From 1070d71da66a60cc965293930006cb9c281b73bf Mon Sep 17 00:00:00 2001 From: tamasmeszaros Date: Wed, 19 Jan 2022 14:18:17 +0100 Subject: [PATCH] Use upstream Qhull, remove duplication in deps and src REALfloat is not defined to 0 on all platforms. --- deps/CMakeLists.txt | 9 +- src/CMakeLists.txt | 11 +- src/qhull/Announce.txt | 47 - src/qhull/CMakeLists.txt | 147 - src/qhull/COPYING.txt | 38 - src/qhull/README.txt | 623 --- src/qhull/REGISTER.txt | 32 - src/qhull/html/index.htm | 935 ---- .../html/normal_voronoi_knauss_oesterle.jpg | Bin 23924 -> 0 bytes src/qhull/html/qconvex.htm | 630 --- src/qhull/html/qdelau_f.htm | 416 -- src/qhull/html/qdelaun.htm | 628 --- src/qhull/html/qh--4d.gif | Bin 4372 -> 0 bytes src/qhull/html/qh--cone.gif | Bin 2946 -> 0 bytes src/qhull/html/qh--dt.gif | Bin 3772 -> 0 bytes src/qhull/html/qh--geom.gif | Bin 318 -> 0 bytes src/qhull/html/qh--half.gif | Bin 2537 -> 0 bytes src/qhull/html/qh--rand.gif | Bin 3875 -> 0 bytes src/qhull/html/qh-code.htm | 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+++ b/deps/CMakeLists.txt @@ -195,19 +195,16 @@ set(_dep_list dep_OpenVDB dep_OpenCSG dep_CGAL + dep_Qhull ${PNG_PKG} ${ZLIB_PKG} ${EXPAT_PKG} ) -if (MSVC) - # Experimental - #list(APPEND _dep_list "dep_qhull") -else() - list(APPEND _dep_list "dep_Qhull") +# if (NOT MSVC) # Not working, static build has different Eigen #list(APPEND _dep_list "dep_libigl") -endif() +# endif() add_custom_target(deps ALL DEPENDS ${_dep_list}) diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt index 98877ece3..f8430e968 100644 --- a/src/CMakeLists.txt +++ b/src/CMakeLists.txt @@ -9,7 +9,6 @@ add_subdirectory(boost) add_subdirectory(clipper) add_subdirectory(miniz) add_subdirectory(glu-libtess) -add_subdirectory(qhull) add_subdirectory(Shiny) add_subdirectory(semver) add_subdirectory(libigl) @@ -19,6 +18,16 @@ add_subdirectory(qoi) # Adding libnest2d project for bin packing... add_subdirectory(libnest2d) +find_package(Qhull 7.2 REQUIRED) +add_library(qhull INTERFACE) +if(SLIC3R_STATIC) + slic3r_remap_configs("Qhull::qhullcpp;Qhull::qhullstatic_r" RelWithDebInfo Release) + target_link_libraries(qhull INTERFACE Qhull::qhullcpp Qhull::qhullstatic_r) +else() + slic3r_remap_configs("Qhull::qhullcpp;Qhull::qhull_r" RelWithDebInfo Release) + target_link_libraries(qhull INTERFACE Qhull::qhullcpp Qhull::qhull_r) +endif() + add_subdirectory(libslic3r) if (SLIC3R_GUI) diff --git a/src/qhull/Announce.txt b/src/qhull/Announce.txt deleted file mode 100644 index 635cff1af..000000000 --- a/src/qhull/Announce.txt +++ /dev/null @@ -1,47 +0,0 @@ - - Qhull 2015.2 2016/01/18 - - http://www.qhull.org - git@github.com:qhull/qhull.git - http://www.geomview.org - -Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams, -furthest-site Voronoi diagrams, and halfspace intersections about a point. -It runs in 2-d, 3-d, 4-d, or higher. It implements the Quickhull algorithm -for computing convex hulls. Qhull handles round-off errors from floating -point arithmetic. It can approximate a convex hull. - -The program includes options for hull volume, facet area, partial hulls, -input transformations, randomization, tracing, multiple output formats, and -execution statistics. The program can be called from within your application. -You can view the results in 2-d, 3-d and 4-d with Geomview. - -To download Qhull: - http://www.qhull.org/download - git@github.com:qhull/qhull.git - -Download qhull-96.ps for: - - Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The - Quickhull Algorithm for Convex Hulls," ACM Trans. on - Mathematical Software, 22(4):469-483, Dec. 1996. - http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/ - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 - -Abstract: - -The convex hull of a set of points is the smallest convex set that contains -the points. This article presents a practical convex hull algorithm that -combines the two-dimensional Quickhull Algorithm with the general dimension -Beneath-Beyond Algorithm. It is similar to the randomized, incremental -algorithms for convex hull and Delaunay triangulation. We provide empirical -evidence that the algorithm runs faster when the input contains non-extreme -points, and that it uses less memory. - -Computational geometry algorithms have traditionally assumed that input sets -are well behaved. When an algorithm is implemented with floating point -arithmetic, this assumption can lead to serious errors. We briefly describe -a solution to this problem when computing the convex hull in two, three, or -four dimensions. The output is a set of "thick" facets that contain all -possible exact convex hulls of the input. A variation is effective in five -or more dimensions. diff --git a/src/qhull/CMakeLists.txt b/src/qhull/CMakeLists.txt deleted file mode 100644 index ab9aba9af..000000000 --- a/src/qhull/CMakeLists.txt +++ /dev/null @@ -1,147 +0,0 @@ - -# This CMake file is written specifically to integrate qhull library with Slic3rPE -# (see https://github.com/prusa3d/PrusaSlicer for more information about the project) -# -# Only original libraries qhullstatic_r and qhullcpp are included. -# They are built as a single statically linked library. -# -# Created by modification of the original qhull CMakeLists. -# Lukas Matena (25.7.2018), lukasmatena@seznam.cz - -# see bug report: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=925540 - -find_package(Qhull 7.2 QUIET) - -add_library(qhull INTERFACE) - -if(Qhull_FOUND) - -message(STATUS "Using qhull from system.") -if(SLIC3R_STATIC) - slic3r_remap_configs("Qhull::qhullcpp;Qhull::qhullstatic_r" RelWithDebInfo Release) - target_link_libraries(qhull INTERFACE Qhull::qhullcpp Qhull::qhullstatic_r) -else() - slic3r_remap_configs("Qhull::qhullcpp;Qhull::qhull_r" RelWithDebInfo Release) - target_link_libraries(qhull INTERFACE Qhull::qhullcpp Qhull::qhull_r) -endif() - -else(Qhull_FOUND) - -project(qhull) -cmake_minimum_required(VERSION 2.6) - -# Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, qhull-warn.pri -set(qhull_VERSION2 "2015.2 2016/01/18") # not used, See global.c, global_r.c, rbox.c, rbox_r.c -set(qhull_VERSION "7.2.0") # Advance every release - -#include(CMakeModules/CheckLFS.cmake) -#option(WITH_LFS "Enable Large File Support" ON) -#check_lfs(WITH_LFS) - - -message(STATUS "qhull Version: ${qhull_VERSION} (static linking)") - - -set(libqhull_HEADERS - # reentrant qhull HEADERS: - src/libqhull_r/libqhull_r.h - src/libqhull_r/geom_r.h - src/libqhull_r/io_r.h - src/libqhull_r/mem_r.h - src/libqhull_r/merge_r.h - src/libqhull_r/poly_r.h - src/libqhull_r/qhull_ra.h - src/libqhull_r/qset_r.h - src/libqhull_r/random_r.h - src/libqhull_r/stat_r.h - src/libqhull_r/user_r.h - - # C++ interface to reentrant Qhull HEADERS: - src/libqhullcpp/Coordinates.h - src/libqhullcpp/functionObjects.h - src/libqhullcpp/PointCoordinates.h - src/libqhullcpp/Qhull.h - src/libqhullcpp/QhullError.h - src/libqhullcpp/QhullFacet.h - src/libqhullcpp/QhullFacetList.h - src/libqhullcpp/QhullFacetSet.h - src/libqhullcpp/QhullHyperplane.h - src/libqhullcpp/QhullIterator.h - src/libqhullcpp/QhullLinkedList.h - src/libqhullcpp/QhullPoint.h - src/libqhullcpp/QhullPoints.h - src/libqhullcpp/QhullPointSet.h - src/libqhullcpp/QhullQh.h - src/libqhullcpp/QhullRidge.h - src/libqhullcpp/QhullSet.h - src/libqhullcpp/QhullSets.h - src/libqhullcpp/QhullStat.h - src/libqhullcpp/QhullVertex.h - src/libqhullcpp/QhullVertexSet.h - src/libqhullcpp/RboxPoints.h - src/libqhullcpp/RoadError.h - src/libqhullcpp/RoadLogEvent.h - src/qhulltest/RoadTest.h -) - -set(libqhull_SOURCES - # reentrant qhull SOURCES: - src/libqhull_r/global_r.c - src/libqhull_r/stat_r.c - src/libqhull_r/geom2_r.c - src/libqhull_r/poly2_r.c - src/libqhull_r/merge_r.c - src/libqhull_r/libqhull_r.c - src/libqhull_r/geom_r.c - src/libqhull_r/poly_r.c - src/libqhull_r/qset_r.c - src/libqhull_r/mem_r.c - src/libqhull_r/random_r.c - src/libqhull_r/usermem_r.c - src/libqhull_r/io_r.c - src/libqhull_r/user_r.c - src/libqhull_r/rboxlib_r.c - - # C++ interface to reentrant Qhull SOURCES: - src/libqhullcpp/Coordinates.cpp - src/libqhullcpp/PointCoordinates.cpp - src/libqhullcpp/Qhull.cpp - src/libqhullcpp/QhullFacet.cpp - src/libqhullcpp/QhullFacetList.cpp - src/libqhullcpp/QhullFacetSet.cpp - src/libqhullcpp/QhullHyperplane.cpp - src/libqhullcpp/QhullPoint.cpp - src/libqhullcpp/QhullPointSet.cpp - src/libqhullcpp/QhullPoints.cpp - src/libqhullcpp/QhullQh.cpp - src/libqhullcpp/QhullRidge.cpp - src/libqhullcpp/QhullSet.cpp - src/libqhullcpp/QhullStat.cpp - src/libqhullcpp/QhullVertex.cpp - src/libqhullcpp/QhullVertexSet.cpp - src/libqhullcpp/RboxPoints.cpp - src/libqhullcpp/RoadError.cpp - src/libqhullcpp/RoadLogEvent.cpp - - # headers for both (libqhullr and libqhullcpp: - ${libqhull_HEADERS} -) - - -################################################## -# combined library (reentrant qhull and qhullcpp) for Slic3r: -set(qhull_STATIC qhullstatic) -add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES}) -set_target_properties(${qhull_STATIC} PROPERTIES - VERSION ${qhull_VERSION}) - -if(UNIX) - target_link_libraries(${qhull_STATIC} m) -endif(UNIX) -################################################## - -# LIBDIR is defined in the main xs CMake file: -target_include_directories(${qhull_STATIC} BEFORE PUBLIC ${LIBDIR}/qhull/src) -target_link_libraries(qhull INTERFACE ${qhull_STATIC}) - -endif() diff --git a/src/qhull/COPYING.txt b/src/qhull/COPYING.txt deleted file mode 100644 index 2895ec6a3..000000000 --- a/src/qhull/COPYING.txt +++ /dev/null @@ -1,38 +0,0 @@ - Qhull, Copyright (c) 1993-2015 - - C.B. Barber - Arlington, MA - - and - - The National Science and Technology Research Center for - Computation and Visualization of Geometric Structures - (The Geometry Center) - University of Minnesota - - email: qhull@qhull.org - -This software includes Qhull from C.B. Barber and The Geometry Center. -Qhull is copyrighted as noted above. Qhull is free software and may -be obtained via http from www.qhull.org. It may be freely copied, modified, -and redistributed under the following conditions: - -1. All copyright notices must remain intact in all files. - -2. A copy of this text file must be distributed along with any copies - of Qhull that you redistribute; this includes copies that you have - modified, or copies of programs or other software products that - include Qhull. - -3. If you modify Qhull, you must include a notice giving the - name of the person performing the modification, the date of - modification, and the reason for such modification. - -4. When distributing modified versions of Qhull, or other software - products that include Qhull, you must provide notice that the original - source code may be obtained as noted above. - -5. There is no warranty or other guarantee of fitness for Qhull, it is - provided solely "as is". Bug reports or fixes may be sent to - qhull_bug@qhull.org; the authors may or may not act on them as - they desire. diff --git a/src/qhull/README.txt b/src/qhull/README.txt deleted file mode 100644 index c811b9f80..000000000 --- a/src/qhull/README.txt +++ /dev/null @@ -1,623 +0,0 @@ -This distribution of qhull library is only meant for interfacing qhull with Slic3rPE -(https://github.com/prusa3d/PrusaSlicer). - -The qhull source file was acquired from https://github.com/qhull/qhull at revision -f0bd8ceeb84b554d7cdde9bbfae7d3351270478c. - -No changes to the qhull library were made, except for -- setting REALfloat=1 in user_r.h to enforce calculations in floats -- modifying CMakeLists.txt (the original was renamed to origCMakeLists.txt) - -Many thanks to C. Bradford Barber and all contributors. - -Lukas Matena (lukasmatena@seznam.cz) -25.7.2018 - - -See original contents of the README file below. - -====================================================================================== -====================================================================================== -====================================================================================== - - -Name - - qhull, rbox 2015.2 2016/01/18 - -Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection - - Documentation: - html/index.htm - - - Available from: - - - (git@github.com:qhull/qhull.git) - - News and a paper: - - - - Version 1 (simplicial only): - - -Purpose - - Qhull is a general dimension convex hull program that reads a set - of points from stdin, and outputs the smallest convex set that contains - the points to stdout. It also generates Delaunay triangulations, Voronoi - diagrams, furthest-site Voronoi diagrams, and halfspace intersections - about a point. - - Rbox is a useful tool in generating input for Qhull; it generates - hypercubes, diamonds, cones, circles, simplices, spirals, - lattices, and random points. - - Qhull produces graphical output for Geomview. This helps with - understanding the output. - -Environment requirements - - Qhull and rbox should run on all 32-bit and 64-bit computers. Use - an ANSI C or C++ compiler to compile the program. The software is - self-contained. It comes with examples and test scripts. - - Qhull's C++ interface uses the STL. The C++ test program uses QTestLib - from the Qt Framework. Qhull's C++ interface may change without - notice. Eventually, it will move into the qhull shared library. - - Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt - before using or distributing Qhull. - -To cite Qhull, please use - - Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull - algorithm for convex hulls," ACM Trans. on Mathematical Software, - 22(4):469-483, Dec 1996, http://www.qhull.org. - -To modify Qhull, particularly the C++ interface - - Qhull is on GitHub - (http://github.com/qhull/qhull, git@github.com:qhull/qhull.git) - - For internal documentation, see html/qh-code.htm - -To install Qhull - - Qhull is precompiled for Windows 32-bit, otherwise it needs compilation. - - Qhull includes Makefiles for gcc and other targets, CMakeLists.txt for CMake, - .sln/.vcproj/.vcxproj files for Microsoft Visual Studio, and .pro files - for Qt Creator. It compiles under Windows with mingw. - - Install and build instructions follow. - - See the end of this document for a list of distributed files. - ------------------ -Installing Qhull on Windows 10, 8, 7 (32- or 64-bit), Windows XP, and Windows NT - - The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe, - qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files, - and source files. Qhull.exe and user-eg3.exe are compiled with the reentrant - library while the other executables use the non-reentrant library. - - To install Qhull: - - Unzip the files into a directory (e.g., named 'qhull') - - Click on QHULL-GO or open a command window into Qhull's bin directory. - - Test with 'rbox D4 | qhull' - - To uninstall Qhull - - Delete the qhull directory - - To learn about Qhull: - - Execute 'qconvex' for a synopsis and examples. - - Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points. - - Execute 'rbox 10 | qconvex i TO file' to write results to 'file'. - - Browse the documentation: qhull\html\index.htm - - If an error occurs, Windows sends the error to stdout instead of stderr. - Use 'TO xxx' to send normal output to xxx - - To improve the command window - - Double-click the window bar to increase the size of the window - - Right-click the window bar - - Select Properties - - Check QuickEdit Mode - Select text with right-click or Enter - Paste text with right-click - - Change Font to Lucinda Console - - Change Layout to Screen Buffer Height 999, Window Size Height 55 - - Change Colors to Screen Background White, Screen Text Black - - Click OK - - Select 'Modify shortcut that started this window', then OK - - If you use qhull a lot, install a bash shell such as - MSYS (www.mingw.org/wiki/msys), Road Bash (www.qhull.org/bash), - or Cygwin (www.cygwin.com). - ------------------ -Installing Qhull on Unix with gcc - - To build Qhull, static libraries, shared library, and C++ interface - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - make - - export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH - - The Makefiles may be edited for other compilers. - If 'testqset' exits with an error, qhull is broken - - A simple Makefile for Qhull is in src/libqhull and src/libqhull_r. - To build the Qhull executables and libqhullstatic - - Extract Qhull from qhull...tgz or qhull...zip - - cd src/libqhull_r # cd src/libqhull - - make - - ------------------ -Installing Qhull with CMake 2.6 or later - - See CMakeLists.txt for examples and further build instructions - - To build Qhull, static libraries, shared library, and C++ interface - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - cd build - - cmake --help # List build generators - - make -G "" .. && cmake .. - - cmake .. - - make - - make install - - The ".." is important. It refers to the parent directory (i.e., qhull/) - - On Windows, CMake installs to C:/Program Files/qhull. 64-bit generators - have a "Win64" tag. - - If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in - - If cmake fails with "No CMAKE_C_COMPILER could be found" - - cmake was not able to find the build environment specified by -G "..." - ------------------ -Installing Qhull with Qt - - To build Qhull, including its C++ test (qhulltest) - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Load src/qhull-all.pro into QtCreator - - Build - -------------------- -Working with Qhull's C++ interface - - See html/qh-code.htm#cpp for calling Qhull from C++ programs - - See html/qh-code.htm#reentrant for converting from Qhull-2012 - - Examples of using the C++ interface - user_eg3_r.cpp - qhulltest/*_test.cpp - - Qhull's C++ interface is likely to change. Stay current with GitHub. - - To clone Qhull's next branch from http://github.com/qhull/qhull - git init - git clone git@github.com:qhull/qhull.git - cd qhull - git checkout next - ... - git pull origin next - - Compile qhullcpp and libqhullstatic_r with the same compiler. Both libraries - use the C routines setjmp() and longjmp() for error handling. They must - be compiled with the same compiler. - -------------------- -Calling Qhull from C programs - - See html/qh-code.htm#library for calling Qhull from C programs - - See html/qh-code.htm#reentrant for converting from Qhull-2012 - - Warning: You will need to understand Qhull's data structures and read the - code. Most users will find it easier to call Qhull as an external command. - - The new, reentrant 'C' code (src/libqhull_r), passes a pointer to qhT - to most Qhull routines. This allows multiple instances of Qhull to run - at the same time. It simplifies the C++ interface. - - The non-reentrant 'C' code (src/libqhull) looks unusual. It refers to - Qhull's global data structure, qhT, through a 'qh' macro (e.g., 'qh ferr'). - This allows the same code to use static memory or heap memory. - If qh_QHpointer is defined, qh_qh is a pointer to an allocated qhT; - otherwise qh_qh is a global static data structure of type qhT. - ------------------- -Compiling Qhull with Microsoft Visual C++ - - To compile 32-bit Qhull with Microsoft Visual C++ 2010 and later - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Load solution build/qhull-32.sln - - Build target 'Win32' - - Project qhulltest requires Qt for DevStudio (http://www.qt.io) - Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012) - If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified' - - To compile 64-bit Qhull with Microsoft Visual C++ 2010 and later - - 64-bit Qhull has larger data structures due to 64-bit pointers - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Load solution build/qhull-64.sln - - Build target 'Win32' - - Project qhulltest requires Qt for DevStudio (http://www.qt.io) - Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012_64) - If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified' - - To compile Qhull with Microsoft Visual C++ 2005 (vcproj files) - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Load solution build/qhull.sln - - Build target 'win32' (not 'x64') - - Project qhulltest requires Qt for DevStudio (http://www.qt.io) - Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/4.7.4) - If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified' - ------------------ -Compiling Qhull with Qt Creator - - Qt (http://www.qt.io) is a C++ framework for Windows, Linux, and Macintosh - - Qhull uses QTestLib to test qhull's C++ interface (see src/qhulltest/) - - To compile Qhull with Qt Creator - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Download the Qt SDK - - Start Qt Creator - - Load src/qhull-all.pro - - Build - ------------------ -Compiling Qhull with mingw on Windows - - To compile Qhull with MINGW - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Install Road Bash (http://www.qhull.org/bash) - or install MSYS (http://www.mingw.org/wiki/msys) - - Install MINGW-w64 (http://sourceforge.net/projects/mingw-w64). - Mingw is included with Qt SDK. - - make - ------------------ -Compiling Qhull with cygwin on Windows - - To compile Qhull with cygwin - - Download and extract Qhull (either GitHub, .tgz file, or .zip file) - - Install cygwin (http://www.cygwin.com) - - Include packages for gcc, make, ar, and ln - - make - ------------------ -Compiling from Makfile without gcc - - The file, qhull-src.tgz, contains documentation and source files for - qhull and rbox. - - To unpack the tgz file - - tar zxf qhull-src.tgz - - cd qhull - - Use qhull/Makefile - Simpler Makefiles are qhull/src/libqhull/Makefile and qhull/src/libqhull_r/Makefile - - Compiling qhull and rbox with Makefile - - in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines - - the defaults are gcc and enscript - - CCOPTS1 should include the ANSI flag. It defines __STDC__ - - in user.h, check the definitions of qh_SECticks and qh_CPUclock. - - use '#define qh_CLOCKtype 2' for timing runs longer than 1 hour - - type: make - - this builds: qhull qconvex qdelaunay qhalf qvoronoi rbox libqhull.a libqhull_r.a - - type: make doc - - this prints the man page - - See also qhull/html/index.htm - - if your compiler reports many errors, it is probably not a ANSI C compiler - - you will need to set the -ansi switch or find another compiler - - if your compiler warns about missing prototypes for fprintf() etc. - - this is ok, your compiler should have these in stdio.h - - if your compiler warns about missing prototypes for memset() etc. - - include memory.h in qhull_a.h - - if your compiler reports "global.c: storage size of 'qh_qh' isn't known" - - delete the initializer "={0}" in global.c, stat.c and mem.c - - if your compiler warns about "stat.c: improper initializer" - - this is ok, the initializer is not used - - if you have trouble building libqhull.a with 'ar' - - try 'make -f Makefile.txt qhullx' - - if the code compiles, the qhull test case will automatically execute - - if an error occurs, there's an incompatibility between machines - - If you can, try a different compiler - - You can turn off the Qhull memory manager with qh_NOmem in mem.h - - You can turn off compiler optimization (-O2 in Makefile) - - If you find the source of the problem, please let us know - - to install the programs and their man pages: - - define MANDIR and BINDIR - - type 'make install' - - - if you have Geomview (www.geomview.org) - - try 'rbox 100 | qconvex G >a' and load 'a' into Geomview - - run 'q_eg' for Geomview examples of Qhull output (see qh-eg.htm) - ------------------- -Compiling on other machines and compilers - - Qhull may compile with Borland C++ 5.0 bcc32. A Makefile is included. - Execute 'cd src/libqhull; make -f Mborland'. If you use the Borland IDE, set - the ANSI option in Options:Project:Compiler:Source:Language-compliance. - - Qhull may compile with Borland C++ 4.02 for Win32 and DOS Power Pack. - Use 'cd src/libqhull; make -f Mborland -D_DPMI'. Qhull 1.0 compiles with - Borland C++ 4.02. For rbox 1.0, use "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". - Use the same options for Qhull 1.0. [D. Zwick] - - If you have troubles with the memory manager, you can turn it off by - defining qh_NOmem in mem.h. - ------------------ -Distributed files - - README.txt // Instructions for installing Qhull - REGISTER.txt // Qhull registration - COPYING.txt // Copyright notice - QHULL-GO.lnk // Windows icon for eg/qhull-go.bat - Announce.txt // Announcement - CMakeLists.txt // CMake build file (2.6 or later) - CMakeModules/CheckLFS.cmake // enables Large File Support in cmake - File_id.diz // Package descriptor - index.htm // Home page - Makefile // Makefile for gcc and other compilers - qhull*.md5sum // md5sum for all files - - bin/* // Qhull executables and dll (.zip only) - build/qhull*.pc.in // pkg-config templates for qhull_r, qhull, and qhull_p - build/qhull-32.sln // 32-bit DevStudio solution and project files (2010 and later) - build/*-32.vcxproj - build/qhull-64.sln // 64-bit DevStudio solution and project files (2010 and later) - build/*-64.vcxproj - build/qhull.sln // DevStudio solution and project files (2005 and 2009) - build/*.vcproj - eg/* // Test scripts and geomview files from q_eg - html/index.htm // Manual - html/qh-faq.htm // Frequently asked questions - html/qh-get.htm // Download page - html/qhull-cpp.xml // C++ style notes as a Road FAQ (www.qhull.org/road) - src/Changes.txt // Change history for Qhull and rbox - src/qhull-all.pro // Qt project - -eg/ - q_eg // shell script for Geomview examples (eg.01.cube) - q_egtest // shell script for Geomview test examples - q_test // shell script to test qhull - q_test-ok.txt // output from q_test - qhulltest-ok.txt // output from qhulltest (Qt only) - make-vcproj.sh // bash shell script to create vcproj and vcxprog files - qhull-zip.sh // bash shell script for distribution files - -rbox consists of (bin, html): - rbox.exe // Win32 executable (.zip only) - rbox.htm // html manual - rbox.man // Unix man page - rbox.txt - -qhull consists of (bin, html): - qconvex.exe // Win32 executables and dlls (.zip download only) - qhull.exe // Built with the reentrant library (about 2% slower) - qdelaunay.exe - qhalf.exe - qvoronoi.exe - qhull_r.dll - qhull-go.bat // command window - qconvex.htm // html manual - qdelaun.htm - qdelau_f.htm - qhalf.htm - qvoronoi.htm - qvoron_f.htm - qh-eg.htm - qh-code.htm - qh-impre.htm - index.htm - qh-opt*.htm - qh-quick.htm - qh--*.gif // images for manual - normal_voronoi_knauss_oesterle.jpg - qhull.man // Unix man page - qhull.txt - -bin/ - msvcr80.dll // Visual C++ redistributable file (.zip download only) - -src/ - qhull/unix.c // Qhull and rbox applications using non-reentrant libqhullstatic.a - rbox/rbox.c - qconvex/qconvex.c - qhalf/qhalf.c - qdelaunay/qdelaunay.c - qvoronoi/qvoronoi.c - - qhull/unix_r.c // Qhull and rbox applications using reentrant libqhullstatic_r.a - rbox/rbox_r.c - qconvex/qconvex_r.c // Qhull applications built with reentrant libqhull_r/Makefile - qhalf/qhalf_r.c - qdelaunay/qdelaun_r.c - qvoronoi/qvoronoi_r.c - - user_eg/user_eg_r.c // example of using qhull_r.dll from a user program - user_eg2/user_eg2_r.c // example of using libqhullstatic_r.a from a user program - user_eg3/user_eg3_r.cpp // example of Qhull's C++ interface libqhullcpp with libqhullstatic_r.a - qhulltest/qhulltest.cpp // Test of Qhull's C++ interface using Qt's QTestLib - qhull-*.pri // Include files for Qt projects - testqset_r/testqset_r.c // Test of reentrant qset_r.c and mem_r.c - testqset/testqset.c // Test of non-rentrant qset.c and mem.c - - -src/libqhull - libqhull.pro // Qt project for non-rentrant, shared library (qhull.dll) - index.htm // design documentation for libqhull - qh-*.htm - qhull-exports.def // Export Definition file for Visual C++ - Makefile // Simple gcc Makefile for qhull and libqhullstatic.a - Mborland // Makefile for Borland C++ 5.0 - - libqhull.h // header file for qhull - user.h // header file of user definable constants - libqhull.c // Quickhull algorithm with partitioning - user.c // user re-definable functions - usermem.c - userprintf.c - userprintf_rbox.c - - qhull_a.h // include files for libqhull/*.c - geom.c // geometric routines - geom2.c - geom.h - global.c // global variables - io.c // input-output routines - io.h - mem.c // memory routines, this is stand-alone code - mem.h - merge.c // merging of non-convex facets - merge.h - poly.c // polyhedron routines - poly2.c - poly.h - qset.c // set routines, this only depends on mem.c - qset.h - random.c // utilities w/ Park & Miller's random number generator - random.h - rboxlib.c // point set generator for rbox - stat.c // statistics - stat.h - -src/libqhull_r - libqhull_r.pro // Qt project for rentrant, shared library (qhull_r.dll) - index.htm // design documentation for libqhull_r - qh-*_r.htm - qhull-exports_r.def // Export Definition file for Visual C++ - Makefile // Simple gcc Makefile for qhull and libqhullstatic.a - - libqhull_r.h // header file for qhull - user_r.h // header file of user definable constants - libqhull_r.c // Quickhull algorithm wi_r.hpartitioning - user_r.c // user re-definable functions - usermem.c - userprintf.c - userprintf_rbox.c - qhull_ra.h // include files for libqhull/*_r.c - geom_r.c // geometric routines - geom2.c - geom_r.h - global_r.c // global variables - io_r.c // input-output routines - io_r.h - mem_r.c // memory routines, this is stand-alone code - mem.h - merge_r.c // merging of non-convex facets - merge.h - poly_r.c // polyhedron routines - poly2.c - poly_r.h - qset_r.c // set routines, this only depends on mem_r.c - qset.h - random_r.c // utilities w/ Park & Miller's random number generator - random.h - rboxlib_r.c // point set generator for rbox - stat_r.c // statistics - stat.h - -src/libqhullcpp/ - libqhullcpp.pro // Qt project for renentrant, static C++ library - Qhull.cpp // Calls libqhull_r.c from C++ - Qhull.h - qt-qhull.cpp // Supporting methods for Qt - - Coordinates.cpp // input classes - Coordinates.h - - PointCoordinates.cpp - PointCoordinates.h - RboxPoints.cpp // call rboxlib.c from C++ - RboxPoints.h - - QhullFacet.cpp // data structure classes - QhullFacet.h - QhullHyperplane.cpp - QhullHyperplane.h - QhullPoint.cpp - QhullPoint.h - QhullQh.cpp - QhullRidge.cpp - QhullRidge.h - QhullVertex.cpp - QhullVertex.h - - QhullFacetList.cpp // collection classes - QhullFacetList.h - QhullFacetSet.cpp - QhullFacetSet.h - QhullIterator.h - QhullLinkedList.h - QhullPoints.cpp - QhullPoints.h - QhullPointSet.cpp - QhullPointSet.h - QhullSet.cpp - QhullSet.h - QhullSets.h - QhullVertexSet.cpp - QhullVertexSet.h - - functionObjects.h // supporting classes - QhullError.cpp - QhullError.h - QhullQh.cpp - QhullQh.h - QhullStat.cpp - QhullStat.h - RoadError.cpp // Supporting base classes - RoadError.h - RoadLogEvent.cpp - RoadLogEvent.h - usermem_r-cpp.cpp // Optional override for qh_exit() to throw an error - -src/libqhullstatic/ - libqhullstatic.pro // Qt project for non-reentrant, static library - -src/libqhullstatic_r/ - libqhullstatic_r.pro // Qt project for reentrant, static library - -src/qhulltest/ - qhulltest.pro // Qt project for test of C++ interface - Coordinates_test.cpp // Test of each class - PointCoordinates_test.cpp - Qhull_test.cpp - QhullFacet_test.cpp - QhullFacetList_test.cpp - QhullFacetSet_test.cpp - QhullHyperplane_test.cpp - QhullLinkedList_test.cpp - QhullPoint_test.cpp - QhullPoints_test.cpp - QhullPointSet_test.cpp - QhullRidge_test.cpp - QhullSet_test.cpp - QhullVertex_test.cpp - QhullVertexSet_test.cpp - RboxPoints_test.cpp - RoadTest.cpp // Run multiple test files with QTestLib - RoadTest.h - ------------------ -Authors: - - C. Bradford Barber Hannu Huhdanpaa (Version 1.0) - bradb@shore.net hannu@qhull.org - - Qhull 1.0 and 2.0 were developed under NSF grants NSF/DMS-8920161 - and NSF-CCR-91-15793 750-7504 at the Geometry Center and Harvard - University. If you find Qhull useful, please let us know. diff --git a/src/qhull/REGISTER.txt b/src/qhull/REGISTER.txt deleted file mode 100644 index 16ccb1a58..000000000 --- a/src/qhull/REGISTER.txt +++ /dev/null @@ -1,32 +0,0 @@ -Dear Qhull User - -We would like to find out how you are using our software. Think of -Qhull as a new kind of shareware: you share your science and successes -with us, and we share our software and support with you. - -If you use Qhull, please send us a note telling -us what you are doing with it. - -We need to know: - - (1) What you are working on - an abstract of your work would be - fine. - - (2) How Qhull has helped you, for example, by increasing your - productivity or allowing you to do things you could not do - before. If Qhull had a direct bearing on your work, please - tell us about this. - -We encourage you to cite Qhull in your publications. - -To cite Qhull, please use - - Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull - algorithm for convex hulls," ACM Trans. on Mathematical Software, - 22(4):469-483, Dec 1996, http://www.qhull.org. - -Please send e-mail to - - bradb@shore.net - -Thank you! diff --git a/src/qhull/html/index.htm b/src/qhull/html/index.htm deleted file mode 100644 index ca4789b47..000000000 --- a/src/qhull/html/index.htm +++ /dev/null @@ -1,935 +0,0 @@ - - - - - - -Qhull manual - - - - - -

Up: Home page for Qhull
-Up:News about Qhull
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-To: Qhull manual: Table of Contents -(please wait while loading)
-To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
- -

- -

[random-fixed] Qhull manual

- -

Qhull is a general dimension code for computing convex hulls, -Delaunay triangulations, halfspace intersections about a point, Voronoi -diagrams, furthest-site Delaunay triangulations, and -furthest-site Voronoi diagrams. These structures have -applications in science, engineering, statistics, and -mathematics. See Fukuda's -introduction to convex hulls, Delaunay triangulations, -Voronoi diagrams, and linear programming. For a detailed -introduction, see O'Rourke ['94], Computational -Geometry in C. -

- -

There are six programs. Except for rbox, they use -the same code. Each program includes instructions and examples. -

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    -
  • qconvex -- convex hulls -
  • qdelaunay -- Delaunay triangulations and - furthest-site Delaunay triangulations -
  • qhalf -- halfspace intersections about a point -
  • qhull -- all structures with additional options -
  • qvoronoi -- Voronoi diagrams and - furthest-site Voronoi diagrams -
  • rbox -- generate point distributions for qhull -
-
- -

Qhull implements the Quickhull algorithm for computing the -convex hull. Qhull includes options -for hull volume, facet area, multiple output formats, and -graphical output. It can approximate a convex hull.

- -

Qhull handles roundoff errors from floating point -arithmetic. It generates a convex hull with "thick" facets. -A facet's outer plane is clearly above all of the points; -its inner plane is clearly below the facet's vertices. Any -exact convex hull must lie between the inner and outer plane. - -

Qhull uses merged facets, triangulated output, or joggled -input. Triangulated output triangulates non-simplicial, merged -facets. Joggled input also -guarantees simplicial output, but it -is less accurate than merged facets. For merged facets, Qhull -reports the maximum outer and inner plane. - -

Brad Barber, Arlington, MA

- -

Copyright © 1995-2015 C.B. Barber

- -
- -

»Qhull manual: Table of -Contents

- - -

»When to use Qhull

-
- -

Qhull constructs convex hulls, Delaunay triangulations, -halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay -triangulations, and furthest-site Voronoi diagrams.

- -

For convex hulls and halfspace intersections, Qhull may be used -for 2-d upto 8-d. For Voronoi diagrams and Delaunay triangulations, Qhull may be -used for 2-d upto 7-d. In higher dimensions, the size of the output -grows rapidly and Qhull does not work well with virtual memory. -If n is the size of -the input and d is the dimension (d>=3), the size of the output -and execution time -grows by n^(floor(d/2) -[see Performance]. For example, do -not try to build a 16-d convex hull of 1000 points. It will -have on the order of 1,000,000,000,000,000,000,000,000 facets. - -

On a 600 MHz Pentium 3, Qhull computes the 2-d convex hull of -300,000 cocircular points in 11 seconds. It computes the -2-d Delaunay triangulation and 3-d convex hull of 120,000 points -in 12 seconds. It computes the -3-d Delaunay triangulation and 4-d convex hull of 40,000 points -in 18 seconds. It computes the -4-d Delaunay triangulation and 5-d convex hull of 6,000 points -in 12 seconds. It computes the -5-d Delaunay triangulation and 6-d convex hull of 1,000 points -in 12 seconds. It computes the -6-d Delaunay triangulation and 7-d convex hull of 300 points -in 15 seconds. It computes the -7-d Delaunay triangulation and 8-d convex hull of 120 points -in 15 seconds. It computes the -8-d Delaunay triangulation and 9-d convex hull of 70 points -in 15 seconds. It computes the -9-d Delaunay triangulation and 10-d convex hull of 50 points -in 17 seconds. The 10-d convex hull of 50 points has about 90,000 facets. - - -

Qhull does not support constrained Delaunay -triangulations, triangulation of non-convex surfaces, mesh -generation of non-convex objects, or medium-sized inputs in 9-D -and higher.

- -

This is a big package with many options. It is one of the -fastest available. It is the only 3-d code that handles precision -problems due to floating point arithmetic. For example, it -implements the identity function for extreme points (see Imprecision in Qhull).

- -

[2016] A newly discovered, bad case for Qhull is multiple, nearly incident points within a 10^-13 ball of 3-d and higher -Delaunay triangulations (input sites in the unit cube). Nearly incident points within substantially -smaller or larger balls are OK. Error QH6271 is reported if a problem occurs. A future release of Qhull -will handle this case. For more information, see "Nearly coincident points on an edge" in Limitations of merged facets - -

If you need a short code for convex hull, Delaunay -triangulation, or Voronoi volumes consider Clarkson's hull -program. If you need 2-d Delaunay triangulations consider -Shewchuk's triangle -program. It is much faster than Qhull and it allows -constraints. Both programs use exact arithmetic. They are in http://www.netlib.org/voronoi/. - -

If your input is in general position (i.e., no coplanar or colinear points), -

  • Tomilov's quickhull.hpp () -or Qhull version -1.0 may meet your needs. Both programs detect precision problems, -but do not handle them.

    - -

    CGAL is a library of efficient and reliable -geometric algorithms. It uses C++ templates and the Boost library to produce dimension-specific -code. This allows more efficient use of memory than Qhull's general-dimension -code. CGAL simulates arbitrary precision while Qhull handles round-off error -with thick facets. Compare the two approaches with Robustness Issues in CGAL, -and Imprecision in Qhull. - - -

    Leda is a -library for writing computational -geometry programs and other combinatorial algorithms. It -includes routines for computing 3-d convex -hulls, 2-d Delaunay triangulations, and 3-d Delaunay triangulations. -It provides rational arithmetic and graphical output. It runs on most -platforms. - -

    If your problem is in high dimensions with a few, -non-simplicial facets, try Fukuda's cdd. -It is much faster than Qhull for these distributions.

    - -

    Custom software for 2-d and 3-d convex hulls may be faster -than Qhull. Custom software should use less memory. Qhull uses -general-dimension data structures and code. The data structures -support non-simplicial facets.

    - -

    Qhull is not suitable for mesh generation or triangulation of -arbitrary surfaces. You may use Qhull if the surface is convex or -completely visible from an interior point (e.g., a star-shaped -polyhedron). First, project each site to a sphere that is -centered at the interior point. Then, compute the convex hull of -the projected sites. The facets of the convex hull correspond to -a triangulation of the surface. For mesh generation of arbitrary -surfaces, see Schneiders' -Finite Element Mesh Generation.

    - -

    Qhull is not suitable for constrained Delaunay triangulations. -With a lot of work, you can write a program that uses Qhull to -add constraints by adding additional points to the triangulation.

    - -

    Qhull is not suitable for the subdivision of arbitrary -objects. Use qdelaunay to subdivide a convex object.

    - -
    • -

    »Description of -Qhull

    -
    - -

    »definition

    -
    - -

    The convex hull of a point set P is the smallest -convex set that contains P. If P is finite, the -convex hull defines a matrix A and a vector b such -that for all x in P, Ax+b <= [0,...].

    - -

    Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher -dimensions. Qhull represents a convex hull as a list of facets. -Each facet has a set of vertices, a set of neighboring facets, -and a halfspace. A halfspace is defined by a unit normal and an -offset (i.e., a row of A and an element of b).

    - -

    Qhull accounts for round-off error. It returns -"thick" facets defined by two parallel hyperplanes. The -outer planes contain all input points. The inner planes exclude -all output vertices. See Imprecise -convex hulls.

    - -

    Qhull may be used for the Delaunay triangulation or the -Voronoi diagram of a set of points. It may be used for the -intersection of halfspaces.

    - -
    -

    »input format

    -
    - -

    The input data on stdin consists of:

    - -
      -
    • first line contains the dimension
      • -
    • second line contains the number of input points
      • -
    • remaining lines contain point coordinates
      • -
    - -

    For example:

    - -
    -    3  #sample 3-d input
-    5
-    0.4 -0.5 1.0
-    1000 -1e-5 -100
-    0.3 0.2 0.1
-    1.0 1.0 1.0
-    0 0 0
-
    - -

    Input may be entered by hand. End the input with a control-D -(^D) character.

    - -

    To input data from a file, use I/O redirection or 'TI file'. The filename may not -include spaces or quotes.

    - -

    A comment starts with a non-numeric character and continues to -the end of line. The first comment is reported in summaries and -statistics. With multiple qhull commands, use option 'FQ' to place a comment in the output.

    - -

    The dimension and number of points can be reversed. Comments -and line breaks are ignored. Error reporting is better if there -is one point per line.

    - -
    -

    »option format

    -
    - -

    Use options to specify the output formats and control -Qhull. The qhull program takes all options. The -other programs use a subset of the options. They disallow -experimental and inappropriate options. - -

    -
      -
    • -qconvex == qhull -
    • -qdelaunay == qhull d Qbb -
    • -qhalf == qhull H -
    • -qvoronoi == qhull v Qbb -
    -
    - -

    Single letters are used for output formats and precision -constants. The other options are grouped into menus for formats -('F'), Geomview ('G '), printing ('P'), Qhull control ('Q '), and tracing ('T'). The menu options may be listed -together (e.g., 'GrD3' for 'Gr' and 'GD3'). Options may be in any -order. Capitalized options take a numeric argument (except for 'PG' and 'F' -options). Use option 'FO' to print -the selected options.

    - -

    Qhull uses zero-relative indexing. If there are n -points, the index of the first point is 0 and the index of -the last point is n-1.

    - -

    The default options are:

    - -
      -
    • summary output ('s')
      • -
    • merged facets ('C-0' in 2-d, - 3-d, 4-d; 'Qx' in 5-d and - up)
      • -
    - -

    Except for bounding box -('Qbk:n', etc.), drop facets -('Pdk:n', etc.), and -Qhull command ('FQ'), only the last -occurence of an option counts. -Bounding box and drop facets may be repeated for each dimension. -Option 'FQ' may be repeated any number of times. - -

    The Unix tcsh and ksh shells make it easy to -try out different options. In Windows 95, use a command window with doskey -and a window scroller (e.g., peruse).

    - -
    -

    »output format

    -
    - -

    To write the results to a file, use I/O redirection or 'TO file'. Windows 95 users should use -'TO file' or the console. If a filename is surrounded by single quotes, -it may include spaces. -

    - -

    The default output option is a short summary ('s') to stdout. There are many -others (see output and formats). You can list vertex incidences, -vertices and facets, vertex coordinates, or facet normals. You -can view Qhull objects with Geomview, Mathematica, or Maple. You can -print the internal data structures. You can call Qhull from your -application (see Qhull library).

    - -

    For example, 'qhull o' lists the -vertices and facets of the convex hull.

    - -

    Error messages and additional summaries ('s') go to stderr. Unless -redirected, stderr is the console.

    - -
    -

    »algorithm

    -
    - -

    Qhull implements the Quickhull algorithm for convex hull -[Barber et al. '96]. This algorithm -combines the 2-d Quickhull algorithm with the n-d -beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized -algorithms of Clarkson and others [Clarkson & Shor '89; Clarkson et al. '93; -Mulmuley '94]. For a demonstration, see How Qhull adds a point. The main -advantages of Quickhull are output sensitive performance (in -terms of the number of extreme points), reduced space -requirements, and floating-point error handling.

    - -
    -

    »data structures

    -
    - -

    Qhull produces the following data structures for dimension d: -

    - -
      -
    • A coordinate is a real number in floating point - format.
      • -
    • A point is an array of d coordinates. - With option 'QJ', the - coordinates are joggled by a small amount.
      • -
    • A vertex is an input point.
      • -
    • A hyperplane is d normal coefficients and - an offset. The length of the normal is one. The - hyperplane defines a halfspace. If V is a normal, b - is an offset, and x is a point inside the convex - hull, then Vx+b <0.
      • -
    • An outer plane is a positive - offset from a hyperplane. When Qhull is done, all points - will be below all outer planes.
      • -
    • An inner plane is a negative - offset from a hyperplane. When Qhull is done, all - vertices will be above the corresponding inner planes.
      • -
    • An orientation is either 'top' or 'bottom'. It is the - topological equivalent of a hyperplane's geometric - orientation.
      • -
    • A simplicial facet is a set of - d neighboring facets, a set of d vertices, a - hyperplane equation, an inner plane, an outer plane, and - an orientation. For example in 3-d, a simplicial facet is - a triangle.
      • -
    • A centrum is a point on a facet's hyperplane. A - centrum is the average of a facet's vertices. Neighboring - facets are convex if each centrum is below the - neighbor facet's hyperplane.
      • -
    • A ridge is a set of d-1 vertices, two - neighboring facets, and an orientation. For example in - 3-d, a ridge is a line segment.
      • -
    • A non-simplicial facet is a set of ridges, a - hyperplane equation, a centrum, an outer plane, and an - inner plane. The ridges determine a set of neighboring - facets, a set of vertices, and an orientation. Qhull - produces a non-simplicial facet when it merges two facets - together. For example, a cube has six non-simplicial - facets.
      • -
    - -

    For examples, use option 'f'. See polyhedron operations for further -design documentation.

    - -
    -

    »Imprecision in Qhull

    -
    - -

    See Imprecision in Qhull and Merged facets or joggled input

    - -
    -

    »Examples of Qhull

    -
    - -

    See Examples of Qhull. Most of these examples require Geomview. -Some of the examples have pictures -.

    - -
    -
    -

    »Options for using Qhull

    -
    - -

    See Options.

    - -
    -

    »Qhull internals

    -
    - -

    See Internals.

    - -
    -

    »Geomview, Qhull's -graphical viewer

    -
    - -

    Geomview -is an interactive geometry viewing program. -Geomview provides a good visualization of Qhull's 2-d and 3-d results. - -

    Qhull includes Examples of Qhull that may be viewed with Geomview. - -

    Geomview can help visulalize a 3-d Delaunay triangulation or the surface of a 4-d convex hull, -Use option 'QVn' to select the 3-D facets adjacent to a vertex. - -

    You may use Geomview to create movies that animate your objects (c.f., How can I create a video animation?). -Geomview helped create the mathematical videos "Not Knot", "Outside In", and "The Shape of Space" from the Geometry Center. - - -

    »Installing Geomview

    -
    - -

    Geomview is an open source project -under SourceForge. - -

    -For build instructions see -Downloading Geomview. -Geomview builds under Linux, Unix, Macintosh OS X, and Windows. - -

    Geomview has installable packages for Debian and Ubuntu. -The OS X build needs Xcode, an X11 SDK, and Lesstif or Motif. -The Windows build uses Cygwin (see Building Geomview below for instructions). - -

    If using Xforms (e.g., for Geomview's External Modules), install the 'libXpm-devel' package from cygwin and move the xforms directory into your geomview directory, e.g.,
    mv xforms-1.2.4 geomview-1.9.5/xforms - -

    Geomview's ndview provides multiple views into 4-d and higher objects. -This module is out-of-date (geomview-users: 4dview). -Download NDview-sgi.tar.Z at newpieces and 4dview at Geomview/modules. - -

    -

    »Using Geomview

    -
    - -

    Use Geomview to view Examples of Qhull. You can spin the convex hull, fly a camera through its facets, -and see how Qhull produces thick facets in response to round-off error. - -

    Follow these instructions to view 'eg,01.cube' from Examples of Qhull -

      -
    1. Launch an XTerm command shell -
        -
      • If needed, start the X terminal server, Use 'xinit' or 'startx' in /usr/X11R6/bin
        xinit -- -multiwindow -clipboard
        startx -
      • Start an XTerm command shell. In Windows, click the Cygwin/bash icon on your desktop. -
      • Set the DISPLAY variable, e.g.,
        export DISPLAY=:0
        export DISPLAY=:0 >>~/.bashenv -
      -
    2. Use Qhull's Geomview options to create a geomview object -
        -
      • rbox c D3 | qconvex G >eg.01.cube -
      • On windows, convert the output to Unix text format with 'd2u'
        rbox c D3 | qconvex G | d2u >eg.01.cube
        d2u eg.* -
      -
    3. Run Geomview -
        -
      • Start Geomview with your example
        ./geomview eg.01.cube -
      • Follow the instructions in Gemoview Tutorial -
      • Geomview creates the Geomview control panel with Targets and External Module, the Geomview toolbar with buttons for controlling Geomview, and the Geomview camera window showing a cube. -
      • Clear the camera window by selecting your object in the Targets list and 'Edit > Delete' or 'dd' -
      • Load the Geomview files panel. Select 'Open' in the 'File' menu. -
      • Set 'Filter' in the files panel to your example directory followed by '/*' (e.g., '/usr/local/qhull-2015.2/eg/*') -
      • Click 'Filter' in the files panel to view your examples in the 'Files' list. -
      • Load another example into the camera window by selecting it and clicking 'OK'. -
      • Review the instructions for Interacting with Geomview -
      • When viewing multiple objects at once, you may want to turn off normalization. In the 'Inspect > Apperance' control panel, set 'Normalize' to 'None'. -
      -
    - -

    Geomview defines GCL (a textual API for controlling Geomview) and OOGL (a textual file format for defining objects). -

      -
    • To control Geomview, you may use any program that reads and writes from stdin and stdout. For example, it could report Qhull's information about a vertex identified by a double-click 'pick' event. -
    • GCL command language for controlling Geomview -
    • OOGL file format for defining objects (tutorial). -
    • External Modules for interacting with Geomview via GCL -
    • Interact with your objects via pick commands in response to right-mouse double clicks. Enable pick events with the interest command. -
    - -
    -

    »Building Geomview for Windows

    -
    - -

    Compile Geomview under Cygwin. For detailed instructions, see -Building Savi and Geomview under Windows. These instructions are somewhat out-of-date. Updated -instructions follow. - -

    How to compile Geomview under 32-bit Cygwin (October 2015)

    -
      -
    1. Note: L. Wood has run into multiple issues with Geomview on Cygwin. He recommends Virtualbox/Ubuntu -and a one-click install of geomview via the Ubuntu package. See his Savi/Geomview link above. -
    2. Install 32-bit Cygwin as follows. -For additional guidance, see Cygwin's Installing and Updating Cygwin Packages -and Setup cygwin. -
        -
      • Launch the cygwin installer. -
      • Select a mirror from Cygwin mirrors (e.g., http://mirrors.kernel.org/sourceware/cygwin/ in California). -
      • Select the packages to install. Besides the cygwin packages listed in the Savi/Windows instructions consider adding -
          -
        • Default -- libXm-devel (required for /usr/include/Xm/Xm.h) -
        • Devel -- bashdb, gcc-core (in place of gcc), gdb -
        • Lib -- libGL-devel, libGLU1 (required, obsolete), libGLU-devel (required, obsolete), libjpeg-devel(XForms), libXext-devel (required), libXpm-devel (Xforms) -libGL and lib -
        • Math -- bc -
        • Net -- autossh, inetutils, openssh -
        • System -- chere -
        • Utils -- dos2unix (required for qhull), keychain -
        • If installing perl, ActiveState Perl may be a better choice than cygwin's perl. Perl is not used by Geomview or Qhull. -
        • Cygwin Package Search -- Search for cygwin programs and packages -
        -
      • Click 'Next' to download and install the packages. -
      • If the download is incomplete, try again. -
      • If you try again after a successful install, cygwin will uninstall and reinstall all modules.. -
      • Click on the 'Cywin Terminal' icon on the Desktop. It sets up a user directory in /home from /etc/skel/... -
      • Mount your disk drives
        mount c: /c # Ignore the warning /c does not exist -
      -
    3. Consider installing the Road Bash scripts (/etc/road-*) from Road. -They define aliases and functions for Unix command shells (Unix, Linux, Mac OS X, Windows), -
        -
      • Download Road Bash and unzip the downloaded file -
      • Copy .../bash/etc/road-* to the Cywin /etc directory (by default, C:\cygwin\etc). -
      • Using the cygwin terminal, convert the road scripts to Unix format
        d2u /etc/road-* -
      • Try it
        source /etc/road-home.bashrc -
      • Install it
        cp /etc/road-home.bashrc ~/.bashrc -
      -
    4. Launch the X terminal server from 'Start > All programs > Cygwin-X > Xwin Server'. Alternatively, run 'startx' -
    5. Launch an XTerm shell -
        -
      • Right click the Cywin icon on the system tray in the Windows taskbar. -
      • Select 'System Tools > XTerm' -
      -
    6. Download and extract Geomview -- Downloading Geomview -
    7. Compile Geomview -
        -
      • ./configure -
      • make -
      -
    8. If './configure' fails, check 'config.log' at the failing step. Look carefully for missing libraries, etc. The Geomview FAQ contains suggestions (e.g., "configure claims it can't find OpenGl"). -
    9. If 'make' fails, read the output carefully for error messages. Usually it is a missing include file or package. Locate and install the missing cygwin packages -(Cygwin Package Search). -
    - -
    -
    -

    »What to do if something -goes wrong

    -
    - -

    Please report bugs to qhull_bug@qhull.org -. Please report if Qhull crashes. Please report if Qhull -generates an "internal error". Please report if Qhull -produces a poor approximate hull in 2-d, 3-d or 4-d. Please -report documentation errors. Please report missing or incorrect -links.

    - -

    If you do not understand something, try a small example. The rbox program is an easy way to generate -test cases. The Geomview program helps to -visualize the output from Qhull.

    - -

    If Qhull does not compile, it is due to an incompatibility -between your system and ours. The first thing to check is that -your compiler is ANSI standard. Qhull produces a compiler error -if __STDC__ is not defined. You may need to set a flag (e.g., -'-A' or '-ansi').

    - -

    If Qhull compiles but crashes on the test case (rbox D4), -there's still incompatibility between your system and ours. -Sometimes it is due to memory management. This can be turned off -with qh_NOmem in mem.h. Please let us know if you figure out how -to fix these problems.

    - -

    If you doubt the output from Qhull, add option 'Tv'. It checks that every point is -inside the outer planes of the convex hull. It checks that every -facet is convex with its neighbors. It checks the topology of the -convex hull.

    - -

    Qhull should work on all inputs. It may report precision -errors if you turn off merged facets with option 'Q0'. This can get as bad as facets with -flipped orientation or two facets with the same vertices. You'll -get a long help message if you run into such a case. They are -easy to generate with rbox.

    - -

    If you do find a problem, try to simplify it before reporting -the error. Try different size inputs to locate the smallest one -that causes an error. You're welcome to hunt through the code -using the execution trace ('T4') as -a guide. This is especially true if you're incorporating Qhull -into your own program.

    - -

    When you report an error, please attach a data set to the end -of your message. Include the options that you used with Qhull, -the results of option 'FO', and any -messages generated by Qhull. This allows me to see the error for -myself. Qhull is maintained part-time.

    - -
    -

    »Email

    -
    - -

    Please send correspondence to Brad Barber at qhull@qhull.org -and report bugs to qhull_bug@qhull.org -. Let me know how you use Qhull. If you mention it in a -paper, please send a reference and abstract.

    - -

    If you would like to get Qhull announcements (e.g., a new -version) and news (any bugs that get fixed, etc.), let us know -and we will add you to our mailing list. For Internet news about geometric algorithms -and convex hulls, look at comp.graphics.algorithms and -sci.math.num-analysis. For Qhull news look at qhull-news.html.

    - -
    -

    »Authors

    -
    - -
    -   C. Bradford Barber                    Hannu Huhdanpaa
-   bradb@shore.net                       hannu@qhull.org
-
    - -
    -

    »Acknowledgments

    -
    - -

    A special thanks to David Dobkin for his guidance. A special -thanks to Albert Marden, Victor Milenkovic, the Geometry Center, -and Harvard University for supporting this work.

    - -

    A special thanks to Mark Phillips, Robert Miner, and Stuart Levy for running the Geometry - Center web site long after the Geometry Center closed. - Stuart moved the web site to the University of Illinois at Champaign-Urbana. -Mark and Robert are founders of Geometry Technologies. -Mark, Stuart, and Tamara Munzner are the original authors of Geomview. - -

    A special thanks to Endocardial -Solutions, Inc. of St. Paul, Minnesota for their support of the -internal documentation (src/libqhull/index.htm). They use Qhull to build 3-d models of -heart chambers.

    - -

    Qhull 1.0 and 2.0 were developed under National Science Foundation -grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. If you find -it useful, please let us know.

    - -

    The Geometry Center was supported by grant DMS-8920161 from the -National Science Foundation, by grant DOE/DE-FG02-92ER25137 from -the Department of Energy, by the University of Minnesota, and by -Minnesota Technology, Inc.

    - -
    -

    »References

    -
    - -

    Aurenhammer, F., "Voronoi diagrams --- A survey of a fundamental geometric data structure," ACM -Computing Surveys, 1991, 23:345-405.

    - -

    Barber, C. B., D.P. Dobkin, and H.T. -Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM -Transactions on Mathematical Software, 22(4):469-483, Dec 1996, www.qhull.org -[http://portal.acm.org; -http://citeseerx.ist.psu.edu]. -

    - -

    Clarkson, K.L. and P.W. Shor, -"Applications of random sampling in computational geometry, -II", Discrete Computational Geometry, 4:387-421, 1989

    - -

    Clarkson, K.L., K. Mehlhorn, and R. -Seidel, "Four results on randomized incremental -construction," Computational Geometry: Theory and -Applications, vol. 3, p. 185-211, 1993.

    - -

    Devillers, et. al., -"Walking in a triangulation," ACM Symposium on -Computational Geometry, June 3-5,2001, Medford MA. - -

    Dobkin, D.P. and D.G. Kirkpatrick, -"Determining the separation of preprocessed polyhedra--a -unified approach," in Proc. 17th Inter. Colloq. Automata -Lang. Program., in Lecture Notes in Computer Science, -Springer-Verlag, 443:400-413, 1990.

    - -

    Edelsbrunner, H, Geometry and Topology for Mesh Generation, -Cambridge University Press, 2001. - -

    Gartner, B., "Fast and robust smallest enclosing balls", Algorithms - ESA '99, LNCS 1643. - -

    Golub, G.H. and van Loan, C.F., Matric Computations, Baltimore, Maryland, USA: John Hopkins Press, 1983 - -

    Fortune, S., "Computational -geometry," in R. Martin, editor, Directions in Geometric -Computation, Information Geometers, 47 Stockers Avenue, -Winchester, SO22 5LB, UK, ISBN 1-874728-02-X, 1993.

    - -

    Milenkovic, V., "Robust polygon -modeling," Computer-Aided Design, vol. 25, p. 546-566, -September 1993.

    - -

    Mucke, E.P., I. Saias, B. Zhu, Fast -randomized point location without preprocessing in Two- and -Three-dimensional Delaunay Triangulations, ACM Symposium on -Computational Geometry, p. 274-283, 1996 [GeomDir]. -

    - -

    Mulmuley, K., Computational Geometry, -An Introduction Through Randomized Algorithms, Prentice-Hall, -NJ, 1994.

    - -

    O'Rourke, J., Computational Geometry -in C, Cambridge University Press, 1994.

    - -

    Preparata, F. and M. Shamos, Computational -Geometry, Springer-Verlag, New York, 1985.

    - -
    - -
    - -

    Up: Home page for Qhull
    -Up:News about Qhull
    -Up: FAQ about Qhull
    -To: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -Dn: Imprecision in Qhull
    -Dn: Description of Qhull examples
    -Dn: Qhull internals
    -Dn: Qhull functions, macros, and data -structures - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

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z0A@ngq!zWCKXx<8g#Q4zPaec)n)8WtyNLOW?)ukB;EVQVmqXOiqJrS=f>s|aQjUi` zf$#M_@k?RuY9XnkJc@|NBr?2HAz340tf#RZYDDTP$Tdpxc&6?8(M2#Dk7`0ajTBG= zN}ozXr#&d5fDozlG~I{NiYNgJA4+LM*il6QG^e#Rr?nJN14C8YrM+T0S~dO&QNhD4+!L{i!w|Lq!w}LWk0m z%RZD*KnBC;X?CAVD4+l*wL53E6i@=}K8BPb^rDJF6em3?;XSCLm=Y|0)hfg@_kT(# RpbH2+s%0FGD58Kr|Jfm)sf+*s diff --git a/src/qhull/html/qconvex.htm b/src/qhull/html/qconvex.htm deleted file mode 100644 index 38a363b08..000000000 --- a/src/qhull/html/qconvex.htm +++ /dev/null @@ -1,630 +0,0 @@ - - - - -qconvex -- convex hull - - - - -Up: -Home page for Qhull
    -Up: Qhull manual -- Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options -
    - -

    [cone]qconvex -- convex hull

    - -

    The convex hull of a set of points is the smallest convex set -containing the points. See the detailed introduction by O'Rourke -['94]. See Description of Qhull and How Qhull adds a point.

    - -
    -
    -
    Example: rbox 10 D3 | qconvex s o TO result
    -
    Compute the 3-d convex hull of 10 random points. Write a - summary to the console and the points and facets to - 'result'.
    - -
     
    -
    Example: rbox c | qconvex n
    -
    Print the normals for each facet of a cube.
    -
     
    -
    Example: rbox c | qconvex i Qt
    -
    Print the triangulated facets of a cube.
    -
     
    -
    Example: rbox y 500 W0 | qconvex
    -
    Compute the convex hull of a simplex with 500 - points on its surface.
    -
     
    -
    Example: rbox x W1e-12 1000 | qconvex - QR0
    -
    Compute the convex hull of 1000 points near the - surface of a randomly rotated simplex. Report - the maximum thickness of a facet.
    -
     
    -
    Example: rbox 1000 s | qconvex s FA
    -
    Compute the convex hull of 1000 cospherical - points. Verify the results and print a summary - with the total area and volume.
    -
     
    -
    Example: rbox d D12 | qconvex QR0 FA
    -
    Compute the convex hull of a 12-d diamond. - Randomly rotate the input. Note the large number - of facets and the small volume.
    -
     
    -
    Example: rbox c D7 | qconvex FA TF1000
    -
    Compute the convex hull of the 7-d hypercube. - Report on progress every 1000 facets. Computing - the convex hull of the 9-d hypercube takes too - much time and space.
    -
     
    -
    Example: rbox c d D2 | qconvex Qc s f Fx | more
    -
    Dump all fields of all facets for a square and a - diamond. Also print a summary and a list of - vertices. Note the coplanar points.
    -
     
    -
    -
    - -

    Except for rbox, all of the qhull programs compute a convex hull. - -

    By default, Qhull merges coplanar facets. For example, the convex -hull of a cube's vertices has six facets. - -

    If you use 'Qt' (triangulated output), -all facets will be simplicial (e.g., triangles in 2-d). For the cube -example, it will have 12 facets. Some facets may be -degenerate and have zero area. - -

    If you use 'QJ' (joggled input), -all facets will be simplicial. The corresponding vertices will be -slightly perturbed and identical points will be joggled apart. -Joggled input is less accurate that triangulated -output.See Merged facets or joggled input.

    - -

    The output for 4-d convex hulls may be confusing if the convex -hull contains non-simplicial facets (e.g., a hypercube). See -Why -are there extra points in a 4-d or higher convex hull?
    -

    -

    - -

    The 'qconvex' program is equivalent to -'qhull' in 2-d to 4-d, and -'qhull Qx' -in 5-d and higher. It disables the following Qhull -options: d v H Qbb Qf Qg Qm -Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc. - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »qconvex synopsis

    -
    -qconvex- compute the convex hull.
-    input (stdin): dimension, number of points, point coordinates
-    comments start with a non-numeric character
-
-options (qconvex.htm):
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Tv   - verify result: structure, convexity, and point inclusion
-    .    - concise list of all options
-    -    - one-line description of all options
-
-output options (subset):
-    s    - summary of results (default)
-    i    - vertices incident to each facet
-    n    - normals with offsets
-    p    - vertex coordinates (includes coplanar points if 'Qc')
-    Fx   - extreme points (convex hull vertices)
-    FA   - compute total area and volume
-    o    - OFF format (dim, n, points, facets)
-    G    - Geomview output (2-d, 3-d, and 4-d)
-    m    - Mathematica output (2-d and 3-d)
-    QVn  - print facets that include point n, -n if not
-    TO file- output results to file, may be enclosed in single quotes
-
-examples:
-    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i
-    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA
-    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n
-    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp
-    rbox c D7 | qconvex FA TF1000
-
    - -

    »qconvex -input

    -
    - -

    The input data on stdin consists of:

    -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex), -or the 'TI' option (e.g., qconvex TI data.txt). - -

    Comments start with a non-numeric character. Error reporting is -simpler if there is one point per line. Dimension -and number of points may be reversed. - -

    Here is the input for computing the convex -hull of the unit cube. The output is the normals, one -per facet.

    - -
    -

    rbox c > data

    - 
    -3 RBOX c
-8
-  -0.5   -0.5   -0.5
-  -0.5   -0.5    0.5
-  -0.5    0.5   -0.5
-  -0.5    0.5    0.5
-   0.5   -0.5   -0.5
-   0.5   -0.5    0.5
-   0.5    0.5   -0.5
-   0.5    0.5    0.5
-
    -

    qconvex s n < data

    - 
    -
-Convex hull of 8 points in 3-d:
-
-  Number of vertices: 8
-  Number of facets: 6
-  Number of non-simplicial facets: 6
-
-Statistics for: RBOX c | QCONVEX s n
-
-  Number of points processed: 8
-  Number of hyperplanes created: 11
-  Number of distance tests for qhull: 35
-  Number of merged facets: 6
-  Number of distance tests for merging: 84
-  CPU seconds to compute hull (after input): 0.081
-
-4
-6
-     0      0     -1   -0.5
-     0     -1      0   -0.5
-     1      0      0   -0.5
-    -1      0      0   -0.5
-     0      1      0   -0.5
-     0      0      1   -0.5
-
    -
    - -
    -

    »qconvex outputs

    -
    - -

    These options control the output of qconvex. They may be used -individually or together.

    -
    -
    -
     
    -
    Vertices
    -
    Fx
    -
    list extreme points (i.e., vertices). The first line is the number of - extreme points. Each point is listed, one per line. The cube example - has eight vertices.
    -
    Fv
    -
    list vertices for each facet. The first line is the number of facets. - Each remaining line starts with the number of vertices. For the cube example, - each facet has four vertices.
    -
    i
    -
    list vertices for each facet. The first line is the number of facets. The - remaining lines list the vertices for each facet. In 4-d and - higher, triangulate non-simplicial facets by adding an extra point.
    -
     
    -
     
    -
    Coordinates
    -
    o
    -
    print vertices and facets of the convex hull in OFF format. The - first line is the dimension. The second line is the number of - vertices, facets, and ridges. The vertex - coordinates are next, followed by the facets. Each facet starts with - the number of vertices. The cube example has four vertices per facet.
    -
    Ft
    -
    print a triangulation of the convex hull in OFF format. The first line - is the dimension. The second line is the number of vertices and added points, - followed by the number of facets and the number of ridges. - The vertex coordinates are next, followed by the centrum coordinates. There is - one centrum for each non-simplicial facet. - The cube example has six centrums, one per square. - Each facet starts with the number of vertices or centrums. - In the cube example, each facet uses two vertices and one centrum.
    -
    p
    -
    print vertex coordinates. The first line is the dimension and the second - line is the number of vertices. The following lines are the coordinates of each - vertex. The cube example has eight vertices.
    -
    Qc p
    -
    print coordinates of vertices and coplanar points. The first line is the dimension. - The second line is the number of vertices and coplanar points. The coordinates - are next, one line per point. Use 'Qc Qi p' - to print the coordinates of all points.
    -
     
    -
     
    -
    Facets
    -
    Fn
    -
    list neighboring facets for each facet. The first line is the - number of facets. Each remaining line starts with the number of - neighboring facets. The cube example has four neighbors per facet.
    -
    FN
    -
    list neighboring facets for each point. The first line is the - total number of points. Each remaining line starts with the number of - neighboring facets. Each vertex of the cube example has three neighboring - facets. Use 'Qc Qi FN' - to include coplanar and interior points.
    -
    Fa
    -
    print area for each facet. The first line is the number of facets. - Facet area follows, one line per facet. For the cube example, each facet has area one.
    -
    FI
    -
    list facet IDs. The first line is the number of - facets. The IDs follow, one per line.
    - -
     
    -
     
    -
    Coplanar and interior points
    -
    Fc
    -
    list coplanar points for each facet. The first line is the number - of facets. The remaining lines start with the number of coplanar points. - A coplanar point is assigned to one facet.
    -
    Qi Fc
    -
    list interior points for each facet. The first line is the number - of facets. The remaining lines start with the number of interior points. - A coplanar point is assigned to one facet.
    -
    FP
    -
    print distance to nearest vertex for coplanar points. The first line is the - number of coplanar points. Each remaining line starts with the point ID of - a vertex, followed by the point ID of a coplanar point, its facet, and distance. - Use 'Qc Qi - FP' for coplanar and interior points.
    - -
     
    -
     
    -
    Hyperplanes
    -
    n
    -
    print hyperplane for each facet. The first line is the dimension. The - second line is the number of facets. Each remaining line is the hyperplane's - coefficients followed by its offset.
    -
    Fo
    -
    print outer plane for each facet. The output plane is above all points. - The first line is the dimension. The - second line is the number of facets. Each remaining line is the outer plane's - coefficients followed by its offset.
    -
    Fi
    -
    print inner plane for each facet. The inner plane of a facet is - below its vertices. - The first line is the dimension. The - second line is the number of facets. Each remaining line is the inner plane's - coefficients followed by its offset.
    - -
     
    -
     
    -
    General
    -
    s
    -
    print summary for the convex hull. Use 'Fs' and 'FS' if you need numeric data.
    -
    FA
    -
    compute total area and volume for 's' and 'FS'
    -
    m
    -
    Mathematica output for the convex hull in 2-d or 3-d.
    -
    FM
    -
    Maple output for the convex hull in 2-d or 3-d.
    -
    G
    -
    Geomview output for the convex hull in 2-d, 3-d, or 4-d.
    - -
     
    -
     
    -
    Scaling and rotation
    -
    Qbk:n
    -
    scale k'th coordinate to lower bound.
    -
    QBk:n
    -
    scale k'th coordinate to upper bound.
    -
    QbB
    -
    scale input to unit cube centered at the origin.
    -
    QRn
    -
    randomly rotate the input with a random seed of n. If n=0, the - seed is the time. If n=-1, use time for the random seed, but do - not rotate the input.
    -
    Qbk:0Bk:0
    -
    remove k'th coordinate from input. This computes the - convex hull in one lower dimension.
    -
    -
    - -
    -

    »qconvex controls

    -
    - -

    These options provide additional control:

    - -
    -
    -
    Qt
    -
    triangulated output. Qhull triangulates non-simplicial facets. It may produce - degenerate facets of zero area.
    -
    QJ
    -
    joggle the input instead of merging facets. This guarantees simplicial facets - (e.g., triangles in 3-d). It is less accurate than triangulated output ('Qt').
    -
    Qc
    -
    keep coplanar points
    -
    Qi
    -
    keep interior points
    -
    f
    -
    facet dump. Print the data structure for each facet.
    -
    QVn
    -
    select facets containing point n as a vertex,
    -
    QGn
    -
    select facets that are visible from point n - (marked 'good'). Use -n for the remainder.
    -
    PDk:0
    -
    select facets with a negative coordinate for dimension k
    -
    TFn
    -
    report progress after constructing n facets
    -
    Tv
    -
    verify result
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    Qs
    -
    search all points for the initial simplex. If Qhull can - not construct an initial simplex, it reports a -descriptive message. Usually, the point set is degenerate and one -or more dimensions should be removed ('Qbk:0Bk:0'). -If not, use option 'Qs'. It performs an exhaustive search for the -best initial simplex. This is expensive is high dimensions.
    -
    -
    - -
    -

    »qconvex graphics

    -
    - -

    Display 2-d, 3-d, and 4-d convex hulls with Geomview ('G').

    - -

    Display 2-d and 3-d convex hulls with Mathematica ('m').

    - -

    To view 4-d convex hulls in 3-d, use 'Pd0d1d2d3' to select the positive -octant and 'GrD2' to drop dimension -2.

    - -
    -

    »qconvex notes

    -
    - -

    Qhull always computes a convex hull. The -convex hull may be used for other geometric structures. The -general technique is to transform the structure into an -equivalent convex hull problem. For example, the Delaunay -triangulation is equivalent to the convex hull of the input sites -after lifting the points to a paraboloid.

    - -
    -

    »qconvex -conventions

    -
    - -

    The following terminology is used for convex hulls in Qhull. -See Qhull's data structures.

    - -
      -
    • point - d coordinates
      • -
    • vertex - extreme point of the input set
      • -
    • ridge - d-1 vertices between two - neighboring facets
      • -
    • hyperplane - halfspace defined by a unit normal - and offset
      • -
    • coplanar point - a nearly incident point to a - hyperplane
      • -
    • centrum - a point on the hyperplane for testing - convexity
      • -
    • facet - a facet with vertices, ridges, coplanar - points, neighboring facets, and hyperplane
      • -
    • simplicial facet - a facet with d - vertices, d ridges, and d neighbors
      • -
    • non-simplicial facet - a facet with more than d - vertices
      • -
    • good facet - a facet selected by 'QVn', etc.
      • -
    -
    -

    »qconvex options

    - -
    -qconvex- compute the convex hull
-    http://www.qhull.org
-
-input (stdin):
-    first lines: dimension and number of points (or vice-versa).
-    other lines: point coordinates, best if one point per line
-    comments:    start with a non-numeric character
-
-options:
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Qc   - keep coplanar points with nearest facet
-    Qi   - keep interior points with nearest facet
-
-Qhull control options:
-    Qbk:n   - scale coord k so that low bound is n
-      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
-    QbB  - scale input to unit cube centered at the origin
-    Qbk:0Bk:0 - remove k-th coordinate from input
-    QJn  - randomly joggle input in range [-n,n]
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
-    Qs   - search all points for the initial simplex
-    QGn  - good facet if visible from point n, -n for not visible
-    QVn  - good facet if it includes point n, -n if not
-
-Trace options:
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
-    Tc   - check frequently during execution
-    Ts   - print statistics
-    Tv   - verify result: structure, convexity, and point inclusion
-    Tz   - send all output to stdout
-    TFn  - report summary when n or more facets created
-    TI file - input data from file, no spaces or single quotes
-    TO file - output results to file, may be enclosed in single quotes
-    TPn  - turn on tracing when point n added to hull
-     TMn - turn on tracing at merge n
-     TWn - trace merge facets when width > n
-    TVn  - stop qhull after adding point n, -n for before (see TCn)
-     TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]
-    Un   - max distance below plane for a new, coplanar point
-    Wn   - min facet width for outside point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
-    f    - facet dump
-    G    - Geomview output (see below)
-    i    - vertices incident to each facet
-    m    - Mathematica output (2-d and 3-d)
-    n    - normals with offsets
-    o    - OFF file format (dim, points and facets; Voronoi regions)
-    p    - point coordinates
-    s    - summary (stderr)
-
-More formats:
-    Fa   - area for each facet
-    FA   - compute total area and volume for option 's'
-    Fc   - count plus coplanar points for each facet
-           use 'Qc' (default) for coplanar and 'Qi' for interior
-    FC   - centrum for each facet
-    Fd   - use cdd format for input (homogeneous with offset first)
-    FD   - use cdd format for numeric output (offset first)
-    FF   - facet dump without ridges
-    Fi   - inner plane for each facet
-    FI   - ID for each facet
-    Fm   - merge count for each facet (511 max)
-    FM   - Maple output (2-d and 3-d)
-    Fn   - count plus neighboring facets for each facet
-    FN   - count plus neighboring facets for each point
-    Fo   - outer plane (or max_outside) for each facet
-    FO   - options and precision constants
-    FP   - nearest vertex for each coplanar point
-    FQ   - command used for qconvex
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
-                      for output: #vertices, #facets,
-                                  #coplanar points, #non-simplicial facets
-                    #real (2), max outer plane, min vertex
-    FS   - sizes:   #int (0)
-                    #real(2) tot area, tot volume
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
-    Fv   - count plus vertices for each facet
-    FV   - average of vertices (a feasible point for 'H')
-    Fx   - extreme points (in order for 2-d)
-
-Geomview output (2-d, 3-d, and 4-d)
-    Ga   - all points as dots
-     Gp  -  coplanar points and vertices as radii
-     Gv  -  vertices as spheres
-    Gi   - inner planes only
-     Gn  -  no planes
-     Go  -  outer planes only
-    Gc   - centrums
-    Gh   - hyperplane intersections
-    Gr   - ridges
-    GDn  - drop dimension n in 3-d and 4-d output
-
-Print options:
-    PAn  - keep n largest facets by area
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)
-    PDk:n - drop facet if normal[k] >= n
-    Pg   - print good facets (needs 'QGn' or 'QVn')
-    PFn  - keep facets whose area is at least n
-    PG   - print neighbors of good facets
-    PMn  - keep n facets with most merges
-    Po   - force output.  If error, output neighborhood of facet
-    Pp   - do not report precision problems
-
-    .    - list of all options
-    -    - one line descriptions of all options
-
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -•Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qdelau_f.htm b/src/qhull/html/qdelau_f.htm deleted file mode 100644 index d8981e16b..000000000 --- a/src/qhull/html/qdelau_f.htm +++ /dev/null @@ -1,416 +0,0 @@ - - - - -qdelaunay Qu -- furthest-site Delaunay triangulation - - - - -Up: -Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -
    - -

    [delaunay]qdelaunay Qu -- furthest-site Delaunay triangulation

    - -

    The furthest-site Delaunay triangulation corresponds to the upper facets of the Delaunay construction. -Its vertices are the -extreme points of the input sites. -It is the dual of the furthest-site Voronoi diagram. - -

    -
    -
    Example: rbox 10 D2 | qdelaunay Qu Qt s - i TO - result
    -
    Compute the 2-d, furthest-site Delaunay triangulation of 10 random - points. Triangulate the output. - Write a summary to the console and the regions to - 'result'.
    -
     
    -
    Example: rbox 10 D2 | qdelaunay Qu QJ s - i TO - result
    -
    Compute the 2-d, furthest-site Delaunay triangulation of 10 random - points. Joggle the input to guarantee triangular output. - Write a summary to the console and the regions to - 'result'.
    -
     
    -
    Example: rbox r y c G1 D2 | qdelaunay Qu s - Fv TO - result
    -
    Compute the 2-d, furthest-site Delaunay triangulation of a triangle inside - a square. - Write a summary to the console and unoriented regions to 'result'. - Merge regions for cocircular input sites (e.g., the square). - The square is the only furthest-site - Delaunay region.
    -
    -
    - -

    As with the Delaunay triangulation, Qhull computes the -furthest-site Delaunay triangulation by lifting the input sites to a -paraboloid. The lower facets correspond to the Delaunay -triangulation while the upper facets correspond to the -furthest-site triangulation. Neither triangulation includes -"vertical" facets (i.e., facets whose last hyperplane -coefficient is nearly zero). Vertical facets correspond to input -sites that are coplanar to the convex hull of the input. An -example is points on the boundary of a lattice.

    - -

    By default, qdelaunay merges cocircular and cospherical regions. -For example, the furthest-site Delaunay triangulation of a square inside a diamond -('rbox D2 c d G4 | qdelaunay Qu') consists of one region (the diamond). - -

    If you use 'Qt' (triangulated output), -all furthest-site Delaunay regions will be simplicial (e.g., triangles in 2-d). -Some regions may be -degenerate and have zero area. - -

    If you use 'QJ' (joggled input), all furthest-site -Delaunay regions -will be simplicial (e.g., triangles in 2-d). Joggled input -is less accurate than triangulated output ('Qt'). See Merged facets or joggled input.

    - -

    The output for 3-d, furthest-site Delaunay triangulations may be confusing if the -input contains cospherical data. See the FAQ item -Why -are there extra points in a 4-d or higher convex hull? -Avoid these problems with triangulated output ('Qt') or -joggled input ('QJ'). -

    - -

    The 'qdelaunay' program is equivalent to -'qhull d Qbb' in 2-d to 3-d, and -'qhull d Qbb Qx' -in 4-d and higher. It disables the following Qhull -options: d n v H U Qb QB Qc Qf Qg Qi -Qm Qr QR Qv Qx TR E V FC Fi Fo Fp FV Q0,etc. - - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »furthest-site qdelaunay synopsis

    -
    - -See qdelaunay synopsis. The same -program is used for both constructions. Use option 'Qu' -for furthest-site Delaunay triangulations. - -
    -

    »furthest-site qdelaunay -input

    - -
    -

    The input data on stdin consists of:

    -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qdelaunay Qu < data.txt), a pipe (e.g., rbox 10 | qdelaunay Qu), -or the 'TI' option (e.g., qdelaunay Qu TI data.txt). - -

    For example, this is a square containing four random points. -Its furthest-site Delaunay -triangulation contains one square. -

    -

    -rbox c 4 D2 > data -
    -2 RBOX c 4 D2
-8
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
-  -0.5   -0.5
-  -0.5    0.5
-   0.5   -0.5
-   0.5    0.5
-
    - -

    qdelaunay Qu i < data -

    -
-Furthest-site Delaunay triangulation by the convex hull of 8 points in 3-d:
-
-  Number of input sites: 8
-  Number of Delaunay regions: 1
-  Number of non-simplicial Delaunay regions: 1
-
-Statistics for: RBOX c 4 D2 | QDELAUNAY s Qu i
-
-  Number of points processed: 8
-  Number of hyperplanes created: 20
-  Number of facets in hull: 11
-  Number of distance tests for qhull: 34
-  Number of merged facets: 1
-  Number of distance tests for merging: 107
-  CPU seconds to compute hull (after input): 0.02
-
-1
-7 6 4 5
-
    -
    - -
    -

    »furthest-site qdelaunay -outputs

    -
    - -

    These options control the output of furthest-site Delaunay triangulations:

    -
    - -
    -
    furthest-site Delaunay regions
    -
    i
    -
    list input sites for each furthest-site Delaunay region. The first line is the number of regions. The - remaining lines list the input sites for each region. The regions are - oriented. In 3-d and - higher, report cospherical sites by adding extra points. For the points-in-square example, - the square is the only furthest-site Delaunay region.
    -
    Fv
    -
    list input sites for each furthest-site Delaunay region. The first line is the number of regions. - Each remaining line starts with the number of input sites. The regions - are unoriented. For the points-in-square example, - the square is the only furthest-site Delaunay region.
    -
    Ft
    -
    print a triangulation of the furthest-site Delaunay regions in OFF format. The first line - is the dimension. The second line is the number of input sites and added points, - followed by the number of simplices and the number of ridges. - The input coordinates are next, followed by the centrum coordinates. There is - one centrum for each non-simplicial furthest-site Delaunay region. Each remaining line starts - with dimension+1. The - simplices are oriented. - For the points-in-square example, the square has a centrum at the - origin. It splits the square into four triangular regions.
    -
    Fn
    -
    list neighboring regions for each furthest-site Delaunay region. The first line is the - number of regions. Each remaining line starts with the number of - neighboring regions. Negative indices (e.g., -1) indicate regions - outside of the furthest-site Delaunay triangulation. - For the points-in-square example, the four neighboring regions - are outside of the triangulation. They belong to the regular - Delaunay triangulation.
    -
    FN
    -
    list the furthest-site Delaunay regions for each input site. The first line is the - total number of input sites. Each remaining line starts with the number of - furthest-site Delaunay regions. Negative indices (e.g., -1) indicate regions - outside of the furthest-site Delaunay triangulation. - For the points-in-square example, the four random points belong to no region - while the square's vertices belong to region 0 and three - regions outside of the furthest-site Delaunay triangulation.
    -
    Fa
    -
    print area for each furthest-site Delaunay region. The first line is the number of regions. - The areas follow, one line per region. For the points-in-square example, the - square has unit area.
    - -
     
    -
     
    -
    Input sites
    -
    Fx
    -
    list extreme points of the input sites. These points are vertices of the furthest-point - Delaunay triangulation. They are on the - boundary of the convex hull. The first line is the number of - extreme points. Each point is listed, one per line. The points-in-square example - has four extreme points.
    -
     
    -
     
    -
    General
    -
    FA
    -
    compute total area for 's' - and 'FS'. This is the - same as the area of the convex hull.
    -
    o
    -
    print upper facets of the corresponding convex hull (a - paraboloid)
    -
    m
    -
    Mathematica output for the upper facets of the paraboloid (2-d triangulations).
    -
    FM
    -
    Maple output for the upper facets of the paraboloid (2-d triangulations).
    -
    G
    -
    Geomview output for the paraboloid (2-d or 3-d triangulations).
    -
    s
    -
    print summary for the furthest-site Delaunay triangulation. Use 'Fs' and 'FS' for numeric data.
    -
    -
    - -
    -

    »furthest-site qdelaunay -controls

    -
    - -

    These options provide additional control:

    -
    - -
    -
    Qu
    -
    must be used for furthest-site Delaunay triangulation.
    -
    Qt
    -
    triangulated output. Qhull triangulates non-simplicial facets. It may produce - degenerate facets of zero area.
    -
    QJ
    -
    joggle the input to avoid cospherical and coincident - sites. It is less accurate than triangulated output ('Qt').
    -
    QVn
    -
    select facets adjacent to input site n (marked - 'good').
    -
    Tv
    -
    verify result.
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    TFn
    -
    report progress after constructing n facets
    -
    PDk:1
    -
    include upper and lower facets in the output. Set k - to the last dimension (e.g., 'PD2:1' for 2-d inputs).
    -
    f
    -
    facet dump. Print the data structure for each facet (i.e., furthest-site Delaunay region).
    -
    -
    - -
    -

    »furthest-site qdelaunay -graphics

    -
    - -See Delaunay graphics. -They are the same except for Mathematica and Maple output. - -
    -

    »furthest-site -qdelaunay notes

    -
    - -

    The furthest-site Delaunay triangulation does not -record coincident input sites. Use qdelaunay instead. - -

    qdelaunay Qu does not work for purely cocircular -or cospherical points (e.g., rbox c | qdelaunay Qu). Instead, -use qdelaunay Qz -- when all points are vertices of the convex -hull of the input sites, the Delaunay triangulation is the same -as the furthest-site Delaunay triangulation. - -

    A non-simplicial, furthest-site Delaunay region indicates nearly cocircular or -cospherical input sites. To avoid non-simplicial regions triangulate -the output ('Qt') or joggle -the input ('QJ'). Joggled input -is less accurate than triangulated output. -You may also triangulate -non-simplicial regions with option 'Ft'. It adds -the centrum to non-simplicial regions. Alternatively, use an exact arithmetic code.

    - -

    Furthest-site Delaunay triangulations do not include facets that are -coplanar with the convex hull of the input sites. A facet is -coplanar if the last coefficient of its normal is -nearly zero (see qh_ZEROdelaunay). - -

    -

    »furthest-site qdelaunay conventions

    -
    - -

    The following terminology is used for furthest-site Delaunay -triangulations in Qhull. The underlying structure is the upper -facets of a convex hull in one higher dimension. See convex hull conventions, Delaunay conventions, -and Qhull's data structures

    -
    -
      -
    • input site - a point in the input (one dimension - lower than a point on the convex hull)
      • -
    • point - d+1 coordinates. The last - coordinate is the sum of the squares of the input site's - coordinates
      • -
    • vertex - a point on the paraboloid. It - corresponds to a unique input site.
      • -
    • furthest-site Delaunay facet - an upper facet of the - paraboloid. The last coefficient of its normal is - clearly positive.
      • -
    • furthest-site Delaunay region - a furthest-site Delaunay - facet projected to the input sites
      • -
    • non-simplicial facet - more than d - points are cocircular or cospherical
      • -
    • good facet - a furthest-site Delaunay facet with optional - restrictions by 'QVn', etc.
      • -
    -
    -
    -

    »furthest-site qdelaunay options

    -
    - -See qdelaunay options. The same -program is used for both constructions. Use option 'Qu' -for furthest-site Delaunay triangulations. - -
    - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qdelaun.htm b/src/qhull/html/qdelaun.htm deleted file mode 100644 index a42223c66..000000000 --- a/src/qhull/html/qdelaun.htm +++ /dev/null @@ -1,628 +0,0 @@ - - - - -qdelaunay -- Delaunay triangulation - - - - -Up: -Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -
    - -

    [delaunay]qdelaunay -- Delaunay triangulation

    - -

    The Delaunay triangulation is the triangulation with empty -circumspheres. It has many useful properties and applications. -See the survey article by Aurenhammer ['91] and the detailed introduction -by O'Rourke ['94].

    - -
    -
    -
    Example: rbox r y c G0.1 D2 | qdelaunay s - Fv TO - result
    -
    Compute the 2-d Delaunay triangulation of a triangle and - a small square. - Write a summary to the console and unoriented regions to 'result'. - Merge regions for cocircular input sites (i.e., the - square).
    -
     
    -
    Example: rbox r y c G0.1 D2 | qdelaunay s - Fv Qt
    -
    Compute the 2-d Delaunay triangulation of a triangle and - a small square. Write a summary and unoriented - regions to the console. Produce triangulated output.
    -
     
    -
    Example: rbox 10 D2 | qdelaunay QJ s - i TO - result
    -
    Compute the 2-d Delaunay triangulation of 10 random - points. Joggle the input to guarantee triangular output. - Write a summary to the console and the regions to - 'result'.
    -
    -
    - -

    Qhull computes the Delaunay triangulation by computing a -convex hull. It lifts the input sites to a paraboloid by adding -the sum of the squares of the coordinates. It scales the height -of the paraboloid to improve numeric precision ('Qbb'). -It computes the convex -hull of the lifted sites, and projects the lower convex hull to -the input. - -

    Each region of the Delaunay triangulation -corresponds to a facet of the lower half of the convex hull. -Facets of the upper half of the convex hull correspond to the furthest-site Delaunay triangulation. -See the examples, Delaunay and -Voronoi diagrams.

    - -

    See Qhull FAQ - Delaunay and -Voronoi diagram questions.

    - -

    By default, qdelaunay merges cocircular and cospherical regions. -For example, the Delaunay triangulation of a square inside a diamond -('rbox D2 c d G4 | qdelaunay') contains one region for the square. - -

    Use option 'Qz' if the input is circular, cospherical, or -nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid. - -

    If you use 'Qt' (triangulated output), -all Delaunay regions will be simplicial (e.g., triangles in 2-d). -Some regions may be -degenerate and have zero area. Triangulated output identifies coincident -points. - -

    If you use 'QJ' (joggled input), all Delaunay regions -will be simplicial (e.g., triangles in 2-d). Coincident points will -create small regions since the points are joggled apart. Joggled input -is less accurate than triangulated output ('Qt'). See Merged facets or joggled input.

    - -

    The output for 3-d Delaunay triangulations may be confusing if the -input contains cospherical data. See the FAQ item -Why -are there extra points in a 4-d or higher convex hull? -Avoid these problems with triangulated output ('Qt') or -joggled input ('QJ'). -

    - -

    The 'qdelaunay' program is equivalent to -'qhull d Qbb' in 2-d to 3-d, and -'qhull d Qbb Qx' -in 4-d and higher. It disables the following Qhull -options: d n v H U Qb QB Qc Qf Qg Qi -Qm Qr QR Qv Qx TR E V FC Fi Fo Fp Ft FV Q0,etc. - - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »qdelaunay synopsis

    - -
    -qdelaunay- compute the Delaunay triangulation.
-    input (stdin): dimension, number of points, point coordinates
-    comments start with a non-numeric character
-
-options (qdelaun.htm):
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Qu   - furthest-site Delaunay triangulation
-    Tv   - verify result: structure, convexity, and in-circle test
-    .    - concise list of all options
-    -    - one-line description of all options
-
-output options (subset):
-    s    - summary of results (default)
-    i    - vertices incident to each Delaunay region
-    Fx   - extreme points (vertices of the convex hull)
-    o    - OFF format (shows the points lifted to a paraboloid)
-    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)
-    m    - Mathematica output (2-d inputs lifted to a paraboloid)
-    QVn  - print Delaunay regions that include point n, -n if not
-    TO file- output results to file, may be enclosed in single quotes
-
-examples:
-    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i
-    rbox c P0 D3 | qdelaunay Fv Qt        rbox c P0 D2 | qdelaunay s Qu Fv
-    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay s i Qt
-    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt
-
    - - -

    »qdelaunay -input

    - -
    -

    The input data on stdin consists of:

    -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qdelaunay < data.txt), a pipe (e.g., rbox 10 | qdelaunay), -or the 'TI' option (e.g., qdelaunay TI data.txt). - -

    For example, this is four cocircular points inside a square. Its Delaunay -triangulation contains 8 triangles and one four-sided -figure. -

    -

    -rbox s 4 W0 c G1 D2 > data -
    -2 RBOX s 4 W0 c D2
-8
--0.4941988586954018 -0.07594397977563715
--0.06448037284989526 0.4958248496365813
-0.4911154367094632 0.09383830681375946
--0.348353580869097 -0.3586778257652367
-    -1     -1
-    -1      1
-     1     -1
-     1      1
-
    - -

    qdelaunay s i < data -

    -
-Delaunay triangulation by the convex hull of 8 points in 3-d
-
-  Number of input sites: 8
-  Number of Delaunay regions: 9
-  Number of non-simplicial Delaunay regions: 1
-
-Statistics for: RBOX s 4 W0 c D2 | QDELAUNAY s i
-
-  Number of points processed: 8
-  Number of hyperplanes created: 18
-  Number of facets in hull: 10
-  Number of distance tests for qhull: 33
-  Number of merged facets: 2
-  Number of distance tests for merging: 102
-  CPU seconds to compute hull (after input): 0.028
-
-9
-1 7 5
-6 3 4
-2 3 6
-7 2 6
-2 7 1
-0 5 4
-3 0 4
-0 1 5
-1 0 3 2
-
    -
    - -
    -

    »qdelaunay -outputs

    -
    - -

    These options control the output of Delaunay triangulations:

    -
    - -
    -
    Delaunay regions
    -
    i
    -
    list input sites for each Delaunay region. The first line is the number of regions. The - remaining lines list the input sites for each region. The regions are - oriented. In 3-d and - higher, report cospherical sites by adding extra points. Use triangulated - output ('Qt') to avoid non-simpicial regions. For the circle-in-square example, - eight Delaunay regions are triangular and the ninth has four input sites.
    -
    Fv
    -
    list input sites for each Delaunay region. The first line is the number of regions. - Each remaining line starts with the number of input sites. The regions - are unoriented. For the circle-in-square example, - eight Delaunay regions are triangular and the ninth has four input sites.
    -
    Fn
    -
    list neighboring regions for each Delaunay region. The first line is the - number of regions. Each remaining line starts with the number of - neighboring regions. Negative indices (e.g., -1) indicate regions - outside of the Delaunay triangulation. - For the circle-in-square example, the four regions on the square are neighbors to - the region-at-infinity.
    -
    FN
    -
    list the Delaunay regions for each input site. The first line is the - total number of input sites. Each remaining line starts with the number of - Delaunay regions. Negative indices (e.g., -1) indicate regions - outside of the Delaunay triangulation. - For the circle-in-square example, each point on the circle belongs to four - Delaunay regions. Use 'Qc FN' - to include coincident input sites and deleted vertices.
    -
    Fa
    -
    print area for each Delaunay region. The first line is the number of regions. - The areas follow, one line per region. For the circle-in-square example, the - cocircular region has area 0.4.
    -
     
    -
     
    -
    Input sites
    -
    Fc
    -
    list coincident input sites for each Delaunay region. - The first line is the number of regions. The remaining lines start with - the number of coincident sites and deleted vertices. Deleted vertices - indicate highly degenerate input (see'Fs'). - A coincident site is assigned to one Delaunay - region. Do not use 'QJ' with 'Fc'; the joggle will separate - coincident sites.
    -
    FP
    -
    print coincident input sites with distance to - nearest site (i.e., vertex). The first line is the - number of coincident sites. Each remaining line starts with the point ID of - an input site, followed by the point ID of a coincident point, its region, and distance. - Includes deleted vertices which - indicate highly degenerate input (see'Fs'). - Do not use 'QJ' with 'FP'; the joggle will separate - coincident sites.
    -
    Fx
    -
    list extreme points of the input sites. These points are on the - boundary of the convex hull. The first line is the number of - extreme points. Each point is listed, one per line. The circle-in-square example - has four extreme points.
    -
     
    -
     
    -
    General
    -
    FA
    -
    compute total area for 's' - and 'FS'
    -
    o
    -
    print lower facets of the corresponding convex hull (a - paraboloid)
    -
    m
    -
    Mathematica output for the lower facets of the paraboloid (2-d triangulations).
    -
    FM
    -
    Maple output for the lower facets of the paraboloid (2-d triangulations).
    -
    G
    -
    Geomview output for the paraboloid (2-d or 3-d triangulations).
    -
    s
    -
    print summary for the Delaunay triangulation. Use 'Fs' and 'FS' for numeric data.
    -
    -
    - -
    -

    »qdelaunay -controls

    -
    - -

    These options provide additional control:

    -
    - -
    -
    Qt
    -
    triangulated output. Qhull triangulates non-simplicial facets. It may produce -degenerate facets of zero area.
    -
    QJ
    -
    joggle the input to avoid cospherical and coincident - sites. It is less accurate than triangulated output ('Qt').
    -
    Qu
    -
    compute the furthest-site Delaunay triangulation.
    -
    Qz
    -
    add a point above the paraboloid to reduce precision - errors. Use it for nearly cocircular/cospherical input - (e.g., 'rbox c | qdelaunay Qz'). The point is printed for - options 'Ft' and 'o'.
    -
    QVn
    -
    select facets adjacent to input site n (marked - 'good').
    -
    Tv
    -
    verify result.
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    TFn
    -
    report progress after constructing n facets
    -
    PDk:1
    -
    include upper and lower facets in the output. Set k - to the last dimension (e.g., 'PD2:1' for 2-d inputs).
    -
    f
    -
    facet dump. Print the data structure for each facet (i.e., Delaunay region).
    -
    -
    - -
    -

    »qdelaunay -graphics

    -
    - -

    For 2-d and 3-d Delaunay triangulations, Geomview ('qdelaunay G') displays the corresponding convex -hull (a paraboloid).

    - -

    To view a 2-d Delaunay triangulation, use 'qdelaunay GrD2' to drop the last dimension. This -is the same as viewing the hull without perspective (see -Geomview's 'cameras' menu).

    - -

    To view a 3-d Delaunay triangulation, use 'qdelaunay GrD3' to drop the last dimension. You -may see extra edges. These are interior edges that Geomview moves -towards the viewer (see 'lines closer' in Geomview's camera -options). Use option 'Gt' to make -the outer ridges transparent in 3-d. See Delaunay and Voronoi examples.

    - -

    For 2-d Delaunay triangulations, Mathematica ('m') and Maple ('FM') output displays the lower facets of the corresponding convex -hull (a paraboloid).

    - -

    For 2-d, furthest-site Delaunay triangulations, Maple and Mathematica output ('Qu m') displays the upper facets of the corresponding convex -hull (a paraboloid).

    - -
    -

    »qdelaunay -notes

    -
    - -

    You can simplify the Delaunay triangulation by enclosing the input -sites in a large square or cube. This is particularly recommended -for cocircular or cospherical input data. - -

    A non-simplicial Delaunay region indicates nearly cocircular or -cospherical input sites. To avoid non-simplicial regions either triangulate -the output ('Qt') or joggle -the input ('QJ'). Triangulated output -is more accurate than joggled input. Alternatively, use an exact arithmetic code.

    - -

    Delaunay triangulations do not include facets that are -coplanar with the convex hull of the input sites. A facet is -coplanar if the last coefficient of its normal is -nearly zero (see qh_ZEROdelaunay). - -

    See Imprecision issues :: Delaunay triangulations -for a discussion of precision issues. Deleted vertices indicate -highly degenerate input. They are listed in the summary output and -option 'Fs'.

    - -

    To compute the Delaunay triangulation of points on a sphere, -compute their convex hull. If the sphere is the unit sphere at -the origin, the facet normals are the Voronoi vertices of the -input. The points may be restricted to a hemisphere. [S. Fortune] -

    - -

    The 3-d Delaunay triangulation of regular points on a half -spiral (e.g., 'rbox 100 l | qdelaunay') has quadratic size, while the Delaunay triangulation -of random 3-d points is -approximately linear for reasonably sized point sets. - -

    With the Qhull library, you -can use qh_findbestfacet in poly2.c to locate the facet -that contains a point. You should first lift the point to the -paraboloid (i.e., the last coordinate is the sum of the squares -of the point's coordinates -- qh_setdelaunay). Do not use options -'Qbb', 'QbB', -'Qbk:n', or 'QBk:n' since these scale the last -coordinate.

    - -

    If a point is interior to the convex hull of the input set, it -is interior to the adjacent vertices of the Delaunay -triangulation. This is demonstrated by the following pipe for -point 0: - -

    -    qdelaunay <data s FQ QV0 p | qconvex s Qb3:0B3:0 p
-
    - -

    The first call to qdelaunay returns the neighboring points of -point 0 in the Delaunay triangulation. The second call to qconvex -returns the vertices of the convex hull of these points (after -dropping the lifted coordinate). If point 0 is interior to the -original point set, it is interior to the reduced point set.

    - -
    -

    »qdelaunay conventions

    -
    - -

    The following terminology is used for Delaunay triangulations -in Qhull for dimension d. The underlying structure is the -lower facets of a convex hull in dimension d+1. For -further information, see data -structures and convex hull -conventions.

    -
    -
      -
    • input site - a point in the input (one dimension - lower than a point on the convex hull)
      • -
    • point - a point has d+1 coordinates. The - last coordinate is the sum of the squares of the input - site's coordinates
      • -
    • coplanar point - a coincident - input site or a deleted vertex. Deleted vertices - indicate highly degenerate input.
      • -
    • vertex - a point on the paraboloid. It - corresponds to a unique input site.
      • -
    • point-at-infinity - a point added above the - paraboloid by option 'Qz'
      • -
    • lower facet - a facet corresponding to a - Delaunay region. The last coefficient of its normal is - clearly negative.
      • -
    • upper facet - a facet corresponding to a - furthest-site Delaunay region. The last coefficient of - its normal is clearly positive.
      • -
    • Delaunay region - a - lower facet projected to the input sites
      • -
    • upper Delaunay region - an upper facet projected - to the input sites
      • -
    • non-simplicial facet - more than d - input sites are cocircular or cospherical
      • -
    • good facet - a Delaunay region with optional - restrictions by 'QVn', etc.
      • -
    -
    -
    -

    »qdelaunay options

    - -
    -qdelaunay- compute the Delaunay triangulation
-    http://www.qhull.org
-
-input (stdin):
-    first lines: dimension and number of points (or vice-versa).
-    other lines: point coordinates, best if one point per line
-    comments:    start with a non-numeric character
-
-options:
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Qu   - compute furthest-site Delaunay triangulation
-
-Qhull control options:
-    QJn  - randomly joggle input in range [-n,n]
-    Qs   - search all points for the initial simplex
-    Qz   - add point-at-infinity to Delaunay triangulation
-    QGn  - print Delaunay region if visible from point n, -n if not
-    QVn  - print Delaunay regions that include point n, -n if not
-
-Trace options:
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
-    Tc   - check frequently during execution
-    Ts   - print statistics
-    Tv   - verify result: structure, convexity, and in-circle test
-    Tz   - send all output to stdout
-    TFn  - report summary when n or more facets created
-    TI file - input data from file, no spaces or single quotes
-    TO file - output results to file, may be enclosed in single quotes
-    TPn  - turn on tracing when point n added to hull
-     TMn - turn on tracing at merge n
-     TWn - trace merge facets when width > n
-    TVn  - stop qhull after adding point n, -n for before (see TCn)
-     TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]
-    Wn   - min facet width for outside point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
-    f    - facet dump
-    G    - Geomview output (see below)
-    i    - vertices incident to each Delaunay region
-    m    - Mathematica output (2-d only, lifted to a paraboloid)
-    o    - OFF format (dim, points, and facets as a paraboloid)
-    p    - point coordinates (lifted to a paraboloid)
-    s    - summary (stderr)
-
-More formats:
-    Fa   - area for each Delaunay region
-    FA   - compute total area for option 's'
-    Fc   - count plus coincident points for each Delaunay region
-    Fd   - use cdd format for input (homogeneous with offset first)
-    FD   - use cdd format for numeric output (offset first)
-    FF   - facet dump without ridges
-    FI   - ID of each Delaunay region
-    Fm   - merge count for each Delaunay region (511 max)
-    FM   - Maple output (2-d only, lifted to a paraboloid)
-    Fn   - count plus neighboring region for each Delaunay region
-    FN   - count plus neighboring region for each point
-    FO   - options and precision constants
-    FP   - nearest point and distance for each coincident point
-    FQ   - command used for qdelaunay
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
-                    for output: #vertices, #Delaunay regions,
-                                #coincident points, #non-simplicial regions
-                    #real (2), max outer plane, min vertex
-    FS   - sizes:   #int (0)
-                    #real (2), tot area, 0
-    Fv   - count plus vertices for each Delaunay region
-    Fx   - extreme points of Delaunay triangulation (on convex hull)
-
-Geomview options (2-d and 3-d)
-    Ga   - all points as dots
-     Gp  -  coplanar points and vertices as radii
-     Gv  -  vertices as spheres
-    Gi   - inner planes only
-     Gn  -  no planes
-     Go  -  outer planes only
-    Gc     - centrums
-    Gh   - hyperplane intersections
-    Gr   - ridges
-    GDn  - drop dimension n in 3-d and 4-d output
-    Gt   - transparent outer ridges to view 3-d Delaunay
-
-Print options:
-    PAn  - keep n largest Delaunay regions by area
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)
-    PDk:n - drop facet if normal[k] >= n
-    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')
-    PFn  - keep Delaunay regions whose area is at least n
-    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')
-    PMn  - keep n Delaunay regions with most merges
-    Po   - force output.  If error, output neighborhood of facet
-    Pp   - do not report precision problems
-
-    .    - list of all options
-    -    - one line descriptions of all options
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

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    [4-d cube] Qhull code

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    This section discusses the code for Qhull.

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    Copyright © 1995-2015 C.B. Barber

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    »Qhull code: Table of -Contents

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    »Reentrant Qhull

    - -

    Qhull-2015 introduces reentrant Qhull (libqhull_r). Reentrant Qhull uses a qhT* argument instead of global data structures. -The qhT* pointer is the first argument to most Qhull routines. It allows multiple instances of Qhull to run at the same time. -It simplifies the C++ interface to Qhull. - -

    New code should be written with libqhull_r. Existing users of libqhull should consider converting to libqhull_r. -Although libqhull will be supported indefinitely, improvements may not be implemented. -Reentrant qhull is 1-2% slower than non-reentrant qhull. - -

    Note: Reentrant Qhull is not thread safe. Do not invoke Qhull routines with the same qhT* pointer from multiple threads. - -

    »How to convert code to reentrant Qhull

    - -

    C++ users need to convert to libqhull_r. -The new C++ interface does a better, but not perfect, job of hiding Qhull's C data structures. -The previous C++ interface was unusual due to Qhull's global data structures. - -

    All other users should consider converting to libqhull_r. The conversion is straight forward. -The original conversion of libqhull to libqhull_r required thousands of changes, mostly global -search and replace. The first run of Qhull (unix_r.c) produced the same -output, and nearly the same log files, as the original (unix.c). - -

    Suggestions to help with conversion. -

      -
    • Compare qconvex_r.c with qconvex.c. Define a qhT object and a pointer it. The qhT* pointer is the first argument to most Qhull functions. -Clear qh_qh-<NOerrext before calling qh_initflags(). Invoke QHULL_LIB_CHECK to check for a compatible Qhull library. -
    • Compare user_eg2_r.c with user_eg2.c -
    • Compare user_eg_r.c with user_eg.c. If you use qhT before invoking qh_init_A, call qh_zero() to clear the qhT object. -user_eg_r.c includes multiple Qhull runs. -
    • Review user_eg3_r.cpp. As with the other programs, invoke QHULL_LIB_CHECK. -Simple C++ programs should compile as is. -
    • Compare QhullFacet.cpp with the same file in Qhull-2012.1. UsingLibQhull was replaced with the macro QH_TRY_() and 'qh_qh-<NOerrext= true'. -
    • For detailed notes on libqhull_r, see "libqhull_r (reentrant Qhull)" and "Source code changes for libqhull_r" in Changes.txt. -
    • For detailed notes on libqhullcpp, see "C++ interface" and following sections in Changes.txt. -
    • For regexps and conversion notes, see README_r.txt (unedited). -
    - -

    »Qhull on 64-bit computers

    - -

    Qhull compiles for 64-bit hosts. Since the size of a pointer on a 64-bit host is double the size on a 32-bit host, -memory consumption increases about 50% for simplicial facets and up-to 100% for non-simplicial facets. - -

    You can check memory consumption with option Ts. It includes the size of -each data structure: -

      -
    • 32-bit -- merge 24 ridge 20 vertex 28 facet 88 normal 24 ridge vertices 16 facet vertices or neighbors 20 -
    • 64-bit -- merge 32 ridge 32 vertex 48 facet 120 normal 32 ridge vertices 40 facet vertices or neighbors 48 -
    - -

    For Qhull 2015, the maximum identifier for ridges, vertices, and facets was increased -from 24-bits to 32-bits. This allows for larger convex hulls, but may increase the size of -the corresponding data structures. The sizes for Qhull 2012.1 were -

      -
    • 32-bit -- merge 24 ridge 16 vertex 24 facet 88 -
    • 64-bit -- merge 32 ridge 32 vertex 40 facet 120 -
    - -

    »Calling Qhull from -C++ programs

    - -

    Qhull 2015 uses reentrant Qhull for its C++ interface. If you used -the C++ interface from qhull 2012.1, you may need to adjust how you initialize and use -the Qhull classes. See How to convert code to reentrant Qhull. - -

    -Qhull's C++ interface allows you to explore the results of running Qhull. -It provides access to Qhull's data structures. -Most of the classes derive from the corresponding qhull data structure. -For example, QhullFacet is an instance of Qhull's facetT. -

    - -

    You can retain most of the data in Qhull and use the C++ interface to explore its results. -Each object contains a reference the Qhull's data structure (via QhullQh), making the C++ representation less memory efficient. -

    - -

    Besides using the C++ interface, you can also use libqhull_r directly. For example, -the FOREACHfacet_(...) macro will visit each facet in turn. -

    - -

    The C++ interface to Qhull is incomplete. You may need to extend the interface. -If so, you will need to understand Qhull's data structures and read the code. - -Example (c.f., user_eg3 eg-100). It prints the facets generated by Qhull. - -

    -    RboxPoints rbox;
-    rbox.appendRandomPoints("100");
-    Qhull qhull;
-    qhull.runQhull("", rbox);
-    QhullFacetList facets(qhull);
-    cout<< facets;
-
    - -

    -The C++ iterface for RboxPoints redefines the fprintf() calls -in rboxlib.c. Instead of writing its output to stdout, RboxPoints appends -the output to a std::vector. -The same technique may be used for calling Qhull from C++. -

    -
    • -Run Qhull with option 'Ta' to annotate the -output with qh_fprintf() identifiers. -
    • -Redefine qh_fprintf() for these identifiers. -
    • -See RboxPoints.cpp for an example. -
    -

    -Since the C++ interface uses reentrant Qhull, multiple threads may run Qhull at the same time. Each thread is -one run of Qhull. -

    - -

    -Do not have two threads accessing the same Qhull instance. Qhull is not thread-safe. -

    - -

    »CoordinateIterator

    -

    -A CoordinateIterator or ConstCoordinateIterator [RboxPoints.cpp] is a std::vector<realT>::iterator for Rbox and Qhull coordinates. -It is the result type of RboxPoints.coordinates(). -

    - -

    Qhull does not use CoordinateIterator for its data structures. A point in Qhull is an array of reals instead of a std::vector. -See QhullPoint. -

    - -

    »Qhull

    -

    -Qhull is the top-level class for running Qhull. -It initializes Qhull, runs the computation, and records errors. -It provides access to the global data structure QhullQh, -Qhull's facets, and vertices. -

    - -

    »QhullError

    -

    -QhullError is derived from std::exception. It reports errors from Qhull and captures the output to stderr. -

    - -

    -If error handling is not set up, Qhull exits with a code from 1 to 5. The codes are defined by -qh_ERR* in libqhull_r.h. The exit is via qh_exit() in usermem_r.c. -The C++ interface does not report the -captured output in QhullError. Call Qhull::setErrorStream to send output to cerr instead. -

    - -

    »QhullFacet

    -

    -A QhullFacet is a facet of the convex hull, a region of the Delaunay triangulation, a vertex of a Voronoi diagram, -or an intersection of the halfspace intersection about a point. -A QhullFacet has a set of QhullVertex, a set of QhullRidge, and -a set of neighboring QhullFacets. -

    - -

    »QhullFacetList

    -

    -A QhullFacetList is a linked list of QhullFacet. The result of Qhull.runQhull is a QhullFacetList stored -in QhullQh. -

    - -

    »QhullFacetSet

    -

    -A QhullFacetSet is a QhullSet of QhullFacet. QhullFacetSet may be ordered or unordered. The neighboring facets of a QhullFacet is a QhullFacetSet. -The neighbors of a QhullFacet is a QhullFacetSet. -The neighbors are ordered for simplicial facets, matching the opposite vertex of the facet. -

    - -

    »QhullIterator

    -

    -QhullIterator contains macros for defining Java-style iterator templates from a STL-style iterator template. -

    - -

    »QhullLinkedList

    -

    -A QhullLinkedLIst is a template for linked lists with next and previous pointers. -QhullFacetList and QhullVertexList are QhullLinkedLists. -

    - -

    »QhullPoint

    -

    -A QhullPoint is an array of point coordinates, typically doubles. The length of the array is QhullQh.hull_dim. -The identifier of a QhullPoint is its 0-based index from QhullQh.first_point followed by QhullQh.other_points. -

    - -

    »QhullPointSet

    -

    -A QhullPointSet is a QhullSet of QhullPoint. The QhullPointSet of a QhullFacet is its coplanar points. -

    - -

    »QhullQh

    -

    -QhullQh is the root of Qhull's data structure. -It contains initialized constants, sets, buffers, and variables. -It contains an array and a set of QhullPoint, -a list of QhullFacet, and a list of QhullVertex. -The points are the input to Qhull. The facets and vertices are the result of running Qhull. -

    - -

    -Qhull's functions access QhullQh through the global variable, qh_qh. -The global data structures, qh_stat and qh_mem, record statistics and manage memory respectively. -

    - -

    »QhullRidge

    - -

    -A QhullRidge represents the edge between two QhullFacet's. -It is always simplicial with qh.hull_dim-1 QhullVertex)'s. -

    - -

    »QhullRidgeSet

    - -

    -A QhullRidgeSet is a QhullSet of QhullRidge. Each QhullFacet contains a QhullRidgeSet. -

    - -

    »QhullSet

    - -

    -A QhullSet is a set of pointers to objects. QhullSets may be ordered or unordered. They are the core data structure for Qhull. -

    - -

    »QhullVertex

    - -

    -A QhullVertex is a vertex of the convex hull. A simplicial QhullFacet has qh.hull_dim-1 vertices. A QhullVertex contains a QhullPoint. -It may list its neighboring QhullFacet's. -

    - -

    »QhullVertexList

    - -

    -A QhullVertexList is a QhullLinkedList of QhullVertex. -The global data structure, QhullQh contains a QhullVertexList of all -the vertices. -

    - -

    »QhullVertexSet

    - -

    -A QhullVertexSet is a QhullSet of QhullVertex. -The QhullVertexSet of a QhullFacet is the vertices of the facet. It is -ordered for simplicial facets and unordered for non-simplicial facets. -

    - -

    »RboxPoints

    - -

    -RboxPoints is a std::vector of point coordinates (QhullPoint). -It's iterator is CoordinateIterator. -

    -

    -RboxPoints.appendRandomPoints() appends points from a variety of distributions such as uniformly distributed within a cube and random points on a sphere. -It can also append a cube's vertices or specific points. -

    - -

    »Cpp questions for Qhull

    - -Developing C++ code requires many conventions, idioms, and technical details. -The following questions have either -mystified the author or do not have a clear answer. See also -C++ and Perl Guidelines. -and FIXUP notes in the code. -Please add notes to Qhull Wiki. - -
      -
    • FIXUP QH11028 Should return reference, but get reference to temporary -
      iterator Coordinates::operator++() { return iterator(++i); }
      -
    • size() as size_t, size_type, or int -
    • Should all containers have a reserve()? -
    • Qhull.feasiblePoint interface -
    • How to avoid copy constructor while logging, maybeThrowQhullMessage() -
    • How to configure Qhull output. Trace and results should go to stdout/stderr -
    • Qhull and RboxPoints messaging. e.g., ~Qhull, hasQhullMessage(). Rename them as QhullErrorMessage? -
    • How to add additional output to an error message, e.g., qh_setprint -
    • Is idx the best name for an index? It's rather cryptic, but BSD strings.h defines index(). -
    • Qhull::feasiblePoint Qhull::useOutputStream as field or getter? -
    • Define virtual functions for user customization of Qhull (e.g., qh_fprintf, qh_memfree,etc.) -
    • Figure out RoadError::global_log. clearQhullMessage currently clearGlobalLog -
    • Should the false QhullFacet be NULL or empty? e.g., QhullFacet::tricoplanarOwner() and QhullFacetSet::end() -
    • Should output format for floats be predefined (qh_REAL_1, 2.2g, 10.7g) or as currently set for stream -
    • Should cout << !point.defined() be blank or 'undefined' -
    • Infinite point as !defined() -
    • qlist and qlinkedlist define pointer, reference, size_type, difference_type, const_pointer, const_reference for the class but not for iterator and const_iterator - vector.h -- 
      reference operator[](difference_type _Off) const
      -
    • When forwarding an implementation is base() an approriate name (e.g., Coordinates::iterator::base() as std::vector::iterator). -
    • When forwarding an implementation, does not work "returning address of temporary" -
    • Also --, +=, and -= - 
      iterator       &operator++() { return iterator(i++); }
      -
    • if vector inheritance is bad, is QhullVertexSet OK? -
    • Should QhullPointSet define pointer and reference data types? -
    - -

    »Calling Qhull from -C programs

    - -

    Warning: Qhull was not designed for calling from C -programs. You may find the C++ interface easier to use. -You will need to understand the data structures and read the code. -Most users will find it easier to call Qhull as an external -command. - -

    For examples of calling Qhull, see GNU Octave's -computational geometry code, -and Qhull's -user_eg_r.c, -user_eg2_r.c, and -user_r.c. To see how Qhull calls its library, read -unix_r.c, -qconvex.c, -qdelaun.c, -qhalf.c, and -qvoronoi.c. The '*_r.c' files are reentrant, otherwise they are non-reentrant. -Either version may be used. New code should use reentrant Qhull. - -

    See Reentrant Qhull functions, macros, and data -structures for internal documentation of Qhull. The -documentation provides an overview and index. To use the library -you will need to read and understand the code. For most users, it -is better to write data to a file, call the qhull program, and -read the results from the output file.

    - -

    If you use non-reentrant Qhull, be aware of the macros "qh" -and "qhstat", e.g., "qh hull_dim". They are -defined in libqhull.h. They allow the global data -structures to be pre-allocated (faster access) or dynamically -allocated (allows multiple copies).

    - -

    Qhull's Makefile produces a library, libqhull_r.a, -for inclusion in your programs. First review libqhull_r.h. -This defines the data structures used by Qhull and provides -prototypes for the top-level functions. -Most users will only need libqhull_r.h in their programs. For -example, the Qhull program is defined with libqhull_r.h and unix_r.c. -To access all functions, use qhull_ra.h. Include the file -with "#include <libqhull_r/qhull_ra.h>". This -avoids potential name conflicts.

    - -

    If you use the Qhull library, you are on your own as far as -bugs go. Start with small examples for which you know the output. -If you get a bug, try to duplicate it with the Qhull program. The -'Tc' option will catch many problems -as they occur. When an error occurs, use 'T4 TPn' -to trace from the last point added to the hull. Compare your -trace with the trace output from the Qhull program.

    - -

    Errors in the Qhull library are more likely than errors in the -Qhull program. These are usually due to feature interactions that -do not occur in the Qhull program. Please report all errors that -you find in the Qhull library. Please include suggestions for -improvement.

    - -

    »How to avoid exit(), fprintf(), stderr, and stdout

    - -

    Qhull sends output to qh.fout and errors, log messages, and summaries to qh.ferr. qh.fout is normally -stdout and qh.ferr is stderr. qh.fout may be redefined by option 'TO' or the caller. qh.ferr may be redirected to qh.fout by option 'Tz'.

    - -

    Qhull does not use stderr, stdout, fprintf(), or exit() directly.

    - -

    Qhull reports errors via qh_errexit() by writting a message to qh.ferr and invoking longjmp(). -This returns the caller to the corresponding setjmp() (c.f., QH_TRY_ in QhullQh.h). If -qh_errexit() is not available, Qhull functions call qh_exit(). qh_exit() normally calls exit(), -but may be redefined by the user. An example is -libqhullcpp/usermem_r-cpp.cpp. It redefines qh_exit() as a 'throw'.

    - -

    If qh_meminit() or qh_new_qhull() is called with ferr==NULL, then they set ferr to stderr. -Otherwise the Qhull libraries use qh->ferr and qh->qhmem.ferr for error output.

    - -

    If an error occurs before qh->ferr is initialized, Qhull invokes qh_fprintf_stderr(). The user -may redefine this function along with qh_exit(), qh_malloc(), and qh_free(). - -

    The Qhull libraries write output via qh_fprintf() [userprintf_r.c]. Otherwise, the Qhull -libraries do not use stdout, fprintf(), or printf(). Like qh_exit(), the user may redefine -qh_fprintf().

    - -

    »sets and quick memory -allocation

    - -

    You can use mem_r.c and qset_r.c individually. Mem_r.c -implements quick-fit memory allocation. It is faster than -malloc/free in applications that allocate and deallocate lots of -memory.

    - -

    Qset_r.c implements sets and related collections. It's -the inner loop of Qhull, so speed is more important than -abstraction. Set iteration is particularly fast. qset_r.c -just includes the functions needed for Qhull.

    - -

    »Delaunay triangulations -and point indices

    - -

    Here some unchecked code to print the point indices of each -Delaunay triangle. Use option 'QJ' if you want to avoid -non-simplicial facets. Note that upper Delaunay regions are -skipped. These facets correspond to the furthest-site Delaunay -triangulation.

    - -
    - 
    -  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  FORALLfacets {
-    if (!facet->upperdelaunay) {
-      printf ("%d", qh_setsize (facet->vertices);
-      FOREACHvertex_(facet->vertices)
-        printf (" %d", qh_pointid (vertex->point));
-      printf ("\n");
-    }
-  }
-
-
    -
    - -

    »locate a facet with -qh_findbestfacet()

    - -

    The routine qh_findbestfacet in poly2_r.c is -particularly useful. It uses a directed search to locate the -facet that is furthest below a point. For Delaunay -triangulations, this facet is the Delaunay triangle that contains -the lifted point. For convex hulls, the distance of a point to -the convex hull is either the distance to this facet or the -distance to a subface of the facet.

    - -
    -

    Warning: If triangulated output ('Qt') and -the best facet is triangulated, qh_findbestfacet() returns one of -the corresponding 'tricoplanar' facets. The actual best facet may be a different -tricoplanar facet. -

    -See qh_nearvertex() in poly2.c for sample code to visit each -tricoplanar facet. To identify the correct tricoplanar facet, -see Devillers, et. al., ['01] -and Mucke, et al ['96]. If you -implement this test in general dimension, please notify -qhull@qhull.org. -

    - -

    qh_findbestfacet performs an exhaustive search if its directed -search returns a facet that is above the point. This occurs when -the point is inside the hull or if the curvature of the convex -hull is less than the curvature of a sphere centered at the point -(e.g., a point near a lens-shaped convex hull). When the later -occurs, the distance function is bimodal and a directed search -may return a facet on the far side of the convex hull.

    - -

    Algorithms that retain the previously constructed hulls -usually avoid an exhaustive search for the best facet. You may -use a hierarchical decomposition of the convex hull [Dobkin and -Kirkpatrick '90].

    - -

    To use qh_findbestfacet with Delaunay triangulations, lift the -point to a paraboloid by summing the squares of its coordinates -(see qh_setdelaunay in geom2_r.c). Do not scale the input with -options 'Qbk', 'QBk', 'QbB' or 'Qbb'. See Mucke, et al ['96] for a good point location -algorithm.

    - -

    The intersection of a ray with the convex hull may be found by -locating the facet closest to a distant point on the ray. -Intersecting the ray with the facet's hyperplane gives a new -point to test.

    - -

    »on-line construction with -qh_addpoint()

    - -

    The Qhull library may be used for the on-line construction of -convex hulls, Delaunay triangulations, and halfspace -intersections about a point. It may be slower than implementations that retain -intermediate convex hulls (e.g., Clarkson's hull -program). These implementations always use a directed search. -For the on-line construction of convex hulls and halfspace -intersections, Qhull may use an exhaustive search -(qh_findbestfacet).

    - -

    You may use qh_findbestfacet and qh_addpoint (libqhull.c) to add a point to -a convex hull. Do not modify the point's coordinates since -qh_addpoint does not make a copy of the coordinates. For Delaunay -triangulations, you need to lift the point to a paraboloid by -summing the squares of the coordinates (see qh_setdelaunay in -geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB' -or 'Qbb'. Do not deallocate the point's coordinates. You need to -provide a facet that is below the point (qh_findbestfacet). -

    - -

    You can not delete points. Another limitation is that Qhull -uses the initial set of points to determine the maximum roundoff -error (via the upper and lower bounds for each coordinate).

    - -

    For many applications, it is better to rebuild the hull from -scratch for each new point. This is especially true if the point -set is small or if many points are added at a time.

    - -

    Calling qh_addpoint from your program may be slower than -recomputing the convex hull with qh_qhull. This is especially -true if the added points are not appended to the qh first_point -array. In this case, Qhull must search a set to determine a -point's ID. [R. Weber]

    - -

    See user_eg.c for examples of the on-line construction of -convex hulls, Delaunay triangulations, and halfspace -intersections. The outline is:

    - -
    - 
    -initialize qhull with an initial set of points
-qh_qhull();
-
-for each additional point p
-   append p to the end of the point array or allocate p separately
-   lift p to the paraboloid by calling qh_setdelaunay
-   facet= qh_findbestfacet (p, !qh_ALL, &bestdist, &isoutside);
-   if (isoutside)
-      if (!qh_addpoint (point, facet, False))
-         break;  /* user requested an early exit with 'TVn' or 'TCn' */
-
-call qh_check_maxout() to compute outer planes
-terminate qhull
    -
    - -

    »Constrained -Delaunay triangulation

    - -

    With a fair amount of work, Qhull is suitable for constrained -Delaunay triangulation. See Shewchuk, ACM Symposium on -Computational Geometry, Minneapolis 1998.

    - -

    Here's a quick way to add a constraint to a Delaunay -triangulation: subdivide the constraint into pieces shorter than -the minimum feature separation. You will need an independent -check of the constraint in the output since the minimum feature -separation may be incorrect. [H. Geron]

    - -

    »Tricoplanar facets and option 'Qt'

    - -

    Option 'Qt' triangulates non-simplicial -facets (e.g., a square facet in 3-d or a cubical facet in 4-d). -All facets share the same apex (i.e., the first vertex in facet->vertices). -For each triangulated facet, Qhull -sets facet->tricoplanar true and copies facet->center, facet->normal, facet->offset, and facet->maxoutside. One of -the facets owns facet->normal; its facet->keepcentrum is true. -If facet->isarea is false, facet->triowner points to the owning -facet. - -

    Qhull sets facet->degenerate if the facet's vertices belong -to the same ridge of the non-simplicial facet. - -

    To visit each tricoplanar facet of a non-simplicial facet, -either visit all neighbors of the apex or recursively visit -all neighbors of a tricoplanar facet. The tricoplanar facets -will have the same facet->center.

    - -

    See qh_detvridge for an example of ignoring tricoplanar facets.

    - -

    »Voronoi vertices of a -region

    - -

    The following code iterates over all Voronoi vertices for each -Voronoi region. Qhull computes Voronoi vertices from the convex -hull that corresponds to a Delaunay triangulation. An input site -corresponds to a vertex of the convex hull and a Voronoi vertex -corresponds to an adjacent facet. A facet is -"upperdelaunay" if it corresponds to a Voronoi vertex -"at-infinity". Qhull uses qh_printvoronoi in io.c -for 'qvoronoi o'

    - -
    - 
    -/* please review this code for correctness */
-qh_setvoronoi_all();
-FORALLvertices {
-   site_id = qh_pointid (vertex->point);
-   if (qh hull_dim == 3)
-      qh_order_vertexneighbors(vertex);
-   infinity_seen = 0;
-   FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay) {
-        if (!infinity_seen) {
-          infinity_seen = 1;
-          ... process a Voronoi vertex "at infinity" ...
-        }
-      }else {
-        voronoi_vertex = neighbor->center;
-        ... your code goes here ...
-      }
-   }
-}
-
    -
    - -

    »Voronoi vertices of a -ridge

    - -

    Qhull uses qh_printvdiagram() in io.c to print the ridges of a -Voronoi diagram for option 'Fv'. -The helper function qh_eachvoronoi() does the real work. It calls -the callback 'printvridge' for each ridge of the Voronoi diagram. -

    - -

    You may call qh_printvdiagram2(), qh_eachvoronoi(), or -qh_eachvoronoi_all() with your own function. If you do not need -the total number of ridges, you can skip the first call to -qh_printvdiagram2(). See qh_printvridge() and qh_printvnorm() in -io.c for examples.

    - -

    »vertex neighbors of -a vertex

    - -

    To visit all of the vertices that share an edge with a vertex: -

    - -
      -
    • Generate neighbors for each vertex with - qh_vertexneighbors in poly2.c.
      • -
    • For simplicial facets, visit the vertices of each - neighbor
      • -
    • For non-simplicial facets,
        -
      • Generate ridges for neighbors with qh_makeridges - in merge.c.
        • -
      • Generate ridges for a vertex with qh_vertexridges - in merge.c.
        • -
      • Visit the vertices of these ridges.
        • -
      -
      • -
    - -

    For non-simplicial facets, the ridges form a simplicial -decomposition of the (d-2)-faces between each pair of facets -- -if you need 1-faces, you probably need to generate the full face -graph of the convex hull.

    - -

    »Performance of -Qhull

    - -

    Empirically, Qhull's performance is balanced in the sense that -the average case happens on average. This may always be true if -the precision of the input is limited to at most O(log n) -bits. Empirically, the maximum number of vertices occurs at the -end of constructing the hull.

    - -

    Let n be the number of input points, v be the -number of output vertices, and f_v be the maximum number -of facets for a convex hull of v vertices. If both -conditions hold, Qhull runs in O(n log v) in 2-d and 3-d -and O(n f_v/v) otherwise. The function f_v -increases rapidly with dimension. It is O(v^floor(d/2) / -floor(d/2)!).

    - -

    The time complexity for merging is unknown. Options 'C-0' and 'Qx' -(defaults) handle precision problems due to floating-point -arithmetic. They are optimized for simplicial outputs.

    - -

    When running large data sets, you should monitor Qhull's -performance with the 'TFn' option. -The time per facet is approximately constant. In high-d with many -merged facets, the size of the ridge sets grows rapidly. For -example the product of 8-d simplices contains 18 facets and -500,000 ridges. This will increase the time needed per facet.

    - -

    As dimension increases, the number of facets and ridges in a -convex hull grows rapidly for the same number of vertices. For -example, the convex hull of 300 cospherical points in 6-d has -30,000 facets.

    - -

    If Qhull appears to stop processing facets, check the memory -usage of Qhull. If more than 5-10% of Qhull is in virtual memory, -its performance will degrade rapidly.

    - -

    When building hulls in 20-d and higher, you can follow the -progress of Qhull with option 'T1'. -It reports each major event in processing a point.

    - -

    To reduce memory requirements, recompile Qhull for -single-precision reals (REALfloat in user.h). -Single-precision does not work with joggle ('QJ'). Check qh_MEMalign in user.h -and the match between free list sizes and data structure sizes -(see the end of the statistics report from 'Ts'). If free list sizes do not match, -you may be able to use a smaller qh_MEMalign. Setting -qh_COMPUTEfurthest saves a small amount of memory, as does -clearing qh_MAXoutside (both in user.h).

    - -

    Shewchuk is working on a 3-d version of his triangle -program. It is optimized for 3-d simplicial Delaunay triangulation -and uses less memory than Qhull.

    - -

    To reduce the size of the Qhull executable, consider -qh_NOtrace and qh_KEEPstatistics 0 in user.h. By -changing user.c you can also remove the input/output -code in io.c. If you don't need facet merging, then -version 1.01 of Qhull is much smaller. It contains some bugs that -prevent Qhull from initializing in simple test cases. It is -slower in high dimensions.

    - -

    The precision options, 'Vn', 'Wn', 'Un'. -'A-n', 'C-n', -'An', 'Cn', -and 'Qx', may have large effects on -Qhull performance. You will need to experiment to find the best -combination for your application.

    - -

    The verify option ('Tv') checks -every point after the hull is complete. If facet merging is used, -it checks that every point is inside every facet. This can take a -very long time if there are many points and many facets. You can -interrupt the verify without losing your output. If facet merging -is not used and there are many points and facets, Qhull uses a -directed search instead of an exhaustive search. This should be -fast enough for most point sets. Directed search is not used for -facet merging because directed search was already used for -updating the facets' outer planes.

    - -

    The check-frequently option ('Tc') -becomes expensive as the dimension increases. The verify option -('Tv') performs many of the same -checks before outputting the results.

    - -

    Options 'Q0' (no pre-merging), 'Q3' (no checks for redundant vertices), -'Q5' (no updates for outer planes), -and 'Q8' (no near-interior points) -increase Qhull's speed. The corresponding operations may not be -needed in your application.

    - -

    In 2-d and 3-d, a partial hull may be faster to produce. -Option 'QgGn' only builds facets -visible to point n. Option 'QgVn' -only builds facets that contain point n. In higher-dimensions, -this does not reduce the number of facets.

    - -

    User.h includes a number of performance-related -constants. Changes may improve Qhull performance on your data -sets. To understand their effect on performance, you will need to -read the corresponding code.

    - -

    GNU gprof reports that the dominate cost for 3-d -convex hull of cosperical points is qh_distplane(), mainly called -from qh_findbestnew(). The dominate cost for 3-d Delaunay triangulation -is creating new facets in qh_addpoint(), while qh_distplane() remains -the most expensive function. - -

    -

    »Enhancements to Qhull

    - -

    There are many ways in which Qhull can be improved.

    - -
    -[Jan 2016] Suggestions
-------------
-To do for a future verson of Qhull
- - Add a post-merge pass for Delaunay slivers.  Merge into a neighbor with a circumsphere that includes the opposite point. [M. Treacy]
- - Add a merge pass before cone creation to remove duplicate subridges between horizon facets
- - Option to add a bounding box for Delaunay triangulations, e,g., nearly coincident points
- - Report error when rbox Cn,r,m does not produce points (e.g., 'r' distributions)
- - Rescale output to match 'QbB' on input [J. Metz, 1/30/2014 12:21p]
- - Run through valgrind
- - Notes to compgeom on conformant triangulation and Voronoi volume
- - Git: Create signed tags for Qhull versions
- - Implement weighted Delaunay triangulation and weighted Voronoi diagram [A. Liebscher]
-   e.g., Sugihara, "Three-dimensional convex hull as a fruitful source of diagrams," Theoretical Computer Science, 2000, 235:325-337
- - testqset: test qh_setdelnth and move-to-front
- - Makefile: Re-review gcc/g++ warnings.  OK in 2011.
- - Break up -Wextra into its components or figure out how to override -Wunused-but-set-variable
-   unused-but-set-variable is reporting incorrectly.  All instances are annotated.
- - CMakelists.txt:  Why are files duplicated for cmake build
- - CMakeLists.txt: configure the 'ctest' target
- - The size of maxpoints in qh_maxsimplex should be d+3 unique points to help avoid QH6154
-
- - Can countT be defined as 'int', 'unsigned int', or 64-bit int?
-   countT is currently defined as 'int' in qset_r.h
-   Vertex ID and ridge ID perhaps should be countT, They are currently 'unsigned'
-   Check use of 'int' vs. countT in all cpp code
-   Check use of 'int' vs. countT in all c code
-   qset_r.h defines countT -- duplicates code in user_r.h -- need to add to qset.h/user.h
-   countT -1 used as a flag in Coordinates.mid(), QhullFacet->id()
-   Also QhullPoints indexOf and lastIndexOf
-   Also QhullPointSet indexOf and lastIndexOf
-   Coordinates.indexOf assumes countT is signed (from end)
-   Coordinates.lastIndexOf assumes countT is signed (from end)
-   All error messages with countT are wrong, convert to int?
-   RboxPoints.qh_fprintf_rbox, etc. message 9393 assumes countT but may be int, va_arg(args, countT);  Need to split
-
-------------
-To do for a furture version of the C++ interface
- - Fix C++ memory leak in user_eg3 [M. Sandim]
- - Document C++ using Doxygen conventions (//! and //!<)
- - Should Qhull manage the output formats for doubles?  QH11010 user_r.h defines qh_REAL_1 as %6.8g
- - Allocate memory for QhullSet using Qhull.qhmem.  Create default constructors for QhullVertexSet etc.  Also mid() etc.
- - Add interior point for automatic translation?
- - Add hasNext() to all next() iterators (e.g., QhullVertex)
- - Add defineAs() to each object
- - Write a program with concurrent Qhull
- - Write QhullStat and QhullStat_test
- - Add QList and vector instance of facetT*, etc.
- - Generalize QhullPointSetIterator
- - qh-code.htm: Document changes to C++ interface.
-      Organize C++ documentation into collection classes, etc.
- - Review all C++ classes and C++ tests
- - QhullVertexSet uses QhullSetBase::referenceSetT() to free it's memory.   Probably needed elsewhere
- - The Boost Graph Library provides C++ classes for graph data structures. It may help
-   enhance Qhull's C++ interface [Dr. Dobb's 9/00 p. 29-38; OOPSLA '99 p. 399-414].
-
-[Jan 2010] Suggestions
- - Generate vcproj from qtpro files
-   cd qtpro && qmake -spec win32-msvc2005 -tp vc -recursive
-   sed -i 's/C\:\/bash\/local\/qhull\/qtpro\///' qhull-all.sln
-   Change qhullcpp to libqhull.dll
-   Allow both builds on same host (keep /tmp separate)
- - Make distribution -- remove tmp, news, .git, leftovers from project, change CRLF
-     search for 2010.1, Dates
-     qhulltest --all added to output
-     Add md5sum
-     Add test of user_eg3, etc.
- - C++ class for access to statistics, accumulate vs. add
- - Add dialog box to RoadError-- a virtual function?
- - Option 'Gt' does not make visible all facets of the mesh example, rbox 32 M1,0,1 | qhull d Gt
- - Option to select bounded Voronoi regions [A. Uzunovic]
- - Merge small volume boundary cells into unbounded regions [Dominik Szczerba]
- - Postmerge with merge options
- - Add const to C code
- - Add modify operators and MutablePointCoordinateIterator to PointCoordinates
- - Add Qtest::toString() functions for QhullPoint and others.  QByteArray and qstrdup()
- - Fix option Qt for conformant triangulations of merged facets
- - Investigate flipped facet -- rbox 100 s D3 t1263080158 | qhull R1e-3 Tcv Qc
- - Add doc comments to c++ code
- - Measure performance of Qhull, seconds per point by dimension
- - Report potential wraparound of 64-bit ints -- e.g., a large set or points
-
-Documentation
-- Qhull::addPoint().  Problems with qh_findbestfacet and otherpoints see
-   qh-code.htm#inc on-line construction with qh_addpoint()
-- How to handle 64-bit possible loss of data.  WARN64, ptr_intT, size_t/int
-- Show custom of qh_fprintf
-- grep 'qh_mem ' x | sort | awk '{ print $2; }' | uniq -c | grep -vE ' (2|4|6|8|10|12|14|16|20|64|162)[^0-9]'
-- qtpro/qhulltest contains .pro and Makefile.  Remove Makefiles by setting shadow directory to ../../tmp/projectname
-- Rules for use of qh_qh and multi processes
-    UsingQhull
-    errorIfAnotherUser
-    ~QhullPoints() needs ownership of qh_qh
-    Does !qh_pointer work?
-    When is qh_qh required?  Minimize the time.
-   qhmem, qhstat.ferr
-   qhull_inuse==1 when qhull globals active [not useful?]
-   rbox_inuse==1 when rbox globals active
-   - Multithreaded -- call largest dimension for infinityPoint() and origin()
- - Better documentation for qhmem totshort, freesize, etc.
- - how to change .h, .c, and .cpp to text/html.  OK in Opera
- - QhullVertex.dimension() is not quite correct, epensive
- - Check globalAngleEpsilon
- - Deprecate save_qhull()
-
-[Dec 2003] Here is a partial list:
- - fix finddelaunay() in user_eg.c for tricoplanar facets
- - write a BGL, C++ interface to Qhull
-     http://www.boost.org/libs/graph/doc/table_of_contents.html
- - change qh_save_qhull to swap the qhT structure instead of using pointers
- - change error handling and tracing to be independent of 'qh ferr'
- - determine the maximum width for a given set of parameters
- - prove that directed search locates all coplanar facets
- - in high-d merging, can a loop of facets become disconnected?
- - find a way to improve inner hulls in 5-d and higher
- - determine the best policy for facet visibility ('Vn')
- - determine the limitations of 'Qg'
-
-Precision improvements:
- - For 'Qt', resolve cross-linked, butterfly ridges.
-     May allow retriangulation in qh_addpoint().
- - for Delaunay triangulations ('d' or 'v') under joggled input ('QJ'),
-     remove vertical facets whose lowest vertex may be coplanar with convex hull
- - review use of 'Qbb' with 'd QJ'.  Is MAXabs_coord better than MAXwidth?
- - check Sugihara and Iri's better in-sphere test [Canadian
-     Conf. on Comp. Geo., 1989; Univ. of Tokyo RMI 89-05]
- - replace centrum with center of mass and facet area
- - handle numeric overflow in qh_normalize and elsewhere
- - merge flipped facets into non-flipped neighbors.
-     currently they merge into best neighbor (appears ok)
- - determine min norm for Cramer's rule (qh_sethyperplane_det).  It looks high.
- - improve facet width for very narrow distributions
-
-New features:
- - implement Matlab's tsearch() using Qhull
- - compute volume of Voronoi regions.  You need to determine the dual face
-   graph in all dimensions [see Clarkson's hull program]
- - compute alpha shapes [see Clarkson's hull program]
- - implement deletion of Delaunay vertices
-      see Devillers, ACM Symposium on Computational Geometry, Minneapolis 1999.
- - compute largest empty circle [see O'Rourke, chapter 5.5.3] [Hase]
- - list redundant (i.e., coincident) vertices [Spitz]
- - implement Mucke, et al, ['96] for point location in Delaunay triangulations
- - implement convex hull of moving points
- - implement constrained Delaunay diagrams
-      see Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.
- - estimate outer volume of hull
- - automatically determine lower dimensional hulls
- - allow "color" data for input points
-      need to insert a coordinate for Delaunay triangulations
-
-Input/output improvements:
- - Support the VTK Visualization Toolkit, http://www.kitware.com/vtk.html
- - generate output data array for Qhull library [Gautier]
- - need improved DOS window with screen fonts, scrollbar, cut/paste
- - generate Geomview output for Voronoi ridges and unbounded rays
- - generate Geomview output for halfspace intersection
- - generate Geomview display of furthest-site Voronoi diagram
- - use 'GDn' to view 5-d facets in 4-d
- - convert Geomview output for other 3-d viewers
- - add interactive output option to avoid recomputing a hull
- - orient vertex neighbors for 'Fv' in 3-d and 2-d
- - track total number of ridges for summary and logging
-
-Performance improvements:
- - optimize Qhull for 2-d Delaunay triangulations
- -   use O'Rourke's '94 vertex->duplicate_edge
- -   add bucketing
- -   better to specialize all of the code (ca. 2-3x faster w/o merging)
- - use updated LU decomposition to speed up hyperplane construction
- -        [Gill et al. 1974, Math. Comp. 28:505-35]
- - construct hyperplanes from the corresponding horizon/visible facets
- - for merging in high d, do not use vertex->neighbors
-
-
    - -

    Please let us know about your applications and improvements.

    - -
    - -

    Up: Home -page for Qhull
    -Up: Qhull manual: Table of -Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: Qhull code: Table of Contents
    -Dn: Qhull functions, macros, and data -structures - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see changes.txt

    - - diff --git a/src/qhull/html/qh-eg.htm b/src/qhull/html/qh-eg.htm deleted file mode 100644 index a08f0d13f..000000000 --- a/src/qhull/html/qh-eg.htm +++ /dev/null @@ -1,693 +0,0 @@ - - - - -Examples of Qhull - - - - -

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    - -

    - -

    [halfspace] Examples of Qhull

    - -

    This section of the Qhull manual will introduce you to Qhull -and its options. Each example is a file for viewing with Geomview. You will need to -use a Unix computer with a copy of Geomview. -

    -If you are not running Unix, you can view pictures -for some of the examples. To understand Qhull without Geomview, try the -examples in Programs and -Programs/input. You can also try small -examples that you compute by hand. Use rbox -to generate examples. -

    -To generate the Geomview examples, execute the shell script eg/q_eg. -It uses rbox. The shell script eg/q_egtest generates -test examples, and eg/q_test exercises the code. If you -find yourself viewing the inside of a 3-d example, use Geomview's -normalization option on the 'obscure' menu.

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »Qhull examples: Table of -Contents

    - - - -
    - - -
    - -

    »2-d and 3-d examples

    - -

    »rbox c D3 | qconvex G ->eg.01.cube

    - -

    The first example is a cube in 3-d. The color of each facet -indicates its normal. For example, normal [0,0,1] along the Z -axis is (r=0.5, g=0.5, b=1.0). With the 'Dn' option in rbox, -you can generate hypercubes in any dimension. Above 7-d the -number of intermediate facets grows rapidly. Use 'TFn' to track qconvex's progress. Note -that each facet is a square that qconvex merged from coplanar -triangles.

    - -

    »rbox c d G3.0 | qconvex G ->eg.02.diamond.cube

    - -

    The second example is a cube plus a diamond ('d') scaled by rbox's -'G' option. In higher dimensions, diamonds are much simpler than -hypercubes.

    - -

    »rbox s 100 D3 | qconvex G ->eg.03.sphere

    - -

    The rbox s option generates random points and -projects them to the d-sphere. All points should be on the convex -hull. Notice that random points look more clustered than you -might expect. You can get a smoother distribution by merging -facets and printing the vertices, e.g., rbox 1000 s | qconvex -A-0.95 p | qconvex G >eg.99.

    - -

    »rbox s 100 D2 | qconvex G ->eg.04.circle

    - -

    In 2-d, there are many ways to generate a convex hull. One of -the earliest algorithms, and one of the fastest, is the 2-d -Quickhull algorithm [c.f., Preparata & Shamos '85]. It was the model for -Qhull.

    - -

    »rbox 10 l | qconvex G ->eg.05.spiral

    - -

    One rotation of a spiral.

    - -

    »rbox 1000 D2 | qconvex C-0.03 -Qc Gapcv >eg.06.merge.square

    - -

    This demonstrates how Qhull handles precision errors. Option 'C-0.03' requires a clearly convex angle -between adjacent facets. Otherwise, Qhull merges the facets.

    - -

    This is the convex hull of random points in a square. The -facets have thickness because they must be outside all points and -must include their vertices. The colored lines represent the -original points and the spheres represent the vertices. Floating -in the middle of each facet is the centrum. Each centrum is at -least 0.03 below the planes of its neighbors. This guarantees -that the facets are convex.

    - -

    »rbox 1000 D3 | qconvex G ->eg.07.box

    - -

    Here's the same distribution but in 3-d with Qhull handling -machine roundoff errors. Note the large number of facets.

    - -

    »rbox c G0.4 s 500 | qconvex G ->eg.08a.cube.sphere

    - -

    The sphere is just barely poking out of the cube. Try the same -distribution with randomization turned on ('Qr'). This turns Qhull into a -randomized incremental algorithm. To compare Qhull and -randomization, look at the number of hyperplanes created and the -number of points partitioned. Don't compare CPU times since Qhull's -implementation of randomization is inefficient. The number of -hyperplanes and partitionings indicate the dominant costs for -Qhull. With randomization, you'll notice that the number of -facets created is larger than before. This is especially true as -you increase the number of points. It is because the randomized -algorithm builds most of the sphere before it adds the cube's -vertices.

    - -

    »rbox d G0.6 s 500 | qconvex G ->eg.08b.diamond.sphere

    - -

    This is a combination of the diamond distribution and the -sphere.

    - -

    »rbox 100 L3 G0.5 s | qconvex -G >eg.09.lens

    - -

    Each half of the lens distribution lies on a sphere of radius -three. A directed search for the furthest facet below a point -(e.g., qh_findbest in geom.c) may fail if started from -an arbitrary facet. For example, if the first facet is on the -opposite side of the lens, a directed search will report that the -point is inside the convex hull even though it is outside. This -problem occurs whenever the curvature of the convex hull is less -than a sphere centered at the test point.

    - -

    To prevent this problem, Qhull does not use directed search -all the time. When Qhull processes a point on the edge of the -lens, it partitions the remaining points with an exhaustive -search instead of a directed search (see qh_findbestnew in geom2.c). -

    - -

    »How Qhull adds a point

    - -

    »rbox 100 s P0.5,0.5,0.5 | -qconvex Ga QG0 >eg.10a.sphere.visible

    - -

    The next 4 examples show how Qhull adds a point. The point -[0.5,0.5,0.5] is at one corner of the bounding box. Qhull adds a -point using the beneath-beyond algorithm. First Qhull finds all -of the facets that are visible from the point. Qhull will replace -these facets with new facets.

    - -

    »rbox 100 s -P0.5,0.5,0.5|qconvex Ga QG-0 >eg.10b.sphere.beyond

    - -

    These are the facets that are not visible from the point. -Qhull will keep these facets.

    - -

    »rbox 100 s P0.5,0.5,0.5 | -qconvex PG Ga QG0 >eg.10c.sphere.horizon

    - -

    These facets are the horizon facets; they border the visible -facets. The inside edges are the horizon ridges. Each horizon -ridge will form the base for a new facet.

    - -

    »rbox 100 s P0.5,0.5,0.5 | -qconvex Ga QV0 PgG >eg.10d.sphere.cone

    - -

    This is the cone of points from the new point to the horizon -facets. Try combining this image with eg.10c.sphere.horizon -and eg.10a.sphere.visible. -

    - -

    »rbox 100 s P0.5,0.5,0.5 | -qconvex Ga >eg.10e.sphere.new

    - -

    This is the convex hull after [0.5,0.5,0.5] has been added. -Note that in actual practice, the above sequence would never -happen. Unlike the randomized algorithms, Qhull always processes -a point that is furthest in an outside set. A point like -[0.5,0.5,0.5] would be one of the first points processed.

    - -

    »rbox 100 s P0.5,0.5,0.5 | -qhull Ga QV0g Q0 >eg.14.sphere.corner

    - -

    The 'QVn', 'QGn ' and 'Pdk' -options define good facets for Qhull. In this case 'QV0' defines the 0'th point -[0.5,0.5,0.5] as the good vertex, and 'Qg' -tells Qhull to only build facets that might be part of a good -facet. This technique reduces output size in low dimensions. It -does not work with facet merging.

    - -

    »Triangulated output or joggled input

    - -

    »rbox 500 W0 | qconvex QR0 Qc Gvp >eg.15a.surface

    - -

    This is the convex hull of 500 points on the surface of -a cube. Note the large, non-simplicial facet for each face. -Qhull merges non-convex facets. - -

    If the facets were not merged, Qhull -would report precision problems. For example, turn off facet merging -with option 'Q0'. Qhull may report concave -facets, flipped facets, or other precision errors: -

    -rbox 500 W0 | qhull QR0 Q0 -
    - -

    -

    »rbox 500 W0 | qconvex QR0 Qt Qc Gvp >eg.15b.triangle

    - -

    Like the previous examples, this is the convex hull of 500 points on the -surface of a cube. Option 'Qt' triangulates the -non-simplicial facets. Triangulated output is -particularly helpful for Delaunay triangulations. - -

    -

    »rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp >eg.15c.joggle

    - -

    This is the convex hull of 500 joggled points on the surface of -a cube. The option 'QJ5e-2' -sets a very large joggle to make the effect visible. Notice -that all of the facets are triangles. If you rotate the cube, -you'll see red-yellow lines for coplanar points. -

    -With option 'QJ', Qhull joggles the -input to avoid precision problems. It adds a small random number -to each input coordinate. If a precision -error occurs, it increases the joggle and tries again. It repeats -this process until no precision problems occur. -

    -Joggled input is a simple solution to precision problems in -computational geometry. Qhull can also merge facets to handle -precision problems. See Merged facets or joggled input. - -

    »Delaunay and Voronoi diagrams

    - -

    »qdelaunay Qt -<eg.data.17 GnraD2 >eg.17a.delaunay.2

    - -

    -The input file, eg.data.17, consists of a square, 15 random -points within the outside half of the square, and 6 co-circular -points centered on the square. - -

    The Delaunay triangulation is the triangulation with empty -circumcircles. The input for this example is unusual because it -includes six co-circular points. Every triangular subset of these -points has the same circumcircle. Option 'Qt' -triangulates the co-circular facet.

    - -

    »qdelaunay <eg.data.17 -GnraD2 >eg.17b.delaunay.2i

    - -

    This is the same example without triangulated output ('Qt'). qdelaunay -merges the non-unique Delaunay triangles into a hexagon.

    - -

    »qdelaunay <eg.data.17 -Ga >eg.17c.delaunay.2-3

    - -

    This is how Qhull generated both diagrams. Use Geomview's -'obscure' menu to turn off normalization, and Geomview's -'cameras' menu to turn off perspective. Then load this object -with one of the previous diagrams.

    - -

    The points are lifted to a paraboloid by summing the squares -of each coordinate. These are the light blue points. Then the -convex hull is taken. That's what you see here. If you look up -the Z-axis, you'll see that points and edges coincide.

    - -

    »qvoronoi QJ -<eg.data.17 Gna >eg.17d.voronoi.2

    - -

    The Voronoi diagram is the dual of the Delaunay triangulation. -Here you see the original sites and the Voronoi vertices. -Notice the each -vertex is equidistant from three sites. The edges indicate the -Voronoi region for a site. Qhull does not draw the unbounded -edges. Instead, it draws extra edges to close the unbounded -Voronoi regions. You may find it helpful to enclose the input -points in a square. You can compute the unbounded -rays from option 'Fo'. -

    - -

    Instead -of triangulated output ('Qt'), this -example uses joggled input ('QJ'). -Normally, you should use neither 'QJ' nor 'Qt' for Voronoi diagrams. - -

    »qvoronoi <eg.data.17 -Gna >eg.17e.voronoi.2i

    - -

    This looks the same as the previous diagrams, but take a look -at the data. Run 'qvoronoi p <eg/eg.data.17'. This prints -the Voronoi vertices. - -

    With 'QJ', there are four nearly identical Voronoi vertices -within 10^-11 of the origin. Option 'QJ' joggled the input. After the joggle, -the cocircular -input sites are no longer cocircular. The corresponding Voronoi vertices are -similar but not identical. - -

    This example does not use options 'Qt' or 'QJ'. The cocircular -input sites define one Voronoi vertex near the origin.

    - -

    Option 'Qt' would triangulate the corresponding Delaunay region into -four triangles. Each triangle is assigned the same Voronoi vertex.

    - -

    » rbox c G0.1 d | -qdelaunay Gt Qz <eg.17f.delaunay.3

    - -

    This is the 3-d Delaunay triangulation of a small cube inside -a prism. Since the outside ridges are transparent, it shows the -interior of the outermost facets. If you slice open the -triangulation with Geomview's ginsu, you will see that the innermost -facet is a cube. Note the use of 'Qz' -to add a point "at infinity". This avoids a degenerate -input due to cospherical points.

    - -

    »rbox 10 D2 d | qdelaunay -Qu G >eg.18a.furthest.2-3

    - -

    The furthest-site Voronoi diagram contains Voronoi regions for -points that are furthest from an input site. It is the -dual of the furthest-site Delaunay triangulation. You can -determine the furthest-site Delaunay triangulation from the -convex hull of the lifted points (eg.17c.delaunay.2-3). -The upper convex hull (blue) generates the furthest-site Delaunay -triangulation.

    - -

    »rbox 10 D2 d | qdelaunay -Qu Pd2 G >eg.18b.furthest-up.2-3

    - -

    This is the upper convex hull of the preceding example. The -furthest-site Delaunay triangulation is the projection of the -upper convex hull back to the input points. The furthest-site -Voronoi vertices are the circumcenters of the furthest-site -Delaunay triangles.

    - -

    »rbox 10 D2 d | qvoronoi -Qu Gv >eg.18c.furthest.2

    - -

    This shows an incomplete furthest-site Voronoi diagram. It -only shows regions with more than two vertices. The regions are -artificially truncated. The actual regions are unbounded. You can -print the regions' vertices with 'qvoronoi Qu o'.

    - -

    Use Geomview's 'obscure' menu to turn off normalization, and -Geomview's 'cameras' menu to turn off perspective. Then load this -with the upper convex hull.

    - -

    »rbox 10 D3 | qvoronoi QV5 -p | qconvex G >eg.19.voronoi.region.3

    - -

    This shows the Voronoi region for input site 5 of a 3-d -Voronoi diagram.

    - -

    »Facet merging for imprecision

    - -

    »rbox r s 20 Z1 G0.2 | -qconvex G >eg.20.cone

    - -

    There are two things unusual about this cone. -One is the large flat disk at one end and the other is the -rectangles about the middle. That's how the points were -generated, and if those points were exact, this is the correct -hull. But rbox used floating point arithmetic to -generate the data. So the precise convex hull should have been -triangles instead of rectangles. By requiring convexity, Qhull -has recovered the original design.

    - -

    »rbox 200 s | qhull Q0 -R0.01 Gav Po >eg.21a.roundoff.errors

    - -

    This is the convex hull of 200 cospherical points with -precision errors ignored ('Q0'). To -demonstrate the effect of roundoff error, we've added a random -perturbation ('R0.01') to every -distance and hyperplane calculation. Qhull, like all other convex -hull algorithms with floating point arithmetic, makes -inconsistent decisions and generates wildly wrong results. In -this case, one or more facets are flipped over. These facets have -the wrong color. You can also turn on 'normals' in Geomview's -appearances menu and turn off 'facing normals'. There should be -some white lines pointing in the wrong direction. These -correspond to flipped facets.

    - -

    Different machines may not produce this picture. If your -machine generated a long error message, decrease the number of -points or the random perturbation ('R0.01'). -If it did not report flipped facets, increase the number of -points or perturbation.

    - -

    »rbox 200 s | qconvex Qc -R0.01 Gpav >eg.21b.roundoff.fixed

    - -

    Qhull handles the random perturbations and returns an -imprecise sphere. -In this case, the output is a weak approximation to the points. -This is because a random perturbation of 'R0.01 ' is equivalent to losing all but -1.8 digits of precision. The outer planes float above the points -because Qhull needs to allow for the maximum roundoff error.

    -

    -If you start with a smaller random perturbation, you -can use joggle ('QJn') to avoid -precision problems. You need to set n significantly -larger than the random perturbation. For example, try -'rbox 200 s | qconvex Qc R1e-4 QJ1e-1'. - -

    »rbox 1000 s| qconvex C0.01 -Qc Gcrp >eg.22a.merge.sphere.01

    - -

    »rbox 1000 s| qconvex -C-0.01 Qc Gcrp >eg.22b.merge.sphere.-01

    - -

    »rbox 1000 s| qconvex C0.05 -Qc Gcrpv >eg.22c.merge.sphere.05

    - -

    »rbox 1000 s| qconvex -C-0.05 Qc Gcrpv >eg.22d.merge.sphere.-05

    - -

    The next four examples compare post-merging and pre-merging ('Cn' vs. 'C-n'). -Qhull uses '-' as a flag to indicate pre-merging.

    - -

    Post-merging happens after the convex hull is built. During -post-merging, Qhull repeatedly merges an independent set of -non-convex facets. For a given set of parameters, the result is -about as good as one can hope for.

    - -

    Pre-merging does the same thing as post-merging, except that -it happens after adding each point to the convex hull. With -pre-merging, Qhull guarantees a convex hull, but the facets are -wider than those from post-merging. If a pre-merge option is not -specified, Qhull handles machine round-off errors.

    - -

    You may see coplanar points appearing slightly outside -the facets of the last example. This is becomes Geomview moves -line segments forward toward the viewer. You can avoid the -effect by setting 'lines closer' to '0' in Geomview's camera menu. - -

    »rbox 1000 | qconvex s -Gcprvah C0.1 Qc >eg.23.merge.cube

    - -

    Here's the 3-d imprecise cube with all of the Geomview -options. There's spheres for the vertices, radii for the coplanar -points, dots for the interior points, hyperplane intersections, -centrums, and inner and outer planes. The radii are shorter than -the spheres because this uses post-merging ('C0.1') -instead of pre-merging. - -

    »4-d objects

    - -

    With Qhull and Geomview you can develop an intuitive sense of -4-d surfaces. When you get into trouble, think of viewing the -surface of a 3-d sphere in a 2-d plane.

    - -

    »rbox 5000 D4 | qconvex s GD0v -Pd0:0.5 C-0.02 C0.1 >eg.24.merge.cube.4d-in-3d

    - -

    Here's one facet of the imprecise cube in 4-d. It's projected -into 3-d (the 'GDn' option drops -dimension n). Each ridge consists of two triangles between this -facet and the neighboring facet. In this case, Geomview displays -the topological ridges, i.e., as triangles between three -vertices. That is why the cube looks lopsided.

    - -

    »rbox 5000 D4 | qconvex s -C-0.02 C0.1 Gh >eg.30.4d.merge.cube

    - -

    Here -is the equivalent in 4-d of the imprecise square -and imprecise cube. It's the imprecise convex -hull of 5000 random points in a hypercube. It's a full 4-d object -so Geomview's ginsu does not work. If you view it in -Geomview, you'll be inside the hypercube. To view 4-d objects -directly, either load the 4dview module or the ndview -module. For 4dview, you must have started Geomview -in the same directory as the object. For ndview, -initialize a set of windows with the prefab menu, and load the -object through Geomview. The 4dview module includes an -option for slicing along any hyperplane. If you do this in the x, -y, or z plane, you'll see the inside of a hypercube.

    - -

    The 'Gh' option prints the -geometric intersections between adjacent facets. Note the strong -convexity constraint for post-merging ('C0.1'). -It deletes the small facets.

    - -

    »rbox 20 D3 | qdelaunay G ->eg.31.4d.delaunay

    - -

    The Delaunay triangulation of 3-d sites corresponds to a 4-d -convex hull. You can't see 4-d directly but each facet is a 3-d -object that you can project to 3-d. This is exactly the same as -projecting a 2-d facet of a soccer ball onto a plane.

    - -

    Here we see all of the facets together. You can use Geomview's -ndview to look at the object from several directions. -Try turning on edges in the appearance menu. You'll notice that -some edges seem to disappear. That's because the object is -actually two sets of overlapping facets.

    - -

    You can slice the object apart using Geomview's 4dview. -With 4dview, try slicing along the w axis to get a -single set of facets and then slice along the x axis to look -inside. Another interesting picture is to slice away the equator -in the w dimension.

    - -

    »rbox 30 s D4 | qconvex s G -Pd0d1d2D3

    - -

    This is the positive octant of the convex hull of 30 4-d -points. When looking at 4-d, it's easier to look at just a few -facets at once. If you picked a facet that was directly above -you, then that facet looks exactly the same in 3-d as it looks in -4-d. If you pick several facets, then you need to imagine that -the space of a facet is rotated relative to its neighbors. Try -Geomview's ndview on this example.

    - -

    »Halfspace intersections

    - -

    »rbox 10 r s Z1 G0.3 | -qconvex G >eg.33a.cone

    - -

    »rbox 10 r s Z1 G0.3 | -qconvex FV n | qhalf G >eg.33b.cone.dual

    - -

    »rbox 10 r s Z1 G0.3 | -qconvex FV n | qhalf Fp | qconvex G >eg.33c.cone.halfspace

    - -

    These examples illustrate halfspace intersection. The first -picture is the convex hull of two 20-gons plus an apex. The -second picture is the dual of the first. Try loading both -at once. Each vertex of the second picture corresponds to a facet -or halfspace of the first. The vertices with four edges -correspond to a facet with four neighbors. Similarly the facets -correspond to vertices. A facet's normal coefficients divided by -its negative offset is the vertice's coordinates. The coordinates -are the intersection of the original halfspaces.

    - -

    The third picture shows how Qhull can go back and forth -between equivalent representations. It starts with a cone, -generates the halfspaces that define each facet of the cone, and -then intersects these halfspaces. Except for roundoff error, the -third picture is a duplicate of the first.

    - -
    - -

    Up: Home -page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
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    - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-faq.htm b/src/qhull/html/qh-faq.htm deleted file mode 100644 index feda544a7..000000000 --- a/src/qhull/html/qh-faq.htm +++ /dev/null @@ -1,1547 +0,0 @@ - - - - - - -Qhull FAQ - - - - - -

    Up: Home page for Qhull -(http://www.qhull.org)
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
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    - -

    - -

    [4-d cube] Frequently Asked Questions about Qhull

    -

    If your question does not appear here, see:

    - - - -

    Qhull is a general dimension code for computing convex hulls, -Delaunay triangulations, halfspace intersections about a point, -Voronoi diagrams, furthest-site Delaunay triangulations, and -furthest-site Voronoi diagrams. These structures have -applications in science, engineering, statistics, and -mathematics. For a detailed introduction, see O'Rourke ['94], Computational Geometry in C. -

    - -

    There are separate programs for each application of -Qhull. These programs disable experimental and inappropriate -options. If you prefer, you may use Qhull directly. All programs -run the same code. - -

    Version 3.1 added triangulated output ('Qt'). -It should be used for Delaunay triangulations instead of -using joggled input ('QJ'). - -

    Brad Barber, Arlington MA, -2010/01/09

    - -

    Copyright © 1998-2015 C.B. Barber

    - -
    - -

    »FAQ: Table of Contents

    - -

    Within each category, the most recently asked questions are -first. -

      -
    • Startup questions
        -
      • How do I run Qhull from Windows? -
      • How do I enter points for Qhull? -
      • How do I learn to use Qhull?
        • -
      -
    • Convex hull questions
        -
      • How do I report just the area and volume of a - convex hull? -
      • Why are there extra points in a 4-d or higher - convex hull? -
      • How do I report duplicate - vertices?
        • -
      -
    • Delaunay triangulation questions
        -
      • How do I get rid of nearly flat Delaunay - triangles? -
      • How do I find the Delaunay triangle or Voronoi - region that is closest to a point? - -
      • How do I compute the Delaunay triangulation of a - non-convex object? - -
      • How do I mesh a volume from a set of triangulated - surface points? - -
      • Can Qhull produce a triangular mesh for an - object? - -
      • For 3-d Delaunay triangulations, how do I - report the triangles of each tetrahedron? - -
      • How do I construct a 3-d Delaunay triangulation? -
      • How do I get the triangles for a 2-d Delaunay - triangulation and the vertices of its Voronoi diagram? -
      • Can Qhull triangulate a - hundred 16-d points?
        • -
      - -
    • Voronoi diagram questions
        -
      • See also "Delaunay diagram questions". Qhull computes the Voronoi diagram from the Delaunay triagulation. -
      • How do I compute the volume of a Voronoi region? -
      • How do I get the radii of the empty - spheres for each Voronoi vertex? - -
      • What is the Voronoi diagram of a square? - -
      • How do I construct the Voronoi diagram of - cospherical points? -
      • Can Qhull compute the unbounded rays of the - Voronoi diagram? -
      -
    • Approximation questions
        -
      • How do I approximate data - with a simplex?
        • -
      -
    • Halfspace questions
        -
      • How do I compute the - intersection of halfspaces with Qhull?
        • -
      -
    • Qhull library questions
        -
      • Is Qhull available for Mathematica, Matlab, or - Maple? - -
      • Why are there too few ridges? -
      • Can Qhull use coordinates without placing them in - a data file? -
      • How large are Qhull's data structures? -
      • Can Qhull construct convex hulls and Delaunay - triangulations one point at a time? -
      • How do I visit the ridges of a Delaunay - triangulation? -
      • How do I visit the Delaunay facets? -
      • When is a point outside or inside a facet? -
      • How do I find the facet that is closest to a - point? -
      • How do I find the Delaunay triangle or Voronoi - region that is closest to a point? -
      • How do I list the vertices? -
      • How do I test code that uses the Qhull library? -
      • When I compute a plane - equation from a facet, I sometimes get an - outward-pointing normal and sometimes an - inward-pointing normal
        • -
      -
      • -
    - -
    - -

    »Startup questions

    - -

    »How do I run Qhull -from Windows?

    - -

    Qhull is a console program. You will first need a command window -(i.e., a "command prompt"). You can double click on -'eg\Qhull-go.bat'.

    - -
      -
    • Type 'qconvex', 'qdelaunay', 'qhalf', 'qvoronoi, - 'qhull', and 'rbox' for a synopsis of each program. - -
    • Type 'rbox c D2 | qconvex s i' to compute the - convex hull of a square. - -
    • Type 'rbox c D2 | qconvex s i TO results.txt' to - write the results to the file 'results.txt'. A summary is still printed on - the the console. - -
    • Type 'rbox c D2' to see the input format for - qconvex. - -
    • Type 'qconvex < data.txt s i TO results.txt' to - read input data from 'data.txt'. - -
    • If you want to enter data by hand, type 'qconvex s i TO - results.txt' to read input data from the console. Type in - the numbers and end with a ctrl-D.
      • -
    - -

    »How do I enter -points for Qhull?

    - -

    Qhull takes its data from standard input. For example, create -a file named 'data.txt' with the following contents:

    - -
    - 
    -2  #sample 2-d input
-5  #number of points
-1 2  #coordinates of points
--1.1 3
-3 2.2
-4 5
--10 -10
-
    -
    - -

    Then call qconvex with 'qconvex < data.txt'. It will print a -summary of the convex hull. Use 'qconvex < data.txt o' to print -the vertices and edges. See also input -format.

    - -

    You can generate sample data with rbox, e.g., 'rbox 10' -generates 10 random points in 3-d. Use a pipe ('|') to run rbox -and qhull together, e.g.,

    - -
    -

    rbox c | qconvex o

    -
    - -

    computes the convex hull of a cube.

    - -

    »How do I learn to -use Qhull?

    - -

    First read:

    - - - -

    Look at Qhull's on-line documentation:

    - -
      -
    • 'qconvex' gives a synopsis of qconvex and its options - -
    • 'rbox' lists all of the options for generating point - sets -
    • 'qconvex - | more' lists the options for qconvex -
    • 'qconvex .' gives a concise list of options -
    • 'qdelaunay', 'qhalf', 'qvoronoi', and 'qhull' also have a synopsis and option list
      • -
    - -

    Then try out the Qhull programs on small examples.

    - -
      -
    • 'rbox c' lists the vertices of a cube -
    • 'rbox c | qconvex' is the convex hull of a cube -
    • 'rbox c | qconvex o' lists the vertices and facets of - a cube -
    • 'rbox c | qconvex Qt o' triangulates the cube -
    • 'rbox c | qconvex QJ o' joggles the input and - triangulates the cube -
    • 'rbox c D2 | qconvex' generates the convex hull of a - square -
    • 'rbox c D4 | qconvex' generates the convex hull of a - hypercube -
    • 'rbox 6 s D2 | qconvex p Fx' lists 6 random points in - a circle and lists the vertices of their convex hull in order -
    • 'rbox c D2 c G2 | qdelaunay' computes the Delaunay - triangulation of two embedded squares. It merges the cospherical facets. -
    • 'rbox c D2 c G2 | qdelaunay Qt' computes the Delaunay - triangulation of two embedded squares. It triangulates the cospherical facets. -
    • 'rbox c D2 c G2 | qvoronoi o' computes the - corresponding Voronoi vertices and regions. -
    • 'rbox c D2 c G2 | qvoronio Fv' shows the Voronoi diagram - for the previous example. Each line is one edge of the - diagram. The first number is 4, the next two numbers list - a pair of input sites, and the last two numbers list the - corresponding pair of Voronoi vertices.
      • -
    - -

    Install Geomview -if you are running SGI Irix, Solaris, SunOS, Linux, HP, IBM -RS/6000, DEC Alpha, or Next. You can then visualize the output of -Qhull. Qhull comes with Geomview examples. -

    - -

    Then try Qhull with a small example of your application. Work -out the results by hand. Then experiment with Qhull's options to -find the ones that you need.

    - -

    You will need to decide how Qhull should handle precision -problems. It can triangulate the output ('Qt'), joggle the input ('QJ'), or merge facets (the default).

    - -
      -
    • With joggle, Qhull produces simplicial (i.e., - triangular) output by joggling the input. After joggle, - no points are cocircular or cospherical. -
    • With facet merging, Qhull produces a better - approximation and does not modify the input. -
    • With triangulated output, Qhull merges facets and triangulates - the result.
      • -
    • See Merged facets or joggled input.
      • -
    - -
    -

    »Convex hull questions

    - -

    »How do I report just the area - and volume of a convex hull?

    - -Use option 'FS'. For example, - -
    -C:\qhull>rbox 10 | qconvex FS
-0
-2 2.192915621644613 0.2027867899638665
-
-C:\qhull>rbox 10 | qconvex FA
-
-Convex hull of 10 points in 3-d:
-
-  Number of vertices: 10
-  Number of facets: 16
-
-Statistics for: RBOX 10 | QCONVEX FA
-
-  Number of points processed: 10
-  Number of hyperplanes created: 28
-  Number of distance tests for qhull: 44
-  CPU seconds to compute hull (after input):  0
-  Total facet area:   2.1929156
-  Total volume:       0.20278679
-
    - -

    »Why are there extra -points in a 4-d or higher convex hull?

    - -

    You may see extra points if you use options 'i' or 'Ft' - without using triangulated output ('Qt'). -The extra points occur when a facet is non-simplicial (i.e., a -facet with more than d vertices). For example, Qhull -reports the following for one facet of the convex hull of a hypercube. -Option 'Pd0:0.5' returns the facet along the positive-x axis:

    - -
    - 
    -rbox c D4 | qconvex i Pd0:0.5
-12
-17 13 14 15
-17 13 12 14
-17 11 13 15
-17 14 11 15
-17 10 11 14
-17 14 12 8
-17 12 13 8
-17 10 14 8
-17 11 10 8
-17 13 9 8
-17 9 11 8
-17 11 9 13
-
    -
    - -

    The 4-d hypercube has 16 vertices; so point "17" was -added by qconvex. Qhull adds the point in order to report a -simplicial decomposition of the facet. The point corresponds to -the "centrum" which Qhull computes to test for -convexity.

    - -

    Triangulate the output ('Qt') to avoid the extra points. -Since the hypercube is 4-d, each simplicial facet is a tetrahedron. -

    -
    -C:\qhull3.1>rbox c D4 | qconvex i Pd0:0.5 Qt
-9
-9 13 14 15
-12 9 13 14
-9 11 13 15
-11 9 14 15
-9 10 11 14
-12 9 14 8
-9 12 13 8
-9 10 14 8
-10 9 11 8
-
    -
    - -

    Use the 'Fv' option to print the -vertices of simplicial and non-simplicial facets. For example, -here is the same hypercube facet with option 'Fv' instead of 'i': -

    - -
    - 
    -C:\qhull>rbox c D4 | qconvex Pd0:0.5 Fv
-1
-8 9 10 12 11 13 14 15 8
-
    -
    - -

    The coordinates of the extra point are printed with the 'Ft' option.

    - -
    - 
    -rbox c D4 | qconvex Pd0:0.5 Ft
-4
-17 12 3
-  -0.5   -0.5   -0.5   -0.5
-  -0.5   -0.5   -0.5    0.5
-  -0.5   -0.5    0.5   -0.5
-  -0.5   -0.5    0.5    0.5
-  -0.5    0.5   -0.5   -0.5
-  -0.5    0.5   -0.5    0.5
-  -0.5    0.5    0.5   -0.5
-  -0.5    0.5    0.5    0.5
-   0.5   -0.5   -0.5   -0.5
-   0.5   -0.5   -0.5    0.5
-   0.5   -0.5    0.5   -0.5
-   0.5   -0.5    0.5    0.5
-   0.5    0.5   -0.5   -0.5
-   0.5    0.5   -0.5    0.5
-   0.5    0.5    0.5   -0.5
-   0.5    0.5    0.5    0.5
-   0.5      0      0      0
-4 16 13 14 15
-4 16 13 12 14
-4 16 11 13 15
-4 16 14 11 15
-4 16 10 11 14
-4 16 14 12 8
-4 16 12 13 8
-4 16 10 14 8
-4 16 11 10 8
-4 16 13 9 8
-4 16 9 11 8
-4 16 11 9 13
-
    -
    - -

    »How do I report -duplicate vertices?

    - -

    There's no direct way. You can use option -'FP' to -report the distance to the nearest vertex for coplanar input -points. Select the minimum distance for a duplicated vertex, and -locate all input sites less than this distance.

    - -

    For Delaunay triangulations, all coplanar points are nearly -incident to a vertex. If you want a report of coincident input -sites, do not use option 'QJ'. By -adding a small random quantity to each input coordinate, it -prevents coincident input sites.

    - -
    -

    »Delaunay triangulation questions

    - -

    »How do I get rid of -nearly flat Delaunay triangles?

    - -

    Nearly flat triangles occur when boundary points are nearly -collinear or coplanar. They also occur for nearly coincident -points. Both events can easily occur when using joggle. For example -(rbox 10 W0 D2 | qdelaunay QJ Fa) lists the areas of the Delaunay -triangles of 10 points on the boundary of a square. Some of -these triangles are nearly flat. This occurs when one point -is joggled inside of two other points. In this case, nearly flat -triangles do not occur with triangulated output (rbox 10 W0 D2 | qdelaunay Qt Fa). - - -

    Another example, (rbox c P0 P0 D2 | qdelaunay QJ Fa), computes the -areas of the Delaunay triangles for the unit square and two -instances of the origin. Four of the triangles have an area -of 0.25 while two have an area of 2.0e-11. The later are due to -the duplicated origin. With triangulated output (rbox c P0 P0 D2 | qdelaunay Qt Fa) -there are four triangles of equal area. - -

    Nearly flat triangles also occur without using joggle. For -example, (rbox c P0 P0,0.4999999999 | qdelaunay Fa), computes -the areas of the Delaunay triangles for the unit square, -a nearly collinear point, and the origin. One triangle has an -area of 3.3e-11. - -

    Unfortunately, none of Qhull's merging options remove nearly -flat Delaunay triangles due to nearly collinear or coplanar boundary -points. -The merging options concern the empty circumsphere -property of Delaunay triangles. This is independent of the area of -the Delaunay triangles. Qhull does handle nearly coincident points. - -

    If you are calling Qhull from a program, you can merge slivers into an adjacent facet. -In d dimensions with simplicial facets (e.g., from 'Qt'), each facet has -d+1 neighbors. Each neighbor shares d vertices of the facet's d+1 vertices. Let the -other vertex be the opposite vertex. For each neighboring facet, if its circumsphere -includes the opposite.vertex, the two facets can be merged. [M. Treacy] - -

    You can handle collinear or coplanar boundary points by -enclosing the points in a box. For example, -(rbox c P0 P0,0.4999999999 c G1 | qdelaunay Fa), surrounds the -previous points with [(1,1), (1,-1), (-1,-1), (-1, 1)]. -Its Delaunay triangulation does not include a -nearly flat triangle. The box also simplifies the graphical -output from Qhull. - -

    Without joggle, Qhull lists coincident points as "coplanar" -points. For example, (rbox c P0 P0 D2 | qdelaunay Fa), ignores -the duplicated origin and lists four triangles of size 0.25. -Use 'Fc' to list the coincident points (e.g., -rbox c P0 P0 D2 | qdelaunay Fc). - -

    There is no easy way to determine coincident points with joggle. -Joggle removes all coincident, cocircular, and cospherical points -before running Qhull. Instead use facet merging (the default) -or triangulated output ('Qt'). - -

    »How do I compute -the Delaunay triangulation of a non-convex object?

    - -

    A similar question is -"How do I mesh a volume from a set of triangulated surface points?" - -

    This is an instance of the constrained Delaunay Triangulation -problem. Qhull does not handle constraints. The boundary of the -Delaunay triangulation is always convex. But if the input set -contains enough points, the triangulation will include the -boundary. The number of points needed depends on the input. - -

    Shewchuk has developed a theory of constrained Delaunay triangulations. -See his -paper at the -1998 Computational Geometry Conference. Using these ideas, constraints -could be added to Qhull. They would have many applications. - -

    There is a large literature on mesh generation and many commercial -offerings. For pointers see -Owen's International Meshing Roundtable -and Schneiders' -Finite Element Mesh Generation page.

    - -

    »Can Qhull -produce a triangular mesh for an object?

    - -

    Yes for convex objects, no for non-convex objects. For -non-convex objects, it triangulates the concavities. Unless the -object has many points on its surface, triangles may cross the -surface.

    - -

    »For 3-d Delaunay -triangulations, how do I report the triangles of each -tetrahedron?

    - -

    For points in general position, a 3-d Delaunay triangulation -generates tetrahedron. Each face of a tetrahedron is a triangle. -For example, the 3-d Delaunay triangulation of random points on -the surface of a cube, is a cellular structure of tetrahedron.

    - -

    Use triangulated output ('qdelaunay Qt i') or joggled input ('qdelaunay QJ i') -to generate the Delaunay triangulation. -Option 'i' reports each tetrahedron. The triangles are -every combination of 3 vertices. Each triangle is a -"ridge" of the Delaunay triangulation.

    - -

    For example,

    - -
    -        rbox 10 | qdelaunay Qt i
-        14
-        9 5 8 7
-        0 9 8 7
-        5 3 8 7
-        3 0 8 7
-        5 4 8 1
-        4 6 8 1
-        2 9 5 8
-        4 2 5 8
-        4 2 9 5
-        6 2 4 8
-        9 2 0 8
-        2 6 0 8
-        2 4 9 1
-        2 6 4 1
-
    - -

    is the Delaunay triangulation of 10 random points. Ridge 9-5-8 -occurs twice. Once for tetrahedron 9 5 8 7 and the other for -tetrahedron 2 9 5 8.

    - -

    You can also use the Qhull library to generate the triangles. -See "How do I visit the ridges of a -Delaunay triangulation?"

    - -

    »How do I construct a -3-d Delaunay triangulation?

    - -

    For 3-d Delaunay triangulations with cospherical input sites, -use triangulated output ('Qt') or -joggled input ('QJ'). Otherwise -option 'i' will -triangulate non-simplicial facets by adding a point to the facet. - -

    If you want non-simplicial output for cospherical sites, use -option -'Fv' or 'o'. -For option 'o', ignore the last coordinate. It is the lifted -coordinate for the corresponding convex hull in 4-d. - -

    The following example is a cube -inside a tetrahedron. The 8-vertex facet is the cube. Ignore the -last coordinates.

    - -
    - 
    -C:\qhull>rbox r y c G0.1 | qdelaunay Fv
-4
-12 20 44
-   0.5      0      0 0.3055555555555555
-   0    0.5      0 0.3055555555555555
-   0      0    0.5 0.3055555555555555
-  -0.5   -0.5   -0.5 0.9999999999999999
-  -0.1   -0.1   -0.1 -6.938893903907228e-018
-  -0.1   -0.1    0.1 -6.938893903907228e-018
-  -0.1    0.1   -0.1 -6.938893903907228e-018
-  -0.1    0.1    0.1 -6.938893903907228e-018
-   0.1   -0.1   -0.1 -6.938893903907228e-018
-   0.1   -0.1    0.1 -6.938893903907228e-018
-   0.1    0.1   -0.1 -6.938893903907228e-018
-   0.1    0.1    0.1 -6.938893903907228e-018
-4 2 11 1 0
-4 10 1 0 3
-4 11 10 1 0
-4 2 9 0 3
-4 9 11 2 0
-4 7 2 1 3
-4 11 7 2 1
-4 8 10 0 3
-4 9 8 0 3
-5 8 9 10 11 0
-4 10 6 1 3
-4 6 7 1 3
-5 6 8 10 4 3
-5 6 7 10 11 1
-4 5 9 2 3
-4 7 5 2 3
-5 5 8 9 4 3
-5 5 6 7 4 3
-8 5 6 8 7 9 10 11 4
-5 5 7 9 11 2
-
    -
    - -

    If you want simplicial output use options -'Qt i' or -'QJ i', e.g., -

    - -
    - 
    -rbox r y c G0.1 | qdelaunay Qt i
-31
-2 11 1 0
-11 10 1 0
-9 11 2 0
-11 7 2 1
-8 10 0 3
-9 8 0 3
-10 6 1 3
-6 7 1 3
-5 9 2 3
-7 5 2 3
-9 8 10 11
-8 10 11 0
-9 8 11 0
-6 8 10 4
-8 6 10 3
-6 8 4 3
-6 7 10 11
-10 6 11 1
-6 7 11 1
-8 5 4 3
-5 8 9 3
-5 6 4 3
-6 5 7 3
-5 9 10 11
-8 5 9 10
-7 5 10 11
-5 6 7 10
-8 5 10 4
-5 6 10 4
-5 9 11 2
-7 5 11 2
-
    -
    - -

    »How do I get the -triangles for a 2-d Delaunay triangulation and the vertices of -its Voronoi diagram?

    - -

    To compute the Delaunay triangles indexed by the indices of -the input sites, use

    - -
    -

    rbox 10 D2 | qdelaunay Qt i

    -
    - -

    To compute the Voronoi vertices and the Voronoi region for -each input site, use

    - -
    -

    rbox 10 D2 | qvoronoi o

    -
    - -

    To compute each edge ("ridge") of the Voronoi -diagram for each pair of adjacent input sites, use

    - -
    -

    rbox 10 D2 | qvoronoi Fv

    -
    - -

    To compute the area and volume of the Voronoi region for input site 5 (site 0 is the first one), -use

    - -
    -

    rbox 10 D2 | qvoronoi QV5 p | qconvex s FS

    -
    - -

    To compute the lines ("hyperplanes") that define the -Voronoi region for input site 5, use

    - -
    -

    rbox 10 D2 | qvoronoi QV5 p | qconvex n

    -
    -or -
    -

    rbox 10 D2 | qvoronoi QV5 Fi Fo

    -
    - -

    To list the extreme points of the input sites use

    - -
    -

    rbox 10 D2 | qdelaunay Fx

    -
    - -

    You will get the same point ids with

    - -
    -

    rbox 10 D2 | qconvex Fx

    -
    - -

    »Can Qhull triangulate -a hundred 16-d points?

    - -

    No. This is an immense structure. A triangulation of 19, 16-d -points has 43 simplices. If you add one point at a time, the -triangulation increased as follows: 43, 189, 523, 1289, 2830, -6071, 11410, 20487. The last triangulation for 26 points used 13 -megabytes of memory. When Qhull uses virtual memory, it becomes -too slow to use.

    - -
    -

    »Voronoi -diagram questions

    - -

    »How do I compute the volume of a Voronoi region?

    - -

    For each Voronoi region, compute the convex hull of the region's Voronoi vertices. The volume of each convex hull is the volume -of the corresponding Vornoi region.

    - -

    For example, to compute the volume of the bounded Voronoi region about [0,0,0]: output the origin's Voronoi vertices and -compute the volume of their convex hull. The last number from option 'FS' is the volume.

    -
    -rbox P0 10 | qvoronoi QV0 p | qhull FS
-0
-2 1.448134756744281 0.1067973560800857
-
    - -

    For another example, see How do I get the triangles for a 2-d Delaunay - triangulation and the vertices of its Voronoi diagram?

    - -

    This approach is slow if you are using the command line. A faster approcach is to call Qhull from -a program. The fastest method is Clarkson's hull program. -It computes the volume for all Voronoi regions.

    - -

    An unbounded Voronoi region does not have a volume.

    - -

    »How do I get the radii of the empty - spheres for each Voronoi vertex?

    - -Use option 'Fi' to list each bisector (i.e. Delaunay ridge). Then compute the -minimum distance for each Voronoi vertex. - -

    There's other ways to get the same information. Let me know if you -find a better method. - -

    »What is the Voronoi diagram - of a square?

    - -

    -Consider a square, -

    -C:\qhull>rbox c D2
-2 RBOX c D2
-4
-  -0.5   -0.5
-  -0.5    0.5
-   0.5   -0.5
-   0.5    0.5
-
    - -

    There's two ways to compute the Voronoi diagram: with facet merging -or with joggle. With facet merging, the -result is: - -

    -C:\qhull>rbox c D2 | qvoronoi Qz
-
-Voronoi diagram by the convex hull of 5 points in 3-d:
-
-  Number of Voronoi regions and at-infinity: 5
-  Number of Voronoi vertices: 1
-  Number of facets in hull: 5
-
-Statistics for: RBOX c D2 | QVORONOI Qz
-
-  Number of points processed: 5
-  Number of hyperplanes created: 7
-  Number of distance tests for qhull: 8
-  Number of merged facets: 1
-  Number of distance tests for merging: 29
-  CPU seconds to compute hull (after input):  0
-
-C:\qhull>rbox c D2 | qvoronoi Qz o
-2
-2 5 1
--10.101 -10.101
-     0      0
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-0
-
-C:\qhull>rbox c D2 | qvoronoi Qz Fv
-4
-4 0 1 0 1
-4 0 2 0 1
-4 1 3 0 1
-4 2 3 0 1
-
    - -

    There is one Voronoi vertex at the origin and rays from the origin -along each of the coordinate axes. -The last line '4 2 3 0 1' means that there is -a ray that bisects input points #2 and #3 from infinity (vertex 0) to -the origin (vertex 1). -Option 'Qz' adds an artificial point since the input is cocircular. -Coordinates -10.101 indicate the -vertex at infinity. - -

    With triangulated output, the Voronoi vertex is -duplicated: - -

    -C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz
-
-Voronoi diagram by the convex hull of 5 points in 3-d:
-
-  Number of Voronoi regions and at-infinity: 5
-  Number of Voronoi vertices: 2
-  Number of triangulated facets: 1
-
-Statistics for: RBOX c D2 | QVORONOI Qt Qz
-
-  Number of points processed: 5
-  Number of hyperplanes created: 7
-  Number of facets in hull: 6
-  Number of distance tests for qhull: 8
-  Number of distance tests for merging: 33
-  Number of distance tests for checking: 30
-  Number of merged facets: 1
-  CPU seconds to compute hull (after input): 0.05
-
-C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz o
-2
-3 5 1
--10.101 -10.101
-     0      0
-     0      0
-3 2 0 1
-2 1 0
-2 2 0
-3 2 0 1
-0
-
-C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz Fv
-4
-4 0 2 0 2
-4 0 1 0 1
-4 1 3 0 1
-4 2 3 0 2
-
    - - -

    With joggle, the input is no longer cocircular and the Voronoi vertex is -split into two: - -

    -C:\qhull>rbox c D2 | qvoronoi Qt Qz
-
-C:\qhull>rbox c D2 | qvoronoi QJ o
-2
-3 4 1
--10.101 -10.101
--4.71511718558304e-012 -1.775812830118184e-011
-9.020340030474472e-012 -4.02267108512433e-012
-2 0 1
-3 2 1 0
-3 2 0 1
-2 2 0
-
-C:\qhull>rbox c D2 | qvoronoi QJ Fv
-5
-4 0 2 0 1
-4 0 1 0 1
-4 1 2 1 2
-4 1 3 0 2
-4 2 3 0 2
-
    - -

    Note that the Voronoi diagram includes the same rays as - before plus a short edge between the two vertices.

    - - -

    »How do I construct -the Voronoi diagram of cospherical points?

    - -

    Three-d terrain data can be approximated with cospherical -points. The Delaunay triangulation of cospherical points is the -same as their convex hull. If the points lie on the unit sphere, -the facet normals are the Voronoi vertices [via S. Fortune].

    - -

    For example, consider the points {[1,0,0], [-1,0,0], [0,1,0], -...}. Their convex hull is:

    - -
    -rbox d G1 | qconvex o
-3
-6 8 12
-     0      0     -1
-     0      0      1
-     0     -1      0
-     0      1      0
-    -1      0      0
-     1      0      0
-3 3 1 4
-3 1 3 5
-3 0 3 4
-3 3 0 5
-3 2 1 5
-3 1 2 4
-3 2 0 4
-3 0 2 5
-
    - -

    The facet normals are:

    - -
    -rbox d G1 | qconvex n
-4
-8
--0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
- 0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
--0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
-
    - -

    If you drop the offset from each line (the last number), each -line is the Voronoi vertex for the corresponding facet. The -neighboring facets for each point define the Voronoi region for -each point. For example:

    - -
    -rbox d G1 | qconvex FN
-6
-4 7 3 2 6
-4 5 0 1 4
-4 7 4 5 6
-4 3 1 0 2
-4 6 2 0 5
-4 7 3 1 4
-
    - -

    The Voronoi vertices {7, 3, 2, 6} define the Voronoi region -for point 0. Point 0 is [0,0,-1]. Its Voronoi vertices are

    - -
    --0.5773502691896258  0.5773502691896258 -0.5773502691896258
- 0.5773502691896258  0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
-
    - -

    In this case, the Voronoi vertices are oriented, but in -general they are unordered.

    - -

    By taking the dual of the Delaunay triangulation, you can -construct the Voronoi diagram. For cospherical points, the convex -hull vertices for each facet, define the input sites for each -Voronoi vertex. In 3-d, the input sites are oriented. For -example:

    - -
    -rbox d G1 | qconvex i
-8
-3 1 4
-1 3 5
-0 3 4
-3 0 5
-2 1 5
-1 2 4
-2 0 4
-0 2 5
-
    - -

    The convex hull vertices for facet 0 are {3, 1, 4}. So Voronoi -vertex 0 (i.e., [-0.577, 0.577, 0.577]) is the Voronoi vertex for -input sites {3, 1, 4} (i.e., {[0,1,0], [0,0,1], [-1,0,0]}).

    - -

    »Can Qhull compute the -unbounded rays of the Voronoi diagram?

    - -

    Use 'Fo' to compute the separating -hyperplanes for unbounded Voronoi regions. The corresponding ray -goes to infinity from the Voronoi vertices. If you enclose the -input sites in a large enough box, the outermost bounded regions -will represent the unbounded regions of the original points.

    - -

    If you do not box the input sites, you can identify the -unbounded regions. They list '0' as a vertex. Vertex 0 represents -"infinity". Each unbounded ray includes vertex 0 in -option 'Fv. See Voronoi graphics and Voronoi notes.

    - -
    -

    »Approximation questions

    - -

    »How do I -approximate data with a simplex

    - -

    Qhull may be used to help select a simplex that approximates a -data set. It will take experimentation. Geomview will help to -visualize the results. This task may be difficult to do in 5-d -and higher. Use rbox options 'x' and 'y' to produce random -distributions within a simplex. Your methods work if you can -recover the simplex.

    - -

    Use Qhull's precision options to get a first approximation to -the hull, say with 10 to 50 facets. For example, try 'C0.05' to -remove small facets after constructing the hull. Use 'W0.05' to -ignore points within 0.05 of a facet. Use 'PA5' to print the five -largest facets by area.

    - -

    Then use other methods to fit a simplex to this data. Remove -outlying vertices with few nearby points. Look for large facets -in different quadrants. You can use option 'Pd0d1d2' to print all -the facets in a quadrant.

    - -

    In 4-d and higher, use the outer planes (option 'Fo' or -'facet->maxoutside') since the hyperplane of an approximate -facet may be below many of the input points.

    - -

    For example, consider fitting a cube to 1000 uniformly random -points in the unit cube. In this case, the first try was good:

    - -
    - 
    -rbox 1000 | qconvex W0.05 C0.05 PA6 Fo
-4
-6
-0.35715408374381 0.08706467018177928 -0.9299788727015564 -0.5985514741284483
-0.995841591359023 -0.02512604712761577 0.08756829720435189 -0.5258834069202866
-0.02448099521570909 -0.02685210459017302 0.9993396046151313 -0.5158104982631999
--0.9990223929415094 -0.01261133513150079 0.04236994958247349 -0.509218270408407
--0.0128069014364698 -0.9998380680115362 0.01264203427283151 -0.5002512653670584
-0.01120895057872914 0.01803671994177704 -0.9997744926535512 -0.5056824072956361
-
    -
    - -
    -

    »Halfspace questions

    - -

    »How do I compute the - intersection of halfspaces with Qhull?

    - -

    Qhull computes the halfspace intersection about a point. The -point must be inside all of the halfspaces. Given a point, a -duality turns a halfspace intersection problem into a convex -hull problem. - -

    Use linear programming if you -do not know a point in the interior of the halfspaces. -See the notes for qhalf. You will need - a linear programming code. This may require a fair amount of work to - implement.

    - - - -
    -

    »Qhull library -questions

    - -

    »Is Qhull available for Mathematica, Matlab, or Maple?

    - -

    MATLAB - -

    Z. You of MathWorks added qhull to MATLAB 6. -See functions convhulln, - delaunayn, - griddata3, - griddatan, - tsearch, - tsearchn, and - voronoin. V. Brumberg update MATLAB R14 for Qhull 2003.1 and triangulated output. - -

    Engwirda wrote mesh2d for unstructured mesh generation in MATLAB. -It is based on the iterative method of Persson and generally results in better quality meshes than delaunay refinement. - - -

    Mathematica and Maple - -

    See qh-math -for a Delaunay interface to Mathematica. It includes projects for CodeWarrior -on the Macintosh and Visual C++ on Win32 PCs. - -

    See Mathematica ('m') and Maple ('FM') output options. - -

    -

    »Why are there too few ridges?

    - -The following sample code may produce fewer ridges than expected: - -
    -  facetT *facetp;
-  ridgeT *ridge, **ridgep;
-
-  FORALLfacets {
-    printf("facet f%d\n", facet->id);
-    FOREACHridge_(facet->ridges) {
-      printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
-    }
-  }
-
    - -

    Qhull does not create ridges for simplicial facets. -Instead it computes ridges from facet->neighbors. To make ridges for a -simplicial facet, use qh_makeridges() in merge.c. Usefacet->visit_id to visit -each ridge once (instead of twice). For example, - -

    -  facetT *facet, *neighbor;
-  ridgeT *ridge, **ridgep;
-
-  qh visit_id++;
-  FORALLfacets {
-    printf("facet f%d\n", facet->id);
-    qh_makeridges(facet);
-    facet->visitId= qh visit_id;
-    FOREACHridge_(facet->ridges) {
-        neighbor= otherfacet_(ridge, visible);
-        if (neighbor->visitid != qh visit_id)
-            printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
-    }
-  }
-
    - -

    »Can Qhull use coordinates without placing - them in a data file?

    - -

    You may call Qhull from a program. Please use the reentrant Qhull library (libqhullstatic_r.a, libqhull_r.so, or qhull_r.dll). - -See user_eg.c and "Qhull-template" in user_r.c for examples.. - -See Qhull internals for an introduction to Qhull's reentrant library and its C++ interface. - -

    Hint: Start with a small example for which you know the - answer.

    - -

    »How large are Qhull's data structures?

    - -

    Qhull uses a general-dimension data structure. -The size depends on the dimension. Use option 'Ts' to print -out the memory statistics [e.g., 'rbox D2 10 | qconvex Ts']. - - -

    »Can Qhull construct -convex hulls and Delaunay triangulations one point at a time?

    - -

    The Qhull library may be used to construct convex hulls and -Delaunay triangulations one point at a time. It may not be used -for deleting points or moving points.

    - -

    Qhull is designed for batch processing. Neither Clarkson's -randomized incremental algorithm nor Qhull are designed for -on-line operation. For many applications, it is better to -reconstruct the convex hull or Delaunay triangulation from -scratch for each new point.

    - -

    With random point sets and on-line processing, Clarkson's -algorithm should run faster than Qhull. Clarkson uses the -intermediate facets to reject new, interior points, while Qhull, -when used on-line, visits every facet to reject such points. If -used on-line for n points, Clarkson may take O(n) times as much -memory as the average off-line case, while Qhull's space -requirement does not change.

    - -

    If you triangulate the output before adding all the points -(option 'Qt' and procedure qh_triangulate), you must set -option 'Q11'. It duplicates the -normals of triangulated facets and recomputes the centrums. -This should be avoided for regular use since triangulated facets -are not clearly convex with their neighbors. It appears to -work most of the time, but fails for cases that Qhull normally -handles well [see the test call to qh_triangulate in qh_addpoint]. - -

    »How do I visit the -ridges of a Delaunay triangulation?

    - -

    To visit the ridges of a Delaunay triangulation, visit each -facet. Each ridge will appear twice since it belongs to two -facets. In pseudo-code:

    - -
    -    for each facet of the triangulation
-        if the facet is Delaunay (i.e., part of the lower convex hull)
-            for each ridge of the facet
-                if the ridge's neighboring facet has not been visited
-                    ... process a ridge of the Delaunay triangulation ...
-
    - -

    In undebugged, C code:

    - -
    -    qh visit_id++;
-    FORALLfacets_(facetlist)
-        if (!facet->upperdelaunay) {
-            facet->visitid= qh visit_id;
-            qh_makeridges(facet);
-            FOREACHridge_(facet->ridges) {
-                neighbor= otherfacet_(ridge, facet);
-                if (neighbor->visitid != qh visit_id) {
-                    /* Print ridge here with facet-id and neighbor-id */
-                    /*fprintf(fp, "f%d\tf%d\t",facet->id,neighbor->ID);*/
-                    FOREACHvertex_(ridge->vertices)
-                        fprintf(fp,"%d ",qh_pointid (vertex->point) );
-                    qh_printfacetNvertex_simplicial (fp, facet, format);
-                    fprintf(fp," ");
-                    if(neighbor->upperdelaunay)
-                        fprintf(fp," -1 -1 -1 -1 ");
-                    else
-                        qh_printfacetNvertex_simplicial (fp, neighbor, format);
-                    fprintf(fp,"\n");
-                }
-            }
-        }
-    }
-
    - -

    Qhull should be redesigned as a class library, or at least as -an API. It currently provides everything needed, but the -programmer has to do a lot of work. Hopefully someone will write -C++ wrapper classes or a Python module for Qhull.

    - -

    »How do I visit the -Delaunay regions?

    - -

    Qhull constructs a Delaunay triangulation by lifting the -input sites to a paraboloid. The Delaunay triangulation -corresponds to the lower convex hull of the lifted points. To -visit each facet of the lower convex hull, use:

    - -
    -    facetT *facet;
-
-    ...
-    FORALLfacets {
-        if (!facet->upperdelaunay) {
-            ... only facets for Delaunay regions ...
-        }
-    }
-
    - -

    »When is a point -outside or inside a facet?

    - -

    A point is outside of a facet if it is clearly outside the -facet's outer plane. The outer plane is defined by an offset -(facet->maxoutside) from the facet's hyperplane.

    - -
    -    facetT *facet;
-    pointT *point;
-    realT dist;
-
-    ...
-    qh_distplane(point, facet, &dist);
-    if (dist > facet->maxoutside + 2 * qh DISTround) {
-        /* point is clearly outside of facet */
-    }
-
    - -

    A point is inside of a facet if it is clearly inside the -facet's inner plane. The inner plane is computed as the maximum -distance of a vertex to the facet. It may be computed for an -individual facet, or you may use the maximum over all facets. For -example:

    - -
    -    facetT *facet;
-    pointT *point;
-    realT dist;
-
-    ...
-    qh_distplane(point, facet, &dist);
-    if (dist < qh min_vertex - 2 * qh DISTround) {
-        /* point is clearly inside of facet */
-    }
-
    - -

    Both tests include two qh.DISTrounds because the computation -of the furthest point from a facet may be off by qh.DISTround and -the computation of the current distance to the facet may be off -by qh.DISTround.

    - -

    »How do I find the -facet that is closest to a point?

    - -

    Use qh_findbestfacet(). For example,

    - -
    -    coordT point[ DIM ];
-    boolT isoutside;
-    realT bestdist;
-    facetT *facet;
-
-    ... set coordinates for point ...
-
-    facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
-
-    /* 'facet' is the closest facet to 'point' */
-
    - -

    qh_findbestfacet() performs a directed search for the facet -furthest below the point. If the point lies inside this facet, -qh_findbestfacet() performs an exhaustive search of all facets. -An exhaustive search may be needed because a facet on the far -side of a lens-shaped distribution may be closer to a point than -all of the facet's neighbors. The exhaustive search may be -skipped for spherical distributions.

    - -

    Also see, "How do I find the -Delaunay triangle that is closest to a -point?"

    - -

    »How do I find the -Delaunay triangle or Voronoi region that is closest to a point?

    - -

    A Delaunay triangulation subdivides the plane, or in general -dimension, subdivides space. Given a point, how do you determine -the subdivision containing the point? Or, given a set of points, -how do you determine the subdivision containing each point of the set? -Efficiency is important -- an exhaustive search of the subdivision -is too slow. - -

    First compute the Delaunay triangle with qh_new_qhull() in user_r.c or Qhull::runQhull(). -Lift the point to the paraboloid by summing the squares of the -coordinates. Use qh_findbestfacet() [poly2.c] to find the closest Delaunay -triangle. Determine the closest vertex to find the corresponding -Voronoi region. Do not use options -'Qbb', 'QbB', -'Qbk:n', or 'QBk:n' since these scale the last -coordinate. Optimizations of qh_findbestfacet() should -be possible for Delaunay triangulations.

    - -

    You first need to lift the point to the paraboloid (i.e., the -last coordinate is the sum of the squares of the point's coordinates). -The -routine, qh_setdelaunay() [geom2.c], lifts an array of points to the -paraboloid. The following excerpt is from findclosest() in -user_eg.c.

    - -
    -    coordT point[ DIM + 1];  /* one extra coordinate for lifting the point */
-    boolT isoutside;
-    realT bestdist;
-    facetT *facet;
-
-    ... set coordinates for point[] ...
-
-    qh_setdelaunay (DIM+1, 1, point);
-    facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
-    /* 'facet' is the closest Delaunay triangle to 'point' */
-
    - -

    The returned facet either contains the point or it is the -closest Delaunay triangle along the convex hull of the input set. - -

    Point location is an active research area in Computational -Geometry. For a practical approach, see Mucke, et al, "Fast randomized -point location without preprocessing in two- and -three-dimensional Delaunay triangulations," Computational -Geometry '96, p. 274-283, May 1996. -For an introduction to planar point location see [O'Rourke '93]. -Also see, "How do I find the facet that is closest to a -point?"

    - -

    To locate the closest Voronoi region, determine the closest -vertex of the closest Delaunay triangle.

    - -
    -    realT dist, bestdist= REALmax;
-        vertexT *bestvertex= NULL, *vertex, **vertexp;
-
-    /* 'facet' is the closest Delaunay triangle to 'point' */
-
-    FOREACHvertex_( facet->vertices ) {
-        dist= qh_pointdist( point, vertex->point, DIM );
-        if (dist < bestdist) {
-            bestdist= dist;
-            bestvertex= vertex;
-        }
-    }
-    /* 'bestvertex' represents the Voronoi region closest to 'point'.  The corresponding
-       input site is 'bestvertex->point' */
-
    - -

    »How do I list the -vertices?

    - -

    To list the vertices (i.e., extreme points) of the convex hull -use

    - -
    - 
    -    vertexT *vertex;
-
-    FORALLvertices {
-      ...
-      // vertex->point is the coordinates of the vertex
-      // qh_pointid(vertex->point) is the point ID of the vertex
-      ...
-    }
-
    -
    - -

    »How do I test code -that uses the Qhull library?

    - -

    Compare the output from your program with the output from the -Qhull program. Use option 'T1' or 'T4' to trace what Qhull is -doing. Prepare a small example for which you know the -output. Run the example through the Qhull program and your code. -Compare the trace outputs. If you do everything right, the two -trace outputs should be almost the same. The trace output will -also guide you to the functions that you need to review.

    - -

    »When I compute a -plane equation from a facet, I sometimes get an outward-pointing -normal and sometimes an inward-pointing normal

    - -

    Qhull orients simplicial facets, and prints oriented output -for 'i', 'Ft', and other options. The orientation depends on both -the vertex order and the flag facet->toporient.

    - -

    Qhull does not orient - non-simplicial facets. Instead it orients the facet's ridges. These are - printed with the 'Qt' and 'Ft' option. The facet's hyperplane is oriented.

    - -
    -
    - -

    Up: Home page for Qhull
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    Up: Home -page for Qhull
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    - -

    [4-d cube] Imprecision in Qhull

    - -

    This section of the Qhull manual discusses the problems caused -by coplanar points and why Qhull uses options 'C-0' or 'Qx' -by default. If you ignore precision issues with option 'Q0', the output from Qhull can be -arbitrarily bad. Qhull avoids precision problems if you merge facets (the default) or joggle -the input ('QJ').

    - -

    Use option 'Tv' to verify the -output from Qhull. It verifies that adjacent facets are clearly -convex. It verifies that all points are on or below all facets.

    - -

    Qhull automatically tests for convexity if it detects -precision errors while constructing the hull.

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »Qhull -imprecision: Table of Contents

    - - - -
    - -

    »Precision problems

    - -

    Since Qhull uses floating point arithmetic, roundoff error -occurs with each calculation. This causes problems for -geometric algorithms. Other floating point codes for convex -hulls, Delaunay triangulations, and Voronoi diagrams also suffer -from these problems. Qhull handles most of them.

    - -

    There are several kinds of precision errors:

    - -
      -
    • Representation error occurs when there are not enough - digits to represent a number, e.g., 1/3.
      • -
    • Measurement error occurs when the input coordinates are - from measurements.
      • -
    • Roundoff error occurs when a calculation is rounded to a - fixed number of digits, e.g., a floating point - calculation.
      • -
    • Approximation error occurs when the user wants an - approximate result because the exact result contains too - much detail.
      • -
    - -

    Under imprecision, calculations may return erroneous results. -For example, roundoff error can turn a small, positive number -into a small, negative number. See Milenkovic ['93] for a discussion of strict -robust geometry. Qhull does not meet Milenkovic's criterion -for accuracy. Qhull's error bound is empirical instead of -theoretical.

    - -

    Qhull 1.0 checked for precision errors but did not handle -them. The output could contain concave facets, facets with -inverted orientation ("flipped" facets), more than two -facets adjacent to a ridge, and two facets with exactly the same -set of vertices.

    - -

    Qhull 2.4 and later automatically handles errors due to -machine round-off. Option 'C-0' or 'Qx' is set by default. In 5-d and -higher, the output is clearly convex but an input point could be -outside of the hull. This may be corrected by using option 'C-0', but then the output may contain -wide facets.

    - -

    Qhull 2.5 and later provides option 'QJ' -to joggled input. Each input coordinate is modified by a -small, random quantity. If a precision error occurs, a larger -modification is tried. When no precision errors occur, Qhull is -done.

    - -

    Qhull 3.1 and later provides option 'Qt' -for triangulated output. This removes the need for -joggled input ('QJ'). -Non-simplicial facets are triangulated. -The facets may have zero area. -Triangulated output is particularly useful for Delaunay triangulations.

    - -

    By handling round-off errors, Qhull can provide a variety of -output formats. For example, it can return the halfspace that -defines each facet ('n'). The -halfspaces include roundoff error. If the halfspaces were exact, -their intersection would return the original extreme points. With -imprecise halfspaces and exact arithmetic, nearly incident points -may be returned for an original extreme point. By handling -roundoff error, Qhull returns one intersection point for each of -the original extreme points. Qhull may split or merge an extreme -point, but this appears to be unlikely.

    - -

    The following pipe implements the identity function for -extreme points (with roundoff): -

    - qconvex FV n | qhalf Fp -
    - -

    Bernd Gartner published his -Miniball -algorithm ["Fast and robust smallest enclosing balls", Algorithms - ESA '99, LNCS 1643]. -It uses floating point arithmetic and a carefully designed primitive operation. -It is practical to 20-D or higher, and identifies at least two points on the -convex hull of the input set. Like Qhull, it is an incremental algorithm that -processes points furthest from the intermediate result and ignores -points that are close to the intermediate result. - -

    »Merged facets or joggled input

    - -

    This section discusses the choice between merged facets and joggled input. -By default, Qhull uses merged facets to handle -precision problems. With option 'QJ', -the input is joggled. See examples -of joggled input and triangulated output. -

      -
    • Use merged facets (the default) -when you want non-simplicial output (e.g., the faces of a cube). -
    • Use merged facets and triangulated output ('Qt') when -you want simplicial output and coplanar facets (e.g., triangles for a Delaunay triangulation). -
    • Use joggled input ('QJ') when you need clearly-convex, -simplicial output. -
    - -

    The choice between merged facets and joggled input depends on -the application. Both run about the same speed. Joggled input may -be faster if the initial joggle is sufficiently large to avoid -precision errors. - -

    Most applications should used merged facets -with triangulated output.

    - -

    Use merged facets (the -default, 'C-0') -or triangulated output ('Qt') if

    - -
      -
    • Your application supports non-simplicial facets, or - it allows degenerate, simplicial facets (option 'Qt').
      • -
    • You do not want the input modified.
      • -
    • You want to set additional options for approximating the - hull.
      • -
    • You use single precision arithmetic (realT). -
      • -
    - -

    Use joggled input ('QJ') if

    - -
      -
    • Your application needs clearly convex, simplicial output
      • -
    • Your application supports perturbed input points and narrow triangles.
      • -
    • Seven significant digits is sufficient accuracy.
      • -
    - -

    You may use both techniques or combine joggle with -post-merging ('Cn').

    - -

    Other researchers have used techniques similar to joggled -input. Sullivan and Beichel [ref?] randomly perturb the input -before computing the Delaunay triangulation. Corkum and Wyllie -[news://comp.graphics, 1990] randomly rotate a polytope before -testing point inclusion. Edelsbrunner and Mucke [Symp. Comp. -Geo., 1988] and Yap [J. Comp. Sys. Sci., 1990] symbolically -perturb the input to remove singularities.

    - -

    Merged facets ('C-0') handles -precision problems directly. If a precision problem occurs, Qhull -merges one of the offending facets into one of its neighbors. -Since all precision problems in Qhull are associated with one or -more facets, Qhull will either fix the problem or attempt to merge the -last remaining facets.

    - -

    »Delaunay -triangulations

    - -

    Programs that use Delaunay triangulations traditionally assume -a triangulated input. By default, qdelaunay -merges regions with cocircular or cospherical input sites. -If you want a simplicial triangulation -use triangulated output ('Qt') or joggled -input ('QJ'). - -

    For Delaunay triangulations, triangulated -output should produce good results. All points are within roundoff error of -a paraboloid. If two points are nearly incident, one will be a -coplanar point. So all points are clearly separated and convex. -If qhull reports deleted vertices, the triangulation -may contain serious precision faults. Deleted vertices are reported -in the summary ('s', 'Fs'

    - -

    You should use option 'Qbb' with Delaunay -triangulations. It scales the last coordinate and may reduce -roundoff error. It is automatically set for qdelaunay, -qvoronoi, and option 'QJ'.

    - -

    Edelsbrunner, H, Geometry and Topology for Mesh Generation, Cambridge University Press, 2001. -Good mathematical treatise on Delaunay triangulation and mesh generation for 2-d -and 3-d surfaces. The chapter on surface simplification is -particularly interesting. It is similar to facet merging in Qhull. - -

    Veron and Leon published an algorithm for shape preserving polyhedral -simplification with bounded error [Computers and Graphics, 22.5:565-585, 1998]. -It remove nodes using front propagation and multiple remeshing. - -

    »Halfspace intersection

    - -

    -The identity pipe for Qhull reveals some precision questions for -halfspace intersections. The identity pipe creates the convex hull of -a set of points and intersects the facets' hyperplanes. It should return the input -points, but narrow distributions may drop points while offset distributions may add -points. It may be better to normalize the input set about the origin. -For example, compare the first results with the later two results: [T. Abraham] -

    - rbox 100 s t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail -
    - rbox 100 L1e5 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail -
    - rbox 100 s O10 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail -
    - - -

    »Merged facets

    - -

    Qhull detects precision -problems when computing distances. A precision problem occurs if -the distance computation is less than the maximum roundoff error. -Qhull treats the result of a hyperplane computation as if it -were exact.

    - -

    Qhull handles precision problems by merging non-convex facets. -The result of merging two facets is a thick facet defined by an inner -plane and an outer plane. The inner and outer planes -are offsets from the facet's hyperplane. The inner plane is -clearly below the facet's vertices. At the end of Qhull, the -outer planes are clearly above all input points. Any exact convex -hull must lie between the inner and outer planes.

    - -

    Qhull tests for convexity by computing a point for each facet. -This point is called the facet's centrum. It is the -arithmetic center of the facet's vertices projected to the -facet's hyperplane. For simplicial facets with d -vertices, the centrum is equivalent to the centroid or center of -gravity.

    - -

    Two neighboring facets are convex if each centrum is clearly -below the other hyperplane. The 'Cn' -or 'C-n' options sets the centrum's -radius to n . A centrum is clearly below a hyperplane if -the computed distance from the centrum to the hyperplane is -greater than the centrum's radius plus two maximum roundoff -errors. Two are required because the centrum can be the maximum -roundoff error above its hyperplane and the distance computation -can be high by the maximum roundoff error.

    - -

    With the 'C-n' or 'A-n ' options, Qhull merges non-convex -facets while constructing the hull. The remaining facets are -clearly convex. With the 'Qx ' -option, Qhull merges coplanar facets after constructing the hull. -While constructing the hull, it merges coplanar horizon facets, -flipped facets, concave facets and duplicated ridges. With 'Qx', coplanar points may be missed, but -it appears to be unlikely.

    - -

    If the user sets the 'An' or 'A-n' option, then all neighboring -facets are clearly convex and the maximum (exact) cosine of an -angle is n.

    - -

    If 'C-0' or 'Qx' is used without other precision -options (default), Qhull tests vertices instead of centrums for -adjacent simplices. In 3-d, if simplex abc is adjacent to -simplex bcd, Qhull tests that vertex a is clearly -below simplex bcd , and vertex d is clearly below -simplex abc. When building the hull, Qhull tests vertices -if the horizon is simplicial and no merges occur.

    - -

    »How Qhull merges facets

    - -

    If two facets are not clearly convex, then Qhull removes one -or the other facet by merging the facet into a neighbor. It -selects the merge which minimizes the distance from the -neighboring hyperplane to the facet's vertices. Qhull also -performs merges when a facet has fewer than d neighbors (called a -degenerate facet), when a facet's vertices are included in a -neighboring facet's vertices (called a redundant facet), when a -facet's orientation is flipped, or when a ridge occurs between -more than two facets.

    - -

    Qhull performs merges in a series of passes sorted by merge -angle. Each pass merges those facets which haven't already been -merged in that pass. After a pass, Qhull checks for redundant -vertices. For example, if a vertex has only two neighbors in 3-d, -the vertex is redundant and Qhull merges it into an adjacent -vertex.

    - -

    Merging two simplicial facets creates a non-simplicial facet -of d+1 vertices. Additional merges create larger facets. -When merging facet A into facet B, Qhull retains facet B's -hyperplane. It merges the vertices, neighbors, and ridges of both -facets. It recomputes the centrum if a wide merge has not -occurred (qh_WIDEcoplanar) and the number of extra vertices is -smaller than a constant (qh_MAXnewcentrum).

    - - -

    »Limitations of merged -facets

    - -
      -
    • Uneven dimensions -- -If one coordinate has a larger absolute value than other -coordinates, it may dominate the effect of roundoff errors on -distance computations. You may use option 'QbB' to scale points to the unit cube. -For Delaunay triangulations and Voronoi diagrams, qdelaunay -and qvoronoi always set -option 'Qbb'. It scales the last -coordinate to [0,m] where m is the maximum width of the -other coordinates. Option 'Qbb' is -needed for Delaunay triangulations of integer coordinates -and nearly cocircular points. - -

      For example, compare -

      -        rbox 1000 W0 t | qconvex Qb2:-1e-14B2:1e-14
-
      -with -
      -        rbox 1000 W0 t | qconvex
-
      -The distributions are the same but the first is compressed to a 2e-14 slab. -

      -

    • Post-merging of coplanar facets -- In 5-d and higher, option 'Qx' -(default) delays merging of coplanar facets until post-merging. -This may allow "dents" to occur in the intermediate -convex hulls. A point may be poorly partitioned and force a poor -approximation. See option 'Qx' for -further discussion.

      - -

      This is difficult to produce in 5-d and higher. Option 'Q6' turns off merging of concave -facets. This is similar to 'Qx'. It may lead to serious precision errors, -for example, -

      -        rbox 10000 W1e-13  | qhull Q6  Tv
-
      - -

      -

    • Maximum facet width -- -Qhull reports the maximum outer plane and inner planes (if -more than roundoff error apart). There is no upper bound -for either figure. This is an area for further research. Qhull -does a good job of post-merging in all dimensions. Qhull does a -good job of pre-merging in 2-d, 3-d, and 4-d. With the 'Qx' option, it does a good job in -higher dimensions. In 5-d and higher, Qhull does poorly at -detecting redundant vertices.

      - -

      In the summary ('s'), look at the -ratio between the maximum facet width and the maximum width of a -single merge, e.g., "(3.4x)". Qhull usually reports a -ratio of four or lower in 3-d and six or lower in 4-d. If it -reports a ratio greater than 10, this may indicate an -implementation error. Narrow distributions (see following) may -produce wide facets. - -

      For example, if special processing for narrow distributions is -turned off ('Q10'), qhull may produce -a wide facet:

      -
      -         rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
-
      - -

      -

    • Narrow distribution -- In 3-d, a narrow distribution may result in a poor -approximation. For example, if you do not use qdelaunay nor option -'Qbb', the furthest-site -Delaunay triangulation of nearly cocircular points may produce a poor -approximation: -
      -         rbox s 5000 W1e-13 D2 t1002151341 | qhull d Qt
-         rbox 1000 s W1e-13 t1002231672 | qhull d Tv
-
      - -

      During -construction of the hull, a point may be above two -facets with opposite orientations that span the input -set. Even though the point may be nearly coplanar with both -facets, and can be distant from the precise convex -hull of the input sites. Additional facets leave the point distant from -a facet. To fix this problem, add option 'Qbb' -(it scales the last coordinate). Option 'Qbb' -is automatically set for qdelaunay and qvoronoi. - -

      Qhull generates a warning if the initial simplex is narrow. -For narrow distributions, Qhull changes how it processes coplanar -points -- it does not make a point coplanar until the hull is -finished. -Use option 'Q10' to try Qhull without -special processing for narrow distributions. -For example, special processing is needed for: -

      -         rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
-
      - -

      You may turn off the warning message by reducing -qh_WARNnarrow in user.h or by setting option -'Pp'.

      - -

      Similar problems occur for distributions with a large flat facet surrounded -with many small facet at a sharp angle to the large facet. -Qhull 3.1 fixes most of these problems, but a poor approximation can occur. -A point may be left outside of the convex hull ('Tv'). -Examples include -the furthest-site Delaunay triangulation of nearly cocircular points plus the origin, and the convex hull of a cone of nearly cocircular points. The width of the band is 10^-13. -

      -        rbox s 1000 W1e-13 P0 D2 t996799242 | qhull d Tv
-        rbox 1000 s Z1 G1e-13 t1002152123 | qhull Tv
-        rbox 1000 s Z1 G1e-13 t1002231668 | qhull Tv
-
      - -

      -

    • Quadratic running time -- If the output contains large, non-simplicial -facets, the running time for Qhull may be quadratic in the size of the triangulated -output. For example, rbox 1000 s W1e-13 c G2 | qhull d is 4 times -faster for 500 points. The convex hull contains two large nearly spherical facets and -many nearly coplanar facets. Each new point retriangulates the spherical facet and repartitions the remaining points into all of the nearly coplanar facets. -In this case, quadratic running time is avoided if you use qdelaunay, -add option 'Qbb', -or add the origin ('P0') to the input. -

      -

    • Nearly coincident points within 1e-13 -- -Multiple, nearly coincident points within a 1e-13 ball of points in the unit cube -may lead to wide facets or quadratic running time. -For example, the convex hull a 1000 coincident, cospherical points in 4-D, -or the 3-D Delaunay triangulation of nearly coincident points, may lead to very -wide facets (e.g., 2267021951.3x). - -

      For Delaunay triangulations, the problem typically occurs for extreme points of the input -set (i.e., on the edge between the upper and lower convex hull). After multiple facet merges, four -facets may share the same, duplicate ridge and must be merged. -Some of these facets may be long and narrow, leading to a very wide merged facet. -If so, error QH6271 is reported. It may be overriden with option 'Q12'. - -

      Duplicate ridges occur when the horizon facets for a new point is "pinched". -In a duplicate ridge, a subridge (e.g., a line segment in 3-d) is shared by two horizon facets. -At least two of its vertices are nearly coincident. It is easy to generate coincident points with -option 'Cn,r,m' of rbox. It generates n points within an r ball for each of m input sites. For example, -every point of the following distributions has a nearly coincident point within a 1e-13 ball. -Substantially smaller or larger balls do not lead to pinched horizons. -

      -        rbox 1000 C1,1e-13 D4 s t | qhull
-        rbox 75 C1,1e-13 t | qhull d
-
      -For Delaunay triangulations, a bounding box may alleviate this error (e.g., rbox 500 C1,1E-13 t c G1 | qhull d). -A later release of qhull will avoid pinched horizons by merging duplicate subridges. A subridge is -merged by merging adjacent vertices. -

      -

    • Facet with zero-area -- -It is possible for a zero-area facet to be convex with its -neighbors. This can occur if the hyperplanes of neighboring -facets are above the facet's centrum, and the facet's hyperplane -is above the neighboring centrums. Qhull computes the facet's -hyperplane so that it passes through the facet's vertices. The -vertices can be collinear.

      - -

      -

    • No more facets -- Qhull reports an error if there are d+1 facets left -and two of the facets are not clearly convex. This typically -occurs when the convexity constraints are too strong or the input -points are degenerate. The former is more likely in 5-d and -higher -- especially with option 'C-n'.

      - -

      -

    • Deleted cone -- Lots of merging can end up deleting all -of the new facets for a point. This is a rare event that has -only been seen while debugging the code. - -

      -

    • Triangulated output leads to precision problems -- With sufficient -merging, the ridges of a non-simplicial facet may have serious topological -and geometric problems. A ridge may be between more than two -neighboring facets. If so, their triangulation ('Qt') -will fail since two facets have the same vertex set. Furthermore, -a triangulated facet may have flipped orientation compared to its -neighbors.
      • - -

      The triangulation process detects degenerate facets with -only two neighbors. These are marked degenerate. They have -zero area. - -

      -

    • Coplanar points -- -Option 'Qc' is determined by -qh_check_maxout() after constructing the hull. Qhull needs to -retain all possible coplanar points in the facets' coplanar sets. -This depends on qh_RATIOnearInside in user.h. -Furthermore, the cutoff for a coplanar point is arbitrarily set -at the minimum vertex. If coplanar points are important to your -application, remove the interior points by hand (set 'Qc Qi') or -make qh_RATIOnearInside sufficiently large.

      - -

      -

    • Maximum roundoff error -- Qhull computes the maximum roundoff error from the maximum -coordinates of the point set. Usually the maximum roundoff error -is a reasonable choice for all distance computations. The maximum -roundoff error could be computed separately for each point or for -each distance computation. This is expensive and it conflicts -with option 'C-n'. - -

      -

    • All flipped or upper Delaunay -- When a lot of merging occurs for -Delaunay triangulations, a new point may lead to no good facets. For example, -try a strong convexity constraint: -
      -        rbox 1000 s t993602376 | qdelaunay C-1e-3
-
      - -
    - -

    »Joggled input

    - -

    Joggled input is a simple work-around for precision problems -in computational geometry ["joggle: to shake or jar -slightly," Amer. Heritage Dictionary]. Other names are -jostled input or random perturbation. -Qhull joggles the -input by modifying each coordinate by a small random quantity. If -a precision problem occurs, Qhull joggles the input with a larger -quantity and the algorithm is restarted. This process continues -until no precision problems occur. Unless all inputs incur -precision problems, Qhull will terminate. Qhull adjusts the inner -and outer planes to account for the joggled input.

    - -

    Neither joggle nor merged facets has an upper bound for the width of the output -facets, but both methods work well in practice. Joggled input is -easier to justify. Precision errors occur when the points are -nearly singular. For example, four points may be coplanar or -three points may be collinear. Consider a line and an incident -point. A precision error occurs if the point is within some -epsilon of the line. Now joggle the point away from the line by a -small, uniformly distributed, random quantity. If the point is -changed by more than epsilon, the precision error is avoided. The -probability of this event depends on the maximum joggle. Once the -maximum joggle is larger than epsilon, doubling the maximum -joggle will halve the probability of a precision error.

    - -

    With actual data, an analysis would need to account for each -point changing independently and other computations. It is easier -to determine the probabilities empirically ('TRn') . For example, consider -computing the convex hull of the unit cube centered on the -origin. The arithmetic has 16 significant decimal digits.

    - -
    -

    Convex hull of unit cube

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    joggleerror prob.
    1.0e-150.983
    2.0e-150.830
    4.0e-150.561
    8.0e-150.325
    1.6e-140.185
    3.2e-140.099
    6.4e-140.051
    1.3e-130.025
    2.6e-130.010
    5.1e-130.004
    1.0e-120.002
    2.0e-120.001
    -
    - -

    A larger joggle is needed for multiple points. Since the -number of potential singularities increases, the probability of -one or more precision errors increases. Here is an example.

    - -
    -

    Convex hull of 1000 points on unit cube

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    joggleerror prob.
    1.0e-120.870
    2.0e-120.700
    4.0e-120.450
    8.0e-120.250
    1.6e-110.110
    3.2e-110.065
    6.4e-110.030
    1.3e-100.010
    2.6e-100.008
    5.1e-090.003
    -
    - -

    Other distributions behave similarly. No distribution should -behave significantly worse. In Euclidean space, the probability -measure of all singularities is zero. With floating point -numbers, the probability of a singularity is non-zero. With -sufficient digits, the probability of a singularity is extremely -small for random data. For a sufficiently large joggle, all data -is nearly random data.

    - -

    Qhull uses an initial joggle of 30,000 times the maximum -roundoff error for a distance computation. This avoids most -potential singularities. If a failure occurs, Qhull retries at -the initial joggle (in case bad luck occurred). If it occurs -again, Qhull increases the joggle by ten-fold and tries again. -This process repeats until the joggle is a hundredth of the width -of the input points. Qhull reports an error after 100 attempts. -This should never happen with double-precision arithmetic. Once -the probability of success is non-zero, the probability of -success increases about ten-fold at each iteration. The -probability of repeated failures becomes extremely small.

    - -

    Merged facets produces a significantly better approximation. -Empirically, the maximum separation between inner and outer -facets is about 30 times the maximum roundoff error for a -distance computation. This is about 2,000 times better than -joggled input. Most applications though will not notice the -difference.

    - -

    »Exact arithmetic

    - -

    Exact arithmetic may be used instead of floating point. -Singularities such as coplanar points can either be handled -directly or the input can be symbolically perturbed. Using exact -arithmetic is slower than using floating point arithmetic and the -output may take more space. Chaining a sequence of operations -increases the time and space required. Some operations are -difficult to do.

    - -

    Clarkson's hull -program and Shewchuk's triangle -program are practical implementations of exact arithmetic.

    - -

    Clarkson limits the input precision to about fifteen digits. -This reduces the number of nearly singular computations. When a -determinant is nearly singular, he uses exact arithmetic to -compute a precise result.

    - -

    »Approximating a -convex hull

    - -

    Qhull may be used for approximating a convex hull. This is -particularly valuable in 5-d and higher where hulls can be -immense. You can use 'Qx C-n' to merge facets as the hull is -being constructed. Then use 'Cn' -and/or 'An' to merge small facets -during post-processing. You can print the n largest facets -with option 'PAn'. You can print -facets whose area is at least n with option 'PFn'. You can output the outer planes -and an interior point with 'FV Fo' and then compute their intersection -with 'qhalf'.

    - -

    To approximate a convex hull in 6-d and higher, use -post-merging with 'Wn' (e.g., qhull -W1e-1 C1e-2 TF2000). Pre-merging with a convexity constraint -(e.g., qhull Qx C-1e-2) often produces a poor approximation or -terminates with a simplex. Option 'QbB' -may help to spread out the data.

    - -

    You will need to experiment to determine a satisfactory set of -options. Use rbox to generate test sets -quickly and Geomview to view -the results. You will probably want to write your own driver for -Qhull using the Qhull library. For example, you could select the -largest facet in each quadrant.

    - - -
    - -

    Up: Home -page for Qhull
    -Up: Qhull manual: Table of -Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: Qhull imprecision: Table of Contents - - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-optc.htm b/src/qhull/html/qh-optc.htm deleted file mode 100644 index 87308180d..000000000 --- a/src/qhull/html/qh-optc.htm +++ /dev/null @@ -1,292 +0,0 @@ - - - - -Qhull precision options - - - - -

    Up: Home page for Qhull
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    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    [delaunay] Qhull precision options

    - -This section lists the precision options for Qhull. These options are -indicated by an upper-case letter followed by a number. - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Precision options

    - -

    Most users will not need to set these options. They are best -used for approximating a -convex hull. They may also be used for testing Qhull's handling -of precision errors.

    - -

    By default, Qhull uses options 'C-0' for -2-d, 3-d and 4-d, and 'Qx' for 5-d -and higher. These options use facet merging to handle precision -errors. You may also use joggled input 'QJ' -to avoid precision problems. -For more information see Imprecision in Qhull.

    - -
    -
     
    -
    General
    -
    Cn
    -
    centrum radius for post-merging
    -
    C-n
    -
    centrum radius for pre-merging
    -
    An
    -
    cosine of maximum angle for post-merging
    -
    A-n
    -
    cosine of maximum angle for pre-merging
    -
    Qx
    -
    exact pre-merges (allows coplanar facets)
    -
    C-0
    -
    handle all precision errors
    -
    Wn
    -
    min distance above plane for outside points
    -
    - -
    -
     
    -
    Experimental
    -
    Un
    -
    max distance below plane for a new, coplanar point
    -
    En
    -
    max roundoff error for distance computation
    -
    Vn
    -
    min distance above plane for a visible facet
    -
    Rn
    -
    randomly perturb computations by a factor of [1-n,1+n]
    -
    - -
    -
    - -
    - -

    »A-n - cosine of maximum -angle for pre-merging.

    - -

    Pre-merging occurs while Qhull constructs the hull. It is -indicated by 'C-n', 'A-n', or 'Qx'.

    - -

    If the angle between a pair of facet normals is greater than n, -Qhull merges one of the facets into a neighbor. It selects the -facet that is closest to a neighboring facet.

    - -

    For example, option 'A-0.99' merges facets during the -construction of the hull. If the cosine of the angle between -facets is greater than 0.99, one or the other facet is merged. -Qhull accounts for the maximum roundoff error.

    - -

    If 'A-n' is set without 'C-n', then 'C-0' is automatically set.

    - -

    In 5-d and higher, you should set 'Qx' -along with 'A-n'. It skips merges of coplanar facets until after -the hull is constructed and before 'An' and 'Cn' are checked.

    - -

    »An - cosine of maximum angle for -post-merging.

    - -

    Post merging occurs after the hull is constructed. For -example, option 'A0.99' merges a facet if the cosine of the angle -between facets is greater than 0.99. Qhull accounts for the -maximum roundoff error.

    - -

    If 'An' is set without 'Cn', then 'C0' is automatically set.

    - -

    »C-0 - handle all precision -errors

    - -

    Qhull handles precision errors by merging facets. The 'C-0' -option handles all precision errors in 2-d, 3-d, and 4-d. It is -set by default. It may be used in higher dimensions, but -sometimes the facet width grows rapidly. It is usually better to -use 'Qx' in 5-d and higher. -Use 'QJ' to joggle the input -instead of merging facets. -Use 'Q0' to turn both options off.

    - -

    Qhull optimizes 'C-0' ("_zero-centrum") by testing -vertices instead of centrums for adjacent simplices. This may be -slower in higher dimensions if merges decrease the number of -processed points. The optimization may be turned off by setting a -small value such as 'C-1e-30'. See How -Qhull handles imprecision.

    - -

    »C-n - centrum radius for -pre-merging

    - -

    Pre-merging occurs while Qhull constructs the hull. It is -indicated by 'C-n', 'A-n', or 'Qx'.

    - -

    The centrum of a facet is a point on the facet for -testing facet convexity. It is the average of the vertices -projected to the facet's hyperplane. Two adjacent facets are -convex if each centrum is clearly below the other facet.

    - -

    If adjacent facets are non-convex, one of the facets is merged -into a neighboring facet. Qhull merges the facet that is closest -to a neighboring facet.

    - -

    For option 'C-n', n is the centrum radius. For example, -'C-0.001' merges facets whenever the centrum is less than 0.001 -from a neighboring hyperplane. Qhull accounts for roundoff error -when testing the centrum.

    - -

    In 5-d and higher, you should set 'Qx' -along with 'C-n'. It skips merges of coplanar facets until after -the hull is constructed and before 'An' and 'Cn' are checked.

    - -

    »Cn - centrum radius for -post-merging

    - -

    Post-merging occurs after Qhull constructs the hull. It is -indicated by 'Cn' or 'An'.

    - -

    For option 'Cn', n is the centrum -radius. For example, 'C0.001' merges facets when the centrum is -less than 0.001 from a neighboring hyperplane. Qhull accounts for -roundoff error when testing the centrum.

    - -

    Both pre-merging and post-merging may be defined. If only -post-merging is used ('Q0' with -'Cn'), Qhull may fail to produce a hull due to precision errors -during the hull's construction.

    - -

    »En - max roundoff error -for distance computations

    - -

    This allows the user to change the maximum roundoff error -computed by Qhull. The value computed by Qhull may be overly -pessimistic. If 'En' is set too small, then the output may not be -convex. The statistic "max. distance of a new vertex to a -facet" (from option 'Ts') is a -reasonable upper bound for the actual roundoff error.

    - -

    »Rn - randomly perturb -computations

    - -

    This option perturbs every distance, hyperplane, and angle -computation by up to (+/- n * max_coord). It simulates the -effect of roundoff errors. Unless 'En' is -explicitly set, it is adjusted for 'Rn'. The command 'qhull Rn' -will generate a convex hull despite the perturbations. See the Examples section for an example.

    - -

    Options 'Rn C-n' have the effect of 'W2n' -and 'C-2n'. To use time as the random number -seed, use option 'QR-1'.

    - -

    »Un - max distance for a -new, coplanar point

    - -

    This allows the user to set coplanarity. When pre-merging ('C-n ', 'A-n' or 'Qx'), Qhull merges a new point into any -coplanar facets. The default value for 'Un' is 'Vn'.

    - -

    »Vn - min distance for a -visible facet

    - -

    This allows the user to set facet visibility. When adding a -point to the convex hull, Qhull determines all facets that are -visible from the point. A facet is visible if the distance from -the point to the facet is greater than 'Vn'.

    - -

    Without merging, the default value for 'Vn' is the roundoff -error ('En'). With merging, the default value -is the pre-merge centrum ('C-n') in 2-d or 3-d, -or three times that in other dimensions. If the outside width is -specified with option 'Wn ', the maximum, -default value for 'Vn' is 'Wn'.

    - -

    Qhull warns if 'Vn' is greater than 'Wn' and -furthest outside ('Qf') is not -selected; this combination usually results in flipped facets -(i.e., reversed normals).

    - -

    »Wn - min distance above -plane for outside points

    - -

    Points are added to the convex hull only if they are clearly -outside of a facet. A point is outside of a facet if its distance -to the facet is greater than 'Wn'. Without pre-merging, the -default value for 'Wn' is 'En '. If the user -specifies pre-merging and does not set 'Wn', than 'Wn' is set to -the maximum of 'C-n' and maxcoord*(1 - A-n).

    - -

    This option is good for approximating -a convex hull.

    - -

    Options 'Qc' and 'Qi' use the minimum vertex to -distinguish coplanar points from interior points.

    - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-optf.htm b/src/qhull/html/qh-optf.htm deleted file mode 100644 index 3c7a2b1db..000000000 --- a/src/qhull/html/qh-optf.htm +++ /dev/null @@ -1,736 +0,0 @@ - - - - -Qhull format options (F) - - - -

    Up: Home page for Qhull
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    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    -
    - -

    [delaunay] Qhull format options (F)

    - -

    This section lists the format options for Qhull. These options -are indicated by 'F' followed by a letter. See Output, Print, -and Geomview for other output -options.

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Additional input & output formats

    - -

    These options allow for automatic processing of Qhull output. -Options 'i', 'o', -'n', and 'p' -may also be used.

    - -
    -
    -
    Summary and control -
    FA -
    compute total area and volume for option 's' - -
    FV -
    print average vertex (interior point for 'qhalf') -
    FQ -
    print command for qhull and input -
    FO -
    print options to stderr or stdout -
    FS -
    print sizes: total area and volume -
    Fs -
    print summary: dim, #points, total vertices and - facets, #vertices, #facets, max outer and inner plane -
    Fd -
    use format for input (offset first) -
    FD -
    use cdd format for normals (offset first) -
    FM -
    print Maple output (2-d and 3-d) -
    -
    -
    Facets, points, and vertices -
    Fa -
    print area for each facet -
    FC -
    print centrum for each facet -
    Fc -
    print coplanar points for each facet -
    Fx -
    print extreme points (i.e., vertices) of convex hull. - -
    FF -
    print facets w/o ridges -
    FI -
    print ID for each facet -
    Fi -
    print inner planes for each facet -
    Fm -
    print merge count for each facet (511 max) -
    FP -
    print nearest vertex for coplanar points -
    Fn -
    print neighboring facets for each facet -
    FN -
    print neighboring facets for each point -
    Fo -
    print outer planes for each facet -
    Ft -
    print triangulation with added points -
    Fv -
    print vertices for each facet -
    -
    -
    Delaunay, Voronoi, and halfspace -
    Fx -
    print extreme input sites of Delaunay triangulation - or Voronoi diagram. -
    Fp -
    print points at halfspace intersections -
    Fi -
    print separating hyperplanes for inner, bounded - Voronoi regions -
    Fo -
    print separating hyperplanes for outer, unbounded - Voronoi regions -
    Fv -
    print Voronoi diagram as ridges for each input pair -
    FC -
    print Voronoi vertex ("center") for each facet
    -
    - -
    - -

    »Fa - print area for each -facet

    - -

    The first line is the number of facets. The remaining lines -are the area for each facet, one facet per line. See 'FA' and 'FS' for computing the total area and volume.

    - -

    Use 'PAn' for printing the n -largest facets. Use option 'PFn' -for printing facets larger than n.

    - -

    For Delaunay triangulations, the area is the area of each -Delaunay triangle. For Voronoi vertices, the area is the area of -the dual facet to each vertex.

    - -

    Qhull uses the centrum and ridges to triangulate -non-simplicial facets. The area for non-simplicial facets is the -sum of the areas for each triangle. It is an approximation of the -actual area. The ridge's vertices are projected to the facet's -hyperplane. If a vertex is far below a facet (qh_WIDEcoplanar in user.h), -the corresponding triangles are ignored.

    - -

    For non-simplicial facets, vertices are often below the -facet's hyperplane. If so, the approximation is less than the -actual value and it may be significantly less.

    - -

    »FA - compute total area -and volume for option 's'

    - -

    With option 'FA', Qhull includes the total area and volume in -the summary ('s'). Option 'FS' also includes the total area and volume. -If facets are -merged, the area and volume are approximations. Option 'FA' is -automatically set for options 'Fa', 'PAn', and 'PFn'. -

    - -

    With 'qdelaunay s FA', Qhull computes the total area of -the Delaunay triangulation. This equals the volume of the convex -hull of the data points. With options 'qdelaunay Qu -s FA', Qhull computes the -total area of the furthest-site Delaunay triangulation. This -equals of the total area of the Delaunay triangulation.

    - -

    See 'Fa' for further details. Option 'FS' also computes the total area and volume.

    - -

    »Fc - print coplanar -points for each facet

    - -

    The output starts with the number of facets. Then each facet -is printed one per line. Each line is the number of coplanar -points followed by the point ids.

    - -

    By default, option 'Fc' reports coplanar points -('Qc'). You may also use -option 'Qi'. Options 'Qi Fc' prints -interior points while 'Qci Fc' prints both coplanar and interior -points. - -

    Each coplanar point or interior point is assigned to the -facet it is furthest above (resp., least below).

    - -

    Use 'Qc p' to print vertex and -coplanar point coordinates. Use 'Fv' -to print vertices.

    - -

    »FC - print centrum or -Voronoi vertex for each facet

    - -

    The output starts with the dimension followed by the number of -facets. Then each facet centrum is printed, one per line. For -qvoronoi, Voronoi vertices are -printed instead.

    - -

    »Fd - use cdd format for -input

    - -

    The input starts with comments. The first comment is reported -in the summary. Data starts after a "begin" line. The -next line is the number of points followed by the dimension plus -one and "real" or "integer". Then the points -are listed with a leading "1" or "1.0". The -data ends with an "end" line.

    - -

    For halfspaces ('qhalf Fd'), -the input format is the same. Each halfspace starts with its -offset. The signs of the offset and coefficients are the -opposite of Qhull's -convention. The first two lines of the input may be an interior -point in 'FV' format.

    - -

    »FD - use cdd format for -normals

    - -

    Option 'FD' prints normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the -command line that invoked Qhull. Data starts with a -"begin" line. The next line is the number of normals or -points followed by the dimension plus one and "real". -Then the normals or points are listed with the offset before the -coefficients. The offset for points is 1.0. For normals, -the offset and coefficients use the opposite sign from Qhull. -The data ends with an "end" line.

    - -

    »FF - print facets w/o -ridges

    - -

    Option 'FF' prints all fields of all facets (as in 'f') without printing the ridges. This is -useful in higher dimensions where a facet may have many ridges. -For simplicial facets, options 'FF' and 'f -' are equivalent.

    - -

    »Fi - print inner planes -for each facet

    - -

    The first line is the dimension plus one. The second line is -the number of facets. The remainder is one inner plane per line. -The format is the same as option 'n'.

    - -

    The inner plane is a plane that is below the facet's vertices. -It is an offset from the facet's hyperplane. It includes a -roundoff error for computing the vertex distance.

    - -

    Note that the inner planes for Geomview output ('Gi') include an additional offset for -vertex visualization and roundoff error.

    - -

    »Fi - print separating -hyperplanes for inner, bounded Voronoi regions

    - -

    With qvoronoi, 'Fi' prints the -separating hyperplanes for inner, bounded regions of the Voronoi -diagram. The first line is the number of ridges. Then each -hyperplane is printed, one per line. A line starts with the -number of indices and floats. The first pair of indices indicates -an adjacent pair of input sites. The next d floats are the -normalized coefficients for the hyperplane, and the last float is -the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input -site of the pair.

    - -

    Use 'Fo' for unbounded regions, -and 'Fv' for the corresponding -Voronoi vertices.

    - -

    Use 'Tv' to verify that the -hyperplanes are perpendicular bisectors. It will list relevant -statistics to stderr. The hyperplane is a perpendicular bisector -if the midpoint of the input sites lies on the plane, all Voronoi -vertices in the ridge lie on the plane, and the angle between the -input sites and the plane is ninety degrees. This is true if all -statistics are zero. Roundoff and computation errors make these -non-zero. The deviations appear to be largest when the -corresponding Delaunay triangles are large and thin; for example, -the Voronoi diagram of nearly cospherical points.

    - -

    »FI - print ID for each -facet

    - -

    Print facet identifiers. These are used internally and listed -with options 'f' and 'FF'. -Options 'Fn ' and 'FN' use -facet identifiers for negative indices.

    - -

    »Fm - print merge count -for each facet

    - -

    The first line is the number of facets. The remainder is the -number of merges for each facet, one per line. At most 511 merges -are reported for a facet. See 'PMn' -for printing the facets with the most merges.

    - -

    »FM - print Maple -output

    - -

    Qhull writes a Maple file for 2-d and 3-d convex hulls, -2-d and 3-d halfspace intersections, -and 2-d Delaunay triangulations. Qhull produces a 2-d -or 3-d plot. - -

    Warning: This option has not been tested in Maple. - -

    [From T. K. Abraham with help from M. R. Feinberg and N. Platinova.] -The following steps apply while working within the -Maple worksheet environment : -

      -
    1. Generate the data and store it as an array . For example, in 3-d, data generated -in Maple is of the form : x[i],y[i],z[i] -

      -

    2. Create a single variable and assign the entire array of data points to this variable. -Use the "seq" command within square brackets as shown in the following example. -(The square brackets are essential for the rest of the steps to work.) -

      ->data:=[seq([x[i],y[i],z[i]],i=1..n)]:# here n is the number of data points - -

    3. Next we need to write the data to a file to be read by qhull. Before -writing the data to a file, make sure that the qhull executable files and -the data file lie in the same subdirectory. If the executable files are -stored in the "C:\qhull3.1\" subdirectory, then save the file in the same -subdirectory, say "C:\qhull3.1\datafile.txt". For the sake of integrity of -the data file , it is best to first ensure that the data file does not -exist before writing into the data file. This can be done by running a -delete command first . To write the data to the file, use the "writedata" -and the "writedata[APPEND]" commands as illustrated in the following example : -

      ->system("del c:\\qhull3.1\\datafile.txt");#To erase any previous versions of the file -
      >writedata("c:\\qhull3.1\\datafile.txt ",[3, nops(data)]);#writing in qhull format -
      >writedata[APPEND]("c:\\ qhull3.1\\datafile.txt ", data);#writing the data points -

    4. -Use the 'FM' option to produce Maple output. Store the output as a ".mpl" file. -For example, using the file we created above, we type the following (in DOS environment) -

      -qconvex s FM <datafile.txt >dataplot.mpl - -

    5. -To read 3-d output in Maple, we use the 'read' command followed by -a 'display3d' command. For example (in Maple environment): -

      ->with (plots): -
      >read `c:\\qhull3.1\\dataplot.mpl`:#IMPORTANT - Note that the punctuation mark used is ' and NOT '. The correct punctuation mark is the one next to the key for "1" (not the punctuation mark near the enter key) -
      > qhullplot:=%: -
      > display3d(qhullplot); -

    - -

    For Delaunay triangulation orthogonal projection is better. - -

    For halfspace intersections, Qhull produces the dual -convex hull. - -

    See Is Qhull available for Maple? -for other URLs. - -

    »Fn - print neighboring -facets for each facet

    - -

    The output starts with the number of facets. Then each facet -is printed one per line. Each line is the number of neighbors -followed by an index for each neighbor. The indices match the -other facet output formats.

    - -

    For simplicial facets, each neighbor is opposite -the corresponding vertex (option 'Fv'). -Do not compare to option 'i'. Option 'i' -orients facets by reversing the order of two vertices. For non-simplicial facets, -the neighbors are unordered. - -

    A negative index indicates an unprinted facet due to printing -only good facets ('Pg', qdelaunay, -qvoronoi). It -is the negation of the facet's ID (option 'FI'). -For example, negative indices are used for facets "at -infinity" in the Delaunay triangulation.

    - -

    »FN - print neighboring -facets for each point

    - -

    The first line is the number of points. Then each point is -printed, one per line. For unassigned points (either interior or -coplanar), the line is "0". For assigned coplanar -points ('Qc'), the line is -"1" followed by the index of the facet that is furthest -below the point. For assigned interior points ('Qi'), the line is "1" -followed by the index of the facet that is least above the point. -For vertices that do not belong to good facet, the line is -"0"

    - -

    For vertices of good facets, the line is the number of -neighboring facets followed by the facet indices. The indices -correspond to the other 'F' formats. In 4-d -and higher, the facets are sorted by index. In 3-d, the facets -are in adjacency order (not oriented).

    - -

    A negative index indicates an unprinted facet due to printing -only good facets (qdelaunay, -qvoronoi, 'Pdk', -'Pg'). It is the negation of the -facet's ID (' FI'). For example, negative -indices are used for facets "at infinity" in the -Delaunay triangulation.

    - -

    For Voronoi vertices, option 'FN' lists the vertices of the -Voronoi region for each input site. Option 'FN' lists the regions -in site ID order. Option 'FN' corresponds to the second half of -option 'o'. To convert from 'FN' to 'o', replace negative indices with zero -and increment non-negative indices by one.

    - -

    If you are using the Qhull -library or C++ interface, option 'FN' has the side effect of reordering the -neighbors for a vertex

    - -

    »Fo - print outer planes -for each facet

    - -

    The first line is the dimension plus one. The second line is -the number of facets. The remainder is one outer plane per line. -The format is the same as option 'n'.

    - -

    The outer plane is a plane that is above all points. It is an -offset from the facet's hyperplane. It includes a roundoff error -for computing the point distance. When testing the outer plane -(e.g., 'Tv'), another roundoff error -should be added for the tested point.

    - -

    If outer planes are not checked ('Q5') -or not computed (!qh_MAXoutside), the maximum, computed outside -distance is used instead. This can be much larger than the actual -outer planes.

    - -

    Note that the outer planes for Geomview output ('G') include an additional offset for -vertex/point visualization, 'lines closer,' and roundoff error.

    - -

    »Fo - print separating -hyperplanes for outer, unbounded Voronoi regions

    - -

    With qvoronoi, 'Fo' prints the -separating hyperplanes for outer, unbounded regions of the -Voronoi diagram. The first line is the number of ridges. Then -each hyperplane is printed, one per line. A line starts with the -number of indices and floats. The first pair of indices indicates -an adjacent pair of input sites. The next d floats are the -normalized coefficients for the hyperplane, and the last float is -the offset. The hyperplane is oriented toward 'QVn' (if defined), or the first input -site of the pair.

    - -

    Option 'Fo' gives the hyperplanes for the unbounded rays of -the unbounded regions of the Voronoi diagram. Each hyperplane -goes through the midpoint of the corresponding input sites. The -rays are directed away from the input sites.

    - -

    Use 'Fi' for bounded regions, -and 'Fv' for the corresponding -Voronoi vertices. Use 'Tv' to verify -that the corresponding Voronoi vertices lie on the hyperplane.

    - -

    »FO - print list of -selected options

    - -

    Lists selected options and default values to stderr. -Additional 'FO's are printed to stdout.

    - -

    »Fp - print points at -halfspace intersections

    - -

    The first line is the number of intersection points. The -remainder is one intersection point per line. A intersection -point is the intersection of d or more halfspaces from -'qhalf'. It corresponds to a -facet of the dual polytope. The "infinity" point -[-10.101,-10.101,...] indicates an unbounded intersection.

    - -

    If [x,y,z] are the dual facet's normal coefficients and b<0 -is its offset, the halfspace intersection occurs at -[x/-b,y/-b,z/-b] plus the interior point. If b>=0, the -halfspace intersection is unbounded.

    - -

    »FP - print nearest -vertex for coplanar points

    - -

    The output starts with the number of coplanar points. Then -each coplanar point is printed one per line. Each line is the -point ID of the closest vertex, the point ID of the coplanar -point, the corresponding facet ID, and the distance. Sort the -lines to list the coplanar points nearest to each vertex.

    - -

    Use options 'Qc' and/or 'Qi' with 'FP'. Options 'Qc FP' prints -coplanar points while 'Qci FP' prints coplanar and interior -points. Option 'Qc' is automatically selected if 'Qi' is not -selected. - -

    For Delaunay triangulations (qdelaunay -or qvoronoi), a coplanar point is nearly -incident to a vertex. The distance is the distance in the -original point set.

    - -

    If imprecision problems are severe, Qhull will delete input -sites when constructing the Delaunay triangulation. Option 'FP' will -list these points along with coincident points.

    - -

    If there are many coplanar or coincident points and non-simplicial -facets are triangulated ('Qt'), option -'FP' may be inefficient. It redetermines the original vertex set -for each coplanar point.

    - -

    »FQ - print command for -qhull and input

    - -

    Prints qhull and input command, e.g., "rbox 10 s | qhull -FQ". Option 'FQ' may be repeated multiple times.

    - -

    »Fs - print summary

    - -

    The first line consists of number of integers ("10") -followed by the: -

      -
    • dimension -
    • number of points -
    • number of vertices -
    • number of facets -
    • number of vertices selected for output -
    • number of facets selected for output -
    • number of coplanar points for selected facets -
    • number of nonsimplicial or merged facets selected for - output -
    • number of deleted vertices
      • -
    • number of triangulated facets ('Qt')
      • -
    - -

    The second line consists of the number of reals -("2") followed by the: -

      -
    • maximum offset to an outer plane -
    • minimum offset to an inner plane.
      • -
    -Roundoff and joggle are included. -

    - -

    For Delaunay triangulations and Voronoi diagrams, the -number of deleted vertices should be zero. If greater than zero, then the -input is highly degenerate and coplanar points are not necessarily coincident -points. For example, 'RBOX 1000 s W1e-13 t995138628 | QHULL d Qbb' reports -deleted vertices; the input is nearly cospherical.

    - -

    Later versions of Qhull may produce additional integers or reals.

    - -

    »FS - print sizes

    - -

    The first line consists of the number of integers -("0"). The second line consists of the number of reals -("2"), followed by the total facet area, and the total -volume. Later versions of Qhull may produce additional integers -or reals.

    - -

    The total volume measures the volume of the intersection of -the halfspaces defined by each facet. It is computed from the -facet area. Both area and volume are approximations for -non-simplicial facets. See option 'Fa ' for -further notes. Option 'FA ' also computes the total area and volume.

    - -

    »Ft - print triangulation

    - -

    Prints a triangulation with added points for non-simplicial -facets. The output is

    - -
      -
    • The first line is the dimension -
    • The second line is the number of points, the number - of facets, and the number of ridges. -
    • All of the input points follow, one per line. -
    • The centrums follow, one per non-simplicial facet -
    • Then the facets follow as a list of point indices - preceded by the number of points. The simplices are - oriented.
      • -
    - -

    For convex hulls with simplicial facets, the output is the -same as option 'o'.

    - -

    The added points are the centrums of the non-simplicial -facets. Except for large facets, the centrum is the average -vertex coordinate projected to the facet's hyperplane. Large -facets may use an old centrum to avoid recomputing the centrum -after each merge. In either case, the centrum is clearly below -neighboring facets. See Precision issues. -

    - -

    The new simplices will not be clearly convex with their -neighbors and they will not satisfy the Delaunay property. They -may even have a flipped orientation. Use triangulated input ('Qt') for Delaunay triangulations. - -

    For Delaunay triangulations with simplicial facets, the output is the -same as option 'o' without the lifted -coordinate. Since 'Ft' is invalid for merged Delaunay facets, option -'Ft' is not available for qdelaunay or qvoronoi. It may be used with -joggled input ('QJ') or triangulated output ('Qt'), for example, rbox 10 c G 0.01 | qhull d QJ Ft

    - -

    If you add a point-at-infinity with 'Qz', -it is printed after the input sites and before any centrums. It -will not be used in a Delaunay facet.

    - -

    »Fv - print vertices for -each facet

    - -

    The first line is the number of facets. Then each facet is -printed, one per line. Each line is the number of vertices -followed by the corresponding point ids. Vertices are listed in -the order they were added to the hull (the last one added is the -first listed). -

    -

    Option 'i' also lists the vertices, -but it orients facets by reversing the order of two -vertices. Option 'i' triangulates non-simplicial, 4-d and higher facets by -adding vertices for the centrums. -

    - -

    »Fv - print Voronoi -diagram

    - -

    With qvoronoi, 'Fv' prints the -Voronoi diagram or furthest-site Voronoi diagram. The first line -is the number of ridges. Then each ridge is printed, one per -line. The first number is the count of indices. The second pair -of indices indicates a pair of input sites. The remaining indices -list the corresponding ridge of Voronoi vertices. Vertex 0 is the -vertex-at-infinity. It indicates an unbounded ray.

    - -

    All vertices of a ridge are coplanar. If the ridge is -unbounded, add the midpoint of the pair of input sites. The -unbounded ray is directed from the Voronoi vertices to infinity.

    - -

    Use 'Fo' for separating -hyperplanes of outer, unbounded regions. Use 'Fi' for separating hyperplanes of -inner, bounded regions.

    - -

    Option 'Fv' does not list ridges that require more than one -midpoint. For example, the Voronoi diagram of cospherical points -lists zero ridges (e.g., 'rbox 10 s | qvoronoi Fv Qz'). -Other examples are the Voronoi diagrams of a rectangular mesh -(e.g., 'rbox 27 M1,0 | qvoronoi Fv') or a point set with -a rectangular corner (e.g., -'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qvoronoi Fv'). -Both cases miss unbounded rays at the corners. -To determine these ridges, surround the points with a -large cube (e.g., 'rbox 10 s c G2.0 | qvoronoi Fv Qz'). -The cube needs to be large enough to bound all Voronoi regions of the original point set. -Please report any other cases that are missed. If you -can formally describe these cases or -write code to handle them, please send email to qhull@qhull.org.

    - -

    »FV - print average -vertex

    - -

    The average vertex is the average of all vertex coordinates. -It is an interior point for halfspace intersection. The first -line is the dimension and "1"; the second line is the -coordinates. For example,

    - -
    -

    qconvex FV n | qhalf Fp

    -
    - -

    prints the extreme points of the original point set (roundoff -included).

    - -

    »Fx - print extreme -points (vertices) of convex hulls and Delaunay triangulations

    - -

    The first line is the number of points. The following lines -give the index of the corresponding points. The first point is -'0'.

    - -

    In 2-d, the extreme points (vertices) are listed in -counterclockwise order (by qh_ORIENTclock in user.h).

    - -

    In 3-d and higher convex hulls, the extreme points (vertices) -are sorted by index. This is the same order as option 'p' when it doesn't include coplanar or -interior points.

    - -

    For Delaunay triangulations, 'Fx' lists the extreme -points of the input sites (i.e., the vertices of their convex hull). The points -are unordered.

    - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: -Sept. 25, 1995 --- Last modified: see top -

    - - diff --git a/src/qhull/html/qh-optg.htm b/src/qhull/html/qh-optg.htm deleted file mode 100644 index a56e29df1..000000000 --- a/src/qhull/html/qh-optg.htm +++ /dev/null @@ -1,274 +0,0 @@ - - - -Qhull Geomview options (G) - - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - - -

    [delaunay] Qhull Geomview options (G)

    - -This section lists the Geomview options for Qhull. These options are -indicated by 'G' followed by a letter. See -Output, Print, -and Format for other output options. - - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Geomview output options

    - -

    Geomview is the graphical -viewer for visualizing Qhull output in 2-d, 3-d and 4-d.

    - -

    Geomview displays each facet of the convex hull. The color of -a facet is determined by the coefficients of the facet's normal -equation. For imprecise hulls, Geomview displays the inner and -outer hull. Geomview can also display points, ridges, vertices, -coplanar points, and facet intersections.

    - -

    For 2-d Delaunay triangulations, Geomview displays the -corresponding paraboloid. Geomview displays the 2-d Voronoi -diagram. For halfspace intersections, it displays the -dual convex hull.

    - -
    -
     
    -
    General
    -
    G
    -
    display Geomview output
    -
    Gt
    -
    display transparent 3-d Delaunay triangulation
    -
    GDn
    -
    drop dimension n in 3-d and 4-d output
    - -
     
    -
     
    -
    Specific
    -
    Ga
    -
    display all points as dots
    -
    Gc
    -
    display centrums (2-d, 3-d)
    -
    Gp
    -
    display coplanar points and vertices as radii
    -
    Gh
    -
    display hyperplane intersections
    -
    Gi
    -
    display inner planes only (2-d, 3-d)
    -
    Go
    -
    display outer planes only (2-d, 3-d)
    -
    Gr
    -
    display ridges (3-d)
    -
    Gv
    -
    display vertices as spheres
    -
    Gn
    -
    do not display planes
    - -
    - -
    - -

    »G - produce output for -viewing with Geomview

    - -

    By default, option 'G' displays edges in 2-d, outer planes in -3-d, and ridges in 4-d.

    - -

    A ridge can be explicit or implicit. An explicit ridge is a (d-1)-dimensional -simplex between two facets. In 4-d, the explicit ridges are -triangles. An implicit ridge is the topological intersection of -two neighboring facets. It is the union of explicit ridges.

    - -

    For non-simplicial 4-d facets, the explicit ridges can be -quite complex. When displaying a ridge in 4-d, Qhull projects the -ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both -hyperplanes. This usually results in a cleaner display.

    - -

    For 2-d Delaunay triangulations, Geomview displays the -corresponding paraboloid. Geomview displays the 2-d Voronoi -diagram. For halfspace intersections, it displays the -dual convex hull. - -

    »Ga - display all -points as dots

    - -

    Each input point is displayed as a green dot.

    - -

    »Gc - display centrums -(3-d)

    - -

    The centrum is defined by a green radius sitting on a blue -plane. The plane corresponds to the facet's hyperplane. If you -sight along a facet's hyperplane, you will see that all -neighboring centrums are below the facet. The radius is defined -by 'C-n' or 'Cn'.

    - -

    »GDn - drop dimension -n in 3-d and 4-d output

    - -

    The result is a 2-d or 3-d object. In 4-d, this corresponds to -viewing the 4-d object from the nth axis without perspective. -It's best to view 4-d objects in pieces. Use the 'Pdk' 'Pg' -'PG' 'QGn' -and 'QVn' options to select a few -facets. If one of the facets is perpendicular to an axis, then -projecting along that axis will show the facet exactly as it is -in 4-d. If you generate many facets, use Geomview's ginsu -module to view the interior

    - -

    To view multiple 4-d dimensions at once, output the object -without 'GDn' and read it with Geomview's ndview. As you -rotate the object in one set of dimensions, you can see how it -changes in other sets of dimensions.

    - -

    For additional control over 4-d objects, output the object -without 'GDn' and read it with Geomview's 4dview. You -can slice the object along any 4-d plane. You can also flip the -halfspace that's deleted when slicing. By combining these -features, you can get some interesting cross sections.

    - -

    »Gh - display -hyperplane intersections (3-d, 4-d)

    - -

    In 3-d, the intersection is a black line. It lies on two -neighboring hyperplanes, c.f., the blue squares associated with -centrums ('Gc '). In 4-d, the ridges are -projected to the intersection of both hyperplanes. If you turn on -edges (Geomview's 'appearances' menu), each triangle corresponds -to one ridge. The ridges may overlap each other.

    - -

    »Gi - display inner -planes only (2-d, 3-d)

    - -

    The inner plane of a facet is below all of its vertices. It is -parallel to the facet's hyperplane. The inner plane's color is -the opposite of the outer plane's color, i.e., [1-r,1-g,1-b] . -Its edges are determined by the vertices.

    - -

    »Gn - do not display -planes

    - -

    By default, Geomview displays the precise plane (no merging) -or both inner and output planes (if merging). If merging, -Geomview does not display the inner plane if the the difference -between inner and outer is too small.

    - -

    »Go - display outer -planes only (2-d, 3-d)

    - -

    The outer plane of a facet is above all input points. It is -parallel to the facet's hyperplane. Its color is determined by -the facet's normal, and its edges are determined by the vertices.

    - -

    »Gp - display coplanar -points and vertices as radii

    - -

    Coplanar points ('Qc'), interior -points ('Qi'), outside points ('TCn' or 'TVn'), -and vertices are displayed as red and yellow radii. The radii are -perpendicular to the corresponding facet. Vertices are aligned -with an interior point. The radii define a ball which corresponds -to the imprecision of the point. The imprecision is the maximum -of the roundoff error, the centrum radius, and maxcoord * (1 - -A-n). It is at -least 1/20'th of the maximum coordinate, and ignores post merging -if pre-merging is done.

    - -

    If 'Gv' (print vertices as -spheres) is also selected, option 'Gp' displays coplanar -points as radii. Select options Qc' -and/or 'Qi'. Options 'Qc Gpv' displays -coplanar points while 'Qci Gpv' displays coplanar and interior -points. Option 'Qc' is automatically selected if 'Qi' is not -selected with options 'Gpv'. - -

    »Gr - display ridges -(3-d)

    - -

    A ridge connects the two vertices that are shared by -neighboring facets. It is displayed in green. A ridge is the -topological edge between two facets while the hyperplane -intersection is the geometric edge between two facets. Ridges are -always displayed in 4-d.

    - -

    »Gt - transparent 3-d -Delaunay

    - -

    A 3-d Delaunay triangulation looks like a convex hull with -interior facets. Option 'Gt' removes the outside ridges to reveal -the outermost facets. It automatically sets options 'Gr' and 'GDn'. See example eg.17f.delaunay.3.

    - -

    »Gv - display vertices -as spheres (2-d, 3-d)

    - -

    The radius of the sphere corresponds to the imprecision of the -data. See 'Gp' for determining the radius.

    - - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-opto.htm b/src/qhull/html/qh-opto.htm deleted file mode 100644 index e7b21745c..000000000 --- a/src/qhull/html/qh-opto.htm +++ /dev/null @@ -1,353 +0,0 @@ - - - - -Qhull output options - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    [delaunay] Qhull output options

    - -

    This section lists the output options for Qhull. These options -are indicated by lower case characters. See Formats, Print, and Geomview for other output -options.

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Output options

    - -

    Qhull prints its output to standard out. All output is printed -text. The default output is a summary (option 's'). -Other outputs may be specified as follows.

    - -
    -
    f
    -
    print all fields of all facets
    -
    n
    -
    print hyperplane normals with offsets
    -
    m
    -
    print Mathematica output (2-d and 3-d)
    -
    o
    -
    print OFF file format (dim, points and facets)
    -
    s
    -
    print summary to stderr
    -
    p
    -
    print vertex and point coordinates
    -
    i
    -
    print vertices incident to each facet
    -
     
    -
     
    -
    Related options
    -
    F
    -
    additional input/output formats
    -
    G
    -
    Geomview output
    -
    P
    -
    Print options
    -
    Ft
    -
    print triangulation with added points
    -
     
    -
    - -
    - -

    »f - print all fields of -all facets

    - -

    Print all fields of all facets. -The facet is the primary data structure for -Qhull. - -

    Option 'f' is for -debugging. Most of the fields are available via the 'F' options. If you need specialized -information from Qhull, you can use the Qhull library or C++ interface.

    - -

    Use the 'FF' option to print the -facets but not the ridges.

    - -

    »i - print vertices -incident to each facet

    - -

    The first line is the number of facets. The remaining lines -list the vertices for each facet, one facet per line. The indices -are 0-relative indices of the corresponding input points. The -facets are oriented. Option 'Fv' -displays an unoriented list of vertices with a vertex count per -line. Options 'o' and 'Ft' displays coordinates for each -vertex prior to the vertices for each facet.

    - -

    Simplicial facets (e.g., triangles in 3-d) consist of d -vertices. Non-simplicial facets in 3-d consist of 4 or more -vertices. For example, a facet of a cube consists of 4 vertices. -Use option 'Qt' to triangulate non-simplicial facets.

    - -

    For 4-d and higher convex hulls and 3-d and higher Delaunay -triangulations, d vertices are listed for all facets. A -non-simplicial facet is triangulated with its centrum and each -ridge. The index of the centrum is higher than any input point. -Use option 'Fv' to list the vertices -of non-simplicial facets as is. Use option 'Ft' to print the coordinates of the -centrums as well as those of the input points.

    - -

    »m - print Mathematica -output

    - -

    Qhull writes a Mathematica file for 2-d and 3-d convex hulls, -2-d and 3-d halfspace intersections, -and 2-d Delaunay triangulations. Qhull produces a list of -objects that you can assign to a variable in Mathematica, for -example: "list= << <outputfilename> ". -If the object is 2-d, it can be visualized by "Show[Graphics[list]] -". For 3-d objects the command is "Show[Graphics3D[list]] -". Now the object can be manipulated by commands of the -form "Show[%, <parametername> -> -<newvalue>]".

    - -

    For Delaunay triangulation orthogonal projection is better. -This can be specified, for example, by "BoxRatios: -Show[%, BoxRatios -> {1, 1, 1e-8}]". To see the -meaningful side of the 3-d object used to visualize 2-d Delaunay, -you need to change the viewpoint: "Show[%, ViewPoint --> {0, 0, -1}]". By specifying different viewpoints -you can slowly rotate objects.

    - -

    For halfspace intersections, Qhull produces the dual -convex hull. - -

    See Is Qhull available for Mathematica? -for URLs. - -

    »n - print hyperplane -normals with offsets

    - -

    The first line is the dimension plus one. The second line is -the number of facets. The remaining lines are the normals for -each facet, one normal per line. The facet's offset follows its -normal coefficients.

    - -

    The normals point outward, i.e., the convex hull satisfies Ax -<= -b where A is the matrix of coefficients and b -is the vector of offsets.

    - -

    A point is inside or below a hyperplane if its distance -to the hyperplane is negative. A point is outside or above a hyperplane -if its distance to the hyperplane is positive. Otherwise a point is on or -coplanar to the hyperplane. - -

    If cdd output is specified ('FD'), -Qhull prints the command line, the keyword "begin", the -number of facets, the dimension (plus one), the keyword -"real", and the normals for each facet. The facet's -negative offset precedes its normal coefficients (i.e., if the -origin is an interior point, the offset is positive). Qhull ends -the output with the keyword "end".

    - -

    »o - print OFF file format -

    - -

    The output is:

    - -
      -
    • The first line is the dimension
      • -
    • The second line is the number of points, the number of - facets, and the number of ridges.
      • -
    • All of the input points follow, one per line.
      • -
    • Then Qhull prints the vertices for each facet. Each facet - is on a separate line. The first number is the number of - vertices. The remainder is the indices of the - corresponding points. The vertices are oriented in 2-d, - 3-d, and in simplicial facets.
      • -
    - -

    Option 'Ft' prints the same -information with added points for non-simplicial facets.

    - -

    Option 'i' displays vertices -without the point coordinates. Option 'p' -displays the point coordinates without vertex and facet information.

    - -

    In 3-d, Geomview can load the file directly if you delete the -first line (e.g., by piping through 'tail +2').

    - -

    For Voronoi diagrams (qvoronoi), option -'o' prints Voronoi vertices and Voronoi regions instead of input -points and facets. The first vertex is the infinity vertex -[-10.101, -10.101, ...]. Then, option 'o' lists the vertices in -the Voronoi region for each input site. The regions appear in -site ID order. In 2-d, the vertices of a Voronoi region are -sorted by adjacency (non-oriented). In 3-d and higher, the -Voronoi vertices are sorted by index. See the 'FN' option for listing Voronoi regions -without listing Voronoi vertices.

    - -

    If you are using the Qhull library, options 'v o' have the -side effect of reordering the neighbors for a vertex.

    - -

    »p - print vertex and -point coordinates

    - -

    The first line is the dimension. The second line is the number -of vertices. The remaining lines are the vertices, one vertex per -line. A vertex consists of its point coordinates

    - -

    With the 'Gc' and 'Gi' options, option 'p' also prints -coplanar and interior points respectively.

    - -

    For qvoronoi, it prints the -coordinates of each Voronoi vertex.

    - -

    For qdelaunay, it prints the -input sites as lifted to a paraboloid. For qhalf -it prints the dual points. For both, option 'p' is the same as the first -section of option 'o'.

    - -

    Use 'Fx' to list the point ids of -the extreme points (i.e., vertices).

    - -

    If a subset of the facets is selected ('Pdk', 'PDk', -'Pg' options), option 'p' only -prints vertices and points associated with those facets.

    - -

    If cdd-output format is selected ('FD'), -the first line is "begin". The second line is the -number of vertices, the dimension plus one, and "real". -The vertices follow with a leading "1". Output ends -with "end".

    - -

    »s - print summary to -stderr

    - -

    The default output of Qhull is a summary to stderr. Options 'FS' and 'Fs' -produce the same information for programs. Note: Windows 95 and 98 -treats stderr the same as stdout. Use option 'TO file' to separate -stderr and stdout.

    - -

    The summary lists the number of input points, the dimension, -the number of vertices in the convex hull, and the number of -facets in the convex hull. It lists the number of selected -("good") facets for options 'Pg', -'Pdk', qdelaunay, -or qvoronoi (Delaunay triangulations only -use the lower half of a convex hull). It lists the number of -coplanar points. For Delaunay triangulations without 'Qc', it lists the total number of -coplanar points. It lists the number of simplicial facets in -the output.

    - -

    The terminology depends on the output structure.

    - -

    The summary lists these statistics:

    - -
      -
    • number of points processed by Qhull
      • -
    • number of hyperplanes created
      • -
    • number of distance tests (not counting statistics, - summary, and checking)
      • -
    • number of merged facets (if any)
      • -
    • number of distance tests for merging (if any)
      • -
    • CPU seconds to compute the hull
      • -
    • the maximum joggle for 'QJ'
      - or, the probability of precision errors for 'QJ TRn' -
      • -
    • total area and volume (if computed, see 'FS' 'FA' - 'Fa' 'PAn')
      • -
    • max. distance of a point above a facet (if non-zero)
      • -
    • max. distance of a vertex below a facet (if non-zero)
      • -
    - -

    The statistics include intermediate hulls. For example 'rbox d -D4 | qhull' reports merged facets even though the final hull is -simplicial.

    - -

    Qhull starts counting CPU seconds after it has read and -projected the input points. It stops counting before producing -output. In the code, CPU seconds measures the execution time of -function qhull() in libqhull.c. If the number of CPU -seconds is clearly wrong, check qh_SECticks in user.h.

    - -

    The last two figures measure the maximum distance from a point -or vertex to a facet. They are not printed if less than roundoff -or if not merging. They account for roundoff error in computing -the distance (c.f., option 'Rn'). -Use 'Fs' to report the maximum outer -and inner plane.

    - -

    A number may appear in parentheses after the maximum distance -(e.g., 2.1x). It is the ratio between the maximum distance and -the worst-case distance due to merging two simplicial facets. It -should be small for 2-d, 3-d, and 4-d, and for higher dimensions -with 'Qx'. It is not printed if less -than 0.05.

    - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-optp.htm b/src/qhull/html/qh-optp.htm deleted file mode 100644 index 9c6df90f5..000000000 --- a/src/qhull/html/qh-optp.htm +++ /dev/null @@ -1,253 +0,0 @@ - - - - -Qhull print options (P) - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    [delaunay] Qhull print options (P)

    - -This section lists the print options for Qhull. These options are -indicated by 'P' followed by a letter. See -Output, Geomview, -and Format for other output options. - - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Print options

    -
    -
    -
     
    -
    General
    -
    Pp
    -
    do not report precision problems
    -
    Po
    -
    force output despite precision problems
    -
    Po
    -
    if error, output neighborhood of facet
    -
     
    -
     
    -
    Select
    -
    Pdk:n
    -
    print facets with normal[k] >= n (default 0.0)
    -
    PDk:n
    -
    print facets with normal[k] <= n
    -
    PFn
    -
    print facets whose area is at least n
    -
    Pg
    -
    print good facets only (needs 'QGn' - or 'QVn ')
    -
    PMn
    -
    print n facets with most merges
    -
    PAn
    -
    print n largest facets by area
    -
    PG
    -
    print neighbors of good facets
    -
    -
    -
    - -

    »PAn - keep n largest -facets by area

    - -

    The n largest facets are marked good for printing. This -may be useful for approximating -a hull. Unless 'PG' is set, 'Pg' -is automatically set.

    - -

    »Pdk:n - print facet if -normal[k] >= n

    - -

    For a given output, print only those facets with normal[k] >= n -and drop the others. For example, 'Pd0:0.5' prints facets with normal[0] ->= 0.5 . The default value of n is zero. For -example in 3-d, 'Pd0d1d2' prints facets in the positive octant. -

    -If no facets match, the closest facet is returned.

    -

    -On Windows 95, do not combine multiple options. A 'd' is considered -part of a number. For example, use 'Pd0:0.5 Pd1:0.5' instead of -'Pd0:0.5d1:0.5'. - -

    »PDk:n - print facet if -normal[k] <= n

    - -

    For a given output, print only those facets with normal[k] <= n -and drop the others. -For example, 'PD0:0.5' prints facets with normal[0] -<= 0.5 . The default value of n is zero. For -example in 3-d, 'PD0D1D2' displays facets in the negative octant. -

    -If no facets match, the closest facet is returned.

    - -

    In 2-d, 'd G PD2' displays the Delaunay triangulation instead -of the corresponding paraboloid.

    - -

    Be careful of placing 'Dk' or 'dk' immediately after a real -number. Some compilers treat the 'D' as a double precision -exponent.

    - -

    »PFn - keep facets whose -area is at least n

    - -

    The facets with area at least n are marked good for -printing. This may be useful for approximating a hull. Unless -'PG' is set, 'Pg' is -automatically set.

    - -

    »Pg - print good facets

    - -

    Qhull can mark facets as "good". This is used to

    - -
      -
    • mark the lower convex hull for Delaunay triangulations - and Voronoi diagrams
      • -
    • mark the facets that are visible from a point (the 'QGn ' option)
      • -
    • mark the facets that contain a point (the 'QVn' option).
      • -
    • indicate facets with a large enough area (options 'PAn' and 'PFn')
      • -
    - -

    Option 'Pg' only prints good facets that -also meet 'Pdk' and 'PDk' -options. It is automatically set for options 'PAn', -'PFn ', 'QGn', -and 'QVn'.

    - -

    »PG - print neighbors of -good facets

    - -

    Option 'PG' can be used with or without option 'Pg' -to print the neighbors of good facets. For example, options 'QGn' and 'QVn' -print the horizon facets for point n.

    - -

    »PMn - keep n facets with -most merges

    - -

    The n facets with the most merges are marked good for -printing. This may be useful for approximating a hull. Unless -'PG' is set, 'Pg' is -automatically set.

    - -

    Use option 'Fm' to print merges -per facet. - -

    »Po - force output despite -precision problems

    - -

    Use options 'Po' and 'Q0' if you -can not merge facets, triangulate the output ('Qt'), -or joggle the input (QJ). - -

    Option 'Po' can not force output when -duplicate ridges or duplicate facets occur. It may produce -erroneous results. For these reasons, merged facets, joggled input, or exact arithmetic are better.

    - -

    If you need a simplicial Delaunay triangulation, use -joggled input 'QJ' or triangulated -output 'Ft'. - -

    Option 'Po' may be used without 'Q0' -to remove some steps from Qhull or to output the neighborhood of -an error.

    - -

    Option 'Po' may be used with option 'Q5') -to skip qh_check_maxout (i.e., do not determine the maximum outside distance). -This can save a significant amount of time. - -

    If option 'Po' is used,

    - -
      -
    • most precision errors allow Qhull to continue.
      • -
    • verify ('Tv') does not check - coplanar points.
      • -
    • points are not partitioned into flipped facets and a - flipped facet is always visible to a point. This may - delete flipped facets from the output.
      • -
    - -

    »Po - if error, output -neighborhood of facet

    - -

    If an error occurs before the completion of Qhull and tracing -is not active, 'Po' outputs a neighborhood of the erroneous -facets (if any). It uses the current output options.

    - -

    See 'Po' - force output despite -precision problems. - -

    »Pp - do not report -precision problems

    - -

    With option 'Pp', Qhull does not print statistics about -precision problems, and it removes some of the warnings. It -removes the narrow hull warning.

    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-optq.htm b/src/qhull/html/qh-optq.htm deleted file mode 100644 index 2edbb1fd4..000000000 --- a/src/qhull/html/qh-optq.htm +++ /dev/null @@ -1,731 +0,0 @@ - - - - -Qhull control options (Q) - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    [delaunay] Qhull control options (Q)

    - -

    This section lists the control options for Qhull. These -options are indicated by 'Q' followed by a letter.

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Qhull control options

    - -
    -
     
    -
    General
    -
    Qu
    -
    compute upper hull for furthest-site Delaunay - triangulation
    -
    Qc
    -
    keep coplanar points with nearest facet
    -
    Qi
    -
    keep interior points with nearest facet
    -
    QJ
    -
    joggled input to avoid precision problems
    -
    Qt
    -
    triangulated output
    -
     
    -
     
    -
    Precision handling
    -
    Qz
    -
    add a point-at-infinity for Delaunay triangulations
    -
    Qx
    -
    exact pre-merges (allows coplanar facets)
    -
    Qs
    -
    search all points for the initial simplex
    -
    Qbb
    -
    scale last coordinate to [0,m] for Delaunay
    -
    Qv
    -
    test vertex neighbors for convexity
    -
     
    -
     
    -
    Transform input
    -
    Qbk:0Bk:0
    -
    drop dimension k from input
    -
    QRn
    -
    random rotation (n=seed, n=0 time, n=-1 time/no rotate)
    -
    Qbk:n
    -
    scale coord[k] to low bound of n (default -0.5)
    -
    QBk:n
    -
    scale coord[k] to upper bound of n (default 0.5)
    -
    QbB
    -
    scale input to fit the unit cube
    -
     
    -
     
    -
    Select facets
    -
    QVn
    -
    good facet if it includes point n, -n if not
    -
    QGn
    -
    good facet if visible from point n, -n for not visible
    -
    Qg
    -
    only build good facets (needs 'QGn', 'QVn ', or 'Pdk')
    -
     
    -
     
    -
    Experimental
    -
    Q4
    -
    avoid merging old facets into new facets
    -
    Q5
    -
    do not correct outer planes at end of qhull
    -
    Q3
    -
    do not merge redundant vertices
    -
    Q6
    -
    do not pre-merge concave or coplanar facets
    -
    Q0
    -
    do not pre-merge facets with 'C-0' or 'Qx'
    -
    Q8
    -
    ignore near-interior points
    -
    Q2
    -
    merge all non-convex at once instead of independent sets
    -
    Qf
    -
    partition point to furthest outside facet
    -
    Q7
    -
    process facets depth-first instead of breadth-first
    -
    Q9
    -
    process furthest of furthest points
    -
    Q10
    -
    no special processing for narrow distributions
    -
    Q11
    -
    copy normals and recompute centrums for tricoplanar facets
    -
    Q12
    -
    do not error on wide merge due to duplicate ridge and nearly coincident points
    -
    Qm
    -
    process points only if they would increase the max. outer - plane
    -
    Qr
    -
    process random outside points instead of furthest one
    -
    Q1
    -
    sort merges by type instead of angle
    -
    - -
    - -

    »Qbb - scale the last -coordinate to [0,m] for Delaunay

    - -

    After scaling with option 'Qbb', the lower bound of the last -coordinate will be 0 and the upper bound will be the maximum -width of the other coordinates. Scaling happens after projecting -the points to a paraboloid and scaling other coordinates.

    - -

    Option 'Qbb' is automatically set for qdelaunay -and qvoronoi. Option 'Qbb' is automatically set for joggled input 'QJ'.

    - -

    Option 'Qbb' should be used for Delaunay triangulations with -integer coordinates. Since the last coordinate is the sum of -squares, it may be much larger than the other coordinates. For -example, rbox 10000 D2 B1e8 | qhull d has precision -problems while rbox 10000 D2 B1e8 | qhull d Qbb is OK.

    - -

    »QbB - scale the input to -fit the unit cube

    - -

    After scaling with option 'QbB', the lower bound will be -0.5 -and the upper bound +0.5 in all dimensions. For different bounds -change qh_DEFAULTbox in user.h (0.5 is best for Geomview).

    - -

    For Delaunay and Voronoi diagrams, scaling happens after -projection to the paraboloid. Under precise arithmetic, scaling -does not change the topology of the convex hull. Scaling may -reduce precision errors if coordinate values vary widely.

    - -

    »Qbk:n - scale coord[k] -to low bound

    - -

    After scaling, the lower bound for dimension k of the input -points will be n. 'Qbk' scales coord[k] to -0.5.

    - -

    »QBk:n - scale coord[k] -to upper bound

    - -

    After scaling, the upper bound for dimension k of the input -points will be n. 'QBk' scales coord[k] to 0.5.

    - -

    »Qbk:0Bk:0 - drop -dimension k from the input points

    - -

    Drop dimension k from the input points. For example, -'Qb1:0B1:0' deletes the y-coordinate from all input points. This -allows the user to take convex hulls of sub-dimensional objects. -It happens before the Delaunay and Voronoi transformation. -It happens after the halfspace transformation for both the data -and the feasible point.

    - -

    »Qc - keep coplanar points -with nearest facet

    - -

    During construction of the hull, a point is coplanar if it is -between 'Wn' above and 'Un' below a facet's hyperplane. A -different definition is used for output from Qhull.

    - -

    For output, a coplanar point is above the minimum vertex -(i.e., above the inner plane). With joggle ('QJ'), a coplanar point includes points -within one joggle of the inner plane.

    - -

    With option 'Qc', output formats 'p ', -'f', 'Gp', -'Fc', 'FN', -and 'FP' will print the coplanar -points. With options 'Qc Qi' these outputs -include the interior points.

    - -

    For Delaunay triangulations (qdelaunay -or qvoronoi), a coplanar point is a point -that is nearly incident to a vertex. All input points are either -vertices of the triangulation or coplanar.

    - -

    Qhull stores coplanar points with a facet. While constructing -the hull, it retains all points within qh_RATIOnearInside -(user.h) of a facet. In qh_check_maxout(), it uses these points -to determine the outer plane for each facet. With option 'Qc', -qh_check_maxout() retains points above the minimum vertex for the -hull. Other points are removed. If qh_RATIOnearInside is wrong or -if options 'Q5 Q8' are set, a -coplanar point may be missed in the output (see Qhull limitations).

    - -

    »Qf - partition point to -furthest outside facet

    - -

    After adding a new point to the convex hull, Qhull partitions -the outside points and coplanar points of the old, visible -facets. Without the 'f ' option and -merging, it assigns a point to the first facet that it is outside -('Wn'). When merging, it assigns a -point to the first facet that is more than several times outside -(see qh_DISToutside in user.h).

    - -

    If option 'Qf' is selected, Qhull performs a directed search -(no merging) or an exhaustive search (merging) of new facets. -Option 'Qf' may reduce precision errors if pre-merging does not -occur.

    - -

    Option 'Q9' processes the furthest of all -furthest points.

    - -

    »Qg - only build good -facets (needs 'QGn' 'QVn' or 'Pdk')

    - -

    Qhull has several options for defining and printing good -facets. With the 'Qg' option, Qhull will only -build those facets that it needs to determine the good facets in -the output. This may speed up Qhull in 2-d and 3-d. It is -useful for furthest-site Delaunay -triangulations (qdelaunay Qu, -invoke with 'qhull d Qbb Qu Qg'). -It is not effective in higher -dimensions because many facets see a given point and contain a -given vertex. It is not guaranteed to work for all combinations.

    - -

    See 'QGn', 'QVn', and 'Pdk' for defining good facets, and 'Pg' and 'PG' -for printing good facets and their neighbors. If pre-merging ('C-n') is not used and there are -coplanar facets, then 'Qg Pg' may produce a different result than -'Pg'.

    - -

    »QGn - good facet if -visible from point n, -n for not visible

    - -

    With option 'QGn', a facet is good (see 'Qg' -and 'Pg') if it is visible from -point n. If n < 0, a facet is good if it is not visible -from point n. Point n is not added to the hull (unless 'TCn' or 'TPn').

    - -

    With rbox, use the 'Pn,m,r' option -to define your point; it will be point 0 ('QG0').

    - -

    »Qi - keep interior points -with nearest facet

    - -

    Normally Qhull ignores points that are clearly interior to the -convex hull. With option 'Qi', Qhull treats interior points the -same as coplanar points. Option 'Qi' does not retain coplanar -points. You will probably want 'Qc ' as well.

    - -

    Option 'Qi' is automatically set for 'qdelaunay -Qc' and 'qvoronoi -Qc'. If you use -'qdelaunay Qi' or 'qvoronoi -Qi', option 's' reports all nearly -incident points while option 'Fs' -reports the number of interior points (should always be zero).

    - -

    With option 'Qi', output formats 'p', -'f','Gp', -'Fc', 'FN', -and 'FP' include interior points.

    - -

    »QJ or QJn - joggled -input to avoid precision errors

    - -

    Option 'QJ' or 'QJn' joggles each input coordinate by adding a -random number in the range [-n,n]. If a precision error occurs, -It tries again. If precision errors still occur, Qhull increases n -ten-fold and tries again. The maximum value for increasing n -is 0.01 times the maximum width of the input. Option 'QJ' selects -a default value for n. User.h -defines these parameters and a maximum number of retries. See Merged facets or joggled input.

    - -

    Users of joggled input should consider converting to -triangulated output ('Qt'). Triangulated output is -approximately 1000 times more accurate than joggled input. - -

    Option 'QJ' also sets 'Qbb' for -Delaunay triangulations and Voronoi diagrams. It does not set -'Qbb' if 'Qbk:n' or 'QBk:n' are set.

    - -

    If 'QJn' is set, Qhull does not merge facets unless requested -to. All facets are simplicial (triangular in 2-d). This may be -important for your application. You may also use triangulated output -('Qt') or Option 'Ft'. - -

    Qhull adjusts the outer and inner planes for 'QJn' ('Fs'). They are increased by sqrt(d)*n -to account for the maximum distance between a joggled point and -the corresponding input point. Coplanar points ('Qc') require an additional sqrt(d)*n -since vertices and coplanar points may be joggled in opposite -directions.

    - -

    For Delaunay triangulations (qdelaunay), joggle -happens before lifting the input sites to a paraboloid. Instead of -'QJ', you may use triangulated output ('Qt')

    - -

    This option is deprecated for Voronoi diagrams (qvoronoi). -It triangulates cospherical points, leading to duplicated Voronoi vertices.

    - -

    By default, 'QJn' uses a fixed random number seed. To use time -as the random number seed, select 'QR-1'. -The summary ('s') will show the -selected seed as 'QR-n'. - -

    With 'QJn', Qhull does not error on degenerate hyperplane -computations. Except for Delaunay and Voronoi computations, Qhull -does not error on coplanar points.

    - -

    Use option 'FO' to display the -selected options. Option 'FO' displays the joggle and the joggle -seed. If Qhull restarts, it will redisplay the options.

    - -

    Use option 'TRn' to estimate the -probability that Qhull will fail for a given 'QJn'. - -

    »Qm - only process points -that increase the maximum outer plane

    - -

    Qhull reports the maximum outer plane in its summary ('s'). With option 'Qm', Qhull does not -process points that are below the current, maximum outer plane. -This is equivalent to always adjusting 'Wn -' to the maximum distance of a coplanar point to a facet. It -is ignored for points above the upper convex hull of a Delaunay -triangulation. Option 'Qm' is no longer important for merging.

    - -

    »Qr - process random -outside points instead of furthest ones

    - -

    Normally, Qhull processes the furthest point of a facet's -outside points. Option 'Qr' instead selects a random outside -point for processing. This makes Qhull equivalent to the -randomized incremental algorithms.

    - -

    The original randomization algorithm by Clarkson and Shor ['89] used a conflict list which -is equivalent to Qhull's outside set. Later randomized algorithms -retained the previously constructed facets.

    - -

    To compare Qhull to the randomized algorithms with option -'Qr', compare "hyperplanes constructed" and -"distance tests". Qhull does not report CPU time -because the randomization is inefficient.

    - -

    »QRn - random rotation

    - -

    Option 'QRn' randomly rotates the input. For Delaunay -triangulations (qdelaunay or qvoronoi), -it rotates the lifted points about -the last axis.

    - -

    If n=0, use time as the random number seed. If n>0, -use n as the random number seed. If n=-1, don't rotate -but use time as the random number seed. If n<-1, -don't rotate but use n as the random number seed.

    - -

    »Qs - search all points -for the initial simplex

    - -

    Qhull constructs an initial simplex from d+1 points. It -selects points with the maximum and minimum coordinates and -non-zero determinants. If this fails, it searches all other -points. In 8-d and higher, Qhull selects points with the minimum -x or maximum coordinate (see qh_initialvertices in poly2.c ). -It rejects points with nearly zero determinants. This should work -for almost all input sets.

    - -

    If Qhull can not construct an initial simplex, it reports a -descriptive message. Usually, the point set is degenerate and one -or more dimensions should be removed ('Qbk:0Bk:0'). -If not, use option 'Qs'. It performs an exhaustive search for the -best initial simplex. This is expensive is high dimensions.

    - -

    »Qt - triangulated output

    - -

    By default, qhull merges facets to handle precision errors. This -produces non-simplicial facets (e.g., the convex hull of a cube has 6 square -facets). Each facet is non-simplicial because it has four vertices. - -

    Use option 'Qt' to triangulate all non-simplicial facets before generating -results. Alternatively, use joggled input ('QJ') to -prevent non-simplical facets. Unless 'Pp' is set, -qhull produces a warning if 'QJ' and 'Qt' are used together. - -

    For Delaunay triangulations (qdelaunay), triangulation -occurs after lifting the input sites to a paraboloid and computing the convex hull. -

    - -

    Option 'Qt' is deprecated for Voronoi diagrams (qvoronoi). -It triangulates cospherical points, leading to duplicated Voronoi vertices.

    - -

    Option 'Qt' may produce degenerate facets with zero area.

    - -

    Facet area and hull volumes may differ with and without -'Qt'. The triangulations are different and different triangles -may be ignored due to precision errors. - -

    With sufficient merging, the ridges of a non-simplicial facet may share more than two neighboring facets. If so, their triangulation ('Qt') will fail since two facets have the same vertex set.

    - -

    »Qu - compute upper hull -for furthest-site Delaunay triangulation

    - -

    When computing a Delaunay triangulation (qdelaunay -or qvoronoi), -Qhull computes both the the convex hull of points on a -paraboloid. It normally prints facets of the lower hull. These -correspond to the Delaunay triangulation. With option 'Qu', Qhull -prints facets of the upper hull. These correspond to the furthest-site Delaunay triangulation -and the furthest-site Voronoi diagram.

    - -

    Option 'qhull d Qbb Qu Qg' may improve the speed of option -'Qu'. If you use the Qhull library, a faster method is 1) use -Qhull to compute the convex hull of the input sites; 2) take the -extreme points (vertices) of the convex hull; 3) add one interior -point (e.g., -'FV', the average of d extreme points); 4) run -'qhull d Qbb Qu' or 'qhull v Qbb Qu' on these points.

    - -

    »Qv - test vertex -neighbors for convexity

    - -

    Normally, Qhull tests all facet neighbors for convexity. -Non-neighboring facets which share a vertex may not satisfy the -convexity constraint. This occurs when a facet undercuts the -centrum of another facet. They should still be convex. Option -'Qv' extends Qhull's convexity testing to all neighboring facets -of each vertex. The extra testing occurs after the hull is -constructed..

    - -

    »QVn - good facet if it -includes point n, -n if not

    - -

    With option 'QVn', a facet is good ('Qg', -'Pg') if one of its vertices is -point n. If n<0, a good facet does not include point n. - -

    If options 'PG' -and 'Qg' are not set, option 'Pg' -(print only good) -is automatically set. -

    - -

    Option 'QVn' behaves oddly with options 'Fx' -and 'qvoronoi Fv'. - -

    If used with option 'Qg' (only process good facets), point n is -either in the initial simplex or it is the first -point added to the hull. Options 'QVn Qg' require either 'QJ' or -'Q0' (no merging).

    - -

    »Qx - exact pre-merges -(allows coplanar facets)

    - -

    Option 'Qx' performs exact merges while building the hull. -Option 'Qx' is set by default in 5-d and higher. Use option 'Q0' to not use 'Qx' by default. Unless otherwise -specified, option 'Qx' sets option 'C-0'. -

    - -

    The "exact" merges are merging a point into a -coplanar facet (defined by 'Vn ', 'Un', and 'C-n'), -merging concave facets, merging duplicate ridges, and merging -flipped facets. Coplanar merges and angle coplanar merges ('A-n') are not performed. Concavity -testing is delayed until a merge occurs.

    - -

    After the hull is built, all coplanar merges are performed -(defined by 'C-n' and 'A-n'), then post-merges are performed -(defined by 'Cn' and 'An'). If facet progress is logged ('TFn'), Qhull reports each phase and -prints intermediate summaries and statistics ('Ts').

    - -

    Without 'Qx' in 5-d and higher, options 'C-n' and 'A-n' -may merge too many facets. Since redundant vertices are not -removed effectively, facets become increasingly wide.

    - -

    Option 'Qx' may report a wide facet. With 'Qx', coplanar -facets are not merged. This can produce a "dent" in an -intermediate hull. If a point is partitioned into a dent and it -is below the surrounding facets but above other facets, one or -more wide facets will occur. In practice, this is unlikely. To -observe this effect, run Qhull with option 'Q6' -which doesn't pre-merge concave facets. A concave facet makes a -large dent in the intermediate hull.

    - -

    Option 'Qx' may set an outer plane below one of the input -points. A coplanar point may be assigned to the wrong facet -because of a "dent" in an intermediate hull. After -constructing the hull, Qhull double checks all outer planes with -qh_check_maxout in poly2.c . If a coplanar point is -assigned to the wrong facet, qh_check_maxout may reach a local -maximum instead of locating all coplanar facets. This appears to -be unlikely.

    - -

    »Qz - add a -point-at-infinity for Delaunay triangulations

    - -

    Option 'Qz' adds a point above the paraboloid of lifted sites -for a Delaunay triangulation. It allows the Delaunay -triangulation of cospherical sites. It reduces precision errors -for nearly cospherical sites.

    - -

    »Q0 - no merging with C-0 -and Qx

    - -

    Turn off default merge options 'C-0' -and 'Qx'.

    - -

    With 'Q0' and without other pre-merge options, Qhull ignores -precision issues while constructing the convex hull. This may -lead to precision errors. If so, a descriptive warning is -generated. See Precision issues.

    - -

    »Q1 - sort merges by type -instead of angle

    - -

    Qhull sorts the coplanar facets before picking a subset of the -facets to merge. It merges concave and flipped facets first. Then -it merges facets that meet at a steep angle. With 'Q1', Qhull -sorts merges by type (coplanar, angle coplanar, concave) instead -of by angle. This may make the facets wider.

    - -

    »Q2 - merge all non-convex -at once instead of independent sets

    - -

    With 'Q2', Qhull merges all facets at once instead of -performing merges in independent sets. This may make the facets -wider.

    - -

    »Q3 - do not merge -redundant vertices

    - -

    With 'Q3', Qhull does not remove redundant vertices. In 6-d -and higher, Qhull never removes redundant vertices (since -vertices are highly interconnected). Option 'Q3' may be faster, -but it may result in wider facets. Its effect is easiest to see -in 3-d and 4-d.

    - -

    »Q4 - avoid merging old -facets into new facets

    - -

    With 'Q4', Qhull avoids merges of an old facet into a new -facet. This sometimes improves facet width and sometimes makes it -worse.

    - -

    »Q5 - do not correct outer -planes at end of qhull

    - -

    When merging facets or approximating a hull, Qhull tests -coplanar points and outer planes after constructing the hull. It -does this by performing a directed search (qh_findbest in geom.c). -It includes points that are just inside the hull.

    - -

    With options 'Q5' or 'Po', Qhull -does not test outer planes. The maximum outer plane is used -instead. Coplanar points ('Qc') are defined by -'Un'. An input point may be outside -of the maximum outer plane (this appears to be unlikely). An -interior point may be above 'Un' -from a hyperplane.

    - -

    Option 'Q5' may be used if outer planes are not needed. Outer -planes are needed for options 's', 'G', 'Go ', -'Fs', 'Fo', -'FF', and 'f'.

    - -

    »Q6 - do not pre-merge -concave or coplanar facets

    - -

    With 'Q6', Qhull does not pre-merge concave or coplanar -facets. This demonstrates the effect of "dents" when -using 'Qx'.

    - -

    »Q7 - depth-first -processing instead of breadth-first

    - -

    With 'Q7', Qhull processes facets in depth-first order instead -of breadth-first order. This may increase the locality of -reference in low dimensions. If so, Qhull may be able to use -virtual memory effectively.

    - -

    In 5-d and higher, many facets are visible from each -unprocessed point. So each iteration may access a large -proportion of allocated memory. This makes virtual memory -ineffectual. Once real memory is used up, Qhull will spend most -of its time waiting for I/O.

    - -

    Under 'Q7', Qhull runs slower and the facets may be wider.

    - -

    »Q8 - ignore near-interior -points

    - -

    With 'Q8' and merging, Qhull does not process interior points -that are near to a facet (as defined by qh_RATIOnearInside in -user.h). This avoids partitioning steps. It may miss a coplanar -point when adjusting outer hulls in qh_check_maxout(). The best -value for qh_RATIOnearInside is not known. Options 'Q8 Qc' may be sufficient.

    - -

    »Q9 - process furthest of -furthest points

    - -

    With 'Q9', Qhull processes the furthest point of all outside -sets. This may reduce precision problems. The furthest point of -all outside sets is not necessarily the furthest point from the -convex hull.

    - -

    »Q10 - no special processing -for narrow distributions

    - -

    With 'Q10', Qhull does not special-case narrow distributions. -See Limitations of merged facets for -more information. - -

    »Q11 - copy normals and recompute -centrums for -tricoplanar facets

    - -Option 'Qt' triangulates non-simplicial facets -into "tricoplanar" facets. -Normally tricoplanar facets share the same normal, centrum, and -Voronoi vertex. They can not be merged or replaced. With -option 'Q11', Qhull duplicates the normal and Voronoi vertex. -It recomputes the centrum. - -

    Use 'Q11' if you use the Qhull library to add points -incrementally and call qh_triangulate() after each point. -Otherwise, Qhull will report an error when it tries to -merge and replace a tricoplanar facet. - -

    With sufficient merging and new points, option 'Q11' may -lead to precision problems such -as duplicate ridges and concave facets. For example, if qh_triangulate() -is added to qh_addpoint(), RBOX 1000 s W1e-12 t1001813667 P0 | QHULL d Q11 Tv, -reports an error due to a duplicate ridge. - -

    »Q12 - do not error -on wide merge due to duplicate ridge and nearly coincident points

    - -

    In 3-d and higher Delaunay Triangulations or 4-d and higher convex hulls, multiple, -nearly coincident points may lead to very wide facets. An error is reported if a -merge across a duplicate ridge would increase the facet width by 100x or more. - -

    Use option 'Q12' to log a warning instead of throwing an error. - -

    For Delaunay triangulations, a bounding box may alleviate this error (e.g., rbox 500 C1,1E-13 t c G1 | qhull d). -This avoids the ill-defined edge between upper and lower convex hulls. -The problem will be fixed in a future release of Qhull. - -

    To demonstrate the problem, use rbox option 'Cn,r,m' to generate nearly coincident points. -For more information, see "Nearly coincident points on an edge" -in Nearly coincident points on an edge. - - -

    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-optt.htm b/src/qhull/html/qh-optt.htm deleted file mode 100644 index 0709f58c6..000000000 --- a/src/qhull/html/qh-optt.htm +++ /dev/null @@ -1,278 +0,0 @@ - - - - -Qhull trace options (T) - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    [delaunay] Qhull trace options (T)

    - -This section lists the trace options for Qhull. These options are -indicated by 'T' followed by a letter. - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    Trace options

    - -
    -
     
    -
    General
    -
    Tz
    -
    output error information to stdout instead of stderr
    -
    TI file
    -
    input data from a file
    -
    TO file
    -
    output results to a file
    -
    Ts
    -
    print statistics
    -
    TFn
    -
    report progress whenever n or more facets created
    -
    TRn
    -
    rerun qhull n times
    -
    Tv
    -
    verify result: structure, convexity, and point inclusion
    - -
     
    -
     
    -
    Debugging
    -
    Tc
    -
    check frequently during execution
    -
    TVn
    -
    stop qhull after adding point n
    -
    TCn
    -
    stop qhull after building cone for point n
    -
    TV-n
    -
    stop qhull before adding point n
    -
    T4
    -
    trace at level n, 4=all, 5=mem/gauss, -1= events
    -
    TWn
    -
    trace merge facets when width > n
    -
    TMn
    -
    turn on tracing at merge n
    -
    TPn
    -
    turn on tracing when point n added to hull
    -
    - -
    - -

    »Tc - check frequently -during execution

    - -

    Qhull includes frequent checks of its data structures. Option -'Tc' will catch most inconsistency errors. It is slow and should -not be used for production runs. Option 'Tv' -performs the same checks after the hull is constructed.

    - -

    »TCn - stop qhull after -building cone for point n

    - -

    Qhull builds a cone from the point to its horizon facets. -Option 'TCn' stops Qhull just after building the cone. The output -for 'f' includes the cone and the old -hull.'.

    - -

    »TFn - report summary -whenever n or more facets created

    - -

    Option 'TFn' reports progress whenever more than n facets are -created. The test occurs just before adding a new point to the -hull. During post-merging, 'TFn' reports progress after more than -n/2 merges.

    - -

    »TI file - input data from file

    - -

    Input data from 'file' instead of stdin. The filename may not -contain spaces or use single quotes. -You may use I/O redirection -instead (e.g., 'rbox 10 | qdelaunay >results').

    - -

    »TMn - turn on tracing at -merge n

    - -

    Turn on tracing at n'th merge.

    - -

    »Tn - trace at level n

    - -

    Qhull includes full execution tracing. 'T-1' traces events. -'T1' traces the overall execution of the program. 'T2' and 'T3' -trace overall execution and geometric and topological events. -'T4' traces the algorithm. 'T5' includes information about memory -allocation and Gaussian elimination. 'T1' is useful for logging -progress of Qhull in high dimensions.

    - -

    Option 'Tn' can produce large amounts of output. Use options 'TPn', 'TWn', and 'TMn' to selectively -turn on tracing. Since all errors report the last processed -point, option 'TPn' is particularly useful.

    - -

    Different executions of the same program may produce different -traces and different results. The reason is that Qhull uses hashing -to match ridges of non-simplicial facets. For performance reasons, -the hash computation uses -memory addresses which may change across executions. - -

    »TO file - output results to file

    - -

    Redirect stdout to 'file'. The filename may be enclosed in -single quotes. Unix and Windows NT users may use I/O redirection -instead (e.g., 'rbox 10 | qdelaunay >results').

    -

    -Windows95 users should always use 'TO file'. If they use I/O redirection, -error output is not sent to the console. Qhull uses single quotes instead -of double quotes because a missing double quote can -freeze Windows95 (e.g., do not run, rbox 10 | qhull TO "x)

    -

    - -

    »TPn - turn on tracing -when point n added to hull

    - -

    Option 'TPn' turns on tracing when point n is added to -the hull. It also traces partitions of point n. This option -reduces the output size when tracing. It is the normal -method to determine the cause of a Qhull error. All Qhull errors -report the last point added. - -

    Use options 'TPn TVn' to -trace the addition of point n to the convex hull and stop when done.

    - -

    If used with option 'TWn', -'TPn' turns off tracing after adding point n to the hull. -Use options 'TPn TWn' to -trace the addition of point n to the convex hull, partitions -of point n, and wide merges.

    - -

    »TRn - rerun qhull n times

    - -

    Option 'TRn' reruns Qhull n times. It is usually used -with 'QJn' to determine the probability -that a given joggle will fail. The summary -('s') lists the failure -rate and the precision errors that occurred. -Option 'Ts' will report statistics for -all of the runs. Trace and output options only apply to the last -run. An event trace, 'T-1' reports events for all runs. - -

    Tracing applies to the last run of Qhull. If an error -is reported, the options list the run number as "_run". -To trace this run, set 'TRn' to the same value.

    - -

    »Ts - print statistics

    - -

    Option 'Ts' collects statistics and prints them to stderr. For -Delaunay triangulations, the angle statistics are restricted to -the lower or upper envelope.

    - -

    »Tv - verify result: -structure, convexity, and point inclusion

    - -

    Option 'Tv' checks the topological structure, convexity, and -point inclusion. If precision problems occurred, facet convexity -is tested whether or not 'Tv' is selected. Option 'Tv' does not -check point inclusion if forcing output with 'Po', or if 'Q5' -is set.

    - -

    The convex hull of a set of points is the smallest polytope -that includes the points. Option 'Tv' tests point inclusion. -Qhull verifies that all points are below all outer planes -(facet->maxoutside). Point inclusion is exhaustive if merging -or if the facet-point product is small enough; otherwise Qhull -verifies each point with a directed search (qh_findbest). To -force an exhaustive test when using option 'C-0' (default), use 'C-1e-30' instead.

    - -

    Point inclusion testing occurs after producing output. It -prints a message to stderr unless option 'Pp' is used. This allows the user to -interrupt Qhull without changing the output.

    - -

    With 'qvoronoi Fi' -and 'qvoronoi Fo', -option 'Tv' collects statistics that verify all Voronoi vertices lie -on the separating hyperplane, and for bounded regions, all -separating hyperplanes are perpendicular bisectors. - -

    »TV-n - stop qhull before -adding point n

    - -

    Qhull adds one point at a time to the convex hull. See how Qhull adds a point. Option 'TV-n' -stops Qhull just before adding a new point. Output shows the hull -at this time.

    - -

    »TVn - stop qhull after -adding point n

    - -

    Option 'TVn' stops Qhull after it has added point n. Output -shows the hull at this time.

    - -

    »TWn - trace merge facets -when width > n

    - -

    Along with TMn, this option allows the user to determine the -cause of a wide merge.

    -

    »Tz - send all output to -stdout

    - -

    Redirect stderr to stdout.

    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qh-quick.htm b/src/qhull/html/qh-quick.htm deleted file mode 100644 index 9d52e7d75..000000000 --- a/src/qhull/html/qh-quick.htm +++ /dev/null @@ -1,495 +0,0 @@ - - - - -Qhull quick reference - - - - -

    Up: Home -page for Qhull
    -Up: Qhull manual
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: Qhull internals
    -To: Qhull functions, macros, and data structures
    -To: Qhull files
    -To: Geom • Global -• Io • Mem -• Merge • Poly -• Qhull • Set -• Stat • User -

    - -
    - -

    [cone] Qhull quick reference

    - -This section lists all programs and options in Qhull. - -

    Copyright © 1995-2015 C.B. Barber

    - -

    -  -

    -Qhull programs -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -
    -
    qconvex -- convex hull
    -
    synopsis • input • outputs • controls • graphics • notes • conventions • options
    -
     
    -
    qdelaunay -- Delaunay triangulation
    -
    synopsis • input • outputs • controls • graphics • notes • conventions • options
    -
     
    -
    qdelaunay Qu -- furthest-site Delaunay triangulation
    -
    synopsis • input • outputs • controls • graphics • notes • conventions • options
    -
     
    -
    qhalf -- halfspace intersection about a point
    -
    synopsis • input • outputs • controls • graphics • notes • conventions • options
    -
     
    -
    qvoronoi -- Voronoi diagram
    -
    synopsis • input • outputs • - controls • graphics • notes • conventions • options
    -
     
    -
    qvoronoi Qu -- furthest-site Voronoi diagram
    -
    synopsis • input • outputs • controls • graphics • notes • conventions • options
    -
     
    -
    rbox -- generate point distributions for qhull
    -
    synopsis • outputs • examples • notes • options
    -
     
    -
    qhull -- convex hull and related structures
    -
    synopsis • input • outputs • controls • options
    -
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    -Qhull options - -

    » Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions

    - -

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    'Fa' -Farea -'FA' -FArea-total -'Fc' -Fcoplanars -'FC' -FCentrums - -
    'Fd' -Fd-cdd-in -'FD' -FD-cdd-out -'FF' -FF-dump-xridge -'Fi' -Finner - -
    'Fi' -Finner_bounded -'FI' -FIDs -'Fm' -Fmerges -'FM' -FMaple - -
    'Fn' -Fneighbors -'FN' -FNeigh-vertex -'Fo' -Fouter -'Fo' -Fouter_unbounded - -
    'FO' -FOptions -'Fp' -Fpoint-intersect -'FP' -FPoint_near -'FQ' -FQhull - -
    'Fs' -Fsummary -'FS' -FSize -'Ft' -Ftriangles -'Fv' -Fvertices - -
    'Fv' -Fvoronoi -'FV' -FVertex-ave -'Fx' -Fxtremes - -Merged facets or joggled input - -
     
    'PAn' -PArea-keep -'Pdk:n' -Pdrop_low -'PDk:n' -Pdrop_high -'Pg' -Pgood - -
    'PFn' -PFacet_area_keep -'PG' -PGood_neighbors -'PMn' -PMerge-keep -'Po' -Poutput_forced - -
    'Po' -Poutput_error -'Pp' -Pprecision_not - -
     
    'd' -delaunay -'v' -voronoi -'G' -Geomview -'H' -Halfspace - -
    'f' -facet_dump -'i' -incidences -'m' -mathematica -'n' -normals - -
    'o' -OFF_format -'p' -points -'s' -summary - -
     
    'Gv' -Gvertices -'Gp' -Gpoints -'Ga' -Gall_points -'Gn' -Gno_planes - -
    'Gi' -Ginner -'Gc' -Gcentrums -'Gh' -Ghyperplanes -'Gr' -Gridges - -
    'Go' -Gouter -'GDn' -GDrop_dim -'Gt' -Gtransparent - -
     
    'T4' -T4_trace -'Tc' -Tcheck_often -'Ts' -Tstatistics -'Tv' -Tverify - -
    'Tz' -Tz_stdout -'TFn' -TFacet_log -'TI file' -TInput_file -'TPn' -TPoint_trace - -
    'TMn' -TMerge_trace -'TO file' -TOutput_file -'TRn' -TRerun -'TWn' -TWide_trace - -
    'TV-n' -TVertex_stop_before -
    'TVn' -TVertex_stop_after -'TCn' -TCone_stop_after - -
     
    'A-n' -Angle_max_pre -'An' -Angle_max_post -'C-0' -Centrum_roundoff -'C-n' -Centrum_size_pre - -
    'Cn' -Centrum_size_post -'En' -Error_round -'Rn' -Random_dist -'Vn' -Visible_min - -
    'Un' -Ucoplanar_max -'Wn' -Wide_outside - -
     
    'Qbk:n' -Qbound_low -'QBk:n' -QBound_high -'Qbk:0Bk:0' -Qbound_drop -'QbB' -QbB-scale-box - -
    'Qbb' -Qbb-scale-last -'Qc' -Qcoplanar -'Qf' -Qfurthest -'Qg' -Qgood_only - -
    'QGn' -QGood_point -'Qi' -Qinterior -'Qm' -Qmax_out -'QJn' -QJoggle - -
    'Qr' -Qrandom -'QRn' -QRotate -'Qs' -Qsearch_1st -'Qt' -Qtriangulate - -
    'Qu' -QupperDelaunay -'QVn' -QVertex_good -'Qv' -Qvneighbors -'Qx' -Qxact_merge - -
    'Qz' -Qzinfinite - -
     
    'Q0' -Q0_no_premerge -'Q1' -Q1_no_angle -'Q2' -Q2_no_independ -'Q3' -Q3_no_redundant - -
    'Q4' -Q4_no_old -'Q5' -Q5_no_check_out -'Q6' -Q6_no_concave -'Q7' -Q7_depth_first - -
    'Q8' -Q8_no_near_in -'Q9' -Q9_pick_furthest -'Q10' -Q10_no_narrow -'Q11' -Q11_trinormals -
    - - -

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    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qhalf.htm b/src/qhull/html/qhalf.htm deleted file mode 100644 index c87fe719e..000000000 --- a/src/qhull/html/qhalf.htm +++ /dev/null @@ -1,626 +0,0 @@ - - - - -qhalf -- halfspace intersection about a point - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    [halfspace]qhalf -- halfspace intersection about a point

    - -

    The intersection of a set of halfspaces is a polytope. The -polytope may be unbounded. See Preparata & Shamos ['85] for a discussion. In low -dimensions, halfspace intersection may be used for linear -programming. - -

    -
    -

    Example: rbox c | qconvex FQ FV - n | qhalf Fp

    -
    Print the intersection of the facets of a cube. rbox c - generates the vertices of a cube. qconvex FV n returns of average - of the cube's vertices (in this case, the origin) and the halfspaces - that define the cube. qhalf Fp computes the intersection of - the halfspaces about the origin. The intersection is the vertices - of the original cube.
    - -

    Example: rbox c d G0.55 | qconvex FQ FV - n | qhalf Fp

    -
    Print the intersection of the facets of a cube and a diamond. There - are 24 facets and 14 intersection points. Four facets define each diamond - vertex. Six facets define each cube vertex. -
    - -

    Example: rbox c d G0.55 | qconvex FQ FV - n | qhalf Fp - Qt

    -
    Same as above except triangulate before computing - the intersection points. Three facets define each intersection - point. There are two duplicates of the diamond and four duplicates of the cube. -
    - -

    Example: rbox 10 s t10 | qconvex FQ FV - n | qhalf Fp Fn

    -
    Print the intersection of the facets of the convex hull of 10 cospherical points. - Include the intersection points and the neighboring intersections. - As in the previous examples, the intersection points are nearly the same as the - original input points. -
    -
    -
    - -

    In Qhull, a halfspace is defined by the points on or below a hyperplane. -The distance of each point to the hyperplane is less than or equal to zero. - -

    Qhull computes a halfspace intersection by the geometric -duality between points and halfspaces. -See halfspace examples, -qhalf notes, and -option 'p' of qhalf outputs.

    - -

    Qhalf's outputs are the intersection -points (Fp) and -the neighboring intersection points (Fn). -For random inputs, halfspace -intersections are usually defined by more than d halfspaces. See the sphere example. - -

    You can try triangulated output ('Qt') and joggled input ('QJ'). -It demonstrates that triangulated output is more accurate than joggled input. - -

    If you use 'Qt' (triangulated output), all -halfspace intersections are simplicial (e.g., three halfspaces per -intersection in 3-d). In 3-d, if more than three halfspaces intersect -at the same point, triangulated output will produce -duplicate intersections, one for each additional halfspace. See the third example, or -add 'Qt' to the sphere example.

    - -

    If you use 'QJ' (joggled input), all halfspace -intersections are simplicial. This may lead to nearly identical -intersections. For example, either replace 'Qt' with 'QJ' above, or add -'QJ' to the sphere example. -See Merged facets or joggled input.

    - -

    The 'qhalf' program is equivalent to -'qhull H' in 2-d to 4-d, and -'qhull H Qx' -in 5-d and higher. It disables the following Qhull -options: d n v Qbb QbB Qf Qg Qm -Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc. - - -

    Copyright © 1995-2015 C.B. Barber

    -
    - -

    »qhalf synopsis

    -
    -qhalf- halfspace intersection about a point.
-    input (stdin): [dim, 1, interior point]
-                   dim+1, n
-                   halfspace coefficients + offset
-    comments start with a non-numeric character
-
-options (qhalf.htm):
-    Hn,n - specify coordinates of interior point
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Tv   - verify result: structure, convexity, and redundancy
-    .    - concise list of all options
-    -    - one-line description of all options
-
-output options (subset):
-    s    - summary of results (default)
-    Fp   - intersection coordinates
-    Fv   - non-redundant halfspaces incident to each intersection
-    Fx   - non-redundant halfspaces
-    o    - OFF file format (dual convex hull)
-    G    - Geomview output (dual convex hull)
-    m    - Mathematica output (dual convex hull)
-    QVn  - print intersections for halfspace n, -n if not
-    TO file - output results to file, may be enclosed in single quotes
-
-examples:
-    rbox d | qconvex n | qhalf s H0,0,0 Fp
-    rbox c | qconvex FV n | qhalf s i
-    rbox c | qconvex FV n | qhalf s o
-
    - -

    »qhalf input

    - -
    -

    The input data on stdin consists of:

    -
      -
    • [optional] interior point -
        -
      • dimension -
      • 1 -
      • coordinates of interior point -
      -
    • dimension + 1 -
    • number of halfspaces
      • -
    • halfspace coefficients followed by offset
      • -
    - -

    Use I/O redirection (e.g., qhalf < data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf), -or the 'TI' option (e.g., qhalf TI data.txt). - -

    Qhull needs an interior point to compute the halfspace -intersection. An interior point is clearly inside all of the halfspaces. -A point is inside a halfspace if its distance to the corresponding hyperplane is negative. - -

    The interior point may be listed at the beginning of the input (as shown above). -If not, option -'Hn,n' defines the interior point as -[n,n,0,...] where 0 is the default coordinate (e.g., -'H0' is the origin). Use linear programming if you do not know -the interior point (see halfspace notes),

    - -

    The input to qhalf is a set of halfspaces that are defined by their hyperplanes. -Each halfspace is defined by -d coefficients followed by a signed offset. This defines -a linear inequality. The coefficients define a vector that is -normal to the halfspace. -The vector may have any length. If it -has length one, the offset is the distance from the origin to the -halfspace's boundary. Points in the halfspace have a negative distance to the hyperplane. -The distance from the interior point to each -halfspace is likewise negative.

    - -

    The halfspace format is the same as Qhull's output options 'n', 'Fo', -and 'Fi'. Use option 'Fd' to use cdd format for the -halfspaces.

    - -

    For example, here is the input for computing the intersection -of halfplanes that form a cube.

    - -
    -

    rbox c | qconvex FQ FV n TO data

    - 
    -RBOX c | QCONVEX FQ FV n
-3 1
-     0      0      0
-4
-6
-     0      0     -1   -0.5
-     0     -1      0   -0.5
-     1      0      0   -0.5
-    -1      0      0   -0.5
-     0      1      0   -0.5
-     0      0      1   -0.5
-
    -

    qhalf s Fp < data

    - 
    -
-Halfspace intersection by the convex hull of 6 points in 3-d:
-
-  Number of halfspaces: 6
-  Number of non-redundant halfspaces: 6
-  Number of intersection points: 8
-
-Statistics for: RBOX c | QCONVEX FQ FV n | QHALF s Fp
-
-  Number of points processed: 6
-  Number of hyperplanes created: 11
-  Number of distance tests for qhull: 11
-  Number of merged facets: 1
-  Number of distance tests for merging: 45
-  CPU seconds to compute hull (after input):  0
-
-3
-3
-8
-  -0.5    0.5    0.5
-   0.5    0.5    0.5
-  -0.5    0.5   -0.5
-   0.5    0.5   -0.5
-   0.5   -0.5    0.5
-  -0.5   -0.5    0.5
-  -0.5   -0.5   -0.5
-   0.5   -0.5   -0.5
-
    -
    - -
    -

    »qhalf outputs

    -
    - -

    The following options control the output for halfspace -intersection.

    -
    -
    -
     
    -
    Intersections
    -
    FN
    -
    list intersection points for each non-redundant - halfspace. The first line - is the number of non-redundant halfspaces. Each remaining - lines starts with the number of intersection points. For the cube - example, each halfspace has four intersection points.
    -
    Fn
    -
    list neighboring intersections for each intersection point. The first line - is the number of intersection points. Each remaining line - starts with the number of neighboring intersections. For the cube - example, each intersection point has three neighboring intersections. -

    - In 3-d, a non-simplicial intersection has more than three neighboring - intersections. For random data (e.g., the sphere example), non-simplicial intersections are the norm. - Option 'Qt' produces three - neighboring intersections per intersection by duplicating the intersection - points. Option QJ' produces three - neighboring intersections per intersection by joggling the hyperplanes and - hence their intersections. -

    -
    Fp
    -
    print intersection coordinates. The first line is the dimension and the - second line is the number of intersection points. The following lines are the - coordinates of each intersection.
    -
    FI
    -
    list intersection IDs. The first line is the number of - intersections. The IDs follow, one per line.
    -
     
    -
     
    -
    Halfspaces
    -
    Fx
    -
    list non-redundant halfspaces. The first line is the number of - non-redundant halfspaces. The other lines list one halfspace per line. - A halfspace is non-redundant if it - defines a facet of the intersection. Redundant halfspaces are ignored. For - the cube example, all of the halfspaces are non-redundant. -
    -
    Fv
    -
    list non-redundant halfspaces incident to each intersection point. - The first line is the number of - non-redundant halfspaces. Each remaining line starts with the number - of non-redundant halfspaces. For the - cube example, each intersection is incident to three halfspaces.
    -
    i
    -
    list non-redundant halfspaces incident to each intersection point. The first - line is the number of intersection points. Each remaining line - lists the incident, non-redundant halfspaces. For the - cube example, each intersection is incident to three halfspaces. -
    -
    Fc
    -
    list coplanar halfspaces for each intersection point. The first line is - the number of intersection points. Each remaining line starts with - the number of coplanar halfspaces. A coplanar halfspace is listed for - one intersection point even though it is coplanar to multiple intersection - points.
    -
    Qi Fc
    -
    list redundant halfspaces for each intersection point. The first line is - the number of intersection points. Each remaining line starts with - the number of redundant halfspaces. Use options 'Qc Qi Fc' to list - coplanar and redundant halfspaces.
    - -
     
    -
     
    -
    General
    -
    s
    -
    print summary for the halfspace intersection. Use 'Fs' if you need numeric data.
    -
    o
    -
    print vertices and facets of the dual convex hull. The - first line is the dimension. The second line is the number of - vertices, facets, and ridges. The vertex - coordinates are next, followed by the facets, one per line.
    -
    p
    -
    print vertex coordinates of the dual convex hull. Each vertex corresponds - to a non-redundant halfspace. Its coordinates are the negative of the hyperplane's coefficients - divided by the offset plus the inner product of the coefficients and - the interior point (-c/(b+a.p). - Options 'p Qc' includes coplanar halfspaces. - Options 'p Qi' includes redundant halfspaces.
    -
    m
    -
    Mathematica output for the dual convex hull in 2-d or 3-d.
    -
    FM
    -
    Maple output for the dual convex hull in 2-d or 3-d.
    -
    G
    -
    Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.
    -
    -
    - -
    -

    »qhalf controls

    -
    - -

    These options provide additional control:

    - -
    -
    -
    Qt
    -
    triangulated output. If a 3-d intersection is defined by more than - three hyperplanes, Qhull produces duplicate intersections -- one for - each extra hyperplane.
    -
    QJ
    -
    joggle the input instead of merging facets. In 3-d, this guarantees that - each intersection is defined by three hyperplanes.
    -
    f
    -
    facet dump. Print the data structure for each intersection (i.e., - facet)
    -
    TFn
    -
    report summary after constructing n - intersections
    -
    QVn
    -
    select intersection points for halfspace n - (marked 'good')
    -
    QGn
    -
    select intersection points that are visible to halfspace n - (marked 'good'). Use -n for the remainder.
    -
    Qbk:0Bk:0
    -
    remove the k-th coordinate from the input. This computes the - halfspace intersection in one lower dimension.
    -
    Tv
    -
    verify result
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    Qs
    -
    search all points for the initial simplex. If Qhull can - not construct an initial simplex, it reports a -descriptive message. Usually, the point set is degenerate and one -or more dimensions should be removed ('Qbk:0Bk:0'). -If not, use option 'Qs'. It performs an exhaustive search for the -best initial simplex. This is expensive is high dimensions.
    -
    -
    - - -
    -

    »qhalf graphics

    -
    - -

    To view the results with Geomview, compute the convex hull of -the intersection points ('qhull FQ H0 Fp | qhull G'). See Halfspace examples.

    - -
    -

    »qhalf notes

    -
    - -

    See halfspace intersection for precision issues related to qhalf.

    - -

    If you do not know an interior point for the halfspaces, use -linear programming to find one. Assume, n halfspaces -defined by: aj*x1+bj*x2+cj*x3+dj<=0, j=1..n. Perform -the following linear program:

    - -
    -

    max(x5) aj*x1+bj*x2+cj*x3+dj*x4+x5<=0, j=1..n

    -
    - -

    Then, if [x1,x2,x3,x4,x5] is an optimal solution with -x4>0 and x5>0 we get:

    - -
    -

    aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj<=(-x5/x4) j=1..n and (-x5/x4)<0, -

    -
    - -

    and conclude that the point [x1/x4,x2/x4,x3/x4] is in -the interior of all the halfspaces. Since x5 is -optimal, this point is "way in" the interior (good -for precision errors).

    - -

    After finding an interior point, the rest of the intersection -algorithm is from Preparata & Shamos ['85, p. 316, "A simple case -..."]. Translate the halfspaces so that the interior point -is the origin. Calculate the dual polytope. The dual polytope is -the convex hull of the vertices dual to the original faces in -regard to the unit sphere (i.e., halfspaces at distance d -from the origin are dual to vertices at distance 1/d). -Then calculate the resulting polytope, which is the dual of the -dual polytope, and translate the origin back to the interior -point [S. Spitz, S. Teller, D. Strawn].

    - - -
    -

    »qhalf -conventions

    -
    - -

    The following terminology is used for halfspace intersection -in Qhull. This is the hardest structure to understand. The -underlying structure is a convex hull with one vertex per -non-redundant halfspace. See convex hull -conventions and Qhull's data structures.

    - -
      -
    • interior point - a point in the intersection of - the halfspaces. Qhull needs an interior point to compute - the intersection. See halfspace input.
      • -
    • halfspace - d coordinates for the - normal and a signed offset. The distance to an interior - point is negative.
      • -
    • non-redundant halfspace - a halfspace that - defines an output facet
      • -
    • vertex - a dual vertex in the convex hull - corresponding to a non-redundant halfspace
      • -
    • coplanar point - the dual point corresponding to - a similar halfspace
      • -
    • interior point - the dual point corresponding to - a redundant halfspace
      • -
    • intersection point- the intersection of d - or more non-redundant halfspaces
      • -
    • facet - a dual facet in the convex hull - corresponding to an intersection point
      • -
    • non-simplicial facet - more than d - halfspaces intersect at a point
      • -
    • good facet - an intersection point that - satisfies restriction 'QVn', - etc.
      • -
    - -
    -

    »qhalf options

    - -
    -qhalf- compute the intersection of halfspaces about a point
-    http://www.qhull.org
-
-input (stdin):
-    optional interior point: dimension, 1, coordinates
-    first lines: dimension+1 and number of halfspaces
-    other lines: halfspace coefficients followed by offset
-    comments:    start with a non-numeric character
-
-options:
-    Hn,n - specify coordinates of interior point
-    Qt   - triangulated ouput
-    QJ   - joggle input instead of merging facets
-    Qc   - keep coplanar halfspaces
-    Qi   - keep other redundant halfspaces
-
-Qhull control options:
-    QJn  - randomly joggle input in range [-n,n]
-    Qbk:0Bk:0 - remove k-th coordinate from input
-    Qs   - search all halfspaces for the initial simplex
-    QGn  - print intersection if redundant to halfspace n, -n for not
-    QVn  - print intersections for halfspace n, -n if not
-
-Trace options:
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
-    Tc   - check frequently during execution
-    Ts   - print statistics
-    Tv   - verify result: structure, convexity, and redundancy
-    Tz   - send all output to stdout
-    TFn  - report summary when n or more facets created
-    TI file - input data from file, no spaces or single quotes
-    TO file - output results to file, may be enclosed in single quotes
-    TPn  - turn on tracing when halfspace n added to intersection
-    TMn  - turn on tracing at merge n
-    TWn  - trace merge facets when width > n
-    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)
-    TCn  - stop qhull after building cone for halfspace n (see TVn)
-
-Precision options:
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]
-    Un   - max distance below plane for a new, coplanar halfspace
-    Wn   - min facet width for outside halfspace (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
-    f    - facet dump
-    G    - Geomview output (dual convex hull)
-    i    - non-redundant halfspaces incident to each intersection
-    m    - Mathematica output (dual convex hull)
-    o    - OFF format (dual convex hull: dimension, points, and facets)
-    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
-    s    - summary (stderr)
-
-More formats:
-    Fc   - count plus redundant halfspaces for each intersection
-         -   Qc (default) for coplanar and Qi for other redundant
-    Fd   - use cdd format for input (homogeneous with offset first)
-    FF   - facet dump without ridges
-    FI   - ID of each intersection
-    Fm   - merge count for each intersection (511 max)
-    FM   - Maple output (dual convex hull)
-    Fn   - count plus neighboring intersections for each intersection
-    FN   - count plus intersections for each non-redundant halfspace
-    FO   - options and precision constants
-    Fp   - dim, count, and intersection coordinates
-    FP   - nearest halfspace and distance for each redundant halfspace
-    FQ   - command used for qhalf
-    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
-                      for output: #non-redundant, #intersections, #coplanar
-                                  halfspaces, #non-simplicial intersections
-                    #real (2), max outer plane, min vertex
-    Fv   - count plus non-redundant halfspaces for each intersection
-    Fx   - non-redundant halfspaces
-
-Geomview output (2-d, 3-d and 4-d; dual convex hull)
-    Ga   - all points (i.e., transformed halfspaces) as dots
-     Gp  -  coplanar points and vertices as radii
-     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres
-    Gi   - inner planes (i.e., halfspace intersections) only
-     Gn  -  no planes
-     Go  -  outer planes only
-    Gc   - centrums
-    Gh   - hyperplane intersections
-    Gr   - ridges
-    GDn  - drop dimension n in 3-d and 4-d output
-
-Print options:
-    PAn  - keep n largest facets (i.e., intersections) by area
-    Pdk:n- drop facet if normal[k] <= n (default 0.0)
-    PDk:n- drop facet if normal[k] >= n
-    Pg   - print good facets (needs 'QGn' or 'QVn')
-    PFn  - keep facets whose area is at least n
-    PG   - print neighbors of good facets
-    PMn  - keep n facets with most merges
-    Po   - force output.  If error, output neighborhood of facet
-    Pp   - do not report precision problems
-
-    .    - list of all options
-    -    - one line descriptions of all options
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - - diff --git a/src/qhull/html/qhull-cpp.xml b/src/qhull/html/qhull-cpp.xml deleted file mode 100644 index ae755e826..000000000 --- a/src/qhull/html/qhull-cpp.xml +++ /dev/null @@ -1,214 +0,0 @@ - - - - -

    Qhull C++ -- C++ interface to Qhull

    - - Copyright (c) 2009-2015, C.B. Barber - - -
    -

    This draft - document records some of the design decisions for Qhull C++. Convert it to HTML by road-faq.xsl from road-faq. - - Please send comments and suggestions to bradb@shore.net -

    -
    -
    -
    - Help -
    • -
    • -
    • -
    -
    -
    -
    • -
    • -
    -
    -
    -
    - . -
    - -     - - - - Qhull's collection APIs are modeled on Qt's collection API (QList, QVector, QHash) w/o QT_STRICT_ITERATORS. They support STL and Qt programming. - -

    Some of Qhull's collection classes derive from STL classes. If so, - please avoid additional STL functions and operators added by inheritance. - These collection classes may be rewritten to derive from Qt classes instead. - See Road's . -

    - - - Qhull's collection API (where applicable). For documentation, see Qt's QList, QMap, QListIterator, QMapIterator, QMutableListIterator, and QMutableMapIterator -
    • - STL types [list, qlinkedlist, qlist, qvector, vector] -- const_iterator, iterator -
    • - STL types describing iterators [list, qlinkedlist, qlist, qvector, vector] -- const_pointer, const_reference, difference_type, - pointer, reference, size_type, value_type. - Pointer and reference types not defined if unavailable (not needed for <algorithm>) -
    • - const_iterator, iterator types -- difference_type, iterator_category, pointer, reference, value_type -
    • - Qt types [qlinkedlist, qlist, qvector] -- ConstIterator, Iterator, QhullclassIterator, MutableQhullclassIterator. - Qt's foreach requires const_iterator. -
    • - Types for sets/maps [hash_map, QHash] -- key_compare, key_type, mapped_type -
    • - Constructor -- default constructor, copy constructor, assignment operator, destructor -
    • - Conversion -- to/from/as corresponding C, STL, and Qt constructs. Include toQList and toStdVector (may be filtered, e.g., QhullFacetSet). - Do not define fromStdList and fromQList if container is not reference counted (i.e., acts like a value) -
    • - Get/set -- configuration options for class -
    • - STL-style iterator - begin, constBegin, constEnd, end, key, value, =, *, [], ->, ++, --, +, -, ==, !=, <, - <=, >, >=, const_iterator(iterator), iterator COMPARE const_iterator. - An iterator is an abstraction of a pointer. It is not aware of its container. -
    • - Java-style iterator [qiterator.h] - countRemaining, findNext, findPrevious, hasNext, hasPrevious, next, peekNext, peekPrevious, previous, toBack, toFront, = Coordinates -
    • - Mutable Java-style iterator adds - insert, remove, setValue, value -
    • - Element access -- back, first, front, last -
    • - Element access w/ index -- [], at (const& only), constData, data, mid, value -
    • - Read-only - (int)count, empty, isEmpty, (size_t)size. Count() and size() may be filtered. If so, they may be zero when !empty(). -
    • - Read-only for sets/maps - capacity, key, keys, reserve, resize, values -
    • - Operator - ==, !=, +, +=, << -
    • - Read-write -- append, clear, erase, insert, move, prepend, pop_back, pop_front, push_back, push_front, removeAll, removeAt, removeFirst, removeLast, replace, - swap, takeAt, takeFirst, takeLast -
    • - Read-write for sets/maps -- insertMulti, squeeze, take, unite -
    • - Search -- contains(const T &), count(const T &), indexOf, lastIndexOf -
    • - Search for sets/maps -- constFind, lowerBound, upperBound -
    • - Stream I/O -- stream << -
    - - STL list and vector -- For unfiltered access to each element. -
    • - Apache: Creating your own containers -- requirements for STL containers. Iterators should define the types from 'iterator_traits'. -
    • - STL types -- allocator_type, const_iterator, const_pointer, const_reference, const_reverse_iterator, difference_type, iterator, iterator_category, pointer, reference, reverse_iterator, size_type, value_type -
    • - STL constructors -- MyType(), MyType(count), MyType(count, value), MyType(first, last), - MyType(MyType&), -
    • - STL getter/setters -- at (random_access only), back, begin, capacity, end, front, rbegin, rend, size, max_size -
    • - STL predicates -- empty -
    • - STL iterator types -- const_pointer, const_reference, difference_type, iterator_category, pointer, reference, value_type -
    • - STL iterator operators -- *, -<, ++, --, +=, -=, +, -, [], ==, !=, <, >, >=, <= -
    • - STL operators -- =, [] (random_access only), ==, !=, <, >, <=, >= -
    • - STL modifiers -- assign, clear, erase, insert, pop_back, push_back, reserve, resize, swap -
    • -
    - - Qt Qlist -- For unfiltered access to each element -
    • -
    • - Additional Qt types -- ConstIterator, Iterator, QListIterator, QMutableListIterator -
    • - Additional Qt get/set -- constBegin, constEnd, count, first, last, value (random_access only) -
    • - Additional Qt predicates -- isEmpty -
    • - Additional Qt -- mid (random_access only) -
    • - Additional Qt search -- contains, count(T&), indexOf (random_access only), lastIndeOf (random_access only) -
    • - Additional Qt modifiers -- append, insert(index,value) (random_access only), move (random_access only), pop_front, prepend, push_front, removeAll, removeAt (random_access only), removeFirst, removeLast, replace, swap by index, takeAt, takeFirst, takeLast -
    • - Additional Qt operators -- +, <<, +=, - stream << and >> -
    • - Unsupported types by Qt -- allocator_type, const_reverse_iterator, reverse_iterator -
    • - Unsupported accessors by Qt -- max_size, rbegin, rend -
    • - Unsupported constructors by Qt -- multi-value constructors -
    • - unsupported modifiers by Qt -- assign, muli-value inserts, STL's swaps -
    • -
    - - STL map and Qt QMap. These use nearly the same API as list and vector classes. They add the following. -
    • - STL types -- key_compare, key_type, mapped_type -
    • - STL search -- equal_range, find, lower_bound, upper_bound -
    • - Qt removes -- equal_range, key_compare -
    • - Qt renames -- lowerBound, upperBound -
    • - Qt adds -- constFind, insertMulti, key, keys, take, uniqueKeys, unite, values -
    • - Not applicable to map and QMap -- at, back, pop_back, pop_front, push_back, push_front, swap -
    • - Not applicable to QMap -- append, first, last, lastIndexOf, mid, move, prepend, removeAll, removeAt, removeFirst, removeLast, replace, squeeze, takeAt, takeFirst, takeLast -
    • - Not applicable to map -- assign -
    - - Qt QHash. STL extensions provide similar classes, e.g., Microsoft's stdext::hash_set. THey are nearly the same as QMap -
    • -
    • -
    • - Not applicable to Qhash -- lowerBound, unite, upperBound, -
    • - Qt adds -- squeeze -
    -     - -
    • - check... -- Throw error on failure -
    • - try... -- Return false on failure. Do not throw errors. -
    • - ...Temporarily -- lifetime depends on source. e.g., toByteArrayTemporarily -
    • - ...p -- indicates pointer-to. -
    • - end... -- points to one beyond the last available -
    • - private functions -- No syntactic indication. They may become public later on. -
    • - Error messages -- Preceed error messages with the name of the class throwing the error (e.g. "ClassName: ..."). If this is an internal error, use "ClassName inconsistent: ..." -
    • - parameter order -- qhRunId, dimension, coordinates, count. -
    • - toClass -- Convert into a Class object (makes a deep copy) -
    • - qRunId -- Requires Qh installed. Some routines allow 0 for limited info (e.g., operator<<) -
    • - Disable methods in derived classes -- If the default constructor, copy constructor, or copy assignment is disabled, it should be also disabled in derived classes (better error messages). -
    • - Constructor order -- default constructor, other constructors, copy constructor, copy assignment, destructor -
    -     -     -     diff --git a/src/qhull/html/qhull.htm b/src/qhull/html/qhull.htm deleted file mode 100644 index 0a2aa75e0..000000000 --- a/src/qhull/html/qhull.htm +++ /dev/null @@ -1,473 +0,0 @@ - - - - -qhull -- convex hull and related structures - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis • input -• outputs • controls -• options -

    - -

    [cone]qhull -- convex hull and related structures

    - -

    The convex hull of a set of points is the smallest convex set -containing the points. The Delaunay triangulation and furthest-site -Delaunay triangulation are equivalent to a convex hull in one -higher dimension. Halfspace intersection about a point is -equivalent to a convex hull by polar duality. - -

    The qhull program provides options to build these -structures and to experiment with the process. Use the -qconvex, -qdelaunay, qhalf, -and qvoronoi programs -to build specific structures. You may use qhull instead. -It takes the same options and uses the same code. -

    -
    -
    Example: rbox 1000 D3 | qhull - C-1e-4 - FO - Ts -
    -
    Compute the 3-d convex hull of 1000 random - points. - Centrums must be 10^-4 below neighboring - hyperplanes. Print the options and precision constants. - When done, print statistics. These options may be - used with any of the Qhull programs.
    -
     
    -
    Example: rbox 1000 D3 | qhull d - Qbb - R1e-4 - Q0
    -
    Compute the 3-d Delaunay triangulation of 1000 random - points. Randomly perturb all calculations by - [0.9999,1.0001]. Do not correct precision problems. - This leads to serious precision errors.
    -
    -
    -

    Use the following equivalences when calling qhull in 2-d to 4-d (a 3-d -Delaunay triangulation is a 4-d convex hull): -

    - -
    - -

    Use the following equivalences when calling qhull in 5-d and higher (a 4-d -Delaunay triangulation is a 5-d convex hull): -

    - -
    - - -

    By default, Qhull merges coplanar facets. For example, the convex -hull of a cube's vertices has six facets. - -

    If you use 'Qt' (triangulated output), -all facets will be simplicial (e.g., triangles in 2-d). For the cube -example, it will have 12 facets. Some facets may be -degenerate and have zero area. - -

    If you use 'QJ' (joggled input), -all facets will be simplicial. The corresponding vertices will be -slightly perturbed. Joggled input is less accurate that triangulated -output.See Merged facets or joggled input.

    - -

    The output for 4-d convex hulls may be confusing if the convex -hull contains non-simplicial facets (e.g., a hypercube). See -Why -are there extra points in a 4-d or higher convex hull?
    -

    - -

    Copyright © 1995-2015 C.B. Barber

    - -
    - -

    »qhull synopsis

    -
    -qhull- compute convex hulls and related structures.
-    input (stdin): dimension, n, point coordinates
-    comments start with a non-numeric character
-    halfspace: use dim+1 and put offsets after coefficients
-
-options (qh-quick.htm):
-    d    - Delaunay triangulation by lifting points to a paraboloid
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)
-    v    - Voronoi diagram as the dual of the Delaunay triangulation
-    v Qu - furthest-site Voronoi diagram
-    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Tv   - verify result: structure, convexity, and point inclusion
-    .    - concise list of all options
-    -    - one-line description of all options
-
-Output options (subset):
-    s    - summary of results (default)
-    i    - vertices incident to each facet
-    n    - normals with offsets
-    p    - vertex coordinates (if 'Qc', includes coplanar points)
-           if 'v', Voronoi vertices
-    Fp   - halfspace intersections
-    Fx   - extreme points (convex hull vertices)
-    FA   - compute total area and volume
-    o    - OFF format (if 'v', outputs Voronoi regions)
-    G    - Geomview output (2-d, 3-d and 4-d)
-    m    - Mathematica output (2-d and 3-d)
-    QVn  - print facets that include point n, -n if not
-    TO file- output results to file, may be enclosed in single quotes
-
-examples:
-    rbox c d D2 | qhull Qc s f Fx | more      rbox 1000 s | qhull Tv s FA
-    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p
-    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o
-    rbox c | qhull n                          rbox c | qhull FV n | qhull H Fp
-    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000
-    rbox y 1000 W0 | qhull                    rbox 10 | qhull v QJ o Fv
-
    - -

    »qhull input

    -
    - -

    The input data on stdin consists of:

    -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qhull < data.txt), a pipe (e.g., rbox 10 | qhull), -or the 'TI' option (e.g., qhull TI data.txt). - -

    Comments start with a non-numeric character. Error reporting is -simpler if there is one point per line. Dimension -and number of points may be reversed. For halfspace intersection, -an interior point may be prepended (see qhalf input). - -

    Here is the input for computing the convex -hull of the unit cube. The output is the normals, one -per facet.

    - -
    -

    rbox c > data

    - 
    -3 RBOX c
-8
-  -0.5   -0.5   -0.5
-  -0.5   -0.5    0.5
-  -0.5    0.5   -0.5
-  -0.5    0.5    0.5
-   0.5   -0.5   -0.5
-   0.5   -0.5    0.5
-   0.5    0.5   -0.5
-   0.5    0.5    0.5
-
    -

    qhull s n < data

    - 
    -
-Convex hull of 8 points in 3-d:
-
-  Number of vertices: 8
-  Number of facets: 6
-  Number of non-simplicial facets: 6
-
-Statistics for: RBOX c | QHULL s n
-
-  Number of points processed: 8
-  Number of hyperplanes created: 11
-  Number of distance tests for qhull: 35
-  Number of merged facets: 6
-  Number of distance tests for merging: 84
-  CPU seconds to compute hull (after input): 0.081
-
-4
-6
-     0      0     -1   -0.5
-     0     -1      0   -0.5
-     1      0      0   -0.5
-    -1      0      0   -0.5
-     0      1      0   -0.5
-     0      0      1   -0.5
-
    -
    - -
    -

    »qhull outputs

    -
    - -

    These options control the output of qhull. They may be used -individually or together.

    -
    -
    -
     
    -
    General
    -
    qhull
    -
    compute the convex hull of the input points. - See qconvex.
    -
    qhull d Qbb
    -
    compute the Delaunay triangulation by lifting the points - to a paraboloid. Use option 'Qbb' - to scale the paraboloid and improve numeric precision. - See qdelaunay.
    -
    qhull v Qbb
    -
    compute the Voronoi diagram by computing the Delaunay - triangulation. Use option 'Qbb' - to scale the paraboloid and improve numeric precision. - See qvoronoi.
    -
    qhull H
    -
    compute the halfspace intersection about a point via polar - duality. The point is below the hyperplane that defines the halfspace. - See qhalf.
    -
    -
    - -

    For a full list of output options see -

    - -
    - -
    -

    »qhull controls

    -
    - -

    For a full list of control options see -

    - -
    - -
    -

    »qhull options

    - -
    -qhull- compute convex hulls and related structures.
-    http://www.qhull.org
-
-input (stdin):
-    first lines: dimension and number of points (or vice-versa).
-    other lines: point coordinates, best if one point per line
-    comments:    start with a non-numeric character
-    halfspaces:  use dim plus one and put offset after coefficients.
-                 May be preceded by a single interior point ('H').
-
-options:
-    d    - Delaunay triangulation by lifting points to a paraboloid
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)
-    v    - Voronoi diagram (dual of the Delaunay triangulation)
-    v Qu - furthest-site Voronoi diagram
-    Hn,n,... - halfspace intersection about point [n,n,0,...]
-    Qt   - triangulated output
-    QJ   - joggle input instead of merging facets
-    Qc   - keep coplanar points with nearest facet
-    Qi   - keep interior points with nearest facet
-
-Qhull control options:
-    Qbk:n   - scale coord k so that low bound is n
-      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
-    QbB  - scale input to unit cube centered at the origin
-    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations
-    Qbk:0Bk:0 - remove k-th coordinate from input
-    QJn  - randomly joggle input in range [-n,n]
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
-    Qf   - partition point to furthest outside facet
-    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')
-    Qm   - only process points that would increase max_outside
-    Qr   - process random outside points instead of furthest ones
-    Qs   - search all points for the initial simplex
-    Qu   - for 'd' or 'v', compute upper hull without point at-infinity
-              returns furthest-site Delaunay triangulation
-    Qv   - test vertex neighbors for convexity
-    Qx   - exact pre-merges (skips coplanar and anglomaniacs facets)
-    Qz   - add point-at-infinity to Delaunay triangulation
-    QGn  - good facet if visible from point n, -n for not visible
-    QVn  - good facet if it includes point n, -n if not
-    Q0   - turn off default p remerge with 'C-0'/'Qx'
-    Q1     - sort merges by type instead of angle
-    Q2   - merge all non-convex at once instead of independent sets
-    Q3   - do not merge redundant vertices
-    Q4   - avoid old>new merges
-    Q5   - do not correct outer planes at end of qhull
-    Q6   - do not pre-merge concave or coplanar facets
-    Q7   - depth-first processing instead of breadth-first
-    Q8   - do not process near-inside points
-    Q9   - process furthest of furthest points
-    Q10  - no special processing for narrow distributions
-    Q11  - copy normals and recompute centrums for tricoplanar facets
-    Q12  - do not error on wide merge due to duplicate ridge and nearly coincident points
-
-Towpaths Trace options:
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
-    Tc   - check frequently during execution
-    Ts   - print statistics
-    Tv   - verify result: structure, convexity, and point inclusion
-    Tz   - send all output to stdout
-    TFn  - report summary when n or more facets created
-    TI file - input data from file, no spaces or single quotes
-    TO file - output results to file, may be enclosed in single quotes
-    TPn  - turn on tracing when point n added to hull
-     TMn - turn on tracing at merge n
-     TWn - trace merge facets when width > n
-    TRn  - rerun qhull n times.  Use with 'QJn'
-    TVn  - stop qhull after adding point n, -n for before (see TCn)
-     TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
-    En   - max roundoff error for distance computation
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]
-    Vn   - min distance above plane for a visible facet (default 3C-n or En)
-    Un   - max distance below plane for a new, coplanar point (default Vn)
-    Wn   - min facet width for outside point (before roundoff, default 2Vn)
-
-Output formats (may be combined; if none, produces a summary to stdout):
-    f    - facet dump
-    G    - Geomview output (see below)
-    i    - vertices incident to each facet
-    m    - Mathematica output (2-d and 3-d)
-    o    - OFF format (dim, points and facets; Voronoi regions)
-    n    - normals with offsets
-    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')
-    s    - summary (stderr)
-
-More formats:
-    Fa   - area for each facet
-    FA   - compute total area and volume for option 's'
-    Fc   - count plus coplanar points for each facet
-           use 'Qc' (default) for coplanar and 'Qi' for interior
-    FC   - centrum or Voronoi center for each facet
-    Fd   - use cdd format for input (homogeneous with offset first)
-    FD   - use cdd format for numeric output (offset first)
-    FF   - facet dump without ridges
-    Fi   - inner plane for each facet
-           for 'v', separating hyperplanes for bounded Voronoi regions
-    FI   - ID of each facet
-    Fm   - merge count for each facet (511 max)
-    FM   - Maple output (2-d and 3-d)
-    Fn   - count plus neighboring facets for each facet
-    FN   - count plus neighboring facets for each point
-    Fo   - outer plane (or max_outside) for each facet
-           for 'v', separating hyperplanes for unbounded Voronoi regions
-    FO   - options and precision constants
-    Fp   - dim, count, and intersection coordinates (halfspace only)
-    FP   - nearest vertex and distance for each coplanar point
-    FQ   - command used for qhull
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
-                      output: #vertices, #facets, #coplanars, #nonsimplicial
-                    #real (2), max outer plane, min vertex
-    FS   - sizes:   #int (0)
-                    #real(2) tot area, tot volume
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
-    Fv   - count plus vertices for each facet
-           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites
-    FV   - average of vertices (a feasible point for 'H')
-    Fx   - extreme points (in order for 2-d)
-
-Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)
-    Ga   - all points as dots
-     Gp  -  coplanar points and vertices as radii
-     Gv  -  vertices as spheres
-    Gi   - inner planes only
-     Gn  -  no planes
-     Go  -  outer planes only
-    Gc   - centrums
-    Gh   - hyperplane intersections
-    Gr   - ridges
-    GDn  - drop dimension n in 3-d and 4-d output
-    Gt   - for 3-d 'd', transparent outer ridges
-
-Print options:
-    PAn  - keep n largest facets by area
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)
-    PDk:n - drop facet if normal[k] >= n
-    Pg   - print good facets (needs 'QGn' or 'QVn')
-    PFn  - keep facets whose area is at least n
-    PG   - print neighbors of good facets
-    PMn  - keep n facets with most merges
-    Po   - force output.  If error, output neighborhood of facet
-    Pp   - do not report precision problems
-
-    .    - list of all options
-    -    - one line descriptions of all options
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis • input -• outputs • controls -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qhull.man b/src/qhull/html/qhull.man deleted file mode 100644 index 8d1dc08ac..000000000 --- a/src/qhull/html/qhull.man +++ /dev/null @@ -1,1008 +0,0 @@ -.\" This is the Unix manual page for qhull, written in nroff, the standard -.\" manual formatter for Unix systems. To format it, type -.\" -.\" nroff -man qhull.man -.\" -.\" This will print a formatted copy to standard output. If you want -.\" to ensure that the output is plain ASCII, free of any control -.\" characters that nroff uses for underlining etc, pipe the output -.\" through "col -b": -.\" -.\" nroff -man qhull.man | col -b -.\" -.\" Warning: a leading quote "'" or dot "." will not format correctly -.\" -.TH qhull 1 "2003/12/30" "Geometry Center" -.SH NAME -qhull \- convex hull, Delaunay triangulation, Voronoi diagram, -halfspace intersection about a point, hull volume, facet area -.SH SYNOPSIS -.nf -qhull- compute convex hulls and related structures - input (stdin): dimension, #points, point coordinates - first comment (non-numeric) is listed in the summary - halfspace: use dim plus one with offsets after coefficients - -options (qh-quick.htm): - d - Delaunay triangulation by lifting points to a paraboloid - v - Voronoi diagram via the Delaunay triangulation - H1,1 - Halfspace intersection about [1,1,0,...] - d Qu - Furthest-site Delaunay triangulation (upper convex hull) - v Qu - Furthest-site Voronoi diagram - Qt - triangulated output - QJ - Joggle the input to avoid precision problems - . - concise list of all options - - - one-line description of all options - -Output options (subset): - FA - compute total area and volume - Fx - extreme points (convex hull vertices) - G - Geomview output (2-d, 3-d and 4-d) - Fp - halfspace intersection coordinates - m - Mathematica output (2-d and 3-d) - n - normals with offsets - o - OFF file format (if Voronoi, outputs regions) - TO file- output results to file, may be enclosed in single quotes - f - print all fields of all facets - s - summary of results (default) - Tv - verify result: structure, convexity, and point inclusion - p - vertex coordinates (centers for Voronoi) - i - vertices incident to each facet - -example: - rbox 1000 s | qhull Tv s FA -.fi - - - html manual: index.htm - - installation: README.txt - - see also: COPYING.txt, REGISTER.txt, Changes.txt - - WWW: - - GIT: - - mirror: - - news: - - Geomview: - - news group: - - FAQ: - - email: qhull@qhull.org - - bug reports: qhull_bug@qhull.org - -The sections are: - - INTRODUCTION - - DESCRIPTION, a description of Qhull - - IMPRECISION, how Qhull handles imprecision - - OPTIONS - - Input and output options - - Additional input/output formats - - Precision options - - Geomview options - - Print options - - Qhull options - - Trace options - - BUGS - - E-MAIL - - SEE ALSO - - AUTHORS - - ACKNOWLEGEMENTS - -This man page briefly describes all Qhull options. Please report -any mismatches with Qhull's html manual (index.htm). - -.PP -.SH INTRODUCTION -Qhull is a general dimension code for computing convex hulls, Delaunay -triangulations, Voronoi diagram, furthest\[hy]site Voronoi diagram, -furthest\[hy]site Delaunay triangulations, and -halfspace intersections about a point. It implements the Quickhull algorithm for -computing the convex hull. Qhull handles round\[hy]off errors from floating -point arithmetic. It can approximate a convex hull. - -The program includes options for hull volume, facet area, partial hulls, -input transformations, randomization, tracing, multiple output formats, and -execution statistics. The program can be called from within your application. -You can view the results in 2\[hy]d, 3\[hy]d and 4\[hy]d with Geomview. -.PP -.SH DESCRIPTION -.PP -The format of input is the following: first line contains the dimension, -second line contains the number of input points, and point coordinates follow. -The dimension and number of points can be reversed. -Comments and line breaks are ignored. A comment starts with a -non\[hy]numeric character and continues to the end of line. The first comment -is reported in summaries and statistics. -Error reporting is -better if there is one point per line. -.PP -The default printout option is a short summary. There are many -other output formats. -.PP -Qhull implements the Quickhull algorithm for convex hull. This algorithm combines -the 2\[hy]d Quickhull algorithm with the n\[hy]d beneath\[hy]beyond algorithm -[c.f., Preparata & Shamos '85]. -It is similar to the randomized algorithms of Clarkson and -others [Clarkson et al. '93]. The main -advantages of Quickhull are output sensitive performance, reduced -space requirements, and automatic handling of precision problems. -.PP -The data structure produced by Qhull consists of vertices, ridges, and facets. -A vertex is a point of the input set. A ridge is a set of d vertices -and two neighboring facets. For example in 3\[hy]d, a ridge is an edge of the -polyhedron. A facet is a set of ridges, a set of neighboring facets, a set -of incident vertices, and a hyperplane equation. For simplicial facets, the -ridges are defined by the vertices and neighboring facets. When Qhull -merges two facets, it produces a non\[hy]simplicial -facet. A non\[hy]simplicial facet has more than d neighbors and may share more than -one ridge with a neighbor. -.PP -.SH IMPRECISION -.PP -Since Qhull uses floating point arithmetic, roundoff error may occur for each -calculation. This causes problems -for most geometric algorithms. -.PP -Qhull automatically sets option 'C\-0' in 2\[hy]d, 3\[hy]d, and 4\[hy]d, or -option 'Qx' in 5\[hy]d and higher. These options handle precision problems -by merging facets. Alternatively, use option 'QJ' to joggle the -input. -.PP -With 'C\-0', Qhull merges non\[hy]convex -facets while constructing the hull. The remaining facets are -clearly convex. With 'Qx', Qhull merges -coplanar horizon facets, flipped facets, concave facets and -duplicated ridges. It merges coplanar facets after constructing -the hull. -With 'Qx', coplanar points may be missed, but it -appears to be unlikely. -.PP -To guarantee triangular output, joggle the input with option 'QJ'. Facet -merging will not occur. -.SH OPTIONS -.PP -To get a list of the most important options, execute 'qhull' by itself. -To get a complete list of options, -execute 'qhull \-'. -To get a complete, concise list of options, execute 'qhull .'. - -Options can be in any order. -Capitalized options take an argument (except 'PG' and 'F' options). -Single letters are used for output formats and precision constants. The -other options are grouped into menus for other output formats ('F'), -Geomview output ('G'), -printing ('P'), Qhull control ('Q'), and tracing ('T'). -.TP -Main options: -.TP -default -Compute the convex hull of the input points. Report a summary of -the result. -.TP -d -Compute the Delaunay triangulation by lifting the input points to a -paraboloid. The 'o' option prints the input points and facets. -The 'QJ' option guarantees triangular output. The 'Ft' -option prints a triangulation. It adds points (the centrums) to non\[hy]simplicial -facets. -.TP -v -Compute the Voronoi diagram from the Delaunay triangulation. -The 'p' option prints the Voronoi vertices. -The 'o' option prints the Voronoi vertices and the -vertices in each Voronoi region. It lists regions in -site ID order. -The 'Fv' option prints each ridge of the Voronoi diagram. -The first or zero'th vertex -indicates the infinity vertex. Its coordinates are -qh_INFINITE (\-10.101). It indicates unbounded Voronoi -regions or degenerate Delaunay triangles. -.TP -Hn,n,... -Compute halfspace intersection about [n,n,0,...]. -The input is a set of halfspaces -defined in the same format as 'n', 'Fo', and 'Fi'. -Use 'Fp' to print the intersection points. Use 'Fv' -to list the intersection points for each halfspace. The -other output formats display the dual convex hull. - -The point [n,n,n,...] is a feasible point for the halfspaces, i.e., -a point that is inside all -of the halfspaces (Hx+b <= 0). The default coordinate value is 0. - -The input may start with a feasible point. If so, use 'H' by itself. -The input starts with a feasible point when the first number is the dimension, -the second number is "1", and the coordinates complete a line. The 'FV' -option produces a feasible point for a convex hull. -.TP -d Qu -Compute the furthest\[hy]site Delaunay triangulation from the upper -convex hull. The 'o' option prints the input points and facets. -The 'QJ' option guarantees triangular otuput. You can also use 'Ft' -to triangulate via the centrums of non\[hy]simplicial -facets. -.TP -v Qu -Compute the furthest\[hy]site Voronoi diagram. -The 'p' option prints the Voronoi vertices. -The 'o' option prints the Voronoi vertices and the -vertices in each Voronoi region. -The 'Fv' option prints each ridge of the Voronoi diagram. -The first or zero'th vertex -indicates the infinity vertex at infinity. Its coordinates are -qh_INFINITE (\-10.101). It indicates unbounded Voronoi regions -and degenerate Delaunay triangles. -.PP -.TP -Input/Output options: -.TP -f -Print out all facets and all fields of each facet. -.TP -G -Output the hull in Geomview format. For imprecise hulls, -Geomview displays the inner and outer hull. Geomview can also -display points, ridges, vertices, coplanar points, and -facet intersections. See below for a list of options. - -For Delaunay triangulations, 'G' displays the -corresponding paraboloid. For halfspace intersection, 'G' displays the -dual polytope. -.TP -i -Output the incident vertices for each facet. -Qhull prints the number of facets followed by the -vertices of each facet. One facet is printed per line. The numbers -are the 0\[hy]relative indices of the corresponding input points. -The facets -are oriented. - -In 4d and higher, -Qhull triangulates non\[hy]simplicial facets. Each apex (the first vertex) is -a created point that corresponds to the facet's centrum. Its index is greater -than the indices of the input points. Each base -corresponds to a simplicial ridge between two facets. -To print the vertices without triangulation, use option 'Fv'. -.TP -m -Output the hull in Mathematica format. Qhull writes a Mathematica file for 2\[hy]d and 3\[hy]d -convex hulls and for 2\[hy]d Delaunay triangulations. Qhull produces a list of objects -that you can assign to a variable in Mathematica, for example: -"list= << ". If the object is 2\[hy]d, it can be -visualized by "Show[Graphics[list]] ". For 3\[hy]d objects the command is -"Show[Graphics3D[list]]". -.TP -n -Output the normal equation for each facet. -Qhull prints the dimension (plus one), the number of facets, -and the normals for each facet. The facet's offset follows its -normal coefficients. -.TP -o -Output the facets in OFF file format. -Qhull prints the dimension, number of points, number -of facets, and number of ridges. Then it prints the coordinates of -the input points and the vertices for each facet. Each facet is on -a separate line. The first number is the number of vertices. The -remainder are the indices of the corresponding points. The vertices are -oriented in 2\[hy]d, 3\[hy]d, and in simplicial facets. - -For 2\[hy]d Voronoi diagrams, -the vertices are sorted by adjacency, but not oriented. In 3\[hy]d and higher, -the Voronoi vertices are sorted by index. -See the 'v' option for more information. -.TP -p -Output the coordinates of each vertex point. -Qhull prints the dimension, the number of points, -and the coordinates for each vertex. -With the 'Gc' and 'Gi' options, it also prints coplanar -and interior points. For Voronoi diagrams, it prints the coordinates -of each Voronoi vertex. -.TP -s -Print a summary to stderr. If no output options -are specified at all, a summary goes to stdout. The summary lists -the number of input points, the dimension, the number of vertices -in the convex hull, the number of facets in the convex hull, the -number of good facets (if 'Pg'), and statistics. - -The last two statistics (if needed) measure the maximum distance -from a point or vertex to a -facet. The number in parenthesis (e.g., 2.1x) is the ratio between the -maximum distance and the worst\[hy]case distance due to merging -two simplicial facets. -.PP -.TP -Precision options -.TP -An -Maximum angle given as a cosine. If the angle between a pair of facet -normals -is greater than n, Qhull merges one of the facets into a neighbor. -If 'n' is negative, Qhull tests angles after adding -each point to the hull (pre\[hy]merging). -If 'n' is positive, Qhull tests angles after -constructing the hull (post\[hy]merging). -Both pre\[hy] and post\[hy]merging can be defined. - -Option 'C0' or 'C\-0' is set if the corresponding 'Cn' or 'C\-n' -is not set. If 'Qx' -is set, then 'A\-n' and 'C\-n' are checked after the hull is constructed -and before 'An' and 'Cn' are checked. -.TP -Cn -Centrum radius. -If a centrum is less than n below a neighboring facet, Qhull merges one -of the facets. -If 'n' is negative or '\-0', Qhull tests and merges facets after adding -each point to the hull. This is called "pre\[hy]merging". If 'n' is positive, -Qhull tests for convexity after constructing the hull ("post\[hy]merging"). -Both pre\[hy] and post\[hy]merging can be defined. - -For 5\[hy]d and higher, 'Qx' should be used -instead of 'C\-n'. Otherwise, most or all facets may be merged -together. -.TP -En -Maximum roundoff error for distance computations. -.TP -Rn -Randomly perturb distance computations up to +/\- n * max_coord. -This option perturbs every distance, hyperplane, and angle computation. -To use time as the random number seed, use option 'QR\-1'. -.TP -Vn -Minimum distance for a facet to be visible. -A facet is visible if the distance from the point to the -facet is greater than 'Vn'. - -Without merging, the default value for 'Vn' is the round\[hy]off error ('En'). -With merging, the default value is the pre\[hy]merge centrum ('C\-n') in 2\[hy]d or -3\[hy]d, or three times that in other dimensions. If the outside width -is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. -.TP -Un -Maximum distance below a facet for a point to be coplanar to the facet. The -default value is 'Vn'. -.TP -Wn -Minimum outside width of the hull. Points are added to the convex hull -only if they are clearly outside of a facet. A point is outside of a -facet if its distance to the facet is greater than 'Wn'. The normal -value for 'Wn' is 'En'. If the user specifies pre\[hy]merging and -does not set 'Wn', than 'Wn' is set -to the premerge 'Cn' and maxcoord*(1\-An). -.PP -.TP -Additional input/output formats -.TP -Fa -Print area for each facet. -For Delaunay triangulations, the area is the area of the triangle. -For Voronoi diagrams, the area is the area of the dual facet. -Use 'PAn' for printing the n largest facets, and option 'PFn' for -printing facets larger than 'n'. - -The area for non\[hy]simplicial facets is the sum of the -areas for each ridge to the centrum. Vertices far below -the facet's hyperplane are ignored. -The reported area may be significantly less than the actual area. -.TP -FA -Compute the total area and volume for option 's'. It is an approximation -for non\[hy]simplicial facets (see 'Fa'). -.TP -Fc -Print coplanar points for each facet. The output starts with the -number of facets. Then each facet is printed one per line. Each line -is the number of coplanar points followed by the point ids. -Option 'Qi' includes the interior points. Each coplanar point (interior point) is -assigned to the facet it is furthest above (resp., least below). -.TP -FC -Print centrums for each facet. The output starts with the -dimension followed by the number of facets. -Then each facet centrum is printed, one per line. -.TP -Fd -Read input in cdd format with homogeneous points. -The input starts with comments. The first comment is reported in -the summary. -Data starts after a "begin" line. The next line is the number of points -followed by the dimension+1 and "real" or "integer". Then the points -are listed with a leading "1" or "1.0". The data ends with an "end" line. - -For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace -starts with its offset. The sign of the offset is the opposite of Qhull's -convention. -.TP -FD -Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. -The first line is the command line that invoked Qhull. -Data starts with a "begin" line. The next line is the number of normals or points -followed by the dimension+1 and "real". Then the normals or points -are listed with the offset before the coefficients. The offset for points is -1.0. The offset for normals has the opposite sign. -The data ends with an "end" line. -.TP -FF -Print facets (as in 'f') without printing the ridges. -.TP -Fi -Print inner planes for each facet. The inner plane is below all vertices. -.TP -Fi -Print separating hyperplanes for bounded, inner regions of the Voronoi -diagram. The first line is the number -of ridges. Then each hyperplane is printed, one per line. A line starts -with the number of indices and floats. The first pair lists -adjacent input -sites, the next d floats are the normalized coefficients for the hyperplane, -and the last float is the offset. The hyperplane is oriented toward 'QVn' -(if defined), or the first input site of the pair. Use 'Tv' to -verify that the hyperplanes are perpendicular bisectors. Use 'Fo' for -unbounded regions, and 'Fv' for the corresponding Voronoi vertices. -.TP -FI -Print facet identifiers. -.TP -Fm -Print number of merges for each facet. At most 511 merges are reported for -a facet. See 'PMn' for printing the facets with the most merges. -.TP -FM -Output the hull in Maple format. Qhull writes a Maple -file for 2\[hy]d and 3\[hy]d -convex hulls and for 2\[hy]d Delaunay triangulations. Qhull produces a '.mpl' -file for displaying with display3d(). -.TP -Fn -Print neighbors for each facet. The output starts with the number of facets. -Then each facet is printed one per line. Each line -is the number of neighbors followed by an index for each neighbor. The indices -match the other facet output formats. - -A negative index indicates an unprinted -facet due to printing only good facets ('Pg'). It is the negation of the facet's -ID (option 'FI'). -For example, negative indices are used for facets -"at infinity" in the Delaunay triangulation. -.TP -FN -Print vertex neighbors or coplanar facet for each point. -The first line is the number -of points. Then each point is printed, one per line. If the -point is coplanar, the line is "1" followed by the facet's ID. -If the point is -not a selected vertex, the line is "0". -Otherwise, each line is the number of -neighbors followed by the corresponding facet indices (see 'Fn'). -.TP -Fo -Print outer planes for each facet in the same format as 'n'. -The outer plane is above all points. -.TP -Fo -Print separating hyperplanes for unbounded, outer regions of the Voronoi -diagram. The first line is the number -of ridges. Then each hyperplane is printed, one per line. A line starts -with the number of indices and floats. The first pair lists -adjacent input -sites, the next d floats are the normalized coefficients for the hyperplane, -and the last float is the offset. The hyperplane is oriented toward 'QVn' -(if defined), or the first input site of the pair. Use 'Tv' to -verify that the hyperplanes are perpendicular bisectors. Use 'Fi' for -bounded regions, and 'Fv' for the corresponding Voronoi vertices. -.TP -FO -List all options to stderr, including the default values. Additional 'FO's -are printed to stdout. -.TP -Fp -Print points for halfspace intersections (option 'Hn,n,...'). Each -intersection corresponds to a facet of the dual polytope. -The "infinity" point [\-10.101,\-10.101,...] -indicates an unbounded intersection. -.TP -FP -For each coplanar point ('Qc') print the point ID of the nearest vertex, -the point ID, the facet ID, and the distance. -.TP -FQ -Print command used for qhull and input. -.TP -Fs -Print a summary. The first line consists of the number of integers ("8"), -followed by the dimension, the number of points, the number of vertices, -the number of facets, the number of vertices selected for output, the -number of facets selected for output, the number of coplanar points selected -for output, number of simplicial, unmerged facets in output - -The second line consists of the number of reals ("2"), -followed by the maxmimum offset to an outer plane and and minimum offset to -an inner plane. Roundoff is included. Later -versions of Qhull may produce additional integers or reals. -.TP -FS -Print the size of the hull. The first line consists of the number of integers ("0"). -The second line consists of the number of reals ("2"), -followed by the total facet area, and the total volume. -Later -versions of Qhull may produce additional integers or reals. - -The total volume measures the volume -of the intersection of the halfspaces defined by each facet. -Both area and volume are -approximations for non\[hy]simplicial facets. See option 'Fa'. -.TP -Ft -Print a triangulation with added points for non\[hy]simplicial -facets. The first line is the dimension and the second line is the -number of points and the number of facets. The points follow, one -per line, then the facets follow as a list of point indices. With option 'Qz', the -points include the point\[hy]at\[hy]infinity. -.TP -Fv -Print vertices for each facet. The first line is the number -of facets. Then each facet is printed, one per line. Each line is -the number of vertices followed by the corresponding point ids. Vertices -are listed in the order they were added to the hull (the last one is first). -.TP -Fv -Print all ridges of a Voronoi diagram. The first line is the number -of ridges. Then each ridge is printed, one per line. A line starts -with the number of indices. The first pair lists adjacent input -sites, the remaining indices list Voronoi vertices. Vertex '0' indicates -the vertex\[hy]at\[hy]infinity (i.e., an unbounded ray). In 3\[hy]d, the vertices -are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. -.TP -FV -Print average vertex. The average vertex is a feasible point -for halfspace intersection. -.TP -Fx -List extreme points (vertices) of the convex hull. The first line -is the number of points. The other lines give the indices of the -corresponding points. The first point is '0'. In 2\[hy]d, the points -occur in counter\[hy]clockwise order; otherwise they occur in input order. -For Delaunay triangulations, 'Fx' lists the extreme points of the -input sites. The points are unordered. -.PP -.TP -Geomview options -.TP -G -Produce a file for viewing with Geomview. Without other options, -Qhull displays edges in 2\[hy]d, outer planes in 3\[hy]d, and ridges in 4\[hy]d. -A ridge can be -explicit or implicit. An explicit ridge is a dim\-1 dimensional simplex -between two facets. -In 4\[hy]d, the explicit ridges are triangles. -When displaying a ridge in 4\[hy]d, Qhull projects the ridge's vertices to -one of its facets' hyperplanes. -Use 'Gh' to -project ridges to the intersection of both hyperplanes. -.TP -Ga -Display all input points as dots. -.TP -Gc -Display the centrum for each facet in 3\[hy]d. The centrum is defined by a -green radius sitting on a blue plane. The plane corresponds to the -facet's hyperplane. -The radius is defined by 'C\-n' or 'Cn'. -.TP -GDn -Drop dimension n in 3\[hy]d or 4\[hy]d. The result is a 2\[hy]d or 3\[hy]d object. -.TP -Gh -Display hyperplane intersections in 3\[hy]d and 4\[hy]d. In 3\[hy]d, the -intersection is a black line. It lies on two neighboring hyperplanes -(c.f., the blue squares associated with centrums ('Gc')). In 4\[hy]d, -the ridges are projected to the intersection of both hyperplanes. -.TP -Gi -Display inner planes in 2\[hy]d and 3\[hy]d. The inner plane of a facet -is below all of its vertices. It is parallel to the facet's hyperplane. -The inner plane's color is the opposite (1\-r,1\-g,1\-b) of the outer -plane. Its edges are determined by the vertices. -.TP -Gn -Do not display inner or outer planes. By default, -Geomview displays the precise plane (no merging) or both -inner and output planes (merging). Under merging, Geomview does -not display the inner plane if the -the difference between inner and outer is too small. -.TP -Go -Display outer planes in 2\[hy]d and 3\[hy]d. The outer plane of a facet -is above all input points. It is parallel to the facet's hyperplane. -Its color is determined by the facet's normal, and its -edges are determined by the vertices. -.TP -Gp -Display coplanar points and vertices as radii. A radius defines a ball -which corresponds to the imprecision of the point. The imprecision is -the maximum of the roundoff error, the centrum radius, and maxcoord * -(1\-An). It is at least 1/20'th of the maximum coordinate, -and ignores post\[hy]merging if pre\[hy]merging is done. -.TP -Gr -Display ridges in 3\[hy]d. A ridge connects the two vertices that are shared -by neighboring facets. Ridges are always displayed in 4\[hy]d. -.TP -Gt -A 3\[hy]d Delaunay triangulation looks like a convex hull with interior -facets. Option 'Gt' removes the outside ridges to reveal the outermost -facets. It automatically sets options 'Gr' and 'GDn'. -.TP -Gv -Display vertices as spheres. The radius of the sphere corresponds to -the imprecision of the data. See 'Gp' for determining the radius. -.PP -.TP -Print options -.TP -PAn -Only the n largest facets are marked good for printing. -Unless 'PG' is set, 'Pg' is automatically set. -.TP -Pdk:n -Drop facet from output if normal[k] <= n. The option 'Pdk' uses the -default value of 0 for n. -.TP -PDk:n -Drop facet from output if normal[k] >= n. The option 'PDk' uses the -default value of 0 for n. -.TP -PFn -Only facets with area at least 'n' are marked good for printing. -Unless 'PG' is set, 'Pg' is automatically set. -.TP -Pg -Print only good facets. A good facet is either visible from a point -(the 'QGn' option) or includes a point (the 'QVn' option). It also meets the -requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically -set for options 'PAn' and 'PFn'. -.TP -PG -Print neighbors of good facets. -.TP -PMn -Only the n facets with the most merges are marked good for printing. -Unless 'PG' is set, 'Pg' is automatically set. -.TP -Po -Force output despite precision problems. Verify ('Tv') does not check -coplanar points. -Flipped facets are reported and concave facets are counted. -If 'Po' is used, points are not -partitioned into flipped facets and a flipped facet is always visible -to a point. -Also, if an error occurs before the completion of Qhull and tracing is -not active, 'Po' outputs a neighborhood of the erroneous facets -(if any). -.TP -Pp -Do not report precision problems. -.PP -.TP -Qhull control options -.TP -Qbk:0Bk:0 -Drop dimension k from the input points. This allows the user to -take convex hulls of sub\[hy]dimensional objects. It happens before -the Delaunay and Voronoi transformation. -.TP -QbB -Scale the input points to fit the unit cube. After scaling, the lower -bound will be \-0.5 and the upper bound +0.5 in all dimensions. -For Delaunay and -Voronoi diagrams, scaling happens after projection to the paraboloid. -Under precise -arithmetic, scaling does not change the topology of the convex hull. -.TP -Qbb -Scale the last coordinate to [0, m] where m is the maximum absolute -value of the other coordinates. For Delaunay and -Voronoi diagrams, scaling happens after projection to the paraboloid. -It reduces roundoff error for inputs with integer coordinates. -Under precise -arithmetic, scaling does not change the topology of the convex hull. -.TP -Qbk:n -Scale the k'th coordinate of the input points. After scaling, the lower -bound of the input points will be n. 'Qbk' scales to \-0.5. -.TP -QBk:n -Scale the k'th coordinate of the input points. After scaling, the upper -bound will be n. 'QBk' scales to +0.5. -.TP -Qc -Keep coplanar points with the nearest facet. Output -formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. -.TP -Qf -Partition points to the furthest outside facet. -.TP -Qg -Only build good facets. With the 'Qg' option, Qhull will only build -those facets that it needs to determine the good facets in the output. -See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' -for printing good facets and their neighbors. -.TP -QGn -A facet is good (see 'Qg' and 'Pg') if it is visible from point n. If n < 0, a facet is -good if it is not visible from point n. Point n is not added to the -hull (unless 'TCn' or 'TPn'). -With rbox, use the 'Pn,m,r' option to define your point; it -will be point 0 (QG0). -.TP -Qi -Keep interior points with the nearest facet. -Output formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. -.TP -QJn -Joggle each input coordinate by adding a random number in [\-n,n]. If a -precision error occurs, then qhull increases n and tries again. It does -not increase n beyond a certain value, and it stops after a certain number -of attempts [see user.h]. Option 'QJ' -selects a default value for n. The output will be simplicial. For -Delaunay triangulations, 'QJn' sets 'Qbb' to scale the last coordinate -(not if 'Qbk:n' or 'QBk:n' is set). -\'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. -.TP -Qm -Only process points that would otherwise increase max_outside. Other -points are treated as coplanar or interior points. -.TP -Qr -Process random outside points instead of furthest ones. This makes -Qhull equivalent to the randomized incremental algorithms. CPU time -is not reported since the randomization is inefficient. -.TP -QRn -Randomly rotate the input points. If n=0, use time as the random number seed. -If n>0, use n as the random number seed. If n=\-1, don't rotate but use -time as the random number seed. For Delaunay triangulations ('d' and 'v'), -rotate about the last axis. -.TP -Qs -Search all points for the initial simplex. -.TP -Qt -Triangulated output. Triangulate all non\[hy]simplicial facets. -\'Qt' is deprecated for Voronoi diagrams. See also 'Qt'. -.TP -Qv -Test vertex neighbors for convexity after post\[hy]merging. -To use the 'Qv' option, you also need to set a merge option -(e.g., 'Qx' or 'C\-0'). -.TP -QVn -A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not -include point n. The point is either in the initial simplex or it -is the first point added to the hull. Option 'QVn' may not be used with merging. -.TP -Qx -Perform exact merges while building the hull. The "exact" merges -are merging a point into a coplanar facet (defined by 'Vn', 'Un', -and 'C\-n'), merging concave facets, merging duplicate ridges, and -merging flipped facets. Coplanar merges and angle coplanar merges ('A\-n') -are not performed. Concavity testing is delayed until a merge occurs. - -After -the hull is built, all coplanar merges are performed (defined by 'C\-n' -and 'A\-n'), then post\[hy]merges are performed -(defined by 'Cn' and 'An'). -.TP -Qz -Add a point "at infinity" that is above the paraboloid for Delaunay triangulations -and Voronoi diagrams. This reduces precision problems and allows the triangulation -of cospherical points. -.PP -.TP -Qhull experiments and speedups -.TP -Q0 -Turn off pre\[hy]merging as a default option. -With 'Q0'/'Qx' and without explicit pre\[hy]merge options, Qhull -ignores precision issues while constructing the convex hull. This -may lead to precision errors. If so, a descriptive warning is -generated. -.TP -Q1 -With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave) -instead of by angle. -.TP -Q2 -With 'Q2', Qhull merges all facets at once instead of using -independent sets of merges and then retesting. -.TP -Q3 -With 'Q3', Qhull does not remove redundant vertices. -.TP -Q4 -With 'Q4', Qhull avoids merges of an old facet into a new facet. -.TP -Q5 -With 'Q5', Qhull does not correct outer planes at the end. The -maximum outer plane is used instead. -.TP -Q6 -With 'Q6', Qhull does not pre\[hy]merge concave or coplanar facets. -.TP -Q7 -With 'Q7', Qhull processes facets in depth\[hy]first order instead of -breadth\[hy]first order. -.TP -Q8 -With 'Q8' and merging, Qhull does not retain near\[hy]interior points for adjusting -outer planes. 'Qc' will probably retain -all points that adjust outer planes. -.TP -Q9 -With 'Q9', Qhull processes the furthest of all outside sets at each iteration. -.TP -Q10 -With 'Q10', Qhull does not use special processing for narrow distributions. -.TP -Q11 -With 'Q11', Qhull copies normals and recompute centrums for tricoplanar facets. -.TP -Q12 -With 'Q12', Qhull does not report a very wide merge due to a duplicated ridge with nearly coincident vertices -.PP -.TP -Trace options -.TP -Tn -Trace at level n. Qhull includes full execution tracing. 'T\-1' -traces events. 'T1' traces -the overall execution of the program. 'T2' and 'T3' trace overall -execution and geometric and topological events. 'T4' traces the -algorithm. 'T5' includes information about memory allocation and -Gaussian elimination. -.TP -Ta -Annotate output with codes that identify the -corresponding qh_fprintf() statement. -.TP -Tc -Check frequently during execution. This will catch most inconsistency -errors. -.TP -TCn -Stop Qhull after building the cone of new facets for point n. The -output for 'f' includes the cone and the old hull. -See also 'TVn'. -.TP -TFn -Report progress whenever more than n facets are created -During post\[hy]merging, 'TFn' -reports progress after more than n/2 merges. -.TP -TI file -Input data from 'file'. The filename may not include spaces or -quotes. -.TP -TO file -Output results to 'file'. The name may be enclosed in single -quotes. -.TP -TPn -Turn on tracing when point n is added to the hull. Trace -partitions of point n. If used with TWn, turn off -tracing after adding point n to the hull. -.TP -TRn -Rerun qhull n times. Usually used with 'QJn' to determine the -probability that a given joggle will fail. -.TP -Ts -Collect statistics and print to stderr at the end of execution. -.TP -Tv -Verify the convex hull. This checks the topological structure, facet -convexity, and point inclusion. -If precision problems occurred, facet convexity is tested whether or -not 'Tv' is selected. -Option 'Tv' does not check point inclusion if forcing output with 'Po', -or if 'Q5' is set. - -For point inclusion testing, Qhull verifies that all points are below -all outer planes (facet\->maxoutside). Point inclusion is exhaustive -if merging or if the facet\[hy]point product is small enough; -otherwise Qhull verifies each point with a directed -search (qh_findbest). - -Point inclusion testing occurs after producing output. It prints -a message to stderr unless option 'Pp' is used. This -allows the user to interrupt Qhull without changing the output. -.TP -TVn -Stop Qhull after adding point n. If n < 0, stop Qhull before adding -point n. Output shows the hull at this time. See also 'TCn' -.TP -TMn -Turn on tracing at n'th merge. -.TP -TWn -Trace merge facets when the width is greater than n. -.TP -Tz -Redirect stderr to stdout. -.PP -.SH BUGS -Please report bugs to Brad Barber at qhull_bug@qhull.org. - -If Qhull does not compile, it is due to an incompatibility between your -system and ours. The first thing to check is that your compiler is -ANSI standard. If it is, check the man page for the best options, or -find someone to help you. If you locate the cause of your problem, -please send email since it might help others. - -If Qhull compiles but crashes on the test case (rbox D4), there's -still incompatibility between your system and ours. Typically it's -been due to mem.c and memory alignment. You can use qh_NOmem in mem.h -to turn off memory management. Please let us know if you figure out -how to fix these problems. - -If you do find a problem, try to simplify it before reporting the -error. Try different size inputs to locate the smallest one that -causes an error. You're welcome to hunt through the code using the -execution trace as a guide. This is especially true if you're -incorporating Qhull into your own program. - -When you do report an error, please attach a data set to the -end of your message. This allows us to see the error for ourselves. -Qhull is maintained part\[hy]time. -.PP -.SH E\[hy]MAIL -Please send correspondence to qhull@qhull.org and report bugs to -qhull_bug@qhull.org. Let us know how you use Qhull. If you -mention it in a paper, please send the reference and an abstract. - -If you would like to get Qhull announcements (e.g., a new version) -and news (any bugs that get fixed, etc.), let us know and we will add you to -our mailing list. If you would like to communicate with other -Qhull users, we will add you to the qhull_users alias. -For Internet news about geometric algorithms and convex hulls, look at -comp.graphics.algorithms and sci.math.num\-analysis - -.SH SEE ALSO -rbox(1) - -Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, -"The Quickhull Algorithm for Convex Hulls," ACM -Trans. on Mathematical Software, 22(4):469\[en]483, Dec. 1996. -http://portal.acm.org/citation.cfm?doid=235815.235821 -http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 - -Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized -incremental construction," Computational Geometry: Theory and Applications, -vol. 3, p. 185\[en]211, 1993. - -Preparata, F. and M. Shamos, Computational -Geometry, Springer\[hy]Verlag, New York, 1985. - -.PP -.SH AUTHORS -.nf - C. Bradford Barber Hannu Huhdanpaa - bradb@shore.net hannu@qhull.org - - .fi - -.SH ACKNOWLEDGEMENTS - -A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, -Harvard University, and Endocardial Solutions, Inc. for supporting this work. - -Qhull 1.0 and 2.0 were developed under National Science Foundation -grants NSF/DMS\[hy]8920161 and NSF\[hy]CCR\[hy]91\[hy]15793 750\[hy]7504. David Dobkin -guided the original work at Princeton University. -If you find it useful, please let us know. - -The Geometry Center is supported by grant DMS\[hy]8920161 from the National -Science Foundation, by grant DOE/DE\[hy]FG02\[hy]92ER25137 from the Department -of Energy, by the University of Minnesota, and by Minnesota Technology, Inc. - -Qhull is available from http://www.qhull.org diff --git a/src/qhull/html/qhull.txt b/src/qhull/html/qhull.txt deleted file mode 100644 index 03753547e..000000000 --- a/src/qhull/html/qhull.txt +++ /dev/null @@ -1,1263 +0,0 @@ - - - -qhull(1) qhull(1) - - -NAME - qhull - convex hull, Delaunay triangulation, Voronoi dia- - gram, halfspace intersection about a point, hull volume, facet area - -SYNOPSIS - qhull- compute convex hulls and related structures - input (stdin): dimension, #points, point coordinates - first comment (non-numeric) is listed in the summary - halfspace: use dim plus one with offsets after coefficients - - options (qh-quick.htm): - d - Delaunay triangulation by lifting points to a paraboloid - v - Voronoi diagram via the Delaunay triangulation - H1,1 - Halfspace intersection about [1,1,0,...] - d Qu - Furthest-site Delaunay triangulation (upper convex hull) - v Qu - Furthest-site Voronoi diagram - QJ - Joggle the input to avoid precision problems - . - concise list of all options - - - one-line description of all options - - Output options (subset): - FA - compute total area and volume - Fx - extreme points (convex hull vertices) - G - Geomview output (2-d, 3-d and 4-d) - Fp - halfspace intersection coordinates - m - Mathematica output (2-d and 3-d) - n - normals with offsets - o - OFF file format (if Voronoi, outputs regions) - TO file- output results to file, may be enclosed in single quotes - f - print all fields of all facets - s - summary of results (default) - Tv - verify result: structure, convexity, and point inclusion - p - vertex coordinates - i - vertices incident to each facet - - example: - rbox 1000 s | qhull Tv s FA - - - html manual: index.htm - - installation: README.txt - - see also: COPYING.txt, REGISTER.txt, Changes.txt - - WWW: - - GIT: - - mirror: - - news: - - Geomview: - - news group: - - FAQ: - - email: qhull@qhull.org - - bug reports: qhull_bug@qhull.org - - - - -Geometry Center 2003/12/30 1 - - - - - -qhull(1) qhull(1) - - - The sections are: - - INTRODUCTION - - DESCRIPTION, a description of Qhull - - IMPRECISION, how Qhull handles imprecision - - OPTIONS - - Input and output options - - Additional input/output formats - - Precision options - - Geomview options - - Print options - - Qhull options - - Trace options - - BUGS - - E-MAIL - - SEE ALSO - - AUTHORS - - ACKNOWLEGEMENTS - - This man page briefly describes all Qhull options. Please - report any mismatches with Qhull's html manual (qh- - man.htm). - - - -INTRODUCTION - Qhull is a general dimension code for computing convex - hulls, Delaunay triangulations, Voronoi diagram, furthest- - site Voronoi diagram, furthest-site Delaunay triangula- - tions, and halfspace intersections about a point. It - implements the Quickhull algorithm for computing the con- - vex hull. Qhull handles round-off errors from floating - point arithmetic. It can approximate a convex hull. - - The program includes options for hull volume, facet area, - partial hulls, input transformations, randomization, trac- - ing, multiple output formats, and execution statistics. - The program can be called from within your application. - You can view the results in 2-d, 3-d and 4-d with - Geomview. - - -DESCRIPTION - The format of input is the following: first line contains - the dimension, second line contains the number of input - points, and point coordinates follow. The dimension and - number of points can be reversed. Comments and line - breaks are ignored. A comment starts with a non-numeric - character and continues to the end of line. The first - comment is reported in summaries and statistics. Error - reporting is better if there is one point per line. - - The default printout option is a short summary. There are - many other output formats. - - - - -Geometry Center 2003/12/30 2 - - - - - -qhull(1) qhull(1) - - - Qhull implements the Quickhull algorithm for convex hull. - This algorithm combines the 2-d Quickhull algorithm with - the n-d beneath-beyond algorithm [c.f., Preparata & Shamos - '85]. It is similar to the randomized algorithms of - Clarkson and others [Clarkson et al. '93]. The main - advantages of Quickhull are output sensitive performance, - reduced space requirements, and automatic handling of pre- - cision problems. - - The data structure produced by Qhull consists of vertices, - ridges, and facets. A vertex is a point of the input set. - A ridge is a set of d vertices and two neighboring facets. - For example in 3-d, a ridge is an edge of the polyhedron. - A facet is a set of ridges, a set of neighboring facets, a - set of incident vertices, and a hyperplane equation. For - simplicial facets, the ridges are defined by the vertices - and neighboring facets. When Qhull merges two facets, it - produces a non-simplicial facet. A non-simplicial facet - has more than d neighbors and may share more than one - ridge with a neighbor. - - -IMPRECISION - Since Qhull uses floating point arithmetic, roundoff error - may occur for each calculation. This causes problems for - most geometric algorithms. - - Qhull automatically sets option 'C-0' in 2-d, 3-d, and - 4-d, or option 'Qx' in 5-d and higher. These options han- - dle precision problems by merging facets. Alternatively, - use option 'QJ' to joggle the input. - - With 'C-0', Qhull merges non-convex facets while con- - structing the hull. The remaining facets are clearly con- - vex. With 'Qx', Qhull merges coplanar horizon facets, - flipped facets, concave facets and duplicated ridges. It - merges coplanar facets after constructing the hull. With - 'Qx', coplanar points may be missed, but it appears to be - unlikely. - - To guarantee triangular output, joggle the input with - option 'QJ'. Facet merging will not occur. - -OPTIONS - To get a list of the most important options, execute - 'qhull' by itself. To get a complete list of options, - execute 'qhull -'. To get a complete, concise list of - options, execute 'qhull .'. - - Options can be in any order. Capitalized options take an - argument (except 'PG' and 'F' options). Single letters - are used for output formats and precision constants. The - other options are grouped into menus for other output for- - mats ('F'), Geomview output ('G'), printing ('P'), Qhull - - - -Geometry Center 2003/12/30 3 - - - - - -qhull(1) qhull(1) - - - control ('Q'), and tracing ('T'). - - Main options: - - default - Compute the convex hull of the input points. - Report a summary of the result. - - d Compute the Delaunay triangulation by lifting the - input points to a paraboloid. The 'o' option - prints the input points and facets. The 'QJ' - option guarantees triangular output. The 'Ft' - option prints a triangulation. It adds points (the - centrums) to non-simplicial facets. - - v Compute the Voronoi diagram from the Delaunay tri- - angulation. The 'p' option prints the Voronoi ver- - tices. The 'o' option prints the Voronoi vertices - and the vertices in each Voronoi region. It lists - regions in site id order. The 'Fv' option prints - each ridge of the Voronoi diagram. The first or - zero'th vertex indicates the infinity vertex. Its - coordinates are qh_INFINITE (-10.101). It indi- - cates unbounded Voronoi regions or degenerate - Delaunay triangles. - - Hn,n,... - Compute halfspace intersection about [n,n,0,...]. - The input is a set of halfspaces defined in the - same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to - print the intersection points. Use 'Fv' to list - the intersection points for each halfspace. The - other output formats display the dual convex hull. - - The point [n,n,n,...] is a feasible point for the - halfspaces, i.e., a point that is inside all of the - halfspaces (Hx+b <= 0). The default coordinate - value is 0. - - The input may start with a feasible point. If so, - use 'H' by itself. The input starts with a feasi- - ble point when the first number is the dimension, - the second number is "1", and the coordinates com- - plete a line. The 'FV' option produces a feasible - point for a convex hull. - - d Qu Compute the furthest-site Delaunay triangulation - from the upper convex hull. The 'o' option prints - the input points and facets. The 'QJ' option guar- - antees triangular otuput. You can also use facets. - - v Qu Compute the furthest-site Voronoi diagram. The 'p' - option prints the Voronoi vertices. The 'o' option - prints the Voronoi vertices and the vertices in - - - -Geometry Center 2003/12/30 4 - - - - - -qhull(1) qhull(1) - - - each Voronoi region. The 'Fv' option prints each - ridge of the Voronoi diagram. The first or zero'th - vertex indicates the infinity vertex at infinity. - Its coordinates are qh_INFINITE (-10.101). It - indicates unbounded Voronoi regions and degenerate - Delaunay triangles. - - Qt Triangulated output. - - - Input/Output options: - - f Print out all facets and all fields of each facet. - - G Output the hull in Geomview format. For imprecise - hulls, Geomview displays the inner and outer hull. - Geomview can also display points, ridges, vertices, - coplanar points, and facet intersections. See - below for a list of options. - - For Delaunay triangulations, 'G' displays the cor- - responding paraboloid. For halfspace intersection, - 'G' displays the dual polytope. - - i Output the incident vertices for each facet. Qhull - prints the number of facets followed by the ver- - tices of each facet. One facet is printed per - line. The numbers are the 0-relative indices of - the corresponding input points. The facets are - oriented. - - In 4-d and higher, Qhull triangulates non-simpli- - cial facets. Each apex (the first vertex) is a - created point that corresponds to the facet's cen- - trum. Its index is greater than the indices of the - input points. Each base corresponds to a simpli- - cial ridge between two facets. To print the ver- - tices without triangulation, use option 'Fv'. - - m Output the hull in Mathematica format. Qhull - writes a Mathematica file for 2-d and 3-d convex - hulls and for 2-d Delaunay triangulations. Qhull - produces a list of objects that you can assign to a - variable in Mathematica, for example: "list= << - ". If the object is 2-d, it can be - visualized by "Show[Graphics[list]] ". For 3-d - objects the command is "Show[Graphics3D[list]]". - - n Output the normal equation for each facet. Qhull - prints the dimension (plus one), the number of - facets, and the normals for each facet. The - facet's offset follows its normal coefficients. - - o Output the facets in OFF file format. Qhull prints - the dimension, number of points, number of facets, - and number of ridges. Then it prints the - - - -Geometry Center 2003/12/30 5 - - - - - -qhull(1) qhull(1) - - - coordinates of the input points and the vertices - for each facet. Each facet is on a separate line. - The first number is the number of vertices. The - remainder are the indices of the corresponding - points. The vertices are oriented in 2-d, 3-d, and - in simplicial facets. - - For 2-d Voronoi diagrams, the vertices are sorted - by adjacency, but not oriented. In 3-d and higher, - the Voronoi vertices are sorted by index. See the - 'v' option for more information. - - p Output the coordinates of each vertex point. Qhull - prints the dimension, the number of points, and the - coordinates for each vertex. With the 'Gc' and - 'Gi' options, it also prints coplanar and interior - points. For Voronoi diagrams, it prints the coor- - dinates of each Voronoi vertex. - - s Print a summary to stderr. If no output options - are specified at all, a summary goes to stdout. - The summary lists the number of input points, the - dimension, the number of vertices in the convex - hull, the number of facets in the convex hull, the - number of good facets (if 'Pg'), and statistics. - - The last two statistics (if needed) measure the - maximum distance from a point or vertex to a facet. - The number in parenthesis (e.g., 2.1x) is the ratio - between the maximum distance and the worst-case - distance due to merging two simplicial facets. - - - Precision options - - An Maximum angle given as a cosine. If the angle - between a pair of facet normals is greater than n, Qhull - merges one of the facets into a neighbor. If 'n' - is negative, Qhull tests angles after adding each - point to the hull (pre-merging). If 'n' is posi- - tive, Qhull tests angles after constructing the - hull (post-merging). Both pre- and post-merging - can be defined. - - Option 'C0' or 'C-0' is set if the corresponding - 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A- - n' and 'C-n' are checked after the hull is con- - structed and before 'An' and 'Cn' are checked. - - Cn Centrum radius. If a centrum is less than n below - a neighboring facet, Qhull merges one of the - facets. If 'n' is negative or '-0', Qhull tests - and merges facets after adding each point to the - hull. This is called "pre-merging". If 'n' is - - - -Geometry Center 2003/12/30 6 - - - - - -qhull(1) qhull(1) - - - positive, Qhull tests for convexity after con- - structing the hull ("post-merging"). Both pre- and - post-merging can be defined. - - For 5-d and higher, 'Qx' should be used instead of - 'C-n'. Otherwise, most or all facets may be merged - together. - - En Maximum roundoff error for distance computations. - - Rn Randomly perturb distance computations up to +/- n - * max_coord. This option perturbs every distance, - hyperplane, and angle computation. To use time as - the random number seed, use option 'QR-1'. - - Vn Minimum distance for a facet to be visible. A - facet is visible if the distance from the point to - the facet is greater than 'Vn'. - - Without merging, the default value for 'Vn' is the - round-off error ('En'). With merging, the default - value is the pre-merge centrum ('C-n') in 2-d or - 3--d, or three times that in other dimensions. If - the outside width is specified ('Wn'), the maximum, - default value for 'Vn' is 'Wn'. - - Un Maximum distance below a facet for a point to be - coplanar to the facet. The default value is 'Vn'. - - Wn Minimum outside width of the hull. Points are - added to the convex hull only if they are clearly - outside of a facet. A point is outside of a facet - if its distance to the facet is greater than 'Wn'. - The normal value for 'Wn' is 'En'. If the user - specifies pre-merging and does not set 'Wn', than - 'Wn' is set to the premerge 'Cn' and maxco- - ord*(1-An). - - - Additional input/output formats - - Fa Print area for each facet. For Delaunay triangula- - tions, the area is the area of the triangle. For - Voronoi diagrams, the area is the area of the dual - facet. Use 'PAn' for printing the n largest - facets, and option 'PFn' for printing facets larger - than 'n'. - - The area for non-simplicial facets is the sum of - the areas for each ridge to the centrum. Vertices - far below the facet's hyperplane are ignored. The - reported area may be significantly less than the - actual area. - - - - -Geometry Center 2003/12/30 7 - - - - - -qhull(1) qhull(1) - - - FA Compute the total area and volume for option 's'. - It is an approximation for non-simplicial facets - (see 'Fa'). - - Fc Print coplanar points for each facet. The output - starts with the number of facets. Then each facet - is printed one per line. Each line is the number - of coplanar points followed by the point ids. - Option 'Qi' includes the interior points. Each - coplanar point (interior point) is assigned to the - facet it is furthest above (resp., least below). - - FC Print centrums for each facet. The output starts - with the dimension followed by the number of - facets. Then each facet centrum is printed, one - per line. - - Fd Read input in cdd format with homogeneous points. - The input starts with comments. The first comment - is reported in the summary. Data starts after a - "begin" line. The next line is the number of - points followed by the dimension+1 and "real" or - "integer". Then the points are listed with a - leading "1" or "1.0". The data ends with an "end" - line. - - For halfspaces ('Fd Hn,n,...'), the input format is - the same. Each halfspace starts with its offset. - The sign of the offset is the opposite of Qhull's - convention. - - FD Print normals ('n', 'Fo', 'Fi') or points ('p') in - cdd format. The first line is the command line - that invoked Qhull. Data starts with a "begin" - line. The next line is the number of normals or - points followed by the dimension+1 and "real". - Then the normals or points are listed with the - offset before the coefficients. The offset for - points is 1.0. The offset for normals has the - opposite sign. The data ends with an "end" line. - - FF Print facets (as in 'f') without printing the - ridges. - - Fi Print inner planes for each facet. The inner plane - is below all vertices. - - Fi Print separating hyperplanes for bounded, inner - regions of the Voronoi diagram. The first line is - the number of ridges. Then each hyperplane is - printed, one per line. A line starts with the num- - ber of indices and floats. The first pair lists - adjacent input sites, the next d floats are the - normalized coefficients for the hyperplane, and the - - - -Geometry Center 2003/12/30 8 - - - - - -qhull(1) qhull(1) - - - last float is the offset. The hyperplane is ori- - ented toward verify that the hyperplanes are per- - pendicular bisectors. Use 'Fo' for unbounded - regions, and 'Fv' for the corresponding Voronoi - vertices. - - FI Print facet identifiers. - - Fm Print number of merges for each facet. At most 511 - merges are reported for a facet. See 'PMn' for - printing the facets with the most merges. - - FM Output the hull in Maple format. See 'm' - - Fn Print neighbors for each facet. The output starts - with the number of facets. Then each facet is - printed one per line. Each line is the number of - neighbors followed by an index for each neighbor. - The indices match the other facet output formats. - - A negative index indicates an unprinted facet due - to printing only good facets ('Pg'). It is the - negation of the facet's id (option 'FI'). For - example, negative indices are used for facets "at - infinity" in the Delaunay triangulation. - - FN Print vertex neighbors or coplanar facet for each - point. The first line is the number of points. - Then each point is printed, one per line. If the - point is coplanar, the line is "1" followed by the - facet's id. If the point is not a selected vertex, - the line is "0". Otherwise, each line is the num- - ber of neighbors followed by the corresponding - facet indices (see 'Fn'). - - Fo Print outer planes for each facet in the same for- - mat as 'n'. The outer plane is above all points. - - Fo Print separating hyperplanes for unbounded, outer - regions of the Voronoi diagram. The first line is - the number of ridges. Then each hyperplane is - printed, one per line. A line starts with the num- - ber of indices and floats. The first pair lists - adjacent input sites, the next d floats are the - normalized coefficients for the hyperplane, and the - last float is the offset. The hyperplane is ori- - ented toward verify that the hyperplanes are per- - pendicular bisectors. Use 'Fi' for bounded - regions, and 'Fv' for the corresponding Voronoi - vertices. - - FO List all options to stderr, including the default - values. Additional 'FO's are printed to stdout. - - Fp Print points for halfspace intersections (option - 'Hn,n,...'). Each intersection corresponds to a - - - -Geometry Center 2003/12/30 9 - - - -qhull(1) qhull(1) - - - facet of the dual polytope. The "infinity" point - [-10.101,-10.101,...] indicates an unbounded - intersection. - - FP For each coplanar point ('Qc') print the point id - of the nearest vertex, the point id, the facet id, - and the distance. - - FQ Print command used for qhull and input. - - Fs Print a summary. The first line consists of the - number of integers ("7"), followed by the dimen- - sion, the number of points, the number of vertices, - the number of facets, the number of vertices - selected for output, the number of facets selected - for output, the number of coplanar points selected - for output. - - The second line consists of the number of reals - ("2"), followed by the maxmimum offset to an outer - plane and and minimum offset to an inner plane. - Roundoff is included. Later versions of Qhull may - produce additional integers or reals. - - FS Print the size of the hull. The first line con- - sists of the number of integers ("0"). The second - line consists of the number of reals ("2"), fol- - lowed by the total facet area, and the total vol- - ume. Later versions of Qhull may produce addi- - tional integers or reals. - - The total volume measures the volume of the inter- - section of the halfspaces defined by each facet. - Both area and volume are approximations for non- - simplicial facets. See option 'Fa'. - - Ft Print a triangulation with added points for non- - simplicial facets. The first line is the dimension - and the second line is the number of points and the - number of facets. The points follow, one per line, - then the facets follow as a list of point indices. - With option points include the point-at-infinity. - - Fv Print vertices for each facet. The first line is - the number of facets. Then each facet is printed, - one per line. Each line is the number of vertices - followed by the corresponding point ids. Vertices - are listed in the order they were added to the hull - (the last one is first). - - Fv Print all ridges of a Voronoi diagram. The first - line is the number of ridges. Then each ridge is - printed, one per line. A line starts with the num- - ber of indices. The first pair lists adjacent - - - -Geometry Center 2003/12/30 10 - - - - - -qhull(1) qhull(1) - - - input sites, the remaining indices list Voronoi - vertices. Vertex '0' indicates the vertex-at- - infinity (i.e., an unbounded ray). In 3-d, the - vertices are listed in order. See 'Fi' and 'Fo' - for separating hyperplanes. - - FV Print average vertex. The average vertex is a fea- - sible point for halfspace intersection. - - Fx List extreme points (vertices) of the convex hull. - The first line is the number of points. The other - lines give the indices of the corresponding points. - The first point is '0'. In 2-d, the points occur - in counter-clockwise order; otherwise they occur in - input order. For Delaunay triangulations, 'Fx' - lists the extreme points of the input sites. The - points are unordered. - - - Geomview options - - G Produce a file for viewing with Geomview. Without - other options, Qhull displays edges in 2-d, outer - planes in 3-d, and ridges in 4-d. A ridge can be - explicit or implicit. An explicit ridge is a dim-1 - dimensional simplex between two facets. In 4-d, - the explicit ridges are triangles. When displaying - a ridge in 4-d, Qhull projects the ridge's vertices - to one of its facets' hyperplanes. Use 'Gh' to - project ridges to the intersection of both hyper- - planes. - - Ga Display all input points as dots. - - Gc Display the centrum for each facet in 3-d. The - centrum is defined by a green radius sitting on a - blue plane. The plane corresponds to the facet's - hyperplane. The radius is defined by 'C-n' or - 'Cn'. - - GDn Drop dimension n in 3-d or 4-d. The result is a - 2-d or 3-d object. - - Gh Display hyperplane intersections in 3-d and 4-d. - In 3-d, the intersection is a black line. It lies - on two neighboring hyperplanes (c.f., the blue - squares associated with centrums ('Gc')). In 4-d, - the ridges are projected to the intersection of - both hyperplanes. - - Gi Display inner planes in 2-d and 3-d. The inner - plane of a facet is below all of its vertices. It - is parallel to the facet's hyperplane. The inner - plane's color is the opposite (1-r,1-g,1-b) of the - - - -Geometry Center 2003/12/30 11 - - - - - -qhull(1) qhull(1) - - - outer plane. Its edges are determined by the ver- - tices. - - Gn Do not display inner or outer planes. By default, - Geomview displays the precise plane (no merging) or - both inner and output planes (merging). Under - merging, Geomview does not display the inner plane - if the the difference between inner and outer is - too small. - - Go Display outer planes in 2-d and 3-d. The outer - plane of a facet is above all input points. It is - parallel to the facet's hyperplane. Its color is - determined by the facet's normal, and its edges are - determined by the vertices. - - Gp Display coplanar points and vertices as radii. A - radius defines a ball which corresponds to the - imprecision of the point. The imprecision is the - maximum of the roundoff error, the centrum radius, - and maxcoord * (1-An). It is at least 1/20'th of - the maximum coordinate, and ignores post-merging if - pre-merging is done. - - Gr Display ridges in 3-d. A ridge connects the two - vertices that are shared by neighboring facets. - Ridges are always displayed in 4-d. - - Gt A 3-d Delaunay triangulation looks like a convex - hull with interior facets. Option 'Gt' removes the - outside ridges to reveal the outermost facets. It - automatically sets options 'Gr' and 'GDn'. - - Gv Display vertices as spheres. The radius of the - sphere corresponds to the imprecision of the data. - See 'Gp' for determining the radius. - - - Print options - - PAn Only the n largest facets are marked good for - printing. Unless 'PG' is set, 'Pg' is automati- - cally set. - - Pdk:n Drop facet from output if normal[k] <= n. The - option 'Pdk' uses the default value of 0 for n. - - PDk:n Drop facet from output if normal[k] >= n. The - option 'PDk' uses the default value of 0 for n. - - PFn Only facets with area at least 'n' are marked good - for printing. Unless 'PG' is set, 'Pg' is automat- - ically set. - - - - -Geometry Center 2003/12/30 12 - - - - - -qhull(1) qhull(1) - - - Pg Print only good facets. A good facet is either - visible from a point (the 'QGn' option) or includes - a point (the 'QVn' option). It also meets the - requirements of 'Pdk' and 'PDk' options. Option - 'Pg' is automatically set for options 'PAn' and - 'PFn'. - - PG Print neighbors of good facets. - - PMn Only the n facets with the most merges are marked - good for printing. Unless 'PG' is set, 'Pg' is - automatically set. - - Po Force output despite precision problems. Verify ('Tv') does not check - coplanar points. Flipped facets are reported and - concave facets are counted. If 'Po' is used, - points are not partitioned into flipped facets and - a flipped facet is always visible to a point. - Also, if an error occurs before the completion of - Qhull and tracing is not active, 'Po' outputs a - neighborhood of the erroneous facets (if any). - - Pp Do not report precision problems. - - - Qhull control options - - Qbk:0Bk:0 - Drop dimension k from the input points. This - allows the user to take convex hulls of sub-dimen- - sional objects. It happens before the Delaunay and - Voronoi transformation. - - QbB Scale the input points to fit the unit cube. After - scaling, the lower bound will be -0.5 and the upper - bound +0.5 in all dimensions. For Delaunay and - Voronoi diagrams, scaling happens after projection - to the paraboloid. Under precise arithmetic, scal- - ing does not change the topology of the convex - hull. - - Qbb Scale the last coordinate to [0, m] where m is the - maximum absolute value of the other coordinates. - For Delaunay and Voronoi diagrams, scaling happens - after projection to the paraboloid. It reduces - roundoff error for inputs with integer coordinates. - Under precise arithmetic, scaling does not change - the topology of the convex hull. - - Qbk:n Scale the k'th coordinate of the input points. - After scaling, the lower bound of the input points - will be n. 'Qbk' scales to -0.5. - - - -Geometry Center 2003/12/30 13 - - - - - -qhull(1) qhull(1) - - - QBk:n Scale the k'th coordinate of the input points. - After scaling, the upper bound will be n. 'QBk' - scales to +0.5. - - Qc Keep coplanar points with the nearest facet. Out- - put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' - will print the points. - - Qf Partition points to the furthest outside facet. - - Qg Only build good facets. With the 'Qg' option, - Qhull will only build those facets that it needs to - determine the good facets in the output. See - 'QGn', 'QVn', and 'PdD' for defining good facets, - and 'Pg' and 'PG' for printing good facets and - their neighbors. - - QGn A facet is good (see 'Qg' and 'Pg') if it is visi- - ble from point n. If n < 0, a facet is good if it - is not visible from point n. Point n is not added - to the hull (unless 'TCn' or 'TPn'). With rbox, - use the 'Pn,m,r' option to define your point; it - will be point 0 (QG0). - - Qi Keep interior points with the nearest facet. Out- - put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' - will print the points. - - QJn Joggle each input coordinate by adding a random - number in [-n,n]. If a precision error occurs, - then qhull increases n and tries again. It does - not increase n beyond a certain value, and it stops - after a certain number of attempts [see user.h]. - Option 'QJ' selects a default value for n. The - output will be simplicial. For Delaunay triangula- - tions, 'QJn' sets 'Qbb' to scale the last coordi- - nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is - deprecated for Voronoi diagrams. See also 'Qt'. - - Qm Only process points that would otherwise increase - max_outside. Other points are treated as coplanar - or interior points. - - Qr Process random outside points instead of furthest - ones. This makes Qhull equivalent to the random- - ized incremental algorithms. CPU time is not - reported since the randomization is inefficient. - - QRn Randomly rotate the input points. If n=0, use time - as the random number seed. If n>0, use n as the - random number seed. If n=-1, don't rotate but use - time as the random number seed. For Delaunay tri- - angulations ('d' and 'v'), rotate about the last - axis. - - - - -Geometry Center 2003/12/30 14 - - - - - -qhull(1) qhull(1) - - - Qs Search all points for the initial simplex. - - Qt Triangulated output. Triangulate non-simplicial - facets. 'Qt' is deprecated for Voronoi diagrams. - See also 'QJn' - - Qv Test vertex neighbors for convexity after post- - merging. To use the 'Qv' option, you also need to - set a merge option (e.g., 'Qx' or 'C-0'). - - QVn A good facet (see 'Qg' and 'Pg') includes point n. - If n<0, then a good facet does not include point n. - The point is either in the initial simplex or it is - the first point added to the hull. Option 'QVn' - may not be used with merging. - - Qx Perform exact merges while building the hull. The - "exact" merges are merging a point into a coplanar - facet (defined by 'Vn', 'Un', and 'C-n'), merging - concave facets, merging duplicate ridges, and merg- - ing flipped facets. Coplanar merges and angle - coplanar merges ('A-n') are not performed. Concav- - ity testing is delayed until a merge occurs. - - After the hull is built, all coplanar merges are - performed (defined by 'C-n' and 'A-n'), then post- - merges are performed (defined by 'Cn' and 'An'). - - Qz Add a point "at infinity" that is above the - paraboloid for Delaunay triangulations and Voronoi - diagrams. This reduces precision problems and - allows the triangulation of cospherical points. - - - Qhull experiments and speedups - - Q0 Turn off pre-merging as a default option. With - 'Q0'/'Qx' and without explicit pre-merge options, - Qhull ignores precision issues while constructing - the convex hull. This may lead to precision - errors. If so, a descriptive warning is generated. - - Q1 With 'Q1', Qhull sorts merges by type (coplanar, - angle coplanar, concave) instead of by angle. - - Q2 With 'Q2', Qhull merges all facets at once instead - of using independent sets of merges and then - retesting. - - Q3 With 'Q3', Qhull does not remove redundant ver- - tices. - - Q4 With 'Q4', Qhull avoids merges of an old facet into - a new facet. - - Q5 With 'Q5', Qhull does not correct outer planes at - the end. The maximum outer plane is used instead. - - - - -Geometry Center 2003/12/30 15 - - - - - -qhull(1) qhull(1) - - - Q6 With 'Q6', Qhull does not pre-merge concave or - coplanar facets. - - Q7 With 'Q7', Qhull processes facets in depth-first - order instead of breadth-first order. - - Q8 With 'Q8' and merging, Qhull does not retain near- - interior points for adjusting outer planes. 'Qc' - will probably retain all points that adjust outer - planes. - - Q9 With 'Q9', Qhull processes the furthest of all out- - side sets at each iteration. - - Q10 With 'Q10', Qhull does not use special processing - for narrow distributions. - - Q11 With 'Q11', Qhull copies normals and recomputes - centrums for tricoplanar facets. - - Q12 With 'Q12', Qhull does not report a very wide merge due - to a duplicated ridge with nearly coincident vertices - - Trace options - - Tn Trace at level n. Qhull includes full execution - tracing. 'T-1' traces events. 'T1' traces the - overall execution of the program. 'T2' and 'T3' - trace overall execution and geometric and topologi- - cal events. 'T4' traces the algorithm. 'T5' - includes information about memory allocation and - Gaussian elimination. - - Ta Annotate output with codes that identify the - corresponding qh_fprintf() statement. - - Tc Check frequently during execution. This will catch - most inconsistency errors. - - TCn Stop Qhull after building the cone of new facets - for point n. The output for 'f' includes the cone - and the old hull. See also 'TVn'. - - TFn Report progress whenever more than n facets are - created During post-merging, 'TFn' reports progress - after more than n/2 merges. - - TI file - Input data from 'file'. The filename may not include - spaces or quotes. - - TO file - Output results to 'file'. The name may be enclosed - in single quotes. - - TPn Turn on tracing when point n is added to the hull. - Trace partitions of point n. If used with TWn, turn off - tracing after adding point n to the hull. - - TRn Rerun qhull n times. Usually used with 'QJn' to - determine the probability that a given joggle will - fail. - - Ts Collect statistics and print to stderr at the end - of execution. - - Tv Verify the convex hull. This checks the topologi- - cal structure, facet convexity, and point inclu- - sion. If precision problems occurred, facet con- - vexity is tested whether or not 'Tv' is selected. - Option 'Tv' does not check point inclusion if - - - -Geometry Center 2003/12/30 16 - - - - - -qhull(1) qhull(1) - - - forcing output with 'Po', or if 'Q5' is set. - - For point inclusion testing, Qhull verifies that - all points are below all outer planes (facet->max- - outside). Point inclusion is exhaustive if merging - or if the facet-point product is small enough; oth- - erwise Qhull verifies each point with a directed - search (qh_findbest). - - Point inclusion testing occurs after producing out- - put. It prints a message to stderr unless option - 'Pp' is used. This allows the user to interrupt - Qhull without changing the output. - - TVn Stop Qhull after adding point n. If n < 0, stop - Qhull before adding point n. Output shows the hull - at this time. See also 'TCn' - - TMn Turn on tracing at n'th merge. - - TWn Trace merge facets when the width is greater than - n. - - Tz Redirect stderr to stdout. - - -BUGS - Please report bugs to Brad Barber at - qhull_bug@qhull.org. - - If Qhull does not compile, it is due to an incompatibility - between your system and ours. The first thing to check is - that your compiler is ANSI standard. If it is, check the - man page for the best options, or find someone to help - you. If you locate the cause of your problem, please send - email since it might help others. - - If Qhull compiles but crashes on the test case (rbox D4), - there's still incompatibility between your system and - ours. Typically it's been due to mem.c and memory align- - ment. You can use qh_NOmem in mem.h to turn off memory - management. Please let us know if you figure out how to - fix these problems. - - If you do find a problem, try to simplify it before - reporting the error. Try different size inputs to locate - the smallest one that causes an error. You're welcome to - hunt through the code using the execution trace as a - guide. This is especially true if you're incorporating - Qhull into your own program. - - When you do report an error, please attach a data set to - the end of your message. This allows us to see the error - for ourselves. Qhull is maintained part-time. - - - -Geometry Center 2003/12/30 17 - - - - - -qhull(1) qhull(1) - - -E-MAIL - Please send correspondence to qhull@qhull.org and - report bugs to qhull_bug@qhull.org. Let us know how - you use Qhull. If you mention it in a paper, please send - the reference and an abstract. - - If you would like to get Qhull announcements (e.g., a new - version) and news (any bugs that get fixed, etc.), let us - know and we will add you to our mailing list. If you - would like to communicate with other Qhull users, we will - add you to the qhull_users alias. For Internet news about - geometric algorithms and convex hulls, look at comp.graph- - ics.algorithms and sci.math.num-analysis - - -SEE ALSO - rbox(1) - - Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The - Quickhull Algorithm for Convex Hulls," ACM Trans. on Math- - ematical Software, 22(4):469-483, Dec. 1996. - http://portal.acm.org/citation.cfm?doid=235815.235821 - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 - - - Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results - on randomized incremental construction," Computational - Geometry: Theory and Applications, vol. 3, p. 185-211, - 1993. - - Preparata, F. and M. Shamos, Computational Geometry, - Springer-Verlag, New York, 1985. - - - -AUTHORS - C. Bradford Barber Hannu Huhdanpaa - bradb@shore.net hannu@qhull.org - - - -ACKNOWLEDGEMENTS - A special thanks to Albert Marden, Victor Milenkovic, the - Geometry Center, Harvard University, and Endocardial Solu- - tions, Inc. for supporting this work. - - Qhull 1.0 and 2.0 were developed under National Science Foundation - grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. David Dobkin - - - -Geometry Center 2003/12/30 18 - - - - - -qhull(1) qhull(1) - - - guided the original work at Princeton University. If you find it - useful, please let us know. - - The Geometry Center was supported by grant DMS-8920161 from the National - Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department - of Energy, by the University of Minnesota, and by Minnesota Technology, Inc. - - Qhull is available from http://www.qhull.org - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Geometry Center 2003/12/30 19 - - diff --git a/src/qhull/html/qvoron_f.htm b/src/qhull/html/qvoron_f.htm deleted file mode 100644 index db538b5ab..000000000 --- a/src/qhull/html/qvoron_f.htm +++ /dev/null @@ -1,396 +0,0 @@ - - - - -qvoronoi Qu -- furthest-site Voronoi diagram - - - - -Up: -Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -
    - -

    [delaunay]qvoronoi Qu -- furthest-site Voronoi diagram

    - -

    The furthest-site Voronoi diagram is the furthest-neighbor map for a set of -points. Each region contains those points that are further -from one input site than any other input site. See the -survey article by Aurenhammer ['91] -and the brief introduction by O'Rourke ['94]. The furthest-site Voronoi diagram is the dual of the furthest-site Delaunay triangulation. -

    - -
    -
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    Example: rbox 10 D2 | qvoronoi Qu s - o TO - result
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    Compute the 2-d, furthest-site Voronoi diagram of 10 - random points. Write a summary to the console and the Voronoi - regions and vertices to 'result'. The first vertex of the - result indicates unbounded regions. Almost all regions - are unbounded.
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    - -
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    Example: rbox r y c G1 D2 | qvoronoi Qu - s - Fn TO - result
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    Compute the 2-d furthest-site Voronoi diagram of a square - and a small triangle. Write a summary to the console and the Voronoi - vertices for each input site to 'result'. - The origin is the only furthest-site Voronoi vertex. The - negative indices indicate vertices-at-infinity.
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    - -

    -Qhull computes the furthest-site Voronoi diagram via the -furthest-site Delaunay triangulation. -Each furthest-site Voronoi vertex is the circumcenter of an upper -facet of the Delaunay triangulation. Each furthest-site Voronoi -region corresponds to a vertex of the Delaunay triangulation -(i.e., an input site).

    - -

    See Qhull FAQ - Delaunay and -Voronoi diagram questions.

    - -

    The 'qvonoroi' program is equivalent to -'qhull v Qbb' in 2-d to 3-d, and -'qhull v Qbb Qx' -in 4-d and higher. It disables the following Qhull -options: d n m v H U Qb -QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Gt Q0,etc. - - -

    Copyright © 1995-2015 C.B. Barber

    - -
    -

    »furthest-site qvoronoi synopsis

    -
    - -See qvoronoi synopsis. The same -program is used for both constructions. Use option 'Qu' -for furthest-site Voronoi diagrams. - - -
    -

    »furthest-site qvoronoi -input

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    The input data on stdin consists of:

    -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qvoronoi Qu < data.txt), a pipe (e.g., rbox 10 | qvoronoi Qu), -or the 'TI' option (e.g., qvoronoi TI data.txt Qu). - -

    For example, this is a square containing four random points. -Its furthest-site Voronoi diagram has on vertex and four unbounded, -separating hyperplanes (i.e., the coordinate axes) -

    -

    -rbox c 4 D2 > data -
    -2 RBOX c 4 D2
-8
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
-  -0.5   -0.5
-  -0.5    0.5
-   0.5   -0.5
-   0.5    0.5
-
    - -

    qvoronoi Qu s Fo < data -

    -
-Furthest-site Voronoi vertices by the convex hull of 8 points in 3-d:
-
-  Number of Voronoi regions: 8
-  Number of Voronoi vertices: 1
-  Number of non-simplicial Voronoi vertices: 1
-
-Statistics for: RBOX c 4 D2 | QVORONOI Qu s Fo
-
-  Number of points processed: 8
-  Number of hyperplanes created: 20
-  Number of facets in hull: 11
-  Number of distance tests for qhull: 34
-  Number of merged facets: 1
-  Number of distance tests for merging: 107
-  CPU seconds to compute hull (after input):  0
-
-4
-5 4 5      0      1      0
-5 4 6      1      0      0
-5 5 7      1      0      0
-5 6 7      0      1      0
-
    -
    - -
    -

    » furthest-site qvoronoi -outputs

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    - -

    These options control the output of furthest-site Voronoi diagrams.

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    - -
    -
     
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    furthest-site Voronoi vertices
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    p
    -
    print the coordinates of the furthest-site Voronoi vertices. The first line - is the dimension. The second line is the number of vertices. Each - remaining line is a furthest-site Voronoi vertex. The points-in-square example - has one furthest-site Voronoi vertex at the origin.
    -
    Fn
    -
    list the neighboring furthest-site Voronoi vertices for each furthest-site Voronoi - vertex. The first line is the number of Voronoi vertices. Each - remaining line starts with the number of neighboring vertices. Negative indices (e.g., -1) indicate vertices - outside of the Voronoi diagram. In the points-in-square example, the - Voronoi vertex at the origin has four neighbors-at-infinity.
    -
    FN
    -
    list the furthest-site Voronoi vertices for each furthest-site Voronoi region. The first line is - the number of Voronoi regions. Each remaining line starts with the - number of Voronoi vertices. Negative indices (e.g., -1) indicate vertices - outside of the Voronoi diagram. - In the points-in-square example, all regions share the Voronoi vertex - at the origin.
    - -
     
    -
     
    -
    furthest-site Voronoi regions
    -
    o
    -
    print the furthest-site Voronoi regions in OFF format. The first line is the - dimension. The second line is the number of vertices, the number - of input sites, and "1". The third line represents the vertex-at-infinity. - Its coordinates are "-10.101". The next lines are the coordinates - of the furthest-site Voronoi vertices. Each remaining line starts with the number - of Voronoi vertices in a Voronoi region. In 2-d, the vertices are -listed in adjacency order (unoriented). In 3-d and higher, the -vertices are listed in numeric order. In the points-in-square - example, each unbounded region includes the Voronoi vertex at - the origin. Lines consisting of 0 indicate - interior input sites.
    -
    Fi
    -
    print separating hyperplanes for inner, bounded furthest-site Voronoi - regions. The first number is the number of separating - hyperplanes. Each remaining line starts with 3+dim. The - next two numbers are adjacent input sites. The next dim - numbers are the coefficients of the separating hyperplane. The - last number is its offset. The are no bounded, separating hyperplanes - for the points-in-square example.
    -
    Fo
    -
    print separating hyperplanes for outer, unbounded furthest-site Voronoi - regions. The first number is the number of separating - hyperplanes. Each remaining line starts with 3+dim. The - next two numbers are adjacent input sites on the convex hull. The - next dim - numbers are the coefficients of the separating hyperplane. The - last number is its offset. The points-in-square example has four - unbounded, separating hyperplanes.
    -
     
    -
     
    -
    Input sites
    -
    Fv
    -
    list ridges of furthest-site Voronoi vertices for pairs of input sites. The - first line is the number of ridges. Each remaining line starts with - two plus the number of Voronoi vertices in the ridge. The next - two numbers are two adjacent input sites. The remaining numbers list - the Voronoi vertices. As with option 'o', a 0 indicates - the vertex-at-infinity - and an unbounded, separating hyperplane. - The perpendicular bisector (separating hyperplane) - of the input sites is a flat through these vertices. - In the points-in-square example, the ridge for each edge of the square - is unbounded.
    -
     
    -
     
    -
    General
    -
    s
    -
    print summary of the furthest-site Voronoi diagram. Use 'Fs' for numeric data.
    -
    i
    -
    list input sites for each furthest-site Delaunay region. Use option 'Pp' - to avoid the warning. The first line is the number of regions. The - remaining lines list the input sites for each region. The regions are - oriented. In the points-in-square example, the square region has four - input sites. In 3-d and higher, report cospherical sites by adding extra points. -
    -
    G
    -
    Geomview output for 2-d furthest-site Voronoi diagrams.
    -
    -
    - -
    -

    » furthest-site qvoronoi -controls

    -
    - -

    These options provide additional control:

    -
    - -
    -
    Qu
    -
    must be used.
    -
    QVn
    -
    select furthest-site Voronoi vertices for input site n
    -
    Tv
    -
    verify result
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    TFn
    -
    report progress after constructing n facets
    -
    PDk:1
    -
    include upper and lower facets in the output. Set k - to the last dimension (e.g., 'PD2:1' for 2-d inputs).
    -
    f
    -
    facet dump. Print the data structure for each facet (i.e., - furthest-site Voronoi vertex).
    -
    - -
    -
    -

    » furthest-site qvoronoi -graphics

    -
    -

    In 2-d, Geomview output ('G') -displays a furthest-site Voronoi diagram with extra edges to -close the unbounded furthest-site Voronoi regions. All regions -will be unbounded. Since the points-in-box example has only -one furthest-site Voronoi vertex, the Geomview output is one -point.

    - -

    See the Delaunay and Voronoi -examples for a 2-d example. Turn off normalization (on -Geomview's 'obscure' menu) when comparing the furthest-site -Voronoi diagram with the corresponding Voronoi diagram.

    - -
    -

    »furthest-site qvoronoi -notes

    -
    - -

    See Voronoi notes.

    - -
    -

    »furthest-site qvoronoi conventions

    -
    - -

    The following terminology is used for furthest-site Voronoi -diagrams in Qhull. The underlying structure is a furthest-site -Delaunay triangulation from a convex hull in one higher -dimension. Upper facets of the Delaunay triangulation correspond -to vertices of the furthest-site Voronoi diagram. Vertices of the -furthest-site Delaunay triangulation correspond to input sites. -They also define regions of the furthest-site Voronoi diagram. -All vertices are extreme points of the input sites. See qconvex conventions, furthest-site delaunay -conventions, and Qhull's data structures.

    - -
      -
    • input site - a point in the input (one dimension - lower than a point on the convex hull)
      • -
    • point - a point has d+1 coordinates. The - last coordinate is the sum of the squares of the input - site's coordinates
      • -
    • vertex - a point on the upper facets of the - paraboloid. It corresponds to a unique input site.
      • -
    • furthest-site Delaunay facet - an upper facet of the - paraboloid. The last coefficient of its normal is - clearly positive.
      • -
    • furthest-site Voronoi vertex - the circumcenter - of a furthest-site Delaunay facet
      • -
    • furthest-site Voronoi region - the region of - Euclidean space further from an input site than any other - input site. Qhull lists the furthest-site Voronoi - vertices that define each furthest-site Voronoi region.
      • -
    • furthest-site Voronoi diagram - the graph of the - furthest-site Voronoi regions with the ridges (edges) - between the regions.
      • -
    • infinity vertex - the Voronoi vertex for - unbounded furthest-site Voronoi regions in 'o' output format. Its - coordinates are -10.101.
      • -
    • good facet - an furthest-site Voronoi vertex with - optional restrictions by 'QVn', - etc.
      • -
    - -
    -

    »furthest-site qvoronoi options

    -
    - -See qvoronoi options. The same -program is used for both constructions. Use option 'Qu' -for furthest-site Voronoi diagrams. -
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/qvoronoi.htm b/src/qhull/html/qvoronoi.htm deleted file mode 100644 index 6d81d48c1..000000000 --- a/src/qhull/html/qvoronoi.htm +++ /dev/null @@ -1,667 +0,0 @@ - - - - -qvoronoi -- Voronoi diagram - - - - -Up: -Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -
    - -

    [voronoi]qvoronoi -- Voronoi diagram

    - -

    The Voronoi diagram is the nearest-neighbor map for a set of -points. Each region contains those points that are nearer -one input site than any other input site. It has many useful properties and applications. See the -survey article by Aurenhammer ['91] -and the detailed introduction by O'Rourke ['94]. The Voronoi diagram is the -dual of the Delaunay triangulation.

    - -
    -
    -
    Example: rbox 10 D3 | qvoronoi s - o TO - result
    -
    Compute the 3-d Voronoi diagram of 10 random points. Write a - summary to the console and the Voronoi vertices and - regions to 'result'. The first vertex of the result - indicates unbounded regions.
    - -
     
    -
    Example: rbox r y c G0.1 D2 | qvoronoi - s - o TO - result
    -
    Compute the 2-d Voronoi diagram of a triangle and a small - square. Write a - summary to the console and Voronoi vertices and regions - to 'result'. Report a single Voronoi vertex for - cocircular input sites. The first vertex of the result - indicates unbounded regions. The origin is the Voronoi - vertex for the square.
    - -
     
    -
    Example: rbox r y c G0.1 D2 | qvoronoi Fv - TO result
    -
    Compute the 2-d Voronoi diagram of a triangle and a small - square. Write a - summary to the console and the Voronoi ridges to - 'result'. Each ridge is the perpendicular bisector of a - pair of input sites. Vertex "0" indicates - unbounded ridges. Vertex "8" is the Voronoi - vertex for the square.
    - -
     
    -
    Example: rbox r y c G0.1 D2 | qvoronoi Fi
    -
    Print the bounded, separating hyperplanes for the 2-d Voronoi diagram of a - triangle and a small - square. Note the four hyperplanes (i.e., lines) for Voronoi vertex - "8". It is at the origin. -
    -
    -
    - -

    Qhull computes the Voronoi diagram via the Delaunay -triangulation. Each Voronoi -vertex is the circumcenter of a facet of the Delaunay -triangulation. Each Voronoi region corresponds to a vertex (i.e., input site) of the -Delaunay triangulation.

    - -

    Qhull outputs the Voronoi vertices for each Voronoi region. With -option 'Fv', -it lists all ridges of the Voronoi diagram with the corresponding -pairs of input sites. With -options 'Fi' and 'Fo', -it lists the bounded and unbounded separating hyperplanes. -You can also output a single Voronoi region -for further processing [see graphics].

    - -

    Use option 'Qz' if the input is circular, cospherical, or -nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid. - -

    See Qhull FAQ - Delaunay and -Voronoi diagram questions.

    - -

    The 'qvonoroi' program is equivalent to -'qhull v Qbb' in 2-d to 3-d, and -'qhull v Qbb Qx' -in 4-d and higher. It disables the following Qhull -options: d n v Qbb QbB Qf Qg Qm -Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc. - -

    Copyright © 1995-2015 C.B. Barber

    - -

    Voronoi image by KOOK Architecture, Silvan Oesterle and Michael Knauss. - -

    -

    »qvoronoi synopsis

    - -
    -qvoronoi- compute the Voronoi diagram.
-    input (stdin): dimension, number of points, point coordinates
-    comments start with a non-numeric character
-
-options (qh-voron.htm):
-    Qu   - compute furthest-site Voronoi diagram
-    Tv   - verify result: structure, convexity, and in-circle test
-    .    - concise list of all options
-    -    - one-line description of all options
-
-output options (subset):
-    s    - summary of results (default)
-    p    - Voronoi vertices
-    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)
-    FN   - count and Voronoi vertices for each Voronoi region
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
-    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded
-    G    - Geomview output (2-d only)
-    QVn  - Voronoi vertices for input point n, -n if not
-    TO file- output results to file, may be enclosed in single quotes
-
-examples:
-rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi
-rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv
-rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo
-rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0
-
    - -

    »qvoronoi input

    -
    -The input data on stdin consists of: -
      -
    • dimension -
    • number of points
      • -
    • point coordinates
      • -
    - -

    Use I/O redirection (e.g., qvoronoi < data.txt), a pipe (e.g., rbox 10 | qvoronoi), -or the 'TI' option (e.g., qvoronoi TI data.txt). - -

    For example, this is four cocircular points inside a square. Their Voronoi -diagram has nine vertices and eight regions. Notice the Voronoi vertex -at the origin, and the Voronoi vertices (on each axis) for the four -sides of the square. -

    -

    -rbox s 4 W0 c G1 D2 > data -
    -2 RBOX s 4 W0 c D2
-8
--0.4941988586954018 -0.07594397977563715
--0.06448037284989526 0.4958248496365813
-0.4911154367094632 0.09383830681375946
--0.348353580869097 -0.3586778257652367
-    -1     -1
-    -1      1
-     1     -1
-     1      1
-
    - -

    qvoronoi s p < data -

    -
-Voronoi diagram by the convex hull of 8 points in 3-d:
-
-  Number of Voronoi regions: 8
-  Number of Voronoi vertices: 9
-  Number of non-simplicial Voronoi vertices: 1
-
-Statistics for: RBOX s 4 W0 c D2 | QVORONOI s p
-
-  Number of points processed: 8
-  Number of hyperplanes created: 18
-  Number of facets in hull: 10
-  Number of distance tests for qhull: 33
-  Number of merged facets: 2
-  Number of distance tests for merging: 102
-  CPU seconds to compute hull (after input): 0.094
-
-2
-9
-4.217546450968612e-17 1.735507986399734
--8.402566836762659e-17 -1.364368854147395
-0.3447488772716865 -0.6395484723719818
-1.719446929853986 2.136555906154247e-17
-0.4967882915039657 0.68662371396699
--1.729928876283549 1.343733067524222e-17
--0.8906163241424728 -0.4594150543829102
--0.6656840313875723 0.5003013793414868
--7.318364664277155e-19 -1.188217818408333e-16
-
    -
    - -
    -

    » qvoronoi -outputs

    -
    - -

    These options control the output of Voronoi diagrams.

    -
    - -
    -
     
    -
    Voronoi vertices
    -
    p
    -
    print the coordinates of the Voronoi vertices. The first line - is the dimension. The second line is the number of vertices. Each - remaining line is a Voronoi vertex.
    -
    Fn
    -
    list the neighboring Voronoi vertices for each Voronoi - vertex. The first line is the number of Voronoi vertices. Each - remaining line starts with the number of neighboring vertices. - Negative vertices (e.g., -1) indicate vertices - outside of the Voronoi diagram. - In the circle-in-box example, the - Voronoi vertex at the origin has four neighbors.
    -
    FN
    -
    list the Voronoi vertices for each Voronoi region. The first line is - the number of Voronoi regions. Each remaining line starts with the - number of Voronoi vertices. Negative indices (e.g., -1) indicate vertices - outside of the Voronoi diagram. - In the circle-in-box example, the four bounded regions are defined by four - Voronoi vertices.
    - -
     
    -
     
    -
    Voronoi regions
    -
    o
    -
    print the Voronoi regions in OFF format. The first line is the - dimension. The second line is the number of vertices, the number - of input sites, and "1". The third line represents the vertex-at-infinity. - Its coordinates are "-10.101". The next lines are the coordinates - of the Voronoi vertices. Each remaining line starts with the number - of Voronoi vertices in a Voronoi region. In 2-d, the vertices are -listed in adjacency order (unoriented). In 3-d and higher, the -vertices are listed in numeric order. In the circle-in-square - example, each bounded region includes the Voronoi vertex at - the origin. Lines consisting of 0 indicate - coplanar input sites or 'Qz'.
    -
    Fi
    -
    print separating hyperplanes for inner, bounded Voronoi - regions. The first number is the number of separating - hyperplanes. Each remaining line starts with 3+dim. The - next two numbers are adjacent input sites. The next dim - numbers are the coefficients of the separating hyperplane. The - last number is its offset. Use 'Tv' to verify that the -hyperplanes are perpendicular bisectors. It will list relevant -statistics to stderr.
    -
    Fo
    -
    print separating hyperplanes for outer, unbounded Voronoi - regions. The first number is the number of separating - hyperplanes. Each remaining line starts with 3+dim. The - next two numbers are adjacent input sites on the convex hull. The - next dim - numbers are the coefficients of the separating hyperplane. The - last number is its offset. Use 'Tv' to verify that the -hyperplanes are perpendicular bisectors. It will list relevant -statistics to stderr,
    -
     
    -
     
    -
    Input sites
    -
    Fv
    -
    list ridges of Voronoi vertices for pairs of input sites. The - first line is the number of ridges. Each remaining line starts with - two plus the number of Voronoi vertices in the ridge. The next - two numbers are two adjacent input sites. The remaining numbers list - the Voronoi vertices. As with option 'o', a 0 indicates - the vertex-at-infinity - and an unbounded, separating hyperplane. - The perpendicular bisector (separating hyperplane) - of the input sites is a flat through these vertices. - In the circle-in-square example, the ridge for each edge of the square - is unbounded.
    -
    Fc
    -
    list coincident input sites for each Voronoi vertex. - The first line is the number of vertices. The remaining lines start with - the number of coincident sites and deleted vertices. Deleted vertices - indicate highly degenerate input (see'Fs'). - A coincident site is assigned to one Voronoi - vertex. Do not use 'QJ' with 'Fc'; the joggle will separate - coincident sites.
    -
    FP
    -
    print coincident input sites with distance to - nearest site (i.e., vertex). The first line is the - number of coincident sites. Each remaining line starts with the point ID of - an input site, followed by the point ID of a coincident point, its vertex, and distance. - Includes deleted vertices which - indicate highly degenerate input (see'Fs'). - Do not use 'QJ' with 'FP'; the joggle will separate - coincident sites.
    -
     
    -
     
    -
    General
    -
    s
    -
    print summary of the Voronoi diagram. Use 'Fs' for numeric data.
    -
    i
    -
    list input sites for each Delaunay region. Use option 'Pp' - to avoid the warning. The first line is the number of regions. The - remaining lines list the input sites for each region. The regions are - oriented. In the circle-in-square example, the cocircular region has four - edges. In 3-d and higher, report cospherical sites by adding extra points. -
    -
    G
    -
    Geomview output for 2-d Voronoi diagrams.
    -
    -
    -
    -

    » qvoronoi -controls

    -
    - -

    These options provide additional control:

    -
    - -
    -
    Qu
    -
    compute the furthest-site Voronoi diagram.
    -
    QVn
    -
    select Voronoi vertices for input site n
    -
    Qz
    -
    add a point above the paraboloid to reduce precision - errors. Use it for nearly cocircular/cospherical input - (e.g., 'rbox c | qvoronoi Qz').
    -
    Tv
    -
    verify result
    -
    TI file
    -
    input data from file. The filename may not use spaces or quotes.
    -
    TO file
    -
    output results to file. Use single quotes if the filename - contains spaces (e.g., TO 'file with spaces.txt'
    -
    TFn
    -
    report progress after constructing n facets
    -
    PDk:1
    -
    include upper and lower facets in the output. Set k - to the last dimension (e.g., 'PD2:1' for 2-d inputs).
    -
    f
    -
    facet dump. Print the data structure for each facet (i.e., - Voronoi vertex).
    -
    - -
    -
    -

    » qvoronoi -graphics

    -
    - -

    In 2-d, Geomview output ('G') -displays a Voronoi diagram with extra edges to close the -unbounded Voronoi regions. To view the unbounded rays, enclose -the input points in a square.

    - -

    You can also view individual Voronoi regions in 3-d. To -view the Voronoi region for site 3 in Geomview, execute

    - -
    -

    qvoronoi <data QV3 p | qconvex s G >output

    -
    - -

    The qvoronoi command returns the Voronoi vertices -for input site 3. The qconvex command computes their convex hull. -This is the Voronoi region for input site 3. Its -hyperplane normals (qconvex 'n') are the same as the separating hyperplanes -from options 'Fi' -and 'Fo' (up to roundoff error). - -

    See the Delaunay and Voronoi -examples for 2-d and 3-d examples. Turn off normalization (on -Geomview's 'obscure' menu) when comparing the Voronoi diagram -with the corresponding Delaunay triangulation.

    - -
    -

    »qvoronoi -notes

    -
    - -

    You can simplify the Voronoi diagram by enclosing the input -sites in a large square or cube. This is particularly recommended -for cocircular or cospherical input data.

    - -

    See Voronoi graphics for computing -the convex hull of a Voronoi region.

    - -

    Voronoi diagrams do not include facets that are -coplanar with the convex hull of the input sites. A facet is -coplanar if the last coefficient of its normal is -nearly zero (see qh_ZEROdelaunay). - -

    Unbounded regions can be confusing. For example, 'rbox c | -qvoronoi Qz o' produces the Voronoi regions for the vertices -of a cube centered at the origin. All regions are unbounded. The -output is

    - -
    - 
    3
-2 9 1
--10.101 -10.101 -10.101
-     0      0      0
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-0
-
    -
    - -

    The first line is the dimension. The second line is the number -of vertices and the number of regions. There is one region per -input point plus a region for the point-at-infinity added by -option 'Qz'. The next two lines -lists the Voronoi vertices. The first vertex is the infinity -vertex. It is indicate by the coordinates -10.101. The -second vertex is the origin. The next nine lines list the -regions. Each region lists two vertices -- the infinity vertex -and the origin. The last line is "0" because no region -is associated with the point-at-infinity. A "0" would -also be listed for nearly incident input sites.

    - -

    To use option 'Fv', add an -interior point. For example,

    - -
    - 
    -rbox c P0 | qvoronoi Fv
-20
-5 0 7 1 3 5
-5 0 3 1 4 5
-5 0 5 1 2 3
-5 0 1 1 2 4
-5 0 6 2 3 6
-5 0 2 2 4 6
-5 0 4 4 5 6
-5 0 8 5 3 6
-5 1 2 0 2 4
-5 1 3 0 1 4
-5 1 5 0 1 2
-5 2 4 0 4 6
-5 2 6 0 2 6
-5 3 4 0 4 5
-5 3 7 0 1 5
-5 4 8 0 6 5
-5 5 6 0 2 3
-5 5 7 0 1 3
-5 6 8 0 6 3
-5 7 8 0 3 5
-
    -
    - -

    The output consists of 20 ridges and each ridge lists a pair -of input sites and a triplet of Voronoi vertices. The first eight -ridges connect the origin ('P0'). The remainder list the edges of -the cube. Each edge generates an unbounded ray through the -midpoint. The corresponding separating planes ('Fo') follow each -pair of coordinate axes.

    - -

    Options 'Qt' (triangulated output) -and 'QJ' (joggled input) are deprecated. They may produce -unexpected results. If you use these options, cocircular and cospherical input sites will -produce duplicate or nearly duplicate Voronoi vertices. See also Merged facets or joggled input.

    - -
    -

    »qvoronoi conventions

    -
    - -

    The following terminology is used for Voronoi diagrams in -Qhull. The underlying structure is a Delaunay triangulation from -a convex hull in one higher dimension. Facets of the Delaunay -triangulation correspond to vertices of the Voronoi diagram. -Vertices of the Delaunay triangulation correspond to input sites. -They also correspond to regions of the Voronoi diagram. See convex hull conventions, Delaunay conventions, and -Qhull's data structures.

    -
    - -
      -
    • input site - a point in the input (one dimension - lower than a point on the convex hull)
      • -
    • point - a point has d+1 coordinates. The - last coordinate is the sum of the squares of the input - site's coordinates
      • -
    • coplanar point - a nearly incident - input site
      • -
    • vertex - a point on the paraboloid. It - corresponds to a unique input site.
      • -
    • point-at-infinity - a point added above the - paraboloid by option 'Qz'
      • -
    • Delaunay facet - a lower facet of the - paraboloid. The last coefficient of its normal is - clearly negative.
      • -
    • Voronoi vertex - the circumcenter of a Delaunay - facet
      • -
    • Voronoi region - the Voronoi vertices for an - input site. The region of Euclidean space nearest to an - input site.
      • -
    • Voronoi diagram - the graph of the Voronoi - regions. It includes the ridges (i.e., edges) between the - regions.
      • -
    • vertex-at-infinity - the Voronoi vertex that - indicates unbounded Voronoi regions in 'o' output format. Its - coordinates are -10.101.
      • -
    • good facet - a Voronoi vertex with optional - restrictions by 'QVn', etc.
      • -
    - -
    -
    -

    »qvoronoi options

    - -
    -qvoronoi- compute the Voronoi diagram
-    http://www.qhull.org
-
-input (stdin):
-    first lines: dimension and number of points (or vice-versa).
-    other lines: point coordinates, best if one point per line
-    comments:    start with a non-numeric character
-
-options:
-    Qu   - compute furthest-site Voronoi diagram
-
-Qhull control options:
-    QJn  - randomly joggle input in range [-n,n]
-    Qs   - search all points for the initial simplex
-    Qz   - add point-at-infinity to Voronoi diagram
-    QGn  - Voronoi vertices if visible from point n, -n if not
-    QVn  - Voronoi vertices for input point n, -n if not
-
-Trace options:
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
-    Tc   - check frequently during execution
-    Ts   - statistics
-    Tv   - verify result: structure, convexity, and in-circle test
-    Tz   - send all output to stdout
-    TFn  - report summary when n or more facets created
-    TI file - input data from file, no spaces or single quotes
-    TO file - output results to file, may be enclosed in single quotes
-    TPn  - turn on tracing when point n added to hull
-     TMn - turn on tracing at merge n
-     TWn - trace merge facets when width > n
-    TVn  - stop qhull after adding point n, -n for before (see TCn)
-     TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]
-    Wn   - min facet width for non-coincident point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
-    s    - summary to stderr
-    p    - Voronoi vertices
-    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)
-    i    - Delaunay regions (use 'Pp' to avoid warning)
-    f    - facet dump
-
-More formats:
-    Fc   - count plus coincident points (by Voronoi vertex)
-    Fd   - use cdd format for input (homogeneous with offset first)
-    FD   - use cdd format for output (offset first)
-    FF   - facet dump without ridges
-    Fi   - separating hyperplanes for bounded Voronoi regions
-    FI   - ID for each Voronoi vertex
-    Fm   - merge count for each Voronoi vertex (511 max)
-    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex
-    FN   - count and Voronoi vertices for each Voronoi region
-    Fo   - separating hyperplanes for unbounded Voronoi regions
-    FO   - options and precision constants
-    FP   - nearest point and distance for each coincident point
-    FQ   - command used for qvoronoi
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
-                    for output: #Voronoi regions, #Voronoi vertices,
-                                #coincident points, #non-simplicial regions
-                    #real (2), max outer plane and min vertex
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
-    Fx   - extreme points of Delaunay triangulation (on convex hull)
-
-Geomview options (2-d only)
-    Ga   - all points as dots
-     Gp  -  coplanar points and vertices as radii
-     Gv  -  vertices as spheres
-    Gi   - inner planes only
-     Gn  -  no planes
-     Go  -  outer planes only
-    Gc   - centrums
-    Gh   - hyperplane intersections
-    Gr   - ridges
-    GDn  - drop dimension n in 3-d and 4-d output
-
-Print options:
-    PAn  - keep n largest Voronoi vertices by 'area'
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)
-    PDk:n - drop facet if normal[k] >= n
-    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')
-    PFn  - keep Voronoi vertices whose 'area' is at least n
-    PG   - print neighbors of good Voronoi vertices
-    PMn  - keep n Voronoi vertices with most merges
-    Po   - force output.  If error, output neighborhood of facet
-    Pp   - do not report precision problems
-
-    .    - list of all options
-    -    - one line descriptions of all options
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis -• input • outputs -• controls • graphics -• notes • conventions -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: see top

    - - diff --git a/src/qhull/html/rbox.htm b/src/qhull/html/rbox.htm deleted file mode 100644 index 9c28face5..000000000 --- a/src/qhull/html/rbox.htm +++ /dev/null @@ -1,277 +0,0 @@ - - - - -rbox -- generate point distributions - - - - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis • outputs -• examples • notes -• options -

    - -

    [CONE]rbox -- generate point distributions

    - -
    - rbox generates random or regular points according to the - options given, and outputs the points to stdout. The - points are generated in a cube, unless 's', 'x', or 'y' - are given. - -
    -

    »rbox synopsis

    -
    -rbox- generate various point distributions.  Default is random in cube.
-
-args (any order, space separated):
-  3000    number of random points in cube, lens, spiral, sphere or grid
-  D3      dimension 3-d
-  c       add a unit cube to the output ('c G2.0' sets size)
-  d       add a unit diamond to the output ('d G2.0' sets size)
-  l       generate a regular 3-d spiral
-  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)
-  s       generate cospherical points
-  x       generate random points in simplex, may use 'r' or 'Wn'
-  y       same as 'x', plus simplex
-  Cn,r,m  add n nearly coincident points within radius r of m points
-  Pn,m,r  add point [n,m,r] first, pads with 0
-
-  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.
-  Mn,m,r  lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
-          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.
-  W0.1    random distribution within 0.1 of the cube's or sphere's surface
-  Z0.5 s  random points in a 0.5 disk projected to a sphere
-  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
-
-  Bn      bounding box coordinates, default 0.5
-  h       output as homogeneous coordinates for cdd
-  n       remove command line from the first line of output
-  On      offset coordinates by n
-  t       use time as the random number seed (default is command line)
-  tn      use n as the random number seed
-  z       print integer coordinates, default 'Bn' is 1e+06
-
    - -

    »rbox outputs

    -
    - -The format of the output is the following: first line contains - the dimension and a comment, second line contains the - number of points, and the following lines contain the points, - one point per line. Points are represented by their coordinate values. - -

    For example, rbox c 10 D2 generates -

    -
    -2 RBOX c 10 D2
-14
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
-0.1792964061529342 0.4346928963760779
--0.1164979223315585 0.01941637230982666
-0.3309653464993139 -0.4654278894564396
--0.4465383649305798 0.02970019358182344
-0.1711493843897706 -0.4923018137852678
--0.1165843490665633 -0.433157762450313
-  -0.5   -0.5
-  -0.5    0.5
-   0.5   -0.5
-   0.5    0.5
-
    - -
    - -
    -

    »rbox examples

    - -
    -       rbox 10
-              10 random points in the unit cube centered  at  the
-              origin.
-
-       rbox 10 s D2
-              10 random points on a 2-d circle.
-
-       rbox 100 W0
-              100 random points on the surface of a cube.
-
-       rbox 1000 s D4
-              1000 random points on a 4-d sphere.
-
-       rbox c D5 O0.5
-              a 5-d hypercube with one corner at the origin.
-
-       rbox d D10
-              a 10-d diamond.
-
-       rbox x 1000 r W0
-              100 random points on the surface of a fixed simplex
-
-       rbox y D12
-              a 12-d simplex.
-
-       rbox l 10
-              10 random points along a spiral
-
-       rbox l 10 r
-              10 regular points  along  a  spiral  plus  two  end
-              points
-
-       rbox 1000 L10000 D4 s
-              1000 random points on the surface of a narrow lens.
-
-           rbox 1000 L100000 s G1e-6
-                  1000 random points near the edge of a narrow lens
-
-       rbox c G2 d G3
-              a cube with coordinates +2/-2 and  a  diamond  with
-              coordinates +3/-3.
-
-       rbox 64 M3,4 z
-              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
-              tice (Mesh) of integer points.
-
-       rbox P0 P0 P0 P0 P0
-              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
-              P0 P0 | qhull QJ'.
-
-       r 100 s Z1 G0.1
-              two  cospherical  100-gons plus another cospherical
-              point.
-
-       100 s Z1
-              a cone of points.
-
-       100 s Z1e-7
-              a narrow cone of points with many precision errors.
-
    - -

    »rbox notes

    -
    -Some combinations of arguments generate odd results. - -
    -

    »rbox options

    - -
    -       n      number of points
-
-       Dn     dimension n-d (default 3-d)
-
-       Bn     bounding box coordinates (default 0.5)
-
-       l      spiral distribution, available only in 3-d
-
-       Ln     lens  distribution  of  radius n.  May be used with
-              's', 'r', 'G', and 'W'.
-
-       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
-              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
-              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
-              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
-              {0,1,2} x {0,1,2}.
-
-       s      cospherical points randomly generated in a cube and
-              projected to the unit sphere
-
-       x      simplicial  distribution.   It  is fixed for option
-              'r'.  May be used with 'W'.
-
-       y      simplicial distribution plus a simplex.   Both  'x'
-              and 'y' generate the same points.
-
-       Wn     restrict  points  to distance n of the surface of a
-              sphere or a cube
-
-       c      add a unit cube to the output
-
-       c Gm   add a cube with all combinations of +m  and  -m  to
-              the output
-
-       d      add a unit diamond to the output.
-
-       d Gm   add a diamond made of 0, +m and -m to the output
-
-       Cn,r,m add n nearly coincident points within radius r of m points
-
-       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
-              nates with 0.0.
-
-       n      Remove the command line from the first line of out-
-              put.
-
-       On     offset the data by adding n to each coordinate.
-
-       t      use  time  in  seconds  as  the  random number seed
-              (default is command line).
-
-       tn     set the random number seed to n.
-
-       z      generate integer coordinates.  Use 'Bn'  to  change
-              the  range.   The  default  is 'B1e6' for six-digit
-              coordinates.  In R^4, seven-digit coordinates  will
-              overflow hyperplane normalization.
-
-       Zn s   restrict points to a disk about the z+ axis and the
-              sphere (default Z1.0).  Includes the opposite pole.
-              'Z1e-6'  generates  degenerate  points under single
-              precision.
-
-       Zn Gm s
-              same as Zn with an empty center (default G0.5).
-
-       r s D2 generate a regular polygon
-
-       r s Z1 G0.1
-              generate a regular cone
-
    - - -
    - -

    Up: Home page for Qhull
    -Up: Qhull manual: Table of Contents
    -To: Programs -• Options -• Output -• Formats -• Geomview -• Print -• Qhull -• Precision -• Trace -• Functions
    -To: synopsis • outputs -• examples • notes -• options - -

    - -

    The Geometry Center -Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: Sept. 25, 1995 --- Last modified: August 12, 1998

    - - diff --git a/src/qhull/html/rbox.man b/src/qhull/html/rbox.man deleted file mode 100644 index 3ea6395e6..000000000 --- a/src/qhull/html/rbox.man +++ /dev/null @@ -1,176 +0,0 @@ -.\" This is the Unix manual page for rbox, written in nroff, the standard -.\" manual formatter for Unix systems. To format it, type -.\" -.\" nroff -man rbox.man -.\" -.\" This will print a formatted copy to standard output. If you want -.\" to ensure that the output is plain ascii, free of any control -.\" characters that nroff uses for underlining etc, pipe the output -.\" through "col -b": -.\" -.\" nroff -man rbox.man | col -b -.\" -.TH rbox 1 "August 10, 1998" "Geometry Center" -.SH NAME -rbox \- generate point distributions for qhull -.SH SYNOPSIS -Command "rbox" (w/o arguments) lists the options. -.SH DESCRIPTION -.PP -rbox generates random or regular points according to the options given, and -outputs -the points to stdout. The points are generated in a cube, unless 's' or 'k' -option is -given. The format of the output is the following: first line -contains the dimension and a comment, -second line contains the number of points, and the -following lines contain the points, one point per line. Points are represented -by their coordinate values. -.SH EXAMPLES -.TP -rbox 10 -10 random points in the unit cube centered at the origin. -.TP -rbox 10 s D2 -10 random points on a 2\[hy]d circle. -.TP -rbox 100 W0 -100 random points on the surface of a cube. -.TP -rbox 1000 s D4 -1000 random points on a 4\[hy]d sphere. -.TP -rbox c D5 O0.5 -a 5\[hy]d hypercube with one corner at the origin. -.TP -rbox d D10 -a 10\[hy]d diamond. -.TP -rbox x 1000 r W0 -100 random points on the surface of a fixed simplex -.TP -rbox y D12 -a 12\[hy]d simplex. -.TP -rbox l 10 -10 random points along a spiral -.TP -rbox l 10 r -10 regular points along a spiral plus two end points -.TP -rbox 1000 L10000 D4 s -1000 random points on the surface of a narrow lens. -.TP -rbox c G2 d G3 -a cube with coordinates +2/\-2 and a diamond with coordinates +3/\-3. -.TP -rbox 64 M3,4 z -a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lattice (Mesh) of integer -points. 'rbox 64 M1,0' is orthogonal. -.TP -rbox P0 P0 P0 P0 P0 -5 copies of the origin in 3\-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'. -.TP -r 100 s Z1 G0.1 -two cospherical 100\-gons plus another cospherical point. -.TP -100 s Z1 -a cone of points. -.TP -100 s Z1e\-7 -a narrow cone of points with many precision errors. -.SH OPTIONS -.TP -n -number of points -.TP -Dn -dimension n\[hy]d (default 3\[hy]d) -.TP -Bn -bounding box coordinates (default 0.5) -.TP -l -spiral distribution, available only in 3\[hy]d -.TP -Ln -lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'. -.TP -Mn,m,r -lattice (Mesh) rotated by {[n,\-m,0], [m,n,0], [0,0,r], ...}. -Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an -orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x -{0,1,2}. '27 M3,4 z' is a rotated integer lattice. -.TP -s -cospherical points randomly generated in a cube and projected to the unit sphere -.TP -x -simplicial distribution. It is fixed for option 'r'. May be used with 'W'. -.TP -y -simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points. -.TP -Wn -restrict points to distance n of the surface of a sphere or a cube -.TP -c -add a unit cube to the output -.TP -c Gm -add a cube with all combinations of +m and \-m to the output -.TP -d -add a unit diamond to the output. -.TP -d Gm -add a diamond made of 0, +m and \-m to the output -.TP -Cn,r,m -add n nearly coincident points within radius r of m points -.TP -Pn,m,r -add point [n,m,r] to the output first. Pad coordinates with 0.0. -.TP -n -Remove the command line from the first line of output. -.TP -On -offset the data by adding n to each coordinate. -.TP -t -use time in seconds as the random number seed (default is command line). -.TP -tn -set the random number seed to n. -.TP -z -generate integer coordinates. Use 'Bn' to change the range. -The default is 'B1e6' for six\[hy]digit coordinates. In R^4, seven\[hy]digit -coordinates will overflow hyperplane normalization. -.TP -Zn s -restrict points to a disk about the z+ axis and the sphere (default Z1.0). -Includes the opposite pole. 'Z1e\-6' generates degenerate points under -single precision. -.TP -Zn Gm s -same as Zn with an empty center (default G0.5). -.TP -r s D2 -generate a regular polygon -.TP -r s Z1 G0.1 -generate a regular cone -.SH BUGS -Some combinations of arguments generate odd results. - -Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org -.SH SEE ALSO -qhull(1) -.SH AUTHOR -.nf -C. Bradford Barber -bradb@shore.net -.fi - diff --git a/src/qhull/html/rbox.txt b/src/qhull/html/rbox.txt deleted file mode 100644 index e3cf72189..000000000 --- a/src/qhull/html/rbox.txt +++ /dev/null @@ -1,195 +0,0 @@ - - - -rbox(1) rbox(1) - - -NAME - rbox - generate point distributions for qhull - -SYNOPSIS - Command "rbox" (w/o arguments) lists the options. - -DESCRIPTION - rbox generates random or regular points according to the - options given, and outputs the points to stdout. The - points are generated in a cube, unless 's' or given. The - format of the output is the following: first line contains - the dimension and a comment, second line contains the num- - ber of points, and the following lines contain the points, - one point per line. Points are represented by their coor- - dinate values. - -EXAMPLES - rbox 10 - 10 random points in the unit cube centered at the - origin. - - rbox 10 s D2 - 10 random points on a 2-d circle. - - rbox 100 W0 - 100 random points on the surface of a cube. - - rbox 1000 s D4 - 1000 random points on a 4-d sphere. - - rbox c D5 O0.5 - a 5-d hypercube with one corner at the origin. - - rbox d D10 - a 10-d diamond. - - rbox x 1000 r W0 - 100 random points on the surface of a fixed simplex - - rbox y D12 - a 12-d simplex. - - rbox l 10 - 10 random points along a spiral - - rbox l 10 r - 10 regular points along a spiral plus two end - points - - rbox 1000 L10000 D4 s - 1000 random points on the surface of a narrow lens. - - rbox c G2 d G3 - a cube with coordinates +2/-2 and a diamond with - - - -Geometry Center August 10, 1998 1 - - - - - -rbox(1) rbox(1) - - - coordinates +3/-3. - - rbox 64 M3,4 z - a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat- - tice (Mesh) of integer points. - - rbox P0 P0 P0 P0 P0 - 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 - P0 P0 | qhull QJ'. - - r 100 s Z1 G0.1 - two cospherical 100-gons plus another cospherical - point. - - 100 s Z1 - a cone of points. - - 100 s Z1e-7 - a narrow cone of points with many precision errors. - -OPTIONS - n number of points - - Dn dimension n-d (default 3-d) - - Bn bounding box coordinates (default 0.5) - - l spiral distribution, available only in 3-d - - Ln lens distribution of radius n. May be used with - 's', 'r', 'G', and 'W'. - - Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0], - [0,0,r], ...}. Use 'Mm,n' for a rigid rotation - with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal - lattice. For example, '27 M1,0' is {0,1,2} x - {0,1,2} x {0,1,2}. - - s cospherical points randomly generated in a cube and - projected to the unit sphere - - x simplicial distribution. It is fixed for option - 'r'. May be used with 'W'. - - y simplicial distribution plus a simplex. Both 'x' - and 'y' generate the same points. - - Wn restrict points to distance n of the surface of a - sphere or a cube - - c add a unit cube to the output - - c Gm add a cube with all combinations of +m and -m to - the output - - - -Geometry Center August 10, 1998 2 - - - - - -rbox(1) rbox(1) - - - d add a unit diamond to the output. - - d Gm add a diamond made of 0, +m and -m to the output - - Cn,r,m add n nearly coincident points within radius r of m points - - Pn,m,r add point [n,m,r] to the output first. Pad coordi- - nates with 0.0. - - n Remove the command line from the first line of out- - put. - - On offset the data by adding n to each coordinate. - - t use time in seconds as the random number seed - (default is command line). - - tn set the random number seed to n. - - z generate integer coordinates. Use 'Bn' to change - the range. The default is 'B1e6' for six-digit - coordinates. In R^4, seven-digit coordinates will - overflow hyperplane normalization. - - Zn s restrict points to a disk about the z+ axis and the - sphere (default Z1.0). Includes the opposite pole. - 'Z1e-6' generates degenerate points under single - precision. - - Zn Gm s - same as Zn with an empty center (default G0.5). - - r s D2 generate a regular polygon - - r s Z1 G0.1 - generate a regular cone - -BUGS - Some combinations of arguments generate odd results. - - Report bugs to qhull_bug@qhull.org, other correspon- - dence to qhull@qhull.org - -SEE ALSO - qhull(1) - -AUTHOR - C. Bradford Barber - bradb@shore.net - - - - - -Geometry Center August 10, 1998 3 - - diff --git a/src/qhull/index.htm b/src/qhull/index.htm deleted file mode 100644 index 4ea7806c9..000000000 --- a/src/qhull/index.htm +++ /dev/null @@ -1,284 +0,0 @@ - - - - -Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point - - - - -URL: http://www.qhull.org -
    To: -News -• Download -• CiteSeer -• Images -• Manual -• FAQ -• Programs -• Options -

    - -
    - - -
    -

    Qhull

    - [CONE] -    		 -Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, -halfspace intersection about a point, furthest-site Delaunay -triangulation, and furthest-site Voronoi diagram. The source code runs in -2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull -algorithm for computing the convex hull. It handles roundoff -errors from floating point arithmetic. It computes volumes, -surface areas, and approximations to the convex hull.

    - - -

    Qhull does not support triangulation of non-convex surfaces, mesh -generation of non-convex objects, medium-sized inputs in 9-D -and higher, alpha shapes, weighted Voronoi diagrams, Voronoi volumes, or -constrained Delaunay triangulations,

    - -

    Qhull 2015.2 introduces reentrant Qhull. It allows concurrent Qhull runs and simplifies the C++ interface to Qhull. -If you call Qhull from your program, you should use reentrant Qhull (libqhull_r) instead of qh_QHpointer (libqhull). -If you use Qhull 2003.1. please upgrade or apply poly.c-qh_gethash.patch. -

    -
    - -
    -
    - - - -
    - -

    Introduction -

      -
    • Fukuda's introduction to convex hulls, Delaunay - triangulations, Voronoi diagrams, and linear programming
      • -
    • Lambert's Java visualization of convex hull algorithms
      • -
    • LEDA Guide to geometry algorithms -
    • MathWorld's Computational Geometry from Wolfram Research -
    • Skiena's Computational Geometry from his Algorithm Design Manual. -
    • Stony Brook Algorithm Repository, computational geometry
      • -
    - -

    Qhull Documentation and Support -

    - -

    Related URLs -

    - -

    FAQs and Newsgroups -

    - -
    - -

    The program includes options for input transformations, -randomization, tracing, multiple output formats, and execution -statistics. The program can be called from within your -application.

    - -

    You can view the results in 2-d, 3-d and 4-d with Geomview. An alternative -is VTK.

    - -

    For an article about Qhull, download from - ACM or CiteSeer: -

    - -
    -

    Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The - Quickhull algorithm for convex hulls," ACM Trans. on - Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org

    -
    - -

    Abstract:

    - -
    -

    The convex hull of a set of points is the smallest convex - set that contains the points. This article presents a - practical convex hull algorithm that combines the - two-dimensional Quickhull Algorithm with the general - dimension Beneath-Beyond Algorithm. It is similar to the - randomized, incremental algorithms for convex hull and - Delaunay triangulation. We provide empirical evidence that - the algorithm runs faster when the input contains non-extreme - points, and that it uses less memory.

    -

    Computational geometry algorithms have traditionally - assumed that input sets are well behaved. When an algorithm - is implemented with floating point arithmetic, this - assumption can lead to serious errors. We briefly describe a - solution to this problem when computing the convex hull in - two, three, or four dimensions. The output is a set of - "thick" facets that contain all possible exact convex hulls - of the input. A variation is effective in five or more - dimensions.

    -
    - -
    - -

    Up: Past Software -Projects of the Geometry Center
    -URL: http://www.qhull.org -
    To: -News -• Download -• CiteSeer -• Images -• Manual -• FAQ -• Programs -• Options -

    - -
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    [HOME] The Geometry Center Home Page

    - -

    Comments to: qhull@qhull.org -
    -Created: May 17 1995 --- - - diff --git a/src/qhull/origCMakeLists.txt b/src/qhull/origCMakeLists.txt deleted file mode 100644 index 1034d1dea..000000000 --- a/src/qhull/origCMakeLists.txt +++ /dev/null @@ -1,426 +0,0 @@ -# CMakeLists.txt -- CMake configuration file for qhull, qhull6, and related programs -# -# To install CMake -# Download from http://www.cmake.org/download/ -# -# To find the available targets for CMake -G "..." -# cmake --help -# -# To build with MSYS/mingw -# cd build && cmake -G "MSYS Makefiles" .. && cmake .. -# make -# make install -# -# To uninstall on unix or MSYS/mingw -# xargs rm [B. Boeckel] - - Moved include file for each C++ source file to the top of the includes - - Prepend cpp includes with "libqhullcpp/" - - RoadLogEvent includes RoadLogEvent.h - - QhullIterator.h: Only QHULL_DECLARE_SEQUENTIAL_ITERATOR is used. - - - Compared src/libqhull/* to src/libqhull_r/* and resolved differences - - qh_printpoint in io.c skips qh_IDnone like io_r.c - - qhull_p-exports.def: Added three missing exports - - set_r.h: Removed countT. Too many issues - - - libqhull_r/Makefile: Add help prompts to 'make qtest' - - libqhull.pro: Add '../libqhull/' to sources and headers - - libqhull/Makefile: Fixed -I,./,,/src - - - qhull-zip.sh: Add CMakeModules to tarball [C. Rosenvik] - - CMakeLists.txt: Add targets qhullp and user_egp for qh_QHpointer and libqhull_p - - Reorganized 'make help' - - Makefile cleanall: Delete testqset and qhulltest from bin/ - - Fix filetype of Unix-only files - - Fix Unix line endings for Makefile and check in qhull-zip.sh - - Fix Windows line-endings and check in qhull-zip.sh - - qhull-zip.sh: Check for Unix text files - - ------------ -Qhull 2015.1 2016/01/03 (7.1.0) - - Add Rbox option 'Cn,r,m' to add nearly coincident points. Trigger for duplicate ridges - - Add Qhull option 'Q12' to ignore error on wide merge due to duplicate ridge - - - qh_findbestlower: Call qh_findfacet_all to fix rare "flipped or upper Delaunay" error QH6228. - QH6228 input provided by J. Metz. Reported (date order): L. Fiaschi, N. Bowler, A. Liebscher, V. Vieira, N. Rhinehart, N. Vance, P. Shafer - - qh_check_dupridge: Check if wide merge due to duplicate ridge from nearly coincident points - - qh_initialhull: Fix error messages for initial simplex is flat - - qh_determinant: increased 2-d and 3-d nearzero by 10x due to a counter-example - - rbox: Add qh_outcoord() to output coordinates w/ or w/o iscdd - - qh_meminit (mem.c): Add call to qh_memcheck - - Compare libqhull/... to libqhull_r/... and resolve differences - - Update builds for DevStudio (qhull.sln for msdev 2005..2009, qhull-32.sln and qhull-64.sln for recent releases) - - - qh-impre.htm: Add a section about precision errors for 'Nearly coincident points on an edge' - - html/index.htm#geomview: Document how to install, build, and use Geomview. - - html/index.htm: Emphasize program links and move related urls to end - - qhull/index.htm: Emphasize manual, geomview, and imprecision - - Fix documentation links in libqhull_r/index.htm - - Add 'Functions' link to documentation headers - - Change '...' to '...' - - libqhull_r/index.htm -- Add instructions for configuring web browsers for source links. - - libqhull_r/ -- Fix source links for ..._r.htm files - ------------- -Qhull 2015.0.7 2015/11/09 (7.0.7) - - Fix return type of operator-> in QhullLinkedList and other collection classes [F. Jares] - - Fix return types for QhullLinkedList - - Fix return types for QhullPoints - - Simplify return type for Coordinates::operator[] (same as QList) - - Add const to operators for QhullSet::iterator and add documentation - - Coordinates.h: Fix return types for operations of iterator and const_iterator - - Drop use of Perforce changelist number in qhull_VERSION of CMakeLists.txt - - Rename the md5sum files as *.tgz.md5sum instead of *-tgz.md5sum - - Fix build dependency for testqset_r [asekez] - - rbox.c depends on Qhull due to qh_lib_check which uses qh_version2 for error messages - - QhullFacet_test.cpp: Annotate Qhull invocations. Allows their repetition. - - QhullFacet_test.cpp: Adjust epsilon on distance tests - - Do not create libqhullcpp as a shared library. Qhull C++ classes may change layout and size. - - qhull-cpp.xml: Make a relative path to road-faq.xsl - ------------- -Qhull 2015.0.6 2015/10/20 (7.0.6.2013) - - In the libraries, exit() is only called from qh_exit(). qh_exit may be redefined. - - Add qh_fprintf_stderr to usermem.c. May be overridden to avoid use of stderr [D. Sterratt] - Add usermem to testqset builds - Used by qh_fprintf_rbox - - Remove most instances of stderr/stdout from libqhull, libqhull_r, and libqhullcpp [D. Sterratt] - qh_fprintf_stderr may be redefined. qh_meminit and qh_new_qhull use stderr as the default ferr - - qh_initflags: Use qh.fout instead of stdout for 'TO file'. A library caller may define a different qh.fout. - - qh_settemppush: Call qh_fprintf() instead of fprintf() on error. - - Rename qh_call_qhull as "Qhull-template" from user.c. Updated its references. - - - qh-code.htm: "How to avoid exit(), fprintf(), stderr, and stdout" - - html/index.htm: Fix table of contents for qh-code - - libqhull_r/index.htm: Rewrite introduction to Reentrant Qhull - - qh-faq.htm: Rewrite "Can Qhull use coordinates without placing them in a data file?" - - qh-get.html: Link to github - - Remove qhull_interface.cpp from the documentation - ------------- -Qhull 2015.0.5 2015/10/12 (7.0.5.1995) -- qh_new_qhull: default 'errfile' is 'stderr'. outfile and errfile are optional [B. Pearlmutter] -- qh_new_qhull: returns qh_ERRinput instead of exit() if qhull_cmd is not "qhull ..." [B. Pearlmutter] -- qhalf_r.c,etc: Add clear of qh.NOerrexit -- global.c: gcc 4.4.0 mingw32 segfault cleared by adding comment -- usermem_r-cpp.cpp: Optional file to redefine qh_exit() as throw "QH10003.." [B. Pearlmutter] - qh_exit() is called by qhull_r when qh_errexit() is not available. - -- html/index.htm: Add bibliographic reference to Golub & van Loan and other references [R. Gaul] -- qhalf.htm: A halfspace is the points on or below a hyperplane [D. Strawn] -- qh-opto.htm#n: Defined inside, outside, on, above, and below a hyperplane [D. Strawn] -- qhalf.htm#notes: Recast the linear program using negative halfspaces (as used by Qhull) [D. Strawn] -- qhull_a.h: Fix comment '#include "libqhull/qhull_a.h" [fe rew] - -- build/qhull*.pc.in: Templates for pkg-config (derived from Fedorra) [P. McMunn] - https://bitbucket.org/mgorny/pkg-config-spec/src/c1bf12afe0df6d95f2fe3f5e1ffb4c50f018825d/pkg-config-spec.txt?at=master&fileviewer=file-view-default -- Makefile: Remove user_eg3.o from LIBQHULLCPP_OBJS -- Makefile: Add .h dependencies for unix_r.o, etc. -- libqhull/Makefile: Fix build of rbox -- libqhull_r/Makefile: Fix build -I -- qhull.sln/user_eg3: Add dependency on libcpp -- Removed bin/libqhull_r.dll (should be qhull_r.dll) -- Removed build/qhulltest.vcproj (see build/qhulltest/qhulltest.vcproj) - ------------- -Qhull 2015.0.4 2015/9/30 (7.0.4.1984) - - qh-get.htm: Unix tarball includes version number (e.g., qhull-2015-src-7.1.0.1940.tgz) [Hauptman] - - qglobal.c: Add qh_version2 with Unix version for "-V" option [Hauptman] - - build/qhull-32.sln, *-32.vcxproj: Add Visual Studio 32-bit build for 2010+ - - build/qhull-64.sln, *-64.vcxproj: Add Visual Studio 64-bit build for 2010+ [G. Lodron] - - make-vcproj.sh: Restore to eg/... It is required for Visual Studio builds - - README.txt: updated builds and reentrant Qhull - - Add documentation for QHULL_LIB_CHECK - - qh_lib_check: Check for unknown QHULL_LIB_TYPE - - qh-code.htm: Add memory requirements for 32- and 64-bit - ------------- -Qhull 2015.0.3 2015/9/22 - - qh_mem, qh_merge: Log before 'delete' instead of afterwards [Coverity, K. Schwehr] - - qh_merge: Test for NULL horizon in qh_checkzero [Coverity, K. Schwehr] - - qh_matchneighbor: Check for matchfacet not a neighbor of facet [Coverity, K. Schwehr] - - qh_triangulate: Explicit check for visible==NULL [Coverity, K. Schwehr] - - qh_findbestfacet (unused by qhull): Fix test of isoutside [Coverity, K. Schwehr] - - qh_check_maxout: Check bestfacet!=0 for logging its id [Coverity, K. Schwehr] - - qh_nearvertex: Check for bestvertex not found [Coverity, K. Schwehr] - - qh_checkfacet: Check for missing neighbors of simplicial facets [Coverity, K. Schwehr] - - qh_setdelnth: Check 'nth' before using it [Coverity, K. Schwehr] - - Annotate code for Coverity warnings (most of these protected by qh_errexit) [K. Schwehr] - - - qh_printfacet3math: explicit format string (duplicates change to io.c) [B. Pearlmutter] - - libqhull_r.h: fix spelling error (duplicates change to libqhull.h) [B. Pearlmutter] - - unix_r.c: fix spelling error (duplicates change to unix.c) [B. Pearlmutter] - - qhull_a.h: define qhullUnused() only if defined(__cplusplus) [R. Stogner] - - qh_version: Use const char str[]= "string" instead of const char * str= "string" [U. Drepper, p. 27] - - qh_newvertex: Use UINT_MAX instead of 0xFFFFFFFF - - qh_newridge: Use UINT_MAX instead of 0xFFFFFFFF - - Reviewed FIXUP notes - - - QhullRidge_test: t_foreach use 'foreach(const QhullVertex &v, vertices) - - Made '#include "RoadTest.h" consistent across all C++ tests - - - qh-code.htm: May also use libqhull_r (e.g., FOREACHfacet_(...)) - - qh-get.htm: Add list of download build repositories - - - Add CMakeModules/CheckLFS.cmake: Enables Large File Support [B. Pearlmutter] - - Makefile: Use -fpic at all times instead of -fPIC, [U. Drepper p. 15] - ------------- -Qhull 2015.0.2 2015/9/1 - - global_r.c: Fixed spelling of /* duplicated in...qh_clear_outputflags */ [K. Schwehr] - - Replaced Gitorious with GitHub - - Moved 'to do' comments into Changes.txt - ------------- -Qhull 2015.0.1 2015/8/31 - - Source code changes - - Increased size of vertexT.id and ridgeT.id to 2^32 [H. Strandenes, C. Carson, K. Nguyen] - Reworded the warning message for ridgeT.id overflow. It does not affect Qhull output - - Add qh_lib_check to check for a compatible Qhull library. - Programs should call QHULL_LIB_CHECK before calling Qhull. - - Include headers prefixed with libqhull/, libqhull_r/, or libqhullcpp/ - - Renamed debugging routines dfacet/dvertex to qh_dfacet/qh_dvertex - - Rewrote user_eg, user_eg2, and user_eg3 as reentrant code - - Renamed 'qh_rand_seed' to 'qh_last_random'. Declare it as DATA - - qh_initqhull_start2 sets qh->NOerrexit on initialization - User must clear NOerrexit after setjmp() - - Other source code changes - - Define ptr_intT as 'long long' for __MINGW64__ [A. Voskov] - - poly_r.c: initialize horizon_skip [K. Schwehr] - - Removed vertexT.dim and MAX_vdim. It is not used by reentrant Qhull. - - Removed qhull_inuse. Not used by C++ - - Removed old __MWERKS__/__POWERPC__ code that speed up SIOUX I/O - - Moved #include libqhull/... before system includes (e.g., - - Comment-out _isatty declaration. Avoids "C4273 ... inconsistent dll linkage" - - Add random.h/random_r.h as an include file to random.c/random_r.c - - Rename rbox routines to qh_roundi/qh_out1/qh_out2n/qh_out3n - - Rename dfacet and dvertex to qh_dfacet and qh_dvertex - - Replace 'qhmem .zzz' with 'qhmem.zzz' - - Removed spaces between function name and parentheses - - Rename 'enum statistics' to 'enum qh_statistics' - - Declare rbox as DATA in qhull-exports.def and qhull_p-exports.def - - In comments, use 'qh.zzz' to reference qhT fields - - In qh_fprintf, use qhmem.ferr to report errors - - qh_fprintf may be called for errors in qh_initstatistics and qh_meminit - - qh_pointid returns qh_IDnone, qh_IDinterior, qh_IDunknown in place of -3, -2, -1 resp. - - getid_() returns qh_IDunknown in place of -1 - - After qh_meminit, qhmem.ferr is non-zero (stderr is the default) - - Update qh_MEMalign in testqset.c to user.h (with realT and void*) - - Split rboxT into a header file - - Add rboxlib.h to libqhull_a.h - - Rename PI to qh_PI and extend to 30 digits - - Rename MAXdim to qh_MAXdim - - Change spacing for type annotations '*' and '&' in C++ header files - - Test for !rbox_output/cpp_object in qh_fprintf_rbox - - Remove 'inline' annotation from explicit inline declarations - - Column 25 formatting for iterators, etc. - - Use '#//!\name' for section headers - - QhullFacet.cpp: zinc_(Zdistio); - - Clear qhT.ALLOWrestart in qh_errexit - - Replace longjmp with qh_errexit_rbox in qh_rboxpoints - - Add jmpExtra after rbox_errexit to protect against compiler errors - - Add qh.ISqhullQh to indicate initialization by QhullQh() - - Add library warnings to 'rbox D4', user_eg, user_eg2, user_eg3 - - Add headers to q_eg, q_egtest, and q_test - - Check that qh.NOerrexit is cleared before call to qh_initflags - -Qhull documentation - - README.txt: Added references to qh-code.htm - - README.txt: Added section 'Calling Qhull from C programs' - - qh-code.htm: Moved Performance after C++ and C interface - - qh-code.htm: Moved Cpp Questions to end of the C++ section - - qh-code.htm: Fixed documentation for 'include' path. It should be include/libqhull - - qconvex.htm: Fixed documentation for 'i'. It triangulates in 4-d and higher [ref] - - Clarified qhalf space documentation for the interior point [J. Santos] - - rbox.c: Version is same date as qh_version in global.c - - gobal_r.c: Version includes a '.r' suffix to indicate 'reentrant' - -Qhull builds - - Development moved to http://github.com/qhull/qhull - git clone git@github.com:qhull/qhull.git - - Exchanged make targets for testing. - 'make test' is a quick test of qhull programs. - 'make testall' is a thorough test - - Added 'make help' and 'make test' to libqhull and libqhull_r Makefiles - - CMakeLists.txt: Remove libqhull, libqhull_r, and libqhullcpp from include_directories - - CMakeLists.txt: Add qhull_SHAREDR for qhull_r - - CMakeLists.txt: Retain qhull_SHARED and qhull_SHAREDP (qh_QHpointer) - - CMakeLists.txt: Move qhull_SHARED and qhull_SHAREDP (qh_QHpointer) to qhull_TARGETS_OLD - Drop qhull_STATICP (use qhull_SHAREDP or qhull_STATIC) - Set SOVERSION and VERSION for shared libraries - - Move qhull_p-exports.def back to libqhull - - Switched to mingw-w64-install for gcc - - Improved prompts for 'make' - - qhull-all.pro: Remove user_eg3.cpp from OTHER_FILES - - libqhull.pro: Ordered object files by frequency of execution, as done before - - Add the folder name to C++ includes and remove libqhullcpp from INCLUDEPATH - - Changed CONFIG+=qtestlib to QT+=testlib - - Changed Makefile to gcc -O3 (was -O2) - - Changed libqhull/libqhull_r Makefiles to both produce rbox, qhull, ..., user_eg, and user_eg2 - - Removed Debian 'config/...'. It was needed for Qhull 2012. - -libqhull_r (reentrant Qhull) - - Replaced qh_qh with a parameter to each procedure [P. Klosterman] - No more globally defined data structures in Qhull - Simplified multithreading and C++ user interface - All functions are reentrant (Qt: "A reentrant function can ... be called simultaneously from multiple threads, but only if each invocation uses its own data.") - No more qh_QHpointer. - See user_eg3 and qhulltest - New libraries - libqhull_r -- Shared library with reentrant sources (e.g., poly_r.h and poly_r.c which replace libqhull's poly.h and poly.c) - libqhullstatic_r -- Static library with the same sources as libqhull_r - libqhullcpp -- The C++ interface using libqhullstatic_r (further notes below) - New executables - testqset_r -- Test qset_r.c (the reentrant version of qset.c - - Source code changes for libqhull_r - - Add qh_zero() to initialize and zero memory for qh_new_qhull - - Remove qh_save_qhull(), qh_restore_qhull(), and qh.old_qhstat from global_r.c - - Remove qh_freeqhull2() (global_r.c) - - Remove qh_freestatistics() (stat_r.c) - - Remove qh_compare_vertexpoint (qhT is not available, unused code) - - Remove conditional code for __POWERPC__ from unix_r.c and rbox_r.c - - Move qh_last_random into qh->last_random (random_r.c) - - Rename sources files with a '_r' suffix. qhull_a.h becomes qhull_ra.h - - Replace 'qh' macro with 'qh->' - - Replace global qhT with parameter-0 - - Add qhmemT to beginning of qhT. It may not be used standalone. - - Add qhstatT to end of qhT - - Remove qhull_inuse - - Change qhmem.zzz to qh->qhmem.zzz - - Replace qh_qhstat with qh->qhstat - - Remove qh_freestatistics - - Replace qh_last_random with qh->last_random - - Replace rboxT with qh->rbox_errexit, rbox_isinteger, rbox_out_offset - - Replace rbox.ferr/fout with qh->ferr/fout - - No qh for qh_exit, qh_free, qh_malloc, qh_strtod, qh_strtol, qh_stddev - - New qmake include files qhull-app-c_r.pri, qhull-app-shared_r.pri, qhull-libqhull-src_r.pri - - Replace 'int' with 'countT' and 'COUNTmax' for large counts and identifiers - - qhset converted to countT - - Removed vertexT.dim -- No longer needed by cpp - Removed MAX_vdim - - Guarantee that qh->run_id!=0. Old code assumed that qh_RANDOMint was 31 bits - -Changes to libqhullcpp - - Added QhullVertexSet.h to libqhullcpp.pro and libqhullpcpp.pro - - QhullVertexSet: error if qhsettemp_defined at copy constructor/assignment (otherwise double free) - - Enable QhullSet.operator=. Copy constructor and assignment only copies pointers - - Changed QhullPoint.operator==() to sqrt(distanceEpsilon) - - Added assignment of base class QhullPoints to PointCoordinates.operator= - - Enable QhullPoints.operator= - - Rename PointCoordinates.point_comment to describe_points - - Add 'typename T' to definition of QhullSet::value() - -C++ interface - - Reimplemented C++ interface on reentrant libqhull_r instead of libqhull - - Prepend include files with libqhullcpp/ - - Replaced UsingLibQhull with QhullQh and macro QH_TRY - Removed UsingLibQhull.currentAngleEpsilon and related routines - Removed UsingLibQhull_test.cpp - Replaced globalDistanceEpsilon with QhullQh.distanceEpsilon - Replaced globalAngleEpsilon with QhullQh.angleEpsilon - Moved UsingQhullLib.checkQhullMemoryEmpty to QhullQh.checkAndFreeQhullMemory - Replaced FACTORepsilon=10 with QhullQh.factor_epsilon=1.0 - - To avoid -Wshadow for QhullQh*, use 'qqh' for parameters and 'qh()' for methods - - Moved messaging from Qhull to QhullQh - - Add check of RboxPoints* in qh_fprintf_rbox - - Renamed Qhull.initializeQhull to Qhull.allocateQhullQh - Added qh_freeqhull(!qh_ALL) as done by unix.c and other programs - - Moved QhullPoints.extraCoordinatesCount into QhullPoints.cpp - - Replaced section tags with '#//!\name ...' - - Removed qhRunId from print() to ostream. - - Removed print() to ostream. Use '<< qhullPoint' or '<< qhullPoint.print("message")' - -C++ interface for most classes - - Remove qhRunId - - Add QhullQh *qh_qh to all types - Pointer comparisons of facetT,etc. do not test corresponding qh_qh - Added to end of type for debugging information, unless wasteful alignment - - Add QhullQh * to all constructors - - All constructors may use Qhull & instead of QhullQh * - - For inherited QhullQh types, change to 'protected' - - Renamed 'o' to 'other' except where used extensively in iterators - - Except for conditional code, merged the Conversion section into GetSet - - Removed empty(). Use isEmpty() instead - - Add operator= instead of keeping it private - - print_message=0 not allowed. Use "" instead. - - Rename isDefined() to isValid() to match Qt conventions - -C++ interface by class - - Coordinates - Removed empty(). Use isEmpty() instead - Added append(dim, coordT*) - Reformated the iterators - Convert to countT - - PointCoordinates - Added constructors for Qhull or QhullQh* (provides access to QhullPoint.operator==) - Removed PointCoordinates(int pointDimension) since PointCoordinates should have a comment. Also, it is ambiguous with PointCoordinates(QhullQh*) - Renamed point_comment to describe_points - Convert to countT - - Qhull - Remove qhull_run_i - Remove qh_active - Replace property feasiblePoint with field feasible_point and methods setFeasiblePoint/feasiblePoint - Returns qh.feasible_point if defined - Moved useOutputStream to QhullQh use_output_stream - Renamed useOutputStream() to hasOutputStream() - Replaced qhull_dimension with qh->input_dim //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi) - Removed global s_qhull_output= 0; - Move qhull_status, qhull_message, error_stream, output_stream to QhullQh - Renamed qhullQh() to qh() - Added check of base address to allocateQhullQh(), Was not needed for qhullpcpp - - QhullFacet - Constructor requires Qhull or QhullQh* pointer - Convert to countT - Dropped implicit conversion from facetT - Dropped runId - Add print("message") to replace print() - - QhullFacetList - Constructor requires Qhull or QhullQh* pointer - Convert to countT - Dropped runId - - QhullFacetSet - Removed empty(). Use isEmpty() instead - Constructor requires Qhull or QhullQh* pointer - Convert to countT - Dropped runId - Add operator= - Implement print("message") - - QhullHyperplane - Add hyperplaneAngle() method - Rewrite operator== to use hyperplaneAngle() - Reorganize fields to keep pointers aligned - Except for default constructor requires Qhull or QhullQh* pointer - Enable copy assignment - Reorganized header - - QhullLinkedList - Add operator= - Removed empty(). Use isEmpty() instead - Convert to countT - iterator(T) made iterator(const T &) - const_iterator(T) made const_iterator(const T &) - const_iterator(iterator) made const_iterator(const iterator &) - - QhullPoint - Add constructors for Qhull or QhullQh* pointer (for id() and operator==) - Add defineAs(coordT*) - Add getBaseT() and base_type for QhullSet - Added checks for point_coordinates==0 - Removed static QhullPoint::id(), use QhullPoint.id() instead - distance() throws an error if dimension doesn't agree or if a point is undefined - Convert to countT - If !qh_qh, operator==() requires equal coordinates - Use cout<

    [R. Richter, S. Pasko] - - Remove deprecated libqhull/qhull.h - Use libqhull/libqhull.h instead. Avoids confusion with libqhullcpp/Qhull.h - - Makefile: Add LIBDIR, INCDIR, and DESTDIR to install [L.H. de Mello] - Separate MAN install from DOC install - Create install directories - Installs headers to include/libqhull, include/libqhullcpp, include/road - - CMakeLists.txt: Add MAN_INSTALL_DIR for qhull.1 and rbox.1 man pages - Add RoadTest.h to include/road for Qt users (road_HEADERS) - - Renamed md5sum files to avoid two extensions - - qh-get.htm: Add Readme links and 2009.1 note. - - qh-optf.htm: Fix link - - index.htm: Updated Google Scholar link - - qhull-zip.sh: Improved error message. - ------------- -Qhull 2011.1 2011/04/17 6.2.0.1373 - -Changes to deliverables - - qvoronoi: Deprecated 'Qt' and 'QJn'. Removed from documentation and prompts. - These options produced duplicate Voronoi vertices for cospherical data. - - Removed doskey from Qhull-go.bat. It is incompatible with Windows 7 - - Added 'facets' argument to user_eg3.cpp - - user_eg links with shared library - - qhulltest.cpp: Add closing prompt. - -Changes to build system - - Reorganized source directories - - Moved executables to bin directory - - Add CMake build for all targets (CMakeFiles.txt) [M. Moll assisted] - - Add gcc build for all targets (Makefile) - - Fixed location of qhull.man and rbox.man [M. Moll] - - Add DevStudio builds for all targets (build/*.vcproj) - - Added shared library (lib/qhull6.dll) - Added qh_QHpointer_dllimport to work around problems with MSVC - - Added static libraries with and without qh_QHpointer (lib/qhullstatic.lib) - - Added eg/make-vcproj.sh to create vcproj/sln files from cmake and qmake - - Document location of qh_QHpointer - - Use shadow build directory - - Made -fno-strict-aliasing conditional on gcc version - - Added src/qhull-app-cpp.pri, src/qhull-app-c.pri, etc. for common settings - - Add .gitignore with ignored files and directories. - - Use .git/info/exclude for locally excluded files. - - Fixed MBorland for new directory structure - - cleanall (Makefile): Delete 'linked' programs due to libqhull_r and libqhull/Makefile - -Changes to documentation - - qvoronoi.htm: Remove quotes from qvoronoi example - - qhull-cpp.xml: Add naming conventions - - index.htm: Add Google Scholar references - - qh-optf.htm: Add note about order of 'Fn' matching 'Fv' order [Q. Pan] - - Add patch for old builds in qh-get.htm - - Added C++ compiling instructions to README.txt - - Add instructions for fixing the DOS window - - Changed DOS window to command window - - Fixed html links - - qh-get.htm: Dropped the Spanish mirror site. It was disabled. - -Changes to C code - - mem.h: Define ptr_intT as 'long long' for Microsoft Windows _win64 builds. - On Linux and Mac, 'long' is 64-bits on a 64-bit host - - Added qh_QHpointer_dllimport to work around MSVC problem - - qconvex.c,etc.: Define prototype for _isatty - - Define MSG_QHULL_ERROR in user.h - - Move MSG_FIXUP to 11000 and updated FIXUP QH11... - -Changes to test code - - Add note to q_test than R1e-3 may error (qh-code.htm, Enhancements) - - Add test for executables to q_eg, etc. - - Fixed Qhull-go.bat. QHULL-GO invokes it with command.com, - -Changes to C++ interface - - QhullFacet: Added isSimplicial, isTopOrient, isTriCoplanar, isUpperDelaunay - - Added Qhull::defineVertexFacetNeighbors() for facetNeighbors of vertices. - Automatically called for facet merging and Voronoi diagrams - Do not print QhullVertex::facetNeighbors is !facetNeighborsDefined() - - Assigned FIXUP identifiers - - QhullError: Add copy constructor, assignment operator, and destructor - - Add throw() specifiers to RoadError and QhullError - - Renamed RoadError::defined() to RoadError::isDefined() - - Add #error to Qhull.h if qh_QHpointer is not defined - -Changes to C++ code - - Fixed bug reported by renangms. Vertex output throws error QH10034 - and defineVertexNeighbors() does not exist. - - Define QHULL_USES_QT for qt-qhull.cpp [renangms] - - Reviewed all copy constructors and copy assignments. Updated comments. - Defined Qhull copy constructor and copy assignment [G. Rivet-Sabourin] - Disabled UsingQhullLib default constructor, copy construct, and copy assign - - Merged changes from J. Obermayr in gitorious/jobermayrs-qhull:next - - Fix strncat limit in rboxlib.c and global.c - - Changes to CMakeLists.txt for openSUSE - - Fixed additional uses of strncat - - Fixed QhullFacet::PrintRidges to check hasNextRidge3d() - - Removed gcc warnings for shadowing from code (src/qhull-warn.pri) - - Removed semicolon after extern "C" {...} - - Removed experimental QhullEvent/QhullLog - - Use fabs() instead of abs() to avoid accidental conversions to int - - Fixed type of vertex->neighbors in qh_printvoronoi [no effect on results] - - Removed unnecessary if statement in qh_printvoronoi - ------------- -qhull 2010.1 2010/01/14 -- Fixed quote for #include in qhull.h [U.Hergenhahn, K.Roland] -- Add qt-qhull.cpp with Qt conditional code -- Add libqhullp.proj -- Add libqhull5 to Readme, Announce, download -- Reviewed #pragma -- Reviewed FIXUP and assigned QH tags -- All projects compile with warnings enabled -- Replaced 'up' glyphs with » -- Moved cpp questions to qh-code.htm#questions-cpp -- Moved suggestions to qh-code.htm#enhance -- Moved documentation requests to qh-code.htm#enhance -- Add md5sum file to distributions -- Switched to DevStudio builds to avoid dependent libraries, 10% slower - Removed user_eg3.exe and qhullcpp.dll from Windows build - Fix qhull.sln and project files for qh_QHpointer -- Add eg/qhull-zip.sh to build qhull distribution files - ------------- -qhull 2010.1 2010/01/10 -- Test for NULL fp in qh_eachvoronoi [D. Szczerba] - -qhull 2010.1 2010/01/09 - -Changes to build and distribution -- Use qh_QHpointer=0 for libqhull.a, qhull, rbox, etc. - Use -Dqh_QHpointer for libqhullp.a, qhullcpp.dll, etc. - qh_QHpointer [2010, gcc] 4% time 4% space, [2003, msvc] 8% time 2% space -- Add config/ and project/debian/ for Autoconf build [R. Laboissiere] - from debian branch in git and http://savannah.nongnu.org/cvs/?group=qhull -- Add CMakeLists.txt [kwilliams] -- Fix tabs in Makefile.txt [mschamschula] -- Add -fno-strict-aliasing to Makefile for gcc 4.1, 4.2, and 4.3 qset segfault -- Remove user_eg.exe and user_eg2.exe from Windows distribution -- Order object files by frequency of execution for better locality. - -Changes to source -- Remove ptr_intT from qh_matchvertices. It was int since the beginning. -- user.h requires for CLOCKS_PER_SEC -- Move ostream<

      ---------------------------------
-
-   geom.c
-   geometric routines of qhull
-
-   see qh-geom.htm and geom.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/geom.c#2 $$Change: 1995 $
-   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
-
-   infrequent code goes into geom2.c
-*/
-
-#include "qhull_a.h"
-
-/*---------------------------------
-
-  qh_distplane( point, facet, dist )
-    return distance from point to facet
-
-  returns:
-    dist
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    dist > 0 if point is above facet (i.e., outside)
-    does not error (for qh_sortfacets, qh_outerinner)
-
-  see:
-    qh_distnorm in geom2.c
-    qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
-*/
-void qh_distplane(pointT *point, facetT *facet, realT *dist) {
-  coordT *normal= facet->normal, *coordp, randr;
-  int k;
-
-  switch (qh hull_dim){
-  case 2:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
-    break;
-  case 3:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
-    break;
-  case 4:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
-    break;
-  case 5:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
-    break;
-  case 6:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
-    break;
-  case 7:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
-    break;
-  case 8:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
-    break;
-  default:
-    *dist= facet->offset;
-    coordp= point;
-    for (k=qh hull_dim; k--; )
-      *dist += *coordp++ * *normal++;
-    break;
-  }
-  zinc_(Zdistplane);
-  if (!qh RANDOMdist && qh IStracing < 4)
-    return;
-  if (qh RANDOMdist) {
-    randr= qh_RANDOMint;
-    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh RANDOMfactor * qh MAXabs_coord;
-  }
-  if (qh IStracing >= 4) {
-    qh_fprintf(qh ferr, 8001, "qh_distplane: ");
-    qh_fprintf(qh ferr, 8002, qh_REAL_1, *dist);
-    qh_fprintf(qh ferr, 8003, "from p%d to f%d\n", qh_pointid(point), facet->id);
-  }
-  return;
-} /* distplane */
-
-
-/*---------------------------------
-
-  qh_findbest( point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
-    find facet that is furthest below a point
-    for upperDelaunay facets
-      returns facet only if !qh_NOupper and clearly above
-
-  input:
-    starts search at 'startfacet' (can not be flipped)
-    if !bestoutside(qh_ALL), stops at qh.MINoutside
-
-  returns:
-    best facet (reports error if NULL)
-    early out if isoutside defined and bestdist > qh.MINoutside
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart counts the number of distance tests
-
-  see also:
-    qh_findbestnew()
-
-  notes:
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
-      avoid calls to distplane, function calls, and real number operations.
-    caller traces result
-    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
-    Made code more complicated.
-
-  when called by qh_partitionvisible():
-    indicated by qh_ISnewfacets
-    qh.newfacet_list is list of simplicial, new facets
-    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
-    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
-
-  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
-                 qh_check_bestdist(), qh_addpoint()
-    indicated by !qh_ISnewfacets
-    returns best facet in neighborhood of given facet
-      this is best facet overall if dist > -   qh.MAXcoplanar
-        or hull has at least a "spherical" curvature
-
-  design:
-    initialize and test for early exit
-    repeat while there are better facets
-      for each neighbor of facet
-        exit if outside facet found
-        test for better facet
-    if point is inside and partitioning
-      test for new facets with a "sharp" intersection
-      if so, future calls go to qh_findbestnew()
-    test horizon facets
-*/
-facetT *qh_findbest(pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT isnewfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  facetT *facet, *neighbor, **neighborp;
-  facetT *bestfacet= NULL, *lastfacet= NULL;
-  int oldtrace= qh IStracing;
-  unsigned int visitid= ++qh visit_id;
-  int numpartnew=0;
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  zinc_(Zfindbest);
-  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
-    if (qh TRACElevel > qh IStracing)
-      qh IStracing= qh TRACElevel;
-    qh_fprintf(qh ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
-             qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
-    qh_fprintf(qh ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
-    qh_fprintf(qh ferr, 8006, "  Last point added was p%d.", qh furthest_id);
-    qh_fprintf(qh ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh max_outside);
-  }
-  if (isoutside)
-    *isoutside= True;
-  if (!startfacet->flipped) {  /* test startfacet */
-    *numpart= 1;
-    qh_distplane(point, startfacet, dist);  /* this code is duplicated below */
-    if (!bestoutside && *dist >= qh MINoutside
-    && (!startfacet->upperdelaunay || !noupper)) {
-      bestfacet= startfacet;
-      goto LABELreturn_best;
-    }
-    bestdist= *dist;
-    if (!startfacet->upperdelaunay) {
-      bestfacet= startfacet;
-    }
-  }else
-    *numpart= 0;
-  startfacet->visitid= visitid;
-  facet= startfacet;
-  while (facet) {
-    trace4((qh ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
-                facet->id, bestdist, getid_(bestfacet)));
-    lastfacet= facet;
-    FOREACHneighbor_(facet) {
-      if (!neighbor->newfacet && isnewfacets)
-        continue;
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {  /* code duplicated above */
-        (*numpart)++;
-        qh_distplane(point, neighbor, dist);
-        if (*dist > bestdist) {
-          if (!bestoutside && *dist >= qh MINoutside
-          && (!neighbor->upperdelaunay || !noupper)) {
-            bestfacet= neighbor;
-            goto LABELreturn_best;
-          }
-          if (!neighbor->upperdelaunay) {
-            bestfacet= neighbor;
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }else if (!bestfacet) {
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }
-        } /* end of *dist>bestdist */
-      } /* end of !flipped */
-    } /* end of FOREACHneighbor */
-    facet= neighbor;  /* non-NULL only if *dist>bestdist */
-  } /* end of while facet (directed search) */
-  if (isnewfacets) {
-    if (!bestfacet) {
-      bestdist= -REALmax/2;
-      bestfacet= qh_findbestnew(point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
-      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-    }else if (!qh findbest_notsharp && bestdist < - qh DISTround) {
-      if (qh_sharpnewfacets()) {
-        /* seldom used, qh_findbestnew will retest all facets */
-        zinc_(Zfindnewsharp);
-        bestfacet= qh_findbestnew(point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
-        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-        qh findbestnew= True;
-      }else
-        qh findbest_notsharp= True;
-    }
-  }
-  if (!bestfacet)
-    bestfacet= qh_findbestlower(lastfacet, point, &bestdist, numpart);
-  if (testhorizon)
-    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
-  *dist= bestdist;
-  if (isoutside && bestdist < qh MINoutside)
-    *isoutside= False;
-LABELreturn_best:
-  zadd_(Zfindbesttot, *numpart);
-  zmax_(Zfindbestmax, *numpart);
-  (*numpart) += numpartnew;
-  qh IStracing= oldtrace;
-  return bestfacet;
-}  /* findbest */
-
-
-/*---------------------------------
-
-  qh_findbesthorizon( qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
-    search coplanar and better horizon facets from startfacet/bestdist
-    ischeckmax turns off statistics and minsearch update
-    all arguments must be initialized
-  returns(ischeckmax):
-    best facet
-  returns(!ischeckmax):
-    best facet that is not upperdelaunay
-    allows upperdelaunay that is clearly outside
-  returns:
-    bestdist is distance to bestfacet
-    numpart -- updates number of distance tests
-
-  notes:
-    no early out -- use qh_findbest() or qh_findbestnew()
-    Searches coplanar or better horizon facets
-
-  when called by qh_check_maxout() (qh_IScheckmax)
-    startfacet must be closest to the point
-      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
-      even though other facets are below the point.
-    updates facet->maxoutside for good, visited facets
-    may return NULL
-
-    searchdist is qh.max_outside + 2 * DISTround
-      + max( MINvisible('Vn'), MAXcoplanar('Un'));
-    This setting is a guess.  It must be at least max_outside + 2*DISTround
-    because a facet may have a geometric neighbor across a vertex
-
-  design:
-    for each horizon facet of coplanar best facets
-      continue if clearly inside
-      unless upperdelaunay or clearly outside
-         update best facet
-*/
-facetT *qh_findbesthorizon(boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
-  facetT *bestfacet= startfacet;
-  realT dist;
-  facetT *neighbor, **neighborp, *facet;
-  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
-  int numpartinit= *numpart, coplanarfacetset_size;
-  unsigned int visitid= ++qh visit_id;
-  boolT newbest= False; /* for tracing */
-  realT minsearch, searchdist;  /* skip facets that are too far from point */
-
-  if (!ischeckmax) {
-    zinc_(Zfindhorizon);
-  }else {
-#if qh_MAXoutside
-    if ((!qh ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
-      startfacet->maxoutside= *bestdist;
-#endif
-  }
-  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
-  minsearch= *bestdist - searchdist;
-  if (ischeckmax) {
-    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
-    minimize_(minsearch, -searchdist);
-  }
-  coplanarfacetset_size= 0;
-  facet= startfacet;
-  while (True) {
-    trace4((qh ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
-                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
-                minsearch, searchdist));
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {
-        qh_distplane(point, neighbor, &dist);
-        (*numpart)++;
-        if (dist > *bestdist) {
-          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh MINoutside)) {
-            bestfacet= neighbor;
-            *bestdist= dist;
-            newbest= True;
-            if (!ischeckmax) {
-              minsearch= dist - searchdist;
-              if (dist > *bestdist + searchdist) {
-                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
-                coplanarfacetset_size= 0;
-              }
-            }
-          }
-        }else if (dist < minsearch)
-          continue;  /* if ischeckmax, dist can't be positive */
-#if qh_MAXoutside
-        if (ischeckmax && dist > neighbor->maxoutside)
-          neighbor->maxoutside= dist;
-#endif
-      } /* end of !flipped */
-      if (nextfacet) {
-        if (!coplanarfacetset_size++) {
-          SETfirst_(qh coplanarfacetset)= nextfacet;
-          SETtruncate_(qh coplanarfacetset, 1);
-        }else
-          qh_setappend(&qh coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
-                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
-      }
-      nextfacet= neighbor;
-    } /* end of EACHneighbor */
-    facet= nextfacet;
-    if (facet)
-      nextfacet= NULL;
-    else if (!coplanarfacetset_size)
-      break;
-    else if (!--coplanarfacetset_size) {
-      facet= SETfirstt_(qh coplanarfacetset, facetT);
-      SETtruncate_(qh coplanarfacetset, 0);
-    }else
-      facet= (facetT*)qh_setdellast(qh coplanarfacetset);
-  } /* while True, for each facet in qh.coplanarfacetset */
-  if (!ischeckmax) {
-    zadd_(Zfindhorizontot, *numpart - numpartinit);
-    zmax_(Zfindhorizonmax, *numpart - numpartinit);
-    if (newbest)
-      zinc_(Zparthorizon);
-  }
-  trace4((qh ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
-  return bestfacet;
-}  /* findbesthorizon */
-
-/*---------------------------------
-
-  qh_findbestnew( point, startfacet, dist, isoutside, numpart )
-    find best newfacet for point
-    searches all of qh.newfacet_list starting at startfacet
-    searches horizon facets of coplanar best newfacets
-    searches all facets if startfacet == qh.facet_list
-  returns:
-    best new or horizon facet that is not upperdelaunay
-    early out if isoutside and not 'Qf'
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart is number of distance tests
-
-  notes:
-    Always used for merged new facets (see qh_USEfindbestnew)
-    Avoids upperdelaunay facet unless (isoutside and outside)
-
-    Uses qh.visit_id, qh.coplanarfacetset.
-    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
-
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    a point maybe coplanar to the bestfacet, below its horizon facet,
-    and above a horizon facet of a coplanar newfacet.  For example,
-      rbox 1000 s Z1 G1e-13 | qhull
-      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
-
-    qh_findbestnew() used if
-       qh_sharpnewfacets -- newfacets contains a sharp angle
-       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
-
-  see also:
-    qh_partitionall() and qh_findbest()
-
-  design:
-    for each new facet starting from startfacet
-      test distance from point to facet
-      return facet if clearly outside
-      unless upperdelaunay and a lowerdelaunay exists
-         update best facet
-    test horizon facets
-*/
-facetT *qh_findbestnew(pointT *point, facetT *startfacet,
-           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2;
-  facetT *bestfacet= NULL, *facet;
-  int oldtrace= qh IStracing, i;
-  unsigned int visitid= ++qh visit_id;
-  realT distoutside= 0.0;
-  boolT isdistoutside; /* True if distoutside is defined */
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  if (!startfacet) {
-    if (qh MERGING)
-      qh_fprintf(qh ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
-    else
-      qh_fprintf(qh ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
-              qh furthest_id);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  zinc_(Zfindnew);
-  if (qh BESToutside || bestoutside)
-    isdistoutside= False;
-  else {
-    isdistoutside= True;
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-  }
-  if (isoutside)
-    *isoutside= True;
-  *numpart= 0;
-  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
-    if (qh TRACElevel > qh IStracing)
-      qh IStracing= qh TRACElevel;
-    qh_fprintf(qh ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
-             qh_pointid(point), startfacet->id, isdistoutside, distoutside);
-    qh_fprintf(qh ferr, 8009, "  Last point added p%d visitid %d.",  qh furthest_id, visitid);
-    qh_fprintf(qh ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
-  }
-  /* visit all new facets starting with startfacet, maybe qh facet_list */
-  for (i=0, facet=startfacet; i < 2; i++, facet= qh newfacet_list) {
-    FORALLfacet_(facet) {
-      if (facet == startfacet && i)
-        break;
-      facet->visitid= visitid;
-      if (!facet->flipped) {
-        qh_distplane(point, facet, dist);
-        (*numpart)++;
-        if (*dist > bestdist) {
-          if (!facet->upperdelaunay || *dist >= qh MINoutside) {
-            bestfacet= facet;
-            if (isdistoutside && *dist >= distoutside)
-              goto LABELreturn_bestnew;
-            bestdist= *dist;
-          }
-        }
-      } /* end of !flipped */
-    } /* FORALLfacet from startfacet or qh newfacet_list */
-  }
-  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
-    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
-                                        !qh_NOupper, &bestdist, numpart);
-  *dist= bestdist;
-  if (isoutside && *dist < qh MINoutside)
-    *isoutside= False;
-LABELreturn_bestnew:
-  zadd_(Zfindnewtot, *numpart);
-  zmax_(Zfindnewmax, *numpart);
-  trace4((qh ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
-  qh IStracing= oldtrace;
-  return bestfacet;
-}  /* findbestnew */
-
-/* ============ hyperplane functions -- keep code together [?] ============ */
-
-/*---------------------------------
-
-  qh_backnormal( rows, numrow, numcol, sign, normal, nearzero )
-    given an upper-triangular rows array and a sign,
-    solve for normal equation x using back substitution over rows U
-
-  returns:
-     normal= x
-
-     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
-       if fails on last row
-         this means that the hyperplane intersects [0,..,1]
-         sets last coordinate of normal to sign
-       otherwise
-         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
-         sets nearzero
-
-  notes:
-     assumes numrow == numcol-1
-
-     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
-
-     solves Ux=b where Ax=b and PA=LU
-     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
-     last row of A= [0,...,0,1]
-
-     1) Ly=Pb == y=b since P only permutes the 0's of   b
-
-  design:
-    for each row from end
-      perform back substitution
-      if near zero
-        use qh_divzero for division
-        if zero divide and not last row
-          set tail of normal to 0
-*/
-void qh_backnormal(realT **rows, int numrow, int numcol, boolT sign,
-        coordT *normal, boolT *nearzero) {
-  int i, j;
-  coordT *normalp, *normal_tail, *ai, *ak;
-  realT diagonal;
-  boolT waszero;
-  int zerocol= -1;
-
-  normalp= normal + numcol - 1;
-  *normalp--= (sign ? -1.0 : 1.0);
-  for (i=numrow; i--; ) {
-    *normalp= 0.0;
-    ai= rows[i] + i + 1;
-    ak= normalp+1;
-    for (j=i+1; j < numcol; j++)
-      *normalp -= *ai++ * *ak++;
-    diagonal= (rows[i])[i];
-    if (fabs_(diagonal) > qh MINdenom_2)
-      *(normalp--) /= diagonal;
-    else {
-      waszero= False;
-      *normalp= qh_divzero(*normalp, diagonal, qh MINdenom_1_2, &waszero);
-      if (waszero) {
-        zerocol= i;
-        *(normalp--)= (sign ? -1.0 : 1.0);
-        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
-          *normal_tail= 0.0;
-      }else
-        normalp--;
-    }
-  }
-  if (zerocol != -1) {
-    zzinc_(Zback0);
-    *nearzero= True;
-    trace4((qh ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
-    qh_precision("zero diagonal on back substitution");
-  }
-} /* backnormal */
-
-/*---------------------------------
-
-  qh_gausselim( rows, numrow, numcol, sign )
-    Gaussian elimination with partial pivoting
-
-  returns:
-    rows is upper triangular (includes row exchanges)
-    flips sign for each row exchange
-    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
-
-  notes:
-    if nearzero, the determinant's sign may be incorrect.
-    assumes numrow <= numcol
-
-  design:
-    for each row
-      determine pivot and exchange rows if necessary
-      test for near zero
-      perform gaussian elimination step
-*/
-void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
-  realT *ai, *ak, *rowp, *pivotrow;
-  realT n, pivot, pivot_abs= 0.0, temp;
-  int i, j, k, pivoti, flip=0;
-
-  *nearzero= False;
-  for (k=0; k < numrow; k++) {
-    pivot_abs= fabs_((rows[k])[k]);
-    pivoti= k;
-    for (i=k+1; i < numrow; i++) {
-      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
-        pivot_abs= temp;
-        pivoti= i;
-      }
-    }
-    if (pivoti != k) {
-      rowp= rows[pivoti];
-      rows[pivoti]= rows[k];
-      rows[k]= rowp;
-      *sign ^= 1;
-      flip ^= 1;
-    }
-    if (pivot_abs <= qh NEARzero[k]) {
-      *nearzero= True;
-      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
-        if (qh IStracing >= 4) {
-          qh_fprintf(qh ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
-          qh_printmatrix(qh ferr, "Matrix:", rows, numrow, numcol);
-        }
-        zzinc_(Zgauss0);
-        qh_precision("zero pivot for Gaussian elimination");
-        goto LABELnextcol;
-      }
-    }
-    pivotrow= rows[k] + k;
-    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
-    for (i=k+1; i < numrow; i++) {
-      ai= rows[i] + k;
-      ak= pivotrow;
-      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
-      for (j= numcol - (k+1); j--; )
-        *ai++ -= n * *ak++;
-    }
-  LABELnextcol:
-    ;
-  }
-  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
-  if (qh IStracing >= 5)
-    qh_printmatrix(qh ferr, "qh_gausselem: result", rows, numrow, numcol);
-} /* gausselim */
-
-
-/*---------------------------------
-
-  qh_getangle( vect1, vect2 )
-    returns the dot product of two vectors
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    the angle may be > 1.0 or < -1.0 because of roundoff errors
-
-*/
-realT qh_getangle(pointT *vect1, pointT *vect2) {
-  realT angle= 0, randr;
-  int k;
-
-  for (k=qh hull_dim; k--; )
-    angle += *vect1++ * *vect2++;
-  if (qh RANDOMdist) {
-    randr= qh_RANDOMint;
-    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh RANDOMfactor;
-  }
-  trace4((qh ferr, 4006, "qh_getangle: %2.2g\n", angle));
-  return(angle);
-} /* getangle */
-
-
-/*---------------------------------
-
-  qh_getcenter( vertices )
-    returns arithmetic center of a set of vertices as a new point
-
-  notes:
-    allocates point array for center
-*/
-pointT *qh_getcenter(setT *vertices) {
-  int k;
-  pointT *center, *coord;
-  vertexT *vertex, **vertexp;
-  int count= qh_setsize(vertices);
-
-  if (count < 2) {
-    qh_fprintf(qh ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  center= (pointT *)qh_memalloc(qh normal_size);
-  for (k=0; k < qh hull_dim; k++) {
-    coord= center+k;
-    *coord= 0.0;
-    FOREACHvertex_(vertices)
-      *coord += vertex->point[k];
-    *coord /= count;  /* count>=2 by QH6003 */
-  }
-  return(center);
-} /* getcenter */
-
-
-/*---------------------------------
-
-  qh_getcentrum( facet )
-    returns the centrum for a facet as a new point
-
-  notes:
-    allocates the centrum
-*/
-pointT *qh_getcentrum(facetT *facet) {
-  realT dist;
-  pointT *centrum, *point;
-
-  point= qh_getcenter(facet->vertices);
-  zzinc_(Zcentrumtests);
-  qh_distplane(point, facet, &dist);
-  centrum= qh_projectpoint(point, facet, dist);
-  qh_memfree(point, qh normal_size);
-  trace4((qh ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
-          facet->id, qh_setsize(facet->vertices), dist));
-  return centrum;
-} /* getcentrum */
-
-
-/*---------------------------------
-
-  qh_getdistance( facet, neighbor, mindist, maxdist )
-    returns the maxdist and mindist distance of any vertex from neighbor
-
-  returns:
-    the max absolute value
-
-  design:
-    for each vertex of facet that is not in neighbor
-      test the distance from vertex to neighbor
-*/
-realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
-  vertexT *vertex, **vertexp;
-  realT dist, maxd, mind;
-
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHvertex_(neighbor->vertices)
-    vertex->seen= True;
-  mind= 0.0;
-  maxd= 0.0;
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      zzinc_(Zbestdist);
-      qh_distplane(vertex->point, neighbor, &dist);
-      if (dist < mind)
-        mind= dist;
-      else if (dist > maxd)
-        maxd= dist;
-    }
-  }
-  *mindist= mind;
-  *maxdist= maxd;
-  mind= -mind;
-  if (maxd > mind)
-    return maxd;
-  else
-    return mind;
-} /* getdistance */
-
-
-/*---------------------------------
-
-  qh_normalize( normal, dim, toporient )
-    normalize a vector and report if too small
-    does not use min norm
-
-  see:
-    qh_normalize2
-*/
-void qh_normalize(coordT *normal, int dim, boolT toporient) {
-  qh_normalize2( normal, dim, toporient, NULL, NULL);
-} /* normalize */
-
-/*---------------------------------
-
-  qh_normalize2( normal, dim, toporient, minnorm, ismin )
-    normalize a vector and report if too small
-    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
-
-  returns:
-    normalized vector
-    flips sign if !toporient
-    if minnorm non-NULL,
-      sets ismin if normal < minnorm
-
-  notes:
-    if zero norm
-       sets all elements to sqrt(1.0/dim)
-    if divide by zero (divzero())
-       sets largest element to   +/-1
-       bumps Znearlysingular
-
-  design:
-    computes norm
-    test for minnorm
-    if not near zero
-      normalizes normal
-    else if zero norm
-      sets normal to standard value
-    else
-      uses qh_divzero to normalize
-      if nearzero
-        sets norm to direction of maximum value
-*/
-void qh_normalize2(coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin) {
-  int k;
-  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
-  boolT zerodiv;
-
-  norm1= normal+1;
-  norm2= normal+2;
-  norm3= normal+3;
-  if (dim == 2)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
-  else if (dim == 3)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
-  else if (dim == 4) {
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3));
-  }else if (dim > 4) {
-    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3);
-    for (k=dim-4, colp=normal+4; k--; colp++)
-      norm += (*colp) * (*colp);
-    norm= sqrt(norm);
-  }
-  if (minnorm) {
-    if (norm < *minnorm)
-      *ismin= True;
-    else
-      *ismin= False;
-  }
-  wmin_(Wmindenom, norm);
-  if (norm > qh MINdenom) {
-    if (!toporient)
-      norm= -norm;
-    *normal /= norm;
-    *norm1 /= norm;
-    if (dim == 2)
-      ; /* all done */
-    else if (dim == 3)
-      *norm2 /= norm;
-    else if (dim == 4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-    }else if (dim >4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-      for (k=dim-4, colp=normal+4; k--; )
-        *colp++ /= norm;
-    }
-  }else if (norm == 0.0) {
-    temp= sqrt(1.0/dim);
-    for (k=dim, colp=normal; k--; )
-      *colp++ = temp;
-  }else {
-    if (!toporient)
-      norm= -norm;
-    for (k=dim, colp=normal; k--; colp++) { /* k used below */
-      temp= qh_divzero(*colp, norm, qh MINdenom_1, &zerodiv);
-      if (!zerodiv)
-        *colp= temp;
-      else {
-        maxp= qh_maxabsval(normal, dim);
-        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
-        for (k=dim, colp=normal; k--; colp++)
-          *colp= 0.0;
-        *maxp= temp;
-        zzinc_(Znearlysingular);
-        trace0((qh ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
-               norm, qh furthest_id));
-        return;
-      }
-    }
-  }
-} /* normalize */
-
-
-/*---------------------------------
-
-  qh_projectpoint( point, facet, dist )
-    project point onto a facet by dist
-
-  returns:
-    returns a new point
-
-  notes:
-    if dist= distplane(point,facet)
-      this projects point to hyperplane
-    assumes qh_memfree_() is valid for normal_size
-*/
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist) {
-  pointT *newpoint, *np, *normal;
-  int normsize= qh normal_size;
-  int k;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(normsize, freelistp, newpoint, pointT);
-  np= newpoint;
-  normal= facet->normal;
-  for (k=qh hull_dim; k--; )
-    *(np++)= *point++ - dist * *normal++;
-  return(newpoint);
-} /* projectpoint */
-
-
-/*---------------------------------
-
-  qh_setfacetplane( facet )
-    sets the hyperplane for a facet
-    if qh.RANDOMdist, joggles hyperplane
-
-  notes:
-    uses global buffers qh.gm_matrix and qh.gm_row
-    overwrites facet->normal if already defined
-    updates Wnewvertex if PRINTstatistics
-    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
-
-  design:
-    copy vertex coordinates to qh.gm_matrix/gm_row
-    compute determinate
-    if nearzero
-      recompute determinate with gaussian elimination
-      if nearzero
-        force outside orientation by testing interior point
-*/
-void qh_setfacetplane(facetT *facet) {
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int normsize= qh normal_size;
-  int k,i, oldtrace= 0;
-  realT dist;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-  coordT *coord, *gmcoord;
-  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
-  boolT nearzero= False;
-
-  zzinc_(Zsetplane);
-  if (!facet->normal)
-    qh_memalloc_(normsize, freelistp, facet->normal, coordT);
-  if (facet == qh tracefacet) {
-    oldtrace= qh IStracing;
-    qh IStracing= 5;
-    qh_fprintf(qh ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
-    qh_fprintf(qh ferr, 8013, "  Last point added to hull was p%d.", qh furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
-    qh_fprintf(qh ferr, 8015, "\n\nCurrent summary is:\n");
-      qh_printsummary(qh ferr);
-  }
-  if (qh hull_dim <= 4) {
-    i= 0;
-    if (qh RANDOMdist) {
-      gmcoord= qh gm_matrix;
-      FOREACHvertex_(facet->vertices) {
-        qh gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        for (k=qh hull_dim; k--; )
-          *(gmcoord++)= *coord++ * qh_randomfactor(qh RANDOMa, qh RANDOMb);
-      }
-    }else {
-      FOREACHvertex_(facet->vertices)
-       qh gm_row[i++]= vertex->point;
-    }
-    qh_sethyperplane_det(qh hull_dim, qh gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-  }
-  if (qh hull_dim > 4 || nearzero) {
-    i= 0;
-    gmcoord= qh gm_matrix;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        qh gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        point= point0;
-        for (k=qh hull_dim; k--; )
-          *(gmcoord++)= *coord++ - *point++;
-      }
-    }
-    qh gm_row[i]= gmcoord;  /* for areasimplex */
-    if (qh RANDOMdist) {
-      gmcoord= qh gm_matrix;
-      for (i=qh hull_dim-1; i--; ) {
-        for (k=qh hull_dim; k--; )
-          *(gmcoord++) *= qh_randomfactor(qh RANDOMa, qh RANDOMb);
-      }
-    }
-    qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-    if (nearzero) {
-      if (qh_orientoutside(facet)) {
-        trace0((qh ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh furthest_id));
-      /* this is part of using Gaussian Elimination.  For example in 5-d
-           1 1 1 1 0
-           1 1 1 1 1
-           0 0 0 1 0
-           0 1 0 0 0
-           1 0 0 0 0
-           norm= 0.38 0.38 -0.76 0.38 0
-         has a determinate of 1, but g.e. after subtracting pt. 0 has
-         0's in the diagonal, even with full pivoting.  It does work
-         if you subtract pt. 4 instead. */
-      }
-    }
-  }
-  facet->upperdelaunay= False;
-  if (qh DELAUNAY) {
-    if (qh UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
-      if (facet->normal[qh hull_dim -1] >= qh ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }else {
-      if (facet->normal[qh hull_dim -1] > -qh ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }
-  }
-  if (qh PRINTstatistics || qh IStracing || qh TRACElevel || qh JOGGLEmax < REALmax) {
-    qh old_randomdist= qh RANDOMdist;
-    qh RANDOMdist= False;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        boolT istrace= False;
-        zinc_(Zdiststat);
-        qh_distplane(vertex->point, facet, &dist);
-        dist= fabs_(dist);
-        zinc_(Znewvertex);
-        wadd_(Wnewvertex, dist);
-        if (dist > wwval_(Wnewvertexmax)) {
-          wwval_(Wnewvertexmax)= dist;
-          if (dist > qh max_outside) {
-            qh max_outside= dist;  /* used by qh_maxouter() */
-            if (dist > qh TRACEdist)
-              istrace= True;
-          }
-        }else if (-dist > qh TRACEdist)
-          istrace= True;
-        if (istrace) {
-          qh_fprintf(qh ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
-                qh_pointid(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
-          qh_errprint("DISTANT", facet, NULL, NULL, NULL);
-        }
-      }
-    }
-    qh RANDOMdist= qh old_randomdist;
-  }
-  if (qh IStracing >= 3) {
-    qh_fprintf(qh ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
-             facet->id, facet->offset);
-    for (k=0; k < qh hull_dim; k++)
-      qh_fprintf(qh ferr, 8018, "%2.2g ", facet->normal[k]);
-    qh_fprintf(qh ferr, 8019, "\n");
-  }
-  if (facet == qh tracefacet)
-    qh IStracing= oldtrace;
-} /* setfacetplane */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_det( dim, rows, point0, toporient, normal, offset, nearzero )
-    given dim X dim array indexed by rows[], one row per point,
-        toporient(flips all signs),
-        and point0 (any row)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-    sets nearzero if hyperplane not through points
-
-  notes:
-    only defined for dim == 2..4
-    rows[] is not modified
-    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
-    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
-
-  derivation of 3-d minnorm
-    Goal: all vertices V_i within qh.one_merge of hyperplane
-    Plan: exactly translate the facet so that V_0 is the origin
-          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
-          exactly rotate the effective perturbation to only effect n_0
-             this introduces a factor of sqrt(3)
-    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
-    Let M_d be the max coordinate difference
-    Let M_a be the greater of M_d and the max abs. coordinate
-    Let u be machine roundoff and distround be max error for distance computation
-    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
-    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
-    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
-
-  derivation of 4-d minnorm
-    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
-     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
-    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
-     [all other terms contain at least two factors nearly zero.]
-    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
-    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
-*/
-void qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
-          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
-  realT maxround, dist;
-  int i;
-  pointT *point;
-
-
-  if (dim == 2) {
-    normal[0]= dY(1,0);
-    normal[1]= dX(0,1);
-    qh_normalize2(normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
-    *nearzero= False;  /* since nearzero norm => incident points */
-  }else if (dim == 3) {
-    normal[0]= det2_(dY(2,0), dZ(2,0),
-                     dY(1,0), dZ(1,0));
-    normal[1]= det2_(dX(1,0), dZ(1,0),
-                     dX(2,0), dZ(2,0));
-    normal[2]= det2_(dX(2,0), dY(2,0),
-                     dX(1,0), dY(1,0));
-    qh_normalize2(normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2]);
-    maxround= qh DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }else if (dim == 4) {
-    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
-                        dY(1,0), dZ(1,0), dW(1,0),
-                        dY(3,0), dZ(3,0), dW(3,0));
-    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
-                        dX(1,0), dZ(1,0), dW(1,0),
-                        dX(3,0), dZ(3,0), dW(3,0));
-    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
-                        dX(1,0), dY(1,0), dW(1,0),
-                        dX(3,0), dY(3,0), dW(3,0));
-    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
-                        dX(1,0), dY(1,0), dZ(1,0),
-                        dX(3,0), dY(3,0), dZ(3,0));
-    qh_normalize2(normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2] + point0[3]*normal[3]);
-    maxround= qh DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2] + point[3]*normal[3]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }
-  if (*nearzero) {
-    zzinc_(Zminnorm);
-    trace0((qh ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
-    zzinc_(Znearlysingular);
-  }
-} /* sethyperplane_det */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_gauss( dim, rows, point0, toporient, normal, offset, nearzero )
-    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-
-  notes:
-    if nearzero
-      orientation may be incorrect because of incorrect sign flips in gausselim
-    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
-        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
-    i.e., N is normal to the hyperplane, and the unnormalized
-        distance to [0 .. 1] is either 1 or   0
-
-  design:
-    perform gaussian elimination
-    flip sign for negative values
-    perform back substitution
-    normalize result
-    compute offset
-*/
-void qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
-                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
-  coordT *pointcoord, *normalcoef;
-  int k;
-  boolT sign= toporient, nearzero2= False;
-
-  qh_gausselim(rows, dim-1, dim, &sign, nearzero);
-  for (k=dim-1; k--; ) {
-    if ((rows[k])[k] < 0)
-      sign ^= 1;
-  }
-  if (*nearzero) {
-    zzinc_(Znearlysingular);
-    trace0((qh ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
-    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
-  }else {
-    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
-    if (nearzero2) {
-      zzinc_(Znearlysingular);
-      trace0((qh ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh furthest_id));
-    }
-  }
-  if (nearzero2)
-    *nearzero= True;
-  qh_normalize2(normal, dim, True, NULL, NULL);
-  pointcoord= point0;
-  normalcoef= normal;
-  *offset= -(*pointcoord++ * *normalcoef++);
-  for (k=dim-1; k--; )
-    *offset -= *pointcoord++ * *normalcoef++;
-} /* sethyperplane_gauss */
-
-
-
diff --git a/src/qhull/src/libqhull/geom.h b/src/qhull/src/libqhull/geom.h
deleted file mode 100644
index 16ef48d2d..000000000
--- a/src/qhull/src/libqhull/geom.h
+++ /dev/null
@@ -1,176 +0,0 @@
-/*
      ---------------------------------
-
-  geom.h
-    header file for geometric routines
-
-   see qh-geom.htm and geom.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/geom.h#1 $$Change: 1981 $
-   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-#include "libqhull.h"
-
-/* ============ -macros- ======================== */
-
-/*----------------------------------
-
-  fabs_(a)
-    returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*----------------------------------
-
-  fmax_(a,b)
-    returns the maximum value of a and b
-*/
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  fmin_(a,b)
-    returns the minimum value of a and b
-*/
-#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  maximize_(maxval, val)
-    set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
-
-/*----------------------------------
-
-  minimize_(minval, val)
-    set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
-
-/*----------------------------------
-
-  det2_(a1, a2,
-        b1, b2)
-
-    compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*----------------------------------
-
-  det3_(a1, a2, a3,
-       b1, b2, b3,
-       c1, c2, c3)
-
-    compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
-                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*----------------------------------
-
-  dX( p1, p2 )
-  dY( p1, p2 )
-  dZ( p1, p2 )
-
-    given two indices into rows[],
-
-    compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-void    qh_backnormal(realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
-void    qh_distplane(pointT *point, facetT *facet, realT *dist);
-facetT *qh_findbest(pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT isnewfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbesthorizon(boolT ischeckmax, pointT *point,
-                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
-facetT *qh_findbestnew(pointT *point, facetT *startfacet, realT *dist,
-                     boolT bestoutside, boolT *isoutside, int *numpart);
-void    qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
-realT   qh_getangle(pointT *vect1, pointT *vect2);
-pointT *qh_getcenter(setT *vertices);
-pointT *qh_getcentrum(facetT *facet);
-realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
-void    qh_normalize(coordT *normal, int dim, boolT toporient);
-void    qh_normalize2(coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin);
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
-
-void    qh_setfacetplane(facetT *newfacets);
-void    qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
-              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
-void    qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
-             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
-boolT   qh_sharpnewfacets(void);
-
-/*========= infrequently used code in geom2.c =============*/
-
-coordT *qh_copypoints(coordT *points, int numpoints, int dimension);
-void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT   qh_determinant(realT **rows, int dim, boolT *nearzero);
-realT   qh_detjoggle(pointT *points, int numpoints, int dimension);
-void    qh_detroundoff(void);
-realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
-realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
-realT   qh_distround(int dimension, realT maxabs, realT maxsumabs);
-realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
-realT   qh_facetarea(facetT *facet);
-realT   qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
-          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
-pointT *qh_facetcenter(setT *vertices);
-facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
-void    qh_getarea(facetT *facetlist);
-boolT   qh_gram_schmidt(int dim, realT **rows);
-boolT   qh_inthresholds(coordT *normal, realT *angle);
-void    qh_joggleinput(void);
-realT  *qh_maxabsval(realT *normal, int dim);
-setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
-realT   qh_maxouter(void);
-void    qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
-realT   qh_minabsval(realT *normal, int dim);
-int     qh_mindiff(realT *vecA, realT *vecB, int dim);
-boolT   qh_orientoutside(facetT *facet);
-void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
-coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
-void    qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol);
-void    qh_printpoints(FILE *fp, const char *string, setT *points);
-void    qh_projectinput(void);
-void    qh_projectpoints(signed char *project, int n, realT *points,
-             int numpoints, int dim, realT *newpoints, int newdim);
-void    qh_rotateinput(realT **rows);
-void    qh_rotatepoints(realT *points, int numpoints, int dim, realT **rows);
-void    qh_scaleinput(void);
-void    qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
-                   coordT high, coordT newhigh);
-void    qh_scalepoints(pointT *points, int numpoints, int dim,
-                realT *newlows, realT *newhighs);
-boolT   qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
-              coordT *normal, coordT *offset, coordT *feasible);
-coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
-pointT *qh_voronoi_center(int dim, setT *points);
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/src/qhull/src/libqhull/geom2.c b/src/qhull/src/libqhull/geom2.c
deleted file mode 100644
index 82ec4936e..000000000
--- a/src/qhull/src/libqhull/geom2.c
+++ /dev/null
@@ -1,2094 +0,0 @@
-/*
      ---------------------------------
-
-
-   geom2.c
-   infrequently used geometric routines of qhull
-
-   see qh-geom.htm and geom.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/geom2.c#6 $$Change: 2065 $
-   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-
-   frequently used code goes into geom.c
-*/
-
-#include "qhull_a.h"
-
-/*================== functions in alphabetic order ============*/
-
-/*---------------------------------
-
-  qh_copypoints( points, numpoints, dimension)
-    return qh_malloc'd copy of points
-  notes:
-    qh_free the returned points to avoid a memory leak
-*/
-coordT *qh_copypoints(coordT *points, int numpoints, int dimension) {
-  int size;
-  coordT *newpoints;
-
-  size= numpoints * dimension * (int)sizeof(coordT);
-  if (!(newpoints=(coordT*)qh_malloc((size_t)size))) {
-    qh_fprintf(qh ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
-        numpoints);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
-  return newpoints;
-} /* copypoints */
-
-/*---------------------------------
-
-  qh_crossproduct( dim, vecA, vecB, vecC )
-    crossproduct of 2 dim vectors
-    C= A x B
-
-  notes:
-    from Glasner, Graphics Gems I, p. 639
-    only defined for dim==3
-*/
-void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
-
-  if (dim == 3) {
-    vecC[0]=   det2_(vecA[1], vecA[2],
-                     vecB[1], vecB[2]);
-    vecC[1]= - det2_(vecA[0], vecA[2],
-                     vecB[0], vecB[2]);
-    vecC[2]=   det2_(vecA[0], vecA[1],
-                     vecB[0], vecB[1]);
-  }
-} /* vcross */
-
-/*---------------------------------
-
-  qh_determinant( rows, dim, nearzero )
-    compute signed determinant of a square matrix
-    uses qh.NEARzero to test for degenerate matrices
-
-  returns:
-    determinant
-    overwrites rows and the matrix
-    if dim == 2 or 3
-      nearzero iff determinant < qh NEARzero[dim-1]
-      (!quite correct, not critical)
-    if dim >= 4
-      nearzero iff diagonal[k] < qh NEARzero[k]
-*/
-realT qh_determinant(realT **rows, int dim, boolT *nearzero) {
-  realT det=0;
-  int i;
-  boolT sign= False;
-
-  *nearzero= False;
-  if (dim < 2) {
-    qh_fprintf(qh ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }else if (dim == 2) {
-    det= det2_(rows[0][0], rows[0][1],
-                 rows[1][0], rows[1][1]);
-    if (fabs_(det) < 10*qh NEARzero[1])  /* not really correct, what should this be? */
-      *nearzero= True;
-  }else if (dim == 3) {
-    det= det3_(rows[0][0], rows[0][1], rows[0][2],
-                 rows[1][0], rows[1][1], rows[1][2],
-                 rows[2][0], rows[2][1], rows[2][2]);
-    if (fabs_(det) < 10*qh NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63  */
-      *nearzero= True;
-  }else {
-    qh_gausselim(rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
-    det= 1.0;
-    for (i=dim; i--; )
-      det *= (rows[i])[i];
-    if (sign)
-      det= -det;
-  }
-  return det;
-} /* determinant */
-
-/*---------------------------------
-
-  qh_detjoggle( points, numpoints, dimension )
-    determine default max joggle for point array
-      as qh_distround * qh_JOGGLEdefault
-
-  returns:
-    initial value for JOGGLEmax from points and REALepsilon
-
-  notes:
-    computes DISTround since qh_maxmin not called yet
-    if qh SCALElast, last dimension will be scaled later to MAXwidth
-
-    loop duplicated from qh_maxmin
-*/
-realT qh_detjoggle(pointT *points, int numpoints, int dimension) {
-  realT abscoord, distround, joggle, maxcoord, mincoord;
-  pointT *point, *pointtemp;
-  realT maxabs= -REALmax;
-  realT sumabs= 0;
-  realT maxwidth= 0;
-  int k;
-
-  for (k=0; k < dimension; k++) {
-    if (qh SCALElast && k == dimension-1)
-      abscoord= maxwidth;
-    else if (qh DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
-      abscoord= 2 * maxabs * maxabs;  /* may be low by qh hull_dim/2 */
-    else {
-      maxcoord= -REALmax;
-      mincoord= REALmax;
-      FORALLpoint_(points, numpoints) {
-        maximize_(maxcoord, point[k]);
-        minimize_(mincoord, point[k]);
-      }
-      maximize_(maxwidth, maxcoord-mincoord);
-      abscoord= fmax_(maxcoord, -mincoord);
-    }
-    sumabs += abscoord;
-    maximize_(maxabs, abscoord);
-  } /* for k */
-  distround= qh_distround(qh hull_dim, maxabs, sumabs);
-  joggle= distround * qh_JOGGLEdefault;
-  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
-  trace2((qh ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
-  return joggle;
-} /* detjoggle */
-
-/*---------------------------------
-
-  qh_detroundoff()
-    determine maximum roundoff errors from
-      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
-      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
-
-    accounts for qh.SETroundoff, qh.RANDOMdist, qh MERGEexact
-      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
-      qh.postmerge_centrum, qh.MINoutside,
-      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
-
-  returns:
-    sets qh.DISTround, etc. (see below)
-    appends precision constants to qh.qhull_options
-
-  see:
-    qh_maxmin() for qh.NEARzero
-
-  design:
-    determine qh.DISTround for distance computations
-    determine minimum denominators for qh_divzero
-    determine qh.ANGLEround for angle computations
-    adjust qh.premerge_cos,... for roundoff error
-    determine qh.ONEmerge for maximum error due to a single merge
-    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
-      qh.MINoutside, qh.WIDEfacet
-    initialize qh.max_vertex and qh.minvertex
-*/
-void qh_detroundoff(void) {
-
-  qh_option("_max-width", NULL, &qh MAXwidth);
-  if (!qh SETroundoff) {
-    qh DISTround= qh_distround(qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
-    if (qh RANDOMdist)
-      qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
-    qh_option("Error-roundoff", NULL, &qh DISTround);
-  }
-  qh MINdenom= qh MINdenom_1 * qh MAXabs_coord;
-  qh MINdenom_1_2= sqrt(qh MINdenom_1 * qh hull_dim) ;  /* if will be normalized */
-  qh MINdenom_2= qh MINdenom_1_2 * qh MAXabs_coord;
-                                              /* for inner product */
-  qh ANGLEround= 1.01 * qh hull_dim * REALepsilon;
-  if (qh RANDOMdist)
-    qh ANGLEround += qh RANDOMfactor;
-  if (qh premerge_cos < REALmax/2) {
-    qh premerge_cos -= qh ANGLEround;
-    if (qh RANDOMdist)
-      qh_option("Angle-premerge-with-random", NULL, &qh premerge_cos);
-  }
-  if (qh postmerge_cos < REALmax/2) {
-    qh postmerge_cos -= qh ANGLEround;
-    if (qh RANDOMdist)
-      qh_option("Angle-postmerge-with-random", NULL, &qh postmerge_cos);
-  }
-  qh premerge_centrum += 2 * qh DISTround;    /*2 for centrum and distplane()*/
-  qh postmerge_centrum += 2 * qh DISTround;
-  if (qh RANDOMdist && (qh MERGEexact || qh PREmerge))
-    qh_option("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
-  if (qh RANDOMdist && qh POSTmerge)
-    qh_option("Centrum-postmerge-with-random", NULL, &qh postmerge_centrum);
-  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
-    realT maxangle= 1.0, maxrho;
-
-    minimize_(maxangle, qh premerge_cos);
-    minimize_(maxangle, qh postmerge_cos);
-    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
-    qh ONEmerge= sqrt((realT)qh hull_dim) * qh MAXwidth *
-      sqrt(1.0 - maxangle * maxangle) + qh DISTround;
-    maxrho= qh hull_dim * qh premerge_centrum + qh DISTround;
-    maximize_(qh ONEmerge, maxrho);
-    maxrho= qh hull_dim * qh postmerge_centrum + qh DISTround;
-    maximize_(qh ONEmerge, maxrho);
-    if (qh MERGING)
-      qh_option("_one-merge", NULL, &qh ONEmerge);
-  }
-  qh NEARinside= qh ONEmerge * qh_RATIOnearinside; /* only used if qh KEEPnearinside */
-  if (qh JOGGLEmax < REALmax/2 && (qh KEEPcoplanar || qh KEEPinside)) {
-    realT maxdist;             /* adjust qh.NEARinside for joggle */
-    qh KEEPnearinside= True;
-    maxdist= sqrt((realT)qh hull_dim) * qh JOGGLEmax + qh DISTround;
-    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
-    maximize_(qh NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
-  }
-  if (qh KEEPnearinside)
-    qh_option("_near-inside", NULL, &qh NEARinside);
-  if (qh JOGGLEmax < qh DISTround) {
-    qh_fprintf(qh ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
-         qh JOGGLEmax, qh DISTround);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh MINvisible > REALmax/2) {
-    if (!qh MERGING)
-      qh MINvisible= qh DISTround;
-    else if (qh hull_dim <= 3)
-      qh MINvisible= qh premerge_centrum;
-    else
-      qh MINvisible= qh_COPLANARratio * qh premerge_centrum;
-    if (qh APPROXhull && qh MINvisible > qh MINoutside)
-      qh MINvisible= qh MINoutside;
-    qh_option("Visible-distance", NULL, &qh MINvisible);
-  }
-  if (qh MAXcoplanar > REALmax/2) {
-    qh MAXcoplanar= qh MINvisible;
-    qh_option("U-coplanar-distance", NULL, &qh MAXcoplanar);
-  }
-  if (!qh APPROXhull) {             /* user may specify qh MINoutside */
-    qh MINoutside= 2 * qh MINvisible;
-    if (qh premerge_cos < REALmax/2)
-      maximize_(qh MINoutside, (1- qh premerge_cos) * qh MAXabs_coord);
-    qh_option("Width-outside", NULL, &qh MINoutside);
-  }
-  qh WIDEfacet= qh MINoutside;
-  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MAXcoplanar);
-  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MINvisible);
-  qh_option("_wide-facet", NULL, &qh WIDEfacet);
-  if (qh MINvisible > qh MINoutside + 3 * REALepsilon
-  && !qh BESToutside && !qh FORCEoutput)
-    qh_fprintf(qh ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
-             qh MINvisible, qh MINoutside);
-  qh max_vertex= qh DISTround;
-  qh min_vertex= -qh DISTround;
-  /* numeric constants reported in printsummary */
-} /* detroundoff */
-
-/*---------------------------------
-
-  qh_detsimplex( apex, points, dim, nearzero )
-    compute determinant of a simplex with point apex and base points
-
-  returns:
-     signed determinant and nearzero from qh_determinant
-
-  notes:
-     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
-
-  design:
-    construct qm_matrix by subtracting apex from points
-    compute determinate
-*/
-realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero) {
-  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
-  coordT **rows;
-  int k,  i=0;
-  realT det;
-
-  zinc_(Zdetsimplex);
-  gmcoord= qh gm_matrix;
-  rows= qh gm_row;
-  FOREACHpoint_(points) {
-    if (i == dim)
-      break;
-    rows[i++]= gmcoord;
-    coordp= point;
-    coorda= apex;
-    for (k=dim; k--; )
-      *(gmcoord++)= *coordp++ - *coorda++;
-  }
-  if (i < dim) {
-    qh_fprintf(qh ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
-               i, dim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  det= qh_determinant(rows, dim, nearzero);
-  trace2((qh ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
-          det, qh_pointid(apex), dim, *nearzero));
-  return det;
-} /* detsimplex */
-
-/*---------------------------------
-
-  qh_distnorm( dim, point, normal, offset )
-    return distance from point to hyperplane at normal/offset
-
-  returns:
-    dist
-
-  notes:
-    dist > 0 if point is outside of hyperplane
-
-  see:
-    qh_distplane in geom.c
-*/
-realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
-  coordT *normalp= normal, *coordp= point;
-  realT dist;
-  int k;
-
-  dist= *offsetp;
-  for (k=dim; k--; )
-    dist += *(coordp++) * *(normalp++);
-  return dist;
-} /* distnorm */
-
-/*---------------------------------
-
-  qh_distround(dimension, maxabs, maxsumabs )
-    compute maximum round-off error for a distance computation
-      to a normalized hyperplane
-    maxabs is the maximum absolute value of a coordinate
-    maxsumabs is the maximum possible sum of absolute coordinate values
-
-  returns:
-    max dist round for REALepsilon
-
-  notes:
-    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
-    use sqrt(dim) since one vector is normalized
-      or use maxsumabs since one vector is < 1
-*/
-realT qh_distround(int dimension, realT maxabs, realT maxsumabs) {
-  realT maxdistsum, maxround;
-
-  maxdistsum= sqrt((realT)dimension) * maxabs;
-  minimize_( maxdistsum, maxsumabs);
-  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
-              /* adds maxabs for offset */
-  trace4((qh ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
-                 maxround, maxabs, maxsumabs, maxdistsum));
-  return maxround;
-} /* distround */
-
-/*---------------------------------
-
-  qh_divzero( numer, denom, mindenom1, zerodiv )
-    divide by a number that's nearly zero
-    mindenom1= minimum denominator for dividing into 1.0
-
-  returns:
-    quotient
-    sets zerodiv and returns 0.0 if it would overflow
-
-  design:
-    if numer is nearly zero and abs(numer) < abs(denom)
-      return numer/denom
-    else if numer is nearly zero
-      return 0 and zerodiv
-    else if denom/numer non-zero
-      return numer/denom
-    else
-      return 0 and zerodiv
-*/
-realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
-  realT temp, numerx, denomx;
-
-
-  if (numer < mindenom1 && numer > -mindenom1) {
-    numerx= fabs_(numer);
-    denomx= fabs_(denom);
-    if (numerx < denomx) {
-      *zerodiv= False;
-      return numer/denom;
-    }else {
-      *zerodiv= True;
-      return 0.0;
-    }
-  }
-  temp= denom/numer;
-  if (temp > mindenom1 || temp < -mindenom1) {
-    *zerodiv= False;
-    return numer/denom;
-  }else {
-    *zerodiv= True;
-    return 0.0;
-  }
-} /* divzero */
-
-
-/*---------------------------------
-
-  qh_facetarea( facet )
-    return area for a facet
-
-  notes:
-    if non-simplicial,
-      uses centrum to triangulate facet and sums the projected areas.
-    if (qh DELAUNAY),
-      computes projected area instead for last coordinate
-    assumes facet->normal exists
-    projecting tricoplanar facets to the hyperplane does not appear to make a difference
-
-  design:
-    if simplicial
-      compute area
-    else
-      for each ridge
-        compute area from centrum to ridge
-    negate area if upper Delaunay facet
-*/
-realT qh_facetarea(facetT *facet) {
-  vertexT *apex;
-  pointT *centrum;
-  realT area= 0.0;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->simplicial) {
-    apex= SETfirstt_(facet->vertices, vertexT);
-    area= qh_facetarea_simplex(qh hull_dim, apex->point, facet->vertices,
-                    apex, facet->toporient, facet->normal, &facet->offset);
-  }else {
-    if (qh CENTERtype == qh_AScentrum)
-      centrum= facet->center;
-    else
-      centrum= qh_getcentrum(facet);
-    FOREACHridge_(facet->ridges)
-      area += qh_facetarea_simplex(qh hull_dim, centrum, ridge->vertices,
-                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
-    if (qh CENTERtype != qh_AScentrum)
-      qh_memfree(centrum, qh normal_size);
-  }
-  if (facet->upperdelaunay && qh DELAUNAY)
-    area= -area;  /* the normal should be [0,...,1] */
-  trace4((qh ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
-  return area;
-} /* facetarea */
-
-/*---------------------------------
-
-  qh_facetarea_simplex( dim, apex, vertices, notvertex, toporient, normal, offset )
-    return area for a simplex defined by
-      an apex, a base of vertices, an orientation, and a unit normal
-    if simplicial or tricoplanar facet,
-      notvertex is defined and it is skipped in vertices
-
-  returns:
-    computes area of simplex projected to plane [normal,offset]
-    returns 0 if vertex too far below plane (qh WIDEfacet)
-      vertex can't be apex of tricoplanar facet
-
-  notes:
-    if (qh DELAUNAY),
-      computes projected area instead for last coordinate
-    uses qh gm_matrix/gm_row and qh hull_dim
-    helper function for qh_facetarea
-
-  design:
-    if Notvertex
-      translate simplex to apex
-    else
-      project simplex to normal/offset
-      translate simplex to apex
-    if Delaunay
-      set last row/column to 0 with -1 on diagonal
-    else
-      set last row to Normal
-    compute determinate
-    scale and flip sign for area
-*/
-realT qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
-        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
-  pointT *coorda, *coordp, *gmcoord;
-  coordT **rows, *normalp;
-  int k,  i=0;
-  realT area, dist;
-  vertexT *vertex, **vertexp;
-  boolT nearzero;
-
-  gmcoord= qh gm_matrix;
-  rows= qh gm_row;
-  FOREACHvertex_(vertices) {
-    if (vertex == notvertex)
-      continue;
-    rows[i++]= gmcoord;
-    coorda= apex;
-    coordp= vertex->point;
-    normalp= normal;
-    if (notvertex) {
-      for (k=dim; k--; )
-        *(gmcoord++)= *coordp++ - *coorda++;
-    }else {
-      dist= *offset;
-      for (k=dim; k--; )
-        dist += *coordp++ * *normalp++;
-      if (dist < -qh WIDEfacet) {
-        zinc_(Znoarea);
-        return 0.0;
-      }
-      coordp= vertex->point;
-      normalp= normal;
-      for (k=dim; k--; )
-        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
-    }
-  }
-  if (i != dim-1) {
-    qh_fprintf(qh ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
-               i, dim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  rows[i]= gmcoord;
-  if (qh DELAUNAY) {
-    for (i=0; i < dim-1; i++)
-      rows[i][dim-1]= 0.0;
-    for (k=dim; k--; )
-      *(gmcoord++)= 0.0;
-    rows[dim-1][dim-1]= -1.0;
-  }else {
-    normalp= normal;
-    for (k=dim; k--; )
-      *(gmcoord++)= *normalp++;
-  }
-  zinc_(Zdetsimplex);
-  area= qh_determinant(rows, dim, &nearzero);
-  if (toporient)
-    area= -area;
-  area *= qh AREAfactor;
-  trace4((qh ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
-          area, qh_pointid(apex), toporient, nearzero));
-  return area;
-} /* facetarea_simplex */
-
-/*---------------------------------
-
-  qh_facetcenter( vertices )
-    return Voronoi center (Voronoi vertex) for a facet's vertices
-
-  returns:
-    return temporary point equal to the center
-
-  see:
-    qh_voronoi_center()
-*/
-pointT *qh_facetcenter(setT *vertices) {
-  setT *points= qh_settemp(qh_setsize(vertices));
-  vertexT *vertex, **vertexp;
-  pointT *center;
-
-  FOREACHvertex_(vertices)
-    qh_setappend(&points, vertex->point);
-  center= qh_voronoi_center(qh hull_dim-1, points);
-  qh_settempfree(&points);
-  return center;
-} /* facetcenter */
-
-/*---------------------------------
-
-  qh_findgooddist( point, facetA, dist, facetlist )
-    find best good facet visible for point from facetA
-    assumes facetA is visible from point
-
-  returns:
-    best facet, i.e., good facet that is furthest from point
-      distance to best facet
-      NULL if none
-
-    moves good, visible facets (and some other visible facets)
-      to end of qh facet_list
-
-  notes:
-    uses qh visit_id
-
-  design:
-    initialize bestfacet if facetA is good
-    move facetA to end of facetlist
-    for each facet on facetlist
-      for each unvisited neighbor of facet
-        move visible neighbors to end of facetlist
-        update best good neighbor
-        if no good neighbors, update best facet
-*/
-facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp,
-               facetT **facetlist) {
-  realT bestdist= -REALmax, dist;
-  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
-  boolT goodseen= False;
-
-  if (facetA->good) {
-    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
-    qh_distplane(point, facetA, &bestdist);
-    bestfacet= facetA;
-    goodseen= True;
-  }
-  qh_removefacet(facetA);
-  qh_appendfacet(facetA);
-  *facetlist= facetA;
-  facetA->visitid= ++qh visit_id;
-  FORALLfacet_(*facetlist) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      if (goodseen && !neighbor->good)
-        continue;
-      zzinc_(Zcheckpart);
-      qh_distplane(point, neighbor, &dist);
-      if (dist > 0) {
-        qh_removefacet(neighbor);
-        qh_appendfacet(neighbor);
-        if (neighbor->good) {
-          goodseen= True;
-          if (dist > bestdist) {
-            bestdist= dist;
-            bestfacet= neighbor;
-          }
-        }
-      }
-    }
-  }
-  if (bestfacet) {
-    *distp= bestdist;
-    trace2((qh ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
-      qh_pointid(point), bestdist, bestfacet->id));
-    return bestfacet;
-  }
-  trace4((qh ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
-      qh_pointid(point), facetA->id));
-  return NULL;
-}  /* findgooddist */
-
-/*---------------------------------
-
-  qh_getarea( facetlist )
-    set area of all facets in facetlist
-    collect statistics
-    nop if hasAreaVolume
-
-  returns:
-    sets qh totarea/totvol to total area and volume of convex hull
-    for Delaunay triangulation, computes projected area of the lower or upper hull
-      ignores upper hull if qh ATinfinity
-
-  notes:
-    could compute outer volume by expanding facet area by rays from interior
-    the following attempt at perpendicular projection underestimated badly:
-      qh.totoutvol += (-dist + facet->maxoutside + qh DISTround)
-                            * area/ qh hull_dim;
-  design:
-    for each facet on facetlist
-      compute facet->area
-      update qh.totarea and qh.totvol
-*/
-void qh_getarea(facetT *facetlist) {
-  realT area;
-  realT dist;
-  facetT *facet;
-
-  if (qh hasAreaVolume)
-    return;
-  if (qh REPORTfreq)
-    qh_fprintf(qh ferr, 8020, "computing area of each facet and volume of the convex hull\n");
-  else
-    trace1((qh ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
-  qh totarea= qh totvol= 0.0;
-  FORALLfacet_(facetlist) {
-    if (!facet->normal)
-      continue;
-    if (facet->upperdelaunay && qh ATinfinity)
-      continue;
-    if (!facet->isarea) {
-      facet->f.area= qh_facetarea(facet);
-      facet->isarea= True;
-    }
-    area= facet->f.area;
-    if (qh DELAUNAY) {
-      if (facet->upperdelaunay == qh UPPERdelaunay)
-        qh totarea += area;
-    }else {
-      qh totarea += area;
-      qh_distplane(qh interior_point, facet, &dist);
-      qh totvol += -dist * area/ qh hull_dim;
-    }
-    if (qh PRINTstatistics) {
-      wadd_(Wareatot, area);
-      wmax_(Wareamax, area);
-      wmin_(Wareamin, area);
-    }
-  }
-  qh hasAreaVolume= True;
-} /* getarea */
-
-/*---------------------------------
-
-  qh_gram_schmidt( dim, row )
-    implements Gram-Schmidt orthogonalization by rows
-
-  returns:
-    false if zero norm
-    overwrites rows[dim][dim]
-
-  notes:
-    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
-    overflow due to small divisors not handled
-
-  design:
-    for each row
-      compute norm for row
-      if non-zero, normalize row
-      for each remaining rowA
-        compute inner product of row and rowA
-        reduce rowA by row * inner product
-*/
-boolT qh_gram_schmidt(int dim, realT **row) {
-  realT *rowi, *rowj, norm;
-  int i, j, k;
-
-  for (i=0; i < dim; i++) {
-    rowi= row[i];
-    for (norm= 0.0, k= dim; k--; rowi++)
-      norm += *rowi * *rowi;
-    norm= sqrt(norm);
-    wmin_(Wmindenom, norm);
-    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
-      return False;
-    for (k=dim; k--; )
-      *(--rowi) /= norm;
-    for (j=i+1; j < dim; j++) {
-      rowj= row[j];
-      for (norm= 0.0, k=dim; k--; )
-        norm += *rowi++ * *rowj++;
-      for (k=dim; k--; )
-        *(--rowj) -= *(--rowi) * norm;
-    }
-  }
-  return True;
-} /* gram_schmidt */
-
-
-/*---------------------------------
-
-  qh_inthresholds( normal, angle )
-    return True if normal within qh.lower_/upper_threshold
-
-  returns:
-    estimate of angle by summing of threshold diffs
-      angle may be NULL
-      smaller "angle" is better
-
-  notes:
-    invalid if qh.SPLITthresholds
-
-  see:
-    qh.lower_threshold in qh_initbuild()
-    qh_initthresholds()
-
-  design:
-    for each dimension
-      test threshold
-*/
-boolT qh_inthresholds(coordT *normal, realT *angle) {
-  boolT within= True;
-  int k;
-  realT threshold;
-
-  if (angle)
-    *angle= 0.0;
-  for (k=0; k < qh hull_dim; k++) {
-    threshold= qh lower_threshold[k];
-    if (threshold > -REALmax/2) {
-      if (normal[k] < threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-    if (qh upper_threshold[k] < REALmax/2) {
-      threshold= qh upper_threshold[k];
-      if (normal[k] > threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-  }
-  return within;
-} /* inthresholds */
-
-
-/*---------------------------------
-
-  qh_joggleinput()
-    randomly joggle input to Qhull by qh.JOGGLEmax
-    initial input is qh.first_point/qh.num_points of qh.hull_dim
-      repeated calls use qh.input_points/qh.num_points
-
-  returns:
-    joggles points at qh.first_point/qh.num_points
-    copies data to qh.input_points/qh.input_malloc if first time
-    determines qh.JOGGLEmax if it was zero
-    if qh.DELAUNAY
-      computes the Delaunay projection of the joggled points
-
-  notes:
-    if qh.DELAUNAY, unnecessarily joggles the last coordinate
-    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
-
-  design:
-    if qh.DELAUNAY
-      set qh.SCALElast for reduced precision errors
-    if first call
-      initialize qh.input_points to the original input points
-      if qh.JOGGLEmax == 0
-        determine default qh.JOGGLEmax
-    else
-      increase qh.JOGGLEmax according to qh.build_cnt
-    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
-    if qh.DELAUNAY
-      sets the Delaunay projection
-*/
-void qh_joggleinput(void) {
-  int i, seed, size;
-  coordT *coordp, *inputp;
-  realT randr, randa, randb;
-
-  if (!qh input_points) { /* first call */
-    qh input_points= qh first_point;
-    qh input_malloc= qh POINTSmalloc;
-    size= qh num_points * qh hull_dim * sizeof(coordT);
-    if (!(qh first_point=(coordT*)qh_malloc((size_t)size))) {
-      qh_fprintf(qh ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
-          qh num_points);
-      qh_errexit(qh_ERRmem, NULL, NULL);
-    }
-    qh POINTSmalloc= True;
-    if (qh JOGGLEmax == 0.0) {
-      qh JOGGLEmax= qh_detjoggle(qh input_points, qh num_points, qh hull_dim);
-      qh_option("QJoggle", NULL, &qh JOGGLEmax);
-    }
-  }else {                 /* repeated call */
-    if (!qh RERUN && qh build_cnt > qh_JOGGLEretry) {
-      if (((qh build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
-        realT maxjoggle= qh MAXwidth * qh_JOGGLEmaxincrease;
-        if (qh JOGGLEmax < maxjoggle) {
-          qh JOGGLEmax *= qh_JOGGLEincrease;
-          minimize_(qh JOGGLEmax, maxjoggle);
-        }
-      }
-    }
-    qh_option("QJoggle", NULL, &qh JOGGLEmax);
-  }
-  if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
-      qh_fprintf(qh ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
-                qh JOGGLEmax);
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  /* for some reason, using qh ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
-  seed= qh_RANDOMint;
-  qh_option("_joggle-seed", &seed, NULL);
-  trace0((qh ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
-    qh JOGGLEmax, seed));
-  inputp= qh input_points;
-  coordp= qh first_point;
-  randa= 2.0 * qh JOGGLEmax/qh_RANDOMmax;
-  randb= -qh JOGGLEmax;
-  size= qh num_points * qh hull_dim;
-  for (i=size; i--; ) {
-    randr= qh_RANDOMint;
-    *(coordp++)= *(inputp++) + (randr * randa + randb);
-  }
-  if (qh DELAUNAY) {
-    qh last_low= qh last_high= qh last_newhigh= REALmax;
-    qh_setdelaunay(qh hull_dim, qh num_points, qh first_point);
-  }
-} /* joggleinput */
-
-/*---------------------------------
-
-  qh_maxabsval( normal, dim )
-    return pointer to maximum absolute value of a dim vector
-    returns NULL if dim=0
-*/
-realT *qh_maxabsval(realT *normal, int dim) {
-  realT maxval= -REALmax;
-  realT *maxp= NULL, *colp, absval;
-  int k;
-
-  for (k=dim, colp= normal; k--; colp++) {
-    absval= fabs_(*colp);
-    if (absval > maxval) {
-      maxval= absval;
-      maxp= colp;
-    }
-  }
-  return maxp;
-} /* maxabsval */
-
-
-/*---------------------------------
-
-  qh_maxmin( points, numpoints, dimension )
-    return max/min points for each dimension
-    determine max and min coordinates
-
-  returns:
-    returns a temporary set of max and min points
-      may include duplicate points. Does not include qh.GOODpoint
-    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
-         qh.MAXlastcoord, qh.MINlastcoord
-    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
-
-  notes:
-    loop duplicated in qh_detjoggle()
-
-  design:
-    initialize global precision variables
-    checks definition of REAL...
-    for each dimension
-      for each point
-        collect maximum and minimum point
-      collect maximum of maximums and minimum of minimums
-      determine qh.NEARzero for Gaussian Elimination
-*/
-setT *qh_maxmin(pointT *points, int numpoints, int dimension) {
-  int k;
-  realT maxcoord, temp;
-  pointT *minimum, *maximum, *point, *pointtemp;
-  setT *set;
-
-  qh max_outside= 0.0;
-  qh MAXabs_coord= 0.0;
-  qh MAXwidth= -REALmax;
-  qh MAXsumcoord= 0.0;
-  qh min_vertex= 0.0;
-  qh WAScoplanar= False;
-  if (qh ZEROcentrum)
-    qh ZEROall_ok= True;
-  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
-  && REALmax > 0.0 && -REALmax < 0.0)
-    ; /* all ok */
-  else {
-    qh_fprintf(qh ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
-REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
-             REALepsilon, REALmin, REALmax, -REALmax);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  set= qh_settemp(2*dimension);
-  for (k=0; k < dimension; k++) {
-    if (points == qh GOODpointp)
-      minimum= maximum= points + dimension;
-    else
-      minimum= maximum= points;
-    FORALLpoint_(points, numpoints) {
-      if (point == qh GOODpointp)
-        continue;
-      if (maximum[k] < point[k])
-        maximum= point;
-      else if (minimum[k] > point[k])
-        minimum= point;
-    }
-    if (k == dimension-1) {
-      qh MINlastcoord= minimum[k];
-      qh MAXlastcoord= maximum[k];
-    }
-    if (qh SCALElast && k == dimension-1)
-      maxcoord= qh MAXwidth;
-    else {
-      maxcoord= fmax_(maximum[k], -minimum[k]);
-      if (qh GOODpointp) {
-        temp= fmax_(qh GOODpointp[k], -qh GOODpointp[k]);
-        maximize_(maxcoord, temp);
-      }
-      temp= maximum[k] - minimum[k];
-      maximize_(qh MAXwidth, temp);
-    }
-    maximize_(qh MAXabs_coord, maxcoord);
-    qh MAXsumcoord += maxcoord;
-    qh_setappend(&set, maximum);
-    qh_setappend(&set, minimum);
-    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
-       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
-       Golub & van Loan say that n^3 can be ignored and 10 be used in
-       place of rho */
-    qh NEARzero[k]= 80 * qh MAXsumcoord * REALepsilon;
-  }
-  if (qh IStracing >=1)
-    qh_printpoints(qh ferr, "qh_maxmin: found the max and min points(by dim):", set);
-  return(set);
-} /* maxmin */
-
-/*---------------------------------
-
-  qh_maxouter()
-    return maximum distance from facet to outer plane
-    normally this is qh.max_outside+qh.DISTround
-    does not include qh.JOGGLEmax
-
-  see:
-    qh_outerinner()
-
-  notes:
-    need to add another qh.DISTround if testing actual point with computation
-
-  for joggle:
-    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
-    need to use Wnewvertexmax since could have a coplanar point for a high
-      facet that is replaced by a low facet
-    need to add qh.JOGGLEmax if testing input points
-*/
-realT qh_maxouter(void) {
-  realT dist;
-
-  dist= fmax_(qh max_outside, qh DISTround);
-  dist += qh DISTround;
-  trace4((qh ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh max_outside));
-  return dist;
-} /* maxouter */
-
-/*---------------------------------
-
-  qh_maxsimplex( dim, maxpoints, points, numpoints, simplex )
-    determines maximum simplex for a set of points
-    starts from points already in simplex
-    skips qh.GOODpointp (assumes that it isn't in maxpoints)
-
-  returns:
-    simplex with dim+1 points
-
-  notes:
-    assumes at least pointsneeded points in points
-    maximizes determinate for x,y,z,w, etc.
-    uses maxpoints as long as determinate is clearly non-zero
-
-  design:
-    initialize simplex with at least two points
-      (find points with max or min x coordinate)
-    for each remaining dimension
-      add point that maximizes the determinate
-        (use points from maxpoints first)
-*/
-void qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
-  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
-  boolT nearzero, maxnearzero= False;
-  int k, sizinit;
-  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
-
-  sizinit= qh_setsize(*simplex);
-  if (sizinit < 2) {
-    if (qh_setsize(maxpoints) >= 2) {
-      FOREACHpoint_(maxpoints) {
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }else {
-      FORALLpoint_(points, numpoints) {
-        if (point == qh GOODpointp)
-          continue;
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }
-    qh_setunique(simplex, minx);
-    if (qh_setsize(*simplex) < 2)
-      qh_setunique(simplex, maxx);
-    sizinit= qh_setsize(*simplex);
-    if (sizinit < 2) {
-      qh_precision("input has same x coordinate");
-      if (zzval_(Zsetplane) > qh hull_dim+1) {
-        qh_fprintf(qh ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
-                 qh_setsize(maxpoints)+numpoints);
-        qh_errexit(qh_ERRprec, NULL, NULL);
-      }else {
-        qh_fprintf(qh ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh hull_dim);
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-    }
-  }
-  for (k=sizinit; k < dim+1; k++) {
-    maxpoint= NULL;
-    maxdet= -REALmax;
-    FOREACHpoint_(maxpoints) {
-      if (!qh_setin(*simplex, point)) {
-        det= qh_detsimplex(point, *simplex, k, &nearzero);
-        if ((det= fabs_(det)) > maxdet) {
-          maxdet= det;
-          maxpoint= point;
-          maxnearzero= nearzero;
-        }
-      }
-    }
-    if (!maxpoint || maxnearzero) {
-      zinc_(Zsearchpoints);
-      if (!maxpoint) {
-        trace0((qh ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
-      }else {
-        trace0((qh ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
-                k+1, qh_pointid(maxpoint), maxdet));
-      }
-      FORALLpoint_(points, numpoints) {
-        if (point == qh GOODpointp)
-          continue;
-        if (!qh_setin(*simplex, point)) {
-          det= qh_detsimplex(point, *simplex, k, &nearzero);
-          if ((det= fabs_(det)) > maxdet) {
-            maxdet= det;
-            maxpoint= point;
-            maxnearzero= nearzero;
-          }
-        }
-      }
-    } /* !maxpoint */
-    if (!maxpoint) {
-      qh_fprintf(qh ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-    qh_setappend(simplex, maxpoint);
-    trace1((qh ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
-            qh_pointid(maxpoint), k+1, maxdet));
-  } /* k */
-} /* maxsimplex */
-
-/*---------------------------------
-
-  qh_minabsval( normal, dim )
-    return minimum absolute value of a dim vector
-*/
-realT qh_minabsval(realT *normal, int dim) {
-  realT minval= 0;
-  realT maxval= 0;
-  realT *colp;
-  int k;
-
-  for (k=dim, colp=normal; k--; colp++) {
-    maximize_(maxval, *colp);
-    minimize_(minval, *colp);
-  }
-  return fmax_(maxval, -minval);
-} /* minabsval */
-
-
-/*---------------------------------
-
-  qh_mindif( vecA, vecB, dim )
-    return index of min abs. difference of two vectors
-*/
-int qh_mindiff(realT *vecA, realT *vecB, int dim) {
-  realT mindiff= REALmax, diff;
-  realT *vecAp= vecA, *vecBp= vecB;
-  int k, mink= 0;
-
-  for (k=0; k < dim; k++) {
-    diff= *vecAp++ - *vecBp++;
-    diff= fabs_(diff);
-    if (diff < mindiff) {
-      mindiff= diff;
-      mink= k;
-    }
-  }
-  return mink;
-} /* mindiff */
-
-
-
-/*---------------------------------
-
-  qh_orientoutside( facet  )
-    make facet outside oriented via qh.interior_point
-
-  returns:
-    True if facet reversed orientation.
-*/
-boolT qh_orientoutside(facetT *facet) {
-  int k;
-  realT dist;
-
-  qh_distplane(qh interior_point, facet, &dist);
-  if (dist > 0) {
-    for (k=qh hull_dim; k--; )
-      facet->normal[k]= -facet->normal[k];
-    facet->offset= -facet->offset;
-    return True;
-  }
-  return False;
-} /* orientoutside */
-
-/*---------------------------------
-
-  qh_outerinner( facet, outerplane, innerplane  )
-    if facet and qh.maxoutdone (i.e., qh_check_maxout)
-      returns outer and inner plane for facet
-    else
-      returns maximum outer and inner plane
-    accounts for qh.JOGGLEmax
-
-  see:
-    qh_maxouter(), qh_check_bestdist(), qh_check_points()
-
-  notes:
-    outerplaner or innerplane may be NULL
-    facet is const
-    Does not error (QhullFacet)
-
-    includes qh.DISTround for actual points
-    adds another qh.DISTround if testing with floating point arithmetic
-*/
-void qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane) {
-  realT dist, mindist;
-  vertexT *vertex, **vertexp;
-
-  if (outerplane) {
-    if (!qh_MAXoutside || !facet || !qh maxoutdone) {
-      *outerplane= qh_maxouter();       /* includes qh.DISTround */
-    }else { /* qh_MAXoutside ... */
-#if qh_MAXoutside
-      *outerplane= facet->maxoutside + qh DISTround;
-#endif
-
-    }
-    if (qh JOGGLEmax < REALmax/2)
-      *outerplane += qh JOGGLEmax * sqrt((realT)qh hull_dim);
-  }
-  if (innerplane) {
-    if (facet) {
-      mindist= REALmax;
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(vertex->point, facet, &dist);
-        minimize_(mindist, dist);
-      }
-      *innerplane= mindist - qh DISTround;
-    }else
-      *innerplane= qh min_vertex - qh DISTround;
-    if (qh JOGGLEmax < REALmax/2)
-      *innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
-  }
-} /* outerinner */
-
-/*---------------------------------
-
-  qh_pointdist( point1, point2, dim )
-    return distance between two points
-
-  notes:
-    returns distance squared if 'dim' is negative
-*/
-coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
-  coordT dist, diff;
-  int k;
-
-  dist= 0.0;
-  for (k= (dim > 0 ? dim : -dim); k--; ) {
-    diff= *point1++ - *point2++;
-    dist += diff * diff;
-  }
-  if (dim > 0)
-    return(sqrt(dist));
-  return dist;
-} /* pointdist */
-
-
-/*---------------------------------
-
-  qh_printmatrix( fp, string, rows, numrow, numcol )
-    print matrix to fp given by row vectors
-    print string as header
-
-  notes:
-    print a vector by qh_printmatrix(fp, "", &vect, 1, len)
-*/
-void qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
-  realT *rowp;
-  realT r; /*bug fix*/
-  int i,k;
-
-  qh_fprintf(fp, 9001, "%s\n", string);
-  for (i=0; i < numrow; i++) {
-    rowp= rows[i];
-    for (k=0; k < numcol; k++) {
-      r= *rowp++;
-      qh_fprintf(fp, 9002, "%6.3g ", r);
-    }
-    qh_fprintf(fp, 9003, "\n");
-  }
-} /* printmatrix */
-
-
-/*---------------------------------
-
-  qh_printpoints( fp, string, points )
-    print pointids to fp for a set of points
-    if string, prints string and 'p' point ids
-*/
-void qh_printpoints(FILE *fp, const char *string, setT *points) {
-  pointT *point, **pointp;
-
-  if (string) {
-    qh_fprintf(fp, 9004, "%s", string);
-    FOREACHpoint_(points)
-      qh_fprintf(fp, 9005, " p%d", qh_pointid(point));
-    qh_fprintf(fp, 9006, "\n");
-  }else {
-    FOREACHpoint_(points)
-      qh_fprintf(fp, 9007, " %d", qh_pointid(point));
-    qh_fprintf(fp, 9008, "\n");
-  }
-} /* printpoints */
-
-
-/*---------------------------------
-
-  qh_projectinput()
-    project input points using qh.lower_bound/upper_bound and qh DELAUNAY
-    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
-      removes dimension k
-    if halfspace intersection
-      removes dimension k from qh.feasible_point
-    input points in qh first_point, num_points, input_dim
-
-  returns:
-    new point array in qh first_point of qh hull_dim coordinates
-    sets qh POINTSmalloc
-    if qh DELAUNAY
-      projects points to paraboloid
-      lowbound/highbound is also projected
-    if qh ATinfinity
-      adds point "at-infinity"
-    if qh POINTSmalloc
-      frees old point array
-
-  notes:
-    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
-
-
-  design:
-    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
-    determines newdim and newnum for qh hull_dim and qh num_points
-    projects points to newpoints
-    projects qh.lower_bound to itself
-    projects qh.upper_bound to itself
-    if qh DELAUNAY
-      if qh ATINFINITY
-        projects points to paraboloid
-        computes "infinity" point as vertex average and 10% above all points
-      else
-        uses qh_setdelaunay to project points to paraboloid
-*/
-void qh_projectinput(void) {
-  int k,i;
-  int newdim= qh input_dim, newnum= qh num_points;
-  signed char *project;
-  int projectsize= (qh input_dim+1)*sizeof(*project);
-  pointT *newpoints, *coord, *infinity;
-  realT paraboloid, maxboloid= 0;
-
-  project= (signed char*)qh_memalloc(projectsize);
-  memset((char*)project, 0, (size_t)projectsize);
-  for (k=0; k < qh input_dim; k++) {   /* skip Delaunay bound */
-    if (qh lower_bound[k] == 0 && qh upper_bound[k] == 0) {
-      project[k]= -1;
-      newdim--;
-    }
-  }
-  if (qh DELAUNAY) {
-    project[k]= 1;
-    newdim++;
-    if (qh ATinfinity)
-      newnum++;
-  }
-  if (newdim != qh hull_dim) {
-    qh_memfree(project, projectsize);
-    qh_fprintf(qh ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (!(newpoints= qh temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
-    qh_memfree(project, projectsize);
-    qh_fprintf(qh ferr, 6016, "qhull error: insufficient memory to project %d points\n",
-           qh num_points);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  /* qh_projectpoints throws error if mismatched dimensions */
-  qh_projectpoints(project, qh input_dim+1, qh first_point,
-                    qh num_points, qh input_dim, newpoints, newdim);
-  trace1((qh ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
-  qh_projectpoints(project, qh input_dim+1, qh lower_bound,
-                    1, qh input_dim+1, qh lower_bound, newdim+1);
-  qh_projectpoints(project, qh input_dim+1, qh upper_bound,
-                    1, qh input_dim+1, qh upper_bound, newdim+1);
-  if (qh HALFspace) {
-    if (!qh feasible_point) {
-      qh_memfree(project, projectsize);
-      qh_fprintf(qh ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-    qh_projectpoints(project, qh input_dim, qh feasible_point,
-                      1, qh input_dim, qh feasible_point, newdim);
-  }
-  qh_memfree(project, projectsize);
-  if (qh POINTSmalloc)
-    qh_free(qh first_point);
-  qh first_point= newpoints;
-  qh POINTSmalloc= True;
-  qh temp_malloc= NULL;
-  if (qh DELAUNAY && qh ATinfinity) {
-    coord= qh first_point;
-    infinity= qh first_point + qh hull_dim * qh num_points;
-    for (k=qh hull_dim-1; k--; )
-      infinity[k]= 0.0;
-    for (i=qh num_points; i--; ) {
-      paraboloid= 0.0;
-      for (k=0; k < qh hull_dim-1; k++) {
-        paraboloid += *coord * *coord;
-        infinity[k] += *coord;
-        coord++;
-      }
-      *(coord++)= paraboloid;
-      maximize_(maxboloid, paraboloid);
-    }
-    /* coord == infinity */
-    for (k=qh hull_dim-1; k--; )
-      *(coord++) /= qh num_points;
-    *(coord++)= maxboloid * 1.1;
-    qh num_points++;
-    trace0((qh ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
-  }else if (qh DELAUNAY)  /* !qh ATinfinity */
-    qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
-} /* projectinput */
-
-
-/*---------------------------------
-
-  qh_projectpoints( project, n, points, numpoints, dim, newpoints, newdim )
-    project points/numpoints/dim to newpoints/newdim
-    if project[k] == -1
-      delete dimension k
-    if project[k] == 1
-      add dimension k by duplicating previous column
-    n is size of project
-
-  notes:
-    newpoints may be points if only adding dimension at end
-
-  design:
-    check that 'project' and 'newdim' agree
-    for each dimension
-      if project == -1
-        skip dimension
-      else
-        determine start of column in newpoints
-        determine start of column in points
-          if project == +1, duplicate previous column
-        copy dimension (column) from points to newpoints
-*/
-void qh_projectpoints(signed char *project, int n, realT *points,
-        int numpoints, int dim, realT *newpoints, int newdim) {
-  int testdim= dim, oldk=0, newk=0, i,j=0,k;
-  realT *newp, *oldp;
-
-  for (k=0; k < n; k++)
-    testdim += project[k];
-  if (testdim != newdim) {
-    qh_fprintf(qh ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
-      newdim, testdim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  for (j=0; j= dim)
-          continue;
-        oldp= points+oldk;
-      }else
-        oldp= points+oldk++;
-      for (i=numpoints; i--; ) {
-        *newp= *oldp;
-        newp += newdim;
-        oldp += dim;
-      }
-    }
-    if (oldk >= dim)
-      break;
-  }
-  trace1((qh ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
-    numpoints, dim, newdim));
-} /* projectpoints */
-
-
-/*---------------------------------
-
-  qh_rotateinput( rows )
-    rotate input using row matrix
-    input points given by qh first_point, num_points, hull_dim
-    assumes rows[dim] is a scratch buffer
-    if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    rotated input
-    sets qh POINTSmalloc
-
-  design:
-    see qh_rotatepoints
-*/
-void qh_rotateinput(realT **rows) {
-
-  if (!qh POINTSmalloc) {
-    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
-    qh POINTSmalloc= True;
-  }
-  qh_rotatepoints(qh first_point, qh num_points, qh hull_dim, rows);
-}  /* rotateinput */
-
-/*---------------------------------
-
-  qh_rotatepoints( points, numpoints, dim, row )
-    rotate numpoints points by a d-dim row matrix
-    assumes rows[dim] is a scratch buffer
-
-  returns:
-    rotated points in place
-
-  design:
-    for each point
-      for each coordinate
-        use row[dim] to compute partial inner product
-      for each coordinate
-        rotate by partial inner product
-*/
-void qh_rotatepoints(realT *points, int numpoints, int dim, realT **row) {
-  realT *point, *rowi, *coord= NULL, sum, *newval;
-  int i,j,k;
-
-  if (qh IStracing >= 1)
-    qh_printmatrix(qh ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
-  for (point= points, j= numpoints; j--; point += dim) {
-    newval= row[dim];
-    for (i=0; i < dim; i++) {
-      rowi= row[i];
-      coord= point;
-      for (sum= 0.0, k= dim; k--; )
-        sum += *rowi++ * *coord++;
-      *(newval++)= sum;
-    }
-    for (k=dim; k--; )
-      *(--coord)= *(--newval);
-  }
-} /* rotatepoints */
-
-
-/*---------------------------------
-
-  qh_scaleinput()
-    scale input points using qh low_bound/high_bound
-    input points given by qh first_point, num_points, hull_dim
-    if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    scales coordinates of points to low_bound[k], high_bound[k]
-    sets qh POINTSmalloc
-
-  design:
-    see qh_scalepoints
-*/
-void qh_scaleinput(void) {
-
-  if (!qh POINTSmalloc) {
-    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
-    qh POINTSmalloc= True;
-  }
-  qh_scalepoints(qh first_point, qh num_points, qh hull_dim,
-       qh lower_bound, qh upper_bound);
-}  /* scaleinput */
-
-/*---------------------------------
-
-  qh_scalelast( points, numpoints, dim, low, high, newhigh )
-    scale last coordinate to [0,m] for Delaunay triangulations
-    input points given by points, numpoints, dim
-
-  returns:
-    changes scale of last coordinate from [low, high] to [0, newhigh]
-    overwrites last coordinate of each point
-    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
-
-  notes:
-    when called by qh_setdelaunay, low/high may not match actual data
-
-  design:
-    compute scale and shift factors
-    apply to last coordinate of each point
-*/
-void qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
-                   coordT high, coordT newhigh) {
-  realT scale, shift;
-  coordT *coord;
-  int i;
-  boolT nearzero= False;
-
-  trace4((qh ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
-    low, high, newhigh));
-  qh last_low= low;
-  qh last_high= high;
-  qh last_newhigh= newhigh;
-  scale= qh_divzero(newhigh, high - low,
-                  qh MINdenom_1, &nearzero);
-  if (nearzero) {
-    if (qh DELAUNAY)
-      qh_fprintf(qh ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
-    else
-      qh_fprintf(qh ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
-                newhigh, low, high, high-low);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  shift= - low * newhigh / (high-low);
-  coord= points + dim - 1;
-  for (i=numpoints; i--; coord += dim)
-    *coord= *coord * scale + shift;
-} /* scalelast */
-
-/*---------------------------------
-
-  qh_scalepoints( points, numpoints, dim, newlows, newhighs )
-    scale points to new lowbound and highbound
-    retains old bound when newlow= -REALmax or newhigh= +REALmax
-
-  returns:
-    scaled points
-    overwrites old points
-
-  design:
-    for each coordinate
-      compute current low and high bound
-      compute scale and shift factors
-      scale all points
-      enforce new low and high bound for all points
-*/
-void qh_scalepoints(pointT *points, int numpoints, int dim,
-        realT *newlows, realT *newhighs) {
-  int i,k;
-  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
-  boolT nearzero= False;
-
-  for (k=0; k < dim; k++) {
-    newhigh= newhighs[k];
-    newlow= newlows[k];
-    if (newhigh > REALmax/2 && newlow < -REALmax/2)
-      continue;
-    low= REALmax;
-    high= -REALmax;
-    for (i=numpoints, coord=points+k; i--; coord += dim) {
-      minimize_(low, *coord);
-      maximize_(high, *coord);
-    }
-    if (newhigh > REALmax/2)
-      newhigh= high;
-    if (newlow < -REALmax/2)
-      newlow= low;
-    if (qh DELAUNAY && k == dim-1 && newhigh < newlow) {
-      qh_fprintf(qh ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
-               k, k, newhigh, newlow);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    scale= qh_divzero(newhigh - newlow, high - low,
-                  qh MINdenom_1, &nearzero);
-    if (nearzero) {
-      qh_fprintf(qh ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
-              k, newlow, newhigh, low, high);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    shift= (newlow * high - low * newhigh)/(high-low);
-    coord= points+k;
-    for (i=numpoints; i--; coord += dim)
-      *coord= *coord * scale + shift;
-    coord= points+k;
-    if (newlow < newhigh) {
-      mincoord= newlow;
-      maxcoord= newhigh;
-    }else {
-      mincoord= newhigh;
-      maxcoord= newlow;
-    }
-    for (i=numpoints; i--; coord += dim) {
-      minimize_(*coord, maxcoord);  /* because of roundoff error */
-      maximize_(*coord, mincoord);
-    }
-    trace0((qh ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
-      k, low, high, newlow, newhigh, numpoints, scale, shift));
-  }
-} /* scalepoints */
-
-
-/*---------------------------------
-
-  qh_setdelaunay( dim, count, points )
-    project count points to dim-d paraboloid for Delaunay triangulation
-
-    dim is one more than the dimension of the input set
-    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
-
-    points is a dim*count realT array.  The first dim-1 coordinates
-    are the coordinates of the first input point.  array[dim] is
-    the first coordinate of the second input point.  array[2*dim] is
-    the first coordinate of the third input point.
-
-    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
-      calls qh_scalelast to scale the last coordinate the same as the other points
-
-  returns:
-    for each point
-      sets point[dim-1] to sum of squares of coordinates
-    scale points to 'Qbb' if needed
-
-  notes:
-    to project one point, use
-      qh_setdelaunay(qh hull_dim, 1, point)
-
-    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
-    the coordinates after the original projection.
-
-*/
-void qh_setdelaunay(int dim, int count, pointT *points) {
-  int i, k;
-  coordT *coordp, coord;
-  realT paraboloid;
-
-  trace0((qh ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
-  coordp= points;
-  for (i=0; i < count; i++) {
-    coord= *coordp++;
-    paraboloid= coord*coord;
-    for (k=dim-2; k--; ) {
-      coord= *coordp++;
-      paraboloid += coord*coord;
-    }
-    *coordp++ = paraboloid;
-  }
-  if (qh last_low < REALmax/2)
-    qh_scalelast(points, count, dim, qh last_low, qh last_high, qh last_newhigh);
-} /* setdelaunay */
-
-
-/*---------------------------------
-
-  qh_sethalfspace( dim, coords, nextp, normal, offset, feasible )
-    set point to dual of halfspace relative to feasible point
-    halfspace is normal coefficients and offset.
-
-  returns:
-    false and prints error if feasible point is outside of hull
-    overwrites coordinates for point at dim coords
-    nextp= next point (coords)
-    does not call qh_errexit
-
-  design:
-    compute distance from feasible point to halfspace
-    divide each normal coefficient by -dist
-*/
-boolT qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
-         coordT *normal, coordT *offset, coordT *feasible) {
-  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
-  realT dist;
-  realT r; /*bug fix*/
-  int k;
-  boolT zerodiv;
-
-  dist= *offset;
-  for (k=dim; k--; )
-    dist += *(normp++) * *(feasiblep++);
-  if (dist > 0)
-    goto LABELerroroutside;
-  normp= normal;
-  if (dist < -qh MINdenom) {
-    for (k=dim; k--; )
-      *(coordp++)= *(normp++) / -dist;
-  }else {
-    for (k=dim; k--; ) {
-      *(coordp++)= qh_divzero(*(normp++), -dist, qh MINdenom_1, &zerodiv);
-      if (zerodiv)
-        goto LABELerroroutside;
-    }
-  }
-  *nextp= coordp;
-  if (qh IStracing >= 4) {
-    qh_fprintf(qh ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
-    for (k=dim, coordp=coords; k--; ) {
-      r= *coordp++;
-      qh_fprintf(qh ferr, 8022, " %6.2g", r);
-    }
-    qh_fprintf(qh ferr, 8023, "\n");
-  }
-  return True;
-LABELerroroutside:
-  feasiblep= feasible;
-  normp= normal;
-  qh_fprintf(qh ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh ferr, 8024, qh_REAL_1, r=*(feasiblep++));
-  qh_fprintf(qh ferr, 8025, "\n     halfspace: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh ferr, 8026, qh_REAL_1, r=*(normp++));
-  qh_fprintf(qh ferr, 8027, "\n     at offset: ");
-  qh_fprintf(qh ferr, 8028, qh_REAL_1, *offset);
-  qh_fprintf(qh ferr, 8029, " and distance: ");
-  qh_fprintf(qh ferr, 8030, qh_REAL_1, dist);
-  qh_fprintf(qh ferr, 8031, "\n");
-  return False;
-} /* sethalfspace */
-
-/*---------------------------------
-
-  qh_sethalfspace_all( dim, count, halfspaces, feasible )
-    generate dual for halfspace intersection with feasible point
-    array of count halfspaces
-      each halfspace is normal coefficients followed by offset
-      the origin is inside the halfspace if the offset is negative
-    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
-
-  returns:
-    malloc'd array of count X dim-1 points
-
-  notes:
-    call before qh_init_B or qh_initqhull_globals
-    free memory when done
-    unused/untested code: please email bradb@shore.net if this works ok for you
-    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
-    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
-
-  design:
-    see qh_sethalfspace
-*/
-coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible) {
-  int i, newdim;
-  pointT *newpoints;
-  coordT *coordp, *normalp, *offsetp;
-
-  trace0((qh ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
-  newdim= dim - 1;
-  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
-    qh_fprintf(qh ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
-          count);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coordp= newpoints;
-  normalp= halfspaces;
-  for (i=0; i < count; i++) {
-    offsetp= normalp + newdim;
-    if (!qh_sethalfspace(newdim, coordp, &coordp, normalp, offsetp, feasible)) {
-      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
-      qh_fprintf(qh ferr, 8032, "The halfspace was at index %d\n", i);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    normalp= offsetp + 1;
-  }
-  return newpoints;
-} /* sethalfspace_all */
-
-
-/*---------------------------------
-
-  qh_sharpnewfacets()
-
-  returns:
-    true if could be an acute angle (facets in different quadrants)
-
-  notes:
-    for qh_findbest
-
-  design:
-    for all facets on qh.newfacet_list
-      if two facets are in different quadrants
-        set issharp
-*/
-boolT qh_sharpnewfacets(void) {
-  facetT *facet;
-  boolT issharp = False;
-  int *quadrant, k;
-
-  quadrant= (int*)qh_memalloc(qh hull_dim * sizeof(int));
-  FORALLfacet_(qh newfacet_list) {
-    if (facet == qh newfacet_list) {
-      for (k=qh hull_dim; k--; )
-        quadrant[ k]= (facet->normal[ k] > 0);
-    }else {
-      for (k=qh hull_dim; k--; ) {
-        if (quadrant[ k] != (facet->normal[ k] > 0)) {
-          issharp= True;
-          break;
-        }
-      }
-    }
-    if (issharp)
-      break;
-  }
-  qh_memfree( quadrant, qh hull_dim * sizeof(int));
-  trace3((qh ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
-  return issharp;
-} /* sharpnewfacets */
-
-/*---------------------------------
-
-  qh_voronoi_center( dim, points )
-    return Voronoi center for a set of points
-    dim is the orginal dimension of the points
-    gh.gm_matrix/qh.gm_row are scratch buffers
-
-  returns:
-    center as a temporary point (qh_memalloc)
-    if non-simplicial,
-      returns center for max simplex of points
-
-  notes:
-    only called by qh_facetcenter
-    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
-
-  design:
-    if non-simplicial
-      determine max simplex for points
-    translate point0 of simplex to origin
-    compute sum of squares of diagonal
-    compute determinate
-    compute Voronoi center (see Bowyer & Woodwark)
-*/
-pointT *qh_voronoi_center(int dim, setT *points) {
-  pointT *point, **pointp, *point0;
-  pointT *center= (pointT*)qh_memalloc(qh center_size);
-  setT *simplex;
-  int i, j, k, size= qh_setsize(points);
-  coordT *gmcoord;
-  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
-  boolT nearzero, infinite;
-
-  if (size == dim+1)
-    simplex= points;
-  else if (size < dim+1) {
-    qh_memfree(center, qh center_size);
-    qh_fprintf(qh ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
-             dim+1);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-    simplex= points;  /* never executed -- avoids warning */
-  }else {
-    simplex= qh_settemp(dim+1);
-    qh_maxsimplex(dim, points, NULL, 0, &simplex);
-  }
-  point0= SETfirstt_(simplex, pointT);
-  gmcoord= qh gm_matrix;
-  for (k=0; k < dim; k++) {
-    qh gm_row[k]= gmcoord;
-    FOREACHpoint_(simplex) {
-      if (point != point0)
-        *(gmcoord++)= point[k] - point0[k];
-    }
-  }
-  sum2row= gmcoord;
-  for (i=0; i < dim; i++) {
-    sum2= 0.0;
-    for (k=0; k < dim; k++) {
-      diffp= qh gm_row[k] + i;
-      sum2 += *diffp * *diffp;
-    }
-    *(gmcoord++)= sum2;
-  }
-  det= qh_determinant(qh gm_row, dim, &nearzero);
-  factor= qh_divzero(0.5, det, qh MINdenom, &infinite);
-  if (infinite) {
-    for (k=dim; k--; )
-      center[k]= qh_INFINITE;
-    if (qh IStracing)
-      qh_printpoints(qh ferr, "qh_voronoi_center: at infinity for ", simplex);
-  }else {
-    for (i=0; i < dim; i++) {
-      gmcoord= qh gm_matrix;
-      sum2p= sum2row;
-      for (k=0; k < dim; k++) {
-        qh gm_row[k]= gmcoord;
-        if (k == i) {
-          for (j=dim; j--; )
-            *(gmcoord++)= *sum2p++;
-        }else {
-          FOREACHpoint_(simplex) {
-            if (point != point0)
-              *(gmcoord++)= point[k] - point0[k];
-          }
-        }
-      }
-      center[i]= qh_determinant(qh gm_row, dim, &nearzero)*factor + point0[i];
-    }
-#ifndef qh_NOtrace
-    if (qh IStracing >= 3) {
-      qh_fprintf(qh ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
-      qh_printmatrix(qh ferr, "center:", ¢er, 1, dim);
-      if (qh IStracing >= 5) {
-        qh_printpoints(qh ferr, "points", simplex);
-        FOREACHpoint_(simplex)
-          qh_fprintf(qh ferr, 8034, "p%d dist %.2g, ", qh_pointid(point),
-                   qh_pointdist(point, center, dim));
-        qh_fprintf(qh ferr, 8035, "\n");
-      }
-    }
-#endif
-  }
-  if (simplex != points)
-    qh_settempfree(&simplex);
-  return center;
-} /* voronoi_center */
-
diff --git a/src/qhull/src/libqhull/global.c b/src/qhull/src/libqhull/global.c
deleted file mode 100644
index 0328fea7b..000000000
--- a/src/qhull/src/libqhull/global.c
+++ /dev/null
@@ -1,2217 +0,0 @@
-
-/*
      ---------------------------------
-
-   global.c
-   initializes all the globals of the qhull application
-
-   see README
-
-   see libqhull.h for qh.globals and function prototypes
-
-   see qhull_a.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/global.c#17 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
- */
-
-#include "qhull_a.h"
-
-/*========= qh definition -- globals defined in libqhull.h =======================*/
-
-#if qh_QHpointer
-qhT *qh_qh= NULL;       /* pointer to all global variables */
-#else
-qhT qh_qh;              /* all global variables.
-                           Add "= {0}" if this causes a compiler error.
-                           Also qh_qhstat in stat.c and qhmem in mem.c.  */
-#endif
-
-/*----------------------------------
-
-  qh_version
-    version string by year and date
-    qh_version2 for Unix users and -V
-
-    the revision increases on code changes only
-
-  notes:
-    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
-                    qhull-news.html, Eudora signatures, CMakeLists.txt
-    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
-    check that CmakeLists @version is the same as qh_version2
-    change year:    Copying.txt
-    check download size
-    recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c, testqset.c
-*/
-
-const char qh_version[]= "2015.2 2016/01/18";
-const char qh_version2[]= "qhull 7.2.0 (2015.2 2016/01/18)";
-
-/*---------------------------------
-
-  qh_appendprint( printFormat )
-    append printFormat to qh.PRINTout unless already defined
-*/
-void qh_appendprint(qh_PRINT format) {
-  int i;
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    if (qh PRINTout[i] == format && format != qh_PRINTqhull)
-      break;
-    if (!qh PRINTout[i]) {
-      qh PRINTout[i]= format;
-      break;
-    }
-  }
-} /* appendprint */
-
-/*---------------------------------
-
-  qh_checkflags( commandStr, hiddenFlags )
-    errors if commandStr contains hiddenFlags
-    hiddenFlags starts and ends with a space and is space delimited (checked)
-
-  notes:
-    ignores first word (e.g., "qconvex i")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initflags() initializes Qhull according to commandStr
-*/
-void qh_checkflags(char *command, char *hiddenflags) {
-  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
-  char key, opt, prevopt;
-  char chkkey[]= "   ";
-  char chkopt[]=  "    ";
-  char chkopt2[]= "     ";
-  boolT waserr= False;
-
-  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
-    qh_fprintf(qh ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (strpbrk(hiddenflags, ",\n\r\t")) {
-    qh_fprintf(qh ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    key = *s++;
-    chkerr = NULL;
-    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
-      s= qh_skipfilename(++s);
-      continue;
-    }
-    chkkey[1]= key;
-    if (strstr(hiddenflags, chkkey)) {
-      chkerr= chkkey;
-    }else if (isupper(key)) {
-      opt= ' ';
-      prevopt= ' ';
-      chkopt[1]= key;
-      chkopt2[1]= key;
-      while (!chkerr && *s && !isspace(*s)) {
-        opt= *s++;
-        if (isalpha(opt)) {
-          chkopt[2]= opt;
-          if (strstr(hiddenflags, chkopt))
-            chkerr= chkopt;
-          if (prevopt != ' ') {
-            chkopt2[2]= prevopt;
-            chkopt2[3]= opt;
-            if (strstr(hiddenflags, chkopt2))
-              chkerr= chkopt2;
-          }
-        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
-              && (prevopt == ' ' || islower(prevopt))) {
-            chkopt[2]= opt;
-            if (strstr(hiddenflags, chkopt))
-              chkerr= chkopt;
-        }else {
-          qh_strtod(s-1, &t);
-          if (s < t)
-            s= t;
-        }
-        prevopt= opt;
-      }
-    }
-    if (chkerr) {
-      *chkerr= '\'';
-      chkerr[strlen(chkerr)-1]=  '\'';
-      qh_fprintf(qh ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
-      waserr= True;
-    }
-  }
-  if (waserr)
-    qh_errexit(qh_ERRinput, NULL, NULL);
-} /* checkflags */
-
-/*---------------------------------
-
-  qh_clear_outputflags()
-    Clear output flags for QhullPoints
-*/
-void qh_clear_outputflags(void) {
-  int i,k;
-
-  qh ANNOTATEoutput= False;
-  qh DOintersections= False;
-  qh DROPdim= -1;
-  qh FORCEoutput= False;
-  qh GETarea= False;
-  qh GOODpoint= 0;
-  qh GOODpointp= NULL;
-  qh GOODthreshold= False;
-  qh GOODvertex= 0;
-  qh GOODvertexp= NULL;
-  qh IStracing= 0;
-  qh KEEParea= False;
-  qh KEEPmerge= False;
-  qh KEEPminArea= REALmax;
-  qh PRINTcentrums= False;
-  qh PRINTcoplanar= False;
-  qh PRINTdots= False;
-  qh PRINTgood= False;
-  qh PRINTinner= False;
-  qh PRINTneighbors= False;
-  qh PRINTnoplanes= False;
-  qh PRINToptions1st= False;
-  qh PRINTouter= False;
-  qh PRINTprecision= True;
-  qh PRINTridges= False;
-  qh PRINTspheres= False;
-  qh PRINTstatistics= False;
-  qh PRINTsummary= False;
-  qh PRINTtransparent= False;
-  qh SPLITthresholds= False;
-  qh TRACElevel= 0;
-  qh TRInormals= False;
-  qh USEstdout= False;
-  qh VERIFYoutput= False;
-  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh lower_threshold[k]= -REALmax;
-    qh upper_threshold[k]= REALmax;
-    qh lower_bound[k]= -REALmax;
-    qh upper_bound[k]= REALmax;
-  }
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    qh PRINTout[i]= qh_PRINTnone;
-  }
-
-  if (!qh qhull_commandsiz2)
-      qh qhull_commandsiz2= (int)strlen(qh qhull_command); /* WARN64 */
-  else {
-      qh qhull_command[qh qhull_commandsiz2]= '\0';
-  }
-  if (!qh qhull_optionsiz2)
-    qh qhull_optionsiz2= (int)strlen(qh qhull_options);  /* WARN64 */
-  else {
-    qh qhull_options[qh qhull_optionsiz2]= '\0';
-    qh qhull_optionlen= qh_OPTIONline;  /* start a new line */
-  }
-} /* clear_outputflags */
-
-/*---------------------------------
-
-  qh_clock()
-    return user CPU time in 100ths (qh_SECtick)
-    only defined for qh_CLOCKtype == 2
-
-  notes:
-    use first value to determine time 0
-    from Stevens '92 8.15
-*/
-unsigned long qh_clock(void) {
-
-#if (qh_CLOCKtype == 2)
-  struct tms time;
-  static long clktck;  /* initialized first call and never updated */
-  double ratio, cpu;
-  unsigned long ticks;
-
-  if (!clktck) {
-    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
-      qh_fprintf(qh ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-  }
-  if (times(&time) == -1) {
-    qh_fprintf(qh ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  ratio= qh_SECticks / (double)clktck;
-  ticks= time.tms_utime * ratio;
-  return ticks;
-#else
-  qh_fprintf(qh ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
-  qh_errexit(qh_ERRqhull, NULL, NULL); /* never returns */
-  return 0;
-#endif
-} /* clock */
-
-/*---------------------------------
-
-  qh_freebuffers()
-    free up global memory buffers
-
-  notes:
-    must match qh_initbuffers()
-*/
-void qh_freebuffers(void) {
-
-  trace5((qh ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
-  /* allocated by qh_initqhull_buffers */
-  qh_memfree(qh NEARzero, qh hull_dim * sizeof(realT));
-  qh_memfree(qh lower_threshold, (qh input_dim+1) * sizeof(realT));
-  qh_memfree(qh upper_threshold, (qh input_dim+1) * sizeof(realT));
-  qh_memfree(qh lower_bound, (qh input_dim+1) * sizeof(realT));
-  qh_memfree(qh upper_bound, (qh input_dim+1) * sizeof(realT));
-  qh_memfree(qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
-  qh_memfree(qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
-  qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
-  qh lower_bound= qh upper_bound= NULL;
-  qh gm_matrix= NULL;
-  qh gm_row= NULL;
-  qh_setfree(&qh other_points);
-  qh_setfree(&qh del_vertices);
-  qh_setfree(&qh coplanarfacetset);
-  if (qh line)                /* allocated by qh_readinput, freed if no error */
-    qh_free(qh line);
-  if (qh half_space)
-    qh_free(qh half_space);
-  if (qh temp_malloc)
-    qh_free(qh temp_malloc);
-  if (qh feasible_point)      /* allocated by qh_readfeasible */
-    qh_free(qh feasible_point);
-  if (qh feasible_string)     /* allocated by qh_initflags */
-    qh_free(qh feasible_string);
-  qh line= qh feasible_string= NULL;
-  qh half_space= qh feasible_point= qh temp_malloc= NULL;
-  /* usually allocated by qh_readinput */
-  if (qh first_point && qh POINTSmalloc) {
-    qh_free(qh first_point);
-    qh first_point= NULL;
-  }
-  if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
-    qh_free(qh input_points);
-    qh input_points= NULL;
-  }
-  trace5((qh ferr, 5002, "qh_freebuffers: finished\n"));
-} /* freebuffers */
-
-
-/*---------------------------------
-
-  qh_freebuild( allmem )
-    free global memory used by qh_initbuild and qh_buildhull
-    if !allmem,
-      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
-
-  design:
-    free centrums
-    free each vertex
-    mark unattached ridges
-    for each facet
-      free ridges
-      free outside set, coplanar set, neighbor set, ridge set, vertex set
-      free facet
-    free hash table
-    free interior point
-    free merge set
-    free temporary sets
-*/
-void qh_freebuild(boolT allmem) {
-  facetT *facet;
-  vertexT *vertex;
-  ridgeT *ridge, **ridgep;
-  mergeT *merge, **mergep;
-
-  trace1((qh ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
-  if (qh del_vertices)
-    qh_settruncate(qh del_vertices, 0);
-  if (allmem) {
-    while ((vertex= qh vertex_list)) {
-      if (vertex->next)
-        qh_delvertex(vertex);
-      else {
-        qh_memfree(vertex, (int)sizeof(vertexT));
-        qh newvertex_list= qh vertex_list= NULL;
-      }
-    }
-  }else if (qh VERTEXneighbors) {
-    FORALLvertices
-      qh_setfreelong(&(vertex->neighbors));
-  }
-  qh VERTEXneighbors= False;
-  qh GOODclosest= NULL;
-  if (allmem) {
-    FORALLfacets {
-      FOREACHridge_(facet->ridges)
-        ridge->seen= False;
-    }
-    FORALLfacets {
-      if (facet->visible) {
-        FOREACHridge_(facet->ridges) {
-          if (!otherfacet_(ridge, facet)->visible)
-            ridge->seen= True;  /* an unattached ridge */
-        }
-      }
-    }
-    while ((facet= qh facet_list)) {
-      FOREACHridge_(facet->ridges) {
-        if (ridge->seen) {
-          qh_setfree(&(ridge->vertices));
-          qh_memfree(ridge, (int)sizeof(ridgeT));
-        }else
-          ridge->seen= True;
-      }
-      qh_setfree(&(facet->outsideset));
-      qh_setfree(&(facet->coplanarset));
-      qh_setfree(&(facet->neighbors));
-      qh_setfree(&(facet->ridges));
-      qh_setfree(&(facet->vertices));
-      if (facet->next)
-        qh_delfacet(facet);
-      else {
-        qh_memfree(facet, (int)sizeof(facetT));
-        qh visible_list= qh newfacet_list= qh facet_list= NULL;
-      }
-    }
-  }else {
-    FORALLfacets {
-      qh_setfreelong(&(facet->outsideset));
-      qh_setfreelong(&(facet->coplanarset));
-      if (!facet->simplicial) {
-        qh_setfreelong(&(facet->neighbors));
-        qh_setfreelong(&(facet->ridges));
-        qh_setfreelong(&(facet->vertices));
-      }
-    }
-  }
-  qh_setfree(&(qh hash_table));
-  qh_memfree(qh interior_point, qh normal_size);
-  qh interior_point= NULL;
-  FOREACHmerge_(qh facet_mergeset)  /* usually empty */
-    qh_memfree(merge, (int)sizeof(mergeT));
-  qh facet_mergeset= NULL;  /* temp set */
-  qh degen_mergeset= NULL;  /* temp set */
-  qh_settempfree_all();
-} /* freebuild */
-
-/*---------------------------------
-
-  qh_freeqhull( allmem )
-    see qh_freeqhull2
-    if qh_QHpointer, frees qh_qh
-*/
-void qh_freeqhull(boolT allmem) {
-    qh_freeqhull2(allmem);
-#if qh_QHpointer
-    qh_free(qh_qh);
-    qh_qh= NULL;
-#endif
-}
-
-/*---------------------------------
-
-qh_freeqhull2( allmem )
-  free global memory and set qhT to 0
-  if !allmem,
-    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
-
-notes:
-  sets qh.NOerrexit in case caller forgets to
-  Does not throw errors
-
-see:
-  see qh_initqhull_start2()
-
-design:
-  free global and temporary memory from qh_initbuild and qh_buildhull
-  free buffers
-  free statistics
-*/
-void qh_freeqhull2(boolT allmem) {
-
-  qh NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
-  trace1((qh ferr, 1006, "qh_freeqhull: free global memory\n"));
-  qh_freebuild(allmem);
-  qh_freebuffers();
-  qh_freestatistics();
-#if qh_QHpointer
-  memset((char *)qh_qh, 0, sizeof(qhT));
-  /* qh_qh freed by caller, qh_freeqhull() */
-#else
-  memset((char *)&qh_qh, 0, sizeof(qhT));
-#endif
-  qh NOerrexit= True;
-} /* freeqhull2 */
-
-/*---------------------------------
-
-  qh_init_A( infile, outfile, errfile, argc, argv )
-    initialize memory and stdio files
-    convert input options to option string (qh.qhull_command)
-
-  notes:
-    infile may be NULL if qh_readpoints() is not called
-
-    errfile should always be defined.  It is used for reporting
-    errors.  outfile is used for output and format options.
-
-    argc/argv may be 0/NULL
-
-    called before error handling initialized
-    qh_errexit() may not be used
-*/
-void qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
-  qh_meminit(errfile);
-  qh_initqhull_start(infile, outfile, errfile);
-  qh_init_qhull_command(argc, argv);
-} /* init_A */
-
-/*---------------------------------
-
-  qh_init_B( points, numpoints, dim, ismalloc )
-    initialize globals for points array
-
-    points has numpoints dim-dimensional points
-      points[0] is the first coordinate of the first point
-      points[1] is the second coordinate of the first point
-      points[dim] is the first coordinate of the second point
-
-    ismalloc=True
-      Qhull will call qh_free(points) on exit or input transformation
-    ismalloc=False
-      Qhull will allocate a new point array if needed for input transformation
-
-    qh.qhull_command
-      is the option string.
-      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
-
-  returns:
-    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
-      projects the input to a new point array
-
-        if qh.DELAUNAY,
-          qh.hull_dim is increased by one
-        if qh.ATinfinity,
-          qh_projectinput adds point-at-infinity for Delaunay tri.
-
-    if qh.SCALEinput
-      changes the upper and lower bounds of the input, see qh_scaleinput()
-
-    if qh.ROTATEinput
-      rotates the input by a random rotation, see qh_rotateinput()
-      if qh.DELAUNAY
-        rotates about the last coordinate
-
-  notes:
-    called after points are defined
-    qh_errexit() may be used
-*/
-void qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc) {
-  qh_initqhull_globals(points, numpoints, dim, ismalloc);
-  if (qhmem.LASTsize == 0)
-    qh_initqhull_mem();
-  /* mem.c and qset.c are initialized */
-  qh_initqhull_buffers();
-  qh_initthresholds(qh qhull_command);
-  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
-    qh_projectinput();
-  if (qh SCALEinput)
-    qh_scaleinput();
-  if (qh ROTATErandom >= 0) {
-    qh_randommatrix(qh gm_matrix, qh hull_dim, qh gm_row);
-    if (qh DELAUNAY) {
-      int k, lastk= qh hull_dim-1;
-      for (k=0; k < lastk; k++) {
-        qh gm_row[k][lastk]= 0.0;
-        qh gm_row[lastk][k]= 0.0;
-      }
-      qh gm_row[lastk][lastk]= 1.0;
-    }
-    qh_gram_schmidt(qh hull_dim, qh gm_row);
-    qh_rotateinput(qh gm_row);
-  }
-} /* init_B */
-
-/*---------------------------------
-
-  qh_init_qhull_command( argc, argv )
-    build qh.qhull_command from argc/argv
-    Calls qh_exit if qhull_command is too short
-
-  returns:
-    a space-delimited string of options (just as typed)
-
-  notes:
-    makes option string easy to input and output
-
-    argc/argv may be 0/NULL
-*/
-void qh_init_qhull_command(int argc, char *argv[]) {
-
-  if (!qh_argv_to_command(argc, argv, qh qhull_command, (int)sizeof(qh qhull_command))){
-    /* Assumes qh.ferr is defined. */
-    qh_fprintf(qh ferr, 6033, "qhull input error: more than %d characters in command line\n",
-          (int)sizeof(qh qhull_command));
-    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
-  }
-} /* init_qhull_command */
-
-/*---------------------------------
-
-  qh_initflags( commandStr )
-    set flags and initialized constants from commandStr
-    calls qh_exit() if qh->NOerrexit
-
-  returns:
-    sets qh.qhull_command to command if needed
-
-  notes:
-    ignores first word (e.g., "qhull d")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
-    'prompt' in unix.c for documentation
-
-  design:
-    for each space-delimited option group
-      if top-level option
-        check syntax
-        append appropriate option to option string
-        set appropriate global variable or append printFormat to print options
-      else
-        for each sub-option
-          check syntax
-          append appropriate option to option string
-          set appropriate global variable or append printFormat to print options
-*/
-void qh_initflags(char *command) {
-  int k, i, lastproject;
-  char *s= command, *t, *prev_s, *start, key;
-  boolT isgeom= False, wasproject;
-  realT r;
-
-  if(qh NOerrexit){/* without this comment, segfault in gcc 4.4.0 mingw32 */
-    qh_fprintf(qh ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
-    qh_exit(6245);
-  }
-  if (command <= &qh qhull_command[0] || command > &qh qhull_command[0] + sizeof(qh qhull_command)) {
-    if (command != &qh qhull_command[0]) {
-      *qh qhull_command= '\0';
-      strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
-    }
-    while (*s && !isspace(*s))  /* skip program name */
-      s++;
-  }
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    prev_s= s;
-    switch (*s++) {
-    case 'd':
-      qh_option("delaunay", NULL, NULL);
-      qh DELAUNAY= True;
-      break;
-    case 'f':
-      qh_option("facets", NULL, NULL);
-      qh_appendprint(qh_PRINTfacets);
-      break;
-    case 'i':
-      qh_option("incidence", NULL, NULL);
-      qh_appendprint(qh_PRINTincidences);
-      break;
-    case 'm':
-      qh_option("mathematica", NULL, NULL);
-      qh_appendprint(qh_PRINTmathematica);
-      break;
-    case 'n':
-      qh_option("normals", NULL, NULL);
-      qh_appendprint(qh_PRINTnormals);
-      break;
-    case 'o':
-      qh_option("offFile", NULL, NULL);
-      qh_appendprint(qh_PRINToff);
-      break;
-    case 'p':
-      qh_option("points", NULL, NULL);
-      qh_appendprint(qh_PRINTpoints);
-      break;
-    case 's':
-      qh_option("summary", NULL, NULL);
-      qh PRINTsummary= True;
-      break;
-    case 'v':
-      qh_option("voronoi", NULL, NULL);
-      qh VORONOI= True;
-      qh DELAUNAY= True;
-      break;
-    case 'A':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh premerge_cos= -qh_strtod(s, &s);
-          qh_option("Angle-premerge-", NULL, &qh premerge_cos);
-          qh PREmerge= True;
-        }else {
-          qh postmerge_cos= qh_strtod(s, &s);
-          qh_option("Angle-postmerge", NULL, &qh postmerge_cos);
-          qh POSTmerge= True;
-        }
-        qh MERGING= True;
-      }
-      break;
-    case 'C':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh premerge_centrum= -qh_strtod(s, &s);
-          qh_option("Centrum-premerge-", NULL, &qh premerge_centrum);
-          qh PREmerge= True;
-        }else {
-          qh postmerge_centrum= qh_strtod(s, &s);
-          qh_option("Centrum-postmerge", NULL, &qh postmerge_centrum);
-          qh POSTmerge= True;
-        }
-        qh MERGING= True;
-      }
-      break;
-    case 'E':
-      if (*s == '-')
-        qh_fprintf(qh ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
-      else {
-        qh DISTround= qh_strtod(s, &s);
-        qh_option("Distance-roundoff", NULL, &qh DISTround);
-        qh SETroundoff= True;
-      }
-      break;
-    case 'H':
-      start= s;
-      qh HALFspace= True;
-      qh_strtod(s, &t);
-      while (t > s)  {
-        if (*t && !isspace(*t)) {
-          if (*t == ',')
-            t++;
-          else
-            qh_fprintf(qh ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
-        }
-        s= t;
-        qh_strtod(s, &t);
-      }
-      if (start < t) {
-        if (!(qh feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
-          qh_fprintf(qh ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
-          qh_errexit(qh_ERRmem, NULL, NULL);
-        }
-        strncpy(qh feasible_string, start, (size_t)(t-start));
-        qh_option("Halfspace-about", NULL, NULL);
-        qh_option(qh feasible_string, NULL, NULL);
-      }else
-        qh_option("Halfspace", NULL, NULL);
-      break;
-    case 'R':
-      if (!isdigit(*s))
-        qh_fprintf(qh ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
-      else {
-        qh RANDOMfactor= qh_strtod(s, &s);
-        qh_option("Random_perturb", NULL, &qh RANDOMfactor);
-        qh RANDOMdist= True;
-      }
-      break;
-    case 'V':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
-      else {
-        qh MINvisible= qh_strtod(s, &s);
-        qh_option("Visible", NULL, &qh MINvisible);
-      }
-      break;
-    case 'U':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
-      else {
-        qh MAXcoplanar= qh_strtod(s, &s);
-        qh_option("U-coplanar", NULL, &qh MAXcoplanar);
-      }
-      break;
-    case 'W':
-      if (*s == '-')
-        qh_fprintf(qh ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
-      else {
-        qh MINoutside= qh_strtod(s, &s);
-        qh_option("W-outside", NULL, &qh MINoutside);
-        qh APPROXhull= True;
-      }
-      break;
-    /************  sub menus ***************/
-    case 'F':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option("Farea", NULL, NULL);
-          qh_appendprint(qh_PRINTarea);
-          qh GETarea= True;
-          break;
-        case 'A':
-          qh_option("FArea-total", NULL, NULL);
-          qh GETarea= True;
-          break;
-        case 'c':
-          qh_option("Fcoplanars", NULL, NULL);
-          qh_appendprint(qh_PRINTcoplanars);
-          break;
-        case 'C':
-          qh_option("FCentrums", NULL, NULL);
-          qh_appendprint(qh_PRINTcentrums);
-          break;
-        case 'd':
-          qh_option("Fd-cdd-in", NULL, NULL);
-          qh CDDinput= True;
-          break;
-        case 'D':
-          qh_option("FD-cdd-out", NULL, NULL);
-          qh CDDoutput= True;
-          break;
-        case 'F':
-          qh_option("FFacets-xridge", NULL, NULL);
-          qh_appendprint(qh_PRINTfacets_xridge);
-          break;
-        case 'i':
-          qh_option("Finner", NULL, NULL);
-          qh_appendprint(qh_PRINTinner);
-          break;
-        case 'I':
-          qh_option("FIDs", NULL, NULL);
-          qh_appendprint(qh_PRINTids);
-          break;
-        case 'm':
-          qh_option("Fmerges", NULL, NULL);
-          qh_appendprint(qh_PRINTmerges);
-          break;
-        case 'M':
-          qh_option("FMaple", NULL, NULL);
-          qh_appendprint(qh_PRINTmaple);
-          break;
-        case 'n':
-          qh_option("Fneighbors", NULL, NULL);
-          qh_appendprint(qh_PRINTneighbors);
-          break;
-        case 'N':
-          qh_option("FNeighbors-vertex", NULL, NULL);
-          qh_appendprint(qh_PRINTvneighbors);
-          break;
-        case 'o':
-          qh_option("Fouter", NULL, NULL);
-          qh_appendprint(qh_PRINTouter);
-          break;
-        case 'O':
-          if (qh PRINToptions1st) {
-            qh_option("FOptions", NULL, NULL);
-            qh_appendprint(qh_PRINToptions);
-          }else
-            qh PRINToptions1st= True;
-          break;
-        case 'p':
-          qh_option("Fpoint-intersect", NULL, NULL);
-          qh_appendprint(qh_PRINTpointintersect);
-          break;
-        case 'P':
-          qh_option("FPoint-nearest", NULL, NULL);
-          qh_appendprint(qh_PRINTpointnearest);
-          break;
-        case 'Q':
-          qh_option("FQhull", NULL, NULL);
-          qh_appendprint(qh_PRINTqhull);
-          break;
-        case 's':
-          qh_option("Fsummary", NULL, NULL);
-          qh_appendprint(qh_PRINTsummary);
-          break;
-        case 'S':
-          qh_option("FSize", NULL, NULL);
-          qh_appendprint(qh_PRINTsize);
-          qh GETarea= True;
-          break;
-        case 't':
-          qh_option("Ftriangles", NULL, NULL);
-          qh_appendprint(qh_PRINTtriangles);
-          break;
-        case 'v':
-          /* option set in qh_initqhull_globals */
-          qh_appendprint(qh_PRINTvertices);
-          break;
-        case 'V':
-          qh_option("FVertex-average", NULL, NULL);
-          qh_appendprint(qh_PRINTaverage);
-          break;
-        case 'x':
-          qh_option("Fxtremes", NULL, NULL);
-          qh_appendprint(qh_PRINTextremes);
-          break;
-        default:
-          s--;
-          qh_fprintf(qh ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'G':
-      isgeom= True;
-      qh_appendprint(qh_PRINTgeom);
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option("Gall-points", NULL, NULL);
-          qh PRINTdots= True;
-          break;
-        case 'c':
-          qh_option("Gcentrums", NULL, NULL);
-          qh PRINTcentrums= True;
-          break;
-        case 'h':
-          qh_option("Gintersections", NULL, NULL);
-          qh DOintersections= True;
-          break;
-        case 'i':
-          qh_option("Ginner", NULL, NULL);
-          qh PRINTinner= True;
-          break;
-        case 'n':
-          qh_option("Gno-planes", NULL, NULL);
-          qh PRINTnoplanes= True;
-          break;
-        case 'o':
-          qh_option("Gouter", NULL, NULL);
-          qh PRINTouter= True;
-          break;
-        case 'p':
-          qh_option("Gpoints", NULL, NULL);
-          qh PRINTcoplanar= True;
-          break;
-        case 'r':
-          qh_option("Gridges", NULL, NULL);
-          qh PRINTridges= True;
-          break;
-        case 't':
-          qh_option("Gtransparent", NULL, NULL);
-          qh PRINTtransparent= True;
-          break;
-        case 'v':
-          qh_option("Gvertices", NULL, NULL);
-          qh PRINTspheres= True;
-          break;
-        case 'D':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
-          else {
-            if (qh DROPdim >= 0)
-              qh_fprintf(qh ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
-                   qh DROPdim);
-            qh DROPdim= qh_strtol(s, &s);
-            qh_option("GDrop-dim", &qh DROPdim, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'P':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'd': case 'D':  /* see qh_initthresholds() */
-          key= s[-1];
-          i= qh_strtol(s, &s);
-          r= 0;
-          if (*s == ':') {
-            s++;
-            r= qh_strtod(s, &s);
-          }
-          if (key == 'd')
-            qh_option("Pdrop-facets-dim-less", &i, &r);
-          else
-            qh_option("PDrop-facets-dim-more", &i, &r);
-          break;
-        case 'g':
-          qh_option("Pgood-facets", NULL, NULL);
-          qh PRINTgood= True;
-          break;
-        case 'G':
-          qh_option("PGood-facet-neighbors", NULL, NULL);
-          qh PRINTneighbors= True;
-          break;
-        case 'o':
-          qh_option("Poutput-forced", NULL, NULL);
-          qh FORCEoutput= True;
-          break;
-        case 'p':
-          qh_option("Pprecision-ignore", NULL, NULL);
-          qh PRINTprecision= False;
-          break;
-        case 'A':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
-          else {
-            qh KEEParea= qh_strtol(s, &s);
-            qh_option("PArea-keep", &qh KEEParea, NULL);
-            qh GETarea= True;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
-          else {
-            qh KEEPminArea= qh_strtod(s, &s);
-            qh_option("PFacet-area-keep", NULL, &qh KEEPminArea);
-            qh GETarea= True;
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
-          else {
-            qh KEEPmerge= qh_strtol(s, &s);
-            qh_option("PMerge-keep", &qh KEEPmerge, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'Q':
-      lastproject= -1;
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'b': case 'B':  /* handled by qh_initthresholds */
-          key= s[-1];
-          if (key == 'b' && *s == 'B') {
-            s++;
-            r= qh_DEFAULTbox;
-            qh SCALEinput= True;
-            qh_option("QbBound-unit-box", NULL, &r);
-            break;
-          }
-          if (key == 'b' && *s == 'b') {
-            s++;
-            qh SCALElast= True;
-            qh_option("Qbbound-last", NULL, NULL);
-            break;
-          }
-          k= qh_strtol(s, &s);
-          r= 0.0;
-          wasproject= False;
-          if (*s == ':') {
-            s++;
-            if ((r= qh_strtod(s, &s)) == 0.0) {
-              t= s;            /* need true dimension for memory allocation */
-              while (*t && !isspace(*t)) {
-                if (toupper(*t++) == 'B'
-                 && k == qh_strtol(t, &t)
-                 && *t++ == ':'
-                 && qh_strtod(t, &t) == 0.0) {
-                  qh PROJECTinput++;
-                  trace2((qh ferr, 2004, "qh_initflags: project dimension %d\n", k));
-                  qh_option("Qb-project-dim", &k, NULL);
-                  wasproject= True;
-                  lastproject= k;
-                  break;
-                }
-              }
-            }
-          }
-          if (!wasproject) {
-            if (lastproject == k && r == 0.0)
-              lastproject= -1;  /* doesn't catch all possible sequences */
-            else if (key == 'b') {
-              qh SCALEinput= True;
-              if (r == 0.0)
-                r= -qh_DEFAULTbox;
-              qh_option("Qbound-dim-low", &k, &r);
-            }else {
-              qh SCALEinput= True;
-              if (r == 0.0)
-                r= qh_DEFAULTbox;
-              qh_option("QBound-dim-high", &k, &r);
-            }
-          }
-          break;
-        case 'c':
-          qh_option("Qcoplanar-keep", NULL, NULL);
-          qh KEEPcoplanar= True;
-          break;
-        case 'f':
-          qh_option("Qfurthest-outside", NULL, NULL);
-          qh BESToutside= True;
-          break;
-        case 'g':
-          qh_option("Qgood-facets-only", NULL, NULL);
-          qh ONLYgood= True;
-          break;
-        case 'i':
-          qh_option("Qinterior-keep", NULL, NULL);
-          qh KEEPinside= True;
-          break;
-        case 'm':
-          qh_option("Qmax-outside-only", NULL, NULL);
-          qh ONLYmax= True;
-          break;
-        case 'r':
-          qh_option("Qrandom-outside", NULL, NULL);
-          qh RANDOMoutside= True;
-          break;
-        case 's':
-          qh_option("Qsearch-initial-simplex", NULL, NULL);
-          qh ALLpoints= True;
-          break;
-        case 't':
-          qh_option("Qtriangulate", NULL, NULL);
-          qh TRIangulate= True;
-          break;
-        case 'T':
-          qh_option("QTestPoints", NULL, NULL);
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
-          else {
-            qh TESTpoints= qh_strtol(s, &s);
-            qh_option("QTestPoints", &qh TESTpoints, NULL);
-          }
-          break;
-        case 'u':
-          qh_option("QupperDelaunay", NULL, NULL);
-          qh UPPERdelaunay= True;
-          break;
-        case 'v':
-          qh_option("Qvertex-neighbors-convex", NULL, NULL);
-          qh TESTvneighbors= True;
-          break;
-        case 'x':
-          qh_option("Qxact-merge", NULL, NULL);
-          qh MERGEexact= True;
-          break;
-        case 'z':
-          qh_option("Qz-infinity-point", NULL, NULL);
-          qh ATinfinity= True;
-          break;
-        case '0':
-          qh_option("Q0-no-premerge", NULL, NULL);
-          qh NOpremerge= True;
-          break;
-        case '1':
-          if (!isdigit(*s)) {
-            qh_option("Q1-no-angle-sort", NULL, NULL);
-            qh ANGLEmerge= False;
-            break;
-          }
-          switch (*s++) {
-          case '0':
-            qh_option("Q10-no-narrow", NULL, NULL);
-            qh NOnarrow= True;
-            break;
-          case '1':
-            qh_option("Q11-trinormals Qtriangulate", NULL, NULL);
-            qh TRInormals= True;
-            qh TRIangulate= True;
-            break;
-          case '2':
-            qh_option("Q12-no-wide-dup", NULL, NULL);
-            qh NOwide= True;
-            break;
-          default:
-            s--;
-            qh_fprintf(qh ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
-            while (*++s && !isspace(*s));
-            break;
-          }
-          break;
-        case '2':
-          qh_option("Q2-no-merge-independent", NULL, NULL);
-          qh MERGEindependent= False;
-          goto LABELcheckdigit;
-          break; /* no warnings */
-        case '3':
-          qh_option("Q3-no-merge-vertices", NULL, NULL);
-          qh MERGEvertices= False;
-        LABELcheckdigit:
-          if (isdigit(*s))
-            qh_fprintf(qh ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
-                     *s++);
-          break;
-        case '4':
-          qh_option("Q4-avoid-old-into-new", NULL, NULL);
-          qh AVOIDold= True;
-          break;
-        case '5':
-          qh_option("Q5-no-check-outer", NULL, NULL);
-          qh SKIPcheckmax= True;
-          break;
-        case '6':
-          qh_option("Q6-no-concave-merge", NULL, NULL);
-          qh SKIPconvex= True;
-          break;
-        case '7':
-          qh_option("Q7-no-breadth-first", NULL, NULL);
-          qh VIRTUALmemory= True;
-          break;
-        case '8':
-          qh_option("Q8-no-near-inside", NULL, NULL);
-          qh NOnearinside= True;
-          break;
-        case '9':
-          qh_option("Q9-pick-furthest", NULL, NULL);
-          qh PICKfurthest= True;
-          break;
-        case 'G':
-          i= qh_strtol(s, &t);
-          if (qh GOODpoint)
-            qh_fprintf(qh ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
-          else if (i < 0 || *s == '-') {
-            qh GOODpoint= i-1;
-            qh_option("QGood-if-dont-see-point", &i, NULL);
-          }else {
-            qh GOODpoint= i+1;
-            qh_option("QGood-if-see-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'J':
-          if (!isdigit(*s) && *s != '-')
-            qh JOGGLEmax= 0.0;
-          else {
-            qh JOGGLEmax= (realT) qh_strtod(s, &s);
-            qh_option("QJoggle", NULL, &qh JOGGLEmax);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s) && *s != '-')
-            qh_fprintf(qh ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
-          else {
-            qh ROTATErandom= i= qh_strtol(s, &s);
-            if (i > 0)
-              qh_option("QRotate-id", &i, NULL );
-            else if (i < -1)
-              qh_option("QRandom-seed", &i, NULL );
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (qh GOODvertex)
-            qh_fprintf(qh ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
-          else if (i < 0) {
-            qh GOODvertex= i - 1;
-            qh_option("QV-good-facets-not-point", &i, NULL);
-          }else {
-            qh_option("QV-good-facets-point", &i, NULL);
-            qh GOODvertex= i + 1;
-          }
-          s= t;
-          break;
-        default:
-          s--;
-          qh_fprintf(qh ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'T':
-      while (*s && !isspace(*s)) {
-        if (isdigit(*s) || *s == '-')
-          qh IStracing= qh_strtol(s, &s);
-        else switch (*s++) {
-        case 'a':
-          qh_option("Tannotate-output", NULL, NULL);
-          qh ANNOTATEoutput= True;
-          break;
-        case 'c':
-          qh_option("Tcheck-frequently", NULL, NULL);
-          qh CHECKfrequently= True;
-          break;
-        case 's':
-          qh_option("Tstatistics", NULL, NULL);
-          qh PRINTstatistics= True;
-          break;
-        case 'v':
-          qh_option("Tverify", NULL, NULL);
-          qh VERIFYoutput= True;
-          break;
-        case 'z':
-          if (qh ferr == qh_FILEstderr) {
-            /* The C++ interface captures the output in qh_fprint_qhull() */
-            qh_option("Tz-stdout", NULL, NULL);
-            qh USEstdout= True;
-          }else if (!qh fout)
-            qh_fprintf(qh ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
-          else {
-            qh_option("Tz-stdout", NULL, NULL);
-            qh USEstdout= True;
-            qh ferr= qh fout;
-            qhmem.ferr= qh fout;
-          }
-          break;
-        case 'C':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
-          else {
-            i= qh_strtol(s, &s);
-            qh_option("TCone-stop", &i, NULL);
-            qh STOPcone= i + 1;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
-          else {
-            qh REPORTfreq= qh_strtol(s, &s);
-            qh_option("TFacet-log", &qh REPORTfreq, NULL);
-            qh REPORTfreq2= qh REPORTfreq/2;  /* for tracemerging() */
-          }
-          break;
-        case 'I':
-          if (!isspace(*s))
-            qh_fprintf(qh ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
-          while (isspace(*s))
-            s++;
-          t= qh_skipfilename(s);
-          {
-            char filename[qh_FILENAMElen];
-
-            qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
-            s= t;
-            if (!freopen(filename, "r", stdin)) {
-              qh_fprintf(qh ferr, 6041, "qhull error: could not open file \"%s\".", filename);
-              qh_errexit(qh_ERRinput, NULL, NULL);
-            }else {
-              qh_option("TInput-file", NULL, NULL);
-              qh_option(filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'O':
-            if (!isspace(*s))
-                qh_fprintf(qh ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
-            while (isspace(*s))
-                s++;
-            t= qh_skipfilename(s);
-            {
-              char filename[qh_FILENAMElen];
-
-              qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
-              s= t;
-              if (!qh fout) {
-                qh_fprintf(qh ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
-              }else if (!freopen(filename, "w", qh fout)) {
-                qh_fprintf(qh ferr, 6044, "qhull error: could not open file \"%s\".", filename);
-                qh_errexit(qh_ERRinput, NULL, NULL);
-              }else {
-                qh_option("TOutput-file", NULL, NULL);
-              qh_option(filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'P':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
-          else {
-            qh TRACEpoint= qh_strtol(s, &s);
-            qh_option("Trace-point", &qh TRACEpoint, NULL);
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
-          else {
-            qh TRACEmerge= qh_strtol(s, &s);
-            qh_option("Trace-merge", &qh TRACEmerge, NULL);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
-          else {
-            qh RERUN= qh_strtol(s, &s);
-            qh_option("TRerun", &qh RERUN, NULL);
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (s == t)
-            qh_fprintf(qh ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
-          else if (i < 0) {
-            qh STOPpoint= i - 1;
-            qh_option("TV-stop-before-point", &i, NULL);
-          }else {
-            qh STOPpoint= i + 1;
-            qh_option("TV-stop-after-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'W':
-          if (!isdigit(*s))
-            qh_fprintf(qh ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
-          else {
-            qh TRACEdist= (realT) qh_strtod(s, &s);
-            qh_option("TWide-trace", NULL, &qh TRACEdist);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    default:
-      qh_fprintf(qh ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
-               (int)s[-1]);
-      break;
-    }
-    if (s-1 == prev_s && *s && !isspace(*s)) {
-      qh_fprintf(qh ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
-               (int)*prev_s, (int)*prev_s);
-      while (*s && !isspace(*s))
-        s++;
-    }
-  }
-  if (qh STOPcone && qh JOGGLEmax < REALmax/2)
-    qh_fprintf(qh ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
-  if (isgeom && !qh FORCEoutput && qh PRINTout[1])
-    qh_fprintf(qh ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
-  /* set derived values in qh_initqhull_globals */
-} /* initflags */
-
-
-/*---------------------------------
-
-  qh_initqhull_buffers()
-    initialize global memory buffers
-
-  notes:
-    must match qh_freebuffers()
-*/
-void qh_initqhull_buffers(void) {
-  int k;
-
-  qh TEMPsize= (qhmem.LASTsize - sizeof(setT))/SETelemsize;
-  if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
-    qh TEMPsize= 8;  /* e.g., if qh_NOmem */
-  qh other_points= qh_setnew(qh TEMPsize);
-  qh del_vertices= qh_setnew(qh TEMPsize);
-  qh coplanarfacetset= qh_setnew(qh TEMPsize);
-  qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
-  qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh lower_threshold[k]= -REALmax;
-    qh upper_threshold[k]= REALmax;
-    qh lower_bound[k]= -REALmax;
-    qh upper_bound[k]= REALmax;
-  }
-  qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
-  qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
-} /* initqhull_buffers */
-
-/*---------------------------------
-
-  qh_initqhull_globals( points, numpoints, dim, ismalloc )
-    initialize globals
-    if ismalloc
-      points were malloc'd and qhull should free at end
-
-  returns:
-    sets qh.first_point, num_points, input_dim, hull_dim and others
-    seeds random number generator (seed=1 if tracing)
-    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
-    adjust user flags as needed
-    also checks DIM3 dependencies and constants
-
-  notes:
-    do not use qh_point() since an input transformation may move them elsewhere
-
-  see:
-    qh_initqhull_start() sets default values for non-zero globals
-
-  design:
-    initialize points array from input arguments
-    test for qh.ZEROcentrum
-      (i.e., use opposite vertex instead of cetrum for convexity testing)
-    initialize qh.CENTERtype, qh.normal_size,
-      qh.center_size, qh.TRACEpoint/level,
-    initialize and test random numbers
-    qh_initqhull_outputflags() -- adjust and test output flags
-*/
-void qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc) {
-  int seed, pointsneeded, extra= 0, i, randi, k;
-  realT randr;
-  realT factorial;
-
-  time_t timedata;
-
-  trace0((qh ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
-      qh qhull_command));
-  qh POINTSmalloc= ismalloc;
-  qh first_point= points;
-  qh num_points= numpoints;
-  qh hull_dim= qh input_dim= dim;
-  if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
-    qh MERGING= True;
-    if (qh hull_dim <= 4) {
-      qh PREmerge= True;
-      qh_option("_pre-merge", NULL, NULL);
-    }else {
-      qh MERGEexact= True;
-      qh_option("Qxact_merge", NULL, NULL);
-    }
-  }else if (qh MERGEexact)
-    qh MERGING= True;
-  if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
-#ifdef qh_NOmerge
-    qh JOGGLEmax= 0.0;
-#endif
-  }
-  if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
-    qh_fprintf(qh ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
-  if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
-    qh SCALElast= True;
-    qh_option("Qbbound-last-qj", NULL, NULL);
-  }
-  if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
-  && qh premerge_centrum == 0) {
-    qh ZEROcentrum= True;
-    qh ZEROall_ok= True;
-    qh_option("_zero-centrum", NULL, NULL);
-  }
-  if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
-    qh_fprintf(qh ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
-          REALepsilon);
-#ifdef qh_NOmerge
-  if (qh MERGING) {
-    qh_fprintf(qh ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-#endif
-  if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
-    qh KEEPinside= True;
-    qh_option("Qinterior-keep", NULL, NULL);
-  }
-  if (qh DELAUNAY && qh HALFspace) {
-    qh_fprintf(qh ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
-    qh_fprintf(qh ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh UPPERdelaunay && qh ATinfinity) {
-    qh_fprintf(qh ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
-    qh_fprintf(qh ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
-  qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
-  qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
-                          && !qh NOnearinside);
-  if (qh MERGING)
-    qh CENTERtype= qh_AScentrum;
-  else if (qh VORONOI)
-    qh CENTERtype= qh_ASvoronoi;
-  if (qh TESTvneighbors && !qh MERGING) {
-    qh_fprintf(qh ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
-    qh_errexit(qh_ERRinput, NULL ,NULL);
-  }
-  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
-    qh hull_dim -= qh PROJECTinput;
-    if (qh DELAUNAY) {
-      qh hull_dim++;
-      if (qh ATinfinity)
-        extra= 1;
-    }
-  }
-  if (qh hull_dim <= 1) {
-    qh_fprintf(qh ferr, 6050, "qhull error: dimension %d must be > 1\n", qh hull_dim);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  for (k=2, factorial=1.0; k < qh hull_dim; k++)
-    factorial *= k;
-  qh AREAfactor= 1.0 / factorial;
-  trace2((qh ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
-        dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
-  qh normal_size= qh hull_dim * sizeof(coordT);
-  qh center_size= qh normal_size - sizeof(coordT);
-  pointsneeded= qh hull_dim+1;
-  if (qh hull_dim > qh_DIMmergeVertex) {
-    qh MERGEvertices= False;
-    qh_option("Q3-no-merge-vertices-dim-high", NULL, NULL);
-  }
-  if (qh GOODpoint)
-    pointsneeded++;
-#ifdef qh_NOtrace
-  if (qh IStracing) {
-    qh_fprintf(qh ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-#endif
-  if (qh RERUN > 1) {
-    qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
-    if (qh IStracing != -1)
-      qh IStracing= 0;
-  }else if (qh TRACEpoint != qh_IDunknown || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
-    qh TRACElevel= (qh IStracing? qh IStracing : 3);
-    qh IStracing= 0;
-  }
-  if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
-    seed= (int)time(&timedata);
-    if (qh ROTATErandom  == -1) {
-      seed= -seed;
-      qh_option("QRandom-seed", &seed, NULL );
-    }else
-      qh_option("QRotate-random", &seed, NULL);
-    qh ROTATErandom= seed;
-  }
-  seed= qh ROTATErandom;
-  if (seed == INT_MIN)    /* default value */
-    seed= 1;
-  else if (seed < 0)
-    seed= -seed;
-  qh_RANDOMseed_(seed);
-  randr= 0.0;
-  for (i=1000; i--; ) {
-    randi= qh_RANDOMint;
-    randr += randi;
-    if (randi > qh_RANDOMmax) {
-      qh_fprintf(qh ferr, 8036, "\
-qhull configuration error (qh_RANDOMmax in user.h):\n\
-   random integer %d > qh_RANDOMmax(%.8g)\n",
-               randi, qh_RANDOMmax);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-  }
-  qh_RANDOMseed_(seed);
-  randr = randr/1000;
-  if (randr < qh_RANDOMmax * 0.1
-  || randr > qh_RANDOMmax * 0.9)
-    qh_fprintf(qh ferr, 8037, "\
-qhull configuration warning (qh_RANDOMmax in user.h):\n\
-   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
-   Is qh_RANDOMmax (%.2g) wrong?\n",
-             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
-  qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
-  qh RANDOMb= 1.0 - qh RANDOMfactor;
-  if (qh_HASHfactor < 1.1) {
-    qh_fprintf(qh ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
-      qh_HASHfactor);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (numpoints+extra < pointsneeded) {
-    qh_fprintf(qh ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
-            numpoints, pointsneeded);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  qh_initqhull_outputflags();
-} /* initqhull_globals */
-
-/*---------------------------------
-
-  qh_initqhull_mem(  )
-    initialize mem.c for qhull
-    qh.hull_dim and qh.normal_size determine some of the allocation sizes
-    if qh.MERGING,
-      includes ridgeT
-    calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
-      (see numsizes below)
-
-  returns:
-    mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
-
-  notes:
-    qh_produceoutput() prints memsizes
-
-*/
-void qh_initqhull_mem(void) {
-  int numsizes;
-  int i;
-
-  numsizes= 8+10;
-  qh_meminitbuffers(qh IStracing, qh_MEMalign, numsizes,
-                     qh_MEMbufsize,qh_MEMinitbuf);
-  qh_memsize((int)sizeof(vertexT));
-  if (qh MERGING) {
-    qh_memsize((int)sizeof(ridgeT));
-    qh_memsize((int)sizeof(mergeT));
-  }
-  qh_memsize((int)sizeof(facetT));
-  i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;  /* ridge.vertices */
-  qh_memsize(i);
-  qh_memsize(qh normal_size);        /* normal */
-  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
-  qh_memsize(i);
-  qh_user_memsizes();
-  qh_memsetup();
-} /* initqhull_mem */
-
-/*---------------------------------
-
-  qh_initqhull_outputflags
-    initialize flags concerned with output
-
-  returns:
-    adjust user flags as needed
-
-  see:
-    qh_clear_outputflags() resets the flags
-
-  design:
-    test for qh.PRINTgood (i.e., only print 'good' facets)
-    check for conflicting print output options
-*/
-void qh_initqhull_outputflags(void) {
-  boolT printgeom= False, printmath= False, printcoplanar= False;
-  int i;
-
-  trace3((qh ferr, 3024, "qh_initqhull_outputflags: %s\n", qh qhull_command));
-  if (!(qh PRINTgood || qh PRINTneighbors)) {
-    if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
-        || (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
-      qh PRINTgood= True;
-      qh_option("Pgood", NULL, NULL);
-    }
-  }
-  if (qh PRINTtransparent) {
-    if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
-      qh_fprintf(qh ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    qh DROPdim = 3;
-    qh PRINTridges = True;
-  }
-  for (i=qh_PRINTEND; i--; ) {
-    if (qh PRINTout[i] == qh_PRINTgeom)
-      printgeom= True;
-    else if (qh PRINTout[i] == qh_PRINTmathematica || qh PRINTout[i] == qh_PRINTmaple)
-      printmath= True;
-    else if (qh PRINTout[i] == qh_PRINTcoplanars)
-      printcoplanar= True;
-    else if (qh PRINTout[i] == qh_PRINTpointnearest)
-      printcoplanar= True;
-    else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
-      qh_fprintf(qh ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
-      qh_fprintf(qh ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
-      qh_fprintf(qh ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTvertices) {
-      if (qh VORONOI)
-        qh_option("Fvoronoi", NULL, NULL);
-      else
-        qh_option("Fvertices", NULL, NULL);
-    }
-  }
-  if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
-    if (qh PRINTprecision)
-      qh_fprintf(qh ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
-  }
-  if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
-    qh_fprintf(qh ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (printgeom) {
-    if (qh hull_dim > 4) {
-      qh_fprintf(qh ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
-     + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
-      qh_fprintf(qh ferr, 6058, "qhull input error: no output specified for Geomview\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
-      qh_fprintf(qh ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    /* can not warn about furthest-site Geomview output: no lower_threshold */
-    if (qh hull_dim == 4 && qh DROPdim == -1 &&
-        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
-      qh_fprintf(qh ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
-available for 4-d output(ignored).  Could use 'GDn' instead.\n");
-      qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
-    }
-  }
-  if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
-    if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
-      if (qh QHULLfinished) {
-        qh_fprintf(qh ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
-      }else {
-        qh KEEPcoplanar = True;
-        qh_option("Qcoplanar", NULL, NULL);
-      }
-    }
-  }
-  qh PRINTdim= qh hull_dim;
-  if (qh DROPdim >=0) {    /* after Geomview checks */
-    if (qh DROPdim < qh hull_dim) {
-      qh PRINTdim--;
-      if (!printgeom || qh hull_dim < 3)
-        qh_fprintf(qh ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
-    }else
-      qh DROPdim= -1;
-  }else if (qh VORONOI) {
-    qh DROPdim= qh hull_dim-1;
-    qh PRINTdim= qh hull_dim-1;
-  }
-} /* qh_initqhull_outputflags */
-
-/*---------------------------------
-
-  qh_initqhull_start( infile, outfile, errfile )
-    allocate memory if needed and call qh_initqhull_start2()
-*/
-void qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile) {
-
-#if qh_QHpointer
-  if (qh_qh) {
-    qh_fprintf(errfile, 6205, "qhull error (qh_initqhull_start): qh_qh already defined.  Call qh_save_qhull() first\n");
-    qh_exit(qh_ERRqhull);  /* no error handler */
-  }
-  if (!(qh_qh= (qhT *)qh_malloc(sizeof(qhT)))) {
-    qh_fprintf(errfile, 6060, "qhull error (qh_initqhull_start): insufficient memory\n");
-    qh_exit(qh_ERRmem);  /* no error handler */
-  }
-#endif
-  qh_initstatistics();
-  qh_initqhull_start2(infile, outfile, errfile);
-} /* initqhull_start */
-
-/*---------------------------------
-
-  qh_initqhull_start2( infile, outfile, errfile )
-    start initialization of qhull
-    initialize statistics, stdio, default values for global variables
-    assumes qh_qh is defined
-  notes:
-    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
-  see:
-    qh_maxmin() determines the precision constants
-    qh_freeqhull2()
-*/
-void qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile) {
-  time_t timedata;
-  int seed;
-
-  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
-#if qh_QHpointer
-  memset((char *)qh_qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
-#else
-  memset((char *)&qh_qh, 0, sizeof(qhT));
-#endif
-  qh ANGLEmerge= True;
-  qh DROPdim= -1;
-  qh ferr= errfile;
-  qh fin= infile;
-  qh fout= outfile;
-  qh furthest_id= qh_IDunknown;
-  qh JOGGLEmax= REALmax;
-  qh KEEPminArea = REALmax;
-  qh last_low= REALmax;
-  qh last_high= REALmax;
-  qh last_newhigh= REALmax;
-  qh max_outside= 0.0;
-  qh max_vertex= 0.0;
-  qh MAXabs_coord= 0.0;
-  qh MAXsumcoord= 0.0;
-  qh MAXwidth= -REALmax;
-  qh MERGEindependent= True;
-  qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
-  qh MINoutside= 0.0;
-  qh MINvisible= REALmax;
-  qh MAXcoplanar= REALmax;
-  qh outside_err= REALmax;
-  qh premerge_centrum= 0.0;
-  qh premerge_cos= REALmax;
-  qh PRINTprecision= True;
-  qh PRINTradius= 0.0;
-  qh postmerge_cos= REALmax;
-  qh postmerge_centrum= 0.0;
-  qh ROTATErandom= INT_MIN;
-  qh MERGEvertices= True;
-  qh totarea= 0.0;
-  qh totvol= 0.0;
-  qh TRACEdist= REALmax;
-  qh TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
-  qh tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
-  qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
-  seed= (int)time(&timedata);
-  qh_RANDOMseed_(seed);
-  qh run_id= qh_RANDOMint;
-  if(!qh run_id)
-      qh run_id++;  /* guarantee non-zero */
-  qh_option("run-id", &qh run_id, NULL);
-  strcat(qh qhull, "qhull");
-} /* initqhull_start2 */
-
-/*---------------------------------
-
-  qh_initthresholds( commandString )
-    set thresholds for printing and scaling from commandString
-
-  returns:
-    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
-
-  see:
-    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
-    qh_inthresholds()
-
-  design:
-    for each 'Pdn' or 'PDn' option
-      check syntax
-      set qh.lower_threshold or qh.upper_threshold
-    set qh.GOODthreshold if an unbounded threshold is used
-    set qh.SPLITthreshold if a bounded threshold is used
-*/
-void qh_initthresholds(char *command) {
-  realT value;
-  int idx, maxdim, k;
-  char *s= command; /* non-const due to strtol */
-  char key;
-
-  maxdim= qh input_dim;
-  if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
-    maxdim++;
-  while (*s) {
-    if (*s == '-')
-      s++;
-    if (*s == 'P') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'd' || key == 'D') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
-                    key, s-1);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= qh hull_dim) {
-            qh_fprintf(qh ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
-                idx, key, qh hull_dim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-            if (fabs((double)value) > 1.0) {
-              qh_fprintf(qh ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
-                      value, key);
-              continue;
-            }
-          }else
-            value= 0.0;
-          if (key == 'd')
-            qh lower_threshold[idx]= value;
-          else
-            qh upper_threshold[idx]= value;
-        }
-      }
-    }else if (*s == 'Q') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'b' && *s == 'B') {
-          s++;
-          for (k=maxdim; k--; ) {
-            qh lower_bound[k]= -qh_DEFAULTbox;
-            qh upper_bound[k]= qh_DEFAULTbox;
-          }
-        }else if (key == 'b' && *s == 'b')
-          s++;
-        else if (key == 'b' || key == 'B') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
-                    key);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= maxdim) {
-            qh_fprintf(qh ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
-                idx, key, maxdim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-          }else if (key == 'b')
-            value= -qh_DEFAULTbox;
-          else
-            value= qh_DEFAULTbox;
-          if (key == 'b')
-            qh lower_bound[idx]= value;
-          else
-            qh upper_bound[idx]= value;
-        }
-      }
-    }else {
-      while (*s && !isspace(*s))
-        s++;
-    }
-    while (isspace(*s))
-      s++;
-  }
-  for (k=qh hull_dim; k--; ) {
-    if (qh lower_threshold[k] > -REALmax/2) {
-      qh GOODthreshold= True;
-      if (qh upper_threshold[k] < REALmax/2) {
-        qh SPLITthresholds= True;
-        qh GOODthreshold= False;
-        break;
-      }
-    }else if (qh upper_threshold[k] < REALmax/2)
-      qh GOODthreshold= True;
-  }
-} /* initthresholds */
-
-/*---------------------------------
-
-  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
-    Report error if library does not agree with caller
-
-  notes:
-    NOerrors -- qh_lib_check can not call qh_errexit()
-*/
-void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
-    boolT iserror= False;
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
-    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
-    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
-    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
-#endif
-
-    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
-        if (qh_QHpointer) {
-            qh_fprintf_stderr(6246, "qh_lib_check: Incorrect qhull library called.  Caller uses a static qhT while library uses a dynamic qhT via qh_QHpointer.  Both caller and library are non-reentrant.\n");
-            iserror= True;
-        }
-    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
-        if (!qh_QHpointer) {
-            qh_fprintf_stderr(6247, "qh_lib_check: Incorrect qhull library called.  Caller uses a dynamic qhT via qh_QHpointer while library uses a static qhT.  Both caller and library are non-reentrant.\n");
-            iserror= True;
-        }
-    }else if (qhullLibraryType==QHULL_REENTRANT) { /* 2 */
-        qh_fprintf_stderr(6248, "qh_lib_check: Incorrect qhull library called.  Caller uses reentrant Qhull while library is non-reentrant\n");
-        iserror= True;
-    }else{
-        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
-        iserror= True;
-    }
-    if (qhTsize != sizeof(qhT)) {
-        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
-        iserror= True;
-    }
-    if (vertexTsize != sizeof(vertexT)) {
-        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
-        iserror= True;
-    }
-    if (ridgeTsize != sizeof(ridgeT)) {
-        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
-        iserror= True;
-    }
-    if (facetTsize != sizeof(facetT)) {
-        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
-        iserror= True;
-    }
-    if (setTsize && setTsize != sizeof(setT)) {
-        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
-        iserror= True;
-    }
-    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
-        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
-        iserror= True;
-    }
-    if (iserror) {
-        if(qh_QHpointer){
-            qh_fprintf_stderr(6255, "qh_lib_check: Cannot continue.  Library '%s' uses a dynamic qhT via qh_QHpointer (e.g., qhull_p.so)\n", qh_version2);
-        }else{
-            qh_fprintf_stderr(6256, "qh_lib_check: Cannot continue.  Library '%s' uses a static qhT (e.g., libqhull.so)\n", qh_version2);
-        }
-        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-    }
-} /* lib_check */
-
-/*---------------------------------
-
-  qh_option( option, intVal, realVal )
-    add an option description to qh.qhull_options
-
-  notes:
-    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
-    will be printed with statistics ('Ts') and errors
-    strlen(option) < 40
-*/
-void qh_option(const char *option, int *i, realT *r) {
-  char buf[200];
-  int len, maxlen;
-
-  sprintf(buf, "  %s", option);
-  if (i)
-    sprintf(buf+strlen(buf), " %d", *i);
-  if (r)
-    sprintf(buf+strlen(buf), " %2.2g", *r);
-  len= (int)strlen(buf);  /* WARN64 */
-  qh qhull_optionlen += len;
-  maxlen= sizeof(qh qhull_options) - len -1;
-  maximize_(maxlen, 0);
-  if (qh qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
-    qh qhull_optionlen= len;
-    strncat(qh qhull_options, "\n", (size_t)(maxlen--));
-  }
-  strncat(qh qhull_options, buf, (size_t)maxlen);
-} /* option */
-
-#if qh_QHpointer
-/*---------------------------------
-
-  qh_restore_qhull( oldqh )
-    restores a previously saved qhull
-    also restores qh_qhstat and qhmem.tempstack
-    Sets *oldqh to NULL
-  notes:
-    errors if current qhull hasn't been saved or freed
-    uses qhmem for error reporting
-
-  NOTE 1998/5/11:
-    Freeing memory after qh_save_qhull and qh_restore_qhull
-    is complicated.  The procedures will be redesigned.
-
-  see:
-    qh_save_qhull(), UsingLibQhull
-*/
-void qh_restore_qhull(qhT **oldqh) {
-
-  if (*oldqh && strcmp((*oldqh)->qhull, "qhull")) {
-    qh_fprintf(qhmem.ferr, 6061, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
-                  *oldqh);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (qh_qh) {
-    qh_fprintf(qhmem.ferr, 6062, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (!*oldqh || !(*oldqh)->old_qhstat) {
-    qh_fprintf(qhmem.ferr, 6063, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
-                  *oldqh);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  qh_qh= *oldqh;
-  *oldqh= NULL;
-  qh_qhstat= qh old_qhstat;
-  qhmem.tempstack= qh old_tempstack;
-  qh old_qhstat= 0;
-  qh old_tempstack= 0;
-  trace1((qh ferr, 1007, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
-} /* restore_qhull */
-
-/*---------------------------------
-
-  qh_save_qhull(  )
-    saves qhull for a later qh_restore_qhull
-    also saves qh_qhstat and qhmem.tempstack
-
-  returns:
-    qh_qh=NULL
-
-  notes:
-    need to initialize qhull or call qh_restore_qhull before continuing
-
-  NOTE 1998/5/11:
-    Freeing memory after qh_save_qhull and qh_restore_qhull
-    is complicated.  The procedures will be redesigned.
-
-  see:
-    qh_restore_qhull()
-*/
-qhT *qh_save_qhull(void) {
-  qhT *oldqh;
-
-  trace1((qhmem.ferr, 1045, "qh_save_qhull: save qhull %p\n", qh_qh));
-  if (!qh_qh) {
-    qh_fprintf(qhmem.ferr, 6064, "qhull internal error (qh_save_qhull): qhull not initialized\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  qh old_qhstat= qh_qhstat;
-  qh_qhstat= NULL;
-  qh old_tempstack= qhmem.tempstack;
-  qhmem.tempstack= NULL;
-  oldqh= qh_qh;
-  qh_qh= NULL;
-  return oldqh;
-} /* save_qhull */
-
-#endif
-
diff --git a/src/qhull/src/libqhull/index.htm b/src/qhull/src/libqhull/index.htm
deleted file mode 100644
index 62b9d9970..000000000
--- a/src/qhull/src/libqhull/index.htm
+++ /dev/null
@@ -1,264 +0,0 @@
-
-
-
-
-Qhull functions, macros, and data structures
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code
    
-To: Qhull files
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
-
    
-
-
-
    Qhull functions, macros, and data structures
    
-
    
-
    The following sections provide an overview and index to
-Qhull's functions, macros, and data structures.
-Each section starts with an introduction.
-See also Calling
-Qhull from C programs and Calling Qhull from C++ programs.
    
-
-
    Qhull uses the following conventions:
    
-
    
-
-
      
-
    • in code, global variables start with "qh "
-
    • in documentation, global variables start with 'qh.'
-
    • constants start with an upper case word
-
    • important globals include an '_'
-
    • functions, macros, and constants start with "qh_"
      • 
-
    • data types end in "T"
      • 
-
    • macros with arguments end in "_"
      • 
-
    • iterators are macros that use local variables
      • 
-
    • iterators for sets start with "FOREACH"
      • 
-
    • iterators for lists start with "FORALL"
      • 
-
    • qhull options are in single quotes (e.g., 'Pdn')
      • 
-
    • lists are sorted alphabetically
      • 
-
    • preprocessor directives on left margin for older compilers
      • 
-
    
-
    
-
    
-When reading the code, please note that the
-global data structure, 'qh', is a macro.  It
-either expands to "qh_qh." or to
-"qh_qh->". The later is used for
-applications which run concurrent calls to qh_qhull().
-
    
-When reading code with an editor, a search for
-'"function'
-will locate the header of qh_function.  A search for '* function'
-will locate the tail of qh_function.
-
-
    A useful starting point is libqhull.h.  It defines most
-of Qhull data structures and top-level functions.  Search for 'PFn' to
-determine the corresponding constant in Qhull.  Search for 'Fp' to
-determine the corresponding qh_PRINT... constant.
-Search io.c to learn how the print function is implemented.
    
-
-
    If your web browser is configured for .c and .h files, the function, macro, and data type links
-go to the corresponding source location.  To configure your web browser for .c and .h files.
-
      
-
    • In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
-
    • Opera 12.10
-
        
-
      1. In Tools > Preferences > Advanced > Downloads
-
      2. Uncheck 'Hide file types opened with Opera'
-
      3. Quick find 'html'
-
      4. Select 'text/html' > Edit
-
      5. Add File extensions 'c,h,'
-
      6. Click 'OK'
-
      
-
    • Internet Explorer -- Mime types are not available from 'Internet Options'.    Is there a registry key for these settings?
-
    • Firefox -- Mime types are not available from 'Preferences'.  Is there an add-on to change the file extensions for a mime type?
-
    • Chrome -- Can Chrome be configured?
-
    
-
-
    
-Please report documentation and link errors
-to qhull-bug@qhull.org.
-
    
-
-
    Copyright © 1997-2015 C.B. Barber
    
-
-
    
-
-
    »Qhull files 
    
-
    
-
-
    This sections lists the .c and .h files for Qhull. Please
-refer to these files for detailed information.
    
-
    
-
-
    
-
    Makefile, CMakeLists.txt
    
-
    Makefile is preconfigured for gcc.  CMakeLists.txt supports multiple
-platforms with CMake.
-Qhull includes project files for Visual Studio and Qt.
-
    
-
-
     
    
-
    libqhull.h 
    
-
    Include file for the Qhull library (libqhull.so, qhull.dll, libqhullstatic.a).
-Data structures are documented under Poly.
-Global variables are documented under Global.
-Other data structures and variables are documented under
-Qhull or Geom.
    
-
-
     
    
-
    Geom, 
-geom.h, 
-geom.c, 
-geom2.c, 
-random.c, 
-random.h
    
-
    Geometric routines. These routines implement mathematical
-functions such as Gaussian elimination and geometric
-routines needed for Qhull. Frequently used routines are
-in geom.c while infrequent ones are in geom2.c.
-
    
-
-
     
    
-
    Global, 
-global.c, 
-libqhull.h 
    
-
    Global routines. Qhull uses a global data structure, qh,
-to store globally defined constants, lists, sets, and
-variables.
-global.c initializes and frees these
-structures. 
    
-
-
     
    
-
    Io, io.h,
-io.c 
    
-
    Input and output routines. Qhull provides a wide range of
-input and output options.
    
-
-
     
    
-
    Mem, 
-mem.h, 
-mem.c 
    
-
    Memory routines. Qhull provides memory allocation and
-deallocation. It uses quick-fit allocation.
    
-
-
     
    
-
    Merge, 
-merge.h, 
-merge.c 
    
-
    Merge routines. Qhull handles precision problems by
-merged facets or joggled input. These routines merge simplicial facets,
-merge non-simplicial facets, merge cycles of facets, and
-rename redundant vertices.
    
-
-
     
    
-
    Poly, 
-poly.h, 
-poly.c, 
-poly2.c, 
-libqhull.h 
    
-
    Polyhedral routines. Qhull produces a polyhedron as a
-list of facets with vertices, neighbors, ridges, and
-geometric information. libqhull.h defines the main
-data structures. Frequently used routines are in poly.c
-while infrequent ones are in poly2.c.
    
-
-
     
    
-
    Qhull, 
-libqhull.c, 
-libqhull.h, 
-qhull_a.h, 
-unix.c , 
-qconvex.c , 
-qdelaun.c , 
-qhalf.c , 
-qvoronoi.c 
    
-
    Top-level routines. The Quickhull algorithm is
-implemented by libqhull.c. qhull_a.h
-includes all header files. 
    
-
-
     
    
-
    Set, 
-qset.h, 
-qset.c 
    
-
    Set routines. Qhull implements its data structures as
-sets. A set is an array of pointers that is expanded as
-needed. This is a separate package that may be used in
-other applications. 
    
-
-
     
    
-
    Stat, 
-stat.h, 
-stat.c 
    
-
    Statistical routines. Qhull maintains statistics about
-its implementation. 
    
-
-
     
    
-
    User, 
-user.h, 
-user.c, 
-user_eg.c, 
-user_eg2.c, 
-
    
-
    User-defined routines. Qhull allows the user to configure
-the code with defined constants and specialized routines.
-
    
-
    
-
    
-
-
    
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull files
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/io.c b/src/qhull/src/libqhull/io.c
deleted file mode 100644
index 401987ec0..000000000
--- a/src/qhull/src/libqhull/io.c
+++ /dev/null
@@ -1,4062 +0,0 @@
-/*
      ---------------------------------
-
-   io.c
-   Input/Output routines of qhull application
-
-   see qh-io.htm and io.h
-
-   see user.c for qh_errprint and qh_printfacetlist
-
-   unix.c calls qh_readpoints and qh_produce_output
-
-   unix.c and user.c are the only callers of io.c functions
-   This allows the user to avoid loading io.o from qhull.a
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/io.c#5 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-/*========= -functions in alphabetical order after qh_produce_output()  =====*/
-
-/*---------------------------------
-
-  qh_produce_output()
-  qh_produce_output2()
-    prints out the result of qhull in desired format
-    qh_produce_output2() does not call qh_prepare_output()
-    if qh.GETarea
-      computes and prints area and volume
-    qh.PRINTout[] is an array of output formats
-
-  notes:
-    prints output in qh.PRINTout order
-*/
-void qh_produce_output(void) {
-    int tempsize= qh_setsize(qhmem.tempstack);
-
-    qh_prepare_output();
-    qh_produce_output2();
-    if (qh_setsize(qhmem.tempstack) != tempsize) {
-        qh_fprintf(qh ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
-            qh_setsize(qhmem.tempstack));
-        qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-} /* produce_output */
-
-
-void qh_produce_output2(void) {
-  int i, tempsize= qh_setsize(qhmem.tempstack), d_1;
-
-  if (qh PRINTsummary)
-    qh_printsummary(qh ferr);
-  else if (qh PRINTout[0] == qh_PRINTnone)
-    qh_printsummary(qh fout);
-  for (i=0; i < qh_PRINTEND; i++)
-    qh_printfacets(qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
-  qh_allstatistics();
-  if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
-    qh_printstats(qh ferr, qhstat precision, NULL);
-  if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
-    qh_printstats(qh ferr, qhstat vridges, NULL);
-  if (qh PRINTstatistics) {
-    qh_printstatistics(qh ferr, "");
-    qh_memstatistics(qh ferr);
-    d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
-    qh_fprintf(qh ferr, 8040, "\
-    size in bytes: merge %d ridge %d vertex %d facet %d\n\
-         normal %d ridge vertices %d facet vertices or neighbors %d\n",
-            (int)sizeof(mergeT), (int)sizeof(ridgeT),
-            (int)sizeof(vertexT), (int)sizeof(facetT),
-            qh normal_size, d_1, d_1 + SETelemsize);
-  }
-  if (qh_setsize(qhmem.tempstack) != tempsize) {
-    qh_fprintf(qh ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
-             qh_setsize(qhmem.tempstack));
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-} /* produce_output2 */
-
-/*---------------------------------
-
-  qh_dfacet( id )
-    print facet by id, for debugging
-
-*/
-void qh_dfacet(unsigned id) {
-  facetT *facet;
-
-  FORALLfacets {
-    if (facet->id == id) {
-      qh_printfacet(qh fout, facet);
-      break;
-    }
-  }
-} /* dfacet */
-
-
-/*---------------------------------
-
-  qh_dvertex( id )
-    print vertex by id, for debugging
-*/
-void qh_dvertex(unsigned id) {
-  vertexT *vertex;
-
-  FORALLvertices {
-    if (vertex->id == id) {
-      qh_printvertex(qh fout, vertex);
-      break;
-    }
-  }
-} /* dvertex */
-
-
-/*---------------------------------
-
-  qh_compare_facetarea( p1, p2 )
-    used by qsort() to order facets by area
-*/
-int qh_compare_facetarea(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  if (!a->isarea)
-    return -1;
-  if (!b->isarea)
-    return 1;
-  if (a->f.area > b->f.area)
-    return 1;
-  else if (a->f.area == b->f.area)
-    return 0;
-  return -1;
-} /* compare_facetarea */
-
-/*---------------------------------
-
-  qh_compare_facetmerge( p1, p2 )
-    used by qsort() to order facets by number of merges
-*/
-int qh_compare_facetmerge(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  return(a->nummerge - b->nummerge);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_facetvisit( p1, p2 )
-    used by qsort() to order facets by visit id or id
-*/
-int qh_compare_facetvisit(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-  int i,j;
-
-  if (!(i= a->visitid))
-    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
-  if (!(j= b->visitid))
-    j= 0 - b->id;
-  return(i - j);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_vertexpoint( p1, p2 )
-    used by qsort() to order vertices by point id
-
-  Not used.  Not available in libqhull_r.h since qh_pointid depends on qh
-*/
-int qh_compare_vertexpoint(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
-} /* compare_vertexpoint */
-
-/*---------------------------------
-
-  qh_copyfilename( dest, size, source, length )
-    copy filename identified by qh_skipfilename()
-
-  notes:
-    see qh_skipfilename() for syntax
-*/
-void qh_copyfilename(char *filename, int size, const char* source, int length) {
-  char c= *source;
-
-  if (length > size + 1) {
-      qh_fprintf(qh ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  strncpy(filename, source, length);
-  filename[length]= '\0';
-  if (c == '\'' || c == '"') {
-    char *s= filename + 1;
-    char *t= filename;
-    while (*s) {
-      if (*s == c) {
-          if (s[-1] == '\\')
-              t[-1]= c;
-      }else
-          *t++= *s;
-      s++;
-    }
-    *t= '\0';
-  }
-} /* copyfilename */
-
-/*---------------------------------
-
-  qh_countfacets( facetlist, facets, printall,
-          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
-    count good facets for printing and set visitid
-    if allfacets, ignores qh_skipfacet()
-
-  notes:
-    qh_printsummary and qh_countfacets must match counts
-
-  returns:
-    numfacets, numsimplicial, total neighbors, numridges, coplanars
-    each facet with ->visitid indicating 1-relative position
-      ->visitid==0 indicates not good
-
-  notes
-    numfacets >= numsimplicial
-    if qh.NEWfacets,
-      does not count visible facets (matches qh_printafacet)
-
-  design:
-    for all facets on facetlist and in facets set
-      unless facet is skipped or visible (i.e., will be deleted)
-        mark facet->visitid
-        update counts
-*/
-void qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
-    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
-  facetT *facet, **facetp;
-  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
-
-  FORALLfacet_(facetlist) {
-    if ((facet->visible && qh NEWfacets)
-    || (!printall && qh_skipfacet(facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(facet->neighbors);
-      if (facet->simplicial) {
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(facet->coplanarset);
-    }
-  }
-
-  FOREACHfacet_(facets) {
-    if ((facet->visible && qh NEWfacets)
-    || (!printall && qh_skipfacet(facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(facet->neighbors);
-      if (facet->simplicial){
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(facet->coplanarset);
-    }
-  }
-  qh visit_id += numfacets+1;
-  *numfacetsp= numfacets;
-  *numsimplicialp= numsimplicial;
-  *totneighborsp= totneighbors;
-  *numridgesp= numridges;
-  *numcoplanarsp= numcoplanars;
-  *numtricoplanarsp= numtricoplanars;
-} /* countfacets */
-
-/*---------------------------------
-
-  qh_detvnorm( vertex, vertexA, centers, offset )
-    compute separating plane of the Voronoi diagram for a pair of input sites
-    centers= set of facets (i.e., Voronoi vertices)
-      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  returns:
-    norm
-      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
-      copy the data before reusing qh.gm_matrix
-    offset
-      if 'QVn'
-        sign adjusted so that qh.GOODvertexp is inside
-      else
-        sign adjusted so that vertex is inside
-
-    qh.gm_matrix= simplex of points from centers relative to first center
-
-  notes:
-    in io.c so that code for 'v Tv' can be removed by removing io.c
-    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
-
-  design:
-    determine midpoint of input sites
-    build points as the set of Voronoi vertices
-    select a simplex from points (if necessary)
-      include midpoint if the Voronoi region is unbounded
-    relocate the first vertex of the simplex to the origin
-    compute the normalized hyperplane through the simplex
-    orient the hyperplane toward 'QVn' or 'vertex'
-    if 'Tv' or 'Ts'
-      if bounded
-        test that hyperplane is the perpendicular bisector of the input sites
-      test that Voronoi vertices not in the simplex are still on the hyperplane
-    free up temporary memory
-*/
-pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
-  facetT *facet, **facetp;
-  int  i, k, pointid, pointidA, point_i, point_n;
-  setT *simplex= NULL;
-  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
-  coordT *coord, *gmcoord, *normalp;
-  setT *points= qh_settemp(qh TEMPsize);
-  boolT nearzero= False;
-  boolT unbounded= False;
-  int numcenters= 0;
-  int dim= qh hull_dim - 1;
-  realT dist, offset, angle, zero= 0.0;
-
-  midpoint= qh gm_matrix + qh hull_dim * qh hull_dim;  /* last row */
-  for (k=0; k < dim; k++)
-    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
-  FOREACHfacet_(centers) {
-    numcenters++;
-    if (!facet->visitid)
-      unbounded= True;
-    else {
-      if (!facet->center)
-        facet->center= qh_facetcenter(facet->vertices);
-      qh_setappend(&points, facet->center);
-    }
-  }
-  if (numcenters > dim) {
-    simplex= qh_settemp(qh TEMPsize);
-    qh_setappend(&simplex, vertex->point);
-    if (unbounded)
-      qh_setappend(&simplex, midpoint);
-    qh_maxsimplex(dim, points, NULL, 0, &simplex);
-    qh_setdelnth(simplex, 0);
-  }else if (numcenters == dim) {
-    if (unbounded)
-      qh_setappend(&points, midpoint);
-    simplex= points;
-  }else {
-    qh_fprintf(qh ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  i= 0;
-  gmcoord= qh gm_matrix;
-  point0= SETfirstt_(simplex, pointT);
-  FOREACHpoint_(simplex) {
-    if (qh IStracing >= 4)
-      qh_printmatrix(qh ferr, "qh_detvnorm: Voronoi vertex or midpoint",
-                              &point, 1, dim);
-    if (point != point0) {
-      qh gm_row[i++]= gmcoord;
-      coord= point0;
-      for (k=dim; k--; )
-        *(gmcoord++)= *point++ - *coord++;
-    }
-  }
-  qh gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
-  normal= gmcoord;
-  qh_sethyperplane_gauss(dim, qh gm_row, point0, True,
-                normal, &offset, &nearzero);
-  if (qh GOODvertexp == vertexA->point)
-    inpoint= vertexA->point;
-  else
-    inpoint= vertex->point;
-  zinc_(Zdistio);
-  dist= qh_distnorm(dim, inpoint, normal, &offset);
-  if (dist > 0) {
-    offset= -offset;
-    normalp= normal;
-    for (k=dim; k--; ) {
-      *normalp= -(*normalp);
-      normalp++;
-    }
-  }
-  if (qh VERIFYoutput || qh PRINTstatistics) {
-    pointid= qh_pointid(vertex->point);
-    pointidA= qh_pointid(vertexA->point);
-    if (!unbounded) {
-      zinc_(Zdiststat);
-      dist= qh_distnorm(dim, midpoint, normal, &offset);
-      if (dist < 0)
-        dist= -dist;
-      zzinc_(Zridgemid);
-      wwmax_(Wridgemidmax, dist);
-      wwadd_(Wridgemid, dist);
-      trace4((qh ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
-                 pointid, pointidA, dist));
-      for (k=0; k < dim; k++)
-        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
-      qh_normalize(midpoint, dim, False);
-      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
-      if (angle < 0.0)
-        angle= angle + 1.0;
-      else
-        angle= angle - 1.0;
-      if (angle < 0.0)
-        angle -= angle;
-      trace4((qh ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
-                 pointid, pointidA, angle, nearzero));
-      if (nearzero) {
-        zzinc_(Zridge0);
-        wwmax_(Wridge0max, angle);
-        wwadd_(Wridge0, angle);
-      }else {
-        zzinc_(Zridgeok)
-        wwmax_(Wridgeokmax, angle);
-        wwadd_(Wridgeok, angle);
-      }
-    }
-    if (simplex != points) {
-      FOREACHpoint_i_(points) {
-        if (!qh_setin(simplex, point)) {
-          facet= SETelemt_(centers, point_i, facetT);
-          zinc_(Zdiststat);
-          dist= qh_distnorm(dim, point, normal, &offset);
-          if (dist < 0)
-            dist= -dist;
-          zzinc_(Zridge);
-          wwmax_(Wridgemax, dist);
-          wwadd_(Wridge, dist);
-          trace4((qh ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
-                             pointid, pointidA, facet->visitid, dist));
-        }
-      }
-    }
-  }
-  *offsetp= offset;
-  if (simplex != points)
-    qh_settempfree(&simplex);
-  qh_settempfree(&points);
-  return normal;
-} /* detvnorm */
-
-/*---------------------------------
-
-  qh_detvridge( vertexA )
-    determine Voronoi ridge from 'seen' neighbors of vertexA
-    include one vertex-at-infinite if an !neighbor->visitid
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    sorted by center id
-*/
-setT *qh_detvridge(vertexT *vertex) {
-  setT *centers= qh_settemp(qh TEMPsize);
-  setT *tricenters= qh_settemp(qh TEMPsize);
-  facetT *neighbor, **neighborp;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->seen) {
-      if (neighbor->visitid) {
-        if (!neighbor->tricoplanar || qh_setunique(&tricenters, neighbor->center))
-          qh_setappend(¢ers, neighbor);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(¢ers, neighbor);
-      }
-    }
-  }
-  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(centers),
-             sizeof(facetT *), qh_compare_facetvisit);
-  qh_settempfree(&tricenters);
-  return centers;
-} /* detvridge */
-
-/*---------------------------------
-
-  qh_detvridge3( atvertex, vertex )
-    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
-    include one vertex-at-infinite for !neighbor->visitid
-    assumes all facet->seen2= True
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    listed in adjacency order (!oriented)
-    all facet->seen2= True
-
-  design:
-    mark all neighbors of atvertex
-    for each adjacent neighbor of both atvertex and vertex
-      if neighbor selected
-        add neighbor to set of Voronoi vertices
-*/
-setT *qh_detvridge3(vertexT *atvertex, vertexT *vertex) {
-  setT *centers= qh_settemp(qh TEMPsize);
-  setT *tricenters= qh_settemp(qh TEMPsize);
-  facetT *neighbor, **neighborp, *facet= NULL;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= False;
-  FOREACHneighbor_(vertex) {
-    if (!neighbor->seen2) {
-      facet= neighbor;
-      break;
-    }
-  }
-  while (facet) {
-    facet->seen2= True;
-    if (neighbor->seen) {
-      if (facet->visitid) {
-        if (!facet->tricoplanar || qh_setunique(&tricenters, facet->center))
-          qh_setappend(¢ers, facet);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(¢ers, facet);
-      }
-    }
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen2) {
-        if (qh_setin(vertex->neighbors, neighbor))
-          break;
-        else
-          neighbor->seen2= True;
-      }
-    }
-    facet= neighbor;
-  }
-  if (qh CHECKfrequently) {
-    FOREACHneighbor_(vertex) {
-      if (!neighbor->seen2) {
-          qh_fprintf(qh ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
-                 qh_pointid(vertex->point), neighbor->id);
-        qh_errexit(qh_ERRqhull, neighbor, NULL);
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= True;
-  qh_settempfree(&tricenters);
-  return centers;
-} /* detvridge3 */
-
-/*---------------------------------
-
-  qh_eachvoronoi( fp, printvridge, vertex, visitall, innerouter, inorder )
-    if visitall,
-      visit all Voronoi ridges for vertex (i.e., an input site)
-    else
-      visit all unvisited Voronoi ridges for vertex
-      all vertex->seen= False if unvisited
-    assumes
-      all facet->seen= False
-      all facet->seen2= True (for qh_detvridge3)
-      all facet->visitid == 0 if vertex_at_infinity
-                         == index of Voronoi vertex
-                         >= qh.num_facets if ignored
-    innerouter:
-      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
-      qh_RIDGEinner- only inner
-      qh_RIDGEouter- only outer
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns:
-    number of visited ridges (does not include previously visited ridges)
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-        fp== any pointer (assumes FILE*)
-        vertex,vertexA= pair of input sites that define a Voronoi ridge
-        centers= set of facets (i.e., Voronoi vertices)
-                 ->visitid == index or 0 if vertex_at_infinity
-                 ordered for 3-d Voronoi diagram
-  notes:
-    uses qh.vertex_visit
-
-  see:
-    qh_eachvoronoi_all()
-
-  design:
-    mark selected neighbors of atvertex
-    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
-      for each unvisited vertex
-        if atvertex and vertex share more than d-1 neighbors
-          bump totalcount
-          if printvridge defined
-            build the set of shared neighbors (i.e., Voronoi vertices)
-            call printvridge
-*/
-int qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
-  boolT unbounded;
-  int count;
-  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
-  setT *centers;
-  setT *tricenters= qh_settemp(qh TEMPsize);
-
-  vertexT *vertex, **vertexp;
-  boolT firstinf;
-  unsigned int numfacets= (unsigned int)qh num_facets;
-  int totridges= 0;
-
-  qh vertex_visit++;
-  atvertex->seen= True;
-  if (visitall) {
-    FORALLvertices
-      vertex->seen= False;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->visitid < numfacets)
-      neighbor->seen= True;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->seen) {
-      FOREACHvertex_(neighbor->vertices) {
-        if (vertex->visitid != qh vertex_visit && !vertex->seen) {
-          vertex->visitid= qh vertex_visit;
-          count= 0;
-          firstinf= True;
-          qh_settruncate(tricenters, 0);
-          FOREACHneighborA_(vertex) {
-            if (neighborA->seen) {
-              if (neighborA->visitid) {
-                if (!neighborA->tricoplanar || qh_setunique(&tricenters, neighborA->center))
-                  count++;
-              }else if (firstinf) {
-                count++;
-                firstinf= False;
-              }
-            }
-          }
-          if (count >= qh hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
-            if (firstinf) {
-              if (innerouter == qh_RIDGEouter)
-                continue;
-              unbounded= False;
-            }else {
-              if (innerouter == qh_RIDGEinner)
-                continue;
-              unbounded= True;
-            }
-            totridges++;
-            trace4((qh ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
-                  count, qh_pointid(atvertex->point), qh_pointid(vertex->point)));
-            if (printvridge && fp) {
-              if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
-                centers= qh_detvridge3(atvertex, vertex);
-              else
-                centers= qh_detvridge(vertex);
-              (*printvridge)(fp, atvertex, vertex, centers, unbounded);
-              qh_settempfree(¢ers);
-            }
-          }
-        }
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen= False;
-  qh_settempfree(&tricenters);
-  return totridges;
-} /* eachvoronoi */
-
-
-/*---------------------------------
-
-  qh_eachvoronoi_all( fp, printvridge, isUpper, innerouter, inorder )
-    visit all Voronoi ridges
-
-    innerouter:
-      see qh_eachvoronoi()
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns
-    total number of ridges
-
-    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
-      facet->visitid= Voronoi vertex index(same as 'o' format)
-    else
-      facet->visitid= 0
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-      [see qh_eachvoronoi]
-
-  notes:
-    Not used for qhull.exe
-    same effect as qh_printvdiagram but ridges not sorted by point id
-*/
-int qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
-  facetT *facet;
-  vertexT *vertex;
-  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
-  int totridges= 0;
-
-  qh_clearcenters(qh_ASvoronoi);
-  qh_vertexneighbors();
-  maximize_(qh visit_id, (unsigned) qh num_facets);
-  FORALLfacets {
-    facet->visitid= 0;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  FORALLfacets {
-    if (facet->upperdelaunay == isUpper)
-      facet->visitid= numcenters++;
-  }
-  FORALLvertices
-    vertex->seen= False;
-  FORALLvertices {
-    if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
-      continue;
-    totridges += qh_eachvoronoi(fp, printvridge, vertex,
-                   !qh_ALL, innerouter, inorder);
-  }
-  return totridges;
-} /* eachvoronoi_all */
-
-/*---------------------------------
-
-  qh_facet2point( facet, point0, point1, mindist )
-    return two projected temporary vertices for a 2-d facet
-    may be non-simplicial
-
-  returns:
-    point0 and point1 oriented and projected to the facet
-    returns mindist (maximum distance below plane)
-*/
-void qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
-  vertexT *vertex0, *vertex1;
-  realT dist;
-
-  if (facet->toporient ^ qh_ORIENTclock) {
-    vertex0= SETfirstt_(facet->vertices, vertexT);
-    vertex1= SETsecondt_(facet->vertices, vertexT);
-  }else {
-    vertex1= SETfirstt_(facet->vertices, vertexT);
-    vertex0= SETsecondt_(facet->vertices, vertexT);
-  }
-  zadd_(Zdistio, 2);
-  qh_distplane(vertex0->point, facet, &dist);
-  *mindist= dist;
-  *point0= qh_projectpoint(vertex0->point, facet, dist);
-  qh_distplane(vertex1->point, facet, &dist);
-  minimize_(*mindist, dist);
-  *point1= qh_projectpoint(vertex1->point, facet, dist);
-} /* facet2point */
-
-
-/*---------------------------------
-
-  qh_facetvertices( facetlist, facets, allfacets )
-    returns temporary set of vertices in a set and/or list of facets
-    if allfacets, ignores qh_skipfacet()
-
-  returns:
-    vertices with qh.vertex_visit
-
-  notes:
-    optimized for allfacets of facet_list
-
-  design:
-    if allfacets of facet_list
-      create vertex set from vertex_list
-    else
-      for each selected facet in facets or facetlist
-        append unvisited vertices to vertex set
-*/
-setT *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets) {
-  setT *vertices;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-
-  qh vertex_visit++;
-  if (facetlist == qh facet_list && allfacets && !facets) {
-    vertices= qh_settemp(qh num_vertices);
-    FORALLvertices {
-      vertex->visitid= qh vertex_visit;
-      qh_setappend(&vertices, vertex);
-    }
-  }else {
-    vertices= qh_settemp(qh TEMPsize);
-    FORALLfacet_(facetlist) {
-      if (!allfacets && qh_skipfacet(facet))
-        continue;
-      FOREACHvertex_(facet->vertices) {
-        if (vertex->visitid != qh vertex_visit) {
-          vertex->visitid= qh vertex_visit;
-          qh_setappend(&vertices, vertex);
-        }
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (!allfacets && qh_skipfacet(facet))
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-        qh_setappend(&vertices, vertex);
-      }
-    }
-  }
-  return vertices;
-} /* facetvertices */
-
-/*---------------------------------
-
-  qh_geomplanes( facet, outerplane, innerplane )
-    return outer and inner planes for Geomview
-    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
-
-  notes:
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-*/
-void qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane) {
-  realT radius;
-
-  if (qh MERGING || qh JOGGLEmax < REALmax/2) {
-    qh_outerinner(facet, outerplane, innerplane);
-    radius= qh PRINTradius;
-    if (qh JOGGLEmax < REALmax/2)
-      radius -= qh JOGGLEmax * sqrt((realT)qh hull_dim);  /* already accounted for in qh_outerinner() */
-    *outerplane += radius;
-    *innerplane -= radius;
-    if (qh PRINTcoplanar || qh PRINTspheres) {
-      *outerplane += qh MAXabs_coord * qh_GEOMepsilon;
-      *innerplane -= qh MAXabs_coord * qh_GEOMepsilon;
-    }
-  }else
-    *innerplane= *outerplane= 0;
-} /* geomplanes */
-
-
-/*---------------------------------
-
-  qh_markkeep( facetlist )
-    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
-    ignores visible facets (!part of convex hull)
-
-  returns:
-    may clear facet->good
-    recomputes qh.num_good
-
-  design:
-    get set of good facets
-    if qh.KEEParea
-      sort facets by area
-      clear facet->good for all but n largest facets
-    if qh.KEEPmerge
-      sort facets by merge count
-      clear facet->good for all but n most merged facets
-    if qh.KEEPminarea
-      clear facet->good if area too small
-    update qh.num_good
-*/
-void qh_markkeep(facetT *facetlist) {
-  facetT *facet, **facetp;
-  setT *facets= qh_settemp(qh num_facets);
-  int size, count;
-
-  trace2((qh ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
-          qh KEEParea, qh KEEPmerge, qh KEEPminArea));
-  FORALLfacet_(facetlist) {
-    if (!facet->visible && facet->good)
-      qh_setappend(&facets, facet);
-  }
-  size= qh_setsize(facets);
-  if (qh KEEParea) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetarea);
-    if ((count= size - qh KEEParea) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh KEEPmerge) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetmerge);
-    if ((count= size - qh KEEPmerge) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh KEEPminArea < REALmax/2) {
-    FOREACHfacet_(facets) {
-      if (!facet->isarea || facet->f.area < qh KEEPminArea)
-        facet->good= False;
-    }
-  }
-  qh_settempfree(&facets);
-  count= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      count++;
-  }
-  qh num_good= count;
-} /* markkeep */
-
-
-/*---------------------------------
-
-  qh_markvoronoi( facetlist, facets, printall, isLower, numcenters )
-    mark voronoi vertices for printing by site pairs
-
-  returns:
-    temporary set of vertices indexed by pointid
-    isLower set if printing lower hull (i.e., at least one facet is lower hull)
-    numcenters= total number of Voronoi vertices
-    bumps qh.printoutnum for vertex-at-infinity
-    clears all facet->seen and sets facet->seen2
-
-    if selected
-      facet->visitid= Voronoi vertex id
-    else if upper hull (or 'Qu' and lower hull)
-      facet->visitid= 0
-    else
-      facet->visitid >= qh num_facets
-
-  notes:
-    ignores qh.ATinfinity, if defined
-*/
-setT *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
-  int numcenters=0;
-  facetT *facet, **facetp;
-  setT *vertices;
-  boolT isLower= False;
-
-  qh printoutnum++;
-  qh_clearcenters(qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
-  qh_vertexneighbors();
-  vertices= qh_pointvertex();
-  if (qh ATinfinity)
-    SETelem_(vertices, qh num_points-1)= NULL;
-  qh visit_id++;
-  maximize_(qh visit_id, (unsigned) qh num_facets);
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FORALLfacets {
-    if (facet->normal && (facet->upperdelaunay == isLower))
-      facet->visitid= 0;  /* facetlist or facets may overwrite */
-    else
-      facet->visitid= qh visit_id;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  numcenters++;  /* qh_INFINITE */
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(facet))
-      facet->visitid= numcenters++;
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(facet))
-      facet->visitid= numcenters++;
-  }
-  *isLowerp= isLower;
-  *numcentersp= numcenters;
-  trace2((qh ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
-  return vertices;
-} /* markvoronoi */
-
-/*---------------------------------
-
-  qh_order_vertexneighbors( vertex )
-    order facet neighbors of a 2-d or 3-d vertex by adjacency
-
-  notes:
-    does not orient the neighbors
-
-  design:
-    initialize a new neighbor set with the first facet in vertex->neighbors
-    while vertex->neighbors non-empty
-      select next neighbor in the previous facet's neighbor set
-    set vertex->neighbors to the new neighbor set
-*/
-void qh_order_vertexneighbors(vertexT *vertex) {
-  setT *newset;
-  facetT *facet, *neighbor, **neighborp;
-
-  trace4((qh ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
-  newset= qh_settemp(qh_setsize(vertex->neighbors));
-  facet= (facetT*)qh_setdellast(vertex->neighbors);
-  qh_setappend(&newset, facet);
-  while (qh_setsize(vertex->neighbors)) {
-    FOREACHneighbor_(vertex) {
-      if (qh_setin(facet->neighbors, neighbor)) {
-        qh_setdel(vertex->neighbors, neighbor);
-        qh_setappend(&newset, neighbor);
-        facet= neighbor;
-        break;
-      }
-    }
-    if (!neighbor) {
-      qh_fprintf(qh ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
-        vertex->id, facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-  }
-  qh_setfree(&vertex->neighbors);
-  qh_settemppop();
-  vertex->neighbors= newset;
-} /* order_vertexneighbors */
-
-/*---------------------------------
-
-  qh_prepare_output( )
-    prepare for qh_produce_output2() according to
-      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
-    does not reset facet->good
-
-  notes
-    except for PRINTstatistics, no-op if previously called with same options
-*/
-void qh_prepare_output(void) {
-  if (qh VORONOI) {
-    qh_clearcenters(qh_ASvoronoi);  /* must be before qh_triangulate */
-    qh_vertexneighbors();
-  }
-  if (qh TRIangulate && !qh hasTriangulation) {
-    qh_triangulate();
-    if (qh VERIFYoutput && !qh CHECKfrequently)
-      qh_checkpolygon(qh facet_list);
-  }
-  qh_findgood_all(qh facet_list);
-  if (qh GETarea)
-    qh_getarea(qh facet_list);
-  if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
-    qh_markkeep(qh facet_list);
-  if (qh PRINTstatistics)
-    qh_collectstatistics();
-}
-
-/*---------------------------------
-
-  qh_printafacet( fp, format, facet, printall )
-    print facet to fp in given output format (see qh.PRINTout)
-
-  returns:
-    nop if !printall and qh_skipfacet()
-    nop if visible facet and NEWfacets and format != PRINTfacets
-    must match qh_countfacets
-
-  notes
-    preserves qh.visit_id
-    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
-
-  see
-    qh_printbegin() and qh_printend()
-
-  design:
-    test for printing facet
-    call appropriate routine for format
-    or output results directly
-*/
-void qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
-  realT color[4], offset, dist, outerplane, innerplane;
-  boolT zerodiv;
-  coordT *point, *normp, *coordp, **pointp, *feasiblep;
-  int k;
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  if (!printall && qh_skipfacet(facet))
-    return;
-  if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
-    return;
-  qh printoutnum++;
-  switch (format) {
-  case qh_PRINTarea:
-    if (facet->isarea) {
-      qh_fprintf(fp, 9009, qh_REAL_1, facet->f.area);
-      qh_fprintf(fp, 9010, "\n");
-    }else
-      qh_fprintf(fp, 9011, "0\n");
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(fp, 9012, "%d", qh_setsize(facet->coplanarset));
-    FOREACHpoint_(facet->coplanarset)
-      qh_fprintf(fp, 9013, " %d", qh_pointid(point));
-    qh_fprintf(fp, 9014, "\n");
-    break;
-  case qh_PRINTcentrums:
-    qh_printcenter(fp, format, NULL, facet);
-    break;
-  case qh_PRINTfacets:
-    qh_printfacet(fp, facet);
-    break;
-  case qh_PRINTfacets_xridge:
-    qh_printfacetheader(fp, facet);
-    break;
-  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
-    if (!facet->normal)
-      break;
-    for (k=qh hull_dim; k--; ) {
-      color[k]= (facet->normal[k]+1.0)/2.0;
-      maximize_(color[k], -1.0);
-      minimize_(color[k], +1.0);
-    }
-    qh_projectdim3(color, color);
-    if (qh PRINTdim != qh hull_dim)
-      qh_normalize2(color, 3, True, NULL, NULL);
-    if (qh hull_dim <= 2)
-      qh_printfacet2geom(fp, facet, color);
-    else if (qh hull_dim == 3) {
-      if (facet->simplicial)
-        qh_printfacet3geom_simplicial(fp, facet, color);
-      else
-        qh_printfacet3geom_nonsimplicial(fp, facet, color);
-    }else {
-      if (facet->simplicial)
-        qh_printfacet4geom_simplicial(fp, facet, color);
-      else
-        qh_printfacet4geom_nonsimplicial(fp, facet, color);
-    }
-    break;
-  case qh_PRINTids:
-    qh_fprintf(fp, 9015, "%d\n", facet->id);
-    break;
-  case qh_PRINTincidences:
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh hull_dim == 3 && format != qh_PRINTtriangles)
-      qh_printfacet3vertex(fp, facet, format);
-    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
-      qh_printfacetNvertex_simplicial(fp, facet, format);
-    else
-      qh_printfacetNvertex_nonsimplicial(fp, facet, qh printoutvar++, format);
-    break;
-  case qh_PRINTinner:
-    qh_outerinner(facet, NULL, &innerplane);
-    offset= facet->offset - innerplane;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTmerges:
-    qh_fprintf(fp, 9016, "%d\n", facet->nummerge);
-    break;
-  case qh_PRINTnormals:
-    offset= facet->offset;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTouter:
-    qh_outerinner(facet, &outerplane, NULL);
-    offset= facet->offset - outerplane;
-  LABELprintnorm:
-    if (!facet->normal) {
-      qh_fprintf(fp, 9017, "no normal for facet f%d\n", facet->id);
-      break;
-    }
-    if (qh CDDoutput) {
-      qh_fprintf(fp, 9018, qh_REAL_1, -offset);
-      for (k=0; k < qh hull_dim; k++)
-        qh_fprintf(fp, 9019, qh_REAL_1, -facet->normal[k]);
-    }else {
-      for (k=0; k < qh hull_dim; k++)
-        qh_fprintf(fp, 9020, qh_REAL_1, facet->normal[k]);
-      qh_fprintf(fp, 9021, qh_REAL_1, offset);
-    }
-    qh_fprintf(fp, 9022, "\n");
-    break;
-  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
-  case qh_PRINTmaple:
-    if (qh hull_dim == 2)
-      qh_printfacet2math(fp, facet, format, qh printoutvar++);
-    else
-      qh_printfacet3math(fp, facet, format, qh printoutvar++);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(fp, 9023, "%d", qh_setsize(facet->neighbors));
-    FOREACHneighbor_(facet)
-      qh_fprintf(fp, 9024, " %d",
-               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
-    qh_fprintf(fp, 9025, "\n");
-    break;
-  case qh_PRINTpointintersect:
-    if (!qh feasible_point) {
-      qh_fprintf(qh ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
-      qh_errexit( qh_ERRinput, NULL, NULL);
-    }
-    if (facet->offset > 0)
-      goto LABELprintinfinite;
-    point= coordp= (coordT*)qh_memalloc(qh normal_size);
-    normp= facet->normal;
-    feasiblep= qh feasible_point;
-    if (facet->offset < -qh MINdenom) {
-      for (k=qh hull_dim; k--; )
-        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
-    }else {
-      for (k=qh hull_dim; k--; ) {
-        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh MINdenom_1,
-                                 &zerodiv) + *(feasiblep++);
-        if (zerodiv) {
-          qh_memfree(point, qh normal_size);
-          goto LABELprintinfinite;
-        }
-      }
-    }
-    qh_printpoint(fp, NULL, point);
-    qh_memfree(point, qh normal_size);
-    break;
-  LABELprintinfinite:
-    for (k=qh hull_dim; k--; )
-      qh_fprintf(fp, 9026, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(fp, 9027, "\n");
-    break;
-  case qh_PRINTpointnearest:
-    FOREACHpoint_(facet->coplanarset) {
-      int id, id2;
-      vertex= qh_nearvertex(facet, point, &dist);
-      id= qh_pointid(vertex->point);
-      id2= qh_pointid(point);
-      qh_fprintf(fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
-    }
-    break;
-  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
-    if (qh CDDoutput)
-      qh_fprintf(fp, 9029, "1 ");
-    qh_printcenter(fp, format, NULL, facet);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(fp, 9030, "%d", qh_setsize(facet->vertices));
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(fp, 9031, " %d", qh_pointid(vertex->point));
-    qh_fprintf(fp, 9032, "\n");
-    break;
-  default:
-    break;
-  }
-} /* printafacet */
-
-/*---------------------------------
-
-  qh_printbegin(  )
-    prints header for all output formats
-
-  returns:
-    checks for valid format
-
-  notes:
-    uses qh.visit_id for 3/4off
-    changes qh.interior_point if printing centrums
-    qh_countfacets clears facet->visitid for non-good facets
-
-  see
-    qh_printend() and qh_printafacet()
-
-  design:
-    count facets and related statistics
-    print header for format
-*/
-void qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  int i, num;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-  pointT *point, **pointp, *pointtemp;
-
-  qh printoutnum= 0;
-  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-  switch (format) {
-  case qh_PRINTnone:
-    break;
-  case qh_PRINTarea:
-    qh_fprintf(fp, 9033, "%d\n", numfacets);
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(fp, 9034, "%d\n", numfacets);
-    break;
-  case qh_PRINTcentrums:
-    if (qh CENTERtype == qh_ASnone)
-      qh_clearcenters(qh_AScentrum);
-    qh_fprintf(fp, 9035, "%d\n%d\n", qh hull_dim, numfacets);
-    break;
-  case qh_PRINTfacets:
-  case qh_PRINTfacets_xridge:
-    if (facetlist)
-      qh_printvertexlist(fp, "Vertices and facets:\n", facetlist, facets, printall);
-    break;
-  case qh_PRINTgeom:
-    if (qh hull_dim > 4)  /* qh_initqhull_globals also checks */
-      goto LABELnoformat;
-    if (qh VORONOI && qh hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
-      goto LABELnoformat;
-    if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))
-      qh_fprintf(qh ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
-    if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||
-                             (qh PRINTdim == 4 && qh PRINTcentrums)))
-      qh_fprintf(qh ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
-    if (qh PRINTdim == 4 && (qh PRINTspheres))
-      qh_fprintf(qh ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
-    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
-      qh_fprintf(qh ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
-    if (qh PRINTdim == 2) {
-      qh_fprintf(fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
-              qh rbox_command, qh qhull_command);
-    }else if (qh PRINTdim == 3) {
-      qh_fprintf(fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
-              qh rbox_command, qh qhull_command);
-    }else if (qh PRINTdim == 4) {
-      qh visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
-        qh_printend4geom(NULL, facet, &num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(NULL, facet, &num, printall);
-      qh ridgeoutnum= num;
-      qh printoutvar= 0;  /* counts number of ridges in output */
-      qh_fprintf(fp, 9038, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
-    }
-
-    if (qh PRINTdots) {
-      qh printoutnum++;
-      num= qh num_points + qh_setsize(qh other_points);
-      if (qh DELAUNAY && qh ATinfinity)
-        num--;
-      if (qh PRINTdim == 4)
-        qh_fprintf(fp, 9039, "4VECT %d %d 1\n", num, num);
-      else
-        qh_fprintf(fp, 9040, "VECT %d %d 1\n", num, num);
-
-      for (i=num; i--; ) {
-        if (i % 20 == 0)
-          qh_fprintf(fp, 9041, "\n");
-        qh_fprintf(fp, 9042, "1 ");
-      }
-      qh_fprintf(fp, 9043, "# 1 point per line\n1 ");
-      for (i=num-1; i--; ) { /* num at least 3 for D2 */
-        if (i % 20 == 0)
-          qh_fprintf(fp, 9044, "\n");
-        qh_fprintf(fp, 9045, "0 ");
-      }
-      qh_fprintf(fp, 9046, "# 1 color for all\n");
-      FORALLpoints {
-        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
-          if (qh PRINTdim == 4)
-            qh_printpoint(fp, NULL, point);
-            else
-              qh_printpoint3(fp, point);
-        }
-      }
-      FOREACHpoint_(qh other_points) {
-        if (qh PRINTdim == 4)
-          qh_printpoint(fp, NULL, point);
-        else
-          qh_printpoint3(fp, point);
-      }
-      qh_fprintf(fp, 9047, "0 1 1 1  # color of points\n");
-    }
-
-    if (qh PRINTdim == 4  && !qh PRINTnoplanes)
-      /* 4dview loads up multiple 4OFF objects slowly */
-      qh_fprintf(fp, 9048, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);
-    qh PRINTcradius= 2 * qh DISTround;  /* include test DISTround */
-    if (qh PREmerge) {
-      maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);
-    }else if (qh POSTmerge)
-      maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);
-    qh PRINTradius= qh PRINTcradius;
-    if (qh PRINTspheres + qh PRINTcoplanar)
-      maximize_(qh PRINTradius, qh MAXabs_coord * qh_MINradius);
-    if (qh premerge_cos < REALmax/2) {
-      maximize_(qh PRINTradius, (1- qh premerge_cos) * qh MAXabs_coord);
-    }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {
-      maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh MAXabs_coord);
-    }
-    maximize_(qh PRINTradius, qh MINvisible);
-    if (qh JOGGLEmax < REALmax/2)
-      qh PRINTradius += qh JOGGLEmax * sqrt((realT)qh hull_dim);
-    if (qh PRINTdim != 4 &&
-        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
-      vertices= qh_facetvertices(facetlist, facets, printall);
-      if (qh PRINTspheres && qh PRINTdim <= 3)
-        qh_printspheres(fp, vertices, qh PRINTradius);
-      if (qh PRINTcoplanar || qh PRINTcentrums) {
-        qh firstcentrum= True;
-        if (qh PRINTcoplanar&& !qh PRINTspheres) {
-          FOREACHvertex_(vertices)
-            qh_printpointvect2(fp, vertex->point, NULL, qh interior_point, qh PRINTradius);
-        }
-        FORALLfacet_(facetlist) {
-          if (!printall && qh_skipfacet(facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh PRINTcentrums && qh PRINTdim <= 3)
-            qh_printcentrum(fp, facet, qh PRINTcradius);
-          if (!qh PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
-        }
-        FOREACHfacet_(facets) {
-          if (!printall && qh_skipfacet(facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh PRINTcentrums && qh PRINTdim <= 3)
-            qh_printcentrum(fp, facet, qh PRINTcradius);
-          if (!qh PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
-        }
-      }
-      qh_settempfree(&vertices);
-    }
-    qh visit_id++; /* for printing hyperplane intersections */
-    break;
-  case qh_PRINTids:
-    qh_fprintf(fp, 9049, "%d\n", numfacets);
-    break;
-  case qh_PRINTincidences:
-    if (qh VORONOI && qh PRINTprecision)
-      qh_fprintf(qh ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
-    qh printoutvar= qh vertex_id;  /* centrum id for non-simplicial facets */
-    if (qh hull_dim <= 3)
-      qh_fprintf(fp, 9050, "%d\n", numfacets);
-    else
-      qh_fprintf(fp, 9051, "%d\n", numsimplicial+numridges);
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh CDDoutput)
-      qh_fprintf(fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,
-            qh qhull_command, numfacets, qh hull_dim+1);
-    else
-      qh_fprintf(fp, 9053, "%d\n%d\n", qh hull_dim+1, numfacets);
-    break;
-  case qh_PRINTmathematica:
-  case qh_PRINTmaple:
-    if (qh hull_dim > 3)  /* qh_initbuffers also checks */
-      goto LABELnoformat;
-    if (qh VORONOI)
-      qh_fprintf(qh ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
-    if (format == qh_PRINTmaple) {
-      if (qh hull_dim == 2)
-        qh_fprintf(fp, 9054, "PLOT(CURVES(\n");
-      else
-        qh_fprintf(fp, 9055, "PLOT3D(POLYGONS(\n");
-    }else
-      qh_fprintf(fp, 9056, "{\n");
-    qh printoutvar= 0;   /* counts number of facets for notfirst */
-    break;
-  case qh_PRINTmerges:
-    qh_fprintf(fp, 9057, "%d\n", numfacets);
-    break;
-  case qh_PRINTpointintersect:
-    qh_fprintf(fp, 9058, "%d\n%d\n", qh hull_dim, numfacets);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(fp, 9059, "%d\n", numfacets);
-    break;
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh VORONOI)
-      goto LABELnoformat;
-    num = qh hull_dim;
-    if (format == qh_PRINToff || qh hull_dim == 2)
-      qh_fprintf(fp, 9060, "%d\n%d %d %d\n", num,
-        qh num_points+qh_setsize(qh other_points), numfacets, totneighbors/2);
-    else { /* qh_PRINTtriangles */
-      qh printoutvar= qh num_points+qh_setsize(qh other_points); /* first centrum */
-      if (qh DELAUNAY)
-        num--;  /* drop last dimension */
-      qh_fprintf(fp, 9061, "%d\n%d %d %d\n", num, qh printoutvar
-        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
-    }
-    FORALLpoints
-      qh_printpointid(qh fout, NULL, num, point, qh_IDunknown);
-    FOREACHpoint_(qh other_points)
-      qh_printpointid(qh fout, NULL, num, point, qh_IDunknown);
-    if (format == qh_PRINTtriangles && qh hull_dim > 2) {
-      FORALLfacets {
-        if (!facet->simplicial && facet->visitid)
-          qh_printcenter(qh fout, format, NULL, facet);
-      }
-    }
-    break;
-  case qh_PRINTpointnearest:
-    qh_fprintf(fp, 9062, "%d\n", numcoplanars);
-    break;
-  case qh_PRINTpoints:
-    if (!qh VORONOI)
-      goto LABELnoformat;
-    if (qh CDDoutput)
-      qh_fprintf(fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
-           qh qhull_command, numfacets, qh hull_dim);
-    else
-      qh_fprintf(fp, 9064, "%d\n%d\n", qh hull_dim-1, numfacets);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(fp, 9065, "%d\n", numfacets);
-    break;
-  case qh_PRINTsummary:
-  default:
-  LABELnoformat:
-    qh_fprintf(qh ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
-         qh hull_dim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-} /* printbegin */
-
-/*---------------------------------
-
-  qh_printcenter( fp, string, facet )
-    print facet->center as centrum or Voronoi center
-    string may be NULL.  Don't include '%' codes.
-    nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum
-    if upper envelope of Delaunay triangulation and point at-infinity
-      prints qh_INFINITE instead;
-
-  notes:
-    defines facet->center if needed
-    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
-    Same as QhullFacet::printCenter
-*/
-void qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
-  int k, num;
-
-  if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)
-    return;
-  if (string)
-    qh_fprintf(fp, 9066, string);
-  if (qh CENTERtype == qh_ASvoronoi) {
-    num= qh hull_dim-1;
-    if (!facet->normal || !facet->upperdelaunay || !qh ATinfinity) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(facet->vertices);
-      for (k=0; k < num; k++)
-        qh_fprintf(fp, 9067, qh_REAL_1, facet->center[k]);
-    }else {
-      for (k=0; k < num; k++)
-        qh_fprintf(fp, 9068, qh_REAL_1, qh_INFINITE);
-    }
-  }else /* qh.CENTERtype == qh_AScentrum */ {
-    num= qh hull_dim;
-    if (format == qh_PRINTtriangles && qh DELAUNAY)
-      num--;
-    if (!facet->center)
-      facet->center= qh_getcentrum(facet);
-    for (k=0; k < num; k++)
-      qh_fprintf(fp, 9069, qh_REAL_1, facet->center[k]);
-  }
-  if (format == qh_PRINTgeom && num == 2)
-    qh_fprintf(fp, 9070, " 0\n");
-  else
-    qh_fprintf(fp, 9071, "\n");
-} /* printcenter */
-
-/*---------------------------------
-
-  qh_printcentrum( fp, facet, radius )
-    print centrum for a facet in OOGL format
-    radius defines size of centrum
-    2-d or 3-d only
-
-  returns:
-    defines facet->center if needed
-*/
-void qh_printcentrum(FILE *fp, facetT *facet, realT radius) {
-  pointT *centrum, *projpt;
-  boolT tempcentrum= False;
-  realT xaxis[4], yaxis[4], normal[4], dist;
-  realT green[3]={0, 1, 0};
-  vertexT *apex;
-  int k;
-
-  if (qh CENTERtype == qh_AScentrum) {
-    if (!facet->center)
-      facet->center= qh_getcentrum(facet);
-    centrum= facet->center;
-  }else {
-    centrum= qh_getcentrum(facet);
-    tempcentrum= True;
-  }
-  qh_fprintf(fp, 9072, "{appearance {-normal -edge normscale 0} ");
-  if (qh firstcentrum) {
-    qh firstcentrum= False;
-    qh_fprintf(fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
--0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3  0.3 0.0001     0 0 1 1\n\
--0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
-  }else
-    qh_fprintf(fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
-  apex= SETfirstt_(facet->vertices, vertexT);
-  qh_distplane(apex->point, facet, &dist);
-  projpt= qh_projectpoint(apex->point, facet, dist);
-  for (k=qh hull_dim; k--; ) {
-    xaxis[k]= projpt[k] - centrum[k];
-    normal[k]= facet->normal[k];
-  }
-  if (qh hull_dim == 2) {
-    xaxis[2]= 0;
-    normal[2]= 0;
-  }else if (qh hull_dim == 4) {
-    qh_projectdim3(xaxis, xaxis);
-    qh_projectdim3(normal, normal);
-    qh_normalize2(normal, qh PRINTdim, True, NULL, NULL);
-  }
-  qh_crossproduct(3, xaxis, normal, yaxis);
-  qh_fprintf(fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
-  qh_fprintf(fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
-  qh_fprintf(fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
-  qh_printpoint3(fp, centrum);
-  qh_fprintf(fp, 9078, "1 }}}\n");
-  qh_memfree(projpt, qh normal_size);
-  qh_printpointvect(fp, centrum, facet->normal, NULL, radius, green);
-  if (tempcentrum)
-    qh_memfree(centrum, qh normal_size);
-} /* printcentrum */
-
-/*---------------------------------
-
-  qh_printend( fp, format )
-    prints trailer for all output formats
-
-  see:
-    qh_printbegin() and qh_printafacet()
-
-*/
-void qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int num;
-  facetT *facet, **facetp;
-
-  if (!qh printoutnum)
-    qh_fprintf(qh ferr, 7055, "qhull warning: no facets printed\n");
-  switch (format) {
-  case qh_PRINTgeom:
-    if (qh hull_dim == 4 && qh DROPdim < 0  && !qh PRINTnoplanes) {
-      qh visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)
-        qh_printend4geom(fp, facet,&num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(fp, facet, &num, printall);
-      if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
-        qh_fprintf(qh ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh ridgeoutnum, qh printoutvar, num);
-        qh_errexit(qh_ERRqhull, NULL, NULL);
-      }
-    }else
-      qh_fprintf(fp, 9079, "}\n");
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh CDDoutput)
-      qh_fprintf(fp, 9080, "end\n");
-    break;
-  case qh_PRINTmaple:
-    qh_fprintf(fp, 9081, "));\n");
-    break;
-  case qh_PRINTmathematica:
-    qh_fprintf(fp, 9082, "}\n");
-    break;
-  case qh_PRINTpoints:
-    if (qh CDDoutput)
-      qh_fprintf(fp, 9083, "end\n");
-    break;
-  default:
-    break;
-  }
-} /* printend */
-
-/*---------------------------------
-
-  qh_printend4geom( fp, facet, numridges, printall )
-    helper function for qh_printbegin/printend
-
-  returns:
-    number of printed ridges
-
-  notes:
-    just counts printed ridges if fp=NULL
-    uses facet->visitid
-    must agree with qh_printfacet4geom...
-
-  design:
-    computes color for facet from its normal
-    prints each ridge of facet
-*/
-void qh_printend4geom(FILE *fp, facetT *facet, int *nump, boolT printall) {
-  realT color[3];
-  int i, num= *nump;
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-
-  if (!printall && qh_skipfacet(facet))
-    return;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  if (!facet->normal)
-    return;
-  if (fp) {
-    for (i=0; i < 3; i++) {
-      color[i]= (facet->normal[i]+1.0)/2.0;
-      maximize_(color[i], -1.0);
-      minimize_(color[i], +1.0);
-    }
-  }
-  facet->visitid= qh visit_id;
-  if (facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        if (fp)
-          qh_fprintf(fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }else {
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh visit_id) {
-        if (fp)
-          qh_fprintf(fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 ridge->id, facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }
-  *nump= num;
-} /* printend4geom */
-
-/*---------------------------------
-
-  qh_printextremes( fp, facetlist, facets, printall )
-    print extreme points for convex hulls or halfspace intersections
-
-  notes:
-    #points, followed by ids, one per line
-
-    sorted by id
-    same order as qh_printpoints_out if no coplanar/interior points
-*/
-void qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices, *points;
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int id;
-  int numpoints=0, point_i, point_n;
-  int allpoints= qh num_points + qh_setsize(qh other_points);
-
-  points= qh_settemp(allpoints);
-  qh_setzero(points, 0, allpoints);
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(vertex->point);
-    if (id >= 0) {
-      SETelem_(points, id)= vertex->point;
-      numpoints++;
-    }
-  }
-  qh_settempfree(&vertices);
-  qh_fprintf(fp, 9086, "%d\n", numpoints);
-  FOREACHpoint_i_(points) {
-    if (point)
-      qh_fprintf(fp, 9087, "%d\n", point_i);
-  }
-  qh_settempfree(&points);
-} /* printextremes */
-
-/*---------------------------------
-
-  qh_printextremes_2d( fp, facetlist, facets, printall )
-    prints point ids for facets in qh_ORIENTclock order
-
-  notes:
-    #points, followed by ids, one per line
-    if facetlist/facets are disjoint than the output includes skips
-    errors if facets form a loop
-    does not print coplanar points
-*/
-void qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
-  setT *vertices;
-  facetT *facet, *startfacet, *nextfacet;
-  vertexT *vertexA, *vertexB;
-
-  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  qh_fprintf(fp, 9088, "%d\n", qh_setsize(vertices));
-  qh_settempfree(&vertices);
-  if (!numfacets)
-    return;
-  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
-  qh vertex_visit++;
-  qh visit_id++;
-  do {
-    if (facet->toporient ^ qh_ORIENTclock) {
-      vertexA= SETfirstt_(facet->vertices, vertexT);
-      vertexB= SETsecondt_(facet->vertices, vertexT);
-      nextfacet= SETfirstt_(facet->neighbors, facetT);
-    }else {
-      vertexA= SETsecondt_(facet->vertices, vertexT);
-      vertexB= SETfirstt_(facet->vertices, vertexT);
-      nextfacet= SETsecondt_(facet->neighbors, facetT);
-    }
-    if (facet->visitid == qh visit_id) {
-      qh_fprintf(qh ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
-                 facet->id, nextfacet->id);
-      qh_errexit2(qh_ERRqhull, facet, nextfacet);
-    }
-    if (facet->visitid) {
-      if (vertexA->visitid != qh vertex_visit) {
-        vertexA->visitid= qh vertex_visit;
-        qh_fprintf(fp, 9089, "%d\n", qh_pointid(vertexA->point));
-      }
-      if (vertexB->visitid != qh vertex_visit) {
-        vertexB->visitid= qh vertex_visit;
-        qh_fprintf(fp, 9090, "%d\n", qh_pointid(vertexB->point));
-      }
-    }
-    facet->visitid= qh visit_id;
-    facet= nextfacet;
-  }while (facet && facet != startfacet);
-} /* printextremes_2d */
-
-/*---------------------------------
-
-  qh_printextremes_d( fp, facetlist, facets, printall )
-    print extreme points of input sites for Delaunay triangulations
-
-  notes:
-    #points, followed by ids, one per line
-
-    unordered
-*/
-void qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  vertexT *vertex, **vertexp;
-  boolT upperseen, lowerseen;
-  facetT *neighbor, **neighborp;
-  int numpoints=0;
-
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  qh_vertexneighbors();
-  FOREACHvertex_(vertices) {
-    upperseen= lowerseen= False;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay)
-        upperseen= True;
-      else
-        lowerseen= True;
-    }
-    if (upperseen && lowerseen) {
-      vertex->seen= True;
-      numpoints++;
-    }else
-      vertex->seen= False;
-  }
-  qh_fprintf(fp, 9091, "%d\n", numpoints);
-  FOREACHvertex_(vertices) {
-    if (vertex->seen)
-      qh_fprintf(fp, 9092, "%d\n", qh_pointid(vertex->point));
-  }
-  qh_settempfree(&vertices);
-} /* printextremes_d */
-
-/*---------------------------------
-
-  qh_printfacet( fp, facet )
-    prints all fields of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-*/
-void qh_printfacet(FILE *fp, facetT *facet) {
-
-  qh_printfacetheader(fp, facet);
-  if (facet->ridges)
-    qh_printfacetridges(fp, facet);
-} /* printfacet */
-
-
-/*---------------------------------
-
-  qh_printfacet2geom( fp, facet, color )
-    print facet as part of a 2-d VECT for Geomview
-
-    notes:
-      assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-      mindist is calculated within io.c.  maxoutside is calculated elsewhere
-      so a DISTround error may have occurred.
-*/
-void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
-  pointT *point0, *point1;
-  realT mindist, innerplane, outerplane;
-  int k;
-
-  qh_facet2point(facet, &point0, &point1, &mindist);
-  qh_geomplanes(facet, &outerplane, &innerplane);
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet2geom_points(fp, point0, point1, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet2geom_points(fp, point0, point1, facet, innerplane, color);
-  }
-  qh_memfree(point1, qh normal_size);
-  qh_memfree(point0, qh normal_size);
-} /* printfacet2geom */
-
-/*---------------------------------
-
-  qh_printfacet2geom_points( fp, point1, point2, facet, offset, color )
-    prints a 2-d facet as a VECT with 2 points at some offset.
-    The points are on the facet's plane.
-*/
-void qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
-                               facetT *facet, realT offset, realT color[3]) {
-  pointT *p1= point1, *p2= point2;
-
-  qh_fprintf(fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
-  if (offset != 0.0) {
-    p1= qh_projectpoint(p1, facet, -offset);
-    p2= qh_projectpoint(p2, facet, -offset);
-  }
-  qh_fprintf(fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
-           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
-  if (offset != 0.0) {
-    qh_memfree(p1, qh normal_size);
-    qh_memfree(p2, qh normal_size);
-  }
-  qh_fprintf(fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printfacet2geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet2math( fp, facet, format, notfirst )
-    print 2-d Maple or Mathematica output for a facet
-    may be non-simplicial
-
-  notes:
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet3math
-*/
-void qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  pointT *point0, *point1;
-  realT mindist;
-  const char *pointfmt;
-
-  qh_facet2point(facet, &point0, &point1, &mindist);
-  if (notfirst)
-    qh_fprintf(fp, 9096, ",");
-  if (format == qh_PRINTmaple)
-    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
-  else
-    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
-  qh_fprintf(fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
-  qh_memfree(point1, qh normal_size);
-  qh_memfree(point0, qh normal_size);
-} /* printfacet2math */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_nonsimplicial( fp, facet, color )
-    print Geomview OFF for a 3-d nonsimplicial facet.
-    if DOintersections, prints ridges to unvisited neighbors(qh visit_id)
-
-  notes
-    uses facet->visitid for intersections and ridges
-*/
-void qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
-  ridgeT *ridge, **ridgep;
-  setT *projectedpoints, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  pointT *projpt, *point, **pointp;
-  facetT *neighbor;
-  realT dist, outerplane, innerplane;
-  int cntvertices, k;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-
-  qh_geomplanes(facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(facet); /* oriented */
-  cntvertices= qh_setsize(vertices);
-  projectedpoints= qh_settemp(cntvertices);
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(vertex->point, facet, &dist);
-    projpt= qh_projectpoint(vertex->point, facet, dist);
-    qh_setappend(&projectedpoints, projpt);
-  }
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet3geom_points(fp, projectedpoints, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(fp, projectedpoints, facet, innerplane, color);
-  }
-  FOREACHpoint_(projectedpoints)
-    qh_memfree(point, qh normal_size);
-  qh_settempfree(&projectedpoints);
-  qh_settempfree(&vertices);
-  if ((qh DOintersections || qh PRINTridges)
-  && (!facet->visible || !qh NEWfacets)) {
-    facet->visitid= qh visit_id;
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh visit_id) {
-        if (qh DOintersections)
-          qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, black);
-        if (qh PRINTridges) {
-          vertexA= SETfirstt_(ridge->vertices, vertexT);
-          vertexB= SETsecondt_(ridge->vertices, vertexT);
-          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
-        }
-      }
-    }
-  }
-} /* printfacet3geom_nonsimplicial */
-
-/*---------------------------------
-
-  qh_printfacet3geom_points( fp, points, facet, offset )
-    prints a 3-d facet as OFF Geomview object.
-    offset is relative to the facet's hyperplane
-    Facet is determined as a list of points
-*/
-void qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
-  int k, n= qh_setsize(points), i;
-  pointT *point, **pointp;
-  setT *printpoints;
-
-  qh_fprintf(fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
-  if (offset != 0.0) {
-    printpoints= qh_settemp(n);
-    FOREACHpoint_(points)
-      qh_setappend(&printpoints, qh_projectpoint(point, facet, -offset));
-  }else
-    printpoints= points;
-  FOREACHpoint_(printpoints) {
-    for (k=0; k < qh hull_dim; k++) {
-      if (k == qh DROPdim)
-        qh_fprintf(fp, 9099, "0 ");
-      else
-        qh_fprintf(fp, 9100, "%8.4g ", point[k]);
-    }
-    if (printpoints != points)
-      qh_memfree(point, qh normal_size);
-    qh_fprintf(fp, 9101, "\n");
-  }
-  if (printpoints != points)
-    qh_settempfree(&printpoints);
-  qh_fprintf(fp, 9102, "%d ", n);
-  for (i=0; i < n; i++)
-    qh_fprintf(fp, 9103, "%d ", i);
-  qh_fprintf(fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
-} /* printfacet3geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_simplicial(  )
-    print Geomview OFF for a 3-d simplicial facet.
-
-  notes:
-    may flip color
-    uses facet->visitid for intersections and ridges
-
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-    innerplane may be off by qh DISTround.  Maxoutside is calculated elsewhere
-    so a DISTround error may have occurred.
-*/
-void qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
-  setT *points, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  facetT *neighbor, **neighborp;
-  realT outerplane, innerplane;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-  int k;
-
-  qh_geomplanes(facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(facet);
-  points= qh_settemp(qh TEMPsize);
-  FOREACHvertex_(vertices)
-    qh_setappend(&points, vertex->point);
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet3geom_points(fp, points, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-              outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(fp, points, facet, innerplane, color);
-  }
-  qh_settempfree(&points);
-  qh_settempfree(&vertices);
-  if ((qh DOintersections || qh PRINTridges)
-  && (!facet->visible || !qh NEWfacets)) {
-    facet->visitid= qh visit_id;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-        if (qh DOintersections)
-           qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
-        if (qh PRINTridges) {
-          vertexA= SETfirstt_(vertices, vertexT);
-          vertexB= SETsecondt_(vertices, vertexT);
-          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
-        }
-        qh_setfree(&vertices);
-      }
-    }
-  }
-} /* printfacet3geom_simplicial */
-
-/*---------------------------------
-
-  qh_printfacet3math( fp, facet, notfirst )
-    print 3-d Maple or Mathematica output for a facet
-
-  notes:
-    may be non-simplicial
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet2math
-*/
-void qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  vertexT *vertex, **vertexp;
-  setT *points, *vertices;
-  pointT *point, **pointp;
-  boolT firstpoint= True;
-  realT dist;
-  const char *pointfmt, *endfmt;
-
-  if (notfirst)
-    qh_fprintf(fp, 9105, ",\n");
-  vertices= qh_facet3vertex(facet);
-  points= qh_settemp(qh_setsize(vertices));
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(vertex->point, facet, &dist);
-    point= qh_projectpoint(vertex->point, facet, dist);
-    qh_setappend(&points, point);
-  }
-  if (format == qh_PRINTmaple) {
-    qh_fprintf(fp, 9106, "[");
-    pointfmt= "[%16.8f, %16.8f, %16.8f]";
-    endfmt= "]";
-  }else {
-    qh_fprintf(fp, 9107, "Polygon[{");
-    pointfmt= "{%16.8f, %16.8f, %16.8f}";
-    endfmt= "}]";
-  }
-  FOREACHpoint_(points) {
-    if (firstpoint)
-      firstpoint= False;
-    else
-      qh_fprintf(fp, 9108, ",\n");
-    qh_fprintf(fp, 9109, pointfmt, point[0], point[1], point[2]);
-  }
-  FOREACHpoint_(points)
-    qh_memfree(point, qh normal_size);
-  qh_settempfree(&points);
-  qh_settempfree(&vertices);
-  qh_fprintf(fp, 9110, "%s", endfmt);
-} /* printfacet3math */
-
-
-/*---------------------------------
-
-  qh_printfacet3vertex( fp, facet, format )
-    print vertices in a 3-d facet as point ids
-
-  notes:
-    prints number of vertices first if format == qh_PRINToff
-    the facet may be non-simplicial
-*/
-void qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facet3vertex(facet);
-  if (format == qh_PRINToff)
-    qh_fprintf(fp, 9111, "%d ", qh_setsize(vertices));
-  FOREACHvertex_(vertices)
-    qh_fprintf(fp, 9112, "%d ", qh_pointid(vertex->point));
-  qh_fprintf(fp, 9113, "\n");
-  qh_settempfree(&vertices);
-} /* printfacet3vertex */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_nonsimplicial(  )
-    print Geomview 4OFF file for a 4d nonsimplicial facet
-    prints all ridges to unvisited neighbors (qh.visit_id)
-    if qh.DROPdim
-      prints in OFF format
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
-  facetT *neighbor;
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  pointT *point;
-  int k;
-  realT dist;
-
-  facet->visitid= qh visit_id;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh visit_id)
-      continue;
-    if (qh PRINTtransparent && !neighbor->good)
-      continue;
-    if (qh DOintersections)
-      qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);
-    else {
-      if (qh DROPdim >= 0)
-        qh_fprintf(fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
-      else {
-        qh printoutvar++;
-        qh_fprintf(fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
-      }
-      FOREACHvertex_(ridge->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(vertex->point,facet, &dist);
-        point=qh_projectpoint(vertex->point,facet, dist);
-        for (k=0; k < qh hull_dim; k++) {
-          if (k != qh DROPdim)
-            qh_fprintf(fp, 9116, "%8.4g ", point[k]);
-        }
-        qh_fprintf(fp, 9117, "\n");
-        qh_memfree(point, qh normal_size);
-      }
-      if (qh DROPdim >= 0)
-        qh_fprintf(fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-  }
-} /* printfacet4geom_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_simplicial( fp, facet, color )
-    print Geomview 4OFF file for a 4d simplicial facet
-    prints triangles for unvisited neighbors (qh.visit_id)
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
-  setT *vertices;
-  facetT *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int k;
-
-  facet->visitid= qh visit_id;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid == qh visit_id)
-      continue;
-    if (qh PRINTtransparent && !neighbor->good)
-      continue;
-    vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-    if (qh DOintersections)
-      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
-    else {
-      if (qh DROPdim >= 0)
-        qh_fprintf(fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
-                facet->id, neighbor->id);
-      else {
-        qh printoutvar++;
-        qh_fprintf(fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
-      }
-      FOREACHvertex_(vertices) {
-        for (k=0; k < qh hull_dim; k++) {
-          if (k != qh DROPdim)
-            qh_fprintf(fp, 9121, "%8.4g ", vertex->point[k]);
-        }
-        qh_fprintf(fp, 9122, "\n");
-      }
-      if (qh DROPdim >= 0)
-        qh_fprintf(fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-    qh_setfree(&vertices);
-  }
-} /* printfacet4geom_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
-    print vertices for an N-d non-simplicial facet
-    triangulates each ridge to the id
-*/
-void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->visible && qh NEWfacets)
-    return;
-  FOREACHridge_(facet->ridges) {
-    if (format == qh_PRINTtriangles)
-      qh_fprintf(fp, 9124, "%d ", qh hull_dim);
-    qh_fprintf(fp, 9125, "%d ", id);
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      FOREACHvertex_(ridge->vertices)
-        qh_fprintf(fp, 9126, "%d ", qh_pointid(vertex->point));
-    }else {
-      FOREACHvertexreverse12_(ridge->vertices)
-        qh_fprintf(fp, 9127, "%d ", qh_pointid(vertex->point));
-    }
-    qh_fprintf(fp, 9128, "\n");
-  }
-} /* printfacetNvertex_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_simplicial( fp, facet, format )
-    print vertices for an N-d simplicial facet
-    prints vertices for non-simplicial facets
-      2-d facets (orientation preserved by qh_mergefacet2d)
-      PRINToff ('o') for 4-d and higher
-*/
-void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-
-  if (format == qh_PRINToff || format == qh_PRINTtriangles)
-    qh_fprintf(fp, 9129, "%d ", qh_setsize(facet->vertices));
-  if ((facet->toporient ^ qh_ORIENTclock)
-  || (qh hull_dim > 2 && !facet->simplicial)) {
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(fp, 9130, "%d ", qh_pointid(vertex->point));
-  }else {
-    FOREACHvertexreverse12_(facet->vertices)
-      qh_fprintf(fp, 9131, "%d ", qh_pointid(vertex->point));
-  }
-  qh_fprintf(fp, 9132, "\n");
-} /* printfacetNvertex_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetheader( fp, facet )
-    prints header fields of a facet to fp
-
-  notes:
-    for 'f' output and debugging
-    Same as QhullFacet::printHeader()
-*/
-void qh_printfacetheader(FILE *fp, facetT *facet) {
-  pointT *point, **pointp, *furthest;
-  facetT *neighbor, **neighborp;
-  realT dist;
-
-  if (facet == qh_MERGEridge) {
-    qh_fprintf(fp, 9133, " MERGEridge\n");
-    return;
-  }else if (facet == qh_DUPLICATEridge) {
-    qh_fprintf(fp, 9134, " DUPLICATEridge\n");
-    return;
-  }else if (!facet) {
-    qh_fprintf(fp, 9135, " NULLfacet\n");
-    return;
-  }
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  qh_fprintf(fp, 9136, "- f%d\n", facet->id);
-  qh_fprintf(fp, 9137, "    - flags:");
-  if (facet->toporient)
-    qh_fprintf(fp, 9138, " top");
-  else
-    qh_fprintf(fp, 9139, " bottom");
-  if (facet->simplicial)
-    qh_fprintf(fp, 9140, " simplicial");
-  if (facet->tricoplanar)
-    qh_fprintf(fp, 9141, " tricoplanar");
-  if (facet->upperdelaunay)
-    qh_fprintf(fp, 9142, " upperDelaunay");
-  if (facet->visible)
-    qh_fprintf(fp, 9143, " visible");
-  if (facet->newfacet)
-    qh_fprintf(fp, 9144, " new");
-  if (facet->tested)
-    qh_fprintf(fp, 9145, " tested");
-  if (!facet->good)
-    qh_fprintf(fp, 9146, " notG");
-  if (facet->seen)
-    qh_fprintf(fp, 9147, " seen");
-  if (facet->coplanar)
-    qh_fprintf(fp, 9148, " coplanar");
-  if (facet->mergehorizon)
-    qh_fprintf(fp, 9149, " mergehorizon");
-  if (facet->keepcentrum)
-    qh_fprintf(fp, 9150, " keepcentrum");
-  if (facet->dupridge)
-    qh_fprintf(fp, 9151, " dupridge");
-  if (facet->mergeridge && !facet->mergeridge2)
-    qh_fprintf(fp, 9152, " mergeridge1");
-  if (facet->mergeridge2)
-    qh_fprintf(fp, 9153, " mergeridge2");
-  if (facet->newmerge)
-    qh_fprintf(fp, 9154, " newmerge");
-  if (facet->flipped)
-    qh_fprintf(fp, 9155, " flipped");
-  if (facet->notfurthest)
-    qh_fprintf(fp, 9156, " notfurthest");
-  if (facet->degenerate)
-    qh_fprintf(fp, 9157, " degenerate");
-  if (facet->redundant)
-    qh_fprintf(fp, 9158, " redundant");
-  qh_fprintf(fp, 9159, "\n");
-  if (facet->isarea)
-    qh_fprintf(fp, 9160, "    - area: %2.2g\n", facet->f.area);
-  else if (qh NEWfacets && facet->visible && facet->f.replace)
-    qh_fprintf(fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
-  else if (facet->newfacet) {
-    if (facet->f.samecycle && facet->f.samecycle != facet)
-      qh_fprintf(fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
-  }else if (facet->tricoplanar /* !isarea */) {
-    if (facet->f.triowner)
-      qh_fprintf(fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
-  }else if (facet->f.newcycle)
-    qh_fprintf(fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
-  if (facet->nummerge)
-    qh_fprintf(fp, 9165, "    - merges: %d\n", facet->nummerge);
-  qh_printpointid(fp, "    - normal: ", qh hull_dim, facet->normal, qh_IDunknown);
-  qh_fprintf(fp, 9166, "    - offset: %10.7g\n", facet->offset);
-  if (qh CENTERtype == qh_ASvoronoi || facet->center)
-    qh_printcenter(fp, qh_PRINTfacets, "    - center: ", facet);
-#if qh_MAXoutside
-  if (facet->maxoutside > qh DISTround)
-    qh_fprintf(fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
-#endif
-  if (!SETempty_(facet->outsideset)) {
-    furthest= (pointT*)qh_setlast(facet->outsideset);
-    if (qh_setsize(facet->outsideset) < 6) {
-      qh_fprintf(fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(furthest));
-      FOREACHpoint_(facet->outsideset)
-        qh_printpoint(fp, "     ", point);
-    }else if (qh_setsize(facet->outsideset) < 21) {
-      qh_printpoints(fp, "    - outside set:", facet->outsideset);
-    }else {
-      qh_fprintf(fp, 9169, "    - outside set:  %d points.", qh_setsize(facet->outsideset));
-      qh_printpoint(fp, "  Furthest", furthest);
-    }
-#if !qh_COMPUTEfurthest
-    qh_fprintf(fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
-#endif
-  }
-  if (!SETempty_(facet->coplanarset)) {
-    furthest= (pointT*)qh_setlast(facet->coplanarset);
-    if (qh_setsize(facet->coplanarset) < 6) {
-      qh_fprintf(fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(furthest));
-      FOREACHpoint_(facet->coplanarset)
-        qh_printpoint(fp, "     ", point);
-    }else if (qh_setsize(facet->coplanarset) < 21) {
-      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);
-    }else {
-      qh_fprintf(fp, 9172, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));
-      qh_printpoint(fp, "  Furthest", furthest);
-    }
-    zinc_(Zdistio);
-    qh_distplane(furthest, facet, &dist);
-    qh_fprintf(fp, 9173, "      furthest distance= %2.2g\n", dist);
-  }
-  qh_printvertices(fp, "    - vertices:", facet->vertices);
-  qh_fprintf(fp, 9174, "    - neighboring facets:");
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      qh_fprintf(fp, 9175, " MERGE");
-    else if (neighbor == qh_DUPLICATEridge)
-      qh_fprintf(fp, 9176, " DUP");
-    else
-      qh_fprintf(fp, 9177, " f%d", neighbor->id);
-  }
-  qh_fprintf(fp, 9178, "\n");
-  qh RANDOMdist= qh old_randomdist;
-} /* printfacetheader */
-
-
-/*---------------------------------
-
-  qh_printfacetridges( fp, facet )
-    prints ridges of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-    assumes the ridges exist
-    for 'f' output
-    same as QhullFacet::printRidges
-*/
-void qh_printfacetridges(FILE *fp, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int numridges= 0;
-
-
-  if (facet->visible && qh NEWfacets) {
-    qh_fprintf(fp, 9179, "    - ridges(ids may be garbage):");
-    FOREACHridge_(facet->ridges)
-      qh_fprintf(fp, 9180, " r%d", ridge->id);
-    qh_fprintf(fp, 9181, "\n");
-  }else {
-    qh_fprintf(fp, 9182, "    - ridges:\n");
-    FOREACHridge_(facet->ridges)
-      ridge->seen= False;
-    if (qh hull_dim == 3) {
-      ridge= SETfirstt_(facet->ridges, ridgeT);
-      while (ridge && !ridge->seen) {
-        ridge->seen= True;
-        qh_printridge(fp, ridge);
-        numridges++;
-        ridge= qh_nextridge3d(ridge, facet, NULL);
-        }
-    }else {
-      FOREACHneighbor_(facet) {
-        FOREACHridge_(facet->ridges) {
-          if (otherfacet_(ridge,facet) == neighbor) {
-            ridge->seen= True;
-            qh_printridge(fp, ridge);
-            numridges++;
-          }
-        }
-      }
-    }
-    if (numridges != qh_setsize(facet->ridges)) {
-      qh_fprintf(fp, 9183, "     - all ridges:");
-      FOREACHridge_(facet->ridges)
-        qh_fprintf(fp, 9184, " r%d", ridge->id);
-        qh_fprintf(fp, 9185, "\n");
-    }
-    FOREACHridge_(facet->ridges) {
-      if (!ridge->seen)
-        qh_printridge(fp, ridge);
-    }
-  }
-} /* printfacetridges */
-
-/*---------------------------------
-
-  qh_printfacets( fp, format, facetlist, facets, printall )
-    prints facetlist and/or facet set in output format
-
-  notes:
-    also used for specialized formats ('FO' and summary)
-    turns off 'Rn' option since want actual numbers
-*/
-void qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  facetT *facet, **facetp;
-  setT *vertices;
-  coordT *center;
-  realT outerplane, innerplane;
-
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  if (qh CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
-    qh_fprintf(qh ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
-  if (format == qh_PRINTnone)
-    ; /* print nothing */
-  else if (format == qh_PRINTaverage) {
-    vertices= qh_facetvertices(facetlist, facets, printall);
-    center= qh_getcenter(vertices);
-    qh_fprintf(fp, 9186, "%d 1\n", qh hull_dim);
-    qh_printpointid(fp, NULL, qh hull_dim, center, qh_IDunknown);
-    qh_memfree(center, qh normal_size);
-    qh_settempfree(&vertices);
-  }else if (format == qh_PRINTextremes) {
-    if (qh DELAUNAY)
-      qh_printextremes_d(fp, facetlist, facets, printall);
-    else if (qh hull_dim == 2)
-      qh_printextremes_2d(fp, facetlist, facets, printall);
-    else
-      qh_printextremes(fp, facetlist, facets, printall);
-  }else if (format == qh_PRINToptions)
-    qh_fprintf(fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
-  else if (format == qh_PRINTpoints && !qh VORONOI)
-    qh_printpoints_out(fp, facetlist, facets, printall);
-  else if (format == qh_PRINTqhull)
-    qh_fprintf(fp, 9188, "%s | %s\n", qh rbox_command, qh qhull_command);
-  else if (format == qh_PRINTsize) {
-    qh_fprintf(fp, 9189, "0\n2 ");
-    qh_fprintf(fp, 9190, qh_REAL_1, qh totarea);
-    qh_fprintf(fp, 9191, qh_REAL_1, qh totvol);
-    qh_fprintf(fp, 9192, "\n");
-  }else if (format == qh_PRINTsummary) {
-    qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-    vertices= qh_facetvertices(facetlist, facets, printall);
-    qh_fprintf(fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
-                qh num_points + qh_setsize(qh other_points),
-                qh num_vertices, qh num_facets - qh num_visible,
-                qh_setsize(vertices), numfacets, numcoplanars,
-                numfacets - numsimplicial, zzval_(Zdelvertextot),
-                numtricoplanars);
-    qh_settempfree(&vertices);
-    qh_outerinner(NULL, &outerplane, &innerplane);
-    qh_fprintf(fp, 9194, qh_REAL_2n, outerplane, innerplane);
-  }else if (format == qh_PRINTvneighbors)
-    qh_printvneighbors(fp, facetlist, facets, printall);
-  else if (qh VORONOI && format == qh_PRINToff)
-    qh_printvoronoi(fp, format, facetlist, facets, printall);
-  else if (qh VORONOI && format == qh_PRINTgeom) {
-    qh_printbegin(fp, format, facetlist, facets, printall);
-    qh_printvoronoi(fp, format, facetlist, facets, printall);
-    qh_printend(fp, format, facetlist, facets, printall);
-  }else if (qh VORONOI
-  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
-    qh_printvdiagram(fp, format, facetlist, facets, printall);
-  else {
-    qh_printbegin(fp, format, facetlist, facets, printall);
-    FORALLfacet_(facetlist)
-      qh_printafacet(fp, format, facet, printall);
-    FOREACHfacet_(facets)
-      qh_printafacet(fp, format, facet, printall);
-    qh_printend(fp, format, facetlist, facets, printall);
-  }
-  qh RANDOMdist= qh old_randomdist;
-} /* printfacets */
-
-
-/*---------------------------------
-
-  qh_printhyperplaneintersection( fp, facet1, facet2, vertices, color )
-    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
-*/
-void qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
-                   setT *vertices, realT color[3]) {
-  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
-  vertexT *vertex, **vertexp;
-  int i, k;
-  boolT nearzero1, nearzero2;
-
-  costheta= qh_getangle(facet1->normal, facet2->normal);
-  denominator= 1 - costheta * costheta;
-  i= qh_setsize(vertices);
-  if (qh hull_dim == 3)
-    qh_fprintf(fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
-  else if (qh hull_dim == 4 && qh DROPdim >= 0)
-    qh_fprintf(fp, 9196, "OFF 3 1 1 ");
-  else
-    qh printoutvar++;
-  qh_fprintf(fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
-  mindenom= 1 / (10.0 * qh MAXabs_coord);
-  FOREACHvertex_(vertices) {
-    zadd_(Zdistio, 2);
-    qh_distplane(vertex->point, facet1, &dist1);
-    qh_distplane(vertex->point, facet2, &dist2);
-    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
-    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
-    if (nearzero1 || nearzero2)
-      s= t= 0.0;
-    for (k=qh hull_dim; k--; )
-      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
-    if (qh PRINTdim <= 3) {
-      qh_projectdim3(p, p);
-      qh_fprintf(fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
-    }else
-      qh_fprintf(fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
-    if (nearzero1+nearzero2)
-      qh_fprintf(fp, 9200, "p%d(coplanar facets)\n", qh_pointid(vertex->point));
-    else
-      qh_fprintf(fp, 9201, "projected p%d\n", qh_pointid(vertex->point));
-  }
-  if (qh hull_dim == 3)
-    qh_fprintf(fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-  else if (qh hull_dim == 4 && qh DROPdim >= 0)
-    qh_fprintf(fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printhyperplaneintersection */
-
-/*---------------------------------
-
-  qh_printline3geom( fp, pointA, pointB, color )
-    prints a line as a VECT
-    prints 0's for qh.DROPdim
-
-  notes:
-    if pointA == pointB,
-      it's a 1 point VECT
-*/
-void qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
-  int k;
-  realT pA[4], pB[4];
-
-  qh_projectdim3(pointA, pA);
-  qh_projectdim3(pointB, pB);
-  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
-      (fabs(pA[1] - pB[1]) > 1e-3) ||
-      (fabs(pA[2] - pB[2]) > 1e-3)) {
-    qh_fprintf(fp, 9204, "VECT 1 2 1 2 1\n");
-    for (k=0; k < 3; k++)
-       qh_fprintf(fp, 9205, "%8.4g ", pB[k]);
-    qh_fprintf(fp, 9206, " # p%d\n", qh_pointid(pointB));
-  }else
-    qh_fprintf(fp, 9207, "VECT 1 1 1 1 1\n");
-  for (k=0; k < 3; k++)
-    qh_fprintf(fp, 9208, "%8.4g ", pA[k]);
-  qh_fprintf(fp, 9209, " # p%d\n", qh_pointid(pointA));
-  qh_fprintf(fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
-}
-
-/*---------------------------------
-
-  qh_printneighborhood( fp, format, facetA, facetB, printall )
-    print neighborhood of one or two facets
-
-  notes:
-    calls qh_findgood_all()
-    bumps qh.visit_id
-*/
-void qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
-  facetT *neighbor, **neighborp, *facet;
-  setT *facets;
-
-  if (format == qh_PRINTnone)
-    return;
-  qh_findgood_all(qh facet_list);
-  if (facetA == facetB)
-    facetB= NULL;
-  facets= qh_settemp(2*(qh_setsize(facetA->neighbors)+1));
-  qh visit_id++;
-  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
-    if (facet->visitid != qh visit_id) {
-      facet->visitid= qh visit_id;
-      qh_setappend(&facets, facet);
-    }
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      if (printall || !qh_skipfacet(neighbor))
-        qh_setappend(&facets, neighbor);
-    }
-  }
-  qh_printfacets(fp, format, NULL, facets, printall);
-  qh_settempfree(&facets);
-} /* printneighborhood */
-
-/*---------------------------------
-
-  qh_printpoint( fp, string, point )
-  qh_printpointid( fp, string, dim, point, id )
-    prints the coordinates of a point
-
-  returns:
-    if string is defined
-      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
-
-  notes:
-    nop if point is NULL
-    Same as QhullPoint's printPoint
-*/
-void qh_printpoint(FILE *fp, const char *string, pointT *point) {
-  int id= qh_pointid( point);
-
-  qh_printpointid( fp, string, qh hull_dim, point, id);
-} /* printpoint */
-
-void qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id) {
-  int k;
-  realT r; /*bug fix*/
-
-  if (!point)
-    return;
-  if (string) {
-    qh_fprintf(fp, 9211, "%s", string);
-    if (id != qh_IDunknown && id != qh_IDnone)
-      qh_fprintf(fp, 9212, " p%d: ", id);
-  }
-  for (k=dim; k--; ) {
-    r= *point++;
-    if (string)
-      qh_fprintf(fp, 9213, " %8.4g", r);
-    else
-      qh_fprintf(fp, 9214, qh_REAL_1, r);
-  }
-  qh_fprintf(fp, 9215, "\n");
-} /* printpointid */
-
-/*---------------------------------
-
-  qh_printpoint3( fp, point )
-    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
-*/
-void qh_printpoint3(FILE *fp, pointT *point) {
-  int k;
-  realT p[4];
-
-  qh_projectdim3(point, p);
-  for (k=0; k < 3; k++)
-    qh_fprintf(fp, 9216, "%8.4g ", p[k]);
-  qh_fprintf(fp, 9217, " # p%d\n", qh_pointid(point));
-} /* printpoint3 */
-
-/*----------------------------------------
--printpoints- print pointids for a set of points starting at index
-   see geom.c
-*/
-
-/*---------------------------------
-
-  qh_printpoints_out( fp, facetlist, facets, printall )
-    prints vertices, coplanar/inside points, for facets by their point coordinates
-    allows qh.CDDoutput
-
-  notes:
-    same format as qhull input
-    if no coplanar/interior points,
-      same order as qh_printextremes
-*/
-void qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int allpoints= qh num_points + qh_setsize(qh other_points);
-  int numpoints=0, point_i, point_n;
-  setT *vertices, *points;
-  facetT *facet, **facetp;
-  pointT *point, **pointp;
-  vertexT *vertex, **vertexp;
-  int id;
-
-  points= qh_settemp(allpoints);
-  qh_setzero(points, 0, allpoints);
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(vertex->point);
-    if (id >= 0)
-      SETelem_(points, id)= vertex->point;
-  }
-  if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
-    FORALLfacet_(facetlist) {
-      if (!printall && qh_skipfacet(facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-    FOREACHfacet_(facets) {
-      if (!printall && qh_skipfacet(facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-  }
-  qh_settempfree(&vertices);
-  FOREACHpoint_i_(points) {
-    if (point)
-      numpoints++;
-  }
-  if (qh CDDoutput)
-    qh_fprintf(fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
-             qh qhull_command, numpoints, qh hull_dim + 1);
-  else
-    qh_fprintf(fp, 9219, "%d\n%d\n", qh hull_dim, numpoints);
-  FOREACHpoint_i_(points) {
-    if (point) {
-      if (qh CDDoutput)
-        qh_fprintf(fp, 9220, "1 ");
-      qh_printpoint(fp, NULL, point);
-    }
-  }
-  if (qh CDDoutput)
-    qh_fprintf(fp, 9221, "end\n");
-  qh_settempfree(&points);
-} /* printpoints_out */
-
-
-/*---------------------------------
-
-  qh_printpointvect( fp, point, normal, center, radius, color )
-    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
-*/
-void qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
-  realT diff[4], pointA[4];
-  int k;
-
-  for (k=qh hull_dim; k--; ) {
-    if (center)
-      diff[k]= point[k]-center[k];
-    else if (normal)
-      diff[k]= normal[k];
-    else
-      diff[k]= 0;
-  }
-  if (center)
-    qh_normalize2(diff, qh hull_dim, True, NULL, NULL);
-  for (k=qh hull_dim; k--; )
-    pointA[k]= point[k]+diff[k] * radius;
-  qh_printline3geom(fp, point, pointA, color);
-} /* printpointvect */
-
-/*---------------------------------
-
-  qh_printpointvect2( fp, point, normal, center, radius )
-    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
-*/
-void qh_printpointvect2(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
-  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
-
-  qh_printpointvect(fp, point, normal, center, radius, red);
-  qh_printpointvect(fp, point, normal, center, -radius, yellow);
-} /* printpointvect2 */
-
-/*---------------------------------
-
-  qh_printridge( fp, ridge )
-    prints the information in a ridge
-
-  notes:
-    for qh_printfacetridges()
-    same as operator<< [QhullRidge.cpp]
-*/
-void qh_printridge(FILE *fp, ridgeT *ridge) {
-
-  qh_fprintf(fp, 9222, "     - r%d", ridge->id);
-  if (ridge->tested)
-    qh_fprintf(fp, 9223, " tested");
-  if (ridge->nonconvex)
-    qh_fprintf(fp, 9224, " nonconvex");
-  qh_fprintf(fp, 9225, "\n");
-  qh_printvertices(fp, "           vertices:", ridge->vertices);
-  if (ridge->top && ridge->bottom)
-    qh_fprintf(fp, 9226, "           between f%d and f%d\n",
-            ridge->top->id, ridge->bottom->id);
-} /* printridge */
-
-/*---------------------------------
-
-  qh_printspheres( fp, vertices, radius )
-    prints 3-d vertices as OFF spheres
-
-  notes:
-    inflated octahedron from Stuart Levy earth/mksphere2
-*/
-void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
-  vertexT *vertex, **vertexp;
-
-  qh printoutnum++;
-  qh_fprintf(fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
-INST geom {define vsphere OFF\n\
-18 32 48\n\
-\n\
-0 0 1\n\
-1 0 0\n\
-0 1 0\n\
--1 0 0\n\
-0 -1 0\n\
-0 0 -1\n\
-0.707107 0 0.707107\n\
-0 -0.707107 0.707107\n\
-0.707107 -0.707107 0\n\
--0.707107 0 0.707107\n\
--0.707107 -0.707107 0\n\
-0 0.707107 0.707107\n\
--0.707107 0.707107 0\n\
-0.707107 0.707107 0\n\
-0.707107 0 -0.707107\n\
-0 0.707107 -0.707107\n\
--0.707107 0 -0.707107\n\
-0 -0.707107 -0.707107\n\
-\n\
-3 0 6 11\n\
-3 0 7 6 \n\
-3 0 9 7 \n\
-3 0 11 9\n\
-3 1 6 8 \n\
-3 1 8 14\n\
-3 1 13 6\n\
-3 1 14 13\n\
-3 2 11 13\n\
-3 2 12 11\n\
-3 2 13 15\n\
-3 2 15 12\n\
-3 3 9 12\n\
-3 3 10 9\n\
-3 3 12 16\n\
-3 3 16 10\n\
-3 4 7 10\n\
-3 4 8 7\n\
-3 4 10 17\n\
-3 4 17 8\n\
-3 5 14 17\n\
-3 5 15 14\n\
-3 5 16 15\n\
-3 5 17 16\n\
-3 6 13 11\n\
-3 7 8 6\n\
-3 9 10 7\n\
-3 11 12 9\n\
-3 14 8 17\n\
-3 15 13 14\n\
-3 16 12 15\n\
-3 17 10 16\n} transforms { TLIST\n");
-  FOREACHvertex_(vertices) {
-    qh_fprintf(fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
-      radius, vertex->id, radius, radius);
-    qh_printpoint3(fp, vertex->point);
-    qh_fprintf(fp, 9229, "1\n");
-  }
-  qh_fprintf(fp, 9230, "}}}\n");
-} /* printspheres */
-
-
-/*----------------------------------------------
--printsummary-
-                see libqhull.c
-*/
-
-/*---------------------------------
-
-  qh_printvdiagram( fp, format, facetlist, facets, printall )
-    print voronoi diagram
-      # of pairs of input sites
-      #indices site1 site2 vertex1 ...
-
-    sites indexed by input point id
-      point 0 is the first input point
-    vertices indexed by 'o' and 'p' order
-      vertex 0 is the 'vertex-at-infinity'
-      vertex 1 is the first Voronoi vertex
-
-  see:
-    qh_printvoronoi()
-    qh_eachvoronoi_all()
-
-  notes:
-    if all facets are upperdelaunay,
-      prints upper hull (furthest-site Voronoi diagram)
-*/
-void qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  int totcount, numcenters;
-  boolT isLower;
-  qh_RIDGE innerouter= qh_RIDGEall;
-  printvridgeT printvridge= NULL;
-
-  if (format == qh_PRINTvertices) {
-    innerouter= qh_RIDGEall;
-    printvridge= qh_printvridge;
-  }else if (format == qh_PRINTinner) {
-    innerouter= qh_RIDGEinner;
-    printvridge= qh_printvnorm;
-  }else if (format == qh_PRINTouter) {
-    innerouter= qh_RIDGEouter;
-    printvridge= qh_printvnorm;
-  }else {
-    qh_fprintf(qh ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
-  totcount= qh_printvdiagram2(NULL, NULL, vertices, innerouter, False);
-  qh_fprintf(fp, 9231, "%d\n", totcount);
-  totcount= qh_printvdiagram2(fp, printvridge, vertices, innerouter, True /* inorder*/);
-  qh_settempfree(&vertices);
-#if 0  /* for testing qh_eachvoronoi_all */
-  qh_fprintf(fp, 9232, "\n");
-  totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
-  qh_fprintf(fp, 9233, "%d\n", totcount);
-#endif
-} /* printvdiagram */
-
-/*---------------------------------
-
-  qh_printvdiagram2( fp, printvridge, vertices, innerouter, inorder )
-    visit all pairs of input sites (vertices) for selected Voronoi vertices
-    vertices may include NULLs
-
-  innerouter:
-    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
-    qh_RIDGEinner print only inner ridges
-    qh_RIDGEouter print only outer ridges
-
-  inorder:
-    print 3-d Voronoi vertices in order
-
-  assumes:
-    qh_markvoronoi marked facet->visitid for Voronoi vertices
-    all facet->seen= False
-    all facet->seen2= True
-
-  returns:
-    total number of Voronoi ridges
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers) for each ridge
-      [see qh_eachvoronoi()]
-
-  see:
-    qh_eachvoronoi_all()
-*/
-int qh_printvdiagram2(FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
-  int totcount= 0;
-  int vertex_i, vertex_n;
-  vertexT *vertex;
-
-  FORALLvertices
-    vertex->seen= False;
-  FOREACHvertex_i_(vertices) {
-    if (vertex) {
-      if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
-        continue;
-      totcount += qh_eachvoronoi(fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
-    }
-  }
-  return totcount;
-} /* printvdiagram2 */
-
-/*---------------------------------
-
-  qh_printvertex( fp, vertex )
-    prints the information in a vertex
-    Duplicated as operator<< [QhullVertex.cpp]
-*/
-void qh_printvertex(FILE *fp, vertexT *vertex) {
-  pointT *point;
-  int k, count= 0;
-  facetT *neighbor, **neighborp;
-  realT r; /*bug fix*/
-
-  if (!vertex) {
-    qh_fprintf(fp, 9234, "  NULLvertex\n");
-    return;
-  }
-  qh_fprintf(fp, 9235, "- p%d(v%d):", qh_pointid(vertex->point), vertex->id);
-  point= vertex->point;
-  if (point) {
-    for (k=qh hull_dim; k--; ) {
-      r= *point++;
-      qh_fprintf(fp, 9236, " %5.2g", r);
-    }
-  }
-  if (vertex->deleted)
-    qh_fprintf(fp, 9237, " deleted");
-  if (vertex->delridge)
-    qh_fprintf(fp, 9238, " ridgedeleted");
-  qh_fprintf(fp, 9239, "\n");
-  if (vertex->neighbors) {
-    qh_fprintf(fp, 9240, "  neighbors:");
-    FOREACHneighbor_(vertex) {
-      if (++count % 100 == 0)
-        qh_fprintf(fp, 9241, "\n     ");
-      qh_fprintf(fp, 9242, " f%d", neighbor->id);
-    }
-    qh_fprintf(fp, 9243, "\n");
-  }
-} /* printvertex */
-
-
-/*---------------------------------
-
-  qh_printvertexlist( fp, string, facetlist, facets, printall )
-    prints vertices used by a facetlist or facet set
-    tests qh_skipfacet() if !printall
-*/
-void qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
-                         setT *facets, boolT printall) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  qh_fprintf(fp, 9244, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_printvertex(fp, vertex);
-  qh_settempfree(&vertices);
-} /* printvertexlist */
-
-
-/*---------------------------------
-
-  qh_printvertices( fp, string, vertices )
-    prints vertices in a set
-    duplicated as printVertexSet [QhullVertex.cpp]
-*/
-void qh_printvertices(FILE *fp, const char* string, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  qh_fprintf(fp, 9245, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_fprintf(fp, 9246, " p%d(v%d)", qh_pointid(vertex->point), vertex->id);
-  qh_fprintf(fp, 9247, "\n");
-} /* printvertices */
-
-/*---------------------------------
-
-  qh_printvneighbors( fp, facetlist, facets, printall )
-    print vertex neighbors of vertices in facetlist and facets ('FN')
-
-  notes:
-    qh_countfacets clears facet->visitid for non-printed facets
-
-  design:
-    collect facet count and related statistics
-    if necessary, build neighbor sets for each vertex
-    collect vertices in facetlist and facets
-    build a point array for point->vertex and point->coplanar facet
-    for each point
-      list vertex neighbors or coplanar facet
-*/
-void qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
-  setT *vertices, *vertex_points, *coplanar_points;
-  int numpoints= qh num_points + qh_setsize(qh other_points);
-  vertexT *vertex, **vertexp;
-  int vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  pointT *point, **pointp;
-
-  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
-  qh_fprintf(fp, 9248, "%d\n", numpoints);
-  qh_vertexneighbors();
-  vertices= qh_facetvertices(facetlist, facets, printall);
-  vertex_points= qh_settemp(numpoints);
-  coplanar_points= qh_settemp(numpoints);
-  qh_setzero(vertex_points, 0, numpoints);
-  qh_setzero(coplanar_points, 0, numpoints);
-  FOREACHvertex_(vertices)
-    qh_point_add(vertex_points, vertex->point, vertex);
-  FORALLfacet_(facetlist) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(coplanar_points, point, facet);
-  }
-  FOREACHfacet_(facets) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(coplanar_points, point, facet);
-  }
-  FOREACHvertex_i_(vertex_points) {
-    if (vertex) {
-      numneighbors= qh_setsize(vertex->neighbors);
-      qh_fprintf(fp, 9249, "%d", numneighbors);
-      if (qh hull_dim == 3)
-        qh_order_vertexneighbors(vertex);
-      else if (qh hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex)
-        qh_fprintf(fp, 9250, " %d",
-                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
-      qh_fprintf(fp, 9251, "\n");
-    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
-      qh_fprintf(fp, 9252, "1 %d\n",
-                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
-    else
-      qh_fprintf(fp, 9253, "0\n");
-  }
-  qh_settempfree(&coplanar_points);
-  qh_settempfree(&vertex_points);
-  qh_settempfree(&vertices);
-} /* printvneighbors */
-
-/*---------------------------------
-
-  qh_printvoronoi( fp, format, facetlist, facets, printall )
-    print voronoi diagram in 'o' or 'G' format
-    for 'o' format
-      prints voronoi centers for each facet and for infinity
-      for each vertex, lists ids of printed facets or infinity
-      assumes facetlist and facets are disjoint
-    for 'G' format
-      prints an OFF object
-      adds a 0 coordinate to center
-      prints infinity but does not list in vertices
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    if 'o',
-      prints a line for each point except "at-infinity"
-    if all facets are upperdelaunay,
-      reverses lower and upper hull
-*/
-void qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  setT *vertices;
-  vertexT *vertex;
-  boolT isLower;
-  unsigned int numfacets= (unsigned int) qh num_facets;
-
-  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
-  FOREACHvertex_i_(vertices) {
-    if (vertex) {
-      numvertices++;
-      numneighbors = numinf = 0;
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-      if (numinf && !numneighbors) {
-        SETelem_(vertices, vertex_i)= NULL;
-        numvertices--;
-      }
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
-                numcenters, numvertices);
-  else
-    qh_fprintf(fp, 9255, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
-  if (format == qh_PRINTgeom) {
-    for (k=qh hull_dim-1; k--; )
-      qh_fprintf(fp, 9256, qh_REAL_1, 0.0);
-    qh_fprintf(fp, 9257, " 0 # infinity not used\n");
-  }else {
-    for (k=qh hull_dim-1; k--; )
-      qh_fprintf(fp, 9258, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(fp, 9259, "\n");
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(fp, 9260, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(fp, format, NULL, facet);
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(fp, 9261, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(fp, format, NULL, facet);
-    }
-  }
-  FOREACHvertex_i_(vertices) {
-    numneighbors= 0;
-    numinf=0;
-    if (vertex) {
-      if (qh hull_dim == 3)
-        qh_order_vertexneighbors(vertex);
-      else if (qh hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT),
-             (size_t)qh_setsize(vertex->neighbors),
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-    }
-    if (format == qh_PRINTgeom) {
-      if (vertex) {
-        qh_fprintf(fp, 9262, "%d", numneighbors);
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid && neighbor->visitid < numfacets)
-            qh_fprintf(fp, 9263, " %d", neighbor->visitid);
-        }
-        qh_fprintf(fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
-      }else
-        qh_fprintf(fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
-    }else {
-      if (numinf)
-        numneighbors++;
-      qh_fprintf(fp, 9266, "%d", numneighbors);
-      if (vertex) {
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid == 0) {
-            if (numinf) {
-              numinf= 0;
-              qh_fprintf(fp, 9267, " %d", neighbor->visitid);
-            }
-          }else if (neighbor->visitid < numfacets)
-            qh_fprintf(fp, 9268, " %d", neighbor->visitid);
-        }
-      }
-      qh_fprintf(fp, 9269, "\n");
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(fp, 9270, "}\n");
-  qh_settempfree(&vertices);
-} /* printvoronoi */
-
-/*---------------------------------
-
-  qh_printvnorm( fp, vertex, vertexA, centers, unbounded )
-    print one separating plane of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  note:
-    parameter unbounded is UNUSED by this callback
-
-  see:
-    qh_printvdiagram()
-    qh_eachvoronoi()
-*/
-void qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  pointT *normal;
-  realT offset;
-  int k;
-  QHULL_UNUSED(unbounded);
-
-  normal= qh_detvnorm(vertex, vertexA, centers, &offset);
-  qh_fprintf(fp, 9271, "%d %d %d ",
-      2+qh hull_dim, qh_pointid(vertex->point), qh_pointid(vertexA->point));
-  for (k=0; k< qh hull_dim-1; k++)
-    qh_fprintf(fp, 9272, qh_REAL_1, normal[k]);
-  qh_fprintf(fp, 9273, qh_REAL_1, offset);
-  qh_fprintf(fp, 9274, "\n");
-} /* printvnorm */
-
-/*---------------------------------
-
-  qh_printvridge( fp, vertex, vertexA, centers, unbounded )
-    print one ridge of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    the user may use a different function
-    parameter unbounded is UNUSED
-*/
-void qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  facetT *facet, **facetp;
-  QHULL_UNUSED(unbounded);
-
-  qh_fprintf(fp, 9275, "%d %d %d", qh_setsize(centers)+2,
-       qh_pointid(vertex->point), qh_pointid(vertexA->point));
-  FOREACHfacet_(centers)
-    qh_fprintf(fp, 9276, " %d", facet->visitid);
-  qh_fprintf(fp, 9277, "\n");
-} /* printvridge */
-
-/*---------------------------------
-
-  qh_projectdim3( source, destination )
-    project 2-d 3-d or 4-d point to a 3-d point
-    uses qh.DROPdim and qh.hull_dim
-    source and destination may be the same
-
-  notes:
-    allocate 4 elements to destination just in case
-*/
-void qh_projectdim3(pointT *source, pointT *destination) {
-  int i,k;
-
-  for (k=0, i=0; k < qh hull_dim; k++) {
-    if (qh hull_dim == 4) {
-      if (k != qh DROPdim)
-        destination[i++]= source[k];
-    }else if (k == qh DROPdim)
-      destination[i++]= 0;
-    else
-      destination[i++]= source[k];
-  }
-  while (i < 3)
-    destination[i++]= 0.0;
-} /* projectdim3 */
-
-/*---------------------------------
-
-  qh_readfeasible( dim, curline )
-    read feasible point from current line and qh.fin
-
-  returns:
-    number of lines read from qh.fin
-    sets qh.feasible_point with malloc'd coordinates
-
-  notes:
-    checks for qh.HALFspace
-    assumes dim > 1
-
-  see:
-    qh_setfeasible
-*/
-int qh_readfeasible(int dim, const char *curline) {
-  boolT isfirst= True;
-  int linecount= 0, tokcount= 0;
-  const char *s;
-  char *t, firstline[qh_MAXfirst+1];
-  coordT *coords, value;
-
-  if (!qh HALFspace) {
-    qh_fprintf(qh ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh feasible_string)
-    qh_fprintf(qh ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
-  if (!(qh feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
-    qh_fprintf(qh ferr, 6071, "qhull error: insufficient memory for feasible point\n");
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coords= qh feasible_point;
-  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh fin)))) {
-    if (isfirst)
-      isfirst= False;
-    else
-      linecount++;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t)
-        break;
-      s= t;
-      *(coords++)= value;
-      if (++tokcount == dim) {
-        while (isspace(*s))
-          s++;
-        qh_strtod(s, &t);
-        if (s != t) {
-          qh_fprintf(qh ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
-               s);
-          qh_errexit(qh_ERRinput, NULL, NULL);
-        }
-        return linecount;
-      }
-    }
-  }
-  qh_fprintf(qh ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
-           tokcount, dim);
-  qh_errexit(qh_ERRinput, NULL, NULL);
-  return 0;
-} /* readfeasible */
-
-/*---------------------------------
-
-  qh_readpoints( numpoints, dimension, ismalloc )
-    read points from qh.fin into qh.first_point, qh.num_points
-    qh.fin is lines of coordinates, one per vertex, first line number of points
-    if 'rbox D4',
-      gives message
-    if qh.ATinfinity,
-      adds point-at-infinity for Delaunay triangulations
-
-  returns:
-    number of points, array of point coordinates, dimension, ismalloc True
-    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
-        and clears qh.PROJECTdelaunay
-    if qh.HALFspace, reads optional feasible point, reads halfspaces,
-        converts to dual.
-
-  for feasible point in "cdd format" in 3-d:
-    3 1
-    coordinates
-    comments
-    begin
-    n 4 real/integer
-    ...
-    end
-
-  notes:
-    dimension will change in qh_initqhull_globals if qh.PROJECTinput
-    uses malloc() since qh_mem not initialized
-    FIXUP QH11012: qh_readpoints needs rewriting, too long
-*/
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc) {
-  coordT *points, *coords, *infinity= NULL;
-  realT paraboloid, maxboloid= -REALmax, value;
-  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
-  char *s= 0, *t, firstline[qh_MAXfirst+1];
-  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
-  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
-  int tokcount= 0, linecount=0, maxcount, coordcount=0;
-  boolT islong, isfirst= True, wasbegin= False;
-  boolT isdelaunay= qh DELAUNAY && !qh PROJECTinput;
-
-  if (qh CDDinput) {
-    while ((s= fgets(firstline, qh_MAXfirst, qh fin))) {
-      linecount++;
-      if (qh HALFspace && linecount == 1 && isdigit(*s)) {
-        dimfeasible= qh_strtol(s, &s);
-        while (isspace(*s))
-          s++;
-        if (qh_strtol(s, &s) == 1)
-          linecount += qh_readfeasible(dimfeasible, s);
-        else
-          dimfeasible= 0;
-      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
-        break;
-      else if (!*qh rbox_command)
-        strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
-    }
-    if (!s) {
-      qh_fprintf(qh ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-  }
-  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh fin))) {
-    linecount++;
-    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
-      wasbegin= True;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      if (!*s)
-        break;
-      if (!isdigit(*s)) {
-        if (!*qh rbox_command) {
-          strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
-          firsttext= linecount;
-        }
-        break;
-      }
-      if (!diminput)
-        diminput= qh_strtol(s, &s);
-      else {
-        numinput= qh_strtol(s, &s);
-        if (numinput == 1 && diminput >= 2 && qh HALFspace && !qh CDDinput) {
-          linecount += qh_readfeasible(diminput, s); /* checks if ok */
-          dimfeasible= diminput;
-          diminput= numinput= 0;
-        }else
-          break;
-      }
-    }
-  }
-  if (!s) {
-    qh_fprintf(qh ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (diminput > numinput) {
-    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
-    diminput= numinput;
-    numinput= tempi;
-  }
-  if (diminput < 2) {
-    qh_fprintf(qh ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
-            diminput);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (isdelaunay) {
-    qh PROJECTdelaunay= False;
-    if (qh CDDinput)
-      *dimension= diminput;
-    else
-      *dimension= diminput+1;
-    *numpoints= numinput;
-    if (qh ATinfinity)
-      (*numpoints)++;
-  }else if (qh HALFspace) {
-    *dimension= diminput - 1;
-    *numpoints= numinput;
-    if (diminput < 3) {
-      qh_fprintf(qh ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
-            diminput);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (dimfeasible) {
-      if (dimfeasible != *dimension) {
-        qh_fprintf(qh ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
-          dimfeasible, diminput);
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-    }else
-      qh_setfeasible(*dimension);
-  }else {
-    if (qh CDDinput)
-      *dimension= diminput-1;
-    else
-      *dimension= diminput;
-    *numpoints= numinput;
-  }
-  qh normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
-  if (qh HALFspace) {
-    qh half_space= coordp= (coordT*)qh_malloc(qh normal_size + sizeof(coordT));
-    if (qh CDDinput) {
-      offsetp= qh half_space;
-      normalp= offsetp + 1;
-    }else {
-      normalp= qh half_space;
-      offsetp= normalp + *dimension;
-    }
-  }
-  qh maxline= diminput * (qh_REALdigits + 5);
-  maximize_(qh maxline, 500);
-  qh line= (char*)qh_malloc((qh maxline+1) * sizeof(char));
-  *ismalloc= True;  /* use malloc since memory not setup */
-  coords= points= qh temp_malloc=  /* numinput and diminput >=2 by QH6220 */
-        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
-  if (!coords || !qh line || (qh HALFspace && !qh half_space)) {
-    qh_fprintf(qh ferr, 6076, "qhull error: insufficient memory to read %d points\n",
-            numinput);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  if (isdelaunay && qh ATinfinity) {
-    infinity= points + numinput * (*dimension);
-    for (k= (*dimension) - 1; k--; )
-      infinity[k]= 0.0;
-  }
-  maxcount= numinput * diminput;
-  paraboloid= 0.0;
-  while ((s= (isfirst ?  s : fgets(qh line, qh maxline, qh fin)))) {
-    if (!isfirst) {
-      linecount++;
-      if (*s == 'e' || *s == 'E') {
-        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
-          if (qh CDDinput )
-            break;
-          else if (wasbegin)
-            qh_fprintf(qh ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
-        }
-      }
-    }
-    islong= False;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t) {
-        if (!*qh rbox_command)
-         strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
-        if (*s && !firsttext)
-          firsttext= linecount;
-        if (!islong && !firstshort && coordcount)
-          firstshort= linecount;
-        break;
-      }
-      if (!firstpoint)
-        firstpoint= linecount;
-      s= t;
-      if (++tokcount > maxcount)
-        continue;
-      if (qh HALFspace) {
-        if (qh CDDinput)
-          *(coordp++)= -value; /* both coefficients and offset */
-        else
-          *(coordp++)= value;
-      }else {
-        *(coords++)= value;
-        if (qh CDDinput && !coordcount) {
-          if (value != 1.0) {
-            qh_fprintf(qh ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
-                   linecount);
-            qh_errexit(qh_ERRinput, NULL, NULL);
-          }
-          coords--;
-        }else if (isdelaunay) {
-          paraboloid += value * value;
-          if (qh ATinfinity) {
-            if (qh CDDinput)
-              infinity[coordcount-1] += value;
-            else
-              infinity[coordcount] += value;
-          }
-        }
-      }
-      if (++coordcount == diminput) {
-        coordcount= 0;
-        if (isdelaunay) {
-          *(coords++)= paraboloid;
-          maximize_(maxboloid, paraboloid);
-          paraboloid= 0.0;
-        }else if (qh HALFspace) {
-          if (!qh_sethalfspace(*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
-            qh_fprintf(qh ferr, 8048, "The halfspace was on line %d\n", linecount);
-            if (wasbegin)
-              qh_fprintf(qh ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
-            qh_errexit(qh_ERRinput, NULL, NULL);
-          }
-          coordp= qh half_space;
-        }
-        while (isspace(*s))
-          s++;
-        if (*s) {
-          islong= True;
-          if (!firstlong)
-            firstlong= linecount;
-        }
-      }
-    }
-    if (!islong && !firstshort && coordcount)
-      firstshort= linecount;
-    if (!isfirst && s - qh line >= qh maxline) {
-      qh_fprintf(qh ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
-              linecount, (int) (s - qh line));   /* WARN64 */
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    isfirst= False;
-  }
-  if (tokcount != maxcount) {
-    newnum= fmin_(numinput, tokcount/diminput);
-    qh_fprintf(qh ferr, 7073,"\
-qhull warning: instead of %d %d-dimensional points, input contains\n\
-%d points and %d extra coordinates.  Line %d is the first\npoint",
-       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
-    if (firsttext)
-      qh_fprintf(qh ferr, 8051, ", line %d is the first comment", firsttext);
-    if (firstshort)
-      qh_fprintf(qh ferr, 8052, ", line %d is the first short\nline", firstshort);
-    if (firstlong)
-      qh_fprintf(qh ferr, 8053, ", line %d is the first long line", firstlong);
-    qh_fprintf(qh ferr, 8054, ".  Continue with %d points.\n", newnum);
-    numinput= newnum;
-    if (isdelaunay && qh ATinfinity) {
-      for (k= tokcount % diminput; k--; )
-        infinity[k] -= *(--coords);
-      *numpoints= newnum+1;
-    }else {
-      coords -= tokcount % diminput;
-      *numpoints= newnum;
-    }
-  }
-  if (isdelaunay && qh ATinfinity) {
-    for (k= (*dimension) -1; k--; )
-      infinity[k] /= numinput;
-    if (coords == infinity)
-      coords += (*dimension) -1;
-    else {
-      for (k=0; k < (*dimension) -1; k++)
-        *(coords++)= infinity[k];
-    }
-    *(coords++)= maxboloid * 1.1;
-  }
-  if (qh rbox_command[0]) {
-    qh rbox_command[strlen(qh rbox_command)-1]= '\0';
-    if (!strcmp(qh rbox_command, "./rbox D4"))
-      qh_fprintf(qh ferr, 8055, "\n\
-This is the qhull test case.  If any errors or core dumps occur,\n\
-recompile qhull with 'make new'.  If errors still occur, there is\n\
-an incompatibility.  You should try a different compiler.  You can also\n\
-change the choices in user.h.  If you discover the source of the problem,\n\
-please send mail to qhull_bug@qhull.org.\n\
-\n\
-Type 'qhull' for a short list of options.\n");
-  }
-  qh_free(qh line);
-  qh line= NULL;
-  if (qh half_space) {
-    qh_free(qh half_space);
-    qh half_space= NULL;
-  }
-  qh temp_malloc= NULL;
-  trace1((qh ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
-          numinput, diminput));
-  return(points);
-} /* readpoints */
-
-
-/*---------------------------------
-
-  qh_setfeasible( dim )
-    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
-
-  notes:
-    "n,n,n" already checked by qh_initflags()
-    see qh_readfeasible()
-    called only once from qh_new_qhull, otherwise leaks memory
-*/
-void qh_setfeasible(int dim) {
-  int tokcount= 0;
-  char *s;
-  coordT *coords, value;
-
-  if (!(s= qh feasible_string)) {
-    qh_fprintf(qh ferr, 6223, "\
-qhull input error: halfspace intersection needs a feasible point.\n\
-Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (!(qh feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
-    qh_fprintf(qh ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coords= qh feasible_point;
-  while (*s) {
-    value= qh_strtod(s, &s);
-    if (++tokcount > dim) {
-      qh_fprintf(qh ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
-          qh feasible_string, dim);
-      break;
-    }
-    *(coords++)= value;
-    if (*s)
-      s++;
-  }
-  while (++tokcount <= dim)
-    *(coords++)= 0.0;
-} /* setfeasible */
-
-/*---------------------------------
-
-  qh_skipfacet( facet )
-    returns 'True' if this facet is not to be printed
-
-  notes:
-    based on the user provided slice thresholds and 'good' specifications
-*/
-boolT qh_skipfacet(facetT *facet) {
-  facetT *neighbor, **neighborp;
-
-  if (qh PRINTneighbors) {
-    if (facet->good)
-      return !qh PRINTgood;
-    FOREACHneighbor_(facet) {
-      if (neighbor->good)
-        return False;
-    }
-    return True;
-  }else if (qh PRINTgood)
-    return !facet->good;
-  else if (!facet->normal)
-    return True;
-  return(!qh_inthresholds(facet->normal, NULL));
-} /* skipfacet */
-
-/*---------------------------------
-
-  qh_skipfilename( string )
-    returns pointer to character after filename
-
-  notes:
-    skips leading spaces
-    ends with spacing or eol
-    if starts with ' or " ends with the same, skipping \' or \"
-    For qhull, qh_argv_to_command() only uses double quotes
-*/
-char *qh_skipfilename(char *filename) {
-  char *s= filename;  /* non-const due to return */
-  char c;
-
-  while (*s && isspace(*s))
-    s++;
-  c= *s++;
-  if (c == '\0') {
-    qh_fprintf(qh ferr, 6204, "qhull input error: filename expected, none found.\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (c == '\'' || c == '"') {
-    while (*s !=c || s[-1] == '\\') {
-      if (!*s) {
-        qh_fprintf(qh ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-      s++;
-    }
-    s++;
-  }
-  else while (*s && !isspace(*s))
-      s++;
-  return s;
-} /* skipfilename */
-
diff --git a/src/qhull/src/libqhull/io.h b/src/qhull/src/libqhull/io.h
deleted file mode 100644
index eca0369d3..000000000
--- a/src/qhull/src/libqhull/io.h
+++ /dev/null
@@ -1,159 +0,0 @@
-/*
      ---------------------------------
-
-   io.h
-   declarations of Input/Output functions
-
-   see README, libqhull.h and io.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/io.h#1 $$Change: 1981 $
-   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-#include "libqhull.h"
-
-/*============ constants and flags ==================*/
-
-/*----------------------------------
-
-  qh_MAXfirst
-    maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst  200
-
-/*----------------------------------
-
-  qh_MINradius
-    min radius for Gp and Gv, fraction of maxcoord
-*/
-#define qh_MINradius 0.02
-
-/*----------------------------------
-
-  qh_GEOMepsilon
-    adjust outer planes for 'lines closer' and geomview roundoff.
-    This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*----------------------------------
-
-  qh_WHITESPACE
-    possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*----------------------------------
-
-  qh_RIDGE
-    to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
-    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*----------------------------------
-
-  printvridgeT
-    prints results of qh_printvdiagram
-
-  see:
-    qh_printvridge for an example
-*/
-typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-void    qh_dfacet(unsigned id);
-void    qh_dvertex(unsigned id);
-int     qh_compare_facetarea(const void *p1, const void *p2);
-int     qh_compare_facetmerge(const void *p1, const void *p2);
-int     qh_compare_facetvisit(const void *p1, const void *p2);
-int     qh_compare_vertexpoint(const void *p1, const void *p2); /* not used, not in libqhull_r.h */
-void    qh_copyfilename(char *filename, int size, const char* source, int length);
-void    qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
-              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
-              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
-pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
-setT   *qh_detvridge(vertexT *vertex);
-setT   *qh_detvridge3(vertexT *atvertex, vertexT *vertex);
-int     qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int     qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
-void    qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
-setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
-void    qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_markkeep(facetT *facetlist);
-setT   *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
-void    qh_order_vertexneighbors(vertexT *vertex);
-void    qh_prepare_output(void);
-void    qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
-void    qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet);
-void    qh_printcentrum(FILE *fp, facetT *facet, realT radius);
-void    qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printend4geom(FILE *fp, facetT *facet, int *num, boolT printall);
-void    qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printfacet(FILE *fp, facetT *facet);
-void    qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
-void    qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
-                               facetT *facet, realT offset, realT color[3]);
-void    qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
-void    qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
-void    qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format);
-void    qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format);
-void    qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format);
-void    qh_printfacetheader(FILE *fp, facetT *facet);
-void    qh_printfacetridges(FILE *fp, facetT *facet);
-void    qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
-                   setT *vertices, realT color[3]);
-void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
-void    qh_printpoint(FILE *fp, const char *string, pointT *point);
-void    qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id);
-void    qh_printpoint3(FILE *fp, pointT *point);
-void    qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
-void    qh_printpointvect2(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
-void    qh_printridge(FILE *fp, ridgeT *ridge);
-void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
-void    qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-int     qh_printvdiagram2(FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
-void    qh_printvertex(FILE *fp, vertexT *vertex);
-void    qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
-                         setT *facets, boolT printall);
-void    qh_printvertices(FILE *fp, const char* string, setT *vertices);
-void    qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall);
-void    qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_produce_output(void);
-void    qh_produce_output2(void);
-void    qh_projectdim3(pointT *source, pointT *destination);
-int     qh_readfeasible(int dim, const char *curline);
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
-void    qh_setfeasible(int dim);
-boolT   qh_skipfacet(facetT *facet);
-char   *qh_skipfilename(char *filename);
-
-#endif /* qhDEFio */
diff --git a/src/qhull/src/libqhull/libqhull.c b/src/qhull/src/libqhull/libqhull.c
deleted file mode 100644
index 7696a8a9f..000000000
--- a/src/qhull/src/libqhull/libqhull.c
+++ /dev/null
@@ -1,1403 +0,0 @@
-/*
      ---------------------------------
-
-   libqhull.c
-   Quickhull algorithm for convex hulls
-
-   qhull() and top-level routines
-
-   see qh-qhull.htm, libqhull.h, unix.c
-
-   see qhull_a.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/libqhull.c#3 $$Change: 2047 $
-   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-/*============= functions in alphabetic order after qhull() =======*/
-
-/*---------------------------------
-
-  qh_qhull()
-    compute DIM3 convex hull of qh.num_points starting at qh.first_point
-    qh contains all global options and variables
-
-  returns:
-    returns polyhedron
-      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
-
-    returns global variables
-      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
-
-    returns precision constants
-      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
-
-  notes:
-    unless needed for output
-      qh.max_vertex and qh.min_vertex are max/min due to merges
-
-  see:
-    to add individual points to either qh.num_points
-      use qh_addpoint()
-
-    if qh.GETarea
-      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
-
-  design:
-    record starting time
-    initialize hull and partition points
-    build convex hull
-    unless early termination
-      update facet->maxoutside for vertices, coplanar, and near-inside points
-    error if temporary sets exist
-    record end time
-*/
-
-void qh_qhull(void) {
-  int numoutside;
-
-  qh hulltime= qh_CPUclock;
-  if (qh RERUN || qh JOGGLEmax < REALmax/2)
-    qh_build_withrestart();
-  else {
-    qh_initbuild();
-    qh_buildhull();
-  }
-  if (!qh STOPpoint && !qh STOPcone) {
-    if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
-      qh_checkzero( qh_ALL);
-    if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
-      trace2((qh ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
-      qh DOcheckmax= False;
-    }else {
-      if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
-        qh_postmerge("First post-merge", qh premerge_centrum, qh premerge_cos,
-             (qh POSTmerge ? False : qh TESTvneighbors));
-      else if (!qh POSTmerge && qh TESTvneighbors)
-        qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
-             qh premerge_cos, True);
-      if (qh POSTmerge)
-        qh_postmerge("For post-merging", qh postmerge_centrum,
-             qh postmerge_cos, qh TESTvneighbors);
-      if (qh visible_list == qh facet_list) { /* i.e., merging done */
-        qh findbestnew= True;
-        qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numoutside);
-        qh findbestnew= False;
-        qh_deletevisible(/*qh.visible_list*/);
-        qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-      }
-    }
-    if (qh DOcheckmax){
-      if (qh REPORTfreq) {
-        qh_buildtracing(NULL, NULL);
-        qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
-      }
-      qh_check_maxout();
-    }
-    if (qh KEEPnearinside && !qh maxoutdone)
-      qh_nearcoplanar();
-  }
-  if (qh_setsize(qhmem.tempstack) != 0) {
-    qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
-             qh_setsize(qhmem.tempstack));
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  qh hulltime= qh_CPUclock - qh hulltime;
-  qh QHULLfinished= True;
-  trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
-} /* qhull */
-
-/*---------------------------------
-
-  qh_addpoint( furthest, facet, checkdist )
-    add point (usually furthest point) above facet to hull
-    if checkdist,
-      check that point is above facet.
-      if point is not outside of the hull, uses qh_partitioncoplanar()
-      assumes that facet is defined by qh_findbestfacet()
-    else if facet specified,
-      assumes that point is above facet (major damage if below)
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns False if user requested an early termination
-     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
-    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
-    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
-    if unknown point, adds a pointer to qh.other_points
-      do not deallocate the point's coordinates
-
-  notes:
-    assumes point is near its best facet and not at a local minimum of a lens
-      distributions.  Use qh_findbestfacet to avoid this case.
-    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
-
-  see also:
-    qh_triangulate() -- triangulate non-simplicial facets
-
-  design:
-    add point to other_points if needed
-    if checkdist
-      if point not above facet
-        partition coplanar point
-        exit
-    exit if pre STOPpoint requested
-    find horizon and visible facets for point
-    make new facets for point to horizon
-    make hyperplanes for point
-    compute balance statistics
-    match neighboring new facets
-    update vertex neighbors and delete interior vertices
-    exit if STOPcone requested
-    merge non-convex new facets
-    if merge found, many merges, or 'Qf'
-       use qh_findbestnew() instead of qh_findbest()
-    partition outside points from visible facets
-    delete visible facets
-    check polyhedron if requested
-    exit if post STOPpoint requested
-    reset working lists of facets and vertices
-*/
-boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist) {
-  int goodvisible, goodhorizon;
-  vertexT *vertex;
-  facetT *newfacet;
-  realT dist, newbalance, pbalance;
-  boolT isoutside= False;
-  int numpart, numpoints, numnew, firstnew;
-
-  qh maxoutdone= False;
-  if (qh_pointid(furthest) == qh_IDunknown)
-    qh_setappend(&qh other_points, furthest);
-  if (!facet) {
-    qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (checkdist) {
-    facet= qh_findbest(furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
-                        &dist, &isoutside, &numpart);
-    zzadd_(Zpartition, numpart);
-    if (!isoutside) {
-      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
-      facet->notfurthest= True;
-      qh_partitioncoplanar(furthest, facet, &dist);
-      return True;
-    }
-  }
-  qh_buildtracing(furthest, facet);
-  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
-    facet->notfurthest= True;
-    return False;
-  }
-  qh_findhorizon(furthest, facet, &goodvisible, &goodhorizon);
-  if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
-    zinc_(Znotgood);
-    facet->notfurthest= True;
-    /* last point of outsideset is no longer furthest.  This is ok
-       since all points of the outside are likely to be bad */
-    qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    return True;
-  }
-  zzinc_(Zprocessed);
-  firstnew= qh facet_id;
-  vertex= qh_makenewfacets(furthest /*visible_list, attaches if !ONLYgood */);
-  qh_makenewplanes(/* newfacet_list */);
-  numnew= qh facet_id - firstnew;
-  newbalance= numnew - (realT) (qh num_facets-qh num_visible)
-                         * qh hull_dim/qh num_vertices;
-  wadd_(Wnewbalance, newbalance);
-  wadd_(Wnewbalance2, newbalance * newbalance);
-  if (qh ONLYgood
-  && !qh_findgood(qh newfacet_list, goodhorizon) && !qh GOODclosest) {
-    FORALLnew_facets
-      qh_delfacet(newfacet);
-    qh_delvertex(vertex);
-    qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    zinc_(Znotgoodnew);
-    facet->notfurthest= True;
-    return True;
-  }
-  if (qh ONLYgood)
-    qh_attachnewfacets(/*visible_list*/);
-  qh_matchnewfacets();
-  qh_updatevertices();
-  if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
-    facet->notfurthest= True;
-    return False;  /* visible_list etc. still defined */
-  }
-  qh findbestnew= False;
-  if (qh PREmerge || qh MERGEexact) {
-    qh_premerge(vertex, qh premerge_centrum, qh premerge_cos);
-    if (qh_USEfindbestnew)
-      qh findbestnew= True;
-    else {
-      FORALLnew_facets {
-        if (!newfacet->simplicial) {
-          qh findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
-          break;
-        }
-      }
-    }
-  }else if (qh BESToutside)
-    qh findbestnew= True;
-  qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numpoints);
-  qh findbestnew= False;
-  qh findbest_notsharp= False;
-  zinc_(Zpbalance);
-  pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
-                * (qh num_points - qh num_vertices)/qh num_vertices;
-  wadd_(Wpbalance, pbalance);
-  wadd_(Wpbalance2, pbalance * pbalance);
-  qh_deletevisible(/*qh.visible_list*/);
-  zmax_(Zmaxvertex, qh num_vertices);
-  qh NEWfacets= False;
-  if (qh IStracing >= 4) {
-    if (qh num_facets < 2000)
-      qh_printlists();
-    qh_printfacetlist(qh newfacet_list, NULL, True);
-    qh_checkpolygon(qh facet_list);
-  }else if (qh CHECKfrequently) {
-    if (qh num_facets < 50)
-      qh_checkpolygon(qh facet_list);
-    else
-      qh_checkpolygon(qh newfacet_list);
-  }
-  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
-    return False;
-  qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  /* qh_triangulate(); to test qh.TRInormals */
-  trace2((qh ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
-    qh_pointid(furthest), numnew, newbalance, pbalance));
-  return True;
-} /* addpoint */
-
-/*---------------------------------
-
-  qh_build_withrestart()
-    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
-       qh_errexit always undoes qh_build_withrestart()
-    qh.FIRSTpoint/qh.NUMpoints is point array
-        it may be moved by qh_joggleinput()
-*/
-void qh_build_withrestart(void) {
-  int restart;
-
-  qh ALLOWrestart= True;
-  while (True) {
-    restart= setjmp(qh restartexit); /* simple statement for CRAY J916 */
-    if (restart) {       /* only from qh_precision() */
-      zzinc_(Zretry);
-      wmax_(Wretrymax, qh JOGGLEmax);
-      /* QH7078 warns about using 'TCn' with 'QJn' */
-      qh STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
-    }
-    if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
-      if (qh build_cnt > qh_JOGGLEmaxretry) {
-        qh_fprintf(qh ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
-        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
-        or modify qh_JOGGLE... parameters in user.h\n",
-           qh build_cnt, qh JOGGLEmax);
-        qh_errexit(qh_ERRqhull, NULL, NULL);
-      }
-      if (qh build_cnt && !restart)
-        break;
-    }else if (qh build_cnt && qh build_cnt >= qh RERUN)
-      break;
-    qh STOPcone= 0;
-    qh_freebuild(True);  /* first call is a nop */
-    qh build_cnt++;
-    if (!qh qhull_optionsiz)
-      qh qhull_optionsiz= (int)strlen(qh qhull_options);   /* WARN64 */
-    else {
-      qh qhull_options [qh qhull_optionsiz]= '\0';
-      qh qhull_optionlen= qh_OPTIONline;  /* starts a new line */
-    }
-    qh_option("_run", &qh build_cnt, NULL);
-    if (qh build_cnt == qh RERUN) {
-      qh IStracing= qh TRACElastrun;  /* duplicated from qh_initqhull_globals */
-      if (qh TRACEpoint != qh_IDunknown || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
-        qh TRACElevel= (qh IStracing? qh IStracing : 3);
-        qh IStracing= 0;
-      }
-      qhmem.IStracing= qh IStracing;
-    }
-    if (qh JOGGLEmax < REALmax/2)
-      qh_joggleinput();
-    qh_initbuild();
-    qh_buildhull();
-    if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
-      qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
-  }
-  qh ALLOWrestart= False;
-} /* qh_build_withrestart */
-
-/*---------------------------------
-
-  qh_buildhull()
-    construct a convex hull by adding outside points one at a time
-
-  returns:
-
-  notes:
-    may be called multiple times
-    checks facet and vertex lists for incorrect flags
-    to recover from STOPcone, call qh_deletevisible and qh_resetlists
-
-  design:
-    check visible facet and newfacet flags
-    check newlist vertex flags and qh.STOPcone/STOPpoint
-    for each facet with a furthest outside point
-      add point to facet
-      exit if qh.STOPcone or qh.STOPpoint requested
-    if qh.NARROWhull for initial simplex
-      partition remaining outside points to coplanar sets
-*/
-void qh_buildhull(void) {
-  facetT *facet;
-  pointT *furthest;
-  vertexT *vertex;
-  int id;
-
-  trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
-  FORALLfacets {
-    if (facet->visible || facet->newfacet) {
-      qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
-                   facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-  }
-  FORALLvertices {
-    if (vertex->newlist) {
-      qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
-                   vertex->id);
-      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-    id= qh_pointid(vertex->point);
-    if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
-        (qh STOPpoint<0 && id == -qh STOPpoint-1) ||
-        (qh STOPcone>0 && id == qh STOPcone-1)) {
-      trace1((qh ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
-      return;
-    }
-  }
-  qh facet_next= qh facet_list;      /* advance facet when processed */
-  while ((furthest= qh_nextfurthest(&facet))) {
-    qh num_outside--;  /* if ONLYmax, furthest may not be outside */
-    if (!qh_addpoint(furthest, facet, qh ONLYmax))
-      break;
-  }
-  if (qh NARROWhull) /* move points from outsideset to coplanarset */
-    qh_outcoplanar( /* facet_list */ );
-  if (qh num_outside && !furthest) {
-    qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
-} /* buildhull */
-
-
-/*---------------------------------
-
-  qh_buildtracing( furthest, facet )
-    trace an iteration of qh_buildhull() for furthest point and facet
-    if !furthest, prints progress message
-
-  returns:
-    tracks progress with qh.lastreport
-    updates qh.furthest_id (-3 if furthest is NULL)
-    also resets visit_id, vertext_visit on wrap around
-
-  see:
-    qh_tracemerging()
-
-  design:
-    if !furthest
-      print progress message
-      exit
-    if 'TFn' iteration
-      print progress message
-    else if tracing
-      trace furthest point and facet
-    reset qh.visit_id and qh.vertex_visit if overflow may occur
-    set qh.furthest_id for tracing
-*/
-void qh_buildtracing(pointT *furthest, facetT *facet) {
-  realT dist= 0;
-  float cpu;
-  int total, furthestid;
-  time_t timedata;
-  struct tm *tp;
-  vertexT *vertex;
-
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  if (!furthest) {
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    qh_fprintf(qh ferr, 8118, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  Last point was p%d\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
-      total, qh num_facets, qh num_vertices, qh furthest_id);
-    return;
-  }
-  furthestid= qh_pointid(furthest);
-  if (qh TRACEpoint == furthestid) {
-    qh IStracing= qh TRACElevel;
-    qhmem.IStracing= qh TRACElevel;
-  }else if (qh TRACEpoint != qh_IDunknown && qh TRACEdist < REALmax/2) {
-    qh IStracing= 0;
-    qhmem.IStracing= 0;
-  }
-  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
-    qh lastreport= qh facet_id-1;
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    zinc_(Zdistio);
-    qh_distplane(furthest, facet, &dist);
-    qh_fprintf(qh ferr, 8119, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  There are %d\n\
- outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
-      total, qh num_facets, qh num_vertices, qh num_outside+1,
-      furthestid, qh vertex_id, dist, getid_(facet));
-  }else if (qh IStracing >=1) {
-    cpu= (float)qh_CPUclock - (float)qh hulltime;
-    cpu /= (float)qh_SECticks;
-    qh_distplane(furthest, facet, &dist);
-    qh_fprintf(qh ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
-      furthestid, qh vertex_id, qh num_facets, dist,
-      getid_(facet), qh num_outside+1, cpu, qh furthest_id);
-  }
-  zmax_(Zvisit2max, (int)qh visit_id/2);
-  if (qh visit_id > (unsigned) INT_MAX) { /* 31 bits */
-    zinc_(Zvisit);
-    qh visit_id= 0;
-    FORALLfacets
-      facet->visitid= 0;
-  }
-  zmax_(Zvvisit2max, (int)qh vertex_visit/2);
-  if (qh vertex_visit > (unsigned) INT_MAX) { /* 31 bits */
-    zinc_(Zvvisit);
-    qh vertex_visit= 0;
-    FORALLvertices
-      vertex->visitid= 0;
-  }
-  qh furthest_id= furthestid;
-  qh RANDOMdist= qh old_randomdist;
-} /* buildtracing */
-
-/*---------------------------------
-
-  qh_errexit2( exitcode, facet, otherfacet )
-    return exitcode to system after an error
-    report two facets
-
-  returns:
-    assumes exitcode non-zero
-
-  see:
-    normally use qh_errexit() in user.c(reports a facet and a ridge)
-*/
-void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
-
-  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
-  qh_errexit(exitcode, NULL, NULL);
-} /* errexit2 */
-
-
-/*---------------------------------
-
-  qh_findhorizon( point, facet, goodvisible, goodhorizon )
-    given a visible facet, find the point's horizon and visible facets
-    for all facets, !facet-visible
-
-  returns:
-    returns qh.visible_list/num_visible with all visible facets
-      marks visible facets with ->visible
-    updates count of good visible and good horizon facets
-    updates qh.max_outside, qh.max_vertex, facet->maxoutside
-
-  see:
-    similar to qh_delpoint()
-
-  design:
-    move facet to qh.visible_list at end of qh.facet_list
-    for all visible facets
-     for each unvisited neighbor of a visible facet
-       compute distance of point to neighbor
-       if point above neighbor
-         move neighbor to end of qh.visible_list
-       else if point is coplanar with neighbor
-         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
-         mark neighbor coplanar (will create a samecycle later)
-         update horizon statistics
-*/
-void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
-  facetT *neighbor, **neighborp, *visible;
-  int numhorizon= 0, coplanar= 0;
-  realT dist;
-
-  trace1((qh ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
-  *goodvisible= *goodhorizon= 0;
-  zinc_(Ztotvisible);
-  qh_removefacet(facet);  /* visible_list at end of qh facet_list */
-  qh_appendfacet(facet);
-  qh num_visible= 1;
-  if (facet->good)
-    (*goodvisible)++;
-  qh visible_list= facet;
-  facet->visible= True;
-  facet->f.replace= NULL;
-  if (qh IStracing >=4)
-    qh_errprint("visible", facet, NULL, NULL, NULL);
-  qh visit_id++;
-  FORALLvisible_facets {
-    if (visible->tricoplanar && !qh TRInormals) {
-      qh_fprintf(qh ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh_ERRqhull, visible, NULL);
-    }
-    visible->visitid= qh visit_id;
-    FOREACHneighbor_(visible) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      zzinc_(Znumvisibility);
-      qh_distplane(point, neighbor, &dist);
-      if (dist > qh MINvisible) {
-        zinc_(Ztotvisible);
-        qh_removefacet(neighbor);  /* append to end of qh visible_list */
-        qh_appendfacet(neighbor);
-        neighbor->visible= True;
-        neighbor->f.replace= NULL;
-        qh num_visible++;
-        if (neighbor->good)
-          (*goodvisible)++;
-        if (qh IStracing >=4)
-          qh_errprint("visible", neighbor, NULL, NULL, NULL);
-      }else {
-        if (dist > - qh MAXcoplanar) {
-          neighbor->coplanar= True;
-          zzinc_(Zcoplanarhorizon);
-          qh_precision("coplanar horizon");
-          coplanar++;
-          if (qh MERGING) {
-            if (dist > 0) {
-              maximize_(qh max_outside, dist);
-              maximize_(qh max_vertex, dist);
-#if qh_MAXoutside
-              maximize_(neighbor->maxoutside, dist);
-#endif
-            }else
-              minimize_(qh min_vertex, dist);  /* due to merge later */
-          }
-          trace2((qh ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
-              qh_pointid(point), neighbor->id, dist, qh MINvisible));
-        }else
-          neighbor->coplanar= False;
-        zinc_(Ztothorizon);
-        numhorizon++;
-        if (neighbor->good)
-          (*goodhorizon)++;
-        if (qh IStracing >=4)
-          qh_errprint("horizon", neighbor, NULL, NULL, NULL);
-      }
-    }
-  }
-  if (!numhorizon) {
-    qh_precision("empty horizon");
-    qh_fprintf(qh ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
-QhullPoint p%d was above all facets.\n", qh_pointid(point));
-    qh_printfacetlist(qh facet_list, NULL, True);
-    qh_errexit(qh_ERRprec, NULL, NULL);
-  }
-  trace1((qh ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
-       numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists();
-} /* findhorizon */
-
-/*---------------------------------
-
-  qh_nextfurthest( visible )
-    returns next furthest point and visible facet for qh_addpoint()
-    starts search at qh.facet_next
-
-  returns:
-    removes furthest point from outside set
-    NULL if none available
-    advances qh.facet_next over facets with empty outside sets
-
-  design:
-    for each facet from qh.facet_next
-      if empty outside set
-        advance qh.facet_next
-      else if qh.NARROWhull
-        determine furthest outside point
-        if furthest point is not outside
-          advance qh.facet_next(point will be coplanar)
-    remove furthest point from outside set
-*/
-pointT *qh_nextfurthest(facetT **visible) {
-  facetT *facet;
-  int size, idx;
-  realT randr, dist;
-  pointT *furthest;
-
-  while ((facet= qh facet_next) != qh facet_tail) {
-    if (!facet->outsideset) {
-      qh facet_next= facet->next;
-      continue;
-    }
-    SETreturnsize_(facet->outsideset, size);
-    if (!size) {
-      qh_setfree(&facet->outsideset);
-      qh facet_next= facet->next;
-      continue;
-    }
-    if (qh NARROWhull) {
-      if (facet->notfurthest)
-        qh_furthestout(facet);
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-#if qh_COMPUTEfurthest
-      qh_distplane(furthest, facet, &dist);
-      zinc_(Zcomputefurthest);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
-        qh facet_next= facet->next;
-        continue;
-      }
-    }
-    if (!qh RANDOMoutside && !qh VIRTUALmemory) {
-      if (qh PICKfurthest) {
-        qh_furthestnext(/* qh.facet_list */);
-        facet= qh facet_next;
-      }
-      *visible= facet;
-      return((pointT*)qh_setdellast(facet->outsideset));
-    }
-    if (qh RANDOMoutside) {
-      int outcoplanar = 0;
-      if (qh NARROWhull) {
-        FORALLfacets {
-          if (facet == qh facet_next)
-            break;
-          if (facet->outsideset)
-            outcoplanar += qh_setsize( facet->outsideset);
-        }
-      }
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor((qh num_outside - outcoplanar) * randr);
-      FORALLfacet_(qh facet_next) {
-        if (facet->outsideset) {
-          SETreturnsize_(facet->outsideset, size);
-          if (!size)
-            qh_setfree(&facet->outsideset);
-          else if (size > idx) {
-            *visible= facet;
-            return((pointT*)qh_setdelnth(facet->outsideset, idx));
-          }else
-            idx -= size;
-        }
-      }
-      qh_fprintf(qh ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
-              qh num_outside, idx+1, randr);
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }else { /* VIRTUALmemory */
-      facet= qh facet_tail->previous;
-      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
-        if (facet->outsideset)
-          qh_setfree(&facet->outsideset);
-        qh_removefacet(facet);
-        qh_prependfacet(facet, &qh facet_list);
-        continue;
-      }
-      *visible= facet;
-      return furthest;
-    }
-  }
-  return NULL;
-} /* nextfurthest */
-
-/*---------------------------------
-
-  qh_partitionall( vertices, points, numpoints )
-    partitions all points in points/numpoints to the outsidesets of facets
-    vertices= vertices in qh.facet_list(!partitioned)
-
-  returns:
-    builds facet->outsideset
-    does not partition qh.GOODpoint
-    if qh.ONLYgood && !qh.MERGING,
-      does not partition qh.GOODvertex
-
-  notes:
-    faster if qh.facet_list sorted by anticipated size of outside set
-
-  design:
-    initialize pointset with all points
-    remove vertices from pointset
-    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
-    for all facets
-      for all remaining points in pointset
-        compute distance from point to facet
-        if point is outside facet
-          remove point from pointset (by not reappending)
-          update bestpoint
-          append point or old bestpoint to facet's outside set
-      append bestpoint to facet's outside set (furthest)
-    for all points remaining in pointset
-      partition point into facets' outside sets and coplanar sets
-*/
-void qh_partitionall(setT *vertices, pointT *points, int numpoints){
-  setT *pointset;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp, *bestpoint;
-  int size, point_i, point_n, point_end, remaining, i, id;
-  facetT *facet;
-  realT bestdist= -REALmax, dist, distoutside;
-
-  trace1((qh ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
-  pointset= qh_settemp(numpoints);
-  qh num_outside= 0;
-  pointp= SETaddr_(pointset, pointT);
-  for (i=numpoints, point= points; i--; point += qh hull_dim)
-    *(pointp++)= point;
-  qh_settruncate(pointset, numpoints);
-  FOREACHvertex_(vertices) {
-    if ((id= qh_pointid(vertex->point)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  id= qh_pointid(qh GOODpointp);
-  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
-    SETelem_(pointset, id)= NULL;
-  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
-    if ((id= qh_pointid(qh GOODvertexp)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  if (!qh BESToutside) {  /* matches conditional for qh_partitionpoint below */
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-    zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
-    remaining= qh num_facets;
-    point_end= numpoints;
-    FORALLfacets {
-      size= point_end/(remaining--) + 100;
-      facet->outsideset= qh_setnew(size);
-      bestpoint= NULL;
-      point_end= 0;
-      FOREACHpoint_i_(pointset) {
-        if (point) {
-          zzinc_(Zpartitionall);
-          qh_distplane(point, facet, &dist);
-          if (dist < distoutside)
-            SETelem_(pointset, point_end++)= point;
-          else {
-            qh num_outside++;
-            if (!bestpoint) {
-              bestpoint= point;
-              bestdist= dist;
-            }else if (dist > bestdist) {
-              qh_setappend(&facet->outsideset, bestpoint);
-              bestpoint= point;
-              bestdist= dist;
-            }else
-              qh_setappend(&facet->outsideset, point);
-          }
-        }
-      }
-      if (bestpoint) {
-        qh_setappend(&facet->outsideset, bestpoint);
-#if !qh_COMPUTEfurthest
-        facet->furthestdist= bestdist;
-#endif
-      }else
-        qh_setfree(&facet->outsideset);
-      qh_settruncate(pointset, point_end);
-    }
-  }
-  /* if !qh BESToutside, pointset contains points not assigned to outsideset */
-  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
-    qh findbestnew= True;
-    FOREACHpoint_i_(pointset) {
-      if (point)
-        qh_partitionpoint(point, qh facet_list);
-    }
-    qh findbestnew= False;
-  }
-  zzadd_(Zpartitionall, zzval_(Zpartition));
-  zzval_(Zpartition)= 0;
-  qh_settempfree(&pointset);
-  if (qh IStracing >= 4)
-    qh_printfacetlist(qh facet_list, NULL, True);
-} /* partitionall */
-
-
-/*---------------------------------
-
-  qh_partitioncoplanar( point, facet, dist )
-    partition coplanar point to a facet
-    dist is distance from point to facet
-    if dist NULL,
-      searches for bestfacet and does nothing if inside
-    if qh.findbestnew set,
-      searches new facets instead of using qh_findbest()
-
-  returns:
-    qh.max_ouside updated
-    if qh.KEEPcoplanar or qh.KEEPinside
-      point assigned to best coplanarset
-
-  notes:
-    facet->maxoutside is updated at end by qh_check_maxout
-
-  design:
-    if dist undefined
-      find best facet for point
-      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
-        exit
-    if keeping coplanar/nearinside/inside points
-      if point is above furthest coplanar point
-        append point to coplanar set (it is the new furthest)
-        update qh.max_outside
-      else
-        append point one before end of coplanar set
-    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
-    and bestfacet is more than perpendicular to facet
-      repartition the point using qh_findbest() -- it may be put on an outsideset
-    else
-      update qh.max_outside
-*/
-void qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist) {
-  facetT *bestfacet;
-  pointT *oldfurthest;
-  realT bestdist, dist2= 0, angle;
-  int numpart= 0, oldfindbest;
-  boolT isoutside;
-
-  qh WAScoplanar= True;
-  if (!dist) {
-    if (qh findbestnew)
-      bestfacet= qh_findbestnew(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
-    else
-      bestfacet= qh_findbest(point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
-                          &bestdist, &isoutside, &numpart);
-    zinc_(Ztotpartcoplanar);
-    zzadd_(Zpartcoplanar, numpart);
-    if (!qh DELAUNAY && !qh KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
-      if (qh KEEPnearinside) {
-        if (bestdist < -qh NEARinside) {
-          zinc_(Zcoplanarinside);
-          trace4((qh ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
-          return;
-        }
-      }else if (bestdist < -qh MAXcoplanar) {
-          trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
-        zinc_(Zcoplanarinside);
-        return;
-      }
-    }
-  }else {
-    bestfacet= facet;
-    bestdist= *dist;
-  }
-  if (bestdist > qh max_outside) {
-    if (!dist && facet != bestfacet) {
-      zinc_(Zpartangle);
-      angle= qh_getangle(facet->normal, bestfacet->normal);
-      if (angle < 0) {
-        /* typically due to deleted vertex and coplanar facets, e.g.,
-             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
-        zinc_(Zpartflip);
-        trace2((qh ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
-                qh_pointid(point), facet->id, bestfacet->id, bestdist));
-        oldfindbest= qh findbestnew;
-        qh findbestnew= False;
-        qh_partitionpoint(point, bestfacet);
-        qh findbestnew= oldfindbest;
-        return;
-      }
-    }
-    qh max_outside= bestdist;
-    if (bestdist > qh TRACEdist) {
-      qh_fprintf(qh ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
-                     qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
-      qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
-    }
-  }
-  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
-    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
-    if (oldfurthest) {
-      zinc_(Zcomputefurthest);
-      qh_distplane(oldfurthest, bestfacet, &dist2);
-    }
-    if (!oldfurthest || dist2 < bestdist)
-      qh_setappend(&bestfacet->coplanarset, point);
-    else
-      qh_setappend2ndlast(&bestfacet->coplanarset, point);
-  }
-  trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
-          qh_pointid(point), bestfacet->id, bestdist));
-} /* partitioncoplanar */
-
-/*---------------------------------
-
-  qh_partitionpoint( point, facet )
-    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
-    if qh.findbestnew
-      uses qh_findbestnew() to search all new facets
-    else
-      uses qh_findbest()
-
-  notes:
-    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
-
-  design:
-    find best facet for point
-      (either exhaustive search of new facets or directed search from facet)
-    if qh.NARROWhull
-      retain coplanar and nearinside points as outside points
-    if point is outside bestfacet
-      if point above furthest point for bestfacet
-        append point to outside set (it becomes the new furthest)
-        if outside set was empty
-          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
-        update bestfacet->furthestdist
-      else
-        append point one before end of outside set
-    else if point is coplanar to bestfacet
-      if keeping coplanar points or need to update qh.max_outside
-        partition coplanar point into bestfacet
-    else if near-inside point
-      partition as coplanar point into bestfacet
-    else is an inside point
-      if keeping inside points
-        partition as coplanar point into bestfacet
-*/
-void qh_partitionpoint(pointT *point, facetT *facet) {
-  realT bestdist;
-  boolT isoutside;
-  facetT *bestfacet;
-  int numpart;
-#if qh_COMPUTEfurthest
-  realT dist;
-#endif
-
-  if (qh findbestnew)
-    bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
-  else
-    bestfacet= qh_findbest(point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
-                          &bestdist, &isoutside, &numpart);
-  zinc_(Ztotpartition);
-  zzadd_(Zpartition, numpart);
-  if (qh NARROWhull) {
-    if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
-      qh_precision("nearly incident point(narrow hull)");
-    if (qh KEEPnearinside) {
-      if (bestdist >= -qh NEARinside)
-        isoutside= True;
-    }else if (bestdist >= -qh MAXcoplanar)
-      isoutside= True;
-  }
-
-  if (isoutside) {
-    if (!bestfacet->outsideset
-    || !qh_setlast(bestfacet->outsideset)) {
-      qh_setappend(&(bestfacet->outsideset), point);
-      if (!bestfacet->newfacet) {
-        qh_removefacet(bestfacet);  /* make sure it's after qh facet_next */
-        qh_appendfacet(bestfacet);
-      }
-#if !qh_COMPUTEfurthest
-      bestfacet->furthestdist= bestdist;
-#endif
-    }else {
-#if qh_COMPUTEfurthest
-      zinc_(Zcomputefurthest);
-      qh_distplane(oldfurthest, bestfacet, &dist);
-      if (dist < bestdist)
-        qh_setappend(&(bestfacet->outsideset), point);
-      else
-        qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#else
-      if (bestfacet->furthestdist < bestdist) {
-        qh_setappend(&(bestfacet->outsideset), point);
-        bestfacet->furthestdist= bestdist;
-      }else
-        qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#endif
-    }
-    qh num_outside++;
-    trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
-          qh_pointid(point), bestfacet->id, bestfacet->newfacet));
-  }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
-    zzinc_(Zcoplanarpart);
-    if (qh DELAUNAY)
-      qh_precision("nearly incident point");
-    if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
-      qh_partitioncoplanar(point, bestfacet, &bestdist);
-    else {
-      trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
-          qh_pointid(point), bestfacet->id));
-    }
-  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
-    zinc_(Zpartnear);
-    qh_partitioncoplanar(point, bestfacet, &bestdist);
-  }else {
-    zinc_(Zpartinside);
-    trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
-          qh_pointid(point), bestfacet->id, bestdist));
-    if (qh KEEPinside)
-      qh_partitioncoplanar(point, bestfacet, &bestdist);
-  }
-} /* partitionpoint */
-
-/*---------------------------------
-
-  qh_partitionvisible( allpoints, numoutside )
-    partitions points in visible facets to qh.newfacet_list
-    qh.visible_list= visible facets
-    for visible facets
-      1st neighbor (if any) points to a horizon facet or a new facet
-    if allpoints(!used),
-      repartitions coplanar points
-
-  returns:
-    updates outside sets and coplanar sets of qh.newfacet_list
-    updates qh.num_outside (count of outside points)
-
-  notes:
-    qh.findbest_notsharp should be clear (extra work if set)
-
-  design:
-    for all visible facets with outside set or coplanar set
-      select a newfacet for visible facet
-      if outside set
-        partition outside set into new facets
-      if coplanar set and keeping coplanar/near-inside/inside points
-        if allpoints
-          partition coplanar set into new facets, may be assigned outside
-        else
-          partition coplanar set into coplanar sets of new facets
-    for each deleted vertex
-      if allpoints
-        partition vertex into new facets, may be assigned outside
-      else
-        partition vertex into coplanar sets of new facets
-*/
-void qh_partitionvisible(/*qh.visible_list*/ boolT allpoints, int *numoutside) {
-  facetT *visible, *newfacet;
-  pointT *point, **pointp;
-  int coplanar=0, size;
-  unsigned count;
-  vertexT *vertex, **vertexp;
-
-  if (qh ONLYmax)
-    maximize_(qh MINoutside, qh max_vertex);
-  *numoutside= 0;
-  FORALLvisible_facets {
-    if (!visible->outsideset && !visible->coplanarset)
-      continue;
-    newfacet= visible->f.replace;
-    count= 0;
-    while (newfacet && newfacet->visible) {
-      newfacet= newfacet->f.replace;
-      if (count++ > qh facet_id)
-        qh_infiniteloop(visible);
-    }
-    if (!newfacet)
-      newfacet= qh newfacet_list;
-    if (newfacet == qh facet_tail) {
-      qh_fprintf(qh ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
-      qh_errexit(qh_ERRprec, NULL, NULL);
-    }
-    if (visible->outsideset) {
-      size= qh_setsize(visible->outsideset);
-      *numoutside += size;
-      qh num_outside -= size;
-      FOREACHpoint_(visible->outsideset)
-        qh_partitionpoint(point, newfacet);
-    }
-    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
-      size= qh_setsize(visible->coplanarset);
-      coplanar += size;
-      FOREACHpoint_(visible->coplanarset) {
-        if (allpoints) /* not used */
-          qh_partitionpoint(point, newfacet);
-        else
-          qh_partitioncoplanar(point, newfacet, NULL);
-      }
-    }
-  }
-  FOREACHvertex_(qh del_vertices) {
-    if (vertex->point) {
-      if (allpoints) /* not used */
-        qh_partitionpoint(vertex->point, qh newfacet_list);
-      else
-        qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL);
-    }
-  }
-  trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
-} /* partitionvisible */
-
-
-
-/*---------------------------------
-
-  qh_precision( reason )
-    restart on precision errors if not merging and if 'QJn'
-*/
-void qh_precision(const char *reason) {
-
-  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
-    if (qh JOGGLEmax < REALmax/2) {
-      trace0((qh ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
-      /* May be called repeatedly if qh->ALLOWrestart */
-      longjmp(qh restartexit, qh_ERRprec);
-    }
-  }
-} /* qh_precision */
-
-/*---------------------------------
-
-  qh_printsummary( fp )
-    prints summary to fp
-
-  notes:
-    not in io.c so that user_eg.c can prevent io.c from loading
-    qh_printsummary and qh_countfacets must match counts
-
-  design:
-    determine number of points, vertices, and coplanar points
-    print summary
-*/
-void qh_printsummary(FILE *fp) {
-  realT ratio, outerplane, innerplane;
-  float cpu;
-  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
-  int goodused;
-  facetT *facet;
-  const char *s;
-  int numdel= zzval_(Zdelvertextot);
-  int numtricoplanars= 0;
-
-  size= qh num_points + qh_setsize(qh other_points);
-  numvertices= qh num_vertices - qh_setsize(qh del_vertices);
-  id= qh_pointid(qh GOODpointp);
-  FORALLfacets {
-    if (facet->coplanarset)
-      numcoplanars += qh_setsize( facet->coplanarset);
-    if (facet->good) {
-      if (facet->simplicial) {
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else if (qh_setsize(facet->vertices) != qh hull_dim)
-        nonsimplicial++;
-    }
-  }
-  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
-    size--;
-  if (qh STOPcone || qh STOPpoint)
-      qh_fprintf(fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
-  if (qh UPPERdelaunay)
-    goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
-  else if (qh DELAUNAY)
-    goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
-  else
-    goodused= qh num_good;
-  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  if (qh VORONOI) {
-    if (qh UPPERdelaunay)
-      qh_fprintf(fp, 9289, "\n\
-Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    else
-      qh_fprintf(fp, 9290, "\n\
-Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    qh_fprintf(fp, 9291, "  Number of Voronoi regions%s: %d\n",
-              qh ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(fp, 9295, "  Number of%s Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", qh num_good);
-    if (nonsimplicial)
-      qh_fprintf(fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh DELAUNAY) {
-    if (qh UPPERdelaunay)
-      qh_fprintf(fp, 9297, "\n\
-Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    else
-      qh_fprintf(fp, 9298, "\n\
-Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    qh_fprintf(fp, 9299, "  Number of input sites%s: %d\n",
-              qh ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(fp, 9303, "  Number of%s Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", qh num_good);
-    if (nonsimplicial)
-      qh_fprintf(fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh HALFspace) {
-    qh_fprintf(fp, 9305, "\n\
-Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    qh_fprintf(fp, 9306, "  Number of halfspaces: %d\n", size);
-    qh_fprintf(fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh KEEPinside && qh KEEPcoplanar)
-        s= "similar and redundant";
-      else if (qh KEEPinside)
-        s= "redundant";
-      else
-        s= "similar";
-      qh_fprintf(fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(fp, 9309, "  Number of intersection points: %d\n", qh num_facets - qh num_visible);
-    if (goodused)
-      qh_fprintf(fp, 9310, "  Number of 'good' intersection points: %d\n", qh num_good);
-    if (nonsimplicial)
-      qh_fprintf(fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else {
-    qh_fprintf(fp, 9312, "\n\
-Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    qh_fprintf(fp, 9313, "  Number of vertices: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh KEEPinside && qh KEEPcoplanar)
-        s= "coplanar and interior";
-      else if (qh KEEPinside)
-        s= "interior";
-      else
-        s= "coplanar";
-      qh_fprintf(fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(fp, 9315, "  Number of facets: %d\n", qh num_facets - qh num_visible);
-    if (goodused)
-      qh_fprintf(fp, 9316, "  Number of 'good' facets: %d\n", qh num_good);
-    if (nonsimplicial)
-      qh_fprintf(fp, 9317, "  Number of%s non-simplicial facets: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }
-  if (numtricoplanars)
-      qh_fprintf(fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
-  qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
-                      qh rbox_command, qh qhull_command);
-  if (qh ROTATErandom != INT_MIN)
-    qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
-  else
-    qh_fprintf(fp, 9321, "\n\n");
-  qh_fprintf(fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
-  qh_fprintf(fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
-  if (qh DELAUNAY)
-    qh_fprintf(fp, 9324, "  Number of facets in hull: %d\n", qh num_facets - qh num_visible);
-  qh_fprintf(fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
-      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
-#if 0  /* NOTE: must print before printstatistics() */
-  {realT stddev, ave;
-  qh_fprintf(fp, 9326, "  average new facet balance: %2.2g\n",
-          wval_(Wnewbalance)/zval_(Zprocessed));
-  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
-  qh_fprintf(fp, 9328, "  average partition balance: %2.2g\n",
-          wval_(Wpbalance)/zval_(Zpbalance));
-  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  qh_fprintf(fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
-  }
-#endif
-  if (nummerged) {
-    qh_fprintf(fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
-          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
-          zzval_(Zdistzero));
-    qh_fprintf(fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
-    qh_fprintf(fp, 9332,"  Number of merged facets: %d\n", nummerged);
-  }
-  if (!qh RANDOMoutside && qh QHULLfinished) {
-    cpu= (float)qh hulltime;
-    cpu /= (float)qh_SECticks;
-    wval_(Wcpu)= cpu;
-    qh_fprintf(fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
-  }
-  if (qh RERUN) {
-    if (!qh PREmerge && !qh MERGEexact)
-      qh_fprintf(fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
-           zzval_(Zretry)*100.0/qh build_cnt);  /* careful of order */
-  }else if (qh JOGGLEmax < REALmax/2) {
-    if (zzval_(Zretry))
-      qh_fprintf(fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
-         zzval_(Zretry), qh JOGGLEmax);
-    else
-      qh_fprintf(fp, 9336, "  Input joggled by: %2.2g\n", qh JOGGLEmax);
-  }
-  if (qh totarea != 0.0)
-    qh_fprintf(fp, 9337, "  %s facet area:   %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
-  if (qh totvol != 0.0)
-    qh_fprintf(fp, 9338, "  %s volume:       %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
-  if (qh MERGING) {
-    qh_outerinner(NULL, &outerplane, &innerplane);
-    if (outerplane > 2 * qh DISTround) {
-      qh_fprintf(fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
-            (qh QHULLfinished ? "" : "merged "), outerplane);
-      ratio= outerplane/(qh ONEmerge + qh DISTround);
-      /* don't report ratio if MINoutside is large */
-      if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
-        qh_fprintf(fp, 9340, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(fp, 9341, "\n");
-    }
-    if (innerplane < -2 * qh DISTround) {
-      qh_fprintf(fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
-            (qh QHULLfinished ? "" : "merged "), innerplane);
-      ratio= -innerplane/(qh ONEmerge+qh DISTround);
-      if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
-        qh_fprintf(fp, 9343, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(fp, 9344, "\n");
-    }
-  }
-  qh_fprintf(fp, 9345, "\n");
-} /* printsummary */
-
-
diff --git a/src/qhull/src/libqhull/libqhull.h b/src/qhull/src/libqhull/libqhull.h
deleted file mode 100644
index 677085808..000000000
--- a/src/qhull/src/libqhull/libqhull.h
+++ /dev/null
@@ -1,1140 +0,0 @@
-/*
      ---------------------------------
-
-   libqhull.h
-   user-level header file for using qhull.a library
-
-   see qh-qhull.htm, qhull_a.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/libqhull.h#7 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-
-   NOTE: access to qh_qh is via the 'qh' macro.  This allows
-   qh_qh to be either a pointer or a structure.  An example
-   of using qh is "qh.DROPdim" which accesses the DROPdim
-   field of qh_qh.  Similarly, access to qh_qhstat is via
-   the 'qhstat' macro.
-
-   includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c
-
-   use mem.h for mem.c
-   use qset.h for qset.c
-
-   see unix.c for an example of using libqhull.h
-
-   recompile qhull if you change this file
-*/
-
-#ifndef qhDEFlibqhull
-#define qhDEFlibqhull 1
-
-/*=========================== -included files ==============*/
-
-/* user_r.h first for QHULL_CRTDBG */
-#include "user.h"      /* user definable constants (e.g., qh_QHpointer) */
-
-#include "mem.h"   /* Needed qhT in libqhull_r.h.  Here for compatibility */
-#include "qset.h"   /* Needed for QHULL_LIB_CHECK */
-/* include stat_r.h after defining boolT.  Needed for qhT in libqhull_r.h.  Here for compatibility and statT */
-
-#include 
-#include 
-#include 
-#include 
-
-#if __MWERKS__ && __POWERPC__
-#include  
-#include  
-#include        
-#endif
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if     !_MSC_VER
-#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
-#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
-#error  your compiler is a standard C compiler, you can delete this warning from libqhull.h
-#endif
-#endif
-#endif
-
-/*============ constants and basic types ====================*/
-
-extern const char qh_version[]; /* defined in global.c */
-extern const char qh_version2[]; /* defined in global.c */
-
-/*----------------------------------
-
-  coordT
-    coordinates and coefficients are stored as realT (i.e., double)
-
-  notes:
-    Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
-
-    Could use 'float' for data and 'double' for calculations (realT vs. coordT)
-      This requires many type casts, and adjusted error bounds.
-      Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*----------------------------------
-
-  pointT
-    a point is an array of coordinates, usually qh.hull_dim
-    qh_pointid returns
-      qh_IDnone if point==0 or qh is undefined
-      qh_IDinterior for qh.interior_point
-      qh_IDunknown if point is neither in qh.first_point... nor qh.other_points
-
-  notes:
-    qh.STOPcone and qh.STOPpoint assume that qh_IDunknown==-1 (other negative numbers indicate points)
-    qh_IDunknown is also returned by getid_() for unknown facet, ridge, or vertex
-*/
-#define pointT coordT
-typedef enum
-{
-    qh_IDnone = -3, qh_IDinterior = -2, qh_IDunknown = -1
-}
-qh_pointT;
-
-/*----------------------------------
-
-  flagT
-    Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*----------------------------------
-
-  boolT
-    boolean value, either True or False
-
-  notes:
-    needed for portability
-    Use qh_False/qh_True as synonyms
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-#define qh_False 0
-#define qh_True 1
-
-#include "stat.h"  /* after define of boolT */
-
-/*----------------------------------
-
-  qh_CENTER
-    to distinguish facet->center
-*/
-typedef enum
-{
-    qh_ASnone = 0,   /* If not MERGING and not VORONOI */
-    qh_ASvoronoi,    /* Set by qh_clearcenters on qh_prepare_output, or if not MERGING and VORONOI */
-    qh_AScentrum     /* If MERGING (assumed during merging) */
-}
-qh_CENTER;
-
-/*----------------------------------
-
-  qh_PRINT
-    output formats for printing (qh.PRINTout).
-    'Fa' 'FV' 'Fc' 'FC'
-
-
-   notes:
-   some of these names are similar to qhT names.  The similar names are only
-   used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone= 0,
-  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
-  qh_PRINTcoplanars, qh_PRINTcentrums,
-  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
-  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
-  qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
-  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
-  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
-  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
-  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
-  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
-  qh_PRINTEND} qh_PRINT;
-
-/*----------------------------------
-
-  qh_ALL
-    argument flag for selecting everything
-*/
-#define qh_ALL      True
-#define qh_NOupper  True     /* argument for qh_findbest */
-#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets  True     /* argument for qh_findbest */
-#define qh_RESETvisible  True     /* argument for qh_resetlists */
-
-/*----------------------------------
-
-  qh_ERR
-    Qhull exit codes, for indicating errors
-    See: MSG_ERROR and MSG_WARNING [user.h]
-*/
-#define qh_ERRnone  0    /* no error occurred during qhull */
-#define qh_ERRinput 1    /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec  3    /* precision error */
-#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5    /* internal error detected, matches mem.h */
-
-/*----------------------------------
-
-qh_FILEstderr
-Fake stderr to distinguish error output from normal output
-For C++ interface.  Must redefine qh_fprintf_qhull
-*/
-#define qh_FILEstderr ((FILE*)1)
-
-/* ============ -structures- ====================
-   each of the following structures is defined by a typedef
-   all realT and coordT fields occur at the beginning of a structure
-        (otherwise space may be wasted due to alignment)
-   define all flags together and pack into 32-bit number
-   DEFsetT is likewise defined in
-   mem.h and qset.h
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
-#endif
-
-/*----------------------------------
-
-  facetT
-    defines a facet
-
-  notes:
-   qhull() generates the hull as a list of facets.
-
-  topological information:
-    f.previous,next     doubly-linked list of facets
-    f.vertices          set of vertices
-    f.ridges            set of ridges
-    f.neighbors         set of neighbors
-    f.toporient         True if facet has top-orientation (else bottom)
-
-  geometric information:
-    f.offset,normal     hyperplane equation
-    f.maxoutside        offset to outer plane -- all points inside
-    f.center            centrum for testing convexity
-    f.simplicial        True if facet is simplicial
-    f.flipped           True if facet does not include qh.interior_point
-
-  for constructing hull:
-    f.visible           True if facet on list of visible facets (will be deleted)
-    f.newfacet          True if facet on list of newly created facets
-    f.coplanarset       set of points coplanar with this facet
-                        (includes near-inside points for later testing)
-    f.outsideset        set of points outside of this facet
-    f.furthestdist      distance to furthest point of outside set
-    f.visitid           marks visited facets during a loop
-    f.replace           replacement facet for to-be-deleted, visible facets
-    f.samecycle,newcycle cycle of facets for merging into horizon facet
-
-  see below for other flags and fields
-*/
-struct facetT {
-#if !qh_COMPUTEfurthest
-  coordT   furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
-  coordT   maxoutside;  /* max computed distance of point to facet
-                        Before QHULLfinished this is an approximation
-                        since maxdist not always set for mergefacet
-                        Actual outer plane is +DISTround and
-                        computed outer plane is +2*DISTround */
-#endif
-  coordT   offset;      /* exact offset of hyperplane from origin */
-  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
-                        /*   if tricoplanar, shared with a neighbor */
-  union {               /* in order of testing */
-   realT   area;        /* area of facet, only in io.c if  ->isarea */
-   facetT *replace;     /*  replacement facet if ->visible and NEWfacets
-                             is NULL only if qh_mergedegen_redundant or interior */
-   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
-                             if ->newfacet */
-   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
-   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
-   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
-  }f;
-  coordT  *center;      /* set according to qh.CENTERtype */
-                        /*   qh_ASnone:    no center (not MERGING) */
-                        /*   qh_AScentrum: centrum for testing convexity (qh_getcentrum) */
-                        /*                 assumed qh_AScentrum while merging */
-                        /*   qh_ASvoronoi: Voronoi center (qh_facetcenter) */
-                        /* after constructing the hull, it may be changed (qh_clearcenter) */
-                        /* if tricoplanar and !keepcentrum, shared with a neighbor */
-  facetT  *previous;    /* previous facet in the facet_list */
-  facetT  *next;        /* next facet in the facet_list */
-  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
-                           if simplicial, 1st vertex was apex/furthest */
-  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
-                           for simplicial facets, neighbors define the ridges */
-  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
-                           neighbor is opposite the kth vertex, and the first
-                           neighbor is the horizon facet for the first vertex*/
-  setT    *outsideset;  /* set of points outside this facet
-                           if non-empty, last point is furthest
-                           if NARROWhull, includes coplanars for partitioning*/
-  setT    *coplanarset; /* set of points coplanar with this facet
-                           > qh.min_vertex and <= facet->max_outside
-                           a point is assigned to the furthest facet
-                           if non-empty, last point is furthest away */
-  unsigned visitid;     /* visit_id, for visiting all neighbors,
-                           all uses are independent */
-  unsigned id;          /* unique identifier from qh.facet_id */
-  unsigned nummerge:9;  /* number of merges */
-#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
-  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
-                          /*   all tricoplanars share the same apex */
-                          /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
-                          /*     ->keepcentrum is true for the owner.  It has the ->coplanareset */
-                          /*   if ->degenerate, does not span facet (one logical ridge) */
-                          /*   during qh_triangulate, f.trivisible points to original facet */
-  flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
-  flagT    visible:1;   /* True if visible facet (will be deleted) */
-  flagT    toporient:1; /* True if created with top orientation
-                           after merging, use ridge orientation */
-  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
-  flagT    seen:1;      /* used to perform operations only once, like visitid */
-  flagT    seen2:1;     /* used to perform operations only once, like visitid */
-  flagT    flipped:1;   /* True if facet is flipped */
-  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
-  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
-
-/*-------- flags primarily for output ---------*/
-  flagT    good:1;      /* True if a facet marked good for output */
-  flagT    isarea:1;    /* True if facet->f.area is defined */
-
-/*-------- flags for merging ------------------*/
-  flagT    dupridge:1;  /* True if duplicate ridge in facet */
-  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
-                            ->normal defined (also defined for mergeridge2) */
-  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
-  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
-  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
-  flagT     cycledone:1;/* True if mergecycle_all already done */
-  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
-  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
-  flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
-  flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
-  flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*----------------------------------
-
-  ridgeT
-    defines a ridge
-
-  notes:
-  a ridge is hull_dim-1 simplex between two neighboring facets.  If the
-  facets are non-simplicial, there may be more than one ridge between
-  two facets.  E.G. a 4-d hypercube has two triangles between each pair
-  of neighboring facets.
-
-  topological information:
-    vertices            a set of vertices
-    top,bottom          neighboring facets with orientation
-
-  geometric information:
-    tested              True if ridge is clearly convex
-    nonconvex           True if ridge is non-convex
-*/
-struct ridgeT {
-  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
-                           NULL if a degen ridge (matchsame) */
-  facetT  *top;         /* top facet this ridge is part of */
-  facetT  *bottom;      /* bottom facet this ridge is part of */
-  unsigned id;          /* unique identifier.  Same size as vertex_id and ridge_id */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    tested:1;    /* True when ridge is tested for convexity */
-  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
-                           only one ridge between neighbors may have nonconvex */
-};
-
-/*----------------------------------
-
-  vertexT
-     defines a vertex
-
-  topological information:
-    next,previous       doubly-linked list of all vertices
-    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
-
-  geometric information:
-    point               array of DIM3 coordinates
-*/
-struct vertexT {
-  vertexT *next;        /* next vertex in vertex_list */
-  vertexT *previous;    /* previous vertex in vertex_list */
-  pointT  *point;       /* hull_dim coordinates (coordT) */
-  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
-                           inits in io.c or after first merge */
-  unsigned id;          /* unique identifier.  Same size as qh.vertex_id and qh.ridge_id */
-  unsigned visitid;     /* for use with qh.vertex_visit, size must match */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    seen2:1;     /* another seen flag */
-  flagT    delridge:1;  /* vertex was part of a deleted ridge */
-  flagT    deleted:1;   /* true if vertex on qh.del_vertices */
-  flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*----------------------------------
-
-  qh
-   all global variables for qhull are in qh, qhmem, and qhstat
-
-  notes:
-   qhmem is defined in mem.h, qhstat is defined in stat.h, qhrbox is defined in rboxpoints.h
-   Access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h
-
-   All global variables for qhull are in qh, qhmem, and qhstat
-   qh must be unique for each instance of qhull
-   qhstat may be shared between qhull instances.
-   qhmem may be shared across multiple instances of Qhull.
-   Rbox uses global variables rbox_inuse and rbox, but does not persist data across calls.
-
-   Qhull is not multi-threaded.  Global state could be stored in thread-local storage.
-
-   QHULL_LIB_CHECK checks that a program and the corresponding
-   qhull library were built with the same type of header files.
-*/
-
-typedef struct qhT qhT;
-
-#define QHULL_NON_REENTRANT 0
-#define QHULL_QH_POINTER 1
-#define QHULL_REENTRANT 2
-
-#if qh_QHpointer_dllimport
-#define qh qh_qh->
-__declspec(dllimport) extern qhT *qh_qh;     /* allocated in global.c */
-#define QHULL_LIB_TYPE QHULL_QH_POINTER
-
-#elif qh_QHpointer
-#define qh qh_qh->
-extern qhT *qh_qh;     /* allocated in global.c */
-#define QHULL_LIB_TYPE QHULL_QH_POINTER
-
-#elif qh_dllimport
-#define qh qh_qh.
-__declspec(dllimport) extern qhT qh_qh;      /* allocated in global.c */
-#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
-
-#else
-#define qh qh_qh.
-extern qhT qh_qh;
-#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
-#endif
-
-#define QHULL_LIB_CHECK qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), sizeof(setT), sizeof(qhmemT));
-#define QHULL_LIB_CHECK_RBOX qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), 0, 0);
-
-struct qhT {
-
-/*----------------------------------
-
-  qh constants
-    configuration flags and constants for Qhull
-
-  notes:
-    The user configures Qhull by defining flags.  They are
-    copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
-*/
-  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
-  boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
-  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
-  realT   MINoutside;     /*   'Wn' min. distance for an outside point */
-  boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
-  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
-                             for improving precision in Delaunay triangulations */
-  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
-  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
-  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
-  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
-  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
-  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
-  realT postmerge_cos;    /*   'An'    cos_max when post merging */
-  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
-  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
-  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
-  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
-  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
-  pointT *GOODpointp;     /*   the actual point */
-  boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
-                             false if qh.SPLITthreshold */
-  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
-  pointT *GOODvertexp;     /*   the actual point */
-  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
-  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
-  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
-  int   KEEParea;         /* 'PAn' number of largest facets to keep */
-  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
-  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
-                              set automatically if 'd Qc' */
-  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
-  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
-  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
-  boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
-  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
-  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
-  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
-  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
-  boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
-  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
-  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
-  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
-  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
-  boolT NOwide;           /* true 'Q12' if no error on wide merge due to duplicate ridge */
-  boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
-  boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
-  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
-  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
-  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
-                        /* NOTE: some of these names are similar to qh_PRINT names */
-  boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
-  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
-  int   PRINTdim;         /* print dimension for Geomview output */
-  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
-  boolT PRINTgood;        /* true 'Pg' if printing good facets */
-  boolT PRINTinner;       /* true 'Gi' if printing inner planes */
-  boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
-  boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
-  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
-  boolT PRINTouter;       /* true 'Go' if printing outer planes */
-  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
-  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
-  boolT PRINTridges;      /* true 'Gr' if print ridges */
-  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
-  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
-  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
-  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
-  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
-                             need projectinput() for Delaunay in qh_init_B */
-  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
-  boolT QUICKhelp;        /* true if quick help message for degen input */
-  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
-  realT RANDOMfactor;     /*    maximum random perturbation */
-  realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
-  realT RANDOMb;
-  boolT RANDOMoutside;    /* true if select a random outside point */
-  int   REPORTfreq;       /* buildtracing reports every n facets */
-  int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
-  int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
-  int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
-  boolT SCALEinput;       /* true 'Qbk' if scaling input */
-  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
-  boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
-  boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
-  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
-  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
-                               used only for printing (!for qh.ONLYgood) */
-  int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
-                          /*       also used by qh_build_withresart for err exit*/
-  int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
-                                        adding point n */
-  int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
-  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
-  int   TRACElevel;       /* 'Tn' conditional IStracing level */
-  int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
-  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
-  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
-  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
-  boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
-  boolT TRInormals;       /* true 'Q11' if triangulate duplicates ->normal and ->center (sets Qt) */
-  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
-  boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
-  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
-  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
-  boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
-
-  /*--------input constants ---------*/
-  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
-  boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */
-  char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
-  coordT *feasible_point;  /*    as coordinates, both malloc'd */
-  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
-  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
-  int   hull_dim;         /* dimension of hull, set by initbuffers */
-  int   input_dim;        /* dimension of input, set by initbuffers */
-  int   num_points;       /* number of input points */
-  pointT *first_point;    /* array of input points, see POINTSmalloc */
-  boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
-  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
-  boolT input_malloc;     /* true if qh.input_points malloc'd */
-  char  qhull_command[256];/* command line that invoked this program */
-  int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
-  char  rbox_command[256]; /* command line that produced the input points */
-  char  qhull_options[512];/* descriptive list of options */
-  int   qhull_optionlen;  /*    length of last line */
-  int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
-  int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
-  int   run_id;           /* non-zero, random identifier for this instance of qhull */
-  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
-  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
-  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
-                             must set either GOODthreshold or SPLITthreshold
-                             if Delaunay, default is 0.0 for upper envelope */
-  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
-  realT *upper_bound;     /* scale point[k] to new upper bound */
-  realT *lower_bound;     /* scale point[k] to new lower bound
-                             project if both upper_ and lower_bound == 0 */
-
-/*----------------------------------
-
-  qh precision constants
-    precision constants for Qhull
-
-  notes:
-    qh_detroundoff() computes the maximum roundoff error for distance
-    and other computations.  It also sets default values for the
-    qh constants above.
-*/
-  realT ANGLEround;       /* max round off error for angles */
-  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
-  realT cos_max;          /* max cosine for convexity (roundoff added) */
-  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
-  realT MAXabs_coord;     /* max absolute coordinate */
-  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
-  realT MAXsumcoord;      /* max sum of coordinates */
-  realT MAXwidth;         /* max rectilinear width of point coordinates */
-  realT MINdenom_1;       /* min. abs. value for 1/x */
-  realT MINdenom;         /*    use divzero if denominator < MINdenom */
-  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
-  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
-  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
-  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
-  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
-  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
-  realT ONEmerge;         /* max distance for merging simplicial facets */
-  realT outside_err;      /* application's epsilon for coplanar points
-                             qh_check_bestdist() qh_check_points() reports error if point outside */
-  realT WIDEfacet;        /* size of wide facet for skipping ridge in
-                             area computation and locking centrum */
-
-/*----------------------------------
-
-  qh internal constants
-    internal constants for Qhull
-*/
-  char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
-  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
-  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
-  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
-  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
-  FILE *fin;              /* pointer to input file, init by qh_initqhull_start2 */
-  FILE *fout;             /* pointer to output file */
-  FILE *ferr;             /* pointer to error file */
-  pointT *interior_point; /* center point of the initial simplex*/
-  int normal_size;     /* size in bytes for facet normals and point coords*/
-  int center_size;     /* size in bytes for Voronoi centers */
-  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
-
-/*----------------------------------
-
-  qh facet and vertex lists
-    defines lists of facets, new facets, visible facets, vertices, and
-    new vertices.  Includes counts, next ids, and trace ids.
-  see:
-    qh_resetlists()
-*/
-  facetT *facet_list;     /* first facet */
-  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
-  facetT *facet_next;     /* next facet for buildhull()
-                             previous facets do not have outside sets
-                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
-  facetT *newfacet_list;  /* list of new facets to end of facet_list */
-  facetT *visible_list;   /* list of visible facets preceding newfacet_list,
-                             facet->visible set */
-  int       num_visible;  /* current number of visible facets */
-  unsigned tracefacet_id;  /* set at init, then can print whenever */
-  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
-  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
-  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
-  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
-  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
-  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
-                             all vertices have 'newlist' set */
-  int   num_facets;       /* number of facets in facet_list
-                             includes visible faces (num_visible) */
-  int   num_vertices;     /* number of vertices in facet_list */
-  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
-                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
-  int   num_good;         /* number of good facets (after findgood_all) */
-  unsigned facet_id;      /* ID of next, new facet from newfacet() */
-  unsigned ridge_id;      /* ID of next, new ridge from newridge() */
-  unsigned vertex_id;     /* ID of next, new vertex from newvertex() */
-
-/*----------------------------------
-
-  qh global variables
-    defines minimum and maximum distances, next visit ids, several flags,
-    and other global variables.
-    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
-*/
-  unsigned long hulltime; /* ignore time to set up input and randomize */
-                          /*   use unsigned to avoid wrap-around errors */
-  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
-  int   build_cnt;        /* number of calls to qh_initbuild */
-  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
-  int   furthest_id;      /* pointid of furthest point, for tracing */
-  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
-  boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
-  boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
-  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
-  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
-  realT max_outside;      /* maximum distance from a point to a facet,
-                               before roundoff, not simplicial vertices
-                               actual outer plane is +DISTround and
-                               computed outer plane is +2*DISTround */
-  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
-                               before roundoff, due to a merge */
-  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
-                               before roundoff, due to a merge
-                               if qh.JOGGLEmax, qh_makenewplanes sets it
-                               recomputed if qh.DOcheckmax, default -qh.DISTround */
-  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
-                              from makecone/attachnewfacets to deletevisible */
-  boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
-  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
-  boolT NOerrexit;        /* true if qh.errexit is not available, cleared after setjmp */
-  realT PRINTcradius;     /* radius for printing centrums */
-  realT PRINTradius;      /* radius for printing vertex spheres and points */
-  boolT POSTmerging;      /* true when post merging */
-  int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
-  int   printoutnum;      /* number of facets printed */
-  boolT QHULLfinished;    /* True after qhull() is finished */
-  realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
-  realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
-  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
-  unsigned int vertex_visit; /* unique ID for searching vertices, reset with qh_buildtracing */
-  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
-  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qh_check_maxout) */
-
-/*----------------------------------
-
-  qh global sets
-    defines sets for merging, initial simplex, hashing, extra input points,
-    and deleted vertices
-*/
-  setT *facet_mergeset;   /* temporary set of merges to be done */
-  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
-  setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
-                             size is setsize() */
-  setT *other_points;     /* additional points */
-  setT *del_vertices;     /* vertices to partition and delete with visible
-                             facets.  Have deleted set for checkfacet */
-
-/*----------------------------------
-
-  qh global buffers
-    defines buffers for maxtrix operations, input, and error messages
-*/
-  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
-  coordT **gm_row;        /* array of gm_matrix rows */
-  char* line;             /* malloc'd input line of maxline+1 chars */
-  int maxline;
-  coordT *half_space;     /* malloc'd input array for halfspace (qh normal_size+coordT) */
-  coordT *temp_malloc;    /* malloc'd input array for points */
-
-/*----------------------------------
-
-  qh static variables
-    defines static variables for individual functions
-
-  notes:
-    do not use 'static' within a function.  Multiple instances of qhull
-    may exist.
-
-    do not assume zero initialization, 'QPn' may cause a restart
-*/
-  boolT ERREXITcalled;    /* true during qh_errexit (prevents duplicate calls */
-  boolT firstcentrum;     /* for qh_printcentrum */
-  boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
-  setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
-  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
-  realT last_high;
-  realT last_newhigh;
-  unsigned lastreport;    /* for qh_buildtracing */
-  int mergereport;        /* for qh_tracemerging */
-  qhstatT *old_qhstat;    /* for saving qh_qhstat in save_qhull() and UsingLibQhull.  Free with qh_free() */
-  setT *old_tempstack;    /* for saving qhmem.tempstack in save_qhull */
-  int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
-};
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  otherfacet_(ridge, facet)
-    return neighboring facet for a ridge in facet
-*/
-#define otherfacet_(ridge, facet) \
-                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
-
-/*----------------------------------
-
-  getid_(p)
-    return int ID for facet, ridge, or vertex
-    return qh_IDunknown(-1) if NULL
-*/
-#define getid_(p)       ((p) ? (int)((p)->id) : qh_IDunknown)
-
-/*============== FORALL macros ===================*/
-
-/*----------------------------------
-
-  FORALLfacets { ... }
-    assign 'facet' to each facet in qh.facet_list
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacet_( facetlist )
-*/
-#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
-
-/*----------------------------------
-
-  FORALLpoints { ... }
-    assign 'point' to each point in qh.first_point, qh.num_points
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
-
-/*----------------------------------
-
-  FORALLpoint_( points, num) { ... }
-    assign 'point' to each point in points array of num points
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoint_(points, num) for (point= (points), \
-      pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
-
-/*----------------------------------
-
-  FORALLvertices { ... }
-    assign 'vertex' to each vertex in qh.vertex_list
-
-  declare:
-    vertexT *vertex;
-
-  notes:
-    assumes qh.vertex_list terminated with a sentinel
-*/
-#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
-
-/*----------------------------------
-
-  FOREACHfacet_( facets ) { ... }
-    assign 'facet' to each facet in facets
-
-  declare:
-    facetT *facet, **facetp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_( facet ) { ... }
-    assign 'neighbor' to each neighbor in facet->neighbors
-
-  FOREACHneighbor_( vertex ) { ... }
-    assign 'neighbor' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor, **neighborp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_( points ) { ... }
-    assign 'point' to each point in points set
-
-  declare:
-    pointT *point, **pointp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_( ridges ) { ... }
-    assign 'ridge' to each ridge in ridges set
-
-  declare:
-    ridgeT *ridge, **ridgep;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices set
-
-  declare:
-    vertexT *vertex, **vertexp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
-
-/*----------------------------------
-
-  FOREACHfacet_i_( facets ) { ... }
-    assign 'facet' and 'facet_i' for each facet in facets set
-
-  declare:
-    facetT *facet;
-    int     facet_n, facet_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHfacet_i_(facets)    FOREACHsetelement_i_(facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_i_( facet ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
-
-  FOREACHneighbor_i_( vertex ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor;
-    int     neighbor_n, neighbor_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHneighbor_i_(facet)  FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_i_( points ) { ... }
-    assign 'point' and 'point_i' for each point in points set
-
-  declare:
-    pointT *point;
-    int     point_n, point_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHpoint_i_(points)    FOREACHsetelement_i_(pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_i_( ridges ) { ... }
-    assign 'ridge' and 'ridge_i' for each ridge in ridges set
-
-  declare:
-    ridgeT *ridge;
-    int     ridge_n, ridge_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHridge_i_(ridges)    FOREACHsetelement_i_(ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_i_( vertices ) { ... }
-    assign 'vertex' and 'vertex_i' for each vertex in vertices set
-
-  declare:
-    vertexT *vertex;
-    int     vertex_n, vertex_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
-
-/********* -libqhull.c prototypes (duplicated from qhull_a.h) **********************/
-
-void    qh_qhull(void);
-boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
-void    qh_printsummary(FILE *fp);
-
-/********* -user.c prototypes (alphabetical) **********************/
-
-void    qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
-void    qh_errprint(const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
-int     qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
-                char *qhull_cmd, FILE *outfile, FILE *errfile);
-void    qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
-void    qh_printhelp_degenerate(FILE *fp);
-void    qh_printhelp_narrowhull(FILE *fp, realT minangle);
-void    qh_printhelp_singular(FILE *fp);
-void    qh_user_memsizes(void);
-
-/********* -usermem.c prototypes (alphabetical) **********************/
-void    qh_exit(int exitcode);
-void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-
-/********* -userprintf.c and userprintf_rbox.c prototypes **********************/
-void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
-void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
-
-/***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/
-
-facetT *qh_findbest(pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT newfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbestnew(pointT *point, facetT *startfacet,
-                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
-boolT   qh_gram_schmidt(int dim, realT **rows);
-void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_printsummary(FILE *fp);
-void    qh_projectinput(void);
-void    qh_randommatrix(realT *buffer, int dim, realT **row);
-void    qh_rotateinput(realT **rows);
-void    qh_scaleinput(void);
-void    qh_setdelaunay(int dim, int count, pointT *points);
-coordT  *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
-
-/***** -global.c prototypes (alphabetical) ***********************/
-
-unsigned long qh_clock(void);
-void    qh_checkflags(char *command, char *hiddenflags);
-void    qh_clear_outputflags(void);
-void    qh_freebuffers(void);
-void    qh_freeqhull(boolT allmem);
-void    qh_freeqhull2(boolT allmem);
-void    qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
-void    qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_init_qhull_command(int argc, char *argv[]);
-void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_initflags(char *command);
-void    qh_initqhull_buffers(void);
-void    qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_initqhull_mem(void);
-void    qh_initqhull_outputflags(void);
-void    qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile);
-void    qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile);
-void    qh_initthresholds(char *command);
-void    qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize);
-void    qh_option(const char *option, int *i, realT *r);
-#if qh_QHpointer
-void    qh_restore_qhull(qhT **oldqh);
-qhT    *qh_save_qhull(void);
-#endif
-
-/***** -io.c prototypes (duplicated from io.h) ***********************/
-
-void    qh_dfacet(unsigned id);
-void    qh_dvertex(unsigned id);
-void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_produce_output(void);
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
-
-
-/********* -mem.c prototypes (duplicated from mem.h) **********************/
-
-void qh_meminit(FILE *ferr);
-void qh_memfreeshort(int *curlong, int *totlong);
-
-/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
-
-void    qh_check_output(void);
-void    qh_check_points(void);
-setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
-facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
-pointT *qh_point(int id);
-setT   *qh_pointfacet(void /*qh.facet_list*/);
-int     qh_pointid(pointT *point);
-setT   *qh_pointvertex(void /*qh.facet_list*/);
-void    qh_setvoronoi_all(void);
-void    qh_triangulate(void /*qh.facet_list*/);
-
-/********* -rboxlib.c prototypes **********************/
-int     qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command);
-void    qh_errexit_rbox(int exitcode);
-
-/********* -stat.c prototypes (duplicated from stat.h) **********************/
-
-void    qh_collectstatistics(void);
-void    qh_printallstatistics(FILE *fp, const char *string);
-
-#endif /* qhDEFlibqhull */
diff --git a/src/qhull/src/libqhull/libqhull.pro b/src/qhull/src/libqhull/libqhull.pro
deleted file mode 100644
index 18005da59..000000000
--- a/src/qhull/src/libqhull/libqhull.pro
+++ /dev/null
@@ -1,67 +0,0 @@
-# -------------------------------------------------
-# libqhull.pro -- Qt project for Qhull shared library
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-DESTDIR = ../../lib
-DLLDESTDIR = ../../bin
-TEMPLATE = lib
-CONFIG += shared warn_on
-CONFIG -= qt
-
-build_pass:CONFIG(debug, debug|release):{
-    TARGET = qhull_d
-    OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release):{
-    TARGET = qhull
-    OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-win32-msvc* : DEF_FILE += ../../src/libqhull/qhull-exports.def
-
-# Order object files by frequency of execution.  Small files at end.
-
-# libqhull/libqhull.pro and ../qhull-libqhull-src.pri have the same SOURCES and HEADERS
-SOURCES += ../libqhull/global.c
-SOURCES += ../libqhull/stat.c
-SOURCES += ../libqhull/geom2.c
-SOURCES += ../libqhull/poly2.c
-SOURCES += ../libqhull/merge.c
-SOURCES += ../libqhull/libqhull.c
-SOURCES += ../libqhull/geom.c
-SOURCES += ../libqhull/poly.c
-SOURCES += ../libqhull/qset.c
-SOURCES += ../libqhull/mem.c
-SOURCES += ../libqhull/random.c
-SOURCES += ../libqhull/usermem.c
-SOURCES += ../libqhull/userprintf.c
-SOURCES += ../libqhull/io.c
-SOURCES += ../libqhull/user.c
-SOURCES += ../libqhull/rboxlib.c
-SOURCES += ../libqhull/userprintf_rbox.c
-
-HEADERS += ../libqhull/geom.h
-HEADERS += ../libqhull/io.h
-HEADERS += ../libqhull/libqhull.h
-HEADERS += ../libqhull/mem.h
-HEADERS += ../libqhull/merge.h
-HEADERS += ../libqhull/poly.h
-HEADERS += ../libqhull/random.h
-HEADERS += ../libqhull/qhull_a.h
-HEADERS += ../libqhull/qset.h
-HEADERS += ../libqhull/stat.h
-HEADERS += ../libqhull/user.h
-
-OTHER_FILES += Mborland
-OTHER_FILES += qh-geom.htm
-OTHER_FILES += qh-globa.htm
-OTHER_FILES += qh-io.htm
-OTHER_FILES += qh-mem.htm
-OTHER_FILES += qh-merge.htm
-OTHER_FILES += qh-poly.htm
-OTHER_FILES += qh-qhull.htm
-OTHER_FILES += qh-set.htm
-OTHER_FILES += qh-stat.htm
-OTHER_FILES += qh-user.htm
diff --git a/src/qhull/src/libqhull/mem.c b/src/qhull/src/libqhull/mem.c
deleted file mode 100644
index db72bb4e1..000000000
--- a/src/qhull/src/libqhull/mem.c
+++ /dev/null
@@ -1,576 +0,0 @@
-/*
      ---------------------------------
-
-  mem.c
-    memory management routines for qhull
-
-  This is a standalone program.
-
-  To initialize memory:
-
-    qh_meminit(stderr);
-    qh_meminitbuffers(qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
-    qh_memsize((int)sizeof(facetT));
-    qh_memsize((int)sizeof(facetT));
-    ...
-    qh_memsetup();
-
-  To free up all memory buffers:
-    qh_memfreeshort(&curlong, &totlong);
-
-  if qh_NOmem,
-    malloc/free is used instead of mem.c
-
-  notes:
-    uses Quickfit algorithm (freelists for commonly allocated sizes)
-    assumes small sizes for freelists (it discards the tail of memory buffers)
-
-  see:
-    qh-mem.htm and mem.h
-    global.c (qh_initbuffers) for an example of using mem.c
-
-  Copyright (c) 1993-2015 The Geometry Center.
-  $Id: //main/2015/qhull/src/libqhull/mem.c#7 $$Change: 2065 $
-  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-*/
-
-#include "user.h"  /* for QHULL_CRTDBG */
-#include "mem.h"
-#include 
-#include 
-#include 
-
-#ifndef qhDEFlibqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4127)  /* conditional expression is constant */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#endif
-void    qh_errexit(int exitcode, facetT *, ridgeT *);
-void    qh_exit(int exitcode);
-void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
-void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-#endif
-
-/*============ -global data structure ==============
-    see mem.h for definition
-*/
-
-qhmemT qhmem= {0,0,0,0,0,0,0,0,0,0,0,
-               0,0,0,0,0,0,0,0,0,0,0,
-               0,0,0,0,0,0,0};     /* remove "= {0}" if this causes a compiler error */
-
-#ifndef qh_NOmem
-
-/*============= internal functions ==============*/
-
-static int qh_intcompare(const void *i, const void *j);
-
-/*========== functions in alphabetical order ======== */
-
-/*---------------------------------
-
-  qh_intcompare( i, j )
-    used by qsort and bsearch to compare two integers
-*/
-static int qh_intcompare(const void *i, const void *j) {
-  return(*((const int *)i) - *((const int *)j));
-} /* intcompare */
-
-
-/*----------------------------------
-
-  qh_memalloc( insize )
-    returns object of insize bytes
-    qhmem is the global memory structure
-
-  returns:
-    pointer to allocated memory
-    errors if insufficient memory
-
-  notes:
-    use explicit type conversion to avoid type warnings on some compilers
-    actual object may be larger than insize
-    use qh_memalloc_() for inline code for quick allocations
-    logs allocations if 'T5'
-    caller is responsible for freeing the memory.
-    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
-
-  design:
-    if size < qhmem.LASTsize
-      if qhmem.freelists[size] non-empty
-        return first object on freelist
-      else
-        round up request to size of qhmem.freelists[size]
-        allocate new allocation buffer if necessary
-        allocate object from allocation buffer
-    else
-      allocate object with qh_malloc() in user.c
-*/
-void *qh_memalloc(int insize) {
-  void **freelistp, *newbuffer;
-  int idx, size, n;
-  int outsize, bufsize;
-  void *object;
-
-  if (insize<0) {
-      qh_fprintf(qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
-      qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  if (insize>=0 && insize <= qhmem.LASTsize) {
-    idx= qhmem.indextable[insize];
-    outsize= qhmem.sizetable[idx];
-    qhmem.totshort += outsize;
-    freelistp= qhmem.freelists+idx;
-    if ((object= *freelistp)) {
-      qhmem.cntquick++;
-      qhmem.totfree -= outsize;
-      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
-#ifdef qh_TRACEshort
-      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
-      if (qhmem.IStracing >= 5)
-          qh_fprintf(qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
-#endif
-      return(object);
-    }else {
-      qhmem.cntshort++;
-      if (outsize > qhmem.freesize) {
-        qhmem.totdropped += qhmem.freesize;
-        if (!qhmem.curbuffer)
-          bufsize= qhmem.BUFinit;
-        else
-          bufsize= qhmem.BUFsize;
-        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
-          qh_fprintf(qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
-          qh_errexit(qhmem_ERRmem, NULL, NULL);
-        }
-        *((void **)newbuffer)= qhmem.curbuffer;  /* prepend newbuffer to curbuffer
-                                                    list.  newbuffer!=0 by QH6080 */
-        qhmem.curbuffer= newbuffer;
-        size= (sizeof(void **) + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
-        qhmem.freemem= (void *)((char *)newbuffer+size);
-        qhmem.freesize= bufsize - size;
-        qhmem.totbuffer += bufsize - size; /* easier to check */
-        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
-        n = qhmem.totshort + qhmem.totfree + qhmem.totdropped + qhmem.freesize - outsize;
-        if (qhmem.totbuffer != n) {
-            qh_fprintf(qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qhmem.totbuffer, n);
-            qh_errexit(qhmem_ERRmem, NULL, NULL);
-        }
-      }
-      object= qhmem.freemem;
-      qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
-      qhmem.freesize -= outsize;
-      qhmem.totunused += outsize - insize;
-#ifdef qh_TRACEshort
-      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
-      if (qhmem.IStracing >= 5)
-          qh_fprintf(qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
-#endif
-      return object;
-    }
-  }else {                     /* long allocation */
-    if (!qhmem.indextable) {
-      qh_fprintf(qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
-      qh_errexit(qhmem_ERRqhull, NULL, NULL);
-    }
-    outsize= insize;
-    qhmem.cntlong++;
-    qhmem.totlong += outsize;
-    if (qhmem.maxlong < qhmem.totlong)
-      qhmem.maxlong= qhmem.totlong;
-    if (!(object= qh_malloc((size_t)outsize))) {
-      qh_fprintf(qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
-      qh_errexit(qhmem_ERRmem, NULL, NULL);
-    }
-    if (qhmem.IStracing >= 5)
-      qh_fprintf(qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, outsize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
-  }
-  return(object);
-} /* memalloc */
-
-
-/*----------------------------------
-
-  qh_memcheck( )
-*/
-void qh_memcheck(void) {
-  int i, count, totfree= 0;
-  void *object;
-
-  if (qhmem.ferr == 0 || qhmem.IStracing < 0 || qhmem.IStracing > 10 || (((qhmem.ALIGNmask+1) & qhmem.ALIGNmask) != 0)) {
-    qh_fprintf_stderr(6244, "qh_memcheck error: either qhmem is overwritten or qhmem is not initialized.  Call qh_meminit() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qhmem.ferr, qhmem.IStracing, qhmem.ALIGNmask);
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (qhmem.IStracing != 0)
-    qh_fprintf(qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qhmem\n");
-  for (i=0; i < qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    totfree += qhmem.sizetable[i] * count;
-  }
-  if (totfree != qhmem.totfree) {
-    qh_fprintf(qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qhmem.totfree, totfree);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qhmem.IStracing != 0)
-    qh_fprintf(qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qhmem.totfree\n", totfree);
-} /* memcheck */
-
-/*----------------------------------
-
-  qh_memfree( object, insize )
-    free up an object of size bytes
-    size is insize from qh_memalloc
-
-  notes:
-    object may be NULL
-    type checking warns if using (void **)object
-    use qh_memfree_() for quick free's of small objects
-
-  design:
-    if size <= qhmem.LASTsize
-      append object to corresponding freelist
-    else
-      call qh_free(object)
-*/
-void qh_memfree(void *object, int insize) {
-  void **freelistp;
-  int idx, outsize;
-
-  if (!object)
-    return;
-  if (insize <= qhmem.LASTsize) {
-    qhmem.freeshort++;
-    idx= qhmem.indextable[insize];
-    outsize= qhmem.sizetable[idx];
-    qhmem.totfree += outsize;
-    qhmem.totshort -= outsize;
-    freelistp= qhmem.freelists + idx;
-    *((void **)object)= *freelistp;
-    *freelistp= object;
-#ifdef qh_TRACEshort
-    idx= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
-    if (qhmem.IStracing >= 5)
-        qh_fprintf(qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
-#endif
-  }else {
-    qhmem.freelong++;
-    qhmem.totlong -= insize;
-    if (qhmem.IStracing >= 5)
-      qh_fprintf(qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
-    qh_free(object);
-  }
-} /* memfree */
-
-
-/*---------------------------------
-
-  qh_memfreeshort( curlong, totlong )
-    frees up all short and qhmem memory allocations
-
-  returns:
-    number and size of current long allocations
-
-  see:
-    qh_freeqhull(allMem)
-    qh_memtotal(curlong, totlong, curshort, totshort, maxlong, totbuffer);
-*/
-void qh_memfreeshort(int *curlong, int *totlong) {
-  void *buffer, *nextbuffer;
-  FILE *ferr;
-
-  *curlong= qhmem.cntlong - qhmem.freelong;
-  *totlong= qhmem.totlong;
-  for (buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
-    nextbuffer= *((void **) buffer);
-    qh_free(buffer);
-  }
-  qhmem.curbuffer= NULL;
-  if (qhmem.LASTsize) {
-    qh_free(qhmem.indextable);
-    qh_free(qhmem.freelists);
-    qh_free(qhmem.sizetable);
-  }
-  ferr= qhmem.ferr;
-  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
-  qhmem.ferr= ferr;
-} /* memfreeshort */
-
-
-/*----------------------------------
-
-  qh_meminit( ferr )
-    initialize qhmem and test sizeof( void*)
-    Does not throw errors.  qh_exit on failure
-*/
-void qh_meminit(FILE *ferr) {
-
-  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-    qhmem.ferr= ferr;
-  else
-    qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (sizeof(void*) > sizeof(ptr_intT)) {
-      qh_fprintf(qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
-      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qh_memcheck();
-} /* meminit */
-
-/*---------------------------------
-
-  qh_meminitbuffers( tracelevel, alignment, numsizes, bufsize, bufinit )
-    initialize qhmem
-    if tracelevel >= 5, trace memory allocations
-    alignment= desired address alignment for memory allocations
-    numsizes= number of freelists
-    bufsize=  size of additional memory buffers for short allocations
-    bufinit=  size of initial memory buffer for short allocations
-*/
-void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qhmem.IStracing= tracelevel;
-  qhmem.NUMsizes= numsizes;
-  qhmem.BUFsize= bufsize;
-  qhmem.BUFinit= bufinit;
-  qhmem.ALIGNmask= alignment-1;
-  if (qhmem.ALIGNmask & ~qhmem.ALIGNmask) {
-    qh_fprintf(qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
-  qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
-  if (!qhmem.sizetable || !qhmem.freelists) {
-    qh_fprintf(qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  if (qhmem.IStracing >= 1)
-    qh_fprintf(qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
-} /* meminitbuffers */
-
-/*---------------------------------
-
-  qh_memsetup()
-    set up memory after running memsize()
-*/
-void qh_memsetup(void) {
-  int k,i;
-
-  qsort(qhmem.sizetable, (size_t)qhmem.TABLEsize, sizeof(int), qh_intcompare);
-  qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
-  if (qhmem.LASTsize >= qhmem.BUFsize || qhmem.LASTsize >= qhmem.BUFinit) {
-    qh_fprintf(qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
-            qhmem.LASTsize, qhmem.BUFsize, qhmem.BUFinit);
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  if (!(qhmem.indextable= (int *)qh_malloc((qhmem.LASTsize+1) * sizeof(int)))) {
-    qh_fprintf(qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  for (k=qhmem.LASTsize+1; k--; )
-    qhmem.indextable[k]= k;
-  i= 0;
-  for (k=0; k <= qhmem.LASTsize; k++) {
-    if (qhmem.indextable[k] <= qhmem.sizetable[i])
-      qhmem.indextable[k]= i;
-    else
-      qhmem.indextable[k]= ++i;
-  }
-} /* memsetup */
-
-/*---------------------------------
-
-  qh_memsize( size )
-    define a free list for this size
-*/
-void qh_memsize(int size) {
-  int k;
-
-  if (qhmem.LASTsize) {
-    qh_fprintf(qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  size= (size + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
-  for (k=qhmem.TABLEsize; k--; ) {
-    if (qhmem.sizetable[k] == size)
-      return;
-  }
-  if (qhmem.TABLEsize < qhmem.NUMsizes)
-    qhmem.sizetable[qhmem.TABLEsize++]= size;
-  else
-    qh_fprintf(qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
-} /* memsize */
-
-
-/*---------------------------------
-
-  qh_memstatistics( fp )
-    print out memory statistics
-
-    Verifies that qhmem.totfree == sum of freelists
-*/
-void qh_memstatistics(FILE *fp) {
-  int i;
-  int count;
-  void *object;
-
-  qh_memcheck();
-  qh_fprintf(fp, 9278, "\nmemory statistics:\n\
-%7d quick allocations\n\
-%7d short allocations\n\
-%7d long allocations\n\
-%7d short frees\n\
-%7d long frees\n\
-%7d bytes of short memory in use\n\
-%7d bytes of short memory in freelists\n\
-%7d bytes of dropped short memory\n\
-%7d bytes of unused short memory (estimated)\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n\
-%7d bytes of short memory buffers (minus links)\n\
-%7d bytes per short memory buffer (initially %d bytes)\n",
-           qhmem.cntquick, qhmem.cntshort, qhmem.cntlong,
-           qhmem.freeshort, qhmem.freelong,
-           qhmem.totshort, qhmem.totfree,
-           qhmem.totdropped + qhmem.freesize, qhmem.totunused,
-           qhmem.maxlong, qhmem.totlong, qhmem.cntlong - qhmem.freelong,
-           qhmem.totbuffer, qhmem.BUFsize, qhmem.BUFinit);
-  if (qhmem.cntlarger) {
-    qh_fprintf(fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
-           qhmem.cntlarger, ((float)qhmem.totlarger)/(float)qhmem.cntlarger);
-    qh_fprintf(fp, 9280, "  freelists(bytes->count):");
-  }
-  for (i=0; i < qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    qh_fprintf(fp, 9281, " %d->%d", qhmem.sizetable[i], count);
-  }
-  qh_fprintf(fp, 9282, "\n\n");
-} /* memstatistics */
-
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    uses qh_malloc() and qh_free() instead
-*/
-#else /* qh_NOmem */
-
-void *qh_memalloc(int insize) {
-  void *object;
-
-  if (!(object= qh_malloc((size_t)insize))) {
-    qh_fprintf(qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  qhmem.cntlong++;
-  qhmem.totlong += insize;
-  if (qhmem.maxlong < qhmem.totlong)
-      qhmem.maxlong= qhmem.totlong;
-  if (qhmem.IStracing >= 5)
-    qh_fprintf(qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
-  return object;
-}
-
-void qh_memfree(void *object, int insize) {
-
-  if (!object)
-    return;
-  qh_free(object);
-  qhmem.freelong++;
-  qhmem.totlong -= insize;
-  if (qhmem.IStracing >= 5)
-    qh_fprintf(qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
-}
-
-void qh_memfreeshort(int *curlong, int *totlong) {
-  *totlong= qhmem.totlong;
-  *curlong= qhmem.cntlong - qhmem.freelong;
-  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
-}
-
-void qh_meminit(FILE *ferr) {
-
-  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-      qhmem.ferr= ferr;
-  else
-      qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-}
-
-void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qhmem.IStracing= tracelevel;
-}
-
-void qh_memsetup(void) {
-
-}
-
-void qh_memsize(int size) {
-
-}
-
-void qh_memstatistics(FILE *fp) {
-
-  qh_fprintf(fp, 9409, "\nmemory statistics:\n\
-%7d long allocations\n\
-%7d long frees\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n",
-           qhmem.cntlong,
-           qhmem.freelong,
-           qhmem.maxlong, qhmem.totlong, qhmem.cntlong - qhmem.freelong);
-}
-
-#endif /* qh_NOmem */
-
-/*---------------------------------
-
-  qh_memtotal( totlong, curlong, totshort, curshort, maxlong, totbuffer )
-    Return the total, allocated long and short memory
-
-  returns:
-    Returns the total current bytes of long and short allocations
-    Returns the current count of long and short allocations
-    Returns the maximum long memory and total short buffer (minus one link per buffer)
-    Does not error (UsingLibQhull.cpp)
-*/
-void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
-    *totlong= qhmem.totlong;
-    *curlong= qhmem.cntlong - qhmem.freelong;
-    *totshort= qhmem.totshort;
-    *curshort= qhmem.cntshort + qhmem.cntquick - qhmem.freeshort;
-    *maxlong= qhmem.maxlong;
-    *totbuffer= qhmem.totbuffer;
-} /* memtotlong */
-
diff --git a/src/qhull/src/libqhull/mem.h b/src/qhull/src/libqhull/mem.h
deleted file mode 100644
index 453f319df..000000000
--- a/src/qhull/src/libqhull/mem.h
+++ /dev/null
@@ -1,222 +0,0 @@
-/*
      ---------------------------------
-
-   mem.h
-     prototypes for memory management functions
-
-   see qh-mem.htm, mem.c and qset.h
-
-   for error handling, writes message and calls
-     qh_errexit(qhmem_ERRmem, NULL, NULL) if insufficient memory
-       and
-     qh_errexit(qhmem_ERRqhull, NULL, NULL) otherwise
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/mem.h#2 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#ifndef qhDEFmem
-#define qhDEFmem 1
-
-#include 
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    mem.c implements Quickfit memory allocation for about 20% time
-    savings.  If it fails on your machine, try to locate the
-    problem, and send the answer to qhull@qhull.org.  If this can
-    not be done, define qh_NOmem to use malloc/free instead.
-
-   #define qh_NOmem
-*/
-
-/*---------------------------------
-
-qh_TRACEshort
-Trace short and quick memory allocations at T5
-
-*/
-#define qh_TRACEshort
-
-/*-------------------------------------------
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
-    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
-   see qh_MEMalign in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull.h */
-#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull.h */
-
-/*----------------------------------
-
-  ptr_intT
-    for casting a void * to an integer-type that holds a pointer
-    Used for integer expressions (e.g., computing qh_gethash() in poly.c)
-
-  notes:
-    WARN64 -- these notes indicate 64-bit issues
-    On 64-bit machines, a pointer may be larger than an 'int'.
-    qh_meminit()/mem.c checks that 'ptr_intT' holds a 'void*'
-    ptr_intT is typically a signed value, but not necessarily so
-    size_t is typically unsigned, but should match the parameter type
-    Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
-    This matches Qt convention and is easier to work with.
-*/
-#if (defined(__MINGW64__)) && defined(_WIN64)
-typedef long long ptr_intT;
-#elif (_MSC_VER) && defined(_WIN64)
-typedef long long ptr_intT;
-#else
-typedef long ptr_intT;
-#endif
-
-/*----------------------------------
-
-  qhmemT
-    global memory structure for mem.c
-
- notes:
-   users should ignore qhmem except for writing extensions
-   qhmem is allocated in mem.c
-
-   qhmem could be swapable like qh and qhstat, but then
-   multiple qh's and qhmem's would need to keep in synch.
-   A swapable qhmem would also waste memory buffers.  As long
-   as memory operations are atomic, there is no problem with
-   multiple qh structures being active at the same time.
-   If you need separate address spaces, you can swap the
-   contents of qhmem.
-*/
-typedef struct qhmemT qhmemT;
-extern qhmemT qhmem;
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
-#endif
-
-/* Update qhmem in mem.c if add or remove fields */
-struct qhmemT {               /* global memory management variables */
-  int      BUFsize;           /* size of memory allocation buffer */
-  int      BUFinit;           /* initial size of memory allocation buffer */
-  int      TABLEsize;         /* actual number of sizes in free list table */
-  int      NUMsizes;          /* maximum number of sizes in free list table */
-  int      LASTsize;          /* last size in free list table */
-  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
-  void   **freelists;          /* free list table, linked by offset 0 */
-  int     *sizetable;         /* size of each freelist */
-  int     *indextable;        /* size->index table */
-  void    *curbuffer;         /* current buffer, linked by offset 0 */
-  void    *freemem;           /*   free memory in curbuffer */
-  int      freesize;          /*   size of freemem in bytes */
-  setT    *tempstack;         /* stack of temporary memory, managed by users */
-  FILE    *ferr;              /* file for reporting errors when 'qh' may be undefined */
-  int      IStracing;         /* =5 if tracing memory allocations */
-  int      cntquick;          /* count of quick allocations */
-                              /* Note: removing statistics doesn't effect speed */
-  int      cntshort;          /* count of short allocations */
-  int      cntlong;           /* count of long allocations */
-  int      freeshort;         /* count of short memfrees */
-  int      freelong;          /* count of long memfrees */
-  int      totbuffer;         /* total short memory buffers minus buffer links */
-  int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
-  int      totfree;           /* total size of free, short memory on freelists */
-  int      totlong;           /* total size of long memory in use */
-  int      maxlong;           /*   maximum totlong */
-  int      totshort;          /* total size of short memory in use */
-  int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
-  int      cntlarger;         /* count of setlarger's */
-  int      totlarger;         /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*----------------------------------
-
-  qh_memalloc_(insize, freelistp, object, type)
-    returns object of size bytes
-        assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#if defined qh_NOmem
-#define qh_memalloc_(insize, freelistp, object, type) {\
-  object= (type*)qh_memalloc(insize); }
-#elif defined qh_TRACEshort
-#define qh_memalloc_(insize, freelistp, object, type) {\
-    freelistp= NULL; /* Avoid warnings */ \
-    object= (type*)qh_memalloc(insize); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(insize, freelistp, object, type) {\
-  freelistp= qhmem.freelists + qhmem.indextable[insize];\
-  if ((object= (type*)*freelistp)) {\
-    qhmem.totshort += qhmem.sizetable[qhmem.indextable[insize]]; \
-    qhmem.totfree -= qhmem.sizetable[qhmem.indextable[insize]]; \
-    qhmem.cntquick++;  \
-    *freelistp= *((void **)*freelistp);\
-  }else object= (type*)qh_memalloc(insize);}
-#endif
-
-/*----------------------------------
-
-  qh_memfree_(object, insize, freelistp)
-    free up an object
-
-  notes:
-    object may be NULL
-    assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-#if defined qh_NOmem
-#define qh_memfree_(object, insize, freelistp) {\
-  qh_memfree(object, insize); }
-#elif defined qh_TRACEshort
-#define qh_memfree_(object, insize, freelistp) {\
-    freelistp= NULL; /* Avoid warnings */ \
-    qh_memfree(object, insize); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(object, insize, freelistp) {\
-  if (object) { \
-    qhmem.freeshort++;\
-    freelistp= qhmem.freelists + qhmem.indextable[insize];\
-    qhmem.totshort -= qhmem.sizetable[qhmem.indextable[insize]]; \
-    qhmem.totfree += qhmem.sizetable[qhmem.indextable[insize]]; \
-    *((void **)object)= *freelistp;\
-    *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-void *qh_memalloc(int insize);
-void qh_memcheck(void);
-void qh_memfree(void *object, int insize);
-void qh_memfreeshort(int *curlong, int *totlong);
-void qh_meminit(FILE *ferr);
-void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
-                        int bufsize, int bufinit);
-void qh_memsetup(void);
-void qh_memsize(int size);
-void qh_memstatistics(FILE *fp);
-void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);
-
-#endif /* qhDEFmem */
diff --git a/src/qhull/src/libqhull/merge.c b/src/qhull/src/libqhull/merge.c
deleted file mode 100644
index 22104dc03..000000000
--- a/src/qhull/src/libqhull/merge.c
+++ /dev/null
@@ -1,3628 +0,0 @@
-/*
      ---------------------------------
-
-   merge.c
-   merges non-convex facets
-
-   see qh-merge.htm and merge.h
-
-   other modules call qh_premerge() and qh_postmerge()
-
-   the user may call qh_postmerge() to perform additional merges.
-
-   To remove deleted facets and vertices (qhull() in libqhull.c):
-     qh_partitionvisible(!qh_ALL, &numoutside);  // visible_list, newfacet_list
-     qh_deletevisible();         // qh.visible_list
-     qh_resetlists(False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
-
-   assumes qh.CENTERtype= centrum
-
-   merges occur in qh_mergefacet and in qh_mergecycle
-   vertex->neighbors not set until the first merge occurs
-
-   Copyright (c) 1993-2015 C.B. Barber.
-   $Id: //main/2015/qhull/src/libqhull/merge.c#4 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-#ifndef qh_NOmerge
-
-/*===== functions(alphabetical after premerge and postmerge) ======*/
-
-/*---------------------------------
-
-  qh_premerge( apex, maxcentrum )
-    pre-merge nonconvex facets in qh.newfacet_list for apex
-    maxcentrum defines coplanar and concave (qh_test_appendmerge)
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible set
-
-  notes:
-    uses globals, qh.MERGEexact, qh.PREmerge
-
-  design:
-    mark duplicate ridges in qh.newfacet_list
-    merge facet cycles in qh.newfacet_list
-    merge duplicate ridges and concave facets in qh.newfacet_list
-    check merged facet cycles for degenerate and redundant facets
-    merge degenerate and redundant facets
-    collect coplanar and concave facets
-    merge concave, coplanar, degenerate, and redundant facets
-*/
-void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
-  boolT othermerge= False;
-  facetT *newfacet;
-
-  if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
-    return;
-  trace2((qh ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
-            maxcentrum, maxangle, apex->id, getid_(qh newfacet_list)));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists();
-  qh centrum_radius= maxcentrum;
-  qh cos_max= maxangle;
-  qh degen_mergeset= qh_settemp(qh TEMPsize);
-  qh facet_mergeset= qh_settemp(qh TEMPsize);
-  if (qh hull_dim >=3) {
-    qh_mark_dupridges(qh newfacet_list); /* facet_mergeset */
-    qh_mergecycle_all(qh newfacet_list, &othermerge);
-    qh_forcedmerges(&othermerge /* qh.facet_mergeset */);
-    FORALLnew_facets {  /* test samecycle merges */
-      if (!newfacet->simplicial && !newfacet->mergeridge)
-        qh_degen_redundant_neighbors(newfacet, NULL);
-    }
-    if (qh_merge_degenredundant())
-      othermerge= True;
-  }else /* qh.hull_dim == 2 */
-    qh_mergecycle_all(qh newfacet_list, &othermerge);
-  qh_flippedmerges(qh newfacet_list, &othermerge);
-  if (!qh MERGEexact || zzval_(Ztotmerge)) {
-    zinc_(Zpremergetot);
-    qh POSTmerging= False;
-    qh_getmergeset_initial(qh newfacet_list);
-    qh_all_merges(othermerge, False);
-  }
-  qh_settempfree(&qh facet_mergeset);
-  qh_settempfree(&qh degen_mergeset);
-} /* premerge */
-
-/*---------------------------------
-
-  qh_postmerge( reason, maxcentrum, maxangle, vneighbors )
-    post-merge nonconvex facets as defined by maxcentrum and maxangle
-    'reason' is for reporting progress
-    if vneighbors,
-      calls qh_test_vneighbors at end of qh_all_merge
-    if firstmerge,
-      calls qh_reducevertices before qh_getmergeset
-
-  returns:
-    if first call (qh.visible_list != qh.facet_list),
-      builds qh.facet_newlist, qh.newvertex_list
-    deleted facets added to qh.visible_list with facet->visible
-    qh.visible_list == qh.facet_list
-
-  notes:
-
-
-  design:
-    if first call
-      set qh.visible_list and qh.newfacet_list to qh.facet_list
-      add all facets to qh.newfacet_list
-      mark non-simplicial facets, facet->newmerge
-      set qh.newvertext_list to qh.vertex_list
-      add all vertices to qh.newvertex_list
-      if a pre-merge occured
-        set vertex->delridge {will retest the ridge}
-        if qh.MERGEexact
-          call qh_reducevertices()
-      if no pre-merging
-        merge flipped facets
-    determine non-convex facets
-    merge all non-convex facets
-*/
-void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-  facetT *newfacet;
-  boolT othermerges= False;
-  vertexT *vertex;
-
-  if (qh REPORTfreq || qh IStracing) {
-    qh_buildtracing(NULL, NULL);
-    qh_printsummary(qh ferr);
-    if (qh PRINTstatistics)
-      qh_printallstatistics(qh ferr, "reason");
-    qh_fprintf(qh ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
-        reason, maxcentrum, maxangle);
-  }
-  trace2((qh ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
-            vneighbors));
-  qh centrum_radius= maxcentrum;
-  qh cos_max= maxangle;
-  qh POSTmerging= True;
-  qh degen_mergeset= qh_settemp(qh TEMPsize);
-  qh facet_mergeset= qh_settemp(qh TEMPsize);
-  if (qh visible_list != qh facet_list) {  /* first call */
-    qh NEWfacets= True;
-    qh visible_list= qh newfacet_list= qh facet_list;
-    FORALLnew_facets {
-      newfacet->newfacet= True;
-       if (!newfacet->simplicial)
-        newfacet->newmerge= True;
-     zinc_(Zpostfacets);
-    }
-    qh newvertex_list= qh vertex_list;
-    FORALLvertices
-      vertex->newlist= True;
-    if (qh VERTEXneighbors) { /* a merge has occurred */
-      FORALLvertices
-        vertex->delridge= True; /* test for redundant, needed? */
-      if (qh MERGEexact) {
-        if (qh hull_dim <= qh_DIMreduceBuild)
-          qh_reducevertices(); /* was skipped during pre-merging */
-      }
-    }
-    if (!qh PREmerge && !qh MERGEexact)
-      qh_flippedmerges(qh newfacet_list, &othermerges);
-  }
-  qh_getmergeset_initial(qh newfacet_list);
-  qh_all_merges(False, vneighbors);
-  qh_settempfree(&qh facet_mergeset);
-  qh_settempfree(&qh degen_mergeset);
-} /* post_merge */
-
-/*---------------------------------
-
-  qh_all_merges( othermerge, vneighbors )
-    merge all non-convex facets
-
-    set othermerge if already merged facets (for qh_reducevertices)
-    if vneighbors
-      tests vertex neighbors for convexity at end
-    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
-    qh.degen_mergeset is defined
-    if qh.MERGEexact && !qh.POSTmerging,
-      does not merge coplanar facets
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible
-    deleted vertices added qh.delvertex_list with vertex->delvertex
-
-  notes:
-    unless !qh.MERGEindependent,
-      merges facets in independent sets
-    uses qh.newfacet_list as argument since merges call qh_removefacet()
-
-  design:
-    while merges occur
-      for each merge in qh.facet_mergeset
-        unless one of the facets was already merged in this pass
-          merge the facets
-        test merged facets for additional merges
-        add merges to qh.facet_mergeset
-      if vertices record neighboring facets
-        rename redundant vertices
-          update qh.facet_mergeset
-    if vneighbors ??
-      tests vertex neighbors for convexity at end
-*/
-void qh_all_merges(boolT othermerge, boolT vneighbors) {
-  facetT *facet1, *facet2;
-  mergeT *merge;
-  boolT wasmerge= True, isreduce;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-  vertexT *vertex;
-  mergeType mergetype;
-  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
-
-  trace2((qh ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
-            getid_(qh newfacet_list)));
-  while (True) {
-    wasmerge= False;
-    while (qh_setsize(qh facet_mergeset)) {
-      while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
-        facet1= merge->facet1;
-        facet2= merge->facet2;
-        mergetype= merge->type;
-        qh_memfree_(merge, (int)sizeof(mergeT), freelistp);
-        if (facet1->visible || facet2->visible) /*deleted facet*/
-          continue;
-        if ((facet1->newfacet && !facet1->tested)
-                || (facet2->newfacet && !facet2->tested)) {
-          if (qh MERGEindependent && mergetype <= MRGanglecoplanar)
-            continue;      /* perform independent sets of merges */
-        }
-        qh_merge_nonconvex(facet1, facet2, mergetype);
-        numdegenredun += qh_merge_degenredundant();
-        numnewmerges++;
-        wasmerge= True;
-        if (mergetype == MRGconcave)
-          numconcave++;
-        else /* MRGcoplanar or MRGanglecoplanar */
-          numcoplanar++;
-      } /* while setdellast */
-      if (qh POSTmerging && qh hull_dim <= qh_DIMreduceBuild
-      && numnewmerges > qh_MAXnewmerges) {
-        numnewmerges= 0;
-        qh_reducevertices();  /* otherwise large post merges too slow */
-      }
-      qh_getmergeset(qh newfacet_list); /* facet_mergeset */
-    } /* while mergeset */
-    if (qh VERTEXneighbors) {
-      isreduce= False;
-      if (qh hull_dim >=4 && qh POSTmerging) {
-        FORALLvertices
-          vertex->delridge= True;
-        isreduce= True;
-      }
-      if ((wasmerge || othermerge) && (!qh MERGEexact || qh POSTmerging)
-          && qh hull_dim <= qh_DIMreduceBuild) {
-        othermerge= False;
-        isreduce= True;
-      }
-      if (isreduce) {
-        if (qh_reducevertices()) {
-          qh_getmergeset(qh newfacet_list); /* facet_mergeset */
-          continue;
-        }
-      }
-    }
-    if (vneighbors && qh_test_vneighbors(/* qh.newfacet_list */))
-      continue;
-    break;
-  } /* while (True) */
-  if (qh CHECKfrequently && !qh MERGEexact) {
-    qh old_randomdist= qh RANDOMdist;
-    qh RANDOMdist= False;
-    qh_checkconvex(qh newfacet_list, qh_ALGORITHMfault);
-    /* qh_checkconnect(); [this is slow and it changes the facet order] */
-    qh RANDOMdist= qh old_randomdist;
-  }
-  trace1((qh ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
-    numcoplanar, numconcave, numdegenredun));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists();
-} /* all_merges */
-
-
-/*---------------------------------
-
-  qh_appendmergeset( facet, neighbor, mergetype, angle )
-    appends an entry to qh.facet_mergeset or qh.degen_mergeset
-
-    angle ignored if NULL or !qh.ANGLEmerge
-
-  returns:
-    merge appended to facet_mergeset or degen_mergeset
-      sets ->degenerate or ->redundant if degen_mergeset
-
-  see:
-    qh_test_appendmerge()
-
-  design:
-    allocate merge entry
-    if regular merge
-      append to qh.facet_mergeset
-    else if degenerate merge and qh.facet_mergeset is all degenerate
-      append to qh.degen_mergeset
-    else if degenerate merge
-      prepend to qh.degen_mergeset
-    else if redundant merge
-      append to qh.degen_mergeset
-*/
-void qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
-  mergeT *merge, *lastmerge;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (facet->redundant)
-    return;
-  if (facet->degenerate && mergetype == MRGdegen)
-    return;
-  qh_memalloc_((int)sizeof(mergeT), freelistp, merge, mergeT);
-  merge->facet1= facet;
-  merge->facet2= neighbor;
-  merge->type= mergetype;
-  if (angle && qh ANGLEmerge)
-    merge->angle= *angle;
-  if (mergetype < MRGdegen)
-    qh_setappend(&(qh facet_mergeset), merge);
-  else if (mergetype == MRGdegen) {
-    facet->degenerate= True;
-    if (!(lastmerge= (mergeT*)qh_setlast(qh degen_mergeset))
-    || lastmerge->type == MRGdegen)
-      qh_setappend(&(qh degen_mergeset), merge);
-    else
-      qh_setaddnth(&(qh degen_mergeset), 0, merge);
-  }else if (mergetype == MRGredundant) {
-    facet->redundant= True;
-    qh_setappend(&(qh degen_mergeset), merge);
-  }else /* mergetype == MRGmirror */ {
-    if (facet->redundant || neighbor->redundant) {
-      qh_fprintf(qh ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh_ERRqhull, facet, neighbor);
-    }
-    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
-      qh_fprintf(qh ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh_ERRqhull, facet, neighbor);
-    }
-    facet->redundant= True;
-    neighbor->redundant= True;
-    qh_setappend(&(qh degen_mergeset), merge);
-  }
-} /* appendmergeset */
-
-
-/*---------------------------------
-
-  qh_basevertices( samecycle )
-    return temporary set of base vertices for samecycle
-    samecycle is first facet in the cycle
-    assumes apex is SETfirst_( samecycle->vertices )
-
-  returns:
-    vertices(settemp)
-    all ->seen are cleared
-
-  notes:
-    uses qh_vertex_visit;
-
-  design:
-    for each facet in samecycle
-      for each unseen vertex in facet->vertices
-        append to result
-*/
-setT *qh_basevertices(facetT *samecycle) {
-  facetT *same;
-  vertexT *apex, *vertex, **vertexp;
-  setT *vertices= qh_settemp(qh TEMPsize);
-
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  apex->visitid= ++qh vertex_visit;
-  FORALLsame_cycle_(samecycle) {
-    if (same->mergeridge)
-      continue;
-    FOREACHvertex_(same->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        qh_setappend(&vertices, vertex);
-        vertex->visitid= qh vertex_visit;
-        vertex->seen= False;
-      }
-    }
-  }
-  trace4((qh ferr, 4019, "qh_basevertices: found %d vertices\n",
-         qh_setsize(vertices)));
-  return vertices;
-} /* basevertices */
-
-/*---------------------------------
-
-  qh_checkconnect()
-    check that new facets are connected
-    new facets are on qh.newfacet_list
-
-  notes:
-    this is slow and it changes the order of the facets
-    uses qh.visit_id
-
-  design:
-    move first new facet to end of qh.facet_list
-    for all newly appended facets
-      append unvisited neighbors to end of qh.facet_list
-    for all new facets
-      report error if unvisited
-*/
-void qh_checkconnect(void /* qh.newfacet_list */) {
-  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
-
-  facet= qh newfacet_list;
-  qh_removefacet(facet);
-  qh_appendfacet(facet);
-  facet->visitid= ++qh visit_id;
-  FORALLfacet_(facet) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        qh_removefacet(neighbor);
-        qh_appendfacet(neighbor);
-        neighbor->visitid= qh visit_id;
-      }
-    }
-  }
-  FORALLnew_facets {
-    if (newfacet->visitid == qh visit_id)
-      break;
-    qh_fprintf(qh ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
-         newfacet->id);
-    errfacet= newfacet;
-  }
-  if (errfacet)
-    qh_errexit(qh_ERRqhull, errfacet, NULL);
-} /* checkconnect */
-
-/*---------------------------------
-
-  qh_checkzero( testall )
-    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
-
-    if testall,
-      test all facets for qh.MERGEexact post-merging
-    else
-      test qh.newfacet_list
-
-    if qh.MERGEexact,
-      allows coplanar ridges
-      skips convexity test while qh.ZEROall_ok
-
-  returns:
-    True if all facets !flipped, !dupridge, normal
-         if all horizon facets are simplicial
-         if all vertices are clearly below neighbor
-         if all opposite vertices of horizon are below
-    clears qh.ZEROall_ok if any problems or coplanar facets
-
-  notes:
-    uses qh.vertex_visit
-    horizon facets may define multiple new facets
-
-  design:
-    for all facets in qh.newfacet_list or qh.facet_list
-      check for flagged faults (flipped, etc.)
-    for all facets in qh.newfacet_list or qh.facet_list
-      for each neighbor of facet
-        skip horizon facets for qh.newfacet_list
-        test the opposite vertex
-      if qh.newfacet_list
-        test the other vertices in the facet's horizon facet
-*/
-boolT qh_checkzero(boolT testall) {
-  facetT *facet, *neighbor, **neighborp;
-  facetT *horizon, *facetlist;
-  int neighbor_i;
-  vertexT *vertex, **vertexp;
-  realT dist;
-
-  if (testall)
-    facetlist= qh facet_list;
-  else {
-    facetlist= qh newfacet_list;
-    FORALLfacet_(facetlist) {
-      horizon= SETfirstt_(facet->neighbors, facetT);
-      if (!horizon->simplicial)
-        goto LABELproblem;
-      if (facet->flipped || facet->dupridge || !facet->normal)
-        goto LABELproblem;
-    }
-    if (qh MERGEexact && qh ZEROall_ok) {
-      trace2((qh ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
-      return True;
-    }
-  }
-  FORALLfacet_(facetlist) {
-    qh vertex_visit++;
-    neighbor_i= 0;
-    horizon= NULL;
-    FOREACHneighbor_(facet) {
-      if (!neighbor_i && !testall) {
-        horizon= neighbor;
-        neighbor_i++;
-        continue; /* horizon facet tested in qh_findhorizon */
-      }
-      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-      vertex->visitid= qh vertex_visit;
-      zzinc_(Zdistzero);
-      qh_distplane(vertex->point, neighbor, &dist);
-      if (dist >= -qh DISTround) {
-        qh ZEROall_ok= False;
-        if (!qh MERGEexact || testall || dist > qh DISTround)
-          goto LABELnonconvex;
-      }
-    }
-    if (!testall && horizon) {
-      FOREACHvertex_(horizon->vertices) {
-        if (vertex->visitid != qh vertex_visit) {
-          zzinc_(Zdistzero);
-          qh_distplane(vertex->point, facet, &dist);
-          if (dist >= -qh DISTround) {
-            qh ZEROall_ok= False;
-            if (!qh MERGEexact || dist > qh DISTround)
-              goto LABELnonconvex;
-          }
-          break;
-        }
-      }
-    }
-  }
-  trace2((qh ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
-        (qh MERGEexact && !testall) ?
-           "not concave, flipped, or duplicate ridged" : "clearly convex"));
-  return True;
-
- LABELproblem:
-  qh ZEROall_ok= False;
-  trace2((qh ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
-       facet->id));
-  return False;
-
- LABELnonconvex:
-  trace2((qh ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
-         facet->id, neighbor->id, vertex->id, dist));
-  return False;
-} /* checkzero */
-
-/*---------------------------------
-
-  qh_compareangle( angle1, angle2 )
-    used by qsort() to order merges by angle
-*/
-int qh_compareangle(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return((a->angle > b->angle) ? 1 : -1);
-} /* compareangle */
-
-/*---------------------------------
-
-  qh_comparemerge( merge1, merge2 )
-    used by qsort() to order merges
-*/
-int qh_comparemerge(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return(a->type - b->type);
-} /* comparemerge */
-
-/*---------------------------------
-
-  qh_comparevisit( vertex1, vertex2 )
-    used by qsort() to order vertices by their visitid
-*/
-int qh_comparevisit(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return(a->visitid - b->visitid);
-} /* comparevisit */
-
-/*---------------------------------
-
-  qh_copynonconvex( atridge )
-    set non-convex flag on other ridges (if any) between same neighbors
-
-  notes:
-    may be faster if use smaller ridge set
-
-  design:
-    for each ridge of atridge's top facet
-      if ridge shares the same neighbor
-        set nonconvex flag
-*/
-void qh_copynonconvex(ridgeT *atridge) {
-  facetT *facet, *otherfacet;
-  ridgeT *ridge, **ridgep;
-
-  facet= atridge->top;
-  otherfacet= atridge->bottom;
-  FOREACHridge_(facet->ridges) {
-    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
-      ridge->nonconvex= True;
-      trace4((qh ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
-              atridge->id, ridge->id));
-      break;
-    }
-  }
-} /* copynonconvex */
-
-/*---------------------------------
-
-  qh_degen_redundant_facet( facet )
-    check facet for degen. or redundancy
-
-  notes:
-    bumps vertex_visit
-    called if a facet was redundant but no longer is (qh_merge_degenredundant)
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-
-  see:
-    qh_degen_redundant_neighbors()
-
-  design:
-    test for redundant neighbor
-    test for degenerate facet
-*/
-void qh_degen_redundant_facet(facetT *facet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  trace4((qh ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
-          facet->id));
-  FOREACHneighbor_(facet) {
-    qh vertex_visit++;
-    FOREACHvertex_(neighbor->vertices)
-      vertex->visitid= qh vertex_visit;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(facet, neighbor, MRGredundant, NULL);
-      trace2((qh ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
-      return;
-    }
-  }
-  if (qh_setsize(facet->neighbors) < qh hull_dim) {
-    qh_appendmergeset(facet, facet, MRGdegen, NULL);
-    trace2((qh ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* degen_redundant_facet */
-
-
-/*---------------------------------
-
-  qh_degen_redundant_neighbors( facet, delfacet,  )
-    append degenerate and redundant neighbors to facet_mergeset
-    if delfacet,
-      only checks neighbors of both delfacet and facet
-    also checks current facet for degeneracy
-
-  notes:
-    bumps vertex_visit
-    called for each qh_mergefacet() and qh_mergecycle()
-    merge and statistics occur in merge_nonconvex
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-      it appends redundant facets after degenerate ones
-
-    a degenerate facet has fewer than hull_dim neighbors
-    a redundant facet's vertices is a subset of its neighbor's vertices
-    tests for redundant merges first (appendmergeset is nop for others)
-    in a merge, only needs to test neighbors of merged facet
-
-  see:
-    qh_merge_degenredundant() and qh_degen_redundant_facet()
-
-  design:
-    test for degenerate facet
-    test for redundant neighbor
-    test for degenerate neighbor
-*/
-void qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-  int size;
-
-  trace4((qh ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
-          facet->id, getid_(delfacet)));
-  if ((size= qh_setsize(facet->neighbors)) < qh hull_dim) {
-    qh_appendmergeset(facet, facet, MRGdegen, NULL);
-    trace2((qh ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
-  }
-  if (!delfacet)
-    delfacet= facet;
-  qh vertex_visit++;
-  FOREACHvertex_(facet->vertices)
-    vertex->visitid= qh vertex_visit;
-  FOREACHneighbor_(delfacet) {
-    /* uses early out instead of checking vertex count */
-    if (neighbor == facet)
-      continue;
-    FOREACHvertex_(neighbor->vertices) {
-      if (vertex->visitid != qh vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(neighbor, facet, MRGredundant, NULL);
-      trace2((qh ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
-    }
-  }
-  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
-    if (neighbor == facet)
-      continue;
-    if ((size= qh_setsize(neighbor->neighbors)) < qh hull_dim) {
-      qh_appendmergeset(neighbor, neighbor, MRGdegen, NULL);
-      trace2((qh ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
-    }
-  }
-} /* degen_redundant_neighbors */
-
-
-/*---------------------------------
-
-  qh_find_newvertex( oldvertex, vertices, ridges )
-    locate new vertex for renaming old vertex
-    vertices is a set of possible new vertices
-      vertices sorted by number of deleted ridges
-
-  returns:
-    newvertex or NULL
-      each ridge includes both vertex and oldvertex
-    vertices sorted by number of deleted ridges
-
-  notes:
-    modifies vertex->visitid
-    new vertex is in one of the ridges
-    renaming will not cause a duplicate ridge
-    renaming will minimize the number of deleted ridges
-    newvertex may not be adjacent in the dual (though unlikely)
-
-  design:
-    for each vertex in vertices
-      set vertex->visitid to number of references in ridges
-    remove unvisited vertices
-    set qh.vertex_visit above all possible values
-    sort vertices by number of references in ridges
-    add each ridge to qh.hash_table
-    for each vertex in vertices
-      look for a vertex that would not cause a duplicate ridge after a rename
-*/
-vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges) {
-  vertexT *vertex, **vertexp;
-  setT *newridges;
-  ridgeT *ridge, **ridgep;
-  int size, hashsize;
-  int hash;
-
-#ifndef qh_NOtrace
-  if (qh IStracing >= 4) {
-    qh_fprintf(qh ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
-             oldvertex->id);
-    FOREACHvertex_(vertices)
-      qh_fprintf(qh ferr, 8064, "v%d ", vertex->id);
-    FOREACHridge_(ridges)
-      qh_fprintf(qh ferr, 8065, "r%d ", ridge->id);
-    qh_fprintf(qh ferr, 8066, "\n");
-  }
-#endif
-  FOREACHvertex_(vertices)
-    vertex->visitid= 0;
-  FOREACHridge_(ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->visitid++;
-  }
-  FOREACHvertex_(vertices) {
-    if (!vertex->visitid) {
-      qh_setdelnth(vertices, SETindex_(vertices,vertex));
-      vertexp--; /* repeat since deleted this vertex */
-    }
-  }
-  qh vertex_visit += (unsigned int)qh_setsize(ridges);
-  if (!qh_setsize(vertices)) {
-    trace4((qh ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
-            oldvertex->id));
-    return NULL;
-  }
-  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(vertices),
-                sizeof(vertexT *), qh_comparevisit);
-  /* can now use qh vertex_visit */
-  if (qh PRINTstatistics) {
-    size= qh_setsize(vertices);
-    zinc_(Zintersect);
-    zadd_(Zintersecttot, size);
-    zmax_(Zintersectmax, size);
-  }
-  hashsize= qh_newhashtable(qh_setsize(ridges));
-  FOREACHridge_(ridges)
-    qh_hashridge(qh hash_table, hashsize, ridge, oldvertex);
-  FOREACHvertex_(vertices) {
-    newridges= qh_vertexridges(vertex);
-    FOREACHridge_(newridges) {
-      if (qh_hashridge_find(qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
-        zinc_(Zdupridge);
-        break;
-      }
-    }
-    qh_settempfree(&newridges);
-    if (!ridge)
-      break;  /* found a rename */
-  }
-  if (vertex) {
-    /* counted in qh_renamevertex */
-    trace2((qh ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
-      vertex->id, oldvertex->id, qh_setsize(vertices), qh_setsize(ridges)));
-  }else {
-    zinc_(Zfindfail);
-    trace0((qh ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
-      oldvertex->id, qh furthest_id));
-  }
-  qh_setfree(&qh hash_table);
-  return vertex;
-} /* find_newvertex */
-
-/*---------------------------------
-
-  qh_findbest_test( testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
-    test neighbor of facet for qh_findbestneighbor()
-    if testcentrum,
-      tests centrum (assumes it is defined)
-    else
-      tests vertices
-
-  returns:
-    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
-      updates bestfacet, dist, mindist, and maxdist
-*/
-void qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
-      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
-  realT dist, mindist, maxdist;
-
-  if (testcentrum) {
-    zzinc_(Zbestdist);
-    qh_distplane(facet->center, neighbor, &dist);
-    dist *= qh hull_dim; /* estimate furthest vertex */
-    if (dist < 0) {
-      maxdist= 0;
-      mindist= dist;
-      dist= -dist;
-    }else {
-      mindist= 0;
-      maxdist= dist;
-    }
-  }else
-    dist= qh_getdistance(facet, neighbor, &mindist, &maxdist);
-  if (dist < *distp) {
-    *bestfacet= neighbor;
-    *mindistp= mindist;
-    *maxdistp= maxdist;
-    *distp= dist;
-  }
-} /* findbest_test */
-
-/*---------------------------------
-
-  qh_findbestneighbor( facet, dist, mindist, maxdist )
-    finds best neighbor (least dist) of a facet for merging
-
-  returns:
-    returns min and max distances and their max absolute value
-
-  notes:
-    error if qh_ASvoronoi
-    avoids merging old into new
-    assumes ridge->nonconvex only set on one ridge between a pair of facets
-    could use an early out predicate but not worth it
-
-  design:
-    if a large facet
-      will test centrum
-    else
-      will test vertices
-    if a large facet
-      test nonconvex neighbors for best merge
-    else
-      test all neighbors for the best merge
-    if testing centrum
-      get distance information
-*/
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  ridgeT *ridge, **ridgep;
-  boolT nonconvex= True, testcentrum= False;
-  int size= qh_setsize(facet->vertices);
-
-  if(qh CENTERtype==qh_ASvoronoi){
-    qh_fprintf(qh ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
-    qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  *distp= REALmax;
-  if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
-    testcentrum= True;
-    zinc_(Zbestcentrum);
-    if (!facet->center)
-       facet->center= qh_getcentrum(facet);
-  }
-  if (size > qh hull_dim + qh_BESTnonconvex) {
-    FOREACHridge_(facet->ridges) {
-      if (ridge->nonconvex) {
-        neighbor= otherfacet_(ridge, facet);
-        qh_findbest_test(testcentrum, facet, neighbor,
-                          &bestfacet, distp, mindistp, maxdistp);
-      }
-    }
-  }
-  if (!bestfacet) {
-    nonconvex= False;
-    FOREACHneighbor_(facet)
-      qh_findbest_test(testcentrum, facet, neighbor,
-                        &bestfacet, distp, mindistp, maxdistp);
-  }
-  if (!bestfacet) {
-    qh_fprintf(qh ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
-
-    qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  if (testcentrum)
-    qh_getdistance(facet, bestfacet, mindistp, maxdistp);
-  trace3((qh ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
-     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
-  return(bestfacet);
-} /* findbestneighbor */
-
-
-/*---------------------------------
-
-  qh_flippedmerges( facetlist, wasmerge )
-    merge flipped facets into best neighbor
-    assumes qh.facet_mergeset at top of temporary stack
-
-  returns:
-    no flipped facets on facetlist
-    sets wasmerge if merge occurred
-    degen/redundant merges passed through
-
-  notes:
-    othermerges not needed since qh.facet_mergeset is empty before & after
-      keep it in case of change
-
-  design:
-    append flipped facets to qh.facetmergeset
-    for each flipped merge
-      find best neighbor
-      merge facet into neighbor
-      merge degenerate and redundant facets
-    remove flipped merges from qh.facet_mergeset
-*/
-void qh_flippedmerges(facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *neighbor, *facet1;
-  realT dist, mindist, maxdist;
-  mergeT *merge, **mergep;
-  setT *othermerges;
-  int nummerge=0;
-
-  trace4((qh ferr, 4024, "qh_flippedmerges: begin\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->flipped && !facet->visible)
-      qh_appendmergeset(facet, facet, MRGflip, NULL);
-  }
-  othermerges= qh_settemppop(); /* was facet_mergeset */
-  qh facet_mergeset= qh_settemp(qh TEMPsize);
-  qh_settemppush(othermerges);
-  FOREACHmerge_(othermerges) {
-    facet1= merge->facet1;
-    if (merge->type != MRGflip || facet1->visible)
-      continue;
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-      qhmem.IStracing= qh IStracing= qh TRACElevel;
-    neighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
-    trace0((qh ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
-      facet1->id, neighbor->id, dist, qh furthest_id));
-    qh_mergefacet(facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
-    nummerge++;
-    if (qh PRINTstatistics) {
-      zinc_(Zflipped);
-      wadd_(Wflippedtot, dist);
-      wmax_(Wflippedmax, dist);
-    }
-    qh_merge_degenredundant();
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->facet1->visible || merge->facet2->visible)
-      qh_memfree(merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(&qh facet_mergeset, merge);
-  }
-  qh_settempfree(&othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
-} /* flippedmerges */
-
-
-/*---------------------------------
-
-  qh_forcedmerges( wasmerge )
-    merge duplicated ridges
-
-  returns:
-    removes all duplicate ridges on facet_mergeset
-    wasmerge set if merge
-    qh.facet_mergeset may include non-forced merges(none for now)
-    qh.degen_mergeset includes degen/redun merges
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-     could rename vertices that pinch the horizon
-    assumes qh_merge_degenredundant() has not be called
-    othermerges isn't needed since facet_mergeset is empty afterwards
-      keep it in case of change
-
-  design:
-    for each duplicate ridge
-      find current facets by chasing f.replace links
-      check for wide merge due to duplicate ridge
-      determine best direction for facet
-      merge one facet into the other
-      remove duplicate ridges from qh.facet_mergeset
-*/
-void qh_forcedmerges(boolT *wasmerge) {
-  facetT *facet1, *facet2;
-  mergeT *merge, **mergep;
-  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
-  setT *othermerges;
-  int nummerge=0, numflip=0;
-
-  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace4((qh ferr, 4025, "qh_forcedmerges: begin\n"));
-  othermerges= qh_settemppop(); /* was facet_mergeset */
-  qh facet_mergeset= qh_settemp(qh TEMPsize);
-  qh_settemppush(othermerges);
-  FOREACHmerge_(othermerges) {
-    if (merge->type != MRGridge)
-        continue;
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-        qhmem.IStracing= qh IStracing= qh TRACElevel;
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
-      facet1= facet1->f.replace; /* previously merged facet */
-    while (facet2->visible)
-      facet2= facet2->f.replace; /* previously merged facet */
-    if (facet1 == facet2)
-      continue;
-    if (!qh_setin(facet2->neighbors, facet1)) {
-      qh_fprintf(qh ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
-               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
-      qh_errexit2(qh_ERRqhull, facet1, facet2);
-    }
-    dist1= qh_getdistance(facet1, facet2, &mindist1, &maxdist1);
-    dist2= qh_getdistance(facet2, facet1, &mindist2, &maxdist2);
-    qh_check_dupridge(facet1, dist1, facet2, dist2);
-    if (dist1 < dist2)
-      qh_mergefacet(facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
-    else {
-      qh_mergefacet(facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
-      dist1= dist2;
-      facet1= facet2;
-    }
-    if (facet1->flipped) {
-      zinc_(Zmergeflipdup);
-      numflip++;
-    }else
-      nummerge++;
-    if (qh PRINTstatistics) {
-      zinc_(Zduplicate);
-      wadd_(Wduplicatetot, dist1);
-      wmax_(Wduplicatemax, dist1);
-    }
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->type == MRGridge)
-      qh_memfree(merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(&qh facet_mergeset, merge);
-  }
-  qh_settempfree(&othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
-                nummerge, numflip));
-} /* forcedmerges */
-
-
-/*---------------------------------
-
-  qh_getmergeset( facetlist )
-    determines nonconvex facets on facetlist
-    tests !tested ridges and nonconvex ridges of !tested facets
-
-  returns:
-    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
-    all ridges tested
-
-  notes:
-    assumes no nonconvex ridges with both facets tested
-    uses facet->tested/ridge->tested to prevent duplicate tests
-    can not limit tests to modified ridges since the centrum changed
-    uses qh.visit_id
-
-  see:
-    qh_getmergeset_initial()
-
-  design:
-    for each facet on facetlist
-      for each ridge of facet
-        if untested ridge
-          test ridge for convexity
-          if non-convex
-            append ridge to qh.facet_mergeset
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset(facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  nummerges= qh_setsize(qh facet_mergeset);
-  trace4((qh ferr, 4026, "qh_getmergeset: started.\n"));
-  qh visit_id++;
-  FORALLfacet_(facetlist) {
-    if (facet->tested)
-      continue;
-    facet->visitid= qh visit_id;
-    facet->tested= True;  /* must be non-simplicial due to merge */
-    FOREACHneighbor_(facet)
-      neighbor->seen= False;
-    FOREACHridge_(facet->ridges) {
-      if (ridge->tested && !ridge->nonconvex)
-        continue;
-      /* if tested & nonconvex, need to append merge */
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->seen) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-      }else if (neighbor->visitid != qh visit_id) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-        neighbor->seen= True;      /* only one ridge is marked nonconvex */
-        if (qh_test_appendmerge(facet, neighbor))
-          ridge->nonconvex= True;
-      }
-    }
-  }
-  nummerges= qh_setsize(qh facet_mergeset);
-  if (qh ANGLEmerge)
-    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh POSTmerging) {
-    zadd_(Zmergesettot2, nummerges);
-  }else {
-    zadd_(Zmergesettot, nummerges);
-    zmax_(Zmergesetmax, nummerges);
-  }
-  trace2((qh ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
-} /* getmergeset */
-
-
-/*---------------------------------
-
-  qh_getmergeset_initial( facetlist )
-    determine initial qh.facet_mergeset for facets
-    tests all facet/neighbor pairs on facetlist
-
-  returns:
-    sorted qh.facet_mergeset with nonconvex ridges
-    sets facet->tested, ridge->tested, and ridge->nonconvex
-
-  notes:
-    uses visit_id, assumes ridge->nonconvex is False
-
-  see:
-    qh_getmergeset()
-
-  design:
-    for each facet on facetlist
-      for each untested neighbor of facet
-        test facet and neighbor for convexity
-        if non-convex
-          append merge to qh.facet_mergeset
-          mark one of the ridges as nonconvex
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset_initial(facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  qh visit_id++;
-  FORALLfacet_(facetlist) {
-    facet->visitid= qh visit_id;
-    facet->tested= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        if (qh_test_appendmerge(facet, neighbor)) {
-          FOREACHridge_(neighbor->ridges) {
-            if (facet == otherfacet_(ridge, neighbor)) {
-              ridge->nonconvex= True;
-              break;    /* only one ridge is marked nonconvex */
-            }
-          }
-        }
-      }
-    }
-    FOREACHridge_(facet->ridges)
-      ridge->tested= True;
-  }
-  nummerges= qh_setsize(qh facet_mergeset);
-  if (qh ANGLEmerge)
-    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh POSTmerging) {
-    zadd_(Zmergeinittot2, nummerges);
-  }else {
-    zadd_(Zmergeinittot, nummerges);
-    zmax_(Zmergeinitmax, nummerges);
-  }
-  trace2((qh ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
-} /* getmergeset_initial */
-
-
-/*---------------------------------
-
-  qh_hashridge( hashtable, hashsize, ridge, oldvertex )
-    add ridge to hashtable without oldvertex
-
-  notes:
-    assumes hashtable is large enough
-
-  design:
-    determine hash value for ridge without oldvertex
-    find next empty slot for ridge
-*/
-void qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
-  int hash;
-  ridgeT *ridgeA;
-
-  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, oldvertex);
-  while (True) {
-    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-      SETelem_(hashtable, hash)= ridge;
-      break;
-    }else if (ridgeA == ridge)
-      break;
-    if (++hash == hashsize)
-      hash= 0;
-  }
-} /* hashridge */
-
-
-/*---------------------------------
-
-  qh_hashridge_find( hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
-    returns matching ridge without oldvertex in hashtable
-      for ridge without vertex
-    if oldvertex is NULL
-      matches with any one skip
-
-  returns:
-    matching ridge or NULL
-    if no match,
-      if ridge already in   table
-        hashslot= -1
-      else
-        hashslot= next NULL index
-
-  notes:
-    assumes hashtable is large enough
-    can't match ridge to itself
-
-  design:
-    get hash value for ridge without vertex
-    for each hashslot
-      return match if ridge matches ridgeA without oldvertex
-*/
-ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
-  int hash;
-  ridgeT *ridgeA;
-
-  *hashslot= 0;
-  zinc_(Zhashridge);
-  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, vertex);
-  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-    if (ridgeA == ridge)
-      *hashslot= -1;
-    else {
-      zinc_(Zhashridgetest);
-      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
-        return ridgeA;
-    }
-    if (++hash == hashsize)
-      hash= 0;
-  }
-  if (!*hashslot)
-    *hashslot= hash;
-  return NULL;
-} /* hashridge_find */
-
-
-/*---------------------------------
-
-  qh_makeridges( facet )
-    creates explicit ridges between simplicial facets
-
-  returns:
-    facet with ridges and without qh_MERGEridge
-    ->simplicial is False
-
-  notes:
-    allows qh_MERGEridge flag
-    uses existing ridges
-    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    look for qh_MERGEridge neighbors
-    mark neighbors that already have ridges
-    for each unprocessed neighbor of facet
-      create a ridge for neighbor and facet
-    if any qh_MERGEridge neighbors
-      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
-*/
-void qh_makeridges(facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int neighbor_i, neighbor_n;
-  boolT toporient, mergeridge= False;
-
-  if (!facet->simplicial)
-    return;
-  trace4((qh ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
-  facet->simplicial= False;
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      mergeridge= True;
-    else
-      neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges)
-    otherfacet_(ridge, facet)->seen= True;
-  FOREACHneighbor_i_(facet) {
-    if (neighbor == qh_MERGEridge)
-      continue;  /* fixed by qh_mark_dupridges */
-    else if (!neighbor->seen) {  /* no current ridges */
-      ridge= qh_newridge();
-      ridge->vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
-                                                          neighbor_i, 0);
-      toporient= facet->toporient ^ (neighbor_i & 0x1);
-      if (toporient) {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }else {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }
-#if 0 /* this also works */
-      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
-      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }else {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }
-#endif
-      qh_setappend(&(facet->ridges), ridge);
-      qh_setappend(&(neighbor->ridges), ridge);
-    }
-  }
-  if (mergeridge) {
-    while (qh_setdel(facet->neighbors, qh_MERGEridge))
-      ; /* delete each one */
-  }
-} /* makeridges */
-
-
-/*---------------------------------
-
-  qh_mark_dupridges( facetlist )
-    add duplicated ridges to qh.facet_mergeset
-    facet->dupridge is true
-
-  returns:
-    duplicate ridges on qh.facet_mergeset
-    ->mergeridge/->mergeridge2 set
-    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
-    no MERGEridges in neighbor sets
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-    could rename vertices that pinch the horizon (thus removing subridge)
-    uses qh.visit_id
-
-  design:
-    for all facets on facetlist
-      if facet contains a duplicate ridge
-        for each neighbor of facet
-          if neighbor marked qh_MERGEridge (one side of the merge)
-            set facet->mergeridge
-          else
-            if neighbor contains a duplicate ridge
-            and the back link is qh_MERGEridge
-              append duplicate ridge to qh.facet_mergeset
-   for each duplicate ridge
-     make ridge sets in preparation for merging
-     remove qh_MERGEridge from neighbor set
-   for each duplicate ridge
-     restore the missing neighbor from the neighbor set that was qh_MERGEridge
-     add the missing ridge for this neighbor
-*/
-void qh_mark_dupridges(facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  int nummerge=0;
-  mergeT *merge, **mergep;
-
-
-  trace4((qh ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->dupridge) {
-      FOREACHneighbor_(facet) {
-        if (neighbor == qh_MERGEridge) {
-          facet->mergeridge= True;
-          continue;
-        }
-        if (neighbor->dupridge
-        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
-          qh_appendmergeset(facet, neighbor, MRGridge, NULL);
-          facet->mergeridge2= True;
-          facet->mergeridge= True;
-          nummerge++;
-        }
-      }
-    }
-  }
-  if (!nummerge)
-    return;
-  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
-    if (facet->mergeridge && !facet->mergeridge2)
-      qh_makeridges(facet);
-  }
-  FOREACHmerge_(qh facet_mergeset) {   /* restore the missing neighbors */
-    if (merge->type == MRGridge) {
-      qh_setappend(&merge->facet2->neighbors, merge->facet1);
-      qh_makeridges(merge->facet1);   /* and the missing ridges */
-    }
-  }
-  trace1((qh ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
-                nummerge));
-} /* mark_dupridges */
-
-/*---------------------------------
-
-  qh_maydropneighbor( facet )
-    drop neighbor relationship if no ridge between facet and neighbor
-
-  returns:
-    neighbor sets updated
-    appends degenerate facets to qh.facet_mergeset
-
-  notes:
-    won't cause redundant facets since vertex inclusion is the same
-    may drop vertex and neighbor if no ridge
-    uses qh.visit_id
-
-  design:
-    visit all neighbors with ridges
-    for each unvisited neighbor of facet
-      delete neighbor and facet from the neighbor sets
-      if neighbor becomes degenerate
-        append neighbor to qh.degen_mergeset
-    if facet is degenerate
-      append facet to qh.degen_mergeset
-*/
-void qh_maydropneighbor(facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  realT angledegen= qh_ANGLEdegen;
-  facetT *neighbor, **neighborp;
-
-  qh visit_id++;
-  trace4((qh ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
-          facet->id));
-  FOREACHridge_(facet->ridges) {
-    ridge->top->visitid= qh visit_id;
-    ridge->bottom->visitid= qh visit_id;
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid != qh visit_id) {
-      trace0((qh ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
-            facet->id, neighbor->id, qh furthest_id));
-      zinc_(Zdropneighbor);
-      qh_setdel(facet->neighbors, neighbor);
-      neighborp--;  /* repeat, deleted a neighbor */
-      qh_setdel(neighbor->neighbors, facet);
-      if (qh_setsize(neighbor->neighbors) < qh hull_dim) {
-        zinc_(Zdropdegen);
-        qh_appendmergeset(neighbor, neighbor, MRGdegen, &angledegen);
-        trace2((qh ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
-      }
-    }
-  }
-  if (qh_setsize(facet->neighbors) < qh hull_dim) {
-    zinc_(Zdropdegen);
-    qh_appendmergeset(facet, facet, MRGdegen, &angledegen);
-    trace2((qh ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* maydropneighbor */
-
-
-/*---------------------------------
-
-  qh_merge_degenredundant()
-    merge all degenerate and redundant facets
-    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
-
-  returns:
-    number of merges performed
-    resets facet->degenerate/redundant
-    if deleted (visible) facet has no neighbors
-      sets ->f.replace to NULL
-
-  notes:
-    redundant merges happen before degenerate ones
-    merging and renaming vertices can result in degen/redundant facets
-
-  design:
-    for each merge on qh.degen_mergeset
-      if redundant merge
-        if non-redundant facet merged into redundant facet
-          recheck facet for redundancy
-        else
-          merge redundant facet into other facet
-*/
-int qh_merge_degenredundant(void) {
-  int size;
-  mergeT *merge;
-  facetT *bestneighbor, *facet1, *facet2;
-  realT dist, mindist, maxdist;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-  mergeType mergetype;
-
-  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(merge, (int)sizeof(mergeT));
-    if (facet1->visible)
-      continue;
-    facet1->degenerate= False;
-    facet1->redundant= False;
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-      qhmem.IStracing= qh IStracing= qh TRACElevel;
-    if (mergetype == MRGredundant) {
-      zinc_(Zneighbor);
-      while (facet2->visible) {
-        if (!facet2->f.replace) {
-          qh_fprintf(qh ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
-               facet1->id, facet2->id);
-          qh_errexit2(qh_ERRqhull, facet1, facet2);
-        }
-        facet2= facet2->f.replace;
-      }
-      if (facet1 == facet2) {
-        qh_degen_redundant_facet(facet1); /* in case of others */
-        continue;
-      }
-      trace2((qh ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
-            facet1->id, facet2->id));
-      qh_mergefacet(facet1, facet2, NULL, NULL, !qh_MERGEapex);
-      /* merge distance is already accounted for */
-      nummerges++;
-    }else {  /* mergetype == MRGdegen, other merges may have fixed */
-      if (!(size= qh_setsize(facet1->neighbors))) {
-        zinc_(Zdelfacetdup);
-        trace2((qh ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
-        qh_willdelete(facet1, NULL);
-        FOREACHvertex_(facet1->vertices) {
-          qh_setdel(vertex->neighbors, facet1);
-          if (!SETfirst_(vertex->neighbors)) {
-            zinc_(Zdegenvertex);
-            trace2((qh ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
-                 vertex->id, facet1->id));
-            vertex->deleted= True;
-            qh_setappend(&qh del_vertices, vertex);
-          }
-        }
-        nummerges++;
-      }else if (size < qh hull_dim) {
-        bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
-        trace2((qh ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
-              facet1->id, size, bestneighbor->id, dist));
-        qh_mergefacet(facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-        nummerges++;
-        if (qh PRINTstatistics) {
-          zinc_(Zdegen);
-          wadd_(Wdegentot, dist);
-          wmax_(Wdegenmax, dist);
-        }
-      } /* else, another merge fixed the degeneracy and redundancy tested */
-    }
-  }
-  return nummerges;
-} /* merge_degenredundant */
-
-/*---------------------------------
-
-  qh_merge_nonconvex( facet1, facet2, mergetype )
-    remove non-convex ridge between facet1 into facet2
-    mergetype gives why the facet's are non-convex
-
-  returns:
-    merges one of the facets into the best neighbor
-
-  design:
-    if one of the facets is a new facet
-      prefer merging new facet into old facet
-    find best neighbors for both facets
-    merge the nearest facet into its best neighbor
-    update the statistics
-*/
-void qh_merge_nonconvex(facetT *facet1, facetT *facet2, mergeType mergetype) {
-  facetT *bestfacet, *bestneighbor, *neighbor;
-  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
-
-  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace3((qh ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
-      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
-  /* concave or coplanar */
-  if (!facet1->newfacet) {
-    bestfacet= facet2;   /* avoid merging old facet if new is ok */
-    facet2= facet1;
-    facet1= bestfacet;
-  }else
-    bestfacet= facet1;
-  bestneighbor= qh_findbestneighbor(bestfacet, &dist, &mindist, &maxdist);
-  neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
-  if (dist < dist2) {
-    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else if (qh AVOIDold && !facet2->newfacet
-  && ((mindist >= -qh MAXcoplanar && maxdist <= qh max_outside)
-       || dist * 1.5 < dist2)) {
-    zinc_(Zavoidold);
-    wadd_(Wavoidoldtot, dist);
-    wmax_(Wavoidoldmax, dist);
-    trace2((qh ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
-           facet2->id, dist2, facet1->id, dist2));
-    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else {
-    qh_mergefacet(facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
-    dist= dist2;
-  }
-  if (qh PRINTstatistics) {
-    if (mergetype == MRGanglecoplanar) {
-      zinc_(Zacoplanar);
-      wadd_(Wacoplanartot, dist);
-      wmax_(Wacoplanarmax, dist);
-    }else if (mergetype == MRGconcave) {
-      zinc_(Zconcave);
-      wadd_(Wconcavetot, dist);
-      wmax_(Wconcavemax, dist);
-    }else { /* MRGcoplanar */
-      zinc_(Zcoplanar);
-      wadd_(Wcoplanartot, dist);
-      wmax_(Wcoplanarmax, dist);
-    }
-  }
-} /* merge_nonconvex */
-
-/*---------------------------------
-
-  qh_mergecycle( samecycle, newfacet )
-    merge a cycle of facets starting at samecycle into a newfacet
-    newfacet is a horizon facet with ->normal
-    samecycle facets are simplicial from an apex
-
-  returns:
-    initializes vertex neighbors on first merge
-    samecycle deleted (placed on qh.visible_list)
-    newfacet at end of qh.facet_list
-    deleted vertices on qh.del_vertices
-
-  see:
-    qh_mergefacet()
-    called by qh_mergecycle_all() for multiple, same cycle facets
-
-  design:
-    make vertex neighbors if necessary
-    make ridges for newfacet
-    merge neighbor sets of samecycle into newfacet
-    merge ridges of samecycle into newfacet
-    merge vertex neighbors of samecycle into newfacet
-    make apex of samecycle the apex of newfacet
-    if newfacet wasn't a new facet
-      add its vertices to qh.newvertex_list
-    delete samecycle facets a make newfacet a newfacet
-*/
-void qh_mergecycle(facetT *samecycle, facetT *newfacet) {
-  int traceonce= False, tracerestore= 0;
-  vertexT *apex;
-#ifndef qh_NOtrace
-  facetT *same;
-#endif
-
-  if (newfacet->tricoplanar) {
-    if (!qh TRInormals) {
-      qh_fprintf(qh ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh_ERRqhull, newfacet, NULL);
-    }
-    newfacet->tricoplanar= False;
-    newfacet->keepcentrum= False;
-  }
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  zzinc_(Ztotmerge);
-  if (qh REPORTfreq2 && qh POSTmerging) {
-    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
-      qh_tracemerging();
-  }
-#ifndef qh_NOtrace
-  if (qh TRACEmerge == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace2((qh ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
-        zzval_(Ztotmerge), samecycle->id, newfacet->id));
-  if (newfacet == qh tracefacet) {
-    tracerestore= qh IStracing;
-    qh IStracing= 4;
-    qh_fprintf(qh ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
-               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh furthest_id);
-    traceonce= True;
-  }
-  if (qh IStracing >=4) {
-    qh_fprintf(qh ferr, 8069, "  same cycle:");
-    FORALLsame_cycle_(samecycle)
-      qh_fprintf(qh ferr, 8070, " f%d", same->id);
-    qh_fprintf(qh ferr, 8071, "\n");
-  }
-  if (qh IStracing >=4)
-    qh_errprint("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
-#endif /* !qh_NOtrace */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_makeridges(newfacet);
-  qh_mergecycle_neighbors(samecycle, newfacet);
-  qh_mergecycle_ridges(samecycle, newfacet);
-  qh_mergecycle_vneighbors(samecycle, newfacet);
-  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
-    qh_setaddnth(&newfacet->vertices, 0, apex);  /* apex has last id */
-  if (!newfacet->newfacet)
-    qh_newvertices(newfacet->vertices);
-  qh_mergecycle_facets(samecycle, newfacet);
-  qh_tracemerge(samecycle, newfacet);
-  /* check for degen_redundant_neighbors after qh_forcedmerges() */
-  if (traceonce) {
-    qh_fprintf(qh ferr, 8072, "qh_mergecycle: end of trace facet\n");
-    qh IStracing= tracerestore;
-  }
-} /* mergecycle */
-
-/*---------------------------------
-
-  qh_mergecycle_all( facetlist, wasmerge )
-    merge all samecycles of coplanar facets into horizon
-    don't merge facets with ->mergeridge (these already have ->normal)
-    all facets are simplicial from apex
-    all facet->cycledone == False
-
-  returns:
-    all newfacets merged into coplanar horizon facets
-    deleted vertices on  qh.del_vertices
-    sets wasmerge if any merge
-
-  see:
-    calls qh_mergecycle for multiple, same cycle facets
-
-  design:
-    for each facet on facetlist
-      skip facets with duplicate ridges and normals
-      check that facet is in a samecycle (->mergehorizon)
-      if facet only member of samecycle
-        sets vertex->delridge for all vertices except apex
-        merge facet into horizon
-      else
-        mark all facets in samecycle
-        remove facets with duplicate ridges from samecycle
-        merge samecycle into horizon (deletes facets from facetlist)
-*/
-void qh_mergecycle_all(facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *same, *prev, *horizon;
-  facetT *samecycle= NULL, *nextfacet, *nextsame;
-  vertexT *apex, *vertex, **vertexp;
-  int cycles=0, total=0, facets, nummerge;
-
-  trace2((qh ferr, 2031, "qh_mergecycle_all: begin\n"));
-  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
-    if (facet->normal)
-      continue;
-    if (!facet->mergehorizon) {
-      qh_fprintf(qh ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-    horizon= SETfirstt_(facet->neighbors, facetT);
-    if (facet->f.samecycle == facet) {
-      zinc_(Zonehorizon);
-      /* merge distance done in qh_findhorizon */
-      apex= SETfirstt_(facet->vertices, vertexT);
-      FOREACHvertex_(facet->vertices) {
-        if (vertex != apex)
-          vertex->delridge= True;
-      }
-      horizon->f.newcycle= NULL;
-      qh_mergefacet(facet, horizon, NULL, NULL, qh_MERGEapex);
-    }else {
-      samecycle= facet;
-      facets= 0;
-      prev= facet;
-      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
-           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
-        nextsame= same->f.samecycle;
-        if (same->cycledone || same->visible)
-          qh_infiniteloop(same);
-        same->cycledone= True;
-        if (same->normal) {
-          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
-          same->f.samecycle= NULL;
-        }else {
-          prev= same;
-          facets++;
-        }
-      }
-      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
-        nextfacet= nextfacet->next;
-      horizon->f.newcycle= NULL;
-      qh_mergecycle(samecycle, horizon);
-      nummerge= horizon->nummerge + facets;
-      if (nummerge > qh_MAXnummerge)
-        horizon->nummerge= qh_MAXnummerge;
-      else
-        horizon->nummerge= (short unsigned int)nummerge;
-      zzinc_(Zcyclehorizon);
-      total += facets;
-      zzadd_(Zcyclefacettot, facets);
-      zmax_(Zcyclefacetmax, facets);
-    }
-    cycles++;
-  }
-  if (cycles)
-    *wasmerge= True;
-  trace1((qh ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
-} /* mergecycle_all */
-
-/*---------------------------------
-
-  qh_mergecycle_facets( samecycle, newfacet )
-    finish merge of samecycle into newfacet
-
-  returns:
-    samecycle prepended to visible_list for later deletion and partitioning
-      each facet->f.replace == newfacet
-
-    newfacet moved to end of qh.facet_list
-      makes newfacet a newfacet (get's facet1->id if it was old)
-      sets newfacet->newmerge
-      clears newfacet->center (unless merging into a large facet)
-      clears newfacet->tested and ridge->tested for facet1
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  design:
-    make newfacet a new facet and set its flags
-    move samecycle facets to qh.visible_list for later deletion
-    unless newfacet is large
-      remove its centrum
-*/
-void qh_mergecycle_facets(facetT *samecycle, facetT *newfacet) {
-  facetT *same, *next;
-
-  trace4((qh ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
-  qh_removefacet(newfacet);  /* append as a newfacet to end of qh facet_list */
-  qh_appendfacet(newfacet);
-  newfacet->newfacet= True;
-  newfacet->simplicial= False;
-  newfacet->newmerge= True;
-
-  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
-    next= same->f.samecycle;  /* reused by willdelete */
-    qh_willdelete(same, newfacet);
-  }
-  if (newfacet->center
-      && qh_setsize(newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
-    qh_memfree(newfacet->center, qh normal_size);
-    newfacet->center= NULL;
-  }
-  trace3((qh ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_facets */
-
-/*---------------------------------
-
-  qh_mergecycle_neighbors( samecycle, newfacet )
-    add neighbors for samecycle facets to newfacet
-
-  returns:
-    newfacet with updated neighbors and vice-versa
-    newfacet has ridges
-    all neighbors of newfacet marked with qh.visit_id
-    samecycle facets marked with qh.visit_id-1
-    ridges updated for simplicial neighbors of samecycle with a ridge
-
-  notes:
-    assumes newfacet not in samecycle
-    usually, samecycle facets are new, simplicial facets without internal ridges
-      not so if horizon facet is coplanar to two different samecycles
-
-  see:
-    qh_mergeneighbors()
-
-  design:
-    check samecycle
-    delete neighbors from newfacet that are also in samecycle
-    for each neighbor of a facet in samecycle
-      if neighbor is simplicial
-        if first visit
-          move the neighbor relation to newfacet
-          update facet links for its ridges
-        else
-          make ridges for neighbor
-          remove samecycle reference
-      else
-        update neighbor sets
-*/
-void qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor, **neighborp;
-  int delneighbors= 0, newneighbors= 0;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-
-  samevisitid= ++qh visit_id;
-  FORALLsame_cycle_(samecycle) {
-    if (same->visitid == samevisitid || same->visible)
-      qh_infiniteloop(samecycle);
-    same->visitid= samevisitid;
-  }
-  newfacet->visitid= ++qh visit_id;
-  trace4((qh ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
-  FOREACHneighbor_(newfacet) {
-    if (neighbor->visitid == samevisitid) {
-      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
-      delneighbors++;
-    }else
-      neighbor->visitid= qh visit_id;
-  }
-  qh_setcompact(newfacet->neighbors);
-
-  trace4((qh ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHneighbor_(same) {
-      if (neighbor->visitid == samevisitid)
-        continue;
-      if (neighbor->simplicial) {
-        if (neighbor->visitid != qh visit_id) {
-          qh_setappend(&newfacet->neighbors, neighbor);
-          qh_setreplace(neighbor->neighbors, same, newfacet);
-          newneighbors++;
-          neighbor->visitid= qh visit_id;
-          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
-            if (ridge->top == same) {
-              ridge->top= newfacet;
-              break;
-            }else if (ridge->bottom == same) {
-              ridge->bottom= newfacet;
-              break;
-            }
-          }
-        }else {
-          qh_makeridges(neighbor);
-          qh_setdel(neighbor->neighbors, same);
-          /* same can't be horizon facet for neighbor */
-        }
-      }else { /* non-simplicial neighbor */
-        qh_setdel(neighbor->neighbors, same);
-        if (neighbor->visitid != qh visit_id) {
-          qh_setappend(&neighbor->neighbors, newfacet);
-          qh_setappend(&newfacet->neighbors, neighbor);
-          neighbor->visitid= qh visit_id;
-          newneighbors++;
-        }
-      }
-    }
-  }
-  trace2((qh ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
-             delneighbors, newneighbors));
-} /* mergecycle_neighbors */
-
-/*---------------------------------
-
-  qh_mergecycle_ridges( samecycle, newfacet )
-    add ridges/neighbors for facets in samecycle to newfacet
-    all new/old neighbors of newfacet marked with qh.visit_id
-    facets in samecycle marked with qh.visit_id-1
-    newfacet marked with qh.visit_id
-
-  returns:
-    newfacet has merged ridges
-
-  notes:
-    ridge already updated for simplicial neighbors of samecycle with a ridge
-
-  see:
-    qh_mergeridges()
-    qh_makeridges()
-
-  design:
-    remove ridges between newfacet and samecycle
-    for each facet in samecycle
-      for each ridge in facet
-        update facet pointers in ridge
-        skip ridges processed in qh_mergecycle_neighors
-        free ridges between newfacet and samecycle
-        free ridges between facets of samecycle (on 2nd visit)
-        append remaining ridges to newfacet
-      if simpilicial facet
-        for each neighbor of facet
-          if simplicial facet
-          and not samecycle facet or newfacet
-            make ridge between neighbor and newfacet
-*/
-void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor= NULL;
-  int numold=0, numnew=0;
-  int neighbor_i, neighbor_n;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-  boolT toporient;
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
-  samevisitid= qh visit_id -1;
-  FOREACHridge_(newfacet->ridges) {
-    neighbor= otherfacet_(ridge, newfacet);
-    if (neighbor->visitid == samevisitid)
-      SETref_(ridge)= NULL; /* ridge free'd below */
-  }
-  qh_setcompact(newfacet->ridges);
-
-  trace4((qh ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHridge_(same->ridges) {
-      if (ridge->top == same) {
-        ridge->top= newfacet;
-        neighbor= ridge->bottom;
-      }else if (ridge->bottom == same) {
-        ridge->bottom= newfacet;
-        neighbor= ridge->top;
-      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
-        qh_setappend(&newfacet->ridges, ridge);
-        numold++;  /* already set by qh_mergecycle_neighbors */
-        continue;
-      }else {
-        qh_fprintf(qh ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
-        qh_errexit(qh_ERRqhull, NULL, ridge);
-      }
-      if (neighbor == newfacet) {
-        qh_setfree(&(ridge->vertices));
-        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else if (neighbor->visitid == samevisitid) {
-        qh_setdel(neighbor->ridges, ridge);
-        qh_setfree(&(ridge->vertices));
-        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else {
-        qh_setappend(&newfacet->ridges, ridge);
-        numold++;
-      }
-    }
-    if (same->ridges)
-      qh_settruncate(same->ridges, 0);
-    if (!same->simplicial)
-      continue;
-    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */
-      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
-        ridge= qh_newridge();
-        ridge->vertices= qh_setnew_delnthsorted(same->vertices, qh hull_dim,
-                                                          neighbor_i, 0);
-        toporient= same->toporient ^ (neighbor_i & 0x1);
-        if (toporient) {
-          ridge->top= newfacet;
-          ridge->bottom= neighbor;
-        }else {
-          ridge->top= neighbor;
-          ridge->bottom= newfacet;
-        }
-        qh_setappend(&(newfacet->ridges), ridge);
-        qh_setappend(&(neighbor->ridges), ridge);
-        numnew++;
-      }
-    }
-  }
-
-  trace2((qh ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
-             numold, numnew));
-} /* mergecycle_ridges */
-
-/*---------------------------------
-
-  qh_mergecycle_vneighbors( samecycle, newfacet )
-    create vertex neighbors for newfacet from vertices of facets in samecycle
-    samecycle marked with visitid == qh.visit_id - 1
-
-  returns:
-    newfacet vertices with updated neighbors
-    marks newfacet with qh.visit_id-1
-    deletes vertices that are merged away
-    sets delridge on all vertices (faster here than in mergecycle_ridges)
-
-  see:
-    qh_mergevertex_neighbors()
-
-  design:
-    for each vertex of samecycle facet
-      set vertex->delridge
-      delete samecycle facets from vertex neighbors
-      append newfacet to vertex neighbors
-      if vertex only in newfacet
-        delete it from newfacet
-        add it to qh.del_vertices for later deletion
-*/
-void qh_mergecycle_vneighbors(facetT *samecycle, facetT *newfacet) {
-  facetT *neighbor, **neighborp;
-  unsigned int mergeid;
-  vertexT *vertex, **vertexp, *apex;
-  setT *vertices;
-
-  trace4((qh ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
-  mergeid= qh visit_id - 1;
-  newfacet->visitid= mergeid;
-  vertices= qh_basevertices(samecycle); /* temp */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_setappend(&vertices, apex);
-  FOREACHvertex_(vertices) {
-    vertex->delridge= True;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == mergeid)
-        SETref_(neighbor)= NULL;
-    }
-    qh_setcompact(vertex->neighbors);
-    qh_setappend(&vertex->neighbors, newfacet);
-    if (!SETsecond_(vertex->neighbors)) {
-      zinc_(Zcyclevertex);
-      trace2((qh ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
-        vertex->id, samecycle->id, newfacet->id));
-      qh_setdelsorted(newfacet->vertices, vertex);
-      vertex->deleted= True;
-      qh_setappend(&qh del_vertices, vertex);
-    }
-  }
-  qh_settempfree(&vertices);
-  trace3((qh ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_vneighbors */
-
-/*---------------------------------
-
-  qh_mergefacet( facet1, facet2, mindist, maxdist, mergeapex )
-    merges facet1 into facet2
-    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
-
-  returns:
-    qh.max_outside and qh.min_vertex updated
-    initializes vertex neighbors on first merge
-
-  returns:
-    facet2 contains facet1's vertices, neighbors, and ridges
-      facet2 moved to end of qh.facet_list
-      makes facet2 a newfacet
-      sets facet2->newmerge set
-      clears facet2->center (unless merging into a large facet)
-      clears facet2->tested and ridge->tested for facet1
-
-    facet1 prepended to visible_list for later deletion and partitioning
-      facet1->f.replace == facet2
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  notes:
-    mindist/maxdist may be NULL (only if both NULL)
-    traces merge if fmax_(maxdist,-mindist) > TRACEdist
-
-  see:
-    qh_mergecycle()
-
-  design:
-    trace merge and check for degenerate simplex
-    make ridges for both facets
-    update qh.max_outside, qh.max_vertex, qh.min_vertex
-    update facet2->maxoutside and keepcentrum
-    update facet2->nummerge
-    update tested flags for facet2
-    if facet1 is simplicial
-      merge facet1 into facet2
-    else
-      merge facet1's neighbors into facet2
-      merge facet1's ridges into facet2
-      merge facet1's vertices into facet2
-      merge facet1's vertex neighbors into facet2
-      add facet2's vertices to qh.new_vertexlist
-      unless qh_MERGEapex
-        test facet2 for degenerate or redundant neighbors
-      move facet1 to qh.visible_list for later deletion
-      move facet2 to end of qh.newfacet_list
-*/
-void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
-  boolT traceonce= False;
-  vertexT *vertex, **vertexp;
-  int tracerestore=0, nummerge;
-
-  if (facet1->tricoplanar || facet2->tricoplanar) {
-    if (!qh TRInormals) {
-      qh_fprintf(qh ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit2(qh_ERRqhull, facet1, facet2);
-    }
-    if (facet2->tricoplanar) {
-      facet2->tricoplanar= False;
-      facet2->keepcentrum= False;
-    }
-  }
-  zzinc_(Ztotmerge);
-  if (qh REPORTfreq2 && qh POSTmerging) {
-    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
-      qh_tracemerging();
-  }
-#ifndef qh_NOtrace
-  if (qh build_cnt >= qh RERUN) {
-    if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {
-      tracerestore= 0;
-      qh IStracing= qh TRACElevel;
-      traceonce= True;
-      qh_fprintf(qh ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
-             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);
-    }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {
-      tracerestore= qh IStracing;
-      qh IStracing= 4;
-      traceonce= True;
-      qh_fprintf(qh ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
-                 zzval_(Ztotmerge), qh tracefacet_id,  qh furthest_id);
-    }
-  }
-  if (qh IStracing >= 2) {
-    realT mergemin= -2;
-    realT mergemax= -2;
-
-    if (mindist) {
-      mergemin= *mindist;
-      mergemax= *maxdist;
-    }
-    qh_fprintf(qh ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
-    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
-  }
-#endif /* !qh_NOtrace */
-  if (facet1 == facet2 || facet1->visible || facet2->visible) {
-    qh_fprintf(qh ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
-             facet1->id, facet2->id);
-    qh_errexit2(qh_ERRqhull, facet1, facet2);
-  }
-  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
-    qh_fprintf(qh ferr, 6227, "\n\
-qhull precision error: Only %d facets remain.  Can not merge another\n\
-pair.  The input is too degenerate or the convexity constraints are\n\
-too strong.\n", qh hull_dim+1);
-    if (qh hull_dim >= 5 && !qh MERGEexact)
-      qh_fprintf(qh ferr, 8079, "Option 'Qx' may avoid this problem.\n");
-    qh_errexit(qh_ERRprec, NULL, NULL);
-  }
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  qh_makeridges(facet1);
-  qh_makeridges(facet2);
-  if (qh IStracing >=4)
-    qh_errprint("MERGING", facet1, facet2, NULL, NULL);
-  if (mindist) {
-    maximize_(qh max_outside, *maxdist);
-    maximize_(qh max_vertex, *maxdist);
-#if qh_MAXoutside
-    maximize_(facet2->maxoutside, *maxdist);
-#endif
-    minimize_(qh min_vertex, *mindist);
-    if (!facet2->keepcentrum
-    && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidefacet);
-    }
-  }
-  nummerge= facet1->nummerge + facet2->nummerge + 1;
-  if (nummerge >= qh_MAXnummerge)
-    facet2->nummerge= qh_MAXnummerge;
-  else
-    facet2->nummerge= (short unsigned int)nummerge;
-  facet2->newmerge= True;
-  facet2->dupridge= False;
-  qh_updatetested(facet1, facet2);
-  if (qh hull_dim > 2 && qh_setsize(facet1->vertices) == qh hull_dim)
-    qh_mergesimplex(facet1, facet2, mergeapex);
-  else {
-    qh vertex_visit++;
-    FOREACHvertex_(facet2->vertices)
-      vertex->visitid= qh vertex_visit;
-    if (qh hull_dim == 2)
-      qh_mergefacet2d(facet1, facet2);
-    else {
-      qh_mergeneighbors(facet1, facet2);
-      qh_mergevertices(facet1->vertices, &facet2->vertices);
-    }
-    qh_mergeridges(facet1, facet2);
-    qh_mergevertex_neighbors(facet1, facet2);
-    if (!facet2->newfacet)
-      qh_newvertices(facet2->vertices);
-  }
-  if (!mergeapex)
-    qh_degen_redundant_neighbors(facet2, facet1);
-  if (facet2->coplanar || !facet2->newfacet) {
-    zinc_(Zmergeintohorizon);
-  }else if (!facet1->newfacet && facet2->newfacet) {
-    zinc_(Zmergehorizon);
-  }else {
-    zinc_(Zmergenew);
-  }
-  qh_willdelete(facet1, facet2);
-  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */
-  qh_appendfacet(facet2);
-  facet2->newfacet= True;
-  facet2->tested= False;
-  qh_tracemerge(facet1, facet2);
-  if (traceonce) {
-    qh_fprintf(qh ferr, 8080, "qh_mergefacet: end of wide tracing\n");
-    qh IStracing= tracerestore;
-  }
-} /* mergefacet */
-
-
-/*---------------------------------
-
-  qh_mergefacet2d( facet1, facet2 )
-    in 2d, merges neighbors and vertices of facet1 into facet2
-
-  returns:
-    build ridges for neighbors if necessary
-    facet2 looks like a simplicial facet except for centrum, ridges
-      neighbors are opposite the corresponding vertex
-      maintains orientation of facet2
-
-  notes:
-    qh_mergefacet() retains non-simplicial structures
-      they are not needed in 2d, but later routines may use them
-    preserves qh.vertex_visit for qh_mergevertex_neighbors()
-
-  design:
-    get vertices and neighbors
-    determine new vertices and neighbors
-    set new vertices and neighbors and adjust orientation
-    make ridges for new neighbor if needed
-*/
-void qh_mergefacet2d(facetT *facet1, facetT *facet2) {
-  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
-  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
-
-  vertex1A= SETfirstt_(facet1->vertices, vertexT);
-  vertex1B= SETsecondt_(facet1->vertices, vertexT);
-  vertex2A= SETfirstt_(facet2->vertices, vertexT);
-  vertex2B= SETsecondt_(facet2->vertices, vertexT);
-  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
-  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
-  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
-  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
-  if (vertex1A == vertex2A) {
-    vertexA= vertex1B;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1A;
-  }else if (vertex1A == vertex2B) {
-    vertexA= vertex1B;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1A;
-  }else if (vertex1B == vertex2A) {
-    vertexA= vertex1A;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1B;
-  }else { /* 1B == 2B */
-    vertexA= vertex1A;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1B;
-  }
-  /* vertexB always from facet2, neighborB always from facet1 */
-  if (vertexA->id > vertexB->id) {
-    SETfirst_(facet2->vertices)= vertexA;
-    SETsecond_(facet2->vertices)= vertexB;
-    if (vertexB == vertex2A)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborA;
-    SETsecond_(facet2->neighbors)= neighborB;
-  }else {
-    SETfirst_(facet2->vertices)= vertexB;
-    SETsecond_(facet2->vertices)= vertexA;
-    if (vertexB == vertex2B)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborB;
-    SETsecond_(facet2->neighbors)= neighborA;
-  }
-  qh_makeridges(neighborB);
-  qh_setreplace(neighborB->neighbors, facet1, facet2);
-  trace4((qh ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
-       vertexA->id, neighborB->id, facet1->id, facet2->id));
-} /* mergefacet2d */
-
-
-/*---------------------------------
-
-  qh_mergeneighbors( facet1, facet2 )
-    merges the neighbors of facet1 into facet2
-
-  see:
-    qh_mergecycle_neighbors()
-
-  design:
-    for each neighbor of facet1
-      if neighbor is also a neighbor of facet2
-        if neighbor is simpilicial
-          make ridges for later deletion as a degenerate facet
-        update its neighbor set
-      else
-        move the neighbor relation to facet2
-    remove the neighbor relation for facet1 and facet2
-*/
-void qh_mergeneighbors(facetT *facet1, facetT *facet2) {
-  facetT *neighbor, **neighborp;
-
-  trace4((qh ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  qh visit_id++;
-  FOREACHneighbor_(facet2) {
-    neighbor->visitid= qh visit_id;
-  }
-  FOREACHneighbor_(facet1) {
-    if (neighbor->visitid == qh visit_id) {
-      if (neighbor->simplicial)    /* is degen, needs ridges */
-        qh_makeridges(neighbor);
-      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
-        qh_setdel(neighbor->neighbors, facet1);
-      else {
-        qh_setdel(neighbor->neighbors, facet2);
-        qh_setreplace(neighbor->neighbors, facet1, facet2);
-      }
-    }else if (neighbor != facet2) {
-      qh_setappend(&(facet2->neighbors), neighbor);
-      qh_setreplace(neighbor->neighbors, facet1, facet2);
-    }
-  }
-  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
-  qh_setdel(facet2->neighbors, facet1);
-} /* mergeneighbors */
-
-
-/*---------------------------------
-
-  qh_mergeridges( facet1, facet2 )
-    merges the ridge set of facet1 into facet2
-
-  returns:
-    may delete all ridges for a vertex
-    sets vertex->delridge on deleted ridges
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    delete ridges between facet1 and facet2
-      mark (delridge) vertices on these ridges for later testing
-    for each remaining ridge
-      rename facet1 to facet2
-*/
-void qh_mergeridges(facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-
-  trace4((qh ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
-          facet1->id, facet2->id));
-  FOREACHridge_(facet2->ridges) {
-    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
-      FOREACHvertex_(ridge->vertices)
-        vertex->delridge= True;
-      qh_delridge(ridge);  /* expensive in high-d, could rebuild */
-      ridgep--; /*repeat*/
-    }
-  }
-  FOREACHridge_(facet1->ridges) {
-    if (ridge->top == facet1)
-      ridge->top= facet2;
-    else
-      ridge->bottom= facet2;
-    qh_setappend(&(facet2->ridges), ridge);
-  }
-} /* mergeridges */
-
-
-/*---------------------------------
-
-  qh_mergesimplex( facet1, facet2, mergeapex )
-    merge simplicial facet1 into facet2
-    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
-      vertex id is latest (most recently created)
-    facet1 may be contained in facet2
-    ridges exist for both facets
-
-  returns:
-    facet2 with updated vertices, ridges, neighbors
-    updated neighbors for facet1's vertices
-    facet1 not deleted
-    sets vertex->delridge on deleted ridges
-
-  notes:
-    special case code since this is the most common merge
-    called from qh_mergefacet()
-
-  design:
-    if qh_MERGEapex
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to facet2
-    else
-      for each ridge between facet1 and facet2
-        set vertex->delridge
-      determine the apex for facet1 (i.e., vertex to be merged)
-      unless apex already in facet2
-        insert apex into vertices for facet2
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to qh.new_vertexlist if necessary
-      for each vertex of facet1
-        if apex
-          rename facet1 to facet2 in its vertex neighbors
-        else
-          delete facet1 from vertex neighors
-          if only in facet2
-            add vertex to qh.del_vertices for later deletion
-      for each ridge of facet1
-        delete ridges between facet1 and facet2
-        append other ridges to facet2 after renaming facet to facet2
-*/
-void qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex) {
-  vertexT *vertex, **vertexp, *apex;
-  ridgeT *ridge, **ridgep;
-  boolT issubset= False;
-  int vertex_i= -1, vertex_n;
-  facetT *neighbor, **neighborp, *otherfacet;
-
-  if (mergeapex) {
-    if (!facet2->newfacet)
-      qh_newvertices(facet2->vertices);  /* apex is new */
-    apex= SETfirstt_(facet1->vertices, vertexT);
-    if (SETfirstt_(facet2->vertices, vertexT) != apex)
-      qh_setaddnth(&facet2->vertices, 0, apex);  /* apex has last id */
-    else
-      issubset= True;
-  }else {
-    zinc_(Zmergesimplex);
-    FOREACHvertex_(facet1->vertices)
-      vertex->seen= False;
-    FOREACHridge_(facet1->ridges) {
-      if (otherfacet_(ridge, facet1) == facet2) {
-        FOREACHvertex_(ridge->vertices) {
-          vertex->seen= True;
-          vertex->delridge= True;
-        }
-        break;
-      }
-    }
-    FOREACHvertex_(facet1->vertices) {
-      if (!vertex->seen)
-        break;  /* must occur */
-    }
-    apex= vertex;
-    trace4((qh ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
-          apex->id, facet1->id, facet2->id));
-    FOREACHvertex_i_(facet2->vertices) {
-      if (vertex->id < apex->id) {
-        break;
-      }else if (vertex->id == apex->id) {
-        issubset= True;
-        break;
-      }
-    }
-    if (!issubset)
-      qh_setaddnth(&facet2->vertices, vertex_i, apex);
-    if (!facet2->newfacet)
-      qh_newvertices(facet2->vertices);
-    else if (!apex->newlist) {
-      qh_removevertex(apex);
-      qh_appendvertex(apex);
-    }
-  }
-  trace4((qh ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
-          facet1->id));
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex == apex && !issubset)
-      qh_setreplace(vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(vertex, facet1, facet2);
-    }
-  }
-  trace4((qh ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
-          facet1->id, facet2->id));
-  qh visit_id++;
-  FOREACHneighbor_(facet2)
-    neighbor->visitid= qh visit_id;
-  FOREACHridge_(facet1->ridges) {
-    otherfacet= otherfacet_(ridge, facet1);
-    if (otherfacet == facet2) {
-      qh_setdel(facet2->ridges, ridge);
-      qh_setfree(&(ridge->vertices));
-      qh_memfree(ridge, (int)sizeof(ridgeT));
-      qh_setdel(facet2->neighbors, facet1);
-    }else {
-      qh_setappend(&facet2->ridges, ridge);
-      if (otherfacet->visitid != qh visit_id) {
-        qh_setappend(&facet2->neighbors, otherfacet);
-        qh_setreplace(otherfacet->neighbors, facet1, facet2);
-        otherfacet->visitid= qh visit_id;
-      }else {
-        if (otherfacet->simplicial)    /* is degen, needs ridges */
-          qh_makeridges(otherfacet);
-        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
-          qh_setdel(otherfacet->neighbors, facet1);
-        else {   /*keep newfacet->neighbors->horizon*/
-          qh_setdel(otherfacet->neighbors, facet2);
-          qh_setreplace(otherfacet->neighbors, facet1, facet2);
-        }
-      }
-      if (ridge->top == facet1) /* wait until after qh_makeridges */
-        ridge->top= facet2;
-      else
-        ridge->bottom= facet2;
-    }
-  }
-  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
-  trace3((qh ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
-          facet1->id, getid_(apex), facet2->id));
-} /* mergesimplex */
-
-/*---------------------------------
-
-  qh_mergevertex_del( vertex, facet1, facet2 )
-    delete a vertex because of merging facet1 into facet2
-
-  returns:
-    deletes vertex from facet2
-    adds vertex to qh.del_vertices for later deletion
-*/
-void qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2) {
-
-  zinc_(Zmergevertex);
-  trace2((qh ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
-          vertex->id, facet1->id, facet2->id));
-  qh_setdelsorted(facet2->vertices, vertex);
-  vertex->deleted= True;
-  qh_setappend(&qh del_vertices, vertex);
-} /* mergevertex_del */
-
-/*---------------------------------
-
-  qh_mergevertex_neighbors( facet1, facet2 )
-    merge the vertex neighbors of facet1 to facet2
-
-  returns:
-    if vertex is current qh.vertex_visit
-      deletes facet1 from vertex->neighbors
-    else
-      renames facet1 to facet2 in vertex->neighbors
-    deletes vertices if only one neighbor
-
-  notes:
-    assumes vertex neighbor sets are good
-*/
-void qh_mergevertex_neighbors(facetT *facet1, facetT *facet2) {
-  vertexT *vertex, **vertexp;
-
-  trace4((qh ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  if (qh tracevertex) {
-    qh_fprintf(qh ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
-             facet1->id, facet2->id, qh furthest_id, qh tracevertex->neighbors->e[0].p);
-    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
-  }
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex->visitid != qh vertex_visit)
-      qh_setreplace(vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(vertex, facet1, facet2);
-    }
-  }
-  if (qh tracevertex)
-    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
-} /* mergevertex_neighbors */
-
-
-/*---------------------------------
-
-  qh_mergevertices( vertices1, vertices2 )
-    merges the vertex set of facet1 into facet2
-
-  returns:
-    replaces vertices2 with merged set
-    preserves vertex_visit for qh_mergevertex_neighbors
-    updates qh.newvertex_list
-
-  design:
-    create a merged set of both vertices (in inverse id order)
-*/
-void qh_mergevertices(setT *vertices1, setT **vertices2) {
-  int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
-  setT *mergedvertices;
-  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
-
-  mergedvertices= qh_settemp(newsize);
-  FOREACHvertex_(vertices1) {
-    if (!*vertex2 || vertex->id > (*vertex2)->id)
-      qh_setappend(&mergedvertices, vertex);
-    else {
-      while (*vertex2 && (*vertex2)->id > vertex->id)
-        qh_setappend(&mergedvertices, *vertex2++);
-      if (!*vertex2 || (*vertex2)->id < vertex->id)
-        qh_setappend(&mergedvertices, vertex);
-      else
-        qh_setappend(&mergedvertices, *vertex2++);
-    }
-  }
-  while (*vertex2)
-    qh_setappend(&mergedvertices, *vertex2++);
-  if (newsize < qh_setsize(mergedvertices)) {
-    qh_fprintf(qh ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(vertices2);
-  *vertices2= mergedvertices;
-  qh_settemppop();
-} /* mergevertices */
-
-
-/*---------------------------------
-
-  qh_neighbor_intersections( vertex )
-    return intersection of all vertices in vertex->neighbors except for vertex
-
-  returns:
-    returns temporary set of vertices
-    does not include vertex
-    NULL if a neighbor is simplicial
-    NULL if empty set
-
-  notes:
-    used for renaming vertices
-
-  design:
-    initialize the intersection set with vertices of the first two neighbors
-    delete vertex from the intersection
-    for each remaining neighbor
-      intersect its vertex set with the intersection set
-      return NULL if empty
-    return the intersection set
-*/
-setT *qh_neighbor_intersections(vertexT *vertex) {
-  facetT *neighbor, **neighborp, *neighborA, *neighborB;
-  setT *intersect;
-  int neighbor_i, neighbor_n;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->simplicial)
-      return NULL;
-  }
-  neighborA= SETfirstt_(vertex->neighbors, facetT);
-  neighborB= SETsecondt_(vertex->neighbors, facetT);
-  zinc_(Zintersectnum);
-  if (!neighborA)
-    return NULL;
-  if (!neighborB)
-    intersect= qh_setcopy(neighborA->vertices, 0);
-  else
-    intersect= qh_vertexintersect_new(neighborA->vertices, neighborB->vertices);
-  qh_settemppush(intersect);
-  qh_setdelsorted(intersect, vertex);
-  FOREACHneighbor_i_(vertex) {
-    if (neighbor_i >= 2) {
-      zinc_(Zintersectnum);
-      qh_vertexintersect(&intersect, neighbor->vertices);
-      if (!SETfirst_(intersect)) {
-        zinc_(Zintersectfail);
-        qh_settempfree(&intersect);
-        return NULL;
-      }
-    }
-  }
-  trace3((qh ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
-          qh_setsize(intersect), vertex->id));
-  return intersect;
-} /* neighbor_intersections */
-
-/*---------------------------------
-
-  qh_newvertices( vertices )
-    add vertices to end of qh.vertex_list (marks as new vertices)
-
-  returns:
-    vertices on qh.newvertex_list
-    vertex->newlist set
-*/
-void qh_newvertices(setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(vertex);
-      qh_appendvertex(vertex);
-    }
-  }
-} /* newvertices */
-
-/*---------------------------------
-
-  qh_reducevertices()
-    reduce extra vertices, shared vertices, and redundant vertices
-    facet->newmerge is set if merged since last call
-    if !qh.MERGEvertices, only removes extra vertices
-
-  returns:
-    True if also merged degen_redundant facets
-    vertices are renamed if possible
-    clears facet->newmerge and vertex->delridge
-
-  notes:
-    ignored if 2-d
-
-  design:
-    merge any degenerate or redundant facets
-    for each newly merged facet
-      remove extra vertices
-    if qh.MERGEvertices
-      for each newly merged facet
-        for each vertex
-          if vertex was on a deleted ridge
-            rename vertex if it is shared
-      remove delridge flag from new vertices
-*/
-boolT qh_reducevertices(void) {
-  int numshare=0, numrename= 0;
-  boolT degenredun= False;
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  if (qh hull_dim == 2)
-    return False;
-  if (qh_merge_degenredundant())
-    degenredun= True;
- LABELrestart:
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      if (!qh MERGEvertices)
-        newfacet->newmerge= False;
-      qh_remove_extravertices(newfacet);
-    }
-  }
-  if (!qh MERGEvertices)
-    return False;
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      newfacet->newmerge= False;
-      FOREACHvertex_(newfacet->vertices) {
-        if (vertex->delridge) {
-          if (qh_rename_sharedvertex(vertex, newfacet)) {
-            numshare++;
-            vertexp--; /* repeat since deleted vertex */
-          }
-        }
-      }
-    }
-  }
-  FORALLvertex_(qh newvertex_list) {
-    if (vertex->delridge && !vertex->deleted) {
-      vertex->delridge= False;
-      if (qh hull_dim >= 4 && qh_redundant_vertex(vertex)) {
-        numrename++;
-        if (qh_merge_degenredundant()) {
-          degenredun= True;
-          goto LABELrestart;
-        }
-      }
-    }
-  }
-  trace1((qh ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
-          numshare, numrename, degenredun));
-  return degenredun;
-} /* reducevertices */
-
-/*---------------------------------
-
-  qh_redundant_vertex( vertex )
-    detect and rename a redundant vertex
-    vertices have full vertex->neighbors
-
-  returns:
-    returns true if find a redundant vertex
-      deletes vertex(vertex->deleted)
-
-  notes:
-    only needed if vertex->delridge and hull_dim >= 4
-    may add degenerate facets to qh.facet_mergeset
-    doesn't change vertex->neighbors or create redundant facets
-
-  design:
-    intersect vertices of all facet neighbors of vertex
-    determine ridges for these vertices
-    if find a new vertex for vertex amoung these ridges and vertices
-      rename vertex to the new vertex
-*/
-vertexT *qh_redundant_vertex(vertexT *vertex) {
-  vertexT *newvertex= NULL;
-  setT *vertices, *ridges;
-
-  trace3((qh ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
-  if ((vertices= qh_neighbor_intersections(vertex))) {
-    ridges= qh_vertexridges(vertex);
-    if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
-      qh_renamevertex(vertex, newvertex, ridges, NULL, NULL);
-    qh_settempfree(&ridges);
-    qh_settempfree(&vertices);
-  }
-  return newvertex;
-} /* redundant_vertex */
-
-/*---------------------------------
-
-  qh_remove_extravertices( facet )
-    remove extra vertices from non-simplicial facets
-
-  returns:
-    returns True if it finds them
-
-  design:
-    for each vertex in facet
-      if vertex not in a ridge (i.e., no longer used)
-        delete vertex from facet
-        delete facet from vertice's neighbors
-        unless vertex in another facet
-          add vertex to qh.del_vertices for later deletion
-*/
-boolT qh_remove_extravertices(facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  boolT foundrem= False;
-
-  trace4((qh ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
-          facet->id));
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHridge_(facet->ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->seen= True;
-  }
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      foundrem= True;
-      zinc_(Zremvertex);
-      qh_setdelsorted(facet->vertices, vertex);
-      qh_setdel(vertex->neighbors, facet);
-      if (!qh_setsize(vertex->neighbors)) {
-        vertex->deleted= True;
-        qh_setappend(&qh del_vertices, vertex);
-        zinc_(Zremvertexdel);
-        trace2((qh ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
-      }else
-        trace3((qh ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
-      vertexp--; /*repeat*/
-    }
-  }
-  return foundrem;
-} /* remove_extravertices */
-
-/*---------------------------------
-
-  qh_rename_sharedvertex( vertex, facet )
-    detect and rename if shared vertex in facet
-    vertices have full ->neighbors
-
-  returns:
-    newvertex or NULL
-    the vertex may still exist in other facets (i.e., a neighbor was pinched)
-    does not change facet->neighbors
-    updates vertex->neighbors
-
-  notes:
-    a shared vertex for a facet is only in ridges to one neighbor
-    this may undo a pinched facet
-
-    it does not catch pinches involving multiple facets.  These appear
-      to be difficult to detect, since an exhaustive search is too expensive.
-
-  design:
-    if vertex only has two neighbors
-      determine the ridges that contain the vertex
-      determine the vertices shared by both neighbors
-      if can find a new vertex in this set
-        rename the vertex to the new vertex
-*/
-vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet) {
-  facetT *neighbor, **neighborp, *neighborA= NULL;
-  setT *vertices, *ridges;
-  vertexT *newvertex;
-
-  if (qh_setsize(vertex->neighbors) == 2) {
-    neighborA= SETfirstt_(vertex->neighbors, facetT);
-    if (neighborA == facet)
-      neighborA= SETsecondt_(vertex->neighbors, facetT);
-  }else if (qh hull_dim == 3)
-    return NULL;
-  else {
-    qh visit_id++;
-    FOREACHneighbor_(facet)
-      neighbor->visitid= qh visit_id;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == qh visit_id) {
-        if (neighborA)
-          return NULL;
-        neighborA= neighbor;
-      }
-    }
-    if (!neighborA) {
-      qh_fprintf(qh ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
-        vertex->id, facet->id);
-      qh_errprint("ERRONEOUS", facet, NULL, NULL, vertex);
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-  }
-  /* the vertex is shared by facet and neighborA */
-  ridges= qh_settemp(qh TEMPsize);
-  neighborA->visitid= ++qh visit_id;
-  qh_vertexridges_facet(vertex, facet, &ridges);
-  trace2((qh ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
-    qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize(ridges), neighborA->id));
-  zinc_(Zintersectnum);
-  vertices= qh_vertexintersect_new(facet->vertices, neighborA->vertices);
-  qh_setdel(vertices, vertex);
-  qh_settemppush(vertices);
-  if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
-    qh_renamevertex(vertex, newvertex, ridges, facet, neighborA);
-  qh_settempfree(&vertices);
-  qh_settempfree(&ridges);
-  return newvertex;
-} /* rename_sharedvertex */
-
-/*---------------------------------
-
-  qh_renameridgevertex( ridge, oldvertex, newvertex )
-    renames oldvertex as newvertex in ridge
-
-  returns:
-
-  design:
-    delete oldvertex from ridge
-    if newvertex already in ridge
-      copy ridge->noconvex to another ridge if possible
-      delete the ridge
-    else
-      insert newvertex into the ridge
-      adjust the ridge's orientation
-*/
-void qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
-  int nth= 0, oldnth;
-  facetT *temp;
-  vertexT *vertex, **vertexp;
-
-  oldnth= qh_setindex(ridge->vertices, oldvertex);
-  qh_setdelnthsorted(ridge->vertices, oldnth);
-  FOREACHvertex_(ridge->vertices) {
-    if (vertex == newvertex) {
-      zinc_(Zdelridge);
-      if (ridge->nonconvex) /* only one ridge has nonconvex set */
-        qh_copynonconvex(ridge);
-      trace2((qh ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
-        ridge->id, oldvertex->id, newvertex->id));
-      qh_delridge(ridge);
-      return;
-    }
-    if (vertex->id < newvertex->id)
-      break;
-    nth++;
-  }
-  qh_setaddnth(&ridge->vertices, nth, newvertex);
-  if (abs(oldnth - nth)%2) {
-    trace3((qh ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
-            ridge->id));
-    temp= ridge->top;
-    ridge->top= ridge->bottom;
-    ridge->bottom= temp;
-  }
-} /* renameridgevertex */
-
-
-/*---------------------------------
-
-  qh_renamevertex( oldvertex, newvertex, ridges, oldfacet, neighborA )
-    renames oldvertex as newvertex in ridges
-    gives oldfacet/neighborA if oldvertex is shared between two facets
-
-  returns:
-    oldvertex may still exist afterwards
-
-
-  notes:
-    can not change neighbors of newvertex (since it's a subset)
-
-  design:
-    for each ridge in ridges
-      rename oldvertex to newvertex and delete degenerate ridges
-    if oldfacet not defined
-      for each neighbor of oldvertex
-        delete oldvertex from neighbor's vertices
-        remove extra vertices from neighbor
-      add oldvertex to qh.del_vertices
-    else if oldvertex only between oldfacet and neighborA
-      delete oldvertex from oldfacet and neighborA
-      add oldvertex to qh.del_vertices
-    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
-      delete oldvertex from oldfacet
-      delete oldfacet from oldvertice's neighbors
-      remove extra vertices (e.g., oldvertex) from neighborA
-*/
-void qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  boolT istrace= False;
-
-  if (qh IStracing >= 2 || oldvertex->id == qh tracevertex_id ||
-        newvertex->id == qh tracevertex_id)
-    istrace= True;
-  FOREACHridge_(ridges)
-    qh_renameridgevertex(ridge, oldvertex, newvertex);
-  if (!oldfacet) {
-    zinc_(Zrenameall);
-    if (istrace)
-      qh_fprintf(qh ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
-               oldvertex->id, newvertex->id);
-    FOREACHneighbor_(oldvertex) {
-      qh_maydropneighbor(neighbor);
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-      if (qh_remove_extravertices(neighbor))
-        neighborp--; /* neighbor may be deleted */
-    }
-    if (!oldvertex->deleted) {
-      oldvertex->deleted= True;
-      qh_setappend(&qh del_vertices, oldvertex);
-    }
-  }else if (qh_setsize(oldvertex->neighbors) == 2) {
-    zinc_(Zrenameshare);
-    if (istrace)
-      qh_fprintf(qh ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id);
-    FOREACHneighbor_(oldvertex)
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-    oldvertex->deleted= True;
-    qh_setappend(&qh del_vertices, oldvertex);
-  }else {
-    zinc_(Zrenamepinch);
-    if (istrace || qh IStracing)
-      qh_fprintf(qh ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
-    qh_setdelsorted(oldfacet->vertices, oldvertex);
-    qh_setdel(oldvertex->neighbors, oldfacet);
-    qh_remove_extravertices(neighborA);
-  }
-} /* renamevertex */
-
-
-/*---------------------------------
-
-  qh_test_appendmerge( facet, neighbor )
-    tests facet/neighbor for convexity
-    appends to mergeset if non-convex
-    if pre-merging,
-      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
-
-  returns:
-    true if appends facet/neighbor to mergeset
-    sets facet->center as needed
-    does not change facet->seen
-
-  design:
-    if qh.cos_max is defined
-      if the angle between facet normals is too shallow
-        append an angle-coplanar merge to qh.mergeset
-        return True
-    make facet's centrum if needed
-    if facet's centrum is above the neighbor
-      set isconcave
-    else
-      if facet's centrum is not below the neighbor
-        set iscoplanar
-      make neighbor's centrum if needed
-      if neighbor's centrum is above the facet
-        set isconcave
-      else if neighbor's centrum is not below the facet
-        set iscoplanar
-   if isconcave or iscoplanar
-     get angle if needed
-     append concave or coplanar merge to qh.mergeset
-*/
-boolT qh_test_appendmerge(facetT *facet, facetT *neighbor) {
-  realT dist, dist2= -REALmax, angle= -REALmax;
-  boolT isconcave= False, iscoplanar= False, okangle= False;
-
-  if (qh SKIPconvex && !qh POSTmerging)
-    return False;
-  if ((!qh MERGEexact || qh POSTmerging) && qh cos_max < REALmax/2) {
-    angle= qh_getangle(facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-    if (angle > qh cos_max) {
-      zinc_(Zcoplanarangle);
-      qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
-      trace2((qh ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
-         angle, facet->id, neighbor->id));
-      return True;
-    }else
-      okangle= True;
-  }
-  if (!facet->center)
-    facet->center= qh_getcentrum(facet);
-  zzinc_(Zcentrumtests);
-  qh_distplane(facet->center, neighbor, &dist);
-  if (dist > qh centrum_radius)
-    isconcave= True;
-  else {
-    if (dist > -qh centrum_radius)
-      iscoplanar= True;
-    if (!neighbor->center)
-      neighbor->center= qh_getcentrum(neighbor);
-    zzinc_(Zcentrumtests);
-    qh_distplane(neighbor->center, facet, &dist2);
-    if (dist2 > qh centrum_radius)
-      isconcave= True;
-    else if (!iscoplanar && dist2 > -qh centrum_radius)
-      iscoplanar= True;
-  }
-  if (!isconcave && (!iscoplanar || (qh MERGEexact && !qh POSTmerging)))
-    return False;
-  if (!okangle && qh ANGLEmerge) {
-    angle= qh_getangle(facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-  }
-  if (isconcave) {
-    zinc_(Zconcaveridge);
-    if (qh ANGLEmerge)
-      angle += qh_ANGLEconcave + 0.5;
-    qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
-    trace0((qh ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
-           facet->id, neighbor->id, dist, dist2, angle, qh furthest_id));
-  }else /* iscoplanar */ {
-    zinc_(Zcoplanarcentrum);
-    qh_appendmergeset(facet, neighbor, MRGcoplanar, &angle);
-    trace2((qh ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
-              facet->id, neighbor->id, dist, dist2, angle));
-  }
-  return True;
-} /* test_appendmerge */
-
-/*---------------------------------
-
-  qh_test_vneighbors()
-    test vertex neighbors for convexity
-    tests all facets on qh.newfacet_list
-
-  returns:
-    true if non-convex vneighbors appended to qh.facet_mergeset
-    initializes vertex neighbors if needed
-
-  notes:
-    assumes all facet neighbors have been tested
-    this can be expensive
-    this does not guarantee that a centrum is below all facets
-      but it is unlikely
-    uses qh.visit_id
-
-  design:
-    build vertex neighbors if necessary
-    for all new facets
-      for all vertices
-        for each unvisited facet neighbor of the vertex
-          test new facet and neighbor for convexity
-*/
-boolT qh_test_vneighbors(void /* qh.newfacet_list */) {
-  facetT *newfacet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-
-  trace1((qh ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  FORALLnew_facets
-    newfacet->seen= False;
-  FORALLnew_facets {
-    newfacet->seen= True;
-    newfacet->visitid= qh visit_id++;
-    FOREACHneighbor_(newfacet)
-      newfacet->visitid= qh visit_id;
-    FOREACHvertex_(newfacet->vertices) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->seen || neighbor->visitid == qh visit_id)
-          continue;
-        if (qh_test_appendmerge(newfacet, neighbor))
-          nummerges++;
-      }
-    }
-  }
-  zadd_(Ztestvneighbor, nummerges);
-  trace1((qh ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
-           nummerges));
-  return (nummerges > 0);
-} /* test_vneighbors */
-
-/*---------------------------------
-
-  qh_tracemerge( facet1, facet2 )
-    print trace message after merge
-*/
-void qh_tracemerge(facetT *facet1, facetT *facet2) {
-  boolT waserror= False;
-
-#ifndef qh_NOtrace
-  if (qh IStracing >= 4)
-    qh_errprint("MERGED", facet2, NULL, NULL, NULL);
-  if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
-    qh_fprintf(qh ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh furthest_id);
-    if (facet2 != qh tracefacet)
-      qh_errprint("TRACE", qh tracefacet,
-        (qh tracevertex && qh tracevertex->neighbors) ?
-           SETfirstt_(qh tracevertex->neighbors, facetT) : NULL,
-        NULL, qh tracevertex);
-  }
-  if (qh tracevertex) {
-    if (qh tracevertex->deleted)
-      qh_fprintf(qh ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
-            qh furthest_id);
-    else
-      qh_checkvertex(qh tracevertex);
-  }
-  if (qh tracefacet) {
-    qh_checkfacet(qh tracefacet, True, &waserror);
-    if (waserror)
-      qh_errexit(qh_ERRqhull, qh tracefacet, NULL);
-  }
-#endif /* !qh_NOtrace */
-  if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
-    qh_checkfacet(facet2, True, &waserror);
-    if (waserror)
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-} /* tracemerge */
-
-/*---------------------------------
-
-  qh_tracemerging()
-    print trace message during POSTmerging
-
-  returns:
-    updates qh.mergereport
-
-  notes:
-    called from qh_mergecycle() and qh_mergefacet()
-
-  see:
-    qh_buildtracing()
-*/
-void qh_tracemerging(void) {
-  realT cpu;
-  int total;
-  time_t timedata;
-  struct tm *tp;
-
-  qh mergereport= zzval_(Ztotmerge);
-  time(&timedata);
-  tp= localtime(&timedata);
-  cpu= qh_CPUclock;
-  cpu /= qh_SECticks;
-  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  qh_fprintf(qh ferr, 8087, "\n\
-At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
-  contains %d facets and %d vertices.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
-      total, qh num_facets - qh num_visible,
-      qh num_vertices-qh_setsize(qh del_vertices));
-} /* tracemerging */
-
-/*---------------------------------
-
-  qh_updatetested( facet1, facet2 )
-    clear facet2->tested and facet1->ridge->tested for merge
-
-  returns:
-    deletes facet2->center unless it's already large
-      if so, clears facet2->ridge->tested
-
-  design:
-    clear facet2->tested
-    clear ridge->tested for facet1's ridges
-    if facet2 has a centrum
-      if facet2 is large
-        set facet2->keepcentrum
-      else if facet2 has 3 vertices due to many merges, or not large and post merging
-        clear facet2->keepcentrum
-      unless facet2->keepcentrum
-        clear facet2->center to recompute centrum later
-        clear ridge->tested for facet2's ridges
-*/
-void qh_updatetested(facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  int size;
-
-  facet2->tested= False;
-  FOREACHridge_(facet1->ridges)
-    ridge->tested= False;
-  if (!facet2->center)
-    return;
-  size= qh_setsize(facet2->vertices);
-  if (!facet2->keepcentrum) {
-    if (size > qh hull_dim + qh_MAXnewcentrum) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidevertices);
-    }
-  }else if (size <= qh hull_dim + qh_MAXnewcentrum) {
-    /* center and keepcentrum was set */
-    if (size == qh hull_dim || qh POSTmerging)
-      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
-  }
-  if (!facet2->keepcentrum) {
-    qh_memfree(facet2->center, qh normal_size);
-    facet2->center= NULL;
-    FOREACHridge_(facet2->ridges)
-      ridge->tested= False;
-  }
-} /* updatetested */
-
-/*---------------------------------
-
-  qh_vertexridges( vertex )
-    return temporary set of ridges adjacent to a vertex
-    vertex->neighbors defined
-
-  ntoes:
-    uses qh.visit_id
-    does not include implicit ridges for simplicial facets
-
-  design:
-    for each neighbor of vertex
-      add ridges that include the vertex to ridges
-*/
-setT *qh_vertexridges(vertexT *vertex) {
-  facetT *neighbor, **neighborp;
-  setT *ridges= qh_settemp(qh TEMPsize);
-  int size;
-
-  qh visit_id++;
-  FOREACHneighbor_(vertex)
-    neighbor->visitid= qh visit_id;
-  FOREACHneighbor_(vertex) {
-    if (*neighborp)   /* no new ridges in last neighbor */
-      qh_vertexridges_facet(vertex, neighbor, &ridges);
-  }
-  if (qh PRINTstatistics || qh IStracing) {
-    size= qh_setsize(ridges);
-    zinc_(Zvertexridge);
-    zadd_(Zvertexridgetot, size);
-    zmax_(Zvertexridgemax, size);
-    trace3((qh ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
-             size, vertex->id));
-  }
-  return ridges;
-} /* vertexridges */
-
-/*---------------------------------
-
-  qh_vertexridges_facet( vertex, facet, ridges )
-    add adjacent ridges for vertex in facet
-    neighbor->visitid==qh.visit_id if it hasn't been visited
-
-  returns:
-    ridges updated
-    sets facet->visitid to qh.visit_id-1
-
-  design:
-    for each ridge of facet
-      if ridge of visited neighbor (i.e., unprocessed)
-        if vertex in ridge
-          append ridge to vertex
-    mark facet processed
-*/
-void qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges) {
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor;
-
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh visit_id
-    && qh_setin(ridge->vertices, vertex))
-      qh_setappend(ridges, ridge);
-  }
-  facet->visitid= qh visit_id-1;
-} /* vertexridges_facet */
-
-/*---------------------------------
-
-  qh_willdelete( facet, replace )
-    moves facet to visible list
-    sets facet->f.replace to replace (may be NULL)
-
-  returns:
-    bumps qh.num_visible
-*/
-void qh_willdelete(facetT *facet, facetT *replace) {
-
-  qh_removefacet(facet);
-  qh_prependfacet(facet, &qh visible_list);
-  qh num_visible++;
-  facet->visible= True;
-  facet->f.replace= replace;
-} /* willdelete */
-
-#else /* qh_NOmerge */
-void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
-}
-void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-}
-boolT qh_checkzero(boolT testall) {
-   }
-#endif /* qh_NOmerge */
-
diff --git a/src/qhull/src/libqhull/merge.h b/src/qhull/src/libqhull/merge.h
deleted file mode 100644
index 7f5ec3fb6..000000000
--- a/src/qhull/src/libqhull/merge.h
+++ /dev/null
@@ -1,178 +0,0 @@
-/*
      ---------------------------------
-
-   merge.h
-   header file for merge.c
-
-   see qh-merge.htm and merge.c
-
-   Copyright (c) 1993-2015 C.B. Barber.
-   $Id: //main/2015/qhull/src/libqhull/merge.h#1 $$Change: 1981 $
-   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-#include "libqhull.h"
-
-
-/*============ -constants- ==============*/
-
-/*----------------------------------
-
-  qh_ANGLEredundant
-    indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*----------------------------------
-
-  qh_ANGLEdegen
-    indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen     5.0
-
-/*----------------------------------
-
-  qh_ANGLEconcave
-    offset to indicate concave facets in mergeT->angle
-
-  notes:
-    concave facets are assigned the range of [2,4] in mergeT->angle
-    roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave  1.5
-
-/*----------------------------------
-
-  MRG... (mergeType)
-    indicates the type of a merge (mergeT->type)
-*/
-typedef enum {  /* in sort order for facet_mergeset */
-  MRGnone= 0,
-  MRGcoplanar,          /* centrum coplanar */
-  MRGanglecoplanar,     /* angle coplanar */
-                        /* could detect half concave ridges */
-  MRGconcave,           /* concave ridge */
-  MRGflip,              /* flipped facet. facet1 == facet2 */
-  MRGridge,             /* duplicate ridge (qh_MERGEridge) */
-                        /* degen and redundant go onto degen_mergeset */
-  MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
-  MRGredundant,         /* redundant facet (vertex subset) */
-                        /* merge_degenredundant assumes degen < redundant */
-  MRGmirror,            /* mirror facet from qh_triangulate */
-  ENDmrg
-} mergeType;
-
-/*----------------------------------
-
-  qh_MERGEapex
-    flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex     True
-
-/*============ -structures- ====================*/
-
-/*----------------------------------
-
-  mergeT
-    structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT {         /* initialize in qh_appendmergeset */
-  realT   angle;        /* angle between normals of facet1 and facet2 */
-  facetT *facet1;       /* will merge facet1 into facet2 */
-  facetT *facet2;
-  mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FOREACHmerge_( merges ) {...}
-    assign 'merge' to each merge in merges
-
-  notes:
-    uses 'mergeT *merge, **mergep;'
-    if qh_mergefacet(),
-      restart since qh.facet_mergeset may change
-    see FOREACHsetelement_
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-void    qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle);
-void    qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
-             boolT vneighbors);
-void    qh_all_merges(boolT othermerge, boolT vneighbors);
-void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
-setT   *qh_basevertices( facetT *samecycle);
-void    qh_checkconnect(void /* qh.new_facets */);
-boolT   qh_checkzero(boolT testall);
-int     qh_compareangle(const void *p1, const void *p2);
-int     qh_comparemerge(const void *p1, const void *p2);
-int     qh_comparevisit(const void *p1, const void *p2);
-void    qh_copynonconvex(ridgeT *atridge);
-void    qh_degen_redundant_facet(facetT *facet);
-void    qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet);
-vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges);
-void    qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
-           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
-void    qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
-void    qh_forcedmerges( boolT *wasmerge);
-void    qh_getmergeset(facetT *facetlist);
-void    qh_getmergeset_initial(facetT *facetlist);
-void    qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
-ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot);
-void    qh_makeridges(facetT *facet);
-void    qh_mark_dupridges(facetT *facetlist);
-void    qh_maydropneighbor(facetT *facet);
-int     qh_merge_degenredundant(void);
-void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
-void    qh_mergecycle(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_all(facetT *facetlist, boolT *wasmerge);
-void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
-void    qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
-void    qh_mergefacet2d(facetT *facet1, facetT *facet2);
-void    qh_mergeneighbors(facetT *facet1, facetT *facet2);
-void    qh_mergeridges(facetT *facet1, facetT *facet2);
-void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
-void    qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2);
-void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
-void    qh_mergevertices(setT *vertices1, setT **vertices);
-setT   *qh_neighbor_intersections(vertexT *vertex);
-void    qh_newvertices(setT *vertices);
-boolT   qh_reducevertices(void);
-vertexT *qh_redundant_vertex(vertexT *vertex);
-boolT   qh_remove_extravertices(facetT *facet);
-vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet);
-void    qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
-void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
-                        facetT *oldfacet, facetT *neighborA);
-boolT   qh_test_appendmerge(facetT *facet, facetT *neighbor);
-boolT   qh_test_vneighbors(void /* qh.newfacet_list */);
-void    qh_tracemerge(facetT *facet1, facetT *facet2);
-void    qh_tracemerging(void);
-void    qh_updatetested( facetT *facet1, facetT *facet2);
-setT   *qh_vertexridges(vertexT *vertex);
-void    qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges);
-void    qh_willdelete(facetT *facet, facetT *replace);
-
-#endif /* qhDEFmerge */
diff --git a/src/qhull/src/libqhull/poly.c b/src/qhull/src/libqhull/poly.c
deleted file mode 100644
index b8db6a9ef..000000000
--- a/src/qhull/src/libqhull/poly.c
+++ /dev/null
@@ -1,1205 +0,0 @@
-/*
      ---------------------------------
-
-   poly.c
-   implements polygons and simplices
-
-   see qh-poly.htm, poly.h and libqhull.h
-
-   infrequent code is in poly2.c
-   (all but top 50 and their callers 12/3/95)
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/poly.c#3 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_appendfacet( facet )
-    appends facet to end of qh.facet_list,
-
-  returns:
-    updates qh.newfacet_list, facet_next, facet_list
-    increments qh.numfacets
-
-  notes:
-    assumes qh.facet_list/facet_tail is defined (createsimplex)
-
-  see:
-    qh_removefacet()
-
-*/
-void qh_appendfacet(facetT *facet) {
-  facetT *tail= qh facet_tail;
-
-  if (tail == qh newfacet_list)
-    qh newfacet_list= facet;
-  if (tail == qh facet_next)
-    qh facet_next= facet;
-  facet->previous= tail->previous;
-  facet->next= tail;
-  if (tail->previous)
-    tail->previous->next= facet;
-  else
-    qh facet_list= facet;
-  tail->previous= facet;
-  qh num_facets++;
-  trace4((qh ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
-} /* appendfacet */
-
-
-/*---------------------------------
-
-  qh_appendvertex( vertex )
-    appends vertex to end of qh.vertex_list,
-
-  returns:
-    sets vertex->newlist
-    updates qh.vertex_list, newvertex_list
-    increments qh.num_vertices
-
-  notes:
-    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
-
-*/
-void qh_appendvertex(vertexT *vertex) {
-  vertexT *tail= qh vertex_tail;
-
-  if (tail == qh newvertex_list)
-    qh newvertex_list= vertex;
-  vertex->newlist= True;
-  vertex->previous= tail->previous;
-  vertex->next= tail;
-  if (tail->previous)
-    tail->previous->next= vertex;
-  else
-    qh vertex_list= vertex;
-  tail->previous= vertex;
-  qh num_vertices++;
-  trace4((qh ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
-} /* appendvertex */
-
-
-/*---------------------------------
-
-  qh_attachnewfacets( )
-    attach horizon facets to new facets in qh.newfacet_list
-    newfacets have neighbor and ridge links to horizon but not vice versa
-    only needed for qh.ONLYgood
-
-  returns:
-    set qh.NEWfacets
-    horizon facets linked to new facets
-      ridges changed from visible facets to new facets
-      simplicial ridges deleted
-    qh.visible_list, no ridges valid
-    facet->f.replace is a newfacet (if any)
-
-  design:
-    delete interior ridges and neighbor sets by
-      for each visible, non-simplicial facet
-        for each ridge
-          if last visit or if neighbor is simplicial
-            if horizon neighbor
-              delete ridge for horizon's ridge set
-            delete ridge
-        erase neighbor set
-    attach horizon facets and new facets by
-      for all new facets
-        if corresponding horizon facet is simplicial
-          locate corresponding visible facet {may be more than one}
-          link visible facet to new facet
-          replace visible facet with new facet in horizon
-        else it's non-simplicial
-          for all visible neighbors of the horizon facet
-            link visible neighbor to new facet
-            delete visible neighbor from horizon facet
-          append new facet to horizon's neighbors
-          the first ridge of the new facet is the horizon ridge
-          link the new facet into the horizon ridge
-*/
-void qh_attachnewfacets(void /* qh.visible_list, newfacet_list */) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
-  ridgeT *ridge, **ridgep;
-
-  qh NEWfacets= True;
-  trace3((qh ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
-  qh visit_id++;
-  FORALLvisible_facets {
-    visible->visitid= qh visit_id;
-    if (visible->ridges) {
-      FOREACHridge_(visible->ridges) {
-        neighbor= otherfacet_(ridge, visible);
-        if (neighbor->visitid == qh visit_id
-            || (!neighbor->visible && neighbor->simplicial)) {
-          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
-            qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(&(ridge->vertices)); /* delete on 2nd visit */
-          qh_memfree(ridge, (int)sizeof(ridgeT));
-        }
-      }
-      SETfirst_(visible->ridges)= NULL;
-    }
-    SETfirst_(visible->neighbors)= NULL;
-  }
-  trace1((qh ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
-  FORALLnew_facets {
-    horizon= SETfirstt_(newfacet->neighbors, facetT);
-    if (horizon->simplicial) {
-      visible= NULL;
-      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
-        if (neighbor->visible) {
-          if (visible) {
-            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
-                                  SETindex_(horizon->neighbors, neighbor))) {
-              visible= neighbor;
-              break;
-            }
-          }else
-            visible= neighbor;
-        }
-      }
-      if (visible) {
-        visible->f.replace= newfacet;
-        qh_setreplace(horizon->neighbors, visible, newfacet);
-      }else {
-        qh_fprintf(qh ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
-                 horizon->id, newfacet->id);
-        qh_errexit2(qh_ERRqhull, horizon, newfacet);
-      }
-    }else { /* non-simplicial, with a ridge for newfacet */
-      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
-        if (neighbor->visible) {
-          neighbor->f.replace= newfacet;
-          qh_setdelnth(horizon->neighbors,
-                        SETindex_(horizon->neighbors, neighbor));
-          neighborp--; /* repeat */
-        }
-      }
-      qh_setappend(&horizon->neighbors, newfacet);
-      ridge= SETfirstt_(newfacet->ridges, ridgeT);
-      if (ridge->top == horizon)
-        ridge->bottom= newfacet;
-      else
-        ridge->top= newfacet;
-      }
-  } /* newfacets */
-  if (qh PRINTstatistics) {
-    FORALLvisible_facets {
-      if (!visible->f.replace)
-        zinc_(Zinsidevisible);
-    }
-  }
-} /* attachnewfacets */
-
-/*---------------------------------
-
-  qh_checkflipped( facet, dist, allerror )
-    checks facet orientation to interior point
-
-    if allerror set,
-      tests against qh.DISTround
-    else
-      tests against 0 since tested against DISTround before
-
-  returns:
-    False if it flipped orientation (sets facet->flipped)
-    distance if non-NULL
-*/
-boolT qh_checkflipped(facetT *facet, realT *distp, boolT allerror) {
-  realT dist;
-
-  if (facet->flipped && !distp)
-    return False;
-  zzinc_(Zdistcheck);
-  qh_distplane(qh interior_point, facet, &dist);
-  if (distp)
-    *distp= dist;
-  if ((allerror && dist > -qh DISTround)|| (!allerror && dist >= 0.0)) {
-    facet->flipped= True;
-    zzinc_(Zflippedfacets);
-    trace0((qh ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
-              facet->id, dist, qh furthest_id));
-    qh_precision("flipped facet");
-    return False;
-  }
-  return True;
-} /* checkflipped */
-
-/*---------------------------------
-
-  qh_delfacet( facet )
-    removes facet from facet_list and frees up its memory
-
-  notes:
-    assumes vertices and ridges already freed
-*/
-void qh_delfacet(facetT *facet) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
-  if (facet == qh tracefacet)
-    qh tracefacet= NULL;
-  if (facet == qh GOODclosest)
-    qh GOODclosest= NULL;
-  qh_removefacet(facet);
-  if (!facet->tricoplanar || facet->keepcentrum) {
-    qh_memfree_(facet->normal, qh normal_size, freelistp);
-    if (qh CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
-      qh_memfree_(facet->center, qh center_size, freelistp);
-    }else /* AScentrum */ {
-      qh_memfree_(facet->center, qh normal_size, freelistp);
-    }
-  }
-  qh_setfree(&(facet->neighbors));
-  if (facet->ridges)
-    qh_setfree(&(facet->ridges));
-  qh_setfree(&(facet->vertices));
-  if (facet->outsideset)
-    qh_setfree(&(facet->outsideset));
-  if (facet->coplanarset)
-    qh_setfree(&(facet->coplanarset));
-  qh_memfree_(facet, (int)sizeof(facetT), freelistp);
-} /* delfacet */
-
-
-/*---------------------------------
-
-  qh_deletevisible()
-    delete visible facets and vertices
-
-  returns:
-    deletes each facet and removes from facetlist
-    at exit, qh.visible_list empty (== qh.newfacet_list)
-
-  notes:
-    ridges already deleted
-    horizon facets do not reference facets on qh.visible_list
-    new facets in qh.newfacet_list
-    uses   qh.visit_id;
-*/
-void qh_deletevisible(void /*qh.visible_list*/) {
-  facetT *visible, *nextfacet;
-  vertexT *vertex, **vertexp;
-  int numvisible= 0, numdel= qh_setsize(qh del_vertices);
-
-  trace1((qh ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
-         qh num_visible, numdel));
-  for (visible= qh visible_list; visible && visible->visible;
-                visible= nextfacet) { /* deleting current */
-    nextfacet= visible->next;
-    numvisible++;
-    qh_delfacet(visible);
-  }
-  if (numvisible != qh num_visible) {
-    qh_fprintf(qh ferr, 6103, "qhull internal error (qh_deletevisible): qh num_visible %d is not number of visible facets %d\n",
-             qh num_visible, numvisible);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  qh num_visible= 0;
-  zadd_(Zvisfacettot, numvisible);
-  zmax_(Zvisfacetmax, numvisible);
-  zzadd_(Zdelvertextot, numdel);
-  zmax_(Zdelvertexmax, numdel);
-  FOREACHvertex_(qh del_vertices)
-    qh_delvertex(vertex);
-  qh_settruncate(qh del_vertices, 0);
-} /* deletevisible */
-
-/*---------------------------------
-
-  qh_facetintersect( facetA, facetB, skipa, skipB, prepend )
-    return vertices for intersection of two simplicial facets
-    may include 1 prepended entry (if more, need to settemppush)
-
-  returns:
-    returns set of qh.hull_dim-1 + prepend vertices
-    returns skipped index for each test and checks for exactly one
-
-  notes:
-    does not need settemp since set in quick memory
-
-  see also:
-    qh_vertexintersect and qh_vertexintersect_new
-    use qh_setnew_delnthsorted to get nth ridge (no skip information)
-
-  design:
-    locate skipped vertex by scanning facet A's neighbors
-    locate skipped vertex by scanning facet B's neighbors
-    intersect the vertex sets
-*/
-setT *qh_facetintersect(facetT *facetA, facetT *facetB,
-                         int *skipA,int *skipB, int prepend) {
-  setT *intersect;
-  int dim= qh hull_dim, i, j;
-  facetT **neighborsA, **neighborsB;
-
-  neighborsA= SETaddr_(facetA->neighbors, facetT);
-  neighborsB= SETaddr_(facetB->neighbors, facetT);
-  i= j= 0;
-  if (facetB == *neighborsA++)
-    *skipA= 0;
-  else if (facetB == *neighborsA++)
-    *skipA= 1;
-  else if (facetB == *neighborsA++)
-    *skipA= 2;
-  else {
-    for (i=3; i < dim; i++) {
-      if (facetB == *neighborsA++) {
-        *skipA= i;
-        break;
-      }
-    }
-  }
-  if (facetA == *neighborsB++)
-    *skipB= 0;
-  else if (facetA == *neighborsB++)
-    *skipB= 1;
-  else if (facetA == *neighborsB++)
-    *skipB= 2;
-  else {
-    for (j=3; j < dim; j++) {
-      if (facetA == *neighborsB++) {
-        *skipB= j;
-        break;
-      }
-    }
-  }
-  if (i >= dim || j >= dim) {
-    qh_fprintf(qh ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
-            facetA->id, facetB->id);
-    qh_errexit2(qh_ERRqhull, facetA, facetB);
-  }
-  intersect= qh_setnew_delnthsorted(facetA->vertices, qh hull_dim, *skipA, prepend);
-  trace4((qh ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
-          facetA->id, *skipA, facetB->id, *skipB));
-  return(intersect);
-} /* facetintersect */
-
-/*---------------------------------
-
-  qh_gethash( hashsize, set, size, firstindex, skipelem )
-    return hashvalue for a set with firstindex and skipelem
-
-  notes:
-    returned hash is in [0,hashsize)
-    assumes at least firstindex+1 elements
-    assumes skipelem is NULL, in set, or part of hash
-
-    hashes memory addresses which may change over different runs of the same data
-    using sum for hash does badly in high d
-*/
-int qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem) {
-  void **elemp= SETelemaddr_(set, firstindex, void);
-  ptr_intT hash = 0, elem;
-  unsigned result;
-  int i;
-#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
-#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
-#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
-#endif
-
-  switch (size-firstindex) {
-  case 1:
-    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
-    break;
-  case 2:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
-    break;
-  case 3:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      - (ptr_intT) skipelem;
-    break;
-  case 4:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
-    break;
-  case 5:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
-    break;
-  case 6:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
-      - (ptr_intT) skipelem;
-    break;
-  default:
-    hash= 0;
-    i= 3;
-    do {     /* this is about 10% in 10-d */
-      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
-        hash ^= (elem << i) + (elem >> (32-i));
-        i += 3;
-        if (i >= 32)
-          i -= 32;
-      }
-    }while (*elemp);
-    break;
-  }
-  if (hashsize<0) {
-    qh_fprintf(qh ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
-    qh_errexit2(qh_ERRqhull, NULL, NULL);
-  }
-  result= (unsigned)hash;
-  result %= (unsigned)hashsize;
-  /* result= 0; for debugging */
-  return result;
-#ifdef _MSC_VER
-#pragma warning( pop)
-#endif
-} /* gethash */
-
-/*---------------------------------
-
-  qh_makenewfacet( vertices, toporient, horizon )
-    creates a toporient? facet from vertices
-
-  returns:
-    returns newfacet
-      adds newfacet to qh.facet_list
-      newfacet->vertices= vertices
-      if horizon
-        newfacet->neighbor= horizon, but not vice versa
-    newvertex_list updated with vertices
-*/
-facetT *qh_makenewfacet(setT *vertices, boolT toporient,facetT *horizon) {
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(vertex);
-      qh_appendvertex(vertex);
-    }
-  }
-  newfacet= qh_newfacet();
-  newfacet->vertices= vertices;
-  newfacet->toporient= (unsigned char)toporient;
-  if (horizon)
-    qh_setappend(&(newfacet->neighbors), horizon);
-  qh_appendfacet(newfacet);
-  return(newfacet);
-} /* makenewfacet */
-
-
-/*---------------------------------
-
-  qh_makenewplanes()
-    make new hyperplanes for facets on qh.newfacet_list
-
-  returns:
-    all facets have hyperplanes or are marked for   merging
-    doesn't create hyperplane if horizon is coplanar (will merge)
-    updates qh.min_vertex if qh.JOGGLEmax
-
-  notes:
-    facet->f.samecycle is defined for facet->mergehorizon facets
-*/
-void qh_makenewplanes(void /* newfacet_list */) {
-  facetT *newfacet;
-
-  FORALLnew_facets {
-    if (!newfacet->mergehorizon)
-      qh_setfacetplane(newfacet);
-  }
-  if (qh JOGGLEmax < REALmax/2)
-    minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
-} /* makenewplanes */
-
-/*---------------------------------
-
-  qh_makenew_nonsimplicial( visible, apex, numnew )
-    make new facets for ridges of a visible facet
-
-  returns:
-    first newfacet, bumps numnew as needed
-    attaches new facets if !qh.ONLYgood
-    marks ridge neighbors for simplicial visible
-    if (qh.ONLYgood)
-      ridges on newfacet, horizon, and visible
-    else
-      ridge and neighbors between newfacet and   horizon
-      visible facet's ridges are deleted
-
-  notes:
-    qh.visit_id if visible has already been processed
-    sets neighbor->seen for building f.samecycle
-      assumes all 'seen' flags initially false
-
-  design:
-    for each ridge of visible facet
-      get neighbor of visible facet
-      if neighbor was already processed
-        delete the ridge (will delete all visible facets later)
-      if neighbor is a horizon facet
-        create a new facet
-        if neighbor coplanar
-          adds newfacet to f.samecycle for later merging
-        else
-          updates neighbor's neighbor set
-          (checks for non-simplicial facet with multiple ridges to visible facet)
-        updates neighbor's ridge set
-        (checks for simplicial neighbor to non-simplicial visible facet)
-        (deletes ridge if neighbor is simplicial)
-
-*/
-#ifndef qh_NOmerge
-facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor, *newfacet= NULL, *samecycle;
-  setT *vertices;
-  boolT toporient;
-  int ridgeid;
-
-  FOREACHridge_(visible->ridges) {
-    ridgeid= ridge->id;
-    neighbor= otherfacet_(ridge, visible);
-    if (neighbor->visible) {
-      if (!qh ONLYgood) {
-        if (neighbor->visitid == qh visit_id) {
-          qh_setfree(&(ridge->vertices));  /* delete on 2nd visit */
-          qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
-        }
-      }
-    }else {  /* neighbor is an horizon facet */
-      toporient= (ridge->top == visible);
-      vertices= qh_setnew(qh hull_dim); /* makes sure this is quick */
-      qh_setappend(&vertices, apex);
-      qh_setappend_set(&vertices, ridge->vertices);
-      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar) {
-        newfacet->mergehorizon= True;
-        if (!neighbor->seen) {
-          newfacet->f.samecycle= newfacet;
-          neighbor->f.newcycle= newfacet;
-        }else {
-          samecycle= neighbor->f.newcycle;
-          newfacet->f.samecycle= samecycle->f.samecycle;
-          samecycle->f.samecycle= newfacet;
-        }
-      }
-      if (qh ONLYgood) {
-        if (!neighbor->simplicial)
-          qh_setappend(&(newfacet->ridges), ridge);
-      }else {  /* qh_attachnewfacets */
-        if (neighbor->seen) {
-          if (neighbor->simplicial) {
-            qh_fprintf(qh ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
-                   neighbor->id, visible->id);
-            qh_errexit2(qh_ERRqhull, neighbor, visible);
-          }
-          qh_setappend(&(neighbor->neighbors), newfacet);
-        }else
-          qh_setreplace(neighbor->neighbors, visible, newfacet);
-        if (neighbor->simplicial) {
-          qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(&(ridge->vertices));
-          qh_memfree(ridge, (int)sizeof(ridgeT));
-        }else {
-          qh_setappend(&(newfacet->ridges), ridge);
-          if (toporient)
-            ridge->top= newfacet;
-          else
-            ridge->bottom= newfacet;
-        }
-      trace4((qh ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
-            newfacet->id, apex->id, ridgeid, neighbor->id));
-      }
-    }
-    neighbor->seen= True;
-  } /* for each ridge */
-  if (!qh ONLYgood)
-    SETfirst_(visible->ridges)= NULL;
-  return newfacet;
-} /* makenew_nonsimplicial */
-#else /* qh_NOmerge */
-facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_makenew_simplicial( visible, apex, numnew )
-    make new facets for simplicial visible facet and apex
-
-  returns:
-    attaches new facets if (!qh.ONLYgood)
-      neighbors between newfacet and horizon
-
-  notes:
-    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
-
-  design:
-    locate neighboring horizon facet for visible facet
-    determine vertices and orientation
-    create new facet
-    if coplanar,
-      add new facet to f.samecycle
-    update horizon facet's neighbor list
-*/
-facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew) {
-  facetT *neighbor, **neighborp, *newfacet= NULL;
-  setT *vertices;
-  boolT flip, toporient;
-  int horizonskip= 0, visibleskip= 0;
-
-  FOREACHneighbor_(visible) {
-    if (!neighbor->seen && !neighbor->visible) {
-      vertices= qh_facetintersect(neighbor,visible, &horizonskip, &visibleskip, 1);
-      SETfirst_(vertices)= apex;
-      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
-      if (neighbor->toporient)
-        toporient= horizonskip & 0x1;
-      else
-        toporient= (horizonskip & 0x1) ^ 0x1;
-      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar && (qh PREmerge || qh MERGEexact)) {
-#ifndef qh_NOmerge
-        newfacet->f.samecycle= newfacet;
-        newfacet->mergehorizon= True;
-#endif
-      }
-      if (!qh ONLYgood)
-        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
-      trace4((qh ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
-            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
-              neighbor->toporient, visible->id, visibleskip, flip));
-    }
-  }
-  return newfacet;
-} /* makenew_simplicial */
-
-/*---------------------------------
-
-  qh_matchneighbor( newfacet, newskip, hashsize, hashcount )
-    either match subridge of newfacet with neighbor or add to hash_table
-
-  returns:
-    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
-
-  notes:
-    ridge is newfacet->vertices w/o newskip vertex
-    do not allocate memory (need to free hash_table cleanly)
-    uses linear hash chains
-
-  see also:
-    qh_matchduplicates
-
-  design:
-    for each possible matching facet in qh.hash_table
-      if vertices match
-        set ismatch, if facets have opposite orientation
-        if ismatch and matching facet doesn't have a match
-          match the facets by updating their neighbor sets
-        else
-          indicate a duplicate ridge
-          set facet hyperplane for later testing
-          add facet to hashtable
-          unless the other facet was already a duplicate ridge
-            mark both facets with a duplicate ridge
-            add other facet (if defined) to hash table
-*/
-void qh_matchneighbor(facetT *newfacet, int newskip, int hashsize, int *hashcount) {
-  boolT newfound= False;   /* True, if new facet is already in hash chain */
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *matchfacet;
-  int skip, matchskip;
-
-  hash= qh_gethash(hashsize, newfacet->vertices, qh hull_dim, 1,
-                     SETelem_(newfacet->vertices, newskip));
-  trace4((qh ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
-          newfacet->id, newskip, hash, *hashcount));
-  zinc_(Zhashlookup);
-  for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (facet == newfacet) {
-      newfound= True;
-      continue;
-    }
-    zinc_(Zhashtests);
-    if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-      if (SETelem_(newfacet->vertices, newskip) ==
-          SETelem_(facet->vertices, skip)) {
-        qh_precision("two facets with the same vertices");
-        qh_fprintf(qh ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
-          facet->id, newfacet->id);
-        qh_errexit2(qh_ERRprec, facet, newfacet);
-      }
-      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
-      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
-      if (ismatch && !matchfacet) {
-        SETelem_(facet->neighbors, skip)= newfacet;
-        SETelem_(newfacet->neighbors, newskip)= facet;
-        (*hashcount)--;
-        trace4((qh ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
-           facet->id, skip, newfacet->id, newskip));
-        return;
-      }
-      if (!qh PREmerge && !qh MERGEexact) {
-        qh_precision("a ridge with more than two neighbors");
-        qh_fprintf(qh ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
-                 facet->id, newfacet->id, getid_(matchfacet));
-        qh_errexit2(qh_ERRprec, facet, newfacet);
-      }
-      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
-      newfacet->dupridge= True;
-      if (!newfacet->normal)
-        qh_setfacetplane(newfacet);
-      qh_addhash(newfacet, qh hash_table, hashsize, hash);
-      (*hashcount)++;
-      if (!facet->normal)
-        qh_setfacetplane(facet);
-      if (matchfacet != qh_DUPLICATEridge) {
-        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
-        facet->dupridge= True;
-        if (!facet->normal)
-          qh_setfacetplane(facet);
-        if (matchfacet) {
-          matchskip= qh_setindex(matchfacet->neighbors, facet);
-          if (matchskip<0) {
-              qh_fprintf(qh ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
-                  matchfacet->id, facet->id);
-              qh_errexit2(qh_ERRqhull, matchfacet, facet);
-          }
-          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
-          matchfacet->dupridge= True;
-          if (!matchfacet->normal)
-            qh_setfacetplane(matchfacet);
-          qh_addhash(matchfacet, qh hash_table, hashsize, hash);
-          *hashcount += 2;
-        }
-      }
-      trace4((qh ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
-           newfacet->id, newskip, facet->id, skip,
-           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
-           ismatch, hash));
-      return; /* end of duplicate ridge */
-    }
-  }
-  if (!newfound)
-    SETelem_(qh hash_table, scan)= newfacet;  /* same as qh_addhash */
-  (*hashcount)++;
-  trace4((qh ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
-           newfacet->id, newskip, hash));
-} /* matchneighbor */
-
-
-/*---------------------------------
-
-  qh_matchnewfacets()
-    match newfacets in qh.newfacet_list to their newfacet neighbors
-
-  returns:
-    qh.newfacet_list with full neighbor sets
-      get vertices with nth neighbor by deleting nth vertex
-    if qh.PREmerge/MERGEexact or qh.FORCEoutput
-      sets facet->flippped if flipped normal (also prevents point partitioning)
-    if duplicate ridges and qh.PREmerge/MERGEexact
-      sets facet->dupridge
-      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
-
-  notes:
-    newfacets already have neighbor[0] (horizon facet)
-    assumes qh.hash_table is NULL
-    vertex->neighbors has not been updated yet
-    do not allocate memory after qh.hash_table (need to free it cleanly)
-
-  design:
-    delete neighbor sets for all new facets
-    initialize a hash table
-    for all new facets
-      match facet with neighbors
-    if unmatched facets (due to duplicate ridges)
-      for each new facet with a duplicate ridge
-        match it with a facet
-    check for flipped facets
-*/
-void qh_matchnewfacets(void /* qh.newfacet_list */) {
-  int numnew=0, hashcount=0, newskip;
-  facetT *newfacet, *neighbor;
-  int dim= qh hull_dim, hashsize, neighbor_i, neighbor_n;
-  setT *neighbors;
-#ifndef qh_NOtrace
-  int facet_i, facet_n, numfree= 0;
-  facetT *facet;
-#endif
-
-  trace1((qh ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
-  FORALLnew_facets {
-    numnew++;
-    {  /* inline qh_setzero(newfacet->neighbors, 1, qh hull_dim); */
-      neighbors= newfacet->neighbors;
-      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
-      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
-    }
-  }
-
-  qh_newhashtable(numnew*(qh hull_dim-1)); /* twice what is normally needed,
-                                     but every ridge could be DUPLICATEridge */
-  hashsize= qh_setsize(qh hash_table);
-  FORALLnew_facets {
-    for (newskip=1; newskip0 because hull_dim>1 and numnew>0 */
-      qh_matchneighbor(newfacet, newskip, hashsize, &hashcount);
-#if 0   /* use the following to trap hashcount errors */
-    {
-      int count= 0, k;
-      facetT *facet, *neighbor;
-
-      count= 0;
-      FORALLfacet_(qh newfacet_list) {  /* newfacet already in use */
-        for (k=1; k < qh hull_dim; k++) {
-          neighbor= SETelemt_(facet->neighbors, k, facetT);
-          if (!neighbor || neighbor == qh_DUPLICATEridge)
-            count++;
-        }
-        if (facet == newfacet)
-          break;
-      }
-      if (count != hashcount) {
-        qh_fprintf(qh ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
-                 newfacet->id, hashcount, count);
-        qh_errexit(qh_ERRqhull, newfacet, NULL);
-      }
-    }
-#endif  /* end of trap code */
-  }
-  if (hashcount) {
-    FORALLnew_facets {
-      if (newfacet->dupridge) {
-        FOREACHneighbor_i_(newfacet) {
-          if (neighbor == qh_DUPLICATEridge) {
-            qh_matchduplicates(newfacet, neighbor_i, hashsize, &hashcount);
-                    /* this may report MERGEfacet */
-          }
-        }
-      }
-    }
-  }
-  if (hashcount) {
-    qh_fprintf(qh ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
-        hashcount);
-    qh_printhashtable(qh ferr);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-#ifndef qh_NOtrace
-  if (qh IStracing >= 2) {
-    FOREACHfacet_i_(qh hash_table) {
-      if (!facet)
-        numfree++;
-    }
-    qh_fprintf(qh ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
-             numnew, numfree, qh_setsize(qh hash_table));
-  }
-#endif /* !qh_NOtrace */
-  qh_setfree(&qh hash_table);
-  if (qh PREmerge || qh MERGEexact) {
-    if (qh IStracing >= 4)
-      qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
-    FORALLnew_facets {
-      if (newfacet->normal)
-        qh_checkflipped(newfacet, NULL, qh_ALL);
-    }
-  }else if (qh FORCEoutput)
-    qh_checkflipped_all(qh newfacet_list);  /* prints warnings for flipped */
-} /* matchnewfacets */
-
-
-/*---------------------------------
-
-  qh_matchvertices( firstindex, verticesA, skipA, verticesB, skipB, same )
-    tests whether vertices match with a single skip
-    starts match at firstindex since all new facets have a common vertex
-
-  returns:
-    true if matched vertices
-    skip index for each set
-    sets same iff vertices have the same orientation
-
-  notes:
-    assumes skipA is in A and both sets are the same size
-
-  design:
-    set up pointers
-    scan both sets checking for a match
-    test orientation
-*/
-boolT qh_matchvertices(int firstindex, setT *verticesA, int skipA,
-       setT *verticesB, int *skipB, boolT *same) {
-  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
-
-  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
-  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
-  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
-  do if (elemAp != skipAp) {
-    while (*elemAp != *elemBp++) {
-      if (skipBp)
-        return False;
-      skipBp= elemBp;  /* one extra like FOREACH */
-    }
-  }while (*(++elemAp));
-  if (!skipBp)
-    skipBp= ++elemBp;
-  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
-  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
-  trace4((qh ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
-          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
-  return(True);
-} /* matchvertices */
-
-/*---------------------------------
-
-  qh_newfacet()
-    return a new facet
-
-  returns:
-    all fields initialized or cleared   (NULL)
-    preallocates neighbors set
-*/
-facetT *qh_newfacet(void) {
-  facetT *facet;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_((int)sizeof(facetT), freelistp, facet, facetT);
-  memset((char *)facet, (size_t)0, sizeof(facetT));
-  if (qh facet_id == qh tracefacet_id)
-    qh tracefacet= facet;
-  facet->id= qh facet_id++;
-  facet->neighbors= qh_setnew(qh hull_dim);
-#if !qh_COMPUTEfurthest
-  facet->furthestdist= 0.0;
-#endif
-#if qh_MAXoutside
-  if (qh FORCEoutput && qh APPROXhull)
-    facet->maxoutside= qh MINoutside;
-  else
-    facet->maxoutside= qh DISTround;
-#endif
-  facet->simplicial= True;
-  facet->good= True;
-  facet->newfacet= True;
-  trace4((qh ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
-  return(facet);
-} /* newfacet */
-
-
-/*---------------------------------
-
-  qh_newridge()
-    return a new ridge
-*/
-ridgeT *qh_newridge(void) {
-  ridgeT *ridge;
-  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_((int)sizeof(ridgeT), freelistp, ridge, ridgeT);
-  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
-  zinc_(Ztotridges);
-  if (qh ridge_id == UINT_MAX) {
-    qh_fprintf(qh ferr, 7074, "\
-qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
-  }
-  ridge->id= qh ridge_id++;
-  trace4((qh ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
-  return(ridge);
-} /* newridge */
-
-
-/*---------------------------------
-
-  qh_pointid(  point )
-    return id for a point,
-    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
-
-  alternative code if point is in qh.first_point...
-    unsigned long id;
-    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
-
-  notes:
-    Valid points are non-negative
-    WARN64 -- id truncated to 32-bits, at most 2G points
-    NOerrors returned (QhullPoint::id)
-    if point not in point array
-      the code does a comparison of unrelated pointers.
-*/
-int qh_pointid(pointT *point) {
-  ptr_intT offset, id;
-
-  if (!point)
-    return qh_IDnone;
-  else if (point == qh interior_point)
-    return qh_IDinterior;
-  else if (point >= qh first_point
-  && point < qh first_point + qh num_points * qh hull_dim) {
-    offset= (ptr_intT)(point - qh first_point);
-    id= offset / qh hull_dim;
-  }else if ((id= qh_setindex(qh other_points, point)) != -1)
-    id += qh num_points;
-  else
-    return qh_IDunknown;
-  return (int)id;
-} /* pointid */
-
-/*---------------------------------
-
-  qh_removefacet( facet )
-    unlinks facet from qh.facet_list,
-
-  returns:
-    updates qh.facet_list .newfacet_list .facet_next visible_list
-    decrements qh.num_facets
-
-  see:
-    qh_appendfacet
-*/
-void qh_removefacet(facetT *facet) {
-  facetT *next= facet->next, *previous= facet->previous;
-
-  if (facet == qh newfacet_list)
-    qh newfacet_list= next;
-  if (facet == qh facet_next)
-    qh facet_next= next;
-  if (facet == qh visible_list)
-    qh visible_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st facet in qh facet_list */
-    qh facet_list= next;
-    qh facet_list->previous= NULL;
-  }
-  qh num_facets--;
-  trace4((qh ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
-} /* removefacet */
-
-
-/*---------------------------------
-
-  qh_removevertex( vertex )
-    unlinks vertex from qh.vertex_list,
-
-  returns:
-    updates qh.vertex_list .newvertex_list
-    decrements qh.num_vertices
-*/
-void qh_removevertex(vertexT *vertex) {
-  vertexT *next= vertex->next, *previous= vertex->previous;
-
-  if (vertex == qh newvertex_list)
-    qh newvertex_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st vertex in qh vertex_list */
-    qh vertex_list= vertex->next;
-    qh vertex_list->previous= NULL;
-  }
-  qh num_vertices--;
-  trace4((qh ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
-} /* removevertex */
-
-
-/*---------------------------------
-
-  qh_updatevertices()
-    update vertex neighbors and delete interior vertices
-
-  returns:
-    if qh.VERTEXneighbors, updates neighbors for each vertex
-      if qh.newvertex_list,
-         removes visible neighbors  from vertex neighbors
-      if qh.newfacet_list
-         adds new facets to vertex neighbors
-    if qh.visible_list
-       interior vertices added to qh.del_vertices for later partitioning
-
-  design:
-    if qh.VERTEXneighbors
-      deletes references to visible facets from vertex neighbors
-      appends new facets to the neighbor list for each vertex
-      checks all vertices of visible facets
-        removes visible facets from neighbor lists
-        marks unused vertices for deletion
-*/
-void qh_updatevertices(void /*qh.newvertex_list, newfacet_list, visible_list*/) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
-  vertexT *vertex, **vertexp;
-
-  trace3((qh ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
-  if (qh VERTEXneighbors) {
-    FORALLvertex_(qh newvertex_list) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visible)
-          SETref_(neighbor)= NULL;
-      }
-      qh_setcompact(vertex->neighbors);
-    }
-    FORALLnew_facets {
-      FOREACHvertex_(newfacet->vertices)
-        qh_setappend(&vertex->neighbors, newfacet);
-    }
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          FOREACHneighbor_(vertex) { /* this can happen under merging */
-            if (!neighbor->visible)
-              break;
-          }
-          if (neighbor)
-            qh_setdel(vertex->neighbors, visible);
-          else {
-            vertex->deleted= True;
-            qh_setappend(&qh del_vertices, vertex);
-            trace2((qh ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(vertex->point), vertex->id, visible->id));
-          }
-        }
-      }
-    }
-  }else {  /* !VERTEXneighbors */
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          vertex->deleted= True;
-          qh_setappend(&qh del_vertices, vertex);
-          trace2((qh ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(vertex->point), vertex->id, visible->id));
-        }
-      }
-    }
-  }
-} /* updatevertices */
-
-
-
diff --git a/src/qhull/src/libqhull/poly.h b/src/qhull/src/libqhull/poly.h
deleted file mode 100644
index af8b42077..000000000
--- a/src/qhull/src/libqhull/poly.h
+++ /dev/null
@@ -1,296 +0,0 @@
-/*
      ---------------------------------
-
-   poly.h
-   header file for poly.c and poly2.c
-
-   see qh-poly.htm, libqhull.h and poly.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/poly.h#3 $$Change: 2047 $
-   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-#include "libqhull.h"
-
-/*===============   constants ========================== */
-
-/*----------------------------------
-
-  ALGORITHMfault
-    use as argument to checkconvex() to report errors during buildhull
-*/
-#define qh_ALGORITHMfault 0
-
-/*----------------------------------
-
-  DATAfault
-    use as argument to checkconvex() to report errors during initialhull
-*/
-#define qh_DATAfault 1
-
-/*----------------------------------
-
-  DUPLICATEridge
-    special value for facet->neighbor to indicate a duplicate ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge (facetT *)1L
-
-/*----------------------------------
-
-  MERGEridge       flag in facet
-    special value for facet->neighbor to indicate a merged ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge (facetT *)2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FORALLfacet_( facetlist ) { ... }
-    assign 'facet' to each facet in facetlist
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )
-
-/*----------------------------------
-
-  FORALLnew_facets { ... }
-    assign 'newfacet' to each facet in qh.newfacet_list
-
-  notes:
-    uses 'facetT *newfacet;'
-    at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for ( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*----------------------------------
-
-  FORALLvertex_( vertexlist ) { ... }
-    assign 'vertex' to each vertex in vertexlist
-
-  notes:
-    uses 'vertexT *vertex;'
-    at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*----------------------------------
-
-  FORALLvisible_facets { ... }
-    assign 'visible' to each visible facet in qh.visible_list
-
-  notes:
-    uses 'vacetT *visible;'
-    at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
-
-/*----------------------------------
-
-  FORALLsame_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*----------------------------------
-
-  FORALLsame_cycle_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
-     for (same= newfacet->f.samecycle; \
-         same; same= (same == newfacet ?  NULL : same->f.samecycle))
-
-/*----------------------------------
-
-  FOREACHneighborA_( facet ) { ... }
-    assign 'neighborA' to each neighbor in facet->neighbors
-
-  FOREACHneighborA_( vertex ) { ... }
-    assign 'neighborA' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighborA, **neighborAp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*----------------------------------
-
-  FOREACHvisible_( facets ) { ... }
-    assign 'visible' to each facet in facets
-
-  notes:
-    uses 'facetT *facet, *facetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*----------------------------------
-
-  FOREACHnewfacet_( facets ) { ... }
-    assign 'newfacet' to each facet in facets
-
-  notes:
-    uses 'facetT *newfacet, *newfacetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*----------------------------------
-
-  FOREACHvertexA_( vertices ) { ... }
-    assign 'vertexA' to each vertex in vertices
-
-  notes:
-    uses 'vertexT *vertexA, *vertexAp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*----------------------------------
-
-  FOREACHvertexreverse12_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices
-    reverse order of first two vertices
-
-  notes:
-    uses 'vertexT *vertex, *vertexp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly.c in alphabetical order ================*/
-
-void    qh_appendfacet(facetT *facet);
-void    qh_appendvertex(vertexT *vertex);
-void    qh_attachnewfacets(void /* qh.visible_list, qh.newfacet_list */);
-boolT   qh_checkflipped(facetT *facet, realT *dist, boolT allerror);
-void    qh_delfacet(facetT *facet);
-void    qh_deletevisible(void /*qh.visible_list, qh.horizon_list*/);
-setT   *qh_facetintersect(facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
-int     qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem);
-facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
-void    qh_makenewplanes(void /* newfacet_list */);
-facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew);
-facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew);
-void    qh_matchneighbor(facetT *newfacet, int newskip, int hashsize,
-                          int *hashcount);
-void    qh_matchnewfacets(void);
-boolT   qh_matchvertices(int firstindex, setT *verticesA, int skipA,
-                          setT *verticesB, int *skipB, boolT *same);
-facetT *qh_newfacet(void);
-ridgeT *qh_newridge(void);
-int     qh_pointid(pointT *point);
-void    qh_removefacet(facetT *facet);
-void    qh_removevertex(vertexT *vertex);
-void    qh_updatevertices(void);
-
-
-/*========== -prototypes poly2.c in alphabetical order ===========*/
-
-void    qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash);
-void    qh_check_bestdist(void);
-void    qh_check_dupridge(facetT *facet1, realT dist1, facetT *facet2, realT dist2);
-void    qh_check_maxout(void);
-void    qh_check_output(void);
-void    qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
-void    qh_check_points(void);
-void    qh_checkconvex(facetT *facetlist, int fault);
-void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
-void    qh_checkflipped_all(facetT *facetlist);
-void    qh_checkpolygon(facetT *facetlist);
-void    qh_checkvertex(vertexT *vertex);
-void    qh_clearcenters(qh_CENTER type);
-void    qh_createsimplex(setT *vertices);
-void    qh_delridge(ridgeT *ridge);
-void    qh_delvertex(vertexT *vertex);
-setT   *qh_facet3vertex(facetT *facet);
-facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
-facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
-                          int *numpart);
-int     qh_findgood(facetT *facetlist, int goodhorizon);
-void    qh_findgood_all(facetT *facetlist);
-void    qh_furthestnext(void /* qh.facet_list */);
-void    qh_furthestout(facetT *facet);
-void    qh_infiniteloop(facetT *facet);
-void    qh_initbuild(void);
-void    qh_initialhull(setT *vertices);
-setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
-vertexT *qh_isvertex(pointT *point, setT *vertices);
-vertexT *qh_makenewfacets(pointT *point /*horizon_list, visible_list*/);
-void    qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount);
-void    qh_nearcoplanar(void /* qh.facet_list */);
-vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
-int     qh_newhashtable(int newsize);
-vertexT *qh_newvertex(pointT *point);
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
-void    qh_outcoplanar(void /* facet_list */);
-pointT *qh_point(int id);
-void    qh_point_add(setT *set, pointT *point, void *elem);
-setT   *qh_pointfacet(void /*qh.facet_list*/);
-setT   *qh_pointvertex(void /*qh.facet_list*/);
-void    qh_prependfacet(facetT *facet, facetT **facetlist);
-void    qh_printhashtable(FILE *fp);
-void    qh_printlists(void);
-void    qh_resetlists(boolT stats, boolT resetVisible /*qh.newvertex_list qh.newfacet_list qh.visible_list*/);
-void    qh_setvoronoi_all(void);
-void    qh_triangulate(void /*qh.facet_list*/);
-void    qh_triangulate_facet(facetT *facetA, vertexT **first_vertex);
-void    qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
-void    qh_triangulate_mirror(facetT *facetA, facetT *facetB);
-void    qh_triangulate_null(facetT *facetA);
-void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
-setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
-void    qh_vertexneighbors(void /*qh.facet_list*/);
-boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
-
-
-#endif /* qhDEFpoly */
diff --git a/src/qhull/src/libqhull/poly2.c b/src/qhull/src/libqhull/poly2.c
deleted file mode 100644
index de3e6ad0b..000000000
--- a/src/qhull/src/libqhull/poly2.c
+++ /dev/null
@@ -1,3222 +0,0 @@
-/*
      ---------------------------------
-
-   poly2.c
-   implements polygons and simplices
-
-   see qh-poly.htm, poly.h and libqhull.h
-
-   frequently used code is in poly.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/poly2.c#11 $$Change: 2069 $
-   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_addhash( newelem, hashtable, hashsize, hash )
-    add newelem to linear hash table at hash if not already there
-*/
-void qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash) {
-  int scan;
-  void *elem;
-
-  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (elem == newelem)
-      break;
-  }
-  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
-  if (!elem)
-    SETelem_(hashtable, scan)= newelem;
-} /* addhash */
-
-/*---------------------------------
-
-  qh_check_bestdist()
-    check that all points are within max_outside of the nearest facet
-    if qh.ONLYgood,
-      ignores !good facets
-
-  see:
-    qh_check_maxout(), qh_outerinner()
-
-  notes:
-    only called from qh_check_points()
-      seldom used since qh.MERGING is almost always set
-    if notverified>0 at end of routine
-      some points were well inside the hull.  If the hull contains
-      a lens-shaped component, these points were not verified.  Use
-      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
-
-  design:
-    determine facet for each point (if any)
-    for each point
-      start with the assigned facet or with the first facet
-      find the best facet for the point and check all coplanar facets
-      error if point is outside of facet
-*/
-void qh_check_bestdist(void) {
-  boolT waserror= False, unassigned;
-  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
-  facetT *facetlist;
-  realT dist, maxoutside, maxdist= -REALmax;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
-  setT *facets;
-
-  trace1((qh ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
-      qh facet_list->id));
-  maxoutside= qh_maxouter();
-  maxoutside += qh DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
-  facets= qh_pointfacet(/*qh.facet_list*/);
-  if (!qh_QUICKhelp && qh PRINTprecision)
-    qh_fprintf(qh ferr, 8091, "\n\
-qhull output completed.  Verifying that %d points are\n\
-below %2.2g of the nearest %sfacet.\n",
-             qh_setsize(facets), maxoutside, (qh ONLYgood ?  "good " : ""));
-  FOREACHfacet_i_(facets) {  /* for each point with facet assignment */
-    if (facet)
-      unassigned= False;
-    else {
-      unassigned= True;
-      facet= qh facet_list;
-    }
-    point= qh_point(facet_i);
-    if (point == qh GOODpointp)
-      continue;
-    qh_distplane(point, facet, &dist);
-    numpart++;
-    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
-    /* occurs after statistics reported */
-    maximize_(maxdist, dist);
-    if (dist > maxoutside) {
-      if (qh ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-        notgood++;
-      else {
-        waserror= True;
-        qh_fprintf(qh ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-                facet_i, bestfacet->id, dist, maxoutside);
-        if (errfacet1 != bestfacet) {
-          errfacet2= errfacet1;
-          errfacet1= bestfacet;
-        }
-      }
-    }else if (unassigned && dist < -qh MAXcoplanar)
-      notverified++;
-  }
-  qh_settempfree(&facets);
-  if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
-    qh_fprintf(qh ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
-a lens-shaped component, these points were not verified.  Use\n\
-options 'Qci Tv' to verify all points.\n", notverified);
-  if (maxdist > qh outside_err) {
-    qh_fprintf(qh ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-              maxdist, qh outside_err);
-    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
-  }else if (waserror && qh outside_err > REALmax/2)
-    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
-  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
-  trace0((qh ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
-} /* check_bestdist */
-
-/*---------------------------------
-
-  qh_check_dupridge(facet1, dist1, facet2, dist2)
-    Check duplicate ridge between facet1 and facet2 for wide merge
-    dist1 is the maximum distance of facet1's vertices to facet2
-    dist2 is the maximum distance of facet2's vertices to facet1
-
-  Returns
-    Level 1 log of the duplicate ridge with the minimum distance between vertices
-    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
-
-  called from:
-    qh_forcedmerges()
-*/
-#ifndef qh_NOmerge
-void qh_check_dupridge(facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
-  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
-  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
-  realT minvertex= REALmax;
-
-  mergedist= fmin_(dist1, dist2);
-  qh_outerinner(NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
-  prevdist= fmax_(outerplane, innerplane);
-  maximize_(prevdist, qh ONEmerge + qh DISTround);
-  maximize_(prevdist, qh MINoutside + qh DISTround);
-  ratio= mergedist/prevdist;
-  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
-    FOREACHvertexA_(facet1->vertices) {
-      if (vertex > vertexA){   /* Test each pair once */
-        dist= qh_pointdist(vertex->point, vertexA->point, qh hull_dim);
-        minimize_(minvertex, dist);
-      }
-    }
-  }
-  trace0((qh ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
-        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh furthest_id));
-  if (ratio > qh_WIDEduplicate) {
-    qh_fprintf(qh ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
-          ratio, minvertex, facet1->id, facet2->id, mergedist, qh furthest_id);
-    if (qh DELAUNAY)
-      qh_fprintf(qh ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
-    if(minvertex > qh_WIDEduplicate*prevdist)
-      qh_fprintf(qh ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
-          minvertex, qh_WIDEduplicate, prevdist);
-    if (!qh NOwide)
-      qh_errexit2(qh_ERRqhull, facet1, facet2);
-  }
-} /* check_dupridge */
-#endif
-
-/*---------------------------------
-
-  qh_check_maxout()
-    updates qh.max_outside by checking all points against bestfacet
-    if qh.ONLYgood, ignores !good facets
-
-  returns:
-    updates facet->maxoutside via qh_findbesthorizon()
-    sets qh.maxoutdone
-    if printing qh.min_vertex (qh_outerinner),
-      it is updated to the current vertices
-    removes inside/coplanar points from coplanarset as needed
-
-  notes:
-    defines coplanar as min_vertex instead of MAXcoplanar
-    may not need to check near-inside points because of qh.MAXcoplanar
-      and qh.KEEPnearinside (before it was -DISTround)
-
-  see also:
-    qh_check_bestdist()
-
-  design:
-    if qh.min_vertex is needed
-      for all neighbors of all vertices
-        test distance from vertex to neighbor
-    determine facet for each point (if any)
-    for each point with an assigned facet
-      find the best facet for the point and check all coplanar facets
-        (updates outer planes)
-    remove near-inside points from coplanar sets
-*/
-#ifndef qh_NOmerge
-void qh_check_maxout(void) {
-  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
-  realT dist, maxoutside, minvertex, old_maxoutside;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0;
-  setT *facets, *vertices;
-  vertexT *vertex;
-
-  trace1((qh ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
-  maxoutside= minvertex= 0;
-  if (qh VERTEXneighbors
-  && (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
-        || qh TRACElevel || qh PRINTstatistics
-        || qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
-    trace1((qh ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
-    vertices= qh_pointvertex(/*qh.facet_list*/);
-    FORALLvertices {
-      FOREACHneighbor_(vertex) {
-        zinc_(Zdistvertex);  /* distance also computed by main loop below */
-        qh_distplane(vertex->point, neighbor, &dist);
-        minimize_(minvertex, dist);
-        if (-dist > qh TRACEdist || dist > qh TRACEdist
-        || neighbor == qh tracefacet || vertex == qh tracevertex)
-          qh_fprintf(qh ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
-                    qh_pointid(vertex->point), vertex->id, dist, neighbor->id);
-      }
-    }
-    if (qh MERGING) {
-      wmin_(Wminvertex, qh min_vertex);
-    }
-    qh min_vertex= minvertex;
-    qh_settempfree(&vertices);
-  }
-  facets= qh_pointfacet(/*qh.facet_list*/);
-  do {
-    old_maxoutside= fmax_(qh max_outside, maxoutside);
-    FOREACHfacet_i_(facets) {     /* for each point with facet assignment */
-      if (facet) {
-        point= qh_point(facet_i);
-        if (point == qh GOODpointp)
-          continue;
-        zzinc_(Ztotcheck);
-        qh_distplane(point, facet, &dist);
-        numpart++;
-        bestfacet= qh_findbesthorizon(qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
-        if (bestfacet && dist > maxoutside) {
-          if (qh ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-            notgood++;
-          else
-            maxoutside= dist;
-        }
-        if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
-          qh_fprintf(qh ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
-                     qh_pointid(point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
-      }
-    }
-  }while
-    (maxoutside > 2*old_maxoutside);
-    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
-          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
-  zzadd_(Zcheckpart, numpart);
-  qh_settempfree(&facets);
-  wval_(Wmaxout)= maxoutside - qh max_outside;
-  wmax_(Wmaxoutside, qh max_outside);
-  qh max_outside= maxoutside;
-  qh_nearcoplanar(/*qh.facet_list*/);
-  qh maxoutdone= True;
-  trace1((qh ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
-       maxoutside, qh min_vertex, notgood));
-} /* check_maxout */
-#else /* qh_NOmerge */
-void qh_check_maxout(void) {
-}
-#endif
-
-/*---------------------------------
-
-  qh_check_output()
-    performs the checks at the end of qhull algorithm
-    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
-*/
-void qh_check_output(void) {
-  int i;
-
-  if (qh STOPcone)
-    return;
-  if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
-    qh_checkpolygon(qh facet_list);
-    qh_checkflipped_all(qh facet_list);
-    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
-  }else if (!qh MERGING && qh_newstats(qhstat precision, &i)) {
-    qh_checkflipped_all(qh facet_list);
-    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
-  }
-} /* check_output */
-
-
-
-/*---------------------------------
-
-  qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
-    check that point is less than maxoutside from facet
-*/
-void qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
-  realT dist;
-
-  /* occurs after statistics reported */
-  qh_distplane(point, facet, &dist);
-  if (dist > *maxoutside) {
-    if (*errfacet1 != facet) {
-      *errfacet2= *errfacet1;
-      *errfacet1= facet;
-    }
-    qh_fprintf(qh ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-              qh_pointid(point), facet->id, dist, *maxoutside);
-  }
-  maximize_(*maxdist, dist);
-} /* qh_check_point */
-
-
-/*---------------------------------
-
-  qh_check_points()
-    checks that all points are inside all facets
-
-  notes:
-    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
-       calls qh_findbesthorizon (seldom done).
-    ignores flipped facets
-    maxoutside includes 2 qh.DISTrounds
-      one qh.DISTround for the computed distances in qh_check_points
-    qh_printafacet and qh_printsummary needs only one qh.DISTround
-    the computation for qh.VERIFYdirect does not account for qh.other_points
-
-  design:
-    if many points
-      use qh_check_bestdist()
-    else
-      for all facets
-        for all points
-          check that point is inside facet
-*/
-void qh_check_points(void) {
-  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
-  realT total, maxoutside, maxdist= -REALmax;
-  pointT *point, **pointp, *pointtemp;
-  boolT testouter;
-
-  maxoutside= qh_maxouter();
-  maxoutside += qh DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
-          maxoutside));
-  if (qh num_good)   /* miss counts other_points and !good facets */
-     total= (float)qh num_good * (float)qh num_points;
-  else
-     total= (float)qh num_facets * (float)qh num_points;
-  if (total >= qh_VERIFYdirect && !qh maxoutdone) {
-    if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
-      qh_fprintf(qh ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
-Verify may report that a point is outside of a facet.\n");
-    qh_check_bestdist();
-  }else {
-    if (qh_MAXoutside && qh maxoutdone)
-      testouter= True;
-    else
-      testouter= False;
-    if (!qh_QUICKhelp) {
-      if (qh MERGEexact)
-        qh_fprintf(qh ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
-is outside of a facet.  See qh-optq.htm#Qx\n");
-      else if (qh SKIPcheckmax || qh NOnearinside)
-        qh_fprintf(qh ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
-near-inside points ('Q8').  Verify may report that a point is outside\n\
-of a facet.\n");
-    }
-    if (qh PRINTprecision) {
-      if (testouter)
-        qh_fprintf(qh ferr, 8098, "\n\
-Output completed.  Verifying that all points are below outer planes of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              (qh ONLYgood ?  "good " : ""), total);
-      else
-        qh_fprintf(qh ferr, 8099, "\n\
-Output completed.  Verifying that all points are below %2.2g of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              maxoutside, (qh ONLYgood ?  "good " : ""), total);
-    }
-    FORALLfacets {
-      if (!facet->good && qh ONLYgood)
-        continue;
-      if (facet->flipped)
-        continue;
-      if (!facet->normal) {
-        qh_fprintf(qh ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
-        continue;
-      }
-      if (testouter) {
-#if qh_MAXoutside
-        maxoutside= facet->maxoutside + 2* qh DISTround;
-        /* one DISTround to actual point and another to computed point */
-#endif
-      }
-      FORALLpoints {
-        if (point != qh GOODpointp)
-          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-      FOREACHpoint_(qh other_points) {
-        if (point != qh GOODpointp)
-          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-    }
-    if (maxdist > qh outside_err) {
-      qh_fprintf(qh ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-                maxdist, qh outside_err );
-      qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
-    }else if (errfacet1 && qh outside_err > REALmax/2)
-        qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
-    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
-    trace0((qh ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
-  }
-} /* check_points */
-
-
-/*---------------------------------
-
-  qh_checkconvex( facetlist, fault )
-    check that each ridge in facetlist is convex
-    fault = qh_DATAfault if reporting errors
-          = qh_ALGORITHMfault otherwise
-
-  returns:
-    counts Zconcaveridges and Zcoplanarridges
-    errors if concaveridge or if merging an coplanar ridge
-
-  note:
-    if not merging,
-      tests vertices for neighboring simplicial facets
-    else if ZEROcentrum,
-      tests vertices for neighboring simplicial   facets
-    else
-      tests centrums of neighboring facets
-
-  design:
-    for all facets
-      report flipped facets
-      if ZEROcentrum and simplicial neighbors
-        test vertices for neighboring simplicial facets
-      else
-        test centrum against all neighbors
-*/
-void qh_checkconvex(facetT *facetlist, int fault) {
-  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
-  vertexT *vertex;
-  realT dist;
-  pointT *centrum;
-  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
-  int neighbor_i;
-
-  trace1((qh ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
-  if (!qh RERUN) {
-    zzval_(Zconcaveridges)= 0;
-    zzval_(Zcoplanarridges)= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->flipped) {
-      qh_precision("flipped facet");
-      qh_fprintf(qh ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
-               facet->id);
-      errfacet1= facet;
-      waserror= True;
-      continue;
-    }
-    if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
-      allsimplicial= False;
-    else {
-      allsimplicial= True;
-      neighbor_i= 0;
-      FOREACHneighbor_(facet) {
-        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-        if (!neighbor->simplicial || neighbor->tricoplanar) {
-          allsimplicial= False;
-          continue;
-        }
-        qh_distplane(vertex->point, neighbor, &dist);
-        if (dist > -qh DISTround) {
-          if (fault == qh_DATAfault) {
-            qh_precision("coplanar or concave ridge");
-            qh_fprintf(qh ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
-            qh_errexit(qh_ERRsingular, NULL, NULL);
-          }
-          if (dist > qh DISTround) {
-            zzinc_(Zconcaveridges);
-            qh_precision("concave ridge");
-            qh_fprintf(qh ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
-              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
-            errfacet1= facet;
-            errfacet2= neighbor;
-            waserror= True;
-          }else if (qh ZEROcentrum) {
-            if (dist > 0) {     /* qh_checkzero checks that dist < - qh DISTround */
-              zzinc_(Zcoplanarridges);
-              qh_precision("coplanar ridge");
-              qh_fprintf(qh ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
-                facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
-              errfacet1= facet;
-              errfacet2= neighbor;
-              waserror= True;
-            }
-          }else {
-            zzinc_(Zcoplanarridges);
-            qh_precision("coplanar ridge");
-            trace0((qh ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
-              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
-          }
-        }
-      }
-    }
-    if (!allsimplicial) {
-      if (qh CENTERtype == qh_AScentrum) {
-        if (!facet->center)
-          facet->center= qh_getcentrum(facet);
-        centrum= facet->center;
-      }else {
-        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
-           centrum_warning= True;
-           qh_fprintf(qh ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
-        }
-        centrum= qh_getcentrum(facet);
-        tempcentrum= True;
-      }
-      FOREACHneighbor_(facet) {
-        if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
-          continue;
-        if (facet->tricoplanar || neighbor->tricoplanar)
-          continue;
-        zzinc_(Zdistconvex);
-        qh_distplane(centrum, neighbor, &dist);
-        if (dist > qh DISTround) {
-          zzinc_(Zconcaveridges);
-          qh_precision("concave ridge");
-          qh_fprintf(qh ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
-                                     can test against centrum radius instead */
-          zzinc_(Zcoplanarridges);
-          qh_precision("coplanar ridge");
-          qh_fprintf(qh ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }
-      }
-      if (tempcentrum)
-        qh_memfree(centrum, qh normal_size);
-    }
-  }
-  if (waserror && !qh FORCEoutput)
-    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
-} /* checkconvex */
-
-
-/*---------------------------------
-
-  qh_checkfacet( facet, newmerge, waserror )
-    checks for consistency errors in facet
-    newmerge set if from merge.c
-
-  returns:
-    sets waserror if any error occurs
-
-  checks:
-    vertex ids are inverse sorted
-    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
-    if non-simplicial, at least as many ridges as neighbors
-    neighbors are not duplicated
-    ridges are not duplicated
-    in 3-d, ridges=verticies
-    (qh.hull_dim-1) ridge vertices
-    neighbors are reciprocated
-    ridge neighbors are facet neighbors and a ridge for every neighbor
-    simplicial neighbors match facetintersect
-    vertex intersection matches vertices of common ridges
-    vertex neighbors and facet vertices agree
-    all ridges have distinct vertex sets
-
-  notes:
-    uses neighbor->seen
-
-  design:
-    check sets
-    check vertices
-    check sizes of neighbors and vertices
-    check for qh_MERGEridge and qh_DUPLICATEridge flags
-    check neighbor set
-    check ridge set
-    check ridges, neighbors, and vertices
-*/
-void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
-  facetT *neighbor, **neighborp, *errother=NULL;
-  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
-  vertexT *vertex, **vertexp;
-  unsigned previousid= INT_MAX;
-  int numneighbors, numvertices, numridges=0, numRvertices=0;
-  boolT waserror= False;
-  int skipA, skipB, ridge_i, ridge_n, i;
-  setT *intersection;
-
-  if (facet->visible) {
-    qh_fprintf(qh ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
-      facet->id);
-    qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  if (!facet->normal) {
-    qh_fprintf(qh ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
-      facet->id);
-    waserror= True;
-  }
-  qh_setcheck(facet->vertices, "vertices for f", facet->id);
-  qh_setcheck(facet->ridges, "ridges for f", facet->id);
-  qh_setcheck(facet->outsideset, "outsideset for f", facet->id);
-  qh_setcheck(facet->coplanarset, "coplanarset for f", facet->id);
-  qh_setcheck(facet->neighbors, "neighbors for f", facet->id);
-  FOREACHvertex_(facet->vertices) {
-    if (vertex->deleted) {
-      qh_fprintf(qh ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
-      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
-      waserror= True;
-    }
-    if (vertex->id >= previousid) {
-      qh_fprintf(qh ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
-      waserror= True;
-      break;
-    }
-    previousid= vertex->id;
-  }
-  numneighbors= qh_setsize(facet->neighbors);
-  numvertices= qh_setsize(facet->vertices);
-  numridges= qh_setsize(facet->ridges);
-  if (facet->simplicial) {
-    if (numvertices+numneighbors != 2*qh hull_dim
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
-                facet->id, numvertices, numneighbors);
-      qh_setprint(qh ferr, "", facet->neighbors);
-      waserror= True;
-    }
-  }else { /* non-simplicial */
-    if (!newmerge
-    &&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
-         facet->id, numvertices, numneighbors);
-       waserror= True;
-    }
-    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
-    if (numridges < numneighbors
-    ||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
-    ||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
-      if (!facet->degenerate && !facet->redundant) {
-        qh_fprintf(qh ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
-            facet->id, numridges, numneighbors, numvertices);
-        waserror= True;
-      }
-    }
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
-      qh_fprintf(qh ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-    neighbor->seen= True;
-  }
-  FOREACHneighbor_(facet) {
-    if (!qh_setin(neighbor->neighbors, facet)) {
-      qh_fprintf(qh ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
-              facet->id, neighbor->id, neighbor->id, facet->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    if (!neighbor->seen) {
-      qh_fprintf(qh ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
-              facet->id, neighbor->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    qh_setcheck(ridge->vertices, "vertices for r", ridge->id);
-    ridge->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    if (ridge->seen) {
-      qh_fprintf(qh ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
-              facet->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-    ridge->seen= True;
-    numRvertices= qh_setsize(ridge->vertices);
-    if (numRvertices != qh hull_dim - 1) {
-      qh_fprintf(qh ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
-                ridge->top->id, ridge->bottom->id, numRvertices);
-      errridge= ridge;
-      waserror= True;
-    }
-    neighbor= otherfacet_(ridge, facet);
-    neighbor->seen= True;
-    if (!qh_setin(facet->neighbors, neighbor)) {
-      qh_fprintf(qh ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
-           facet->id, neighbor->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-  }
-  if (!facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen) {
-        qh_fprintf(qh ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
-              facet->id, neighbor->id);
-        errother= neighbor;
-        waserror= True;
-      }
-      intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
-      qh_settemppush(intersection);
-      FOREACHvertex_(facet->vertices) {
-        vertex->seen= False;
-        vertex->seen2= False;
-      }
-      FOREACHvertex_(intersection)
-        vertex->seen= True;
-      FOREACHridge_(facet->ridges) {
-        if (neighbor != otherfacet_(ridge, facet))
-            continue;
-        FOREACHvertex_(ridge->vertices) {
-          if (!vertex->seen) {
-            qh_fprintf(qh ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
-                  vertex->id, ridge->id, facet->id, neighbor->id);
-            qh_errexit(qh_ERRqhull, facet, ridge);
-          }
-          vertex->seen2= True;
-        }
-      }
-      if (!newmerge) {
-        FOREACHvertex_(intersection) {
-          if (!vertex->seen2) {
-            if (qh IStracing >=3 || !qh MERGING) {
-              qh_fprintf(qh ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
- not in a ridge.  This is ok under merging.  Last point was p%d\n",
-                     vertex->id, facet->id, neighbor->id, qh furthest_id);
-              if (!qh FORCEoutput && !qh MERGING) {
-                qh_errprint("ERRONEOUS", facet, neighbor, NULL, vertex);
-                if (!qh MERGING)
-                  qh_errexit(qh_ERRqhull, NULL, NULL);
-              }
-            }
-          }
-        }
-      }
-      qh_settempfree(&intersection);
-    }
-  }else { /* simplicial */
-    FOREACHneighbor_(facet) {
-      if (neighbor->simplicial) {
-        skipA= SETindex_(facet->neighbors, neighbor);
-        skipB= qh_setindex(neighbor->neighbors, facet);
-        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
-          qh_fprintf(qh ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
-                   facet->id, skipA, neighbor->id, skipB);
-          errother= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
-    FOREACHridge_i_(facet->ridges) {           /* expensive */
-      for (i=ridge_i+1; i < ridge_n; i++) {
-        ridge2= SETelemt_(facet->ridges, i, ridgeT);
-        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
-          qh_fprintf(qh ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
-                  ridge->id, ridge2->id);
-          errridge= ridge;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
-    *waserrorp= True;
-  }
-} /* checkfacet */
-
-
-/*---------------------------------
-
-  qh_checkflipped_all( facetlist )
-    checks orientation of facets in list against interior point
-*/
-void qh_checkflipped_all(facetT *facetlist) {
-  facetT *facet;
-  boolT waserror= False;
-  realT dist;
-
-  if (facetlist == qh facet_list)
-    zzval_(Zflippedfacets)= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->normal && !qh_checkflipped(facet, &dist, !qh_ALL)) {
-      qh_fprintf(qh ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
-              facet->id, dist);
-      if (!qh FORCEoutput) {
-        qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
-        waserror= True;
-      }
-    }
-  }
-  if (waserror) {
-    qh_fprintf(qh ferr, 8101, "\n\
-A flipped facet occurs when its distance to the interior point is\n\
-greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
-    qh_errexit(qh_ERRprec, NULL, NULL);
-  }
-} /* checkflipped_all */
-
-/*---------------------------------
-
-  qh_checkpolygon( facetlist )
-    checks the correctness of the structure
-
-  notes:
-    call with either qh.facet_list or qh.newfacet_list
-    checks num_facets and num_vertices if qh.facet_list
-
-  design:
-    for each facet
-      checks facet and outside set
-    initializes vertexlist
-    for each facet
-      checks vertex set
-    if checking all facets(qh.facetlist)
-      check facet count
-      if qh.VERTEXneighbors
-        check vertex neighbors and count
-      check vertex count
-*/
-void qh_checkpolygon(facetT *facetlist) {
-  facetT *facet;
-  vertexT *vertex, **vertexp, *vertexlist;
-  int numfacets= 0, numvertices= 0, numridges= 0;
-  int totvneighbors= 0, totvertices= 0;
-  boolT waserror= False, nextseen= False, visibleseen= False;
-
-  trace1((qh ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
-  if (facetlist != qh facet_list || qh ONLYgood)
-    nextseen= True;
-  FORALLfacet_(facetlist) {
-    if (facet == qh visible_list)
-      visibleseen= True;
-    if (!facet->visible) {
-      if (!nextseen) {
-        if (facet == qh facet_next)
-          nextseen= True;
-        else if (qh_setsize(facet->outsideset)) {
-          if (!qh NARROWhull
-#if !qh_COMPUTEfurthest
-               || facet->furthestdist >= qh MINoutside
-#endif
-                        ) {
-            qh_fprintf(qh ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
-                     facet->id);
-            qh_errexit(qh_ERRqhull, facet, NULL);
-          }
-        }
-      }
-      numfacets++;
-      qh_checkfacet(facet, False, &waserror);
-    }
-  }
-  if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
-    qh_fprintf(qh ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
-    qh_printlists();
-    qh_errexit(qh_ERRqhull, qh visible_list, NULL);
-  }
-  if (facetlist == qh facet_list)
-    vertexlist= qh vertex_list;
-  else if (facetlist == qh newfacet_list)
-    vertexlist= qh newvertex_list;
-  else
-    vertexlist= NULL;
-  FORALLvertex_(vertexlist) {
-    vertex->seen= False;
-    vertex->visitid= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visible)
-      continue;
-    if (facet->simplicial)
-      numridges += qh hull_dim;
-    else
-      numridges += qh_setsize(facet->ridges);
-    FOREACHvertex_(facet->vertices) {
-      vertex->visitid++;
-      if (!vertex->seen) {
-        vertex->seen= True;
-        numvertices++;
-        if (qh_pointid(vertex->point) == qh_IDunknown) {
-          qh_fprintf(qh ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
-                   vertex->point, vertex->id, qh first_point);
-          waserror= True;
-        }
-      }
-    }
-  }
-  qh vertex_visit += (unsigned int)numfacets;
-  if (facetlist == qh facet_list) {
-    if (numfacets != qh num_facets - qh num_visible) {
-      qh_fprintf(qh ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
-              numfacets, qh num_facets, qh num_visible);
-      waserror= True;
-    }
-    qh vertex_visit++;
-    if (qh VERTEXneighbors) {
-      FORALLvertices {
-        qh_setcheck(vertex->neighbors, "neighbors for v", vertex->id);
-        if (vertex->deleted)
-          continue;
-        totvneighbors += qh_setsize(vertex->neighbors);
-      }
-      FORALLfacet_(facetlist)
-        totvertices += qh_setsize(facet->vertices);
-      if (totvneighbors != totvertices) {
-        qh_fprintf(qh ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
-                totvneighbors, totvertices);
-        waserror= True;
-      }
-    }
-    if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
-      qh_fprintf(qh ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
-              numvertices, qh num_vertices - qh_setsize(qh del_vertices));
-      waserror= True;
-    }
-    if (qh hull_dim == 2 && numvertices != numfacets) {
-      qh_fprintf(qh ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
-        numvertices, numfacets);
-      waserror= True;
-    }
-    if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
-      qh_fprintf(qh ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
-        A vertex appears twice in a edge list.  May occur during merging.",
-        numvertices, numfacets, numridges/2);
-      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
-    }
-  }
-  if (waserror)
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-} /* checkpolygon */
-
-
-/*---------------------------------
-
-  qh_checkvertex( vertex )
-    check vertex for consistency
-    checks vertex->neighbors
-
-  notes:
-    neighbors checked efficiently in checkpolygon
-*/
-void qh_checkvertex(vertexT *vertex) {
-  boolT waserror= False;
-  facetT *neighbor, **neighborp, *errfacet=NULL;
-
-  if (qh_pointid(vertex->point) == qh_IDunknown) {
-    qh_fprintf(qh ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
-    waserror= True;
-  }
-  if (vertex->id >= qh vertex_id) {
-    qh_fprintf(qh ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
-    waserror= True;
-  }
-  if (!waserror && !vertex->deleted) {
-    if (qh_setsize(vertex->neighbors)) {
-      FOREACHneighbor_(vertex) {
-        if (!qh_setin(neighbor->vertices, vertex)) {
-          qh_fprintf(qh ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
-          errfacet= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
-    qh_errexit(qh_ERRqhull, errfacet, NULL);
-  }
-} /* checkvertex */
-
-/*---------------------------------
-
-  qh_clearcenters( type )
-    clear old data from facet->center
-
-  notes:
-    sets new centertype
-    nop if CENTERtype is the same
-*/
-void qh_clearcenters(qh_CENTER type) {
-  facetT *facet;
-
-  if (qh CENTERtype != type) {
-    FORALLfacets {
-      if (facet->tricoplanar && !facet->keepcentrum)
-          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
-      else if (qh CENTERtype == qh_ASvoronoi){
-        if (facet->center) {
-          qh_memfree(facet->center, qh center_size);
-          facet->center= NULL;
-        }
-      }else /* qh.CENTERtype == qh_AScentrum */ {
-        if (facet->center) {
-          qh_memfree(facet->center, qh normal_size);
-          facet->center= NULL;
-        }
-      }
-    }
-    qh CENTERtype= type;
-  }
-  trace2((qh ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
-} /* clearcenters */
-
-/*---------------------------------
-
-  qh_createsimplex( vertices )
-    creates a simplex from a set of vertices
-
-  returns:
-    initializes qh.facet_list to the simplex
-    initializes qh.newfacet_list, .facet_tail
-    initializes qh.vertex_list, .newvertex_list, .vertex_tail
-
-  design:
-    initializes lists
-    for each vertex
-      create a new facet
-    for each new facet
-      create its neighbor set
-*/
-void qh_createsimplex(setT *vertices) {
-  facetT *facet= NULL, *newfacet;
-  boolT toporient= True;
-  int vertex_i, vertex_n, nth;
-  setT *newfacets= qh_settemp(qh hull_dim+1);
-  vertexT *vertex;
-
-  qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
-  qh num_facets= qh num_vertices= qh num_visible= 0;
-  qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
-  FOREACHvertex_i_(vertices) {
-    newfacet= qh_newfacet();
-    newfacet->vertices= qh_setnew_delnthsorted(vertices, vertex_n,
-                                                vertex_i, 0);
-    newfacet->toporient= (unsigned char)toporient;
-    qh_appendfacet(newfacet);
-    newfacet->newfacet= True;
-    qh_appendvertex(vertex);
-    qh_setappend(&newfacets, newfacet);
-    toporient ^= True;
-  }
-  FORALLnew_facets {
-    nth= 0;
-    FORALLfacet_(qh newfacet_list) {
-      if (facet != newfacet)
-        SETelem_(newfacet->neighbors, nth++)= facet;
-    }
-    qh_settruncate(newfacet->neighbors, qh hull_dim);
-  }
-  qh_settempfree(&newfacets);
-  trace1((qh ferr, 1028, "qh_createsimplex: created simplex\n"));
-} /* createsimplex */
-
-/*---------------------------------
-
-  qh_delridge( ridge )
-    deletes ridge from data structures it belongs to
-    frees up its memory
-
-  notes:
-    in merge.c, caller sets vertex->delridge for each vertex
-    ridges also freed in qh_freeqhull
-*/
-void qh_delridge(ridgeT *ridge) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  qh_setdel(ridge->top->ridges, ridge);
-  qh_setdel(ridge->bottom->ridges, ridge);
-  qh_setfree(&(ridge->vertices));
-  qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
-} /* delridge */
-
-
-/*---------------------------------
-
-  qh_delvertex( vertex )
-    deletes a vertex and frees its memory
-
-  notes:
-    assumes vertex->adjacencies have been updated if needed
-    unlinks from vertex_list
-*/
-void qh_delvertex(vertexT *vertex) {
-
-  if (vertex == qh tracevertex)
-    qh tracevertex= NULL;
-  qh_removevertex(vertex);
-  qh_setfree(&vertex->neighbors);
-  qh_memfree(vertex, (int)sizeof(vertexT));
-} /* delvertex */
-
-
-/*---------------------------------
-
-  qh_facet3vertex(  )
-    return temporary set of 3-d vertices in qh_ORIENTclock order
-
-  design:
-    if simplicial facet
-      build set from facet->vertices with facet->toporient
-    else
-      for each ridge in order
-        build set from ridge's vertices
-*/
-setT *qh_facet3vertex(facetT *facet) {
-  ridgeT *ridge, *firstridge;
-  vertexT *vertex;
-  int cntvertices, cntprojected=0;
-  setT *vertices;
-
-  cntvertices= qh_setsize(facet->vertices);
-  vertices= qh_settemp(cntvertices);
-  if (facet->simplicial) {
-    if (cntvertices != 3) {
-      qh_fprintf(qh ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
-                  cntvertices, facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-    qh_setappend(&vertices, SETfirst_(facet->vertices));
-    if (facet->toporient ^ qh_ORIENTclock)
-      qh_setappend(&vertices, SETsecond_(facet->vertices));
-    else
-      qh_setaddnth(&vertices, 0, SETsecond_(facet->vertices));
-    qh_setappend(&vertices, SETelem_(facet->vertices, 2));
-  }else {
-    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
-    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
-      qh_setappend(&vertices, vertex);
-      if (++cntprojected > cntvertices || ridge == firstridge)
-        break;
-    }
-    if (!ridge || cntprojected != cntvertices) {
-      qh_fprintf(qh ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
-                  facet->id, cntprojected);
-      qh_errexit(qh_ERRqhull, facet, ridge);
-    }
-  }
-  return vertices;
-} /* facet3vertex */
-
-/*---------------------------------
-
-  qh_findbestfacet( point, bestoutside, bestdist, isoutside )
-    find facet that is furthest below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    if bestoutside is set (e.g., qh_ALL)
-      returns best facet that is not upperdelaunay
-      if Delaunay and inside, point is outside circumsphere of bestfacet
-    else
-      returns first facet below point
-      if point is inside, returns nearest, !upperdelaunay facet
-    distance to facet
-    isoutside set if outside of facet
-
-  notes:
-    For tricoplanar facets, this finds one of the tricoplanar facets closest
-    to the point.  For Delaunay triangulations, the point may be inside a
-    different tricoplanar facet. See locate a facet with qh_findbestfacet()
-
-    If inside, qh_findbestfacet performs an exhaustive search
-       this may be too conservative.  Sometimes it is clearly required.
-
-    qh_findbestfacet is not used by qhull.
-    uses qh.visit_id and qh.coplanarset
-
-  see:
-    qh_findbest
-*/
-facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside) {
-  facetT *bestfacet= NULL;
-  int numpart, totpart= 0;
-
-  bestfacet= qh_findbest(point, qh facet_list,
-                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
-                            bestdist, isoutside, &totpart);
-  if (*bestdist < -qh DISTround) {
-    bestfacet= qh_findfacet_all(point, bestdist, isoutside, &numpart);
-    totpart += numpart;
-    if ((isoutside && *isoutside && bestoutside)
-    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
-      bestfacet= qh_findbest(point, bestfacet,
-                            bestoutside, False, bestoutside,
-                            bestdist, isoutside, &totpart);
-      totpart += numpart;
-    }
-  }
-  trace3((qh ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
-      bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
-  return bestfacet;
-} /* findbestfacet */
-
-/*---------------------------------
-
-  qh_findbestlower( facet, point, bestdist, numpart )
-    returns best non-upper, non-flipped neighbor of facet for point
-    if needed, searches vertex neighbors
-
-  returns:
-    returns bestdist and updates numpart
-
-  notes:
-    if Delaunay and inside, point is outside of circumsphere of bestfacet
-    called by qh_findbest() for points above an upperdelaunay facet
-
-*/
-facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  realT dist;
-  vertexT *vertex;
-  boolT isoutside= False;  /* not used */
-
-  zinc_(Zbestlower);
-  FOREACHneighbor_(upperfacet) {
-    if (neighbor->upperdelaunay || neighbor->flipped)
-      continue;
-    (*numpart)++;
-    qh_distplane(point, neighbor, &dist);
-    if (dist > bestdist) {
-      bestfacet= neighbor;
-      bestdist= dist;
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerv);
-    /* rarely called, numpart does not count nearvertex computations */
-    vertex= qh_nearvertex(upperfacet, point, &dist);
-    qh_vertexneighbors();
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay || neighbor->flipped)
-        continue;
-      (*numpart)++;
-      qh_distplane(point, neighbor, &dist);
-      if (dist > bestdist) {
-        bestfacet= neighbor;
-        bestdist= dist;
-      }
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
-    zmax_(Zbestloweralln, qh num_facets);
-    /* [dec'15] Previously reported as QH6228 */
-    trace3((qh ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
-        upperfacet->id));
-    /* rarely called */
-    bestfacet= qh_findfacet_all(point, &bestdist, &isoutside, numpart);
-  }
-  *bestdistp= bestdist;
-  trace3((qh ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
-          bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
-  return bestfacet;
-} /* findbestlower */
-
-/*---------------------------------
-
-  qh_findfacet_all( point, bestdist, isoutside, numpart )
-    exhaustive search for facet below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns first facet below point
-    if point is inside,
-      returns nearest facet
-    distance to facet
-    isoutside if point is outside of the hull
-    number of distance tests
-
-  notes:
-    primarily for library users, rarely used by Qhull
-*/
-facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
-                          int *numpart) {
-  facetT *bestfacet= NULL, *facet;
-  realT dist;
-  int totpart= 0;
-
-  *bestdist= -REALmax;
-  *isoutside= False;
-  FORALLfacets {
-    if (facet->flipped || !facet->normal)
-      continue;
-    totpart++;
-    qh_distplane(point, facet, &dist);
-    if (dist > *bestdist) {
-      *bestdist= dist;
-      bestfacet= facet;
-      if (dist > qh MINoutside) {
-        *isoutside= True;
-        break;
-      }
-    }
-  }
-  *numpart= totpart;
-  trace3((qh ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
-          getid_(bestfacet), *bestdist, *isoutside, totpart));
-  return bestfacet;
-} /* findfacet_all */
-
-/*---------------------------------
-
-  qh_findgood( facetlist, goodhorizon )
-    identify good facets for qh.PRINTgood
-    if qh.GOODvertex>0
-      facet includes point as vertex
-      if !match, returns goodhorizon
-      inactive if qh.MERGING
-    if qh.GOODpoint
-      facet is visible or coplanar (>0) or not visible (<0)
-    if qh.GOODthreshold
-      facet->normal matches threshold
-    if !goodhorizon and !match,
-      selects facet with closest angle
-      sets GOODclosest
-
-  returns:
-    number of new, good facets found
-    determines facet->good
-    may update qh.GOODclosest
-
-  notes:
-    qh_findgood_all further reduces the good region
-
-  design:
-    count good facets
-    mark good facets for qh.GOODpoint
-    mark good facets for qh.GOODthreshold
-    if necessary
-      update qh.GOODclosest
-*/
-int qh_findgood(facetT *facetlist, int goodhorizon) {
-  facetT *facet, *bestfacet= NULL;
-  realT angle, bestangle= REALmax, dist;
-  int  numgood=0;
-
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh GOODvertex>0 && !qh MERGING) {
-    FORALLfacet_(facetlist) {
-      if (!qh_isvertex(qh GOODvertexp, facet->vertices)) {
-        facet->good= False;
-        numgood--;
-      }
-    }
-  }
-  if (qh GOODpoint && numgood) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        zinc_(Zdistgood);
-        qh_distplane(qh GOODpointp, facet, &dist);
-        if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
-          facet->good= False;
-          numgood--;
-        }
-      }
-    }
-  }
-  if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        if (!qh_inthresholds(facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && (!goodhorizon || qh GOODclosest)) {
-      if (qh GOODclosest) {
-        if (qh GOODclosest->visible)
-          qh GOODclosest= NULL;
-        else {
-          qh_inthresholds(qh GOODclosest->normal, &angle);
-          if (angle < bestangle)
-            bestfacet= qh GOODclosest;
-        }
-      }
-      if (bestfacet && bestfacet != qh GOODclosest) {
-        if (qh GOODclosest)
-          qh GOODclosest->good= False;
-        qh GOODclosest= bestfacet;
-        bestfacet->good= True;
-        numgood++;
-        trace2((qh ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-        return numgood;
-      }
-    }else if (qh GOODclosest) { /* numgood > 0 */
-      qh GOODclosest->good= False;
-      qh GOODclosest= NULL;
-    }
-  }
-  zadd_(Zgoodfacet, numgood);
-  trace2((qh ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
-               numgood, goodhorizon));
-  if (!numgood && qh GOODvertex>0 && !qh MERGING)
-    return goodhorizon;
-  return numgood;
-} /* findgood */
-
-/*---------------------------------
-
-  qh_findgood_all( facetlist )
-    apply other constraints for good facets (used by qh.PRINTgood)
-    if qh.GOODvertex
-      facet includes (>0) or doesn't include (<0) point as vertex
-      if last good facet and ONLYgood, prints warning and continues
-    if qh.SPLITthresholds
-      facet->normal matches threshold, or if none, the closest one
-    calls qh_findgood
-    nop if good not used
-
-  returns:
-    clears facet->good if not good
-    sets qh.num_good
-
-  notes:
-    this is like qh_findgood but more restrictive
-
-  design:
-    uses qh_findgood to mark good facets
-    marks facets for qh.GOODvertex
-    marks facets for qh.SPLITthreholds
-*/
-void qh_findgood_all(facetT *facetlist) {
-  facetT *facet, *bestfacet=NULL;
-  realT angle, bestangle= REALmax;
-  int  numgood=0, startgood;
-
-  if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
-  && !qh SPLITthresholds)
-    return;
-  if (!qh ONLYgood)
-    qh_findgood(qh facet_list, 0);
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex(qh GOODvertexp, facet->vertices))) {
-        if (!--numgood) {
-          if (qh ONLYgood) {
-            qh_fprintf(qh ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
-               qh_pointid(qh GOODvertexp), facet->id);
-            return;
-          }else if (qh GOODvertex > 0)
-            qh_fprintf(qh ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
-                qh GOODvertex-1, qh GOODvertex-1);
-          else
-            qh_fprintf(qh ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
-                -qh GOODvertex - 1, -qh GOODvertex - 1);
-        }
-        facet->good= False;
-      }
-    }
-  }
-  startgood= numgood;
-  if (qh SPLITthresholds) {
-    FORALLfacet_(facetlist) {
-      if (facet->good) {
-        if (!qh_inthresholds(facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && bestfacet) {
-      bestfacet->good= True;
-      numgood++;
-      trace0((qh ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-      return;
-    }
-  }
-  qh num_good= numgood;
-  trace0((qh ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
-        numgood, startgood));
-} /* findgood_all */
-
-/*---------------------------------
-
-  qh_furthestnext()
-    set qh.facet_next to facet with furthest of all furthest points
-    searches all facets on qh.facet_list
-
-  notes:
-    this may help avoid precision problems
-*/
-void qh_furthestnext(void /* qh.facet_list */) {
-  facetT *facet, *bestfacet= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FORALLfacets {
-    if (facet->outsideset) {
-#if qh_COMPUTEfurthest
-      pointT *furthest;
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-      zinc_(Zcomputefurthest);
-      qh_distplane(furthest, facet, &dist);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist > bestdist) {
-        bestfacet= facet;
-        bestdist= dist;
-      }
-    }
-  }
-  if (bestfacet) {
-    qh_removefacet(bestfacet);
-    qh_prependfacet(bestfacet, &qh facet_next);
-    trace1((qh ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
-            bestfacet->id, bestdist));
-  }
-} /* furthestnext */
-
-/*---------------------------------
-
-  qh_furthestout( facet )
-    make furthest outside point the last point of outsideset
-
-  returns:
-    updates facet->outsideset
-    clears facet->notfurthest
-    sets facet->furthestdist
-
-  design:
-    determine best point of outsideset
-    make it the last point of outsideset
-*/
-void qh_furthestout(facetT *facet) {
-  pointT *point, **pointp, *bestpoint= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FOREACHpoint_(facet->outsideset) {
-    qh_distplane(point, facet, &dist);
-    zinc_(Zcomputefurthest);
-    if (dist > bestdist) {
-      bestpoint= point;
-      bestdist= dist;
-    }
-  }
-  if (bestpoint) {
-    qh_setdel(facet->outsideset, point);
-    qh_setappend(&facet->outsideset, point);
-#if !qh_COMPUTEfurthest
-    facet->furthestdist= bestdist;
-#endif
-  }
-  facet->notfurthest= False;
-  trace3((qh ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
-          qh_pointid(point), facet->id));
-} /* furthestout */
-
-
-/*---------------------------------
-
-  qh_infiniteloop( facet )
-    report infinite loop error due to facet
-*/
-void qh_infiniteloop(facetT *facet) {
-
-  qh_fprintf(qh ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
-  qh_errexit(qh_ERRqhull, facet, NULL);
-} /* qh_infiniteloop */
-
-/*---------------------------------
-
-  qh_initbuild()
-    initialize hull and outside sets with point array
-    qh.FIRSTpoint/qh.NUMpoints is point array
-    if qh.GOODpoint
-      adds qh.GOODpoint to initial hull
-
-  returns:
-    qh_facetlist with initial hull
-    points partioned into outside sets, coplanar sets, or inside
-    initializes qh.GOODpointp, qh.GOODvertexp,
-
-  design:
-    initialize global variables used during qh_buildhull
-    determine precision constants and points with max/min coordinate values
-      if qh.SCALElast, scale last coordinate(for 'd')
-    build initial simplex
-    partition input points into facets of initial simplex
-    set up lists
-    if qh.ONLYgood
-      check consistency
-      add qh.GOODvertex if defined
-*/
-void qh_initbuild( void) {
-  setT *maxpoints, *vertices;
-  facetT *facet;
-  int i, numpart;
-  realT dist;
-  boolT isoutside;
-
-  qh furthest_id= qh_IDunknown;
-  qh lastreport= 0;
-  qh facet_id= qh vertex_id= qh ridge_id= 0;
-  qh visit_id= qh vertex_visit= 0;
-  qh maxoutdone= False;
-
-  if (qh GOODpoint > 0)
-    qh GOODpointp= qh_point(qh GOODpoint-1);
-  else if (qh GOODpoint < 0)
-    qh GOODpointp= qh_point(-qh GOODpoint-1);
-  if (qh GOODvertex > 0)
-    qh GOODvertexp= qh_point(qh GOODvertex-1);
-  else if (qh GOODvertex < 0)
-    qh GOODvertexp= qh_point(-qh GOODvertex-1);
-  if ((qh GOODpoint
-       && (qh GOODpointp < qh first_point  /* also catches !GOODpointp */
-           || qh GOODpointp > qh_point(qh num_points-1)))
-    || (qh GOODvertex
-        && (qh GOODvertexp < qh first_point  /* also catches !GOODvertexp */
-            || qh GOODvertexp > qh_point(qh num_points-1)))) {
-    qh_fprintf(qh ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
-             qh num_points-1);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
-  if (qh SCALElast)
-    qh_scalelast(qh first_point, qh num_points, qh hull_dim,
-               qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
-  qh_detroundoff();
-  if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
-                  && qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
-    for (i=qh_PRINTEND; i--; ) {
-      if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
-          && !qh GOODthreshold && !qh SPLITthresholds)
-        break;  /* in this case, don't set upper_threshold */
-    }
-    if (i < 0) {
-      if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
-        qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
-        qh GOODthreshold= True;
-      }else {
-        qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
-        if (!qh GOODthreshold)
-          qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
-          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
-      }
-    }
-  }
-  vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
-  qh_initialhull(vertices);  /* initial qh facet_list */
-  qh_partitionall(vertices, qh first_point, qh num_points);
-  if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
-    if (qh TRACElevel || qh IStracing)
-      qh_fprintf(qh ferr, 8103, "\nTrace level %d for %s | %s\n",
-         qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
-    qh_fprintf(qh ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
-  }
-  qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  qh facet_next= qh facet_list;
-  qh_furthestnext(/* qh.facet_list */);
-  if (qh PREmerge) {
-    qh cos_max= qh premerge_cos;
-    qh centrum_radius= qh premerge_centrum;
-  }
-  if (qh ONLYgood) {
-    if (qh GOODvertex > 0 && qh MERGING) {
-      qh_fprintf(qh ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (!(qh GOODthreshold || qh GOODpoint
-         || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
-      qh_fprintf(qh ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
-good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (qh GOODvertex > 0  && !qh MERGING  /* matches qh_partitionall */
-        && !qh_isvertex(qh GOODvertexp, vertices)) {
-      facet= qh_findbestnew(qh GOODvertexp, qh facet_list,
-                          &dist, !qh_ALL, &isoutside, &numpart);
-      zadd_(Zdistgood, numpart);
-      if (!isoutside) {
-        qh_fprintf(qh ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
-               qh_pointid(qh GOODvertexp));
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-      if (!qh_addpoint(qh GOODvertexp, facet, False)) {
-        qh_settempfree(&vertices);
-        qh_settempfree(&maxpoints);
-        return;
-      }
-    }
-    qh_findgood(qh facet_list, 0);
-  }
-  qh_settempfree(&vertices);
-  qh_settempfree(&maxpoints);
-  trace1((qh ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
-} /* initbuild */
-
-/*---------------------------------
-
-  qh_initialhull( vertices )
-    constructs the initial hull as a DIM3 simplex of vertices
-
-  design:
-    creates a simplex (initializes lists)
-    determines orientation of simplex
-    sets hyperplanes for facets
-    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
-    checks for flipped facets and qh.NARROWhull
-    checks the result
-*/
-void qh_initialhull(setT *vertices) {
-  facetT *facet, *firstfacet, *neighbor, **neighborp;
-  realT dist, angle, minangle= REALmax;
-#ifndef qh_NOtrace
-  int k;
-#endif
-
-  qh_createsimplex(vertices);  /* qh.facet_list */
-  qh_resetlists(False, qh_RESETvisible);
-  qh facet_next= qh facet_list;      /* advance facet when processed */
-  qh interior_point= qh_getcenter(vertices);
-  firstfacet= qh facet_list;
-  qh_setfacetplane(firstfacet);
-  zinc_(Znumvisibility); /* needs to be in printsummary */
-  qh_distplane(qh interior_point, firstfacet, &dist);
-  if (dist > 0) {
-    FORALLfacets
-      facet->toporient ^= (unsigned char)True;
-  }
-  FORALLfacets
-    qh_setfacetplane(facet);
-  FORALLfacets {
-    if (!qh_checkflipped(facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
-      trace1((qh ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
-      facet->flipped= False;
-      FORALLfacets {
-        facet->toporient ^= (unsigned char)True;
-        qh_orientoutside(facet);
-      }
-      break;
-    }
-  }
-  FORALLfacets {
-    if (!qh_checkflipped(facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
-      if (qh DELAUNAY && ! qh ATinfinity) {
-        if (qh UPPERdelaunay)
-          qh_fprintf(qh ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
-        else
-          qh_fprintf(qh ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".    Use option 'Qs' to search all points for the initial simplex.\n");
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-      qh_precision("initial simplex is flat");
-      qh_fprintf(qh ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
-                 facet->id);
-      qh_errexit(qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
-    }
-    FOREACHneighbor_(facet) {
-      angle= qh_getangle(facet->normal, neighbor->normal);
-      minimize_( minangle, angle);
-    }
-  }
-  if (minangle < qh_MAXnarrow && !qh NOnarrow) {
-    realT diff= 1.0 + minangle;
-
-    qh NARROWhull= True;
-    qh_option("_narrow-hull", NULL, &diff);
-    if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
-      qh_printhelp_narrowhull(qh ferr, minangle);
-  }
-  zzval_(Zprocessed)= qh hull_dim+1;
-  qh_checkpolygon(qh facet_list);
-  qh_checkconvex(qh facet_list,   qh_DATAfault);
-#ifndef qh_NOtrace
-  if (qh IStracing >= 1) {
-    qh_fprintf(qh ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
-    for (k=0; k < qh hull_dim; k++)
-      qh_fprintf(qh ferr, 8106, " %6.4g", qh interior_point[k]);
-    qh_fprintf(qh ferr, 8107, "\n");
-  }
-#endif
-} /* initialhull */
-
-/*---------------------------------
-
-  qh_initialvertices( dim, maxpoints, points, numpoints )
-    determines a non-singular set of initial vertices
-    maxpoints may include duplicate points
-
-  returns:
-    temporary set of dim+1 vertices in descending order by vertex id
-    if qh.RANDOMoutside && !qh.ALLpoints
-      picks random points
-    if dim >= qh_INITIALmax,
-      uses min/max x and max points with non-zero determinants
-
-  notes:
-    unless qh.ALLpoints,
-      uses maxpoints as long as determinate is non-zero
-*/
-setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
-  pointT *point, **pointp;
-  setT *vertices, *simplex, *tested;
-  realT randr;
-  int idx, point_i, point_n, k;
-  boolT nearzero= False;
-
-  vertices= qh_settemp(dim + 1);
-  simplex= qh_settemp(dim+1);
-  if (qh ALLpoints)
-    qh_maxsimplex(dim, NULL, points, numpoints, &simplex);
-  else if (qh RANDOMoutside) {
-    while (qh_setsize(simplex) != dim+1) {
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor(qh num_points * randr);
-      while (qh_setin(simplex, qh_point(idx))) {
-        idx++; /* in case qh_RANDOMint always returns the same value */
-        idx= idx < qh num_points ? idx : 0;
-      }
-      qh_setappend(&simplex, qh_point(idx));
-    }
-  }else if (qh hull_dim >= qh_INITIALmax) {
-    tested= qh_settemp(dim+1);
-    qh_setappend(&simplex, SETfirst_(maxpoints));   /* max and min X coord */
-    qh_setappend(&simplex, SETsecond_(maxpoints));
-    qh_maxsimplex(fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
-    k= qh_setsize(simplex);
-    FOREACHpoint_i_(maxpoints) {
-      if (point_i & 0x1) {     /* first pick up max. coord. points */
-        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-          qh_detsimplex(point, simplex, k, &nearzero);
-          if (nearzero)
-            qh_setappend(&tested, point);
-          else {
-            qh_setappend(&simplex, point);
-            if (++k == dim)  /* use search for last point */
-              break;
-          }
-        }
-      }
-    }
-    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(point, simplex, k, &nearzero);
-        if (nearzero)
-          qh_setappend(&tested, point);
-        else {
-          qh_setappend(&simplex, point);
-          k++;
-        }
-      }
-    }
-    idx= 0;
-    while (k != dim && (point= qh_point(idx++))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(point, simplex, k, &nearzero);
-        if (!nearzero){
-          qh_setappend(&simplex, point);
-          k++;
-        }
-      }
-    }
-    qh_settempfree(&tested);
-    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
-  }else
-    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
-  FOREACHpoint_(simplex)
-    qh_setaddnth(&vertices, 0, qh_newvertex(point)); /* descending order */
-  qh_settempfree(&simplex);
-  return vertices;
-} /* initialvertices */
-
-
-/*---------------------------------
-
-  qh_isvertex( point, vertices )
-    returns vertex if point is in vertex set, else returns NULL
-
-  notes:
-    for qh.GOODvertex
-*/
-vertexT *qh_isvertex(pointT *point, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (vertex->point == point)
-      return vertex;
-  }
-  return NULL;
-} /* isvertex */
-
-/*---------------------------------
-
-  qh_makenewfacets( point )
-    make new facets from point and qh.visible_list
-
-  returns:
-    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
-    qh.newvertex_list= list of vertices in new facets with ->newlist set
-
-    if (qh.ONLYgood)
-      newfacets reference horizon facets, but not vice versa
-      ridges reference non-simplicial horizon ridges, but not vice versa
-      does not change existing facets
-    else
-      sets qh.NEWfacets
-      new facets attached to horizon facets and ridges
-      for visible facets,
-        visible->r.replace is corresponding new facet
-
-  see also:
-    qh_makenewplanes() -- make hyperplanes for facets
-    qh_attachnewfacets() -- attachnewfacets if not done here(qh ONLYgood)
-    qh_matchnewfacets() -- match up neighbors
-    qh_updatevertices() -- update vertex neighbors and delvertices
-    qh_deletevisible() -- delete visible facets
-    qh_checkpolygon() --check the result
-    qh_triangulate() -- triangulate a non-simplicial facet
-
-  design:
-    for each visible facet
-      make new facets to its horizon facets
-      update its f.replace
-      clear its neighbor set
-*/
-vertexT *qh_makenewfacets(pointT *point /*visible_list*/) {
-  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  qh newfacet_list= qh facet_tail;
-  qh newvertex_list= qh vertex_tail;
-  apex= qh_newvertex(point);
-  qh_appendvertex(apex);
-  qh visit_id++;
-  if (!qh ONLYgood)
-    qh NEWfacets= True;
-  FORALLvisible_facets {
-    FOREACHneighbor_(visible)
-      neighbor->seen= False;
-    if (visible->ridges) {
-      visible->visitid= qh visit_id;
-      newfacet2= qh_makenew_nonsimplicial(visible, apex, &numnew);
-    }
-    if (visible->simplicial)
-      newfacet= qh_makenew_simplicial(visible, apex, &numnew);
-    if (!qh ONLYgood) {
-      if (newfacet2)  /* newfacet is null if all ridges defined */
-        newfacet= newfacet2;
-      if (newfacet)
-        visible->f.replace= newfacet;
-      else
-        zinc_(Zinsidevisible);
-      SETfirst_(visible->neighbors)= NULL;
-    }
-  }
-  trace1((qh ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
-          numnew, qh_pointid(point)));
-  if (qh IStracing >= 4)
-    qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
-  return apex;
-} /* makenewfacets */
-
-/*---------------------------------
-
-  qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
-    match duplicate ridges in qh.hash_table for atfacet/atskip
-    duplicates marked with ->dupridge and qh_DUPLICATEridge
-
-  returns:
-    picks match with worst merge (min distance apart)
-    updates hashcount
-
-  see also:
-    qh_matchneighbor
-
-  notes:
-
-  design:
-    compute hash value for atfacet and atskip
-    repeat twice -- once to make best matches, once to match the rest
-      for each possible facet in qh.hash_table
-        if it is a matching facet and pass 2
-          make match
-          unless tricoplanar, mark match for merging (qh_MERGEridge)
-          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
-        if it is a matching facet and pass 1
-          test if this is a better match
-      if pass 1,
-        make best match (it will not be merged)
-*/
-#ifndef qh_NOmerge
-void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
-  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
-  realT maxdist= -REALmax, mindist, dist2, low, high;
-
-  hash= qh_gethash(hashsize, atfacet->vertices, qh hull_dim, 1,
-                     SETelem_(atfacet->vertices, atskip));
-  trace2((qh ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
-          atfacet->id, atskip, hash, *hashcount));
-  for (makematch= 0; makematch < 2; makematch++) {
-    qh visit_id++;
-    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
-      zinc_(Zhashlookup);
-      nextfacet= NULL;
-      newfacet->visitid= qh visit_id;
-      for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
-           scan= (++scan >= hashsize ? 0 : scan)) {
-        if (!facet->dupridge || facet->visitid == qh visit_id)
-          continue;
-        zinc_(Zhashtests);
-        if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
-          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
-            if (!makematch) {
-              qh_fprintf(qh ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
-                     facet->id, skip, newfacet->id, newskip, hash);
-              qh_errexit2(qh_ERRqhull, facet, newfacet);
-            }
-          }else if (ismatch && makematch) {
-            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
-              SETelem_(facet->neighbors, skip)= newfacet;
-              if (newfacet->tricoplanar)
-                SETelem_(newfacet->neighbors, newskip)= facet;
-              else
-                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
-              *hashcount -= 2; /* removed two unmatched facets */
-              trace4((qh ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
-                    facet->id, skip, newfacet->id, newskip));
-            }
-          }else if (ismatch) {
-            mindist= qh_getdistance(facet, newfacet, &low, &high);
-            dist2= qh_getdistance(newfacet, facet, &low, &high);
-            minimize_(mindist, dist2);
-            if (mindist > maxdist) {
-              maxdist= mindist;
-              maxmatch= facet;
-              maxskip= skip;
-              maxmatch2= newfacet;
-              maxskip2= newskip;
-            }
-            trace3((qh ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
-                    facet->id, skip, newfacet->id, newskip, mindist,
-                    maxmatch->id, maxmatch2->id));
-          }else { /* !ismatch */
-            nextfacet= facet;
-            nextskip= skip;
-          }
-        }
-        if (makematch && !facet
-        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
-          qh_fprintf(qh ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
-                     newfacet->id, newskip, hash);
-          qh_errexit(qh_ERRqhull, newfacet, NULL);
-        }
-      }
-    } /* end of for each new facet at hash */
-    if (!makematch) {
-      if (!maxmatch) {
-        qh_fprintf(qh ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
-                     atfacet->id, atskip, hash);
-        qh_errexit(qh_ERRqhull, atfacet, NULL);
-      }
-      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
-      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
-      *hashcount -= 2; /* removed two unmatched facets */
-      zzinc_(Zmultiridge);
-      trace0((qh ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
-              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
-      qh_precision("ridge with multiple neighbors");
-      if (qh IStracing >= 4)
-        qh_errprint("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
-    }
-  }
-} /* matchduplicates */
-
-/*---------------------------------
-
-  qh_nearcoplanar()
-    for all facets, remove near-inside points from facet->coplanarset
-    coplanar points defined by innerplane from qh_outerinner()
-
-  returns:
-    if qh KEEPcoplanar && !qh KEEPinside
-      facet->coplanarset only contains coplanar points
-    if qh.JOGGLEmax
-      drops inner plane by another qh.JOGGLEmax diagonal since a
-        vertex could shift out while a coplanar point shifts in
-
-  notes:
-    used for qh.PREmerge and qh.JOGGLEmax
-    must agree with computation of qh.NEARcoplanar in qh_detroundoff()
-  design:
-    if not keeping coplanar or inside points
-      free all coplanar sets
-    else if not keeping both coplanar and inside points
-      remove !coplanar or !inside points from coplanar sets
-*/
-void qh_nearcoplanar(void /* qh.facet_list */) {
-  facetT *facet;
-  pointT *point, **pointp;
-  int numpart;
-  realT dist, innerplane;
-
-  if (!qh KEEPcoplanar && !qh KEEPinside) {
-    FORALLfacets {
-      if (facet->coplanarset)
-        qh_setfree( &facet->coplanarset);
-    }
-  }else if (!qh KEEPcoplanar || !qh KEEPinside) {
-    qh_outerinner(NULL, NULL, &innerplane);
-    if (qh JOGGLEmax < REALmax/2)
-      innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
-    numpart= 0;
-    FORALLfacets {
-      if (facet->coplanarset) {
-        FOREACHpoint_(facet->coplanarset) {
-          numpart++;
-          qh_distplane(point, facet, &dist);
-          if (dist < innerplane) {
-            if (!qh KEEPinside)
-              SETref_(point)= NULL;
-          }else if (!qh KEEPcoplanar)
-            SETref_(point)= NULL;
-        }
-        qh_setcompact(facet->coplanarset);
-      }
-    }
-    zzadd_(Zcheckpart, numpart);
-  }
-} /* nearcoplanar */
-
-/*---------------------------------
-
-  qh_nearvertex( facet, point, bestdist )
-    return nearest vertex in facet to point
-
-  returns:
-    vertex and its distance
-
-  notes:
-    if qh.DELAUNAY
-      distance is measured in the input set
-    searches neighboring tricoplanar facets (requires vertexneighbors)
-      Slow implementation.  Recomputes vertex set for each point.
-    The vertex set could be stored in the qh.keepcentrum facet.
-*/
-vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp) {
-  realT bestdist= REALmax, dist;
-  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
-  coordT *center;
-  facetT *neighbor, **neighborp;
-  setT *vertices;
-  int dim= qh hull_dim;
-
-  if (qh DELAUNAY)
-    dim--;
-  if (facet->tricoplanar) {
-    if (!qh VERTEXneighbors || !facet->center) {
-      qh_fprintf(qh ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-    vertices= qh_settemp(qh TEMPsize);
-    apex= SETfirstt_(facet->vertices, vertexT);
-    center= facet->center;
-    FOREACHneighbor_(apex) {
-      if (neighbor->center == center) {
-        FOREACHvertex_(neighbor->vertices)
-          qh_setappend(&vertices, vertex);
-      }
-    }
-  }else
-    vertices= facet->vertices;
-  FOREACHvertex_(vertices) {
-    dist= qh_pointdist(vertex->point, point, -dim);
-    if (dist < bestdist) {
-      bestdist= dist;
-      bestvertex= vertex;
-    }
-  }
-  if (facet->tricoplanar)
-    qh_settempfree(&vertices);
-  *bestdistp= sqrt(bestdist);
-  if (!bestvertex) {
-      qh_fprintf(qh ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(point));
-      qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  trace3((qh ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
-        bestvertex->id, *bestdistp, facet->id, qh_pointid(point))); /* bestvertex!=0 by QH2161 */
-  return bestvertex;
-} /* nearvertex */
-
-/*---------------------------------
-
-  qh_newhashtable( newsize )
-    returns size of qh.hash_table of at least newsize slots
-
-  notes:
-    assumes qh.hash_table is NULL
-    qh_HASHfactor determines the number of extra slots
-    size is not divisible by 2, 3, or 5
-*/
-int qh_newhashtable(int newsize) {
-  int size;
-
-  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
-  while (True) {
-    if (newsize<0 || size<0) {
-        qh_fprintf(qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
-        qh_errexit(qhmem_ERRmem, NULL, NULL);
-    }
-    if ((size%3) && (size%5))
-      break;
-    size += 2;
-    /* loop terminates because there is an infinite number of primes */
-  }
-  qh hash_table= qh_setnew(size);
-  qh_setzero(qh hash_table, 0, size);
-  return size;
-} /* newhashtable */
-
-/*---------------------------------
-
-  qh_newvertex( point )
-    returns a new vertex for point
-*/
-vertexT *qh_newvertex(pointT *point) {
-  vertexT *vertex;
-
-  zinc_(Ztotvertices);
-  vertex= (vertexT *)qh_memalloc((int)sizeof(vertexT));
-  memset((char *) vertex, (size_t)0, sizeof(vertexT));
-  if (qh vertex_id == UINT_MAX) {
-    qh_memfree(vertex, (int)sizeof(vertexT));
-    qh_fprintf(qh ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (qh vertex_id == qh tracevertex_id)
-    qh tracevertex= vertex;
-  vertex->id= qh vertex_id++;
-  vertex->point= point;
-  trace4((qh ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(vertex->point),
-          vertex->id));
-  return(vertex);
-} /* newvertex */
-
-/*---------------------------------
-
-  qh_nextridge3d( atridge, facet, vertex )
-    return next ridge and vertex for a 3d facet
-    returns NULL on error
-    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qh_qh.
-
-  notes:
-    in qh_ORIENTclock order
-    this is a O(n^2) implementation to trace all ridges
-    be sure to stop on any 2nd visit
-    same as QhullRidge::nextRidge3d
-    does not use qh_qh or qh_errexit [QhullFacet.cpp]
-
-  design:
-    for each ridge
-      exit if it is the ridge after atridge
-*/
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-  vertexT *atvertex, *vertex, *othervertex;
-  ridgeT *ridge, **ridgep;
-
-  if ((atridge->top == facet) ^ qh_ORIENTclock)
-    atvertex= SETsecondt_(atridge->vertices, vertexT);
-  else
-    atvertex= SETfirstt_(atridge->vertices, vertexT);
-  FOREACHridge_(facet->ridges) {
-    if (ridge == atridge)
-      continue;
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      othervertex= SETsecondt_(ridge->vertices, vertexT);
-      vertex= SETfirstt_(ridge->vertices, vertexT);
-    }else {
-      vertex= SETsecondt_(ridge->vertices, vertexT);
-      othervertex= SETfirstt_(ridge->vertices, vertexT);
-    }
-    if (vertex == atvertex) {
-      if (vertexp)
-        *vertexp= othervertex;
-      return ridge;
-    }
-  }
-  return NULL;
-} /* nextridge3d */
-#else /* qh_NOmerge */
-void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-}
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_outcoplanar()
-    move points from all facets' outsidesets to their coplanarsets
-
-  notes:
-    for post-processing under qh.NARROWhull
-
-  design:
-    for each facet
-      for each outside point for facet
-        partition point into coplanar set
-*/
-void qh_outcoplanar(void /* facet_list */) {
-  pointT *point, **pointp;
-  facetT *facet;
-  realT dist;
-
-  trace1((qh ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
-  FORALLfacets {
-    FOREACHpoint_(facet->outsideset) {
-      qh num_outside--;
-      if (qh KEEPcoplanar || qh KEEPnearinside) {
-        qh_distplane(point, facet, &dist);
-        zinc_(Zpartition);
-        qh_partitioncoplanar(point, facet, &dist);
-      }
-    }
-    qh_setfree(&facet->outsideset);
-  }
-} /* outcoplanar */
-
-/*---------------------------------
-
-  qh_point( id )
-    return point for a point id, or NULL if unknown
-
-  alternative code:
-    return((pointT *)((unsigned   long)qh.first_point
-           + (unsigned long)((id)*qh.normal_size)));
-*/
-pointT *qh_point(int id) {
-
-  if (id < 0)
-    return NULL;
-  if (id < qh num_points)
-    return qh first_point + id * qh hull_dim;
-  id -= qh num_points;
-  if (id < qh_setsize(qh other_points))
-    return SETelemt_(qh other_points, id, pointT);
-  return NULL;
-} /* point */
-
-/*---------------------------------
-
-  qh_point_add( set, point, elem )
-    stores elem at set[point.id]
-
-  returns:
-    access function for qh_pointfacet and qh_pointvertex
-
-  notes:
-    checks point.id
-*/
-void qh_point_add(setT *set, pointT *point, void *elem) {
-  int id, size;
-
-  SETreturnsize_(set, size);
-  if ((id= qh_pointid(point)) < 0)
-    qh_fprintf(qh ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
-      point, id);
-  else if (id >= size) {
-    qh_fprintf(qh ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
-             id, size);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }else
-    SETelem_(set, id)= elem;
-} /* point_add */
-
-
-/*---------------------------------
-
-  qh_pointfacet()
-    return temporary set of facet for each point
-    the set is indexed by point id
-
-  notes:
-    vertices assigned to one of the facets
-    coplanarset assigned to the facet
-    outside set assigned to the facet
-    NULL if no facet for point (inside)
-      includes qh.GOODpointp
-
-  access:
-    FOREACHfacet_i_(facets) { ... }
-    SETelem_(facets, i)
-
-  design:
-    for each facet
-      add each vertex
-      add each coplanar point
-      add each outside point
-*/
-setT *qh_pointfacet(void /*qh.facet_list*/) {
-  int numpoints= qh num_points + qh_setsize(qh other_points);
-  setT *facets;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp;
-
-  facets= qh_settemp(numpoints);
-  qh_setzero(facets, 0, numpoints);
-  qh vertex_visit++;
-  FORALLfacets {
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-        qh_point_add(facets, vertex->point, facet);
-      }
-    }
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(facets, point, facet);
-    FOREACHpoint_(facet->outsideset)
-      qh_point_add(facets, point, facet);
-  }
-  return facets;
-} /* pointfacet */
-
-/*---------------------------------
-
-  qh_pointvertex(  )
-    return temporary set of vertices indexed by point id
-    entry is NULL if no vertex for a point
-      this will include qh.GOODpointp
-
-  access:
-    FOREACHvertex_i_(vertices) { ... }
-    SETelem_(vertices, i)
-*/
-setT *qh_pointvertex(void /*qh.facet_list*/) {
-  int numpoints= qh num_points + qh_setsize(qh other_points);
-  setT *vertices;
-  vertexT *vertex;
-
-  vertices= qh_settemp(numpoints);
-  qh_setzero(vertices, 0, numpoints);
-  FORALLvertices
-    qh_point_add(vertices, vertex->point, vertex);
-  return vertices;
-} /* pointvertex */
-
-
-/*---------------------------------
-
-  qh_prependfacet( facet, facetlist )
-    prepend facet to the start of a facetlist
-
-  returns:
-    increments qh.numfacets
-    updates facetlist, qh.facet_list, facet_next
-
-  notes:
-    be careful of prepending since it can lose a pointer.
-      e.g., can lose _next by deleting and then prepending before _next
-*/
-void qh_prependfacet(facetT *facet, facetT **facetlist) {
-  facetT *prevfacet, *list;
-
-
-  trace4((qh ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
-          facet->id, getid_(*facetlist)));
-  if (!*facetlist)
-    (*facetlist)= qh facet_tail;
-  list= *facetlist;
-  prevfacet= list->previous;
-  facet->previous= prevfacet;
-  if (prevfacet)
-    prevfacet->next= facet;
-  list->previous= facet;
-  facet->next= *facetlist;
-  if (qh facet_list == list)  /* this may change *facetlist */
-    qh facet_list= facet;
-  if (qh facet_next == list)
-    qh facet_next= facet;
-  *facetlist= facet;
-  qh num_facets++;
-} /* prependfacet */
-
-
-/*---------------------------------
-
-  qh_printhashtable( fp )
-    print hash table to fp
-
-  notes:
-    not in I/O to avoid bringing io.c in
-
-  design:
-    for each hash entry
-      if defined
-        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
-          print entry and neighbors
-*/
-void qh_printhashtable(FILE *fp) {
-  facetT *facet, *neighbor;
-  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
-  vertexT *vertex, **vertexp;
-
-  FOREACHfacet_i_(qh hash_table) {
-    if (facet) {
-      FOREACHneighbor_i_(facet) {
-        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
-          break;
-      }
-      if (neighbor_i == neighbor_n)
-        continue;
-      qh_fprintf(fp, 9283, "hash %d f%d ", facet_i, facet->id);
-      FOREACHvertex_(facet->vertices)
-        qh_fprintf(fp, 9284, "v%d ", vertex->id);
-      qh_fprintf(fp, 9285, "\n neighbors:");
-      FOREACHneighbor_i_(facet) {
-        if (neighbor == qh_MERGEridge)
-          id= -3;
-        else if (neighbor == qh_DUPLICATEridge)
-          id= -2;
-        else
-          id= getid_(neighbor);
-        qh_fprintf(fp, 9286, " %d", id);
-      }
-      qh_fprintf(fp, 9287, "\n");
-    }
-  }
-} /* printhashtable */
-
-
-/*---------------------------------
-
-  qh_printlists( fp )
-    print out facet and vertex list for debugging (without 'f/v' tags)
-*/
-void qh_printlists(void) {
-  facetT *facet;
-  vertexT *vertex;
-  int count= 0;
-
-  qh_fprintf(qh ferr, 8108, "qh_printlists: facets:");
-  FORALLfacets {
-    if (++count % 100 == 0)
-      qh_fprintf(qh ferr, 8109, "\n     ");
-    qh_fprintf(qh ferr, 8110, " %d", facet->id);
-  }
-  qh_fprintf(qh ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
-     getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
-     getid_(qh newvertex_list));
-  count = 0;
-  FORALLvertices {
-    if (++count % 100 == 0)
-      qh_fprintf(qh ferr, 8112, "\n     ");
-    qh_fprintf(qh ferr, 8113, " %d", vertex->id);
-  }
-  qh_fprintf(qh ferr, 8114, "\n");
-} /* printlists */
-
-/*---------------------------------
-
-  qh_resetlists( stats, qh_RESETvisible )
-    reset newvertex_list, newfacet_list, visible_list
-    if stats,
-      maintains statistics
-
-  returns:
-    visible_list is empty if qh_deletevisible was called
-*/
-void qh_resetlists(boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
-  vertexT *vertex;
-  facetT *newfacet, *visible;
-  int totnew=0, totver=0;
-
-  if (stats) {
-    FORALLvertex_(qh newvertex_list)
-      totver++;
-    FORALLnew_facets
-      totnew++;
-    zadd_(Zvisvertextot, totver);
-    zmax_(Zvisvertexmax, totver);
-    zadd_(Znewfacettot, totnew);
-    zmax_(Znewfacetmax, totnew);
-  }
-  FORALLvertex_(qh newvertex_list)
-    vertex->newlist= False;
-  qh newvertex_list= NULL;
-  FORALLnew_facets
-    newfacet->newfacet= False;
-  qh newfacet_list= NULL;
-  if (resetVisible) {
-    FORALLvisible_facets {
-      visible->f.replace= NULL;
-      visible->visible= False;
-    }
-    qh num_visible= 0;
-  }
-  qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
-  qh NEWfacets= False;
-} /* resetlists */
-
-/*---------------------------------
-
-  qh_setvoronoi_all()
-    compute Voronoi centers for all facets
-    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
-
-  returns:
-    facet->center is the Voronoi center
-
-  notes:
-    this is unused/untested code
-      please email bradb@shore.net if this works ok for you
-
-  use:
-    FORALLvertices {...} to locate the vertex for a point.
-    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
-*/
-void qh_setvoronoi_all(void) {
-  facetT *facet;
-
-  qh_clearcenters(qh_ASvoronoi);
-  qh_vertexneighbors();
-
-  FORALLfacets {
-    if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(facet->vertices);
-    }
-  }
-} /* setvoronoi_all */
-
-#ifndef qh_NOmerge
-
-/*---------------------------------
-
-  qh_triangulate()
-    triangulate non-simplicial facets on qh.facet_list,
-    if qh VORONOI, sets Voronoi centers of non-simplicial facets
-    nop if hasTriangulation
-
-  returns:
-    all facets simplicial
-    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
-
-  notes:
-    call after qh_check_output since may switch to Voronoi centers
-    Output may overwrite ->f.triowner with ->f.area
-*/
-void qh_triangulate(void /*qh.facet_list*/) {
-  facetT *facet, *nextfacet, *owner;
-  int onlygood= qh ONLYgood;
-  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
-  facetT *orig_neighbor= NULL, *otherfacet;
-  vertexT *new_vertex_list= NULL;
-  mergeT *merge;
-  mergeType mergetype;
-  int neighbor_i, neighbor_n;
-
-  if (qh hasTriangulation)
-      return;
-  trace1((qh ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
-  if (qh hull_dim == 2)
-    return;
-  if (qh VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
-    qh_clearcenters(qh_ASvoronoi);
-    qh_vertexneighbors();
-  }
-  qh ONLYgood= False; /* for makenew_nonsimplicial */
-  qh visit_id++;
-  qh NEWfacets= True;
-  qh degen_mergeset= qh_settemp(qh TEMPsize);
-  qh newvertex_list= qh vertex_tail;
-  for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible || facet->simplicial)
-      continue;
-    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
-    if (!new_facet_list)
-      new_facet_list= facet;  /* will be moved to end */
-    qh_triangulate_facet(facet, &new_vertex_list);
-  }
-  trace2((qh ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible)
-      continue;
-    if (facet->ridges) {
-      if (qh_setsize(facet->ridges) > 0) {
-        qh_fprintf(qh ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
-        qh_errexit(qh_ERRqhull, facet, NULL);
-      }
-      qh_setfree(&facet->ridges);
-    }
-    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
-      zinc_(Ztrinull);
-      qh_triangulate_null(facet);
-    }
-  }
-  trace2((qh ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
-  qh visible_list= qh facet_tail;
-  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(merge, (int)sizeof(mergeT));
-    if (mergetype == MRGmirror) {
-      zinc_(Ztrimirror);
-      qh_triangulate_mirror(facet1, facet2);
-    }
-  }
-  qh_settempfree(&qh degen_mergeset);
-  trace2((qh ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
-  qh newvertex_list= new_vertex_list;  /* all vertices of new facets */
-  qh visible_list= NULL;
-  qh_updatevertices(/*qh.newvertex_list, empty newfacet_list and visible_list*/);
-  qh_resetlists(False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
-
-  trace2((qh ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
-  trace2((qh ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
-  FORALLfacet_(new_facet_list) {
-    if (facet->tricoplanar && !facet->visible) {
-      FOREACHneighbor_i_(facet) {
-        if (neighbor_i == 0) {  /* first iteration */
-          if (neighbor->tricoplanar)
-            orig_neighbor= neighbor->f.triowner;
-          else
-            orig_neighbor= neighbor;
-        }else {
-          if (neighbor->tricoplanar)
-            otherfacet= neighbor->f.triowner;
-          else
-            otherfacet= neighbor;
-          if (orig_neighbor == otherfacet) {
-            zinc_(Ztridegen);
-            facet->degenerate= True;
-            break;
-          }
-        }
-      }
-    }
-  }
-
-  trace2((qh ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
-  owner= NULL;
-  visible= NULL;
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
-    nextfacet= facet->next;
-    if (facet->visible) {
-      if (facet->tricoplanar) { /* a null or mirrored facet */
-        qh_delfacet(facet);
-        qh num_visible--;
-      }else {  /* a non-simplicial facet followed by its tricoplanars */
-        if (visible && !owner) {
-          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
-          trace2((qh ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
-                       visible->id));
-          qh_delfacet(visible);
-          qh num_visible--;
-        }
-        visible= facet;
-        owner= NULL;
-      }
-    }else if (facet->tricoplanar) {
-      if (facet->f.triowner != visible || visible==NULL) {
-        qh_fprintf(qh ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
-        qh_errexit2(qh_ERRqhull, facet, visible);
-      }
-      if (owner)
-        facet->f.triowner= owner;
-      else if (!facet->degenerate) {
-        owner= facet;
-        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
-        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
-        facet->coplanarset= visible->coplanarset;
-        facet->outsideset= visible->outsideset;
-        visible->coplanarset= NULL;
-        visible->outsideset= NULL;
-        if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
-          visible->center= NULL;
-          visible->normal= NULL;
-        }
-        qh_delfacet(visible);
-        qh num_visible--;
-      }
-    }
-  }
-  if (visible && !owner) {
-    trace2((qh ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
-                 visible->id));
-    qh_delfacet(visible);
-    qh num_visible--;
-  }
-  qh NEWfacets= False;
-  qh ONLYgood= onlygood; /* restore value */
-  if (qh CHECKfrequently)
-    qh_checkpolygon(qh facet_list);
-  qh hasTriangulation= True;
-} /* triangulate */
-
-
-/*---------------------------------
-
-  qh_triangulate_facet(qh, facetA, &firstVertex )
-    triangulate a non-simplicial facet
-      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
-  returns:
-    qh.newfacet_list == simplicial facets
-      facet->tricoplanar set and ->keepcentrum false
-      facet->degenerate set if duplicated apex
-      facet->f.trivisible set to facetA
-      facet->center copied from facetA (created if qh_ASvoronoi)
-        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
-      facet->normal,offset,maxoutside copied from facetA
-
-  notes:
-      only called by qh_triangulate
-      qh_makenew_nonsimplicial uses neighbor->seen for the same
-      if qh.TRInormals, newfacet->normal will need qh_free
-        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
-        keepcentrum is also set on Zwidefacet in qh_mergefacet
-        freed by qh_clearcenters
-
-  see also:
-      qh_addpoint() -- add a point
-      qh_makenewfacets() -- construct a cone of facets for a new vertex
-
-  design:
-      if qh_ASvoronoi,
-         compute Voronoi center (facet->center)
-      select first vertex (highest ID to preserve ID ordering of ->vertices)
-      triangulate from vertex to ridges
-      copy facet->center, normal, offset
-      update vertex neighbors
-*/
-void qh_triangulate_facet(facetT *facetA, vertexT **first_vertex) {
-  facetT *newfacet;
-  facetT *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  trace3((qh ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
-
-  if (qh IStracing >= 4)
-    qh_printfacet(qh ferr, facetA);
-  FOREACHneighbor_(facetA) {
-    neighbor->seen= False;
-    neighbor->coplanar= False;
-  }
-  if (qh CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
-        && fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
-    facetA->center= qh_facetcenter(facetA->vertices);
-  }
-  qh_willdelete(facetA, NULL);
-  qh newfacet_list= qh facet_tail;
-  facetA->visitid= qh visit_id;
-  apex= SETfirstt_(facetA->vertices, vertexT);
-  qh_makenew_nonsimplicial(facetA, apex, &numnew);
-  SETfirst_(facetA->neighbors)= NULL;
-  FORALLnew_facets {
-    newfacet->tricoplanar= True;
-    newfacet->f.trivisible= facetA;
-    newfacet->degenerate= False;
-    newfacet->upperdelaunay= facetA->upperdelaunay;
-    newfacet->good= facetA->good;
-    if (qh TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
-      newfacet->keepcentrum= True;
-      if(facetA->normal){
-        newfacet->normal= qh_memalloc(qh normal_size);
-        memcpy((char *)newfacet->normal, facetA->normal, qh normal_size);
-      }
-      if (qh CENTERtype == qh_AScentrum)
-        newfacet->center= qh_getcentrum(newfacet);
-      else if (qh CENTERtype == qh_ASvoronoi && facetA->center){
-        newfacet->center= qh_memalloc(qh center_size);
-        memcpy((char *)newfacet->center, facetA->center, qh center_size);
-      }
-    }else {
-      newfacet->keepcentrum= False;
-      /* one facet will have keepcentrum=True at end of qh_triangulate */
-      newfacet->normal= facetA->normal;
-      newfacet->center= facetA->center;
-    }
-    newfacet->offset= facetA->offset;
-#if qh_MAXoutside
-    newfacet->maxoutside= facetA->maxoutside;
-#endif
-  }
-  qh_matchnewfacets(/*qh.newfacet_list*/);
-  zinc_(Ztricoplanar);
-  zadd_(Ztricoplanartot, numnew);
-  zmax_(Ztricoplanarmax, numnew);
-  qh visible_list= NULL;
-  if (!(*first_vertex))
-    (*first_vertex)= qh newvertex_list;
-  qh newvertex_list= NULL;
-  qh_updatevertices(/*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-  qh_resetlists(False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-} /* triangulate_facet */
-
-/*---------------------------------
-
-  qh_triangulate_link(oldfacetA, facetA, oldfacetB, facetB)
-    relink facetA to facetB via oldfacets
-  returns:
-    adds mirror facets to qh degen_mergeset (4-d and up only)
-  design:
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
-  int errmirror= False;
-
-  trace3((qh ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
-         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
-  if (qh_setin(facetA->neighbors, facetB)) {
-    if (!qh_setin(facetB->neighbors, facetA))
-      errmirror= True;
-    else
-      qh_appendmergeset(facetA, facetB, MRGmirror, NULL);
-  }else if (qh_setin(facetB->neighbors, facetA))
-    errmirror= True;
-  if (errmirror) {
-    qh_fprintf(qh ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
-       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
-    qh_errexit2(qh_ERRqhull, facetA, facetB);
-  }
-  qh_setreplace(facetB->neighbors, oldfacetB, facetA);
-  qh_setreplace(facetA->neighbors, oldfacetA, facetB);
-} /* triangulate_link */
-
-/*---------------------------------
-
-  qh_triangulate_mirror(facetA, facetB)
-    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
-      a mirrored facet shares the same vertices of a logical ridge
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_mirror(facetT *facetA, facetT *facetB) {
-  facetT *neighbor, *neighborB;
-  int neighbor_i, neighbor_n;
-
-  trace3((qh ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
-         facetA->id, facetB->id));
-  FOREACHneighbor_i_(facetA) {
-    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
-    if (neighbor == neighborB)
-      continue; /* occurs twice */
-    qh_triangulate_link(facetA, neighbor, facetB, neighborB);
-  }
-  qh_willdelete(facetA, NULL);
-  qh_willdelete(facetB, NULL);
-} /* triangulate_mirror */
-
-/*---------------------------------
-
-  qh_triangulate_null(facetA)
-    remove null facetA from qh_triangulate_facet()
-      a null facet has vertex #1 (apex) == vertex #2
-  returns:
-    adds facetA to ->visible for deletion after qh_updatevertices
-    qh degen_mergeset contains mirror facets (4-d and up only)
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_null(facetT *facetA) {
-  facetT *neighbor, *otherfacet;
-
-  trace3((qh ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
-  neighbor= SETfirstt_(facetA->neighbors, facetT);
-  otherfacet= SETsecondt_(facetA->neighbors, facetT);
-  qh_triangulate_link(facetA, neighbor, facetA, otherfacet);
-  qh_willdelete(facetA, NULL);
-} /* triangulate_null */
-
-#else /* qh_NOmerge */
-void qh_triangulate(void) {
-}
-#endif /* qh_NOmerge */
-
-   /*---------------------------------
-
-  qh_vertexintersect( vertexsetA, vertexsetB )
-    intersects two vertex sets (inverse id ordered)
-    vertexsetA is a temporary set at the top of qhmem.tempstack
-
-  returns:
-    replaces vertexsetA with the intersection
-
-  notes:
-    could overwrite vertexsetA if currently too slow
-*/
-void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
-  setT *intersection;
-
-  intersection= qh_vertexintersect_new(*vertexsetA, vertexsetB);
-  qh_settempfree(vertexsetA);
-  *vertexsetA= intersection;
-  qh_settemppush(intersection);
-} /* vertexintersect */
-
-/*---------------------------------
-
-  qh_vertexintersect_new(  )
-    intersects two vertex sets (inverse id ordered)
-
-  returns:
-    a new set
-*/
-setT *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB) {
-  setT *intersection= qh_setnew(qh hull_dim - 1);
-  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
-
-  while (*vertexA && *vertexB) {
-    if (*vertexA  == *vertexB) {
-      qh_setappend(&intersection, *vertexA);
-      vertexA++; vertexB++;
-    }else {
-      if ((*vertexA)->id > (*vertexB)->id)
-        vertexA++;
-      else
-        vertexB++;
-    }
-  }
-  return intersection;
-} /* vertexintersect_new */
-
-/*---------------------------------
-
-  qh_vertexneighbors()
-    for each vertex in qh.facet_list,
-      determine its neighboring facets
-
-  returns:
-    sets qh.VERTEXneighbors
-      nop if qh.VERTEXneighbors already set
-      qh_addpoint() will maintain them
-
-  notes:
-    assumes all vertex->neighbors are NULL
-
-  design:
-    for each facet
-      for each vertex
-        append facet to vertex->neighbors
-*/
-void qh_vertexneighbors(void /*qh.facet_list*/) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  if (qh VERTEXneighbors)
-    return;
-  trace1((qh ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
-  qh vertex_visit++;
-  FORALLfacets {
-    if (facet->visible)
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-        vertex->neighbors= qh_setnew(qh hull_dim);
-      }
-      qh_setappend(&vertex->neighbors, facet);
-    }
-  }
-  qh VERTEXneighbors= True;
-} /* vertexneighbors */
-
-/*---------------------------------
-
-  qh_vertexsubset( vertexsetA, vertexsetB )
-    returns True if vertexsetA is a subset of vertexsetB
-    assumes vertexsets are sorted
-
-  note:
-    empty set is a subset of any other set
-*/
-boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
-  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
-
-  while (True) {
-    if (!*vertexA)
-      return True;
-    if (!*vertexB)
-      return False;
-    if ((*vertexA)->id > (*vertexB)->id)
-      return False;
-    if (*vertexA  == *vertexB)
-      vertexA++;
-    vertexB++;
-  }
-  return False; /* avoid warnings */
-} /* vertexsubset */
diff --git a/src/qhull/src/libqhull/qh-geom.htm b/src/qhull/src/libqhull/qh-geom.htm
deleted file mode 100644
index 6dc7465eb..000000000
--- a/src/qhull/src/libqhull/qh-geom.htm
+++ /dev/null
@@ -1,295 +0,0 @@
-
-
-
-
-geom.c, geom2.c -- geometric and floating point routines
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
-
    
-
-
-
    geom.c, geom2.c, random.c -- geometric and floating point routines
    
-
    
-
    Geometrically, a vertex is a point with d coordinates
-and a facet is a halfspace. A halfspace is defined by an
-oriented hyperplane through the facet's vertices. A hyperplane
-is defined by d normalized coefficients and an offset. A
-point is above a facet if its distance to the facet is
-positive.
    
-
-
    Qhull uses floating point coordinates for input points,
-vertices, halfspace equations, centrums, and an interior point.
    
-
-
    Qhull may be configured for single precision or double
-precision floating point arithmetic (see realT
-). 
    
-
-
    Each floating point operation may incur round-off error (see
-Merge). The maximum error for distance
-computations is determined at initialization. The roundoff error
-in halfspace computation is accounted for by computing the
-distance from vertices to the halfspace. 
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly •
-Qhull • Set •
-Stat • User 
    
-
-
    Index to geom.c,
-geom2.c, geom.h,
-random.c, random.h
-
    
-
-
-
-
    »geometric data types
-and constants
    
-
-
      
-
    • coordT coordinates and
-coefficients are stored as realT
      • 
-
    • pointT a point is an array
-of DIM3 coordinates 
      • 
-
    
-
-
    »mathematical macros
    
-
-
      
-
    • fabs_ returns the absolute
-value of a 
      • 
-
    • fmax_ returns the maximum
-value of a and b 
      • 
-
    • fmin_ returns the minimum
-value of a and b 
      • 
-
    • maximize_ maximize a value
-
      • 
-
    • minimize_ minimize a value
-
      • 
-
    • det2_ compute a 2-d
-determinate 
      • 
-
    • det3_ compute a 3-d
-determinate 
      • 
-
    • dX, dY, dZ compute the difference
-between two coordinates 
      • 
-
    
-
-
    »mathematical functions
    
-
-
-
-
    »computational geometry functions
    
-
-
-
-
    »point array functions
    
-
-
-
    »geometric facet functions
    
-
-
-
    »geometric roundoff functions
    
-
      
-
    • qh_detjoggle determine
-default joggle for points and distance roundoff error
      • 
-
    • qh_detroundoff
-determine maximum roundoff error and other precision constants
      • 
-
    • qh_distround compute
-maximum roundoff error due to a distance computation to a
-normalized hyperplane
      • 
-
    • qh_divzero divide by a
-number that is nearly zero 
      • 
-
    • qh_maxouter return maximum outer
-plane
      • 
-
    • qh_outerinner return actual
-outer and inner planes
-
    
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
-
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-globa.htm b/src/qhull/src/libqhull/qh-globa.htm
deleted file mode 100644
index c87508b66..000000000
--- a/src/qhull/src/libqhull/qh-globa.htm
+++ /dev/null
@@ -1,165 +0,0 @@
-
-
-
-
-global.c -- global variables and their functions
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
-
    
-
-
-
    global.c -- global variables and their functions
    
-
    
-
    Qhull uses a global data structure, qh, to store
-globally defined constants, lists, sets, and variables. This
-allows multiple instances of Qhull to execute at the same time.
-The structure may be statically allocated or
-dynamically allocated with malloc().  See
-QHpointer.
-
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly •
-Qhull • Set •
-Stat • User 
    
-
-
    Index to global.c and
-libqhull.h
    
-
-
-
-
    »Qhull's global
-variables
    
-
-
-
-
    »Global variable and
-initialization routines
    
-
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-io.htm b/src/qhull/src/libqhull/qh-io.htm
deleted file mode 100644
index 5cb591d87..000000000
--- a/src/qhull/src/libqhull/qh-io.htm
+++ /dev/null
@@ -1,305 +0,0 @@
-
-
-
-
-io.c -- input and output operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    io.c -- input and output operations
    
-
    
-
-
    Qhull provides a wide range of input
-and output options. To organize the code, most output formats use
-the same driver: 
    
-
-
    -    qh_printbegin( fp, format, facetlist, facets, printall );
-
-    FORALLfacet_( facetlist )
-      qh_printafacet( fp, format, facet, printall );
-
-    FOREACHfacet_( facets )
-      qh_printafacet( fp, format, facet, printall );
-
-    qh_printend( fp, format );
-
    
-
-
    Note the 'printall' flag. It selects whether or not
-qh_skipfacet() is tested. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom •
-Global • Io •
-Mem • Merge •
-Poly • Qhull •
-Set • Stat •
-User 
    
-
-
    Index to io.c and io.h
    
-
-
-
-
    »io.h constants and types
    
-
-
      
-
    • qh_MAXfirst maximum length
-of first two lines of stdin 
      • 
-
    • qh_WHITESPACE possible
-values of white space 
      • 
-
    • printvridgeT function to
-print results of qh_printvdiagram or qh_eachvoronoi
      • 
-
    
-
-
    »User level functions
    
-
-
-
-
    »Print functions for all
-output formats
    
-
-
-
-
    »Text output functions
    
-
-
-
    »Text utility functions
    
-
-
-
    »Geomview output functions
    
-
-
    »Geomview utility functions
    
-
-
    
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-mem.htm b/src/qhull/src/libqhull/qh-mem.htm
deleted file mode 100644
index b993b2229..000000000
--- a/src/qhull/src/libqhull/qh-mem.htm
+++ /dev/null
@@ -1,145 +0,0 @@
-
-
-
-
-mem.c -- memory operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    mem.c -- memory operations
    
-
    
-
    Qhull uses quick-fit memory allocation. It maintains a
-set of free lists for a variety of small allocations. A
-small request returns a block from the best fitting free
-list. If the free list is empty, Qhull allocates a block
-from a reserved buffer. 
    
-
    Use 'T5' to trace memory allocations.
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to mem.c and
-mem.h
    
-
-
    »mem.h data types and constants
    
-
      
-
    • ptr_intT for casting
-a void* to an integer-type 
      • 
-
    • qhmemT global memory
-structure for mem.c 
      • 
-
    • qh_NOmem disable memory allocation
      • 
-
    
-
    »mem.h macros
    
-
-
    »User level
-functions
    
-
-
-
    »Initialization and
-termination functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-merge.htm b/src/qhull/src/libqhull/qh-merge.htm
deleted file mode 100644
index 54b97c88e..000000000
--- a/src/qhull/src/libqhull/qh-merge.htm
+++ /dev/null
@@ -1,366 +0,0 @@
-
-
-
-
-merge.c -- facet merge operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    merge.c -- facet merge operations
    
-
    
-
    Qhull handles precision problems by merged facets or joggled input.
-Except for redundant vertices, it corrects a problem by
-merging two facets. When done, all facets are clearly
-convex. See Imprecision in Qhull
-for further information. 
    
-
    Users may joggle the input ('QJn')
-instead of merging facets. 
    
-
    Qhull detects and corrects the following problems: 
    
-
      
-
    • More than two facets meeting at a ridge. When
-Qhull creates facets, it creates an even number
-of facets for each ridge. A convex hull always
-has two facets for each ridge. More than two
-facets may be created if non-adjacent facets
-share a vertex. This is called a duplicate
-ridge. In 2-d, a duplicate ridge would
-create a loop of facets. 
      • 
-
    
-
      
-
    • A facet contained in another facet. Facet
-merging may leave all vertices of one facet as a
-subset of the vertices of another facet. This is
-called a redundant facet. 
      • 
-
    
-
      
-
    • A facet with fewer than three neighbors. Facet
-merging may leave a facet with one or two
-neighbors. This is called a degenerate facet.
-
      • 
-
    
-
      
-
    • A facet with flipped orientation. A
-facet's hyperplane may define a halfspace that
-does not include the interior point.This is
-called a flipped facet. 
      • 
-
    
-
      
-
    • A coplanar horizon facet. A
-newly processed point may be coplanar with an
-horizon facet. Qhull creates a new facet without
-a hyperplane. It links new facets for the same
-horizon facet together. This is called a samecycle.
-The new facet or samecycle is merged into the
-horizon facet. 
      • 
-
    
-
      
-
    • Concave facets. A facet's centrum may be
-above a neighboring facet. If so, the facets meet
-at a concave angle. 
      • 
-
    
-
      
-
    • Coplanar facets. A facet's centrum may be
-coplanar with a neighboring facet (i.e., it is
-neither clearly below nor clearly above the
-facet's hyperplane). Qhull removes coplanar
-facets in independent sets sorted by angle.
      • 
-
    
-
      
-
    • Redundant vertex. A vertex may have fewer
-than three neighboring facets. If so, it is
-redundant and may be renamed to an adjacent
-vertex without changing the topological
-structure.This is called a redundant vertex.
-
      • 
-
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to merge.c and
-merge.h
    
-
-
-
    »merge.h data
-types, macros, and global sets
    
-
      
-
    • mergeT structure to
-identify a merge of two facets
      • 
-
    • FOREACHmerge_
-assign 'merge' to each merge in merges 
      • 
-
    • qh global sets
-qh.facet_mergeset contains non-convex merges
-while qh.degen_mergeset contains degenerate and
-redundant facets
      • 
-
    
-
    »merge.h
-constants
    
-
-
    »top-level merge
-functions
    
-
-
-
    »functions for
-identifying merges
    
-
-
-
    »functions for
-determining the best merge
    
-
-
-
    »functions for
-merging facets
    
-
-
-
    »functions for
-merging a cycle of facets
    
-
    If a point is coplanar with an horizon facet, the
-corresponding new facets are linked together (a samecycle)
-for merging.
    
-
-
    »functions
-for renaming a vertex
    
-
-
-
    »functions
-for identifying vertices for renaming
    
-
-
-
    »functions for check and
-trace
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-poly.htm b/src/qhull/src/libqhull/qh-poly.htm
deleted file mode 100644
index c8f6b38b0..000000000
--- a/src/qhull/src/libqhull/qh-poly.htm
+++ /dev/null
@@ -1,485 +0,0 @@
-
-
-
-
-poly.c, poly2.c -- polyhedron operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    poly.c, poly2.c -- polyhedron operations
    
-
    
-
-
    Qhull uses dimension-free terminology. Qhull builds a
-polyhedron in dimension d. A polyhedron is a
-simplicial complex of faces with geometric information for the
-top and bottom-level faces. A (d-1)-face is a facet,
-a (d-2)-face is a ridge, and a 0-face
-is a vertex. For example in 3-d, a facet is a polygon
-and a ridge is an edge. A facet is built from a ridge (the base)
-and a vertex (the apex). See
-Qhull's data structures.
    
-
-
    Qhull's primary data structure is a polyhedron. A
-polyhedron is a list of facets. Each facet has a set of
-neighboring facets and a set of vertices. Each facet has a
-hyperplane. For example, a tetrahedron has four facets.
-If its vertices are a, b, c, d, and its facets
-are 1, 2, 3, 4, the tetrahedron is 
    
-
    
-
      
-
    • facet 1 
        
-    
      • vertices: b c d 
        • 
-    
      • neighbors: 2 3 4 
        • 
-
      
-
      • 
-
    • facet 2 
        
-    
      • vertices: a c d 
        • 
-    
      • neighbors: 1 3 4 
        • 
-
      
-
      • 
-
    • facet 3 
        
-    
      • vertices: a b d 
        • 
-    
      • neighbors: 1 2 4 
        • 
-
      
-
      • 
-
    • facet 4 
        
-    
      • vertices: a b c 
        • 
-    
      • neighbors: 1 2 3 
        • 
-
      
-
      • 
-
    
-
    
-
    A facet may be simplicial or non-simplicial. In 3-d, a
-simplicial facet has three vertices and three
-neighbors. A nonsimplicial facet has more than
-three vertices and more than three neighbors. A
-nonsimplicial facet has a set of ridges and a centrum. 
    
-
    
-A simplicial facet has an orientation. An orientation
-is either top or bottom.
-The flag, facet->toporient,
-defines the orientation of the facet's vertices.  For example in 3-d,
-'top' is left-handed orientation (i.e., the vertex order follows the direction
-of the left-hand fingers when the thumb is pointing away from the center).
-Except for axis-parallel facets in 5-d and higher, topological orientation
-determines the geometric orientation of the facet's hyperplane.
-
-
    A nonsimplicial facet is due to merging two or more
-facets. The facet's ridge set determine a simplicial
-decomposition of the facet. Each ridge is a 1-face (i.e.,
-it has two vertices and two neighboring facets). The
-orientation of a ridge is determined by the order of the
-neighboring facets. The flag, facet->toporient,is
-ignored. 
    
-
    A nonsimplicial facet has a centrum for testing
-convexity. A centrum is a point on the facet's
-hyperplane that is near the center of the facet. Except
-for large facets, it is the arithmetic average of the
-facet's vertices. 
    
-
    A nonsimplicial facet is an approximation that is
-defined by offsets from the facet's hyperplane. When
-Qhull finishes, the outer plane is above all
-points while the inner plane is below the facet's
-vertices. This guarantees that any exact convex hull
-passes between the inner and outer planes. The outer
-plane is defined by facet->maxoutside while
-the inner plane is computed from the facet's vertices.
    
-
-
    Qhull 3.1 includes triangulation of non-simplicial facets
-('Qt').
-These facets,
-called tricoplanar, share the same normal. centrum, and Voronoi center.
-One facet (keepcentrum) owns these data structures.
-While tricoplanar facets are more accurate than the simplicial facets from
-joggled input, they
-may have zero area or flipped orientation.
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to poly.c,
-poly2.c, poly.h,
-and libqhull.h
    
-
-
    »Data
-types and global lists for polyhedrons
    
-
-
    »poly.h constants
    
-
      
-
    • ALGORITHMfault
-flag to not report errors in qh_checkconvex() 
      • 
-
    • DATAfault flag to
-report errors in qh_checkconvex() 
      • 
-
    • DUPLICATEridge
-special value for facet->neighbor to indicate
-a duplicate ridge 
      • 
-
    • MERGEridge
-special value for facet->neighbor to indicate
-a merged ridge 
      • 
-
    
-
    »Global FORALL
-macros
    
-
-
    »FORALL macros
    
-
-
    »FOREACH macros
    
-
-
    »Indexed
-FOREACH macros
    
-
      
-
    • FOREACHfacet_i_
-assign 'facet' and 'facet_i' to each facet in
-facet set 
      • 
-
    • FOREACHneighbor_i_
-assign 'neighbor' and 'neighbor_i' to each facet
-in facet->neighbors or vertex->neighbors
      • 
-
    • FOREACHpoint_i_
-assign 'point' and 'point_i' to each point in
-points set 
      • 
-
    • FOREACHridge_i_
-assign 'ridge' and 'ridge_i' to each ridge in
-ridges set 
      • 
-
    • FOREACHvertex_i_
-assign 'vertex' and 'vertex_i' to each vertex in
-vertices set 
      • 
-
    • FOREACHvertexreverse12_
-assign 'vertex' to each vertex in vertex set;
-reverse the order of first two vertices 
      • 
-
    
-
    »Other macros for polyhedrons
    
-
      
-
    • getid_ return ID for
-a facet, ridge, or vertex 
      • 
-
    • otherfacet_
-return neighboring facet for a ridge in a facet 
      • 
-
    
-
    »Facetlist
-functions
    
-
-
    »Facet
-functions
    
-
-
    »Vertex,
-ridge, and point functions
    
-
-
    »Hashtable functions
    
-
-
    »Allocation and
-deallocation functions
    
-
-
    »Check
-functions
    
-
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-qhull.htm b/src/qhull/src/libqhull/qh-qhull.htm
deleted file mode 100644
index 5212c6422..000000000
--- a/src/qhull/src/libqhull/qh-qhull.htm
+++ /dev/null
@@ -1,279 +0,0 @@
-
-
-
-
-libqhull.c -- top-level functions and basic data types
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    libqhull.c -- top-level functions and basic data types
    
-
    
-
    Qhull implements the Quickhull algorithm for computing
-the convex hull. The Quickhull algorithm combines two
-well-known algorithms: the 2-d quickhull algorithm and
-the n-d beneath-beyond algorithm. See
-Description of Qhull. 
    
-
    This section provides an index to the top-level
-functions and base data types.  The top-level header file, libqhull.h,
-contains prototypes for these functions.
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to libqhull.c,
-libqhull.h, and
-unix.c
    
-
-
-
    »libqhull.h and unix.c
-data types and constants
    
-
      
-
    • flagT Boolean flag as
-a bit 
      • 
-
    • boolT boolean value,
-either True or False 
      • 
-
    • CENTERtype to
-distinguish facet->center 
      • 
-
    • qh_PRINT output
-formats for printing (qh.PRINTout) 
      • 
-
    • qh_ALL argument flag
-for selecting everything 
      • 
-
    • qh_ERR Qhull exit
-codes for indicating errors 
      • 
-
    • qh_FILEstderr Fake stderr
-to distinguish error output from normal output [C++ only]
      • 
-
    • qh_prompt version and long prompt for Qhull
      • 
-
    • qh_prompt2 synopsis for Qhull
      • 
-
    • qh_prompt3 concise prompt for Qhull
      • 
-
    • qh_version version stamp
      • 
-
    
-
-
    »libqhull.h other
-macros
    
-
      
-
    • traceN print trace
-message if qh.IStracing >= N. 
      • 
-
    • QHULL_UNUSED declare an
- unused variable to avoid warnings. 
      • 
-
    
-
-
    »Quickhull
-routines in call order
    
-
-
-
    »Top-level routines for initializing and terminating Qhull (in other modules)
    
-
-
-
    »Top-level routines for reading and modifying the input (in other modules)
    
-
-
-
    »Top-level routines for calling Qhull (in other modules)
    
-
-
-
    »Top-level routines for returning results (in other modules)
    
-
-
-
    »Top-level routines for testing and debugging (in other modules)
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-set.htm b/src/qhull/src/libqhull/qh-set.htm
deleted file mode 100644
index 06e71bbc9..000000000
--- a/src/qhull/src/libqhull/qh-set.htm
+++ /dev/null
@@ -1,308 +0,0 @@
-
-
-
-
-qset.c -- set data type and operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    qset.c -- set data type and operations
    
-
    
-
    Qhull's data structures are constructed from sets. The
-functions and macros in qset.c construct, iterate, and
-modify these sets. They are the most frequently called
-functions in Qhull. For this reason, efficiency is the
-primary concern. 
    
-
    In Qhull, a set is represented by an unordered
-array of pointers with a maximum size and a NULL
-terminator (setT).
-Most sets correspond to mathematical sets
-(i.e., the pointers are unique). Some sets are sorted to
-enforce uniqueness. Some sets are ordered. For example,
-the order of vertices in a ridge determine the ridge's
-orientation. If you reverse the order of adjacent
-vertices, the orientation reverses. Some sets are not
-mathematical sets. They may be indexed as an array and
-they may include NULL pointers. 
    
-
    The most common operation on a set is to iterate its
-members. This is done with a 'FOREACH...' macro. Each set
-has a custom macro. For example, 'FOREACHvertex_'
-iterates over a set of vertices. Each vertex is assigned
-to the variable 'vertex' from the pointer 'vertexp'. 
    
-
    Most sets are constructed by appending elements to the
-set. The last element of a set is either NULL or the
-index of the terminating NULL for a partially full set.
-If a set is full, appending an element copies the set to
-a larger array. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to qset.c and
-qset.h
    
-
-
    »Data types and
-constants
    
-
      
-
    • SETelemsize size
-of a set element in bytes 
      • 
-
    • setT a set with a
-maximum size and a current size
      • 
-
    • qh global sets
-global sets for temporary sets, etc. 
      • 
-
    
-
    »FOREACH macros
    
-
-
    »Access and
-size macros
    
-
-
    »Internal macros
    
-
      
-
    • SETsizeaddr_
-return pointer to end element of a set (indicates
-current size) 
      • 
-
    
-
-
    »address macros
    
-
      
-
    • SETaddr_ return
-address of a set's elements 
      • 
-
    • SETelemaddr_
-return address of the n'th element of a set 
      • 
-
    • SETref_ l.h.s. for
-modifying the current element in a FOREACH
-iteration 
      • 
-
    
-
-
    »Allocation and
-deallocation functions
    
-
-
-
    »Access and
-predicate functions 
    
-
-
-
    »Add functions
    
-
-
-
    »Check and print functions
    
-
-
-
    »Copy, compact, and zero functions
    
-
-
-
    »Delete functions
    
-
-
-
    »Temporary set functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-stat.htm b/src/qhull/src/libqhull/qh-stat.htm
deleted file mode 100644
index b96854031..000000000
--- a/src/qhull/src/libqhull/qh-stat.htm
+++ /dev/null
@@ -1,163 +0,0 @@
-
-
-
-
-stat.c -- statistical operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    stat.c -- statistical operations
    
-
    
-
    Qhull records many statistics. These functions and
-macros make it inexpensive to add a statistic.
-
    As with Qhull's global variables, the statistics data structure is
-accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
-is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
-Statistics
-may be turned off in user.h. If so, all but the 'zz'
-statistics are ignored.
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to stat.c and
-stat.h
    
-
-
-
    »stat.h types
    
-
      
-
    • intrealT union of
-integer and real
      • 
-
    • qhstat global data
-structure for statistics 
      • 
-
    
-
    »stat.h
-constants
    
-
      
-
    • qh_KEEPstatistics 0 turns off most statistics
      • 
-
    • Z..., W... integer (Z) and real (W) statistics
-
      • 
-
    • ZZstat Z.../W... statistics that
-remain defined if qh_KEEPstatistics=0
-
      • 
-
    • ztype zdoc, zinc, etc.
-for definining statistics 
      • 
-
    
-
    »stat.h macros
    
-
      
-
    • MAYdebugx called
-frequently for error trapping 
      • 
-
    • zadd_/wadd_ add value
-to an integer or real statistic 
      • 
-
    • zdef_ define a
-statistic 
      • 
-
    • zinc_ increment an
-integer statistic 
      • 
-
    • zmax_/wmax_ update
-integer or real maximum statistic 
      • 
-
    • zmin_/wmin_ update
-integer or real minimum statistic 
      • 
-
    • zval_/wval_ set or
-return value of a statistic 
      • 
-
    
-
-
    »stat.c
-functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qh-user.htm b/src/qhull/src/libqhull/qh-user.htm
deleted file mode 100644
index 6682f4b2f..000000000
--- a/src/qhull/src/libqhull/qh-user.htm
+++ /dev/null
@@ -1,271 +0,0 @@
-
-
-
-
-user.c -- user-definable operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
    user.c -- user-definable operations
    
-
    
-
    This section contains functions and constants that the
-user may want to change. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to user.c, usermem.c, userprintf.c, userprintf_rbox.c and
-user.h
    
-
-
-
    »Qhull library constants
    
-
-
-
-
    »user.h data
-types and configuration macros
    
-
-
-
    »definition constants
    
-
      
-
    • qh_DEFAULTbox
-define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) 
      • 
-
    • qh_INFINITE on
-output, indicates Voronoi center at infinity 
      • 
-
    • qh_ORIENTclock
-define convention for orienting facets
      • 
-
    • qh_ZEROdelaunay
-define facets that are ignored in Delaunay triangulations
      • 
-
    
-
-
    »joggle constants
    
-
-
-
    »performance
-related constants
    
-
-
-
    »memory constants
    
-
-
-
    »conditional compilation
    
-
      
-
    • compiler defined symbols,
-e.g., _STDC_ and _cplusplus
-
-
    • qh_COMPUTEfurthest
-    compute furthest distance to an outside point instead of storing it with the facet
-
    • qh_KEEPstatistics
-    enable statistic gathering and reporting with option 'Ts'
-
    • qh_MAXoutside
-record outer plane for each facet
-
    • qh_NOmerge
-disable facet merging
-
    • qh_NOtrace
-disable tracing with option 'T4'
-
    • qh_QHpointer
-access global data with pointer or static structure
-
    • qh_QUICKhelp
-use abbreviated help messages, e.g., for degenerate inputs
-
    
-
-
    »merge
-constants
    
-
-
-
    »user.c
-functions
    
-
-
-
    »usermem.c
-functions
    
-
      
-
    • qh_exit exit program, same as exit().  May be redefined as throw "QH10003.." by libqhullcpp/usermem_r-cpp.cpp
      • 
-
    • qh_fprintf_stderr print to stderr when qh.ferr is not defined.
      • 
-
    • qh_free free memory, same as free().
      • 
-
    • qh_malloc allocate memory, same as malloc()
      • 
-
    
-
-
    »userprintf.c
- and userprintf_rbox,c functions
    
-
      
-
    • qh_fprintf print
-information from Qhull, sames as fprintf(). 
      • 
-
    • qh_fprintf_rbox print
-information from Rbox, sames as fprintf(). 
      • 
-
    
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull/qhull-exports.def b/src/qhull/src/libqhull/qhull-exports.def
deleted file mode 100644
index 11a42b57e..000000000
--- a/src/qhull/src/libqhull/qhull-exports.def
+++ /dev/null
@@ -1,417 +0,0 @@
-; qhull-exports.def -- msvc module-definition file
-;
-;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
-;   [mar'11] 399 symbols 
-;   Annotate as DATA qh_last_random qh_qh qh_qhstat qhmem rbox rbox_inuse
-;   Annotate as __declspec for outside access in win32 -- qh_qh qh_qhstat
-;   Same as ../libqhullp/qhull_p-exports.def without qh_save_qhull and qh_restore_qhull
-;
-; $Id: //main/2015/qhull/src/libqhull/qhull-exports.def#3 $$Change: 2047 $
-; $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-; 
-; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
-VERSION 7.0
-EXPORTS
-qh_addhash
-qh_addpoint
-qh_all_merges
-qh_allstatA
-qh_allstatB
-qh_allstatC
-qh_allstatD
-qh_allstatE
-qh_allstatE2
-qh_allstatF
-qh_allstatG
-qh_allstatH
-qh_allstatI
-qh_allstatistics
-qh_appendfacet
-qh_appendmergeset
-qh_appendprint
-qh_appendvertex
-qh_argv_to_command
-qh_argv_to_command_size
-qh_attachnewfacets
-qh_backnormal
-qh_basevertices
-qh_build_withrestart
-qh_buildhull
-qh_buildtracing
-qh_check_bestdist
-qh_check_dupridge
-qh_check_maxout
-qh_check_output
-qh_check_point
-qh_check_points
-qh_checkconnect
-qh_checkconvex
-qh_checkfacet
-qh_checkflags
-qh_checkflipped
-qh_checkflipped_all
-qh_checkpolygon
-qh_checkvertex
-qh_checkzero
-qh_clear_outputflags
-qh_clearcenters
-qh_clock
-qh_collectstatistics
-qh_compare_facetarea
-qh_compare_facetmerge
-qh_compare_facetvisit
-qh_compare_vertexpoint
-qh_compareangle
-qh_comparemerge
-qh_comparevisit
-qh_copyfilename
-qh_copynonconvex
-qh_copypoints
-qh_countfacets
-qh_createsimplex
-qh_crossproduct
-qh_degen_redundant_facet
-qh_degen_redundant_neighbors
-qh_deletevisible
-qh_delfacet
-qh_delridge
-qh_delvertex
-qh_determinant
-qh_detjoggle
-qh_detroundoff
-qh_detsimplex
-qh_detvnorm
-qh_detvridge
-qh_detvridge3
-qh_dfacet
-qh_distnorm
-qh_distplane
-qh_distround
-qh_divzero
-qh_dvertex
-qh_eachvoronoi
-qh_eachvoronoi_all
-qh_errexit
-qh_errexit2
-qh_errexit_rbox
-qh_errprint
-qh_exit
-qh_facet2point
-qh_facet3vertex
-qh_facetarea
-qh_facetarea_simplex
-qh_facetcenter
-qh_facetintersect
-qh_facetvertices
-qh_find_newvertex
-qh_findbest
-qh_findbest_test
-qh_findbestfacet
-qh_findbesthorizon
-qh_findbestlower
-qh_findbestneighbor
-qh_findbestnew
-qh_findfacet_all
-qh_findgood
-qh_findgood_all
-qh_findgooddist
-qh_findhorizon
-qh_flippedmerges
-qh_forcedmerges
-qh_fprintf
-qh_fprintf_rbox
-qh_fprintf_stderr
-qh_free
-qh_freebuffers
-qh_freebuild
-qh_freeqhull
-qh_freeqhull2
-qh_freestatistics
-qh_furthestnext
-qh_furthestout
-qh_gausselim
-qh_geomplanes
-qh_getangle
-qh_getarea
-qh_getcenter
-qh_getcentrum
-qh_getdistance
-qh_gethash
-qh_getmergeset
-qh_getmergeset_initial
-qh_gram_schmidt
-qh_hashridge
-qh_hashridge_find
-qh_infiniteloop
-qh_init_A
-qh_init_B
-qh_init_qhull_command
-qh_initbuild
-qh_initflags
-qh_initialhull
-qh_initialvertices
-qh_initqhull_buffers
-qh_initqhull_globals
-qh_initqhull_mem
-qh_initqhull_outputflags
-qh_initqhull_start
-qh_initqhull_start2
-qh_initstatistics
-qh_initthresholds
-qh_inthresholds
-qh_isvertex
-qh_joggleinput
-; Mark as DATA, otherwise links a separate qh_last_random.  No __declspec.
-qh_last_random      DATA
-qh_lib_check
-qh_makenew_nonsimplicial
-qh_makenew_simplicial
-qh_makenewfacet
-qh_makenewfacets
-qh_makenewplanes
-qh_makeridges
-qh_malloc
-qh_mark_dupridges
-qh_markkeep
-qh_markvoronoi
-qh_matchduplicates
-qh_matchneighbor
-qh_matchnewfacets
-qh_matchvertices
-qh_maxabsval
-qh_maxmin
-qh_maxouter
-qh_maxsimplex
-qh_maydropneighbor
-qh_memalloc
-qh_memfree
-qh_memfreeshort
-qh_meminit
-qh_meminitbuffers
-qh_memsetup
-qh_memsize
-qh_memstatistics
-qh_memtotal
-qh_merge_degenredundant
-qh_merge_nonconvex
-qh_mergecycle
-qh_mergecycle_all
-qh_mergecycle_facets
-qh_mergecycle_neighbors
-qh_mergecycle_ridges
-qh_mergecycle_vneighbors
-qh_mergefacet
-qh_mergefacet2d
-qh_mergeneighbors
-qh_mergeridges
-qh_mergesimplex
-qh_mergevertex_del
-qh_mergevertex_neighbors
-qh_mergevertices
-qh_minabsval
-qh_mindiff
-qh_nearcoplanar
-qh_nearvertex
-qh_neighbor_intersections
-qh_new_qhull
-qh_newfacet
-qh_newhashtable
-qh_newridge
-qh_newstats
-qh_newvertex
-qh_newvertices
-qh_nextfurthest
-qh_nextridge3d
-qh_normalize
-qh_normalize2
-qh_nostatistic
-qh_option
-qh_order_vertexneighbors
-qh_orientoutside
-qh_out1
-qh_out2n
-qh_out3n
-qh_outcoplanar
-qh_outerinner
-qh_partitionall
-qh_partitioncoplanar
-qh_partitionpoint
-qh_partitionvisible
-qh_point
-qh_point_add
-qh_pointdist
-qh_pointfacet
-qh_pointid
-qh_pointvertex
-qh_postmerge
-qh_precision
-qh_premerge
-qh_prepare_output
-qh_prependfacet
-qh_printafacet
-qh_printallstatistics
-qh_printbegin
-qh_printcenter
-qh_printcentrum
-qh_printend
-qh_printend4geom
-qh_printextremes
-qh_printextremes_2d
-qh_printextremes_d
-qh_printfacet
-qh_printfacet2geom
-qh_printfacet2geom_points
-qh_printfacet2math
-qh_printfacet3geom_nonsimplicial
-qh_printfacet3geom_points
-qh_printfacet3geom_simplicial
-qh_printfacet3math
-qh_printfacet3vertex
-qh_printfacet4geom_nonsimplicial
-qh_printfacet4geom_simplicial
-qh_printfacetNvertex_nonsimplicial
-qh_printfacetNvertex_simplicial
-qh_printfacetheader
-qh_printfacetlist
-qh_printfacetridges
-qh_printfacets
-qh_printhashtable
-qh_printhelp_degenerate
-qh_printhelp_narrowhull
-qh_printhelp_singular
-qh_printhyperplaneintersection
-qh_printline3geom
-qh_printlists
-qh_printmatrix
-qh_printneighborhood
-qh_printpoint
-qh_printpoint3
-qh_printpointid
-qh_printpoints
-qh_printpoints_out
-qh_printpointvect
-qh_printpointvect2
-qh_printridge
-qh_printspheres
-qh_printstatistics
-qh_printstatlevel
-qh_printstats
-qh_printsummary
-qh_printvdiagram
-qh_printvdiagram2
-qh_printvertex
-qh_printvertexlist
-qh_printvertices
-qh_printvneighbors
-qh_printvnorm
-qh_printvoronoi
-qh_printvridge
-qh_produce_output
-qh_produce_output2
-qh_projectdim3
-qh_projectinput
-qh_projectpoint
-qh_projectpoints
-; Mark as DATA, otherwise links a separate qh_qh.  qh_qh and qh_qhstat requires __declspec
-qh_qh               DATA
-qh_qhstat           DATA
-qh_qhull
-qh_rand
-qh_randomfactor
-qh_randommatrix
-qh_rboxpoints
-qh_readfeasible
-qh_readpoints
-qh_reducevertices
-qh_redundant_vertex
-qh_remove_extravertices
-qh_removefacet
-qh_removevertex
-qh_rename_sharedvertex
-qh_renameridgevertex
-qh_renamevertex
-qh_resetlists
-qh_rotateinput
-qh_rotatepoints
-qh_roundi
-qh_scaleinput
-qh_scalelast
-qh_scalepoints
-qh_setaddnth
-qh_setaddsorted
-qh_setappend
-qh_setappend2ndlast
-qh_setappend_set
-qh_setcheck
-qh_setcompact
-qh_setcopy
-qh_setdel
-qh_setdelaunay
-qh_setdellast
-qh_setdelnth
-qh_setdelnthsorted
-qh_setdelsorted
-qh_setduplicate
-qh_setequal
-qh_setequal_except
-qh_setequal_skip
-qh_setfacetplane
-qh_setfeasible
-qh_setfree
-qh_setfree2
-qh_setfreelong
-qh_sethalfspace
-qh_sethalfspace_all
-qh_sethyperplane_det
-qh_sethyperplane_gauss
-qh_setin
-qh_setindex
-qh_setlarger
-qh_setlast
-qh_setnew
-qh_setnew_delnthsorted
-qh_setprint
-qh_setreplace
-qh_setsize
-qh_settemp
-qh_settempfree
-qh_settempfree_all
-qh_settemppop
-qh_settemppush
-qh_settruncate
-qh_setunique
-qh_setvoronoi_all
-qh_setzero
-qh_sharpnewfacets
-qh_skipfacet
-qh_skipfilename
-qh_srand
-qh_stddev
-qh_strtod
-qh_strtol
-qh_test_appendmerge
-qh_test_vneighbors
-qh_tracemerge
-qh_tracemerging
-qh_triangulate
-qh_triangulate_facet
-qh_triangulate_link
-qh_triangulate_mirror
-qh_triangulate_null
-qh_updatetested
-qh_updatevertices
-qh_user_memsizes
-qh_version
-qh_version2
-qh_vertexintersect
-qh_vertexintersect_new
-qh_vertexneighbors
-qh_vertexridges
-qh_vertexridges_facet
-qh_vertexsubset
-qh_voronoi_center
-qh_willdelete
-; Mark as DATA, otherwise links a separate qhmem.  No __declspec
-qhmem                   DATA
-rbox			DATA
-rbox_inuse              DATA
diff --git a/src/qhull/src/libqhull/qhull_a.h b/src/qhull/src/libqhull/qhull_a.h
deleted file mode 100644
index 729b72327..000000000
--- a/src/qhull/src/libqhull/qhull_a.h
+++ /dev/null
@@ -1,150 +0,0 @@
-/*
      ---------------------------------
-
-   qhull_a.h
-   all header files for compiling qhull with non-reentrant code
-   included before C++ headers for user_r.h:QHULL_CRTDBG
-
-   see qh-qhull.htm
-
-   see libqhull.h for user-level definitions
-
-   see user.h for user-definable constants
-
-   defines internal functions for libqhull.c global.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/qhull_a.h#4 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-
-   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
-           full parens around (x?y:z)
-           use '#include "libqhull/qhull_a.h"' to avoid name clashes
-*/
-
-#ifndef qhDEFqhulla
-#define qhDEFqhulla 1
-
-#include "libqhull.h"  /* Includes user_r.h and data types */
-
-#include "stat.h"
-#include "random.h"
-#include "mem.h"
-#include "qset.h"
-#include "geom.h"
-#include "merge.h"
-#include "poly.h"
-#include "io.h"
-
-#include 
-#include 
-#include 
-#include     /* some compilers will not need float.h */
-#include 
-#include 
-#include 
-#include 
-#include 
-/*** uncomment here and qset.c
-     if string.h does not define memcpy()
-#include 
-*/
-
-#if qh_CLOCKtype == 2  /* defined in user.h from libqhull.h */
-#include 
-#include 
-#include 
-#endif
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4100)  /* unreferenced formal parameter */
-#pragma warning( disable : 4127)  /* conditional expression is constant */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/* ======= -macros- =========== */
-
-/*----------------------------------
-
-  traceN((qh ferr, 0Nnnn, "format\n", vars));
-    calls qh_fprintf if qh.IStracing >= N
-
-    Add debugging traps to the end of qh_fprintf
-
-  notes:
-    removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh IStracing) qh_fprintf args;}
-#define trace1(args) {if (qh IStracing >= 1) qh_fprintf args;}
-#define trace2(args) {if (qh IStracing >= 2) qh_fprintf args;}
-#define trace3(args) {if (qh IStracing >= 3) qh_fprintf args;}
-#define trace4(args) {if (qh IStracing >= 4) qh_fprintf args;}
-#define trace5(args) {if (qh IStracing >= 5) qh_fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/*----------------------------------
-
-  Define an unused variable to avoid compiler warnings
-
-  Derived from Qt's corelib/global/qglobal.h
-
-*/
-
-#if defined(__cplusplus) && defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
-template 
-inline void qhullUnused(T &x) { (void)x; }
-#  define QHULL_UNUSED(x) qhullUnused(x);
-#else
-#  define QHULL_UNUSED(x) (void)x;
-#endif
-
-/***** -libqhull.c prototypes (alphabetical after qhull) ********************/
-
-void    qh_qhull(void);
-boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
-void    qh_buildhull(void);
-void    qh_buildtracing(pointT *furthest, facetT *facet);
-void    qh_build_withrestart(void);
-void    qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet);
-void    qh_findhorizon(pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
-pointT *qh_nextfurthest(facetT **visible);
-void    qh_partitionall(setT *vertices, pointT *points,int npoints);
-void    qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist);
-void    qh_partitionpoint(pointT *point, facetT *facet);
-void    qh_partitionvisible(boolT allpoints, int *numpoints);
-void    qh_precision(const char *reason);
-void    qh_printsummary(FILE *fp);
-
-/***** -global.c internal prototypes (alphabetical) ***********************/
-
-void    qh_appendprint(qh_PRINT format);
-void    qh_freebuild(boolT allmem);
-void    qh_freebuffers(void);
-void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
-
-/***** -stat.c internal prototypes (alphabetical) ***********************/
-
-void    qh_allstatA(void);
-void    qh_allstatB(void);
-void    qh_allstatC(void);
-void    qh_allstatD(void);
-void    qh_allstatE(void);
-void    qh_allstatE2(void);
-void    qh_allstatF(void);
-void    qh_allstatG(void);
-void    qh_allstatH(void);
-void    qh_freebuffers(void);
-void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
-
-#endif /* qhDEFqhulla */
diff --git a/src/qhull/src/libqhull/qhull_p-exports.def b/src/qhull/src/libqhull/qhull_p-exports.def
deleted file mode 100644
index cadf8a4fa..000000000
--- a/src/qhull/src/libqhull/qhull_p-exports.def
+++ /dev/null
@@ -1,418 +0,0 @@
-; qhull_p-exports.def -- msvc module-definition file
-;
-;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
-;   [mar'11] 399 symbols [jan'15] added 3 symbols
-;   Annotate as DATA qh_last_random qh_qh qh_qhstat qhmem rbox rbox_inuse
-;   Annotate as __declspec for outside access in win32 -- qh_qh qh_qhstat
-;
-; $Id: //main/2011/qhull/src/libqhull/qhull-exports.def#2 $$Change: 1368 $
-; $DateTime: 2011/04/16 08:12:32 $$Author: bbarber $
-;
-; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
-VERSION 7.0
-EXPORTS
-qh_addhash
-qh_addpoint
-qh_all_merges
-qh_allstatA
-qh_allstatB
-qh_allstatC
-qh_allstatD
-qh_allstatE
-qh_allstatE2
-qh_allstatF
-qh_allstatG
-qh_allstatH
-qh_allstatI
-qh_allstatistics
-qh_appendfacet
-qh_appendmergeset
-qh_appendprint
-qh_appendvertex
-qh_argv_to_command
-qh_argv_to_command_size
-qh_attachnewfacets
-qh_backnormal
-qh_basevertices
-qh_build_withrestart
-qh_buildhull
-qh_buildtracing
-qh_check_bestdist
-qh_check_dupridge
-qh_check_maxout
-qh_check_output
-qh_check_point
-qh_check_points
-qh_checkconnect
-qh_checkconvex
-qh_checkfacet
-qh_checkflags
-qh_checkflipped
-qh_checkflipped_all
-qh_checkpolygon
-qh_checkvertex
-qh_checkzero
-qh_clear_outputflags
-qh_clearcenters
-qh_clock
-qh_collectstatistics
-qh_compare_facetarea
-qh_compare_facetmerge
-qh_compare_facetvisit
-qh_compare_vertexpoint
-qh_compareangle
-qh_comparemerge
-qh_comparevisit
-qh_copyfilename
-qh_copynonconvex
-qh_copypoints
-qh_countfacets
-qh_createsimplex
-qh_crossproduct
-qh_degen_redundant_facet
-qh_degen_redundant_neighbors
-qh_deletevisible
-qh_delfacet
-qh_delridge
-qh_delvertex
-qh_determinant
-qh_detjoggle
-qh_detroundoff
-qh_detsimplex
-qh_detvnorm
-qh_detvridge
-qh_detvridge3
-qh_dfacet
-qh_distnorm
-qh_distplane
-qh_distround
-qh_divzero
-qh_dvertex
-qh_eachvoronoi
-qh_eachvoronoi_all
-qh_errexit
-qh_errexit2
-qh_errexit_rbox
-qh_errprint
-qh_exit
-qh_facet2point
-qh_facet3vertex
-qh_facetarea
-qh_facetarea_simplex
-qh_facetcenter
-qh_facetintersect
-qh_facetvertices
-qh_find_newvertex
-qh_findbest
-qh_findbest_test
-qh_findbestfacet
-qh_findbesthorizon
-qh_findbestlower
-qh_findbestneighbor
-qh_findbestnew
-qh_findfacet_all
-qh_findgood
-qh_findgood_all
-qh_findgooddist
-qh_findhorizon
-qh_flippedmerges
-qh_forcedmerges
-qh_fprintf
-qh_fprintf_rbox
-qh_fprintf_stderr
-qh_free
-qh_freebuffers
-qh_freebuild
-qh_freeqhull
-qh_freeqhull2
-qh_freestatistics
-qh_furthestnext
-qh_furthestout
-qh_gausselim
-qh_geomplanes
-qh_getangle
-qh_getarea
-qh_getcenter
-qh_getcentrum
-qh_getdistance
-qh_gethash
-qh_getmergeset
-qh_getmergeset_initial
-qh_gram_schmidt
-qh_hashridge
-qh_hashridge_find
-qh_infiniteloop
-qh_init_A
-qh_init_B
-qh_init_qhull_command
-qh_initbuild
-qh_initflags
-qh_initialhull
-qh_initialvertices
-qh_initqhull_buffers
-qh_initqhull_globals
-qh_initqhull_mem
-qh_initqhull_outputflags
-qh_initqhull_start
-qh_initqhull_start2
-qh_initstatistics
-qh_initthresholds
-qh_inthresholds
-qh_isvertex
-qh_joggleinput
-; Mark as DATA, otherwise links a separate qh_last_random.  No __declspec.
-qh_last_random      DATA
-qh_lib_check
-qh_makenew_nonsimplicial
-qh_makenew_simplicial
-qh_makenewfacet
-qh_makenewfacets
-qh_makenewplanes
-qh_makeridges
-qh_malloc
-qh_mark_dupridges
-qh_markkeep
-qh_markvoronoi
-qh_matchduplicates
-qh_matchneighbor
-qh_matchnewfacets
-qh_matchvertices
-qh_maxabsval
-qh_maxmin
-qh_maxouter
-qh_maxsimplex
-qh_maydropneighbor
-qh_memalloc
-qh_memfree
-qh_memfreeshort
-qh_meminit
-qh_meminitbuffers
-qh_memsetup
-qh_memsize
-qh_memstatistics
-qh_memtotal
-qh_merge_degenredundant
-qh_merge_nonconvex
-qh_mergecycle
-qh_mergecycle_all
-qh_mergecycle_facets
-qh_mergecycle_neighbors
-qh_mergecycle_ridges
-qh_mergecycle_vneighbors
-qh_mergefacet
-qh_mergefacet2d
-qh_mergeneighbors
-qh_mergeridges
-qh_mergesimplex
-qh_mergevertex_del
-qh_mergevertex_neighbors
-qh_mergevertices
-qh_minabsval
-qh_mindiff
-qh_nearcoplanar
-qh_nearvertex
-qh_neighbor_intersections
-qh_new_qhull
-qh_newfacet
-qh_newhashtable
-qh_newridge
-qh_newstats
-qh_newvertex
-qh_newvertices
-qh_nextfurthest
-qh_nextridge3d
-qh_normalize
-qh_normalize2
-qh_nostatistic
-qh_option
-qh_order_vertexneighbors
-qh_orientoutside
-qh_out1
-qh_out2n
-qh_out3n
-qh_outcoplanar
-qh_outerinner
-qh_partitionall
-qh_partitioncoplanar
-qh_partitionpoint
-qh_partitionvisible
-qh_point
-qh_point_add
-qh_pointdist
-qh_pointfacet
-qh_pointid
-qh_pointvertex
-qh_postmerge
-qh_precision
-qh_premerge
-qh_prepare_output
-qh_prependfacet
-qh_printafacet
-qh_printallstatistics
-qh_printbegin
-qh_printcenter
-qh_printcentrum
-qh_printend
-qh_printend4geom
-qh_printextremes
-qh_printextremes_2d
-qh_printextremes_d
-qh_printfacet
-qh_printfacet2geom
-qh_printfacet2geom_points
-qh_printfacet2math
-qh_printfacet3geom_nonsimplicial
-qh_printfacet3geom_points
-qh_printfacet3geom_simplicial
-qh_printfacet3math
-qh_printfacet3vertex
-qh_printfacet4geom_nonsimplicial
-qh_printfacet4geom_simplicial
-qh_printfacetNvertex_nonsimplicial
-qh_printfacetNvertex_simplicial
-qh_printfacetheader
-qh_printfacetlist
-qh_printfacetridges
-qh_printfacets
-qh_printhashtable
-qh_printhelp_degenerate
-qh_printhelp_narrowhull
-qh_printhelp_singular
-qh_printhyperplaneintersection
-qh_printline3geom
-qh_printlists
-qh_printmatrix
-qh_printneighborhood
-qh_printpoint
-qh_printpoint3
-qh_printpointid
-qh_printpoints
-qh_printpoints_out
-qh_printpointvect
-qh_printpointvect2
-qh_printridge
-qh_printspheres
-qh_printstatistics
-qh_printstatlevel
-qh_printstats
-qh_printsummary
-qh_printvdiagram
-qh_printvdiagram2
-qh_printvertex
-qh_printvertexlist
-qh_printvertices
-qh_printvneighbors
-qh_printvnorm
-qh_printvoronoi
-qh_printvridge
-qh_produce_output
-qh_produce_output2
-qh_projectdim3
-qh_projectinput
-qh_projectpoint
-qh_projectpoints
-; Mark as DATA, otherwise links a separate qh_qh.  qh_qh and qh_qhstat requires __declspec
-qh_qh               DATA
-qh_qhstat           DATA
-qh_qhull
-qh_rand
-qh_randomfactor
-qh_randommatrix
-qh_rboxpoints
-qh_readfeasible
-qh_readpoints
-qh_reducevertices
-qh_redundant_vertex
-qh_remove_extravertices
-qh_removefacet
-qh_removevertex
-qh_rename_sharedvertex
-qh_renameridgevertex
-qh_renamevertex
-qh_resetlists
-qh_restore_qhull
-qh_rotateinput
-qh_rotatepoints
-qh_roundi
-qh_save_qhull
-qh_scaleinput
-qh_scalelast
-qh_scalepoints
-qh_setaddnth
-qh_setaddsorted
-qh_setappend
-qh_setappend2ndlast
-qh_setappend_set
-qh_setcheck
-qh_setcompact
-qh_setcopy
-qh_setdel
-qh_setdelaunay
-qh_setdellast
-qh_setdelnth
-qh_setdelnthsorted
-qh_setdelsorted
-qh_setduplicate
-qh_setequal
-qh_setequal_except
-qh_setequal_skip
-qh_setfacetplane
-qh_setfeasible
-qh_setfree
-qh_setfree2
-qh_setfreelong
-qh_sethalfspace
-qh_sethalfspace_all
-qh_sethyperplane_det
-qh_sethyperplane_gauss
-qh_setin
-qh_setindex
-qh_setlarger
-qh_setlast
-qh_setnew
-qh_setnew_delnthsorted
-qh_setprint
-qh_setreplace
-qh_setsize
-qh_settemp
-qh_settempfree
-qh_settempfree_all
-qh_settemppop
-qh_settemppush
-qh_settruncate
-qh_setunique
-qh_setvoronoi_all
-qh_setzero
-qh_sharpnewfacets
-qh_skipfacet
-qh_skipfilename
-qh_srand
-qh_stddev
-qh_strtod
-qh_strtol
-qh_test_appendmerge
-qh_test_vneighbors
-qh_tracemerge
-qh_tracemerging
-qh_triangulate
-qh_triangulate_facet
-qh_triangulate_link
-qh_triangulate_mirror
-qh_triangulate_null
-qh_updatetested
-qh_updatevertices
-qh_user_memsizes
-qh_version
-qh_version2
-qh_vertexintersect
-qh_vertexintersect_new
-qh_vertexneighbors
-qh_vertexridges
-qh_vertexridges_facet
-qh_vertexsubset
-qh_voronoi_center
-qh_willdelete
-; Mark as DATA, otherwise links a separate qhmem.  No __declspec
-qhmem                   DATA
-rbox			DATA
-rbox_inuse              DATA
diff --git a/src/qhull/src/libqhull/qset.c b/src/qhull/src/libqhull/qset.c
deleted file mode 100644
index a969252a7..000000000
--- a/src/qhull/src/libqhull/qset.c
+++ /dev/null
@@ -1,1340 +0,0 @@
-/*
      ---------------------------------
-
-   qset.c
-   implements set manipulations needed for quickhull
-
-   see qh-set.htm and qset.h
-
-   Be careful of strict aliasing (two pointers of different types
-   that reference the same location).  The last slot of a set is
-   either the actual size of the set plus 1, or the NULL terminator
-   of the set (i.e., setelemT).
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/qset.c#3 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "user.h" /* for QHULL_CRTDBG */
-#include "qset.h"
-#include "mem.h"
-#include 
-#include 
-/*** uncomment here and qhull_a.h
-     if string.h does not define memcpy()
-#include 
-*/
-
-#ifndef qhDEFlibqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void    qh_errexit(int exitcode, facetT *, ridgeT *);
-void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
-#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#  pragma warning( disable : 4127)  /* conditional expression is constant */
-#  pragma warning( disable : 4706)  /* assignment within conditional function */
-#  endif
-#endif
-
-/*=============== internal macros ===========================*/
-
-/*============ functions in alphabetical order ===================*/
-
-/*----------------------------------
-
-  qh_setaddnth( setp, nth, newelem)
-    adds newelem as n'th element of sorted or unsorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nth=0 is first element
-    errors if nth is out of bounds
-
-  design:
-    expand *setp if empty or full
-    move tail of *setp up one
-    insert newelem
-*/
-void qh_setaddnth(setT **setp, int nth, void *newelem) {
-  int oldsize, i;
-  setelemT *sizep;          /* avoid strict aliasing */
-  setelemT *oldp, *newp;
-
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  oldsize= sizep->i - 1;
-  if (nth < 0 || nth > oldsize) {
-    qh_fprintf(qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qhmem.ferr, "", *setp);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  sizep->i++;
-  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
-  newp= oldp+1;
-  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
-    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
-  newp->p= newelem;
-} /* setaddnth */
-
-
-/*----------------------------------
-
-  setaddsorted( setp, newelem )
-    adds an newelem into sorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nop if newelem already in set
-
-  design:
-    find newelem's position in *setp
-    insert newelem
-*/
-void qh_setaddsorted(setT **setp, void *newelem) {
-  int newindex=0;
-  void *elem, **elemp;
-
-  FOREACHelem_(*setp) {          /* could use binary search instead */
-    if (elem < newelem)
-      newindex++;
-    else if (elem == newelem)
-      return;
-    else
-      break;
-  }
-  qh_setaddnth(setp, newindex, newelem);
-} /* setaddsorted */
-
-
-/*---------------------------------
-
-  qh_setappend( setp, newelem)
-    append newelem to *setp
-
-  notes:
-    *setp may be a temp set
-    *setp and newelem may be NULL
-
-  design:
-    expand *setp if empty or full
-    append newelem to *setp
-
-*/
-void qh_setappend(setT **setp, void *newelem) {
-  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-  setelemT *endp;
-  int count;
-
-  if (!newelem)
-    return;
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  count= (sizep->i)++ - 1;
-  endp= (setelemT *)SETelemaddr_(*setp, count, void);
-  (endp++)->p= newelem;
-  endp->p= NULL;
-} /* setappend */
-
-/*---------------------------------
-
-  qh_setappend_set( setp, setA)
-    appends setA to *setp
-
-  notes:
-    *setp can not be a temp set
-    *setp and setA may be NULL
-
-  design:
-    setup for copy
-    expand *setp if it is too small
-    append all elements of setA to *setp
-*/
-void qh_setappend_set(setT **setp, setT *setA) {
-  int sizeA, size;
-  setT *oldset;
-  setelemT *sizep;
-
-  if (!setA)
-    return;
-  SETreturnsize_(setA, sizeA);
-  if (!*setp)
-    *setp= qh_setnew(sizeA);
-  sizep= SETsizeaddr_(*setp);
-  if (!(size= sizep->i))
-    size= (*setp)->maxsize;
-  else
-    size--;
-  if (size + sizeA > (*setp)->maxsize) {
-    oldset= *setp;
-    *setp= qh_setcopy(oldset, sizeA);
-    qh_setfree(&oldset);
-    sizep= SETsizeaddr_(*setp);
-  }
-  if (sizeA > 0) {
-    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
-    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
-  }
-} /* setappend_set */
-
-
-/*---------------------------------
-
-  qh_setappend2ndlast( setp, newelem )
-    makes newelem the next to the last element in *setp
-
-  notes:
-    *setp must have at least one element
-    newelem must be defined
-    *setp may be a temp set
-
-  design:
-    expand *setp if empty or full
-    move last element of *setp up one
-    insert newelem
-*/
-void qh_setappend2ndlast(setT **setp, void *newelem) {
-    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-    setelemT *endp, *lastp;
-    int count;
-
-    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-        qh_setlarger(setp);
-        sizep= SETsizeaddr_(*setp);
-    }
-    count= (sizep->i)++ - 1;
-    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
-    lastp= endp-1;
-    *(endp++)= *lastp;
-    endp->p= NULL;    /* may overwrite *sizep */
-    lastp->p= newelem;
-} /* setappend2ndlast */
-
-/*---------------------------------
-
-  qh_setcheck( set, typename, id )
-    check set for validity
-    report errors with typename and id
-
-  design:
-    checks that maxsize, actual size, and NULL terminator agree
-*/
-void qh_setcheck(setT *set, const char *tname, unsigned id) {
-  int maxsize, size;
-  int waserr= 0;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  maxsize= set->maxsize;
-  if (size > maxsize || !maxsize) {
-    qh_fprintf(qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
-             size, tname, id, maxsize);
-    waserr= 1;
-  }else if (set->e[size].p) {
-    qh_fprintf(qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
-             tname, id, size-1, maxsize);
-    waserr= 1;
-  }
-  if (waserr) {
-    qh_setprint(qhmem.ferr, "ERRONEOUS", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setcheck */
-
-
-/*---------------------------------
-
-  qh_setcompact( set )
-    remove internal NULLs from an unsorted set
-
-  returns:
-    updated set
-
-  notes:
-    set may be NULL
-    it would be faster to swap tail of set into holes, like qh_setdel
-
-  design:
-    setup pointers into set
-    skip NULLs while copying elements to start of set
-    update the actual size
-*/
-void qh_setcompact(setT *set) {
-  int size;
-  void **destp, **elemp, **endp, **firstp;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  destp= elemp= firstp= SETaddr_(set, void);
-  endp= destp + size;
-  while (1) {
-    if (!(*destp++ = *elemp++)) {
-      destp--;
-      if (elemp > endp)
-        break;
-    }
-  }
-  qh_settruncate(set, (int)(destp-firstp));   /* WARN64 */
-} /* setcompact */
-
-
-/*---------------------------------
-
-  qh_setcopy( set, extra )
-    make a copy of a sorted or unsorted set with extra slots
-
-  returns:
-    new set
-
-  design:
-    create a newset with extra slots
-    copy the elements to the newset
-
-*/
-setT *qh_setcopy(setT *set, int extra) {
-  setT *newset;
-  int size;
-
-  if (extra < 0)
-    extra= 0;
-  SETreturnsize_(set, size);
-  newset= qh_setnew(size+extra);
-  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
-  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
-  return(newset);
-} /* setcopy */
-
-
-/*---------------------------------
-
-  qh_setdel( set, oldelem )
-    delete oldelem from an unsorted set
-
-  returns:
-    returns oldelem if found
-    returns NULL otherwise
-
-  notes:
-    set may be NULL
-    oldelem must not be NULL;
-    only deletes one copy of oldelem in set
-
-  design:
-    locate oldelem
-    update actual size if it was full
-    move the last element to the oldelem's location
-*/
-void *qh_setdel(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *elemp;
-  setelemT *lastp;
-
-  if (!set)
-    return NULL;
-  elemp= (setelemT *)SETaddr_(set, void);
-  while (elemp->p != oldelem && elemp->p)
-    elemp++;
-  if (elemp->p) {
-    sizep= SETsizeaddr_(set);
-    if (!(sizep->i)--)         /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-    elemp->p= lastp->p;      /* may overwrite itself */
-    lastp->p= NULL;
-    return oldelem;
-  }
-  return NULL;
-} /* setdel */
-
-
-/*---------------------------------
-
-  qh_setdellast( set)
-    return last element of set or NULL
-
-  notes:
-    deletes element from set
-    set may be NULL
-
-  design:
-    return NULL if empty
-    if full set
-      delete last element and set actual size
-    else
-      delete last element and update actual size
-*/
-void *qh_setdellast(setT *set) {
-  int setsize;  /* actually, actual_size + 1 */
-  int maxsize;
-  setelemT *sizep;
-  void *returnvalue;
-
-  if (!set || !(set->e[0].p))
-    return NULL;
-  sizep= SETsizeaddr_(set);
-  if ((setsize= sizep->i)) {
-    returnvalue= set->e[setsize - 2].p;
-    set->e[setsize - 2].p= NULL;
-    sizep->i--;
-  }else {
-    maxsize= set->maxsize;
-    returnvalue= set->e[maxsize - 1].p;
-    set->e[maxsize - 1].p= NULL;
-    sizep->i= maxsize;
-  }
-  return returnvalue;
-} /* setdellast */
-
-
-/*---------------------------------
-
-  qh_setdelnth( set, nth )
-    deletes nth element from unsorted set
-    0 is first element
-
-  returns:
-    returns the element (needs type conversion)
-
-  notes:
-    errors if nth invalid
-
-  design:
-    setup points and check nth
-    delete nth element and overwrite with last element
-*/
-void *qh_setdelnth(setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *elemp, *lastp;
-
-  sizep= SETsizeaddr_(set);
-  if ((sizep->i--)==0)         /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-  if (nth < 0 || nth >= sizep->i) {
-    qh_fprintf(qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
-  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-  elem= elemp->p;
-  elemp->p= lastp->p;      /* may overwrite itself */
-  lastp->p= NULL;
-  return elem;
-} /* setdelnth */
-
-/*---------------------------------
-
-  qh_setdelnthsorted( set, nth )
-    deletes nth element from sorted set
-
-  returns:
-    returns the element (use type conversion)
-
-  notes:
-    errors if nth invalid
-
-  see also:
-    setnew_delnthsorted
-
-  design:
-    setup points and check nth
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelnthsorted(setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  sizep= SETsizeaddr_(set);
-  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
-    qh_fprintf(qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  newp= (setelemT *)SETelemaddr_(set, nth, void);
-  elem= newp->p;
-  oldp= newp+1;
-  while (((newp++)->p= (oldp++)->p))
-    ; /* copy remaining elements and NULL */
-  if ((sizep->i--)==0)         /*  if was a full set */
-    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-  return elem;
-} /* setdelnthsorted */
-
-
-/*---------------------------------
-
-  qh_setdelsorted( set, oldelem )
-    deletes oldelem from sorted set
-
-  returns:
-    returns oldelem if it was deleted
-
-  notes:
-    set may be NULL
-
-  design:
-    locate oldelem in set
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelsorted(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (!set)
-    return NULL;
-  newp= (setelemT *)SETaddr_(set, void);
-  while(newp->p != oldelem && newp->p)
-    newp++;
-  if (newp->p) {
-    oldp= newp+1;
-    while (((newp++)->p= (oldp++)->p))
-      ; /* copy remaining elements */
-    sizep= SETsizeaddr_(set);
-    if ((sizep->i--)==0)    /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-    return oldelem;
-  }
-  return NULL;
-} /* setdelsorted */
-
-
-/*---------------------------------
-
-  qh_setduplicate( set, elemsize )
-    duplicate a set of elemsize elements
-
-  notes:
-    use setcopy if retaining old elements
-
-  design:
-    create a new set
-    for each elem of the old set
-      create a newelem
-      append newelem to newset
-*/
-setT *qh_setduplicate(setT *set, int elemsize) {
-  void          *elem, **elemp, *newElem;
-  setT          *newSet;
-  int           size;
-
-  if (!(size= qh_setsize(set)))
-    return NULL;
-  newSet= qh_setnew(size);
-  FOREACHelem_(set) {
-    newElem= qh_memalloc(elemsize);
-    memcpy(newElem, elem, (size_t)elemsize);
-    qh_setappend(&newSet, newElem);
-  }
-  return newSet;
-} /* setduplicate */
-
-
-/*---------------------------------
-
-  qh_setendpointer( set )
-    Returns pointer to NULL terminator of a set's elements
-    set can not be NULL
-
-*/
-void **qh_setendpointer(setT *set) {
-
-  setelemT *sizep= SETsizeaddr_(set);
-  int n= sizep->i;
-  return (n ? &set->e[n-1].p : &sizep->p);
-} /* qh_setendpointer */
-
-/*---------------------------------
-
-  qh_setequal( setA, setB )
-    returns 1 if two sorted sets are equal, otherwise returns 0
-
-  notes:
-    either set may be NULL
-
-  design:
-    check size of each set
-    setup pointers
-    compare elements of each set
-*/
-int qh_setequal(setT *setA, setT *setB) {
-  void **elemAp, **elemBp;
-  int sizeA= 0, sizeB= 0;
-
-  if (setA) {
-    SETreturnsize_(setA, sizeA);
-  }
-  if (setB) {
-    SETreturnsize_(setB, sizeB);
-  }
-  if (sizeA != sizeB)
-    return 0;
-  if (!sizeA)
-    return 1;
-  elemAp= SETaddr_(setA, void);
-  elemBp= SETaddr_(setB, void);
-  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
-    return 1;
-  return 0;
-} /* setequal */
-
-
-/*---------------------------------
-
-  qh_setequal_except( setA, skipelemA, setB, skipelemB )
-    returns 1 if sorted setA and setB are equal except for skipelemA & B
-
-  returns:
-    false if either skipelemA or skipelemB are missing
-
-  notes:
-    neither set may be NULL
-
-    if skipelemB is NULL,
-      can skip any one element of setB
-
-  design:
-    setup pointers
-    search for skipelemA, skipelemB, and mismatches
-    check results
-*/
-int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
-  void **elemA, **elemB;
-  int skip=0;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  while (1) {
-    if (*elemA == skipelemA) {
-      skip++;
-      elemA++;
-    }
-    if (skipelemB) {
-      if (*elemB == skipelemB) {
-        skip++;
-        elemB++;
-      }
-    }else if (*elemA != *elemB) {
-      skip++;
-      if (!(skipelemB= *elemB++))
-        return 0;
-    }
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (skip != 2 || *elemB)
-    return 0;
-  return 1;
-} /* setequal_except */
-
-
-/*---------------------------------
-
-  qh_setequal_skip( setA, skipA, setB, skipB )
-    returns 1 if sorted setA and setB are equal except for elements skipA & B
-
-  returns:
-    false if different size
-
-  notes:
-    neither set may be NULL
-
-  design:
-    setup pointers
-    search for mismatches while skipping skipA and skipB
-*/
-int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
-  void **elemA, **elemB, **skipAp, **skipBp;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  skipAp= SETelemaddr_(setA, skipA, void);
-  skipBp= SETelemaddr_(setB, skipB, void);
-  while (1) {
-    if (elemA == skipAp)
-      elemA++;
-    if (elemB == skipBp)
-      elemB++;
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (*elemB)
-    return 0;
-  return 1;
-} /* setequal_skip */
-
-
-/*---------------------------------
-
-  qh_setfree( setp )
-    frees the space occupied by a sorted or unsorted set
-
-  returns:
-    sets setp to NULL
-
-  notes:
-    set may be NULL
-
-  design:
-    free array
-    free set
-*/
-void qh_setfree(setT **setp) {
-  int size;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size <= qhmem.LASTsize) {
-      qh_memfree_(*setp, size, freelistp);
-    }else
-      qh_memfree(*setp, size);
-    *setp= NULL;
-  }
-} /* setfree */
-
-
-/*---------------------------------
-
-  qh_setfree2( setp, elemsize )
-    frees the space occupied by a set and its elements
-
-  notes:
-    set may be NULL
-
-  design:
-    free each element
-    free set
-*/
-void qh_setfree2(setT **setp, int elemsize) {
-  void          *elem, **elemp;
-
-  FOREACHelem_(*setp)
-    qh_memfree(elem, elemsize);
-  qh_setfree(setp);
-} /* setfree2 */
-
-
-
-/*---------------------------------
-
-  qh_setfreelong( setp )
-    frees a set only if it's in long memory
-
-  returns:
-    sets setp to NULL if it is freed
-
-  notes:
-    set may be NULL
-
-  design:
-    if set is large
-      free it
-*/
-void qh_setfreelong(setT **setp) {
-  int size;
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size > qhmem.LASTsize) {
-      qh_memfree(*setp, size);
-      *setp= NULL;
-    }
-  }
-} /* setfreelong */
-
-
-/*---------------------------------
-
-  qh_setin( set, setelem )
-    returns 1 if setelem is in a set, 0 otherwise
-
-  notes:
-    set may be NULL or unsorted
-
-  design:
-    scans set for setelem
-*/
-int qh_setin(setT *set, void *setelem) {
-  void *elem, **elemp;
-
-  FOREACHelem_(set) {
-    if (elem == setelem)
-      return 1;
-  }
-  return 0;
-} /* setin */
-
-
-/*---------------------------------
-
-  qh_setindex( set, atelem )
-    returns the index of atelem in set.
-    returns -1, if not in set or maxsize wrong
-
-  notes:
-    set may be NULL and may contain nulls.
-    NOerrors returned (qh_pointid, QhullPoint::id)
-
-  design:
-    checks maxsize
-    scans set for atelem
-*/
-int qh_setindex(setT *set, void *atelem) {
-  void **elem;
-  int size, i;
-
-  if (!set)
-    return -1;
-  SETreturnsize_(set, size);
-  if (size > set->maxsize)
-    return -1;
-  elem= SETaddr_(set, void);
-  for (i=0; i < size; i++) {
-    if (*elem++ == atelem)
-      return i;
-  }
-  return -1;
-} /* setindex */
-
-
-/*---------------------------------
-
-  qh_setlarger( oldsetp )
-    returns a larger set that contains all elements of *oldsetp
-
-  notes:
-    the set is at least twice as large
-    if temp set, updates qhmem.tempstack
-
-  design:
-    creates a new set
-    copies the old set to the new set
-    updates pointers in tempstack
-    deletes the old set
-*/
-void qh_setlarger(setT **oldsetp) {
-  int size= 1;
-  setT *newset, *set, **setp, *oldset;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (*oldsetp) {
-    oldset= *oldsetp;
-    SETreturnsize_(oldset, size);
-    qhmem.cntlarger++;
-    qhmem.totlarger += size+1;
-    newset= qh_setnew(2 * size);
-    oldp= (setelemT *)SETaddr_(oldset, void);
-    newp= (setelemT *)SETaddr_(newset, void);
-    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
-    sizep= SETsizeaddr_(newset);
-    sizep->i= size+1;
-    FOREACHset_((setT *)qhmem.tempstack) {
-      if (set == oldset)
-        *(setp-1)= newset;
-    }
-    qh_setfree(oldsetp);
-  }else
-    newset= qh_setnew(3);
-  *oldsetp= newset;
-} /* setlarger */
-
-
-/*---------------------------------
-
-  qh_setlast( set )
-    return last element of set or NULL (use type conversion)
-
-  notes:
-    set may be NULL
-
-  design:
-    return last element
-*/
-void *qh_setlast(setT *set) {
-  int size;
-
-  if (set) {
-    size= SETsizeaddr_(set)->i;
-    if (!size)
-      return SETelem_(set, set->maxsize - 1);
-    else if (size > 1)
-      return SETelem_(set, size - 2);
-  }
-  return NULL;
-} /* setlast */
-
-
-/*---------------------------------
-
-  qh_setnew( setsize )
-    creates and allocates space for a set
-
-  notes:
-    setsize means the number of elements (!including the NULL terminator)
-    use qh_settemp/qh_setfreetemp if set is temporary
-
-  design:
-    allocate memory for set
-    roundup memory if small set
-    initialize as empty set
-*/
-setT *qh_setnew(int setsize) {
-  setT *set;
-  int sizereceived; /* used if !qh_NOmem */
-  int size;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (!setsize)
-    setsize++;
-  size= sizeof(setT) + setsize * SETelemsize;
-  if (size>0 && size <= qhmem.LASTsize) {
-    qh_memalloc_(size, freelistp, set, setT);
-#ifndef qh_NOmem
-    sizereceived= qhmem.sizetable[ qhmem.indextable[size]];
-    if (sizereceived > size)
-      setsize += (sizereceived - size)/SETelemsize;
-#endif
-  }else
-    set= (setT*)qh_memalloc(size);
-  set->maxsize= setsize;
-  set->e[setsize].i= 1;
-  set->e[0].p= NULL;
-  return(set);
-} /* setnew */
-
-
-/*---------------------------------
-
-  qh_setnew_delnthsorted( set, size, nth, prepend )
-    creates a sorted set not containing nth element
-    if prepend, the first prepend elements are undefined
-
-  notes:
-    set must be defined
-    checks nth
-    see also: setdelnthsorted
-
-  design:
-    create new set
-    setup pointers and allocate room for prepend'ed entries
-    append head of old set to new set
-    append tail of old set to new set
-*/
-setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend) {
-  setT *newset;
-  void **oldp, **newp;
-  int tailsize= size - nth -1, newsize;
-
-  if (tailsize < 0) {
-    qh_fprintf(qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  newsize= size-1 + prepend;
-  newset= qh_setnew(newsize);
-  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
-  oldp= SETaddr_(set, void);
-  newp= SETaddr_(newset, void) + prepend;
-  switch (nth) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
-    newp += nth;
-    oldp += nth;
-    break;
-  }
-  oldp++;
-  switch (tailsize) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
-    newp += tailsize;
-  }
-  *newp= NULL;
-  return(newset);
-} /* setnew_delnthsorted */
-
-
-/*---------------------------------
-
-  qh_setprint( fp, string, set )
-    print set elements to fp with identifying string
-
-  notes:
-    never errors
-*/
-void qh_setprint(FILE *fp, const char* string, setT *set) {
-  int size, k;
-
-  if (!set)
-    qh_fprintf(fp, 9346, "%s set is null\n", string);
-  else {
-    SETreturnsize_(set, size);
-    qh_fprintf(fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
-             string, set, set->maxsize, size);
-    if (size > set->maxsize)
-      size= set->maxsize+1;
-    for (k=0; k < size; k++)
-      qh_fprintf(fp, 9348, " %p", set->e[k].p);
-    qh_fprintf(fp, 9349, "\n");
-  }
-} /* setprint */
-
-/*---------------------------------
-
-  qh_setreplace( set, oldelem, newelem )
-    replaces oldelem in set with newelem
-
-  notes:
-    errors if oldelem not in the set
-    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
-
-  design:
-    find oldelem
-    replace with newelem
-*/
-void qh_setreplace(setT *set, void *oldelem, void *newelem) {
-  void **elemp;
-
-  elemp= SETaddr_(set, void);
-  while (*elemp != oldelem && *elemp)
-    elemp++;
-  if (*elemp)
-    *elemp= newelem;
-  else {
-    qh_fprintf(qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
-       oldelem);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setreplace */
-
-
-/*---------------------------------
-
-  qh_setsize( set )
-    returns the size of a set
-
-  notes:
-    errors if set's maxsize is incorrect
-    same as SETreturnsize_(set)
-    same code for qh_setsize [qset.c] and QhullSetBase::count
-
-  design:
-    determine actual size of set from maxsize
-*/
-int qh_setsize(setT *set) {
-  int size;
-  setelemT *sizep;
-
-  if (!set)
-    return(0);
-  sizep= SETsizeaddr_(set);
-  if ((size= sizep->i)) {
-    size--;
-    if (size > set->maxsize) {
-      qh_fprintf(qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
-               size, set->maxsize);
-      qh_setprint(qhmem.ferr, "set: ", set);
-      qh_errexit(qhmem_ERRqhull, NULL, NULL);
-    }
-  }else
-    size= set->maxsize;
-  return size;
-} /* setsize */
-
-/*---------------------------------
-
-  qh_settemp( setsize )
-    return a stacked, temporary set of upto setsize elements
-
-  notes:
-    use settempfree or settempfree_all to release from qhmem.tempstack
-    see also qh_setnew
-
-  design:
-    allocate set
-    append to qhmem.tempstack
-
-*/
-setT *qh_settemp(int setsize) {
-  setT *newset;
-
-  newset= qh_setnew(setsize);
-  qh_setappend(&qhmem.tempstack, newset);
-  if (qhmem.IStracing >= 5)
-    qh_fprintf(qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
-       newset, newset->maxsize, qh_setsize(qhmem.tempstack));
-  return newset;
-} /* settemp */
-
-/*---------------------------------
-
-  qh_settempfree( set )
-    free temporary set at top of qhmem.tempstack
-
-  notes:
-    nop if set is NULL
-    errors if set not from previous   qh_settemp
-
-  to locate errors:
-    use 'T2' to find source and then find mis-matching qh_settemp
-
-  design:
-    check top of qhmem.tempstack
-    free it
-*/
-void qh_settempfree(setT **set) {
-  setT *stackedset;
-
-  if (!*set)
-    return;
-  stackedset= qh_settemppop();
-  if (stackedset != *set) {
-    qh_settemppush(stackedset);
-    qh_fprintf(qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
-             *set, qh_setsize(*set), qh_setsize(qhmem.tempstack)+1,
-             stackedset, qh_setsize(stackedset));
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(set);
-} /* settempfree */
-
-/*---------------------------------
-
-  qh_settempfree_all(  )
-    free all temporary sets in qhmem.tempstack
-
-  design:
-    for each set in tempstack
-      free set
-    free qhmem.tempstack
-*/
-void qh_settempfree_all(void) {
-  setT *set, **setp;
-
-  FOREACHset_(qhmem.tempstack)
-    qh_setfree(&set);
-  qh_setfree(&qhmem.tempstack);
-} /* settempfree_all */
-
-/*---------------------------------
-
-  qh_settemppop(  )
-    pop and return temporary set from qhmem.tempstack
-
-  notes:
-    the returned set is permanent
-
-  design:
-    pop and check top of qhmem.tempstack
-*/
-setT *qh_settemppop(void) {
-  setT *stackedset;
-
-  stackedset= (setT*)qh_setdellast(qhmem.tempstack);
-  if (!stackedset) {
-    qh_fprintf(qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qhmem.IStracing >= 5)
-    qh_fprintf(qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
-       qh_setsize(qhmem.tempstack)+1, stackedset, qh_setsize(stackedset));
-  return stackedset;
-} /* settemppop */
-
-/*---------------------------------
-
-  qh_settemppush( set )
-    push temporary set unto qhmem.tempstack (makes it temporary)
-
-  notes:
-    duplicates settemp() for tracing
-
-  design:
-    append set to tempstack
-*/
-void qh_settemppush(setT *set) {
-  if (!set) {
-    qh_fprintf(qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setappend(&qhmem.tempstack, set);
-  if (qhmem.IStracing >= 5)
-    qh_fprintf(qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
-      qh_setsize(qhmem.tempstack), set, qh_setsize(set));
-} /* settemppush */
-
-
-/*---------------------------------
-
-  qh_settruncate( set, size )
-    truncate set to size elements
-
-  notes:
-    set must be defined
-
-  see:
-    SETtruncate_
-
-  design:
-    check size
-    update actual size of set
-*/
-void qh_settruncate(setT *set, int size) {
-
-  if (size < 0 || size > set->maxsize) {
-    qh_fprintf(qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
-  set->e[size].p= NULL;
-} /* settruncate */
-
-/*---------------------------------
-
-  qh_setunique( set, elem )
-    add elem to unsorted set unless it is already in set
-
-  notes:
-    returns 1 if it is appended
-
-  design:
-    if elem not in set
-      append elem to set
-*/
-int qh_setunique(setT **set, void *elem) {
-
-  if (!qh_setin(*set, elem)) {
-    qh_setappend(set, elem);
-    return 1;
-  }
-  return 0;
-} /* setunique */
-
-/*---------------------------------
-
-  qh_setzero( set, index, size )
-    zero elements from index on
-    set actual size of set to size
-
-  notes:
-    set must be defined
-    the set becomes an indexed set (can not use FOREACH...)
-
-  see also:
-    qh_settruncate
-
-  design:
-    check index and size
-    update actual size
-    zero elements starting at e[index]
-*/
-void qh_setzero(setT *set, int idx, int size) {
-  int count;
-
-  if (idx < 0 || idx >= size || size > set->maxsize) {
-    qh_fprintf(qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
-    qh_setprint(qhmem.ferr, "", set);
-    qh_errexit(qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
-  count= size - idx + 1;   /* +1 for NULL terminator */
-  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
-} /* setzero */
-
-
diff --git a/src/qhull/src/libqhull/qset.h b/src/qhull/src/libqhull/qset.h
deleted file mode 100644
index 7e4e7d14f..000000000
--- a/src/qhull/src/libqhull/qset.h
+++ /dev/null
@@ -1,490 +0,0 @@
-/*
      ---------------------------------
-
-   qset.h
-     header file for qset.c that implements set
-
-   see qh-set.htm and qset.c
-
-   only uses mem.c, malloc/free
-
-   for error handling, writes message and calls
-      qh_errexit(qhmem_ERRqhull, NULL, NULL);
-
-   set operations satisfy the following properties:
-    - sets have a max size, the actual size (if different) is stored at the end
-    - every set is NULL terminated
-    - sets may be sorted or unsorted, the caller must distinguish this
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/qset.h#2 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#ifndef qhDEFset
-#define qhDEFset 1
-
-#include 
-
-/*================= -structures- ===============*/
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
-#endif
-
-/* [jan'15] Decided not to use countT.  Most sets are small.  The code uses signed tests */
-
-/*------------------------------------------
-
-setT
-  a set or list of pointers with maximum size and actual size.
-
-variations:
-  unsorted, unique   -- a list of unique pointers with NULL terminator
-                           user guarantees uniqueness
-  sorted             -- a sorted list of unique pointers with NULL terminator
-                           qset.c guarantees uniqueness
-  unsorted           -- a list of pointers terminated with NULL
-  indexed            -- an array of pointers with NULL elements
-
-structure for set of n elements:
-
-        --------------
-        |  maxsize
-        --------------
-        |  e[0] - a pointer, may be NULL for indexed sets
-        --------------
-        |  e[1]
-
-        --------------
-        |  ...
-        --------------
-        |  e[n-1]
-        --------------
-        |  e[n] = NULL
-        --------------
-        |  ...
-        --------------
-        |  e[maxsize] - n+1 or NULL (determines actual size of set)
-        --------------
-
-*/
-
-/*-- setelemT -- internal type to allow both pointers and indices
-*/
-typedef union setelemT setelemT;
-union setelemT {
-  void    *p;
-  int      i;         /* integer used for e[maxSize] */
-};
-
-struct setT {
-  int maxsize;          /* maximum number of elements (except NULL) */
-  setelemT e[1];        /* array of pointers, tail is NULL */
-                        /* last slot (unless NULL) is actual size+1
-                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
-                        /* this may generate a warning since e[] contains
-                           maxsize elements */
-};
-
-/*=========== -constants- =========================*/
-
-/*-------------------------------------
-
-  SETelemsize
-    size of a set element in bytes
-*/
-#define SETelemsize ((int)sizeof(setelemT))
-
-
-/*=========== -macros- =========================*/
-
-/*-------------------------------------
-
-   FOREACHsetelement_(type, set, variable)
-     define FOREACH iterator
-
-   declare:
-     assumes *variable and **variablep are declared
-     no space in "variable)" [DEC Alpha cc compiler]
-
-   each iteration:
-     variable is set element
-     variablep is one beyond variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example:
-     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
-
-   notes:
-     use FOREACHsetelement_i_() if need index or include NULLs
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##p= (type **)&((set)->e[0].p); \
-          (variable= *variable##p++);)
-
-/*------------------------------------------
-
-   FOREACHsetelement_i_(type, set, variable)
-     define indexed FOREACH iterator
-
-   declare:
-     type *variable, variable_n, variable_i;
-
-   each iteration:
-     variable is set element, may be NULL
-     variable_i is index, variable_n is qh_setsize()
-
-   to repeat an element:
-     variable_i--; variable_n-- repeats for deleted element
-
-   at exit:
-     variable==NULL and variable_i==variable_n
-
-   example:
-     #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_i_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##_i= 0, variable= (type *)((set)->e[0].p), \
-                   variable##_n= qh_setsize(set);\
-          variable##_i < variable##_n;\
-          variable= (type *)((set)->e[++variable##_i].p) )
-
-/*----------------------------------------
-
-   FOREACHsetelementreverse_(type, set, variable)-
-     define FOREACH iterator in reverse order
-
-   declare:
-     assumes *variable and **variablep are declared
-     also declare 'int variabletemp'
-
-   each iteration:
-     variable is set element
-
-   to repeat an element:
-     variabletemp++; / *repeat* /
-
-   at exit:
-     variable is NULL
-
-   example:
-     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
-
-   notes:
-     use FOREACHsetelementreverse12_() to reverse first two elements
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-           variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
-           variable; variable= \
-           ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
-
-/*-------------------------------------
-
-   FOREACHsetelementreverse12_(type, set, variable)-
-     define FOREACH iterator with e[1] and e[0] reversed
-
-   declare:
-     assumes *variable and **variablep are declared
-
-   each iteration:
-     variable is set element
-     variablep is one after variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example
-     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse12_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##p= (type **)&((set)->e[1].p); \
-          (variable= *variable##p); \
-          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
-              (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
-
-/*-------------------------------------
-
-   FOREACHelem_( set )-
-     iterate elements in a set
-
-   declare:
-     void *elem, *elemp;
-
-   each iteration:
-     elem is set element
-     elemp is one beyond
-
-   to repeat an element:
-     elemp--; / *repeat* /
-
-   at exit:
-     elem == NULL at end of loop
-
-   example:
-     FOREACHelem_(set) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
-
-/*-------------------------------------
-
-   FOREACHset_( set )-
-     iterate a set of sets
-
-   declare:
-     setT *set, **setp;
-
-   each iteration:
-     set is set element
-     setp is one beyond
-
-   to repeat an element:
-     setp--; / *repeat* /
-
-   at exit:
-     set == NULL at end of loop
-
-   example
-     FOREACHset_(sets) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
-
-/*-------------------------------------------
-
-   SETindex_( set, elem )
-     return index of elem in set
-
-   notes:
-     for use with FOREACH iteration
-     WARN64 -- Maximum set size is 2G
-
-   example:
-     i= SETindex_(ridges, ridge)
-*/
-#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))
-
-/*-----------------------------------------
-
-   SETref_( elem )
-     l.h.s. for modifying the current element in a FOREACH iteration
-
-   example:
-     SETref_(ridge)= anotherridge;
-*/
-#define SETref_(elem) (elem##p[-1])
-
-/*-----------------------------------------
-
-   SETelem_(set, n)
-     return the n'th element of set
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-      use SETelemt_() for type cast
-*/
-#define SETelem_(set, n)           ((set)->e[n].p)
-
-/*-----------------------------------------
-
-   SETelemt_(set, n, type)
-     return the n'th element of set as a type
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-*/
-#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
-
-/*-----------------------------------------
-
-   SETelemaddr_(set, n, type)
-     return address of the n'th element of a set
-
-   notes:
-      assumes that n is valid [0..size] and set is defined
-*/
-#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
-
-/*-----------------------------------------
-
-   SETfirst_(set)
-     return first element of set
-
-*/
-#define SETfirst_(set)             ((set)->e[0].p)
-
-/*-----------------------------------------
-
-   SETfirstt_(set, type)
-     return first element of set as a type
-
-*/
-#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
-
-/*-----------------------------------------
-
-   SETsecond_(set)
-     return second element of set
-
-*/
-#define SETsecond_(set)            ((set)->e[1].p)
-
-/*-----------------------------------------
-
-   SETsecondt_(set, type)
-     return second element of set as a type
-*/
-#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
-
-/*-----------------------------------------
-
-   SETaddr_(set, type)
-       return address of set's elements
-*/
-#define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))
-
-/*-----------------------------------------
-
-   SETreturnsize_(set, size)
-     return size of a set
-
-   notes:
-      set must be defined
-      use qh_setsize(set) unless speed is critical
-*/
-#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
-
-/*-----------------------------------------
-
-   SETempty_(set)
-     return true(1) if set is empty
-
-   notes:
-      set may be NULL
-*/
-#define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))
-
-/*---------------------------------
-
-  SETsizeaddr_(set)
-    return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
-    Its type is setelemT* for strict aliasing
-    All SETelemaddr_ must be cast to setelemT
-
-
-  notes:
-    *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
-*/
-#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))
-
-/*-----------------------------------------
-
-   SETtruncate_(set, size)
-     truncate set to size
-
-   see:
-     qh_settruncate()
-
-*/
-#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
-      set->e[size].p= NULL;}
-
-/*======= prototypes in alphabetical order ============*/
-
-void  qh_setaddsorted(setT **setp, void *elem);
-void  qh_setaddnth(setT **setp, int nth, void *newelem);
-void  qh_setappend(setT **setp, void *elem);
-void  qh_setappend_set(setT **setp, setT *setA);
-void  qh_setappend2ndlast(setT **setp, void *elem);
-void  qh_setcheck(setT *set, const char *tname, unsigned id);
-void  qh_setcompact(setT *set);
-setT *qh_setcopy(setT *set, int extra);
-void *qh_setdel(setT *set, void *elem);
-void *qh_setdellast(setT *set);
-void *qh_setdelnth(setT *set, int nth);
-void *qh_setdelnthsorted(setT *set, int nth);
-void *qh_setdelsorted(setT *set, void *newelem);
-setT *qh_setduplicate( setT *set, int elemsize);
-void **qh_setendpointer(setT *set);
-int   qh_setequal(setT *setA, setT *setB);
-int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
-int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
-void  qh_setfree(setT **set);
-void  qh_setfree2( setT **setp, int elemsize);
-void  qh_setfreelong(setT **set);
-int   qh_setin(setT *set, void *setelem);
-int   qh_setindex(setT *set, void *setelem);
-void  qh_setlarger(setT **setp);
-void *qh_setlast(setT *set);
-setT *qh_setnew(int size);
-setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend);
-void  qh_setprint(FILE *fp, const char* string, setT *set);
-void  qh_setreplace(setT *set, void *oldelem, void *newelem);
-int   qh_setsize(setT *set);
-setT *qh_settemp(int setsize);
-void  qh_settempfree(setT **set);
-void  qh_settempfree_all(void);
-setT *qh_settemppop(void);
-void  qh_settemppush(setT *set);
-void  qh_settruncate(setT *set, int size);
-int   qh_setunique(setT **set, void *elem);
-void  qh_setzero(setT *set, int idx, int size);
-
-
-#endif /* qhDEFset */
diff --git a/src/qhull/src/libqhull/random.c b/src/qhull/src/libqhull/random.c
deleted file mode 100644
index 176d697ae..000000000
--- a/src/qhull/src/libqhull/random.c
+++ /dev/null
@@ -1,245 +0,0 @@
-/*
      ---------------------------------
-
-   random.c and utilities
-     Park & Miller's minimimal standard random number generator
-     argc/argv conversion
-
-     Used by rbox.  Do not use 'qh' 
-*/
-
-#include "libqhull.h"
-#include "random.h"
-
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/*---------------------------------
-
- qh_argv_to_command( argc, argv, command, max_size )
-
-    build command from argc/argv
-    max_size is at least
-
- returns:
-    a space-delimited string of options (just as typed)
-    returns false if max_size is too short
-
- notes:
-    silently removes
-    makes option string easy to input and output
-    matches qh_argv_to_command_size()
-
-    argc may be 0
-*/
-int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
-  int i, remaining;
-  char *s;
-  *command= '\0';  /* max_size > 0 */
-
-  if (argc) {
-    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
-    || (s= strrchr( argv[0], '/')))
-        s++;
-    else
-        s= argv[0];
-    if ((int)strlen(s) < max_size)   /* WARN64 */
-        strcpy(command, s);
-    else
-        goto error_argv;
-    if ((s= strstr(command, ".EXE"))
-    ||  (s= strstr(command, ".exe")))
-        *s= '\0';
-  }
-  for (i=1; i < argc; i++) {
-    s= argv[i];
-    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
-    if (!*s || strchr(s, ' ')) {
-      char *t= command + strlen(command);
-      remaining -= 2;
-      if (remaining < 0) {
-        goto error_argv;
-      }
-      *t++= ' ';
-      *t++= '"';
-      while (*s) {
-        if (*s == '"') {
-          if (--remaining < 0)
-            goto error_argv;
-          *t++= '\\';
-        }
-        *t++= *s++;
-      }
-      *t++= '"';
-      *t= '\0';
-    }else if (remaining < 0) {
-      goto error_argv;
-    }else
-      strcat(command, " ");
-      strcat(command, s);
-  }
-  return 1;
-
-error_argv:
-  return 0;
-} /* argv_to_command */
-
-/*---------------------------------
-
-qh_argv_to_command_size( argc, argv )
-
-    return size to allocate for qh_argv_to_command()
-
-notes:
-    argc may be 0
-    actual size is usually shorter
-*/
-int qh_argv_to_command_size(int argc, char *argv[]) {
-    unsigned int count= 1; /* null-terminator if argc==0 */
-    int i;
-    char *s;
-
-    for (i=0; i0 && strchr(argv[i], ' ')) {
-        count += 2;  /* quote delimiters */
-        for (s=argv[i]; *s; s++) {
-          if (*s == '"') {
-            count++;
-          }
-        }
-      }
-    }
-    return count;
-} /* argv_to_command_size */
-
-/*---------------------------------
-
-  qh_rand()
-  qh_srand( seed )
-    generate pseudo-random number between 1 and 2^31 -2
-
-  notes:
-    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
-
-    From Park & Miller's minimal standard random number generator
-      Communications of the ACM, 31:1192-1201, 1988.
-    Does not use 0 or 2^31 -1
-      this is silently enforced by qh_srand()
-    Can make 'Rn' much faster by moving qh_rand to qh_distplane
-*/
-
-/* Global variables and constants */
-
-int qh_last_random= 1;  /* define as global variable instead of using qh */
-
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773  /* m div a */
-#define qh_rand_r 2836    /* m mod a */
-
-int qh_rand( void) {
-    int lo, hi, test;
-    int seed = qh_last_random;
-
-    hi = seed / qh_rand_q;  /* seed div q */
-    lo = seed % qh_rand_q;  /* seed mod q */
-    test = qh_rand_a * lo - qh_rand_r * hi;
-    if (test > 0)
-        seed= test;
-    else
-        seed= test + qh_rand_m;
-    qh_last_random= seed;
-    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
-    /* seed = qh_RANDOMmax;  for testing */
-    return seed;
-} /* rand */
-
-void qh_srand( int seed) {
-    if (seed < 1)
-        qh_last_random= 1;
-    else if (seed >= qh_rand_m)
-        qh_last_random= qh_rand_m - 1;
-    else
-        qh_last_random= seed;
-} /* qh_srand */
-
-/*---------------------------------
-
-qh_randomfactor( scale, offset )
-  return a random factor r * scale + offset
-
-notes:
-  qh.RANDOMa/b are defined in global.c
-*/
-realT qh_randomfactor(realT scale, realT offset) {
-    realT randr;
-
-    randr= qh_RANDOMint;
-    return randr * scale + offset;
-} /* randomfactor */
-
-/*---------------------------------
-
-qh_randommatrix( buffer, dim, rows )
-  generate a random dim X dim matrix in range [-1,1]
-  assumes buffer is [dim+1, dim]
-
-returns:
-  sets buffer to random numbers
-  sets rows to rows of buffer
-  sets row[dim] as scratch row
-*/
-void qh_randommatrix(realT *buffer, int dim, realT **rows) {
-    int i, k;
-    realT **rowi, *coord, realr;
-
-    coord= buffer;
-    rowi= rows;
-    for (i=0; i < dim; i++) {
-        *(rowi++)= coord;
-        for (k=0; k < dim; k++) {
-            realr= qh_RANDOMint;
-            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
-        }
-    }
-    *rowi= coord;
-} /* randommatrix */
-
-/*---------------------------------
-
-  qh_strtol( s, endp) qh_strtod( s, endp)
-    internal versions of strtol() and strtod()
-    does not skip trailing spaces
-  notes:
-    some implementations of strtol()/strtod() skip trailing spaces
-*/
-double qh_strtod(const char *s, char **endp) {
-  double result;
-
-  result= strtod(s, endp);
-  if (s < (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtod */
-
-int qh_strtol(const char *s, char **endp) {
-  int result;
-
-  result= (int) strtol(s, endp, 10);     /* WARN64 */
-  if (s< (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtol */
diff --git a/src/qhull/src/libqhull/random.h b/src/qhull/src/libqhull/random.h
deleted file mode 100644
index 0c6896b76..000000000
--- a/src/qhull/src/libqhull/random.h
+++ /dev/null
@@ -1,34 +0,0 @@
-/*
      ---------------------------------
-
-  random.h
-    header file for random and utility routines
-
-   see qh-geom.htm and random.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/random.h#2 $$Change: 2026 $
-   $DateTime: 2015/11/07 22:44:39 $$Author: bbarber $
-*/
-
-#ifndef qhDEFrandom
-#define qhDEFrandom 1
-
-#include "libqhull.h"
-
-/*============= prototypes in alphabetical order ======= */
-
-
-int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
-int     qh_argv_to_command_size(int argc, char *argv[]);
-int     qh_rand( void);
-void    qh_srand( int seed);
-realT   qh_randomfactor(realT scale, realT offset);
-void    qh_randommatrix(realT *buffer, int dim, realT **row);
-int     qh_strtol(const char *s, char **endp);
-double  qh_strtod(const char *s, char **endp);
-
-#endif /* qhDEFrandom */
-
-
-
diff --git a/src/qhull/src/libqhull/rboxlib.c b/src/qhull/src/libqhull/rboxlib.c
deleted file mode 100644
index f945133fa..000000000
--- a/src/qhull/src/libqhull/rboxlib.c
+++ /dev/null
@@ -1,870 +0,0 @@
-/*
      ---------------------------------
-
-   rboxlib.c
-     Generate input points
-
-   notes:
-     For documentation, see prompt[] of rbox.c
-     50 points generated for 'rbox D4'
-
-   WARNING:
-     incorrect range if qh_RANDOMmax is defined wrong (user.h)
-*/
-
-#include "libqhull.h"  /* First for user.h */
-#include "random.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ */
-#pragma warning( disable : 4706)  /* assignment within conditional expression. */
-#pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
-#endif
-
-#define MAXdim 200
-#define PI 3.1415926535897932384
-
-/* ------------------------------ prototypes ----------------*/
-int qh_roundi( double a);
-void qh_out1( double a);
-void qh_out2n( double a, double b);
-void qh_out3n( double a, double b, double c);
-void qh_outcoord(int iscdd, double *coord, int dim);
-void qh_outcoincident(int coincidentpoints, double radius, int iscdd, double *coord, int dim);
-
-void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-int     qh_rand( void);
-void    qh_srand( int seed);
-
-
-/* ------------------------------ globals -------------------*/
-
-/* No state is carried between rbox requests */
-typedef struct rboxT rboxT;
-struct rboxT {
-  FILE *fout;
-  FILE *ferr;
-  int isinteger;
-  double out_offset;
-  jmp_buf errexit;        /* exit label for rboxpoints, defined by setjmp(), called by qh_errexit_rbox() */
-  char  jmpXtra[40];      /* extra bytes in case jmp_buf is defined wrong by compiler */
-};
-
-
-int rbox_inuse= 0;
-rboxT rbox;
-
-/*---------------------------------
-
-  qh_rboxpoints( fout, ferr, rbox_command )
-    Generate points to fout according to rbox options
-    Report errors on ferr
-
-  returns:
-    0 (qh_ERRnone) on success
-    1 (qh_ERRinput) on input error
-    4 (qh_ERRmem) on memory error
-    5 (qh_ERRqhull) on internal error
-
-  notes:
-    To avoid using stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
-
-  design:
-    Straight line code (consider defining a struct and functions):
-
-    Parse arguments into variables
-    Determine the number of points
-    Generate the points
-*/
-int qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command) {
-  int i,j,k;
-  int gendim;
-  int coincidentcount=0, coincidenttotal=0, coincidentpoints=0;
-  int cubesize, diamondsize, seed=0, count, apex;
-  int dim=3, numpoints=0, totpoints, addpoints=0;
-  int issphere=0, isaxis=0,  iscdd=0, islens=0, isregular=0, iswidth=0, addcube=0;
-  int isgap=0, isspiral=0, NOcommand=0, adddiamond=0;
-  int israndom=0, istime=0;
-  int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
-  double width=0.0, gap=0.0, radius=0.0, coincidentradius=0.0;
-  double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
-  double *coordp, *simplex= NULL, *simplexp;
-  int nthroot, mult[MAXdim];
-  double norm, factor, randr, rangap, lensangle=0, lensbase=1;
-  double anglediff, angle, x, y, cube=0.0, diamond=0.0;
-  double box= qh_DEFAULTbox; /* scale all numbers before output */
-  double randmax= qh_RANDOMmax;
-  char command[200], seedbuf[200];
-  char *s= command, *t, *first_point= NULL;
-  time_t timedata;
-  int exitcode;
-
-  if (rbox_inuse) {
-    qh_fprintf_rbox(rbox.ferr, 6188, "rbox error: rbox in use by another process.  Please lock calls to rbox.\n");
-    return qh_ERRqhull;
-  }
-  rbox_inuse= True;
-  rbox.ferr= ferr;
-  rbox.fout= fout;
-
-  exitcode= setjmp(rbox.errexit);
-  if (exitcode) {
-    /* same code for error exit and normal return.  qh.NOerrexit is set */
-    if (simplex)
-        qh_free(simplex);
-    rbox_inuse= False;
-    return exitcode;
-  }
-
-  *command= '\0';
-  strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
-
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    if (isdigit(*s)) {
-      numpoints= qh_strtol(s, &s);
-      continue;
-    }
-    /* ============= read flags =============== */
-    switch (*s++) {
-    case 'c':
-      addcube= 1;
-      t= s;
-      while (isspace(*t))
-        t++;
-      if (*t == 'G')
-        cube= qh_strtod(++t, &s);
-      break;
-    case 'd':
-      adddiamond= 1;
-      t= s;
-      while (isspace(*t))
-        t++;
-      if (*t == 'G')
-        diamond= qh_strtod(++t, &s);
-      break;
-    case 'h':
-      iscdd= 1;
-      break;
-    case 'l':
-      isspiral= 1;
-      break;
-    case 'n':
-      NOcommand= 1;
-      break;
-    case 'r':
-      isregular= 1;
-      break;
-    case 's':
-      issphere= 1;
-      break;
-    case 't':
-      istime= 1;
-      if (isdigit(*s)) {
-        seed= qh_strtol(s, &s);
-        israndom= 0;
-      }else
-        israndom= 1;
-      break;
-    case 'x':
-      issimplex= 1;
-      break;
-    case 'y':
-      issimplex2= 1;
-      break;
-    case 'z':
-      rbox.isinteger= 1;
-      break;
-    case 'B':
-      box= qh_strtod(s, &s);
-      isbox= 1;
-      break;
-    case 'C':
-      if (*s)
-        coincidentpoints=  qh_strtol(s, &s);
-      if (*s == ',') {
-        ++s;
-        coincidentradius=  qh_strtod(s, &s);
-      }
-      if (*s == ',') {
-        ++s;
-        coincidenttotal=  qh_strtol(s, &s);
-      }
-      if (*s && !isspace(*s)) {
-        qh_fprintf_rbox(rbox.ferr, 7080, "rbox error: arguments for 'Cn,r,m' are not 'int', 'float', and 'int'.  Remaining string is '%s'\n", s);
-        qh_errexit_rbox(qh_ERRinput);
-      }
-      if (coincidentpoints==0){
-        qh_fprintf_rbox(rbox.ferr, 6268, "rbox error: missing arguments for 'Cn,r,m' where n is the number of coincident points, r is the radius (default 0.0), and m is the number of points\n");
-        qh_errexit_rbox(qh_ERRinput);
-      }
-      if (coincidentpoints<0 || coincidenttotal<0 || coincidentradius<0.0){
-        qh_fprintf_rbox(rbox.ferr, 6269, "rbox error: negative arguments for 'Cn,m,r' where n (%d) is the number of coincident points, m (%d) is the number of points, and r (%.2g) is the radius (default 0.0)\n", coincidentpoints, coincidenttotal, coincidentradius);
-        qh_errexit_rbox(qh_ERRinput);
-      }
-      break;
-    case 'D':
-      dim= qh_strtol(s, &s);
-      if (dim < 1
-      || dim > MAXdim) {
-        qh_fprintf_rbox(rbox.ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
-        qh_errexit_rbox(qh_ERRinput);
-      }
-      break;
-    case 'G':
-      if (isdigit(*s))
-        gap= qh_strtod(s, &s);
-      else
-        gap= 0.5;
-      isgap= 1;
-      break;
-    case 'L':
-      if (isdigit(*s))
-        radius= qh_strtod(s, &s);
-      else
-        radius= 10;
-      islens= 1;
-      break;
-    case 'M':
-      ismesh= 1;
-      if (*s)
-        meshn= qh_strtod(s, &s);
-      if (*s == ',') {
-        ++s;
-        meshm= qh_strtod(s, &s);
-      }else
-        meshm= 0.0;
-      if (*s == ',') {
-        ++s;
-        meshr= qh_strtod(s, &s);
-      }else
-        meshr= sqrt(meshn*meshn + meshm*meshm);
-      if (*s && !isspace(*s)) {
-        qh_fprintf_rbox(rbox.ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
-        meshn= 3.0, meshm=4.0, meshr=5.0;
-      }
-      break;
-    case 'O':
-      rbox.out_offset= qh_strtod(s, &s);
-      break;
-    case 'P':
-      if (!first_point)
-        first_point= s-1;
-      addpoints++;
-      while (*s && !isspace(*s))   /* read points later */
-        s++;
-      break;
-    case 'W':
-      width= qh_strtod(s, &s);
-      iswidth= 1;
-      break;
-    case 'Z':
-      if (isdigit(*s))
-        radius= qh_strtod(s, &s);
-      else
-        radius= 1.0;
-      isaxis= 1;
-      break;
-    default:
-      qh_fprintf_rbox(rbox.ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
-      qh_errexit_rbox(qh_ERRinput);
-    }
-    if (*s && !isspace(*s)) {
-      qh_fprintf_rbox(rbox.ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
-      qh_errexit_rbox(qh_ERRinput);
-    }
-  }
-
-  /* ============= defaults, constants, and sizes =============== */
-  if (rbox.isinteger && !isbox)
-    box= qh_DEFAULTzbox;
-  if (addcube) {
-    cubesize= (int)floor(ldexp(1.0,dim)+0.5);
-    if (cube == 0.0)
-      cube= box;
-  }else
-    cubesize= 0;
-  if (adddiamond) {
-    diamondsize= 2*dim;
-    if (diamond == 0.0)
-      diamond= box;
-  }else
-    diamondsize= 0;
-  if (islens) {
-    if (isaxis) {
-        qh_fprintf_rbox(rbox.ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
-        qh_errexit_rbox(qh_ERRinput);
-    }
-    if (radius <= 1.0) {
-        qh_fprintf_rbox(rbox.ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
-               radius);
-        qh_errexit_rbox(qh_ERRinput);
-    }
-    lensangle= asin(1.0/radius);
-    lensbase= radius * cos(lensangle);
-  }
-
-  if (!numpoints) {
-    if (issimplex2)
-        ; /* ok */
-    else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
-        qh_fprintf_rbox(rbox.ferr, 6192, "rbox error: missing count\n");
-        qh_errexit_rbox(qh_ERRinput);
-    }else if (adddiamond + addcube + addpoints)
-        ; /* ok */
-    else {
-        numpoints= 50;  /* ./rbox D4 is the test case */
-        issphere= 1;
-    }
-  }
-  if ((issimplex + islens + isspiral + ismesh > 1)
-  || (issimplex + issphere + isspiral + ismesh > 1)) {
-    qh_fprintf_rbox(rbox.ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
-    qh_errexit_rbox(qh_ERRinput);
-  }
-  if (coincidentpoints>0 && (numpoints == 0 || coincidenttotal > numpoints)) {
-    qh_fprintf_rbox(rbox.ferr, 6270, "rbox error: 'Cn,r,m' requested n coincident points for each of m points.  Either there is no points or m (%d) is greater than the number of points (%d).\n", coincidenttotal, numpoints);
-    qh_errexit_rbox(qh_ERRinput);
-  }
-  if (coincidenttotal == 0)
-    coincidenttotal= numpoints;
-
-  /* ============= print header with total points =============== */
-  if (issimplex || ismesh)
-    totpoints= numpoints;
-  else if (issimplex2)
-    totpoints= numpoints+dim+1;
-  else if (isregular) {
-    totpoints= numpoints;
-    if (dim == 2) {
-        if (islens)
-          totpoints += numpoints - 2;
-    }else if (dim == 3) {
-        if (islens)
-          totpoints += 2 * numpoints;
-      else if (isgap)
-        totpoints += 1 + numpoints;
-      else
-        totpoints += 2;
-    }
-  }else
-    totpoints= numpoints + isaxis;
-  totpoints += cubesize + diamondsize + addpoints;
-  totpoints += coincidentpoints*coincidenttotal;
-
-  /* ============= seed randoms =============== */
-  if (istime == 0) {
-    for (s=command; *s; s++) {
-      if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
-        i= 'x';
-      else
-        i= *s;
-      seed= 11*seed + i;
-    }
-  }else if (israndom) {
-    seed= (int)time(&timedata);
-    sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
-    strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
-    t= strstr(command, " t ");
-    if (t)
-      strcpy(t+1, t+3); /* remove " t " */
-  } /* else, seed explicitly set to n */
-  qh_RANDOMseed_(seed);
-
-  /* ============= print header =============== */
-
-  if (iscdd)
-      qh_fprintf_rbox(rbox.fout, 9391, "%s\nbegin\n        %d %d %s\n",
-      NOcommand ? "" : command,
-      totpoints, dim+1,
-      rbox.isinteger ? "integer" : "real");
-  else if (NOcommand)
-      qh_fprintf_rbox(rbox.fout, 9392, "%d\n%d\n", dim, totpoints);
-  else
-      /* qh_fprintf_rbox special cases 9393 to append 'command' to the RboxPoints.comment() */
-      qh_fprintf_rbox(rbox.fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
-
-  /* ============= explicit points =============== */
-  if ((s= first_point)) {
-    while (s && *s) { /* 'P' */
-      count= 0;
-      if (iscdd)
-        qh_out1( 1.0);
-      while (*++s) {
-        qh_out1( qh_strtod(s, &s));
-        count++;
-        if (isspace(*s) || !*s)
-          break;
-        if (*s != ',') {
-          qh_fprintf_rbox(rbox.ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
-          qh_errexit_rbox(qh_ERRinput);
-        }
-      }
-      if (count < dim) {
-        for (k=dim-count; k--; )
-          qh_out1( 0.0);
-      }else if (count > dim) {
-        qh_fprintf_rbox(rbox.ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
-                  count, dim, s);
-        qh_errexit_rbox(qh_ERRinput);
-      }
-      qh_fprintf_rbox(rbox.fout, 9394, "\n");
-      while ((s= strchr(s, 'P'))) {
-        if (isspace(s[-1]))
-          break;
-      }
-    }
-  }
-
-  /* ============= simplex distribution =============== */
-  if (issimplex+issimplex2) {
-    if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
-      qh_fprintf_rbox(rbox.ferr, 6196, "rbox error: insufficient memory for simplex\n");
-      qh_errexit_rbox(qh_ERRmem); /* qh_ERRmem */
-    }
-    simplexp= simplex;
-    if (isregular) {
-      for (i=0; i randmax/2)
-          coord[dim-1]= -coord[dim-1];
-      /* ============= project 'Wn' point toward boundary =============== */
-      }else if (iswidth && !issphere) {
-        j= qh_RANDOMint % gendim;
-        if (coord[j] < 0)
-          coord[j]= -1.0 - coord[j] * width;
-        else
-          coord[j]= 1.0 - coord[j] * width;
-      }
-      /* ============= scale point to box =============== */
-      for (k=0; k=0; k--) {
-        if (j & ( 1 << k))
-          qh_out1( cube);
-        else
-          qh_out1( -cube);
-      }
-      qh_fprintf_rbox(rbox.fout, 9400, "\n");
-    }
-  }
-
-  /* ============= write diamond vertices =============== */
-  if (adddiamond) {
-    for (j=0; j=0; k--) {
-        if (j/2 != k)
-          qh_out1( 0.0);
-        else if (j & 0x1)
-          qh_out1( diamond);
-        else
-          qh_out1( -diamond);
-      }
-      qh_fprintf_rbox(rbox.fout, 9401, "\n");
-    }
-  }
-
-  if (iscdd)
-    qh_fprintf_rbox(rbox.fout, 9402, "end\nhull\n");
-
-  /* same code for error exit and normal return */
-  qh_free(simplex);
-  rbox_inuse= False;
-  return qh_ERRnone;
-} /* rboxpoints */
-
-/*------------------------------------------------
-outxxx - output functions for qh_rboxpoints
-*/
-int qh_roundi( double a) {
-  if (a < 0.0) {
-    if (a - 0.5 < INT_MIN) {
-      qh_fprintf_rbox(rbox.ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
-      qh_errexit_rbox(qh_ERRinput);
-    }
-    return (int)(a - 0.5);
-  }else {
-    if (a + 0.5 > INT_MAX) {
-      qh_fprintf_rbox(rbox.ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
-      qh_errexit_rbox(qh_ERRinput);
-    }
-    return (int)(a + 0.5);
-  }
-} /* qh_roundi */
-
-void qh_out1(double a) {
-
-  if (rbox.isinteger)
-    qh_fprintf_rbox(rbox.fout, 9403, "%d ", qh_roundi( a+rbox.out_offset));
-  else
-    qh_fprintf_rbox(rbox.fout, 9404, qh_REAL_1, a+rbox.out_offset);
-} /* qh_out1 */
-
-void qh_out2n( double a, double b) {
-
-  if (rbox.isinteger)
-    qh_fprintf_rbox(rbox.fout, 9405, "%d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset));
-  else
-    qh_fprintf_rbox(rbox.fout, 9406, qh_REAL_2n, a+rbox.out_offset, b+rbox.out_offset);
-} /* qh_out2n */
-
-void qh_out3n( double a, double b, double c) {
-
-  if (rbox.isinteger)
-    qh_fprintf_rbox(rbox.fout, 9407, "%d %d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset), qh_roundi(c+rbox.out_offset));
-  else
-    qh_fprintf_rbox(rbox.fout, 9408, qh_REAL_3n, a+rbox.out_offset, b+rbox.out_offset, c+rbox.out_offset);
-} /* qh_out3n */
-
-void qh_outcoord(int iscdd, double *coord, int dim) {
-    double *p= coord;
-    int k;
-
-    if (iscdd)
-      qh_out1( 1.0);
-    for (k=0; k < dim; k++)
-      qh_out1(*(p++));
-    qh_fprintf_rbox(rbox.fout, 9396, "\n");
-} /* qh_outcoord */
-
-void qh_outcoincident(int coincidentpoints, double radius, int iscdd, double *coord, int dim) {
-  double *p;
-  double randr, delta;
-  int i,k;
-  double randmax= qh_RANDOMmax;
-
-  for (i= 0; i
      ---------------------------------
-
-   stat.c
-   contains all statistics that are collected for qhull
-
-   see qh-stat.htm and stat.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/stat.c#5 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "qhull_a.h"
-
-/*============ global data structure ==========*/
-
-#if qh_QHpointer
-qhstatT *qh_qhstat=NULL;  /* global data structure */
-#else
-qhstatT qh_qhstat;   /* add "={0}" if this causes a compiler error */
-#endif
-
-/*========== functions in alphabetic order ================*/
-
-/*---------------------------------
-
-  qh_allstatA()
-    define statistics in groups of 20
-
-  notes:
-    (otherwise, 'gcc -O2' uses too much memory)
-    uses qhstat.next
-*/
-void qh_allstatA(void) {
-
-   /* zdef_(type,name,doc,average) */
-  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
-  zdef_(zinc, Znewvertex, NULL, -1);
-  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
-  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
-  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
-
-  qhstat precision= qhstat next;  /* call qh_precision for each of these */
-  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
-  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
-  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
-  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
-  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
-  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
-  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
-  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
-  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
-  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
-  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
-}
-void qh_allstatB(void) {
-  zzdef_(zdoc, Zdoc1, "summary information", -1);
-  zdef_(zinc, Zvertices, "number of vertices in output", -1);
-  zdef_(zinc, Znumfacets, "number of facets in output", -1);
-  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
-  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
-  zdef_(zinc, Znumridges, "number of ridges in output", -1);
-  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
-  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
-  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
-  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
-  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
-  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
-  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
-  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
-  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
-  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
-  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
-  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
-  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
-  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
-  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
-  zdef_(zinc, Zangle, NULL, -1);
-  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
-  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wadd, Wareatot, "total area of facets", -1);
-  zdef_(wmax, Wareamax, "  maximum facet area", -1);
-  zdef_(wmin, Wareamin, "  minimum facet area", -1);
-}
-void qh_allstatC(void) {
-  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
-  zzdef_(zinc, Zprocessed, "points processed", -1);
-  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
-  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
-  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
-  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
-  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
-  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
-  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
-  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
-  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
-  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
-  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
-  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
-  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
-  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
-  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
-  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
-  zdef_(zinc, Zpbalance, "  number of trials", -1);
-  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
-  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
-  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
-  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
-  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
-  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
-  zdef_(zinc, Zgoodfacet, "good facets found", -1);
-  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
-  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
-  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
-  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
-}
-void qh_allstatD(void) {
-  zdef_(zinc, Zvisit, "resets of visit_id", -1);
-  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
-  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
-  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
-
-  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
-  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
-  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
-  zdef_(zinc, Zfindbest, "calls to findbest", -1);
-  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
-  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
-  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
-  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
-  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
-  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
-  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
-  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
-  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
-  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
-  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
-  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
-  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
-}
-void qh_allstatE(void) {
-  zdef_(zinc, Zpartinside, "inside points", -1);
-  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
-  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
-  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
-  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
-  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
-  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
-  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
-  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
-  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
-  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
-  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
-  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
-  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
-  zdef_(zinc, Zdistio, "distance tests for output", -1);
-  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
-  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
-  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
-  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
-  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
-}
-void qh_allstatE2(void) {
-  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
-  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
-  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
-  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
-  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
-  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
-  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
-
-  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
-  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
-  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
-  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
-  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
-  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
-  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
-  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
-  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
-}
-void qh_allstatF(void) {
-  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
-  zdef_(zinc, Zpremergetot, "merge iterations", -1);
-  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
-  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
-  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
-  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
-  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
-  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
-  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
-  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
-  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
-  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
-  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
-  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
-  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
-  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
-  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
-  zdef_(zinc, Zmergenew, "new facets merged", -1);
-  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
-  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
-  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
-  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
-  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
-  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
-  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
-}
-void qh_allstatG(void) {
-  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
-  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
-  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
-  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
-  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
-  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
-  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
-  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
-  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
-  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
-  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
-  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
-  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
-  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
-  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
-  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
-}
-void qh_allstatH(void) {
-  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
-  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
-  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
-  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
-  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
-  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
-  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
-  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
-  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
-  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
-  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
-  zdef_(zinc, Zremvertexdel, "  deleted", -1);
-  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
-  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
-  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
-  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
-  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
-  zdef_(zinc, Zvertexridge, NULL, -1);
-  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
-  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
-
-  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
-  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
-  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
-  zdef_(zadd, Zmempoints, "for input points and outside and coplanar sets",-1);
-  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
-} /* allstat */
-
-void qh_allstatI(void) {
-  qhstat vridges= qhstat next;
-  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
-  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
-  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
-  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
-  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
-  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
-  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
-  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
-  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
-  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
-  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
-  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
-  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
-
-  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
-  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
-  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
-  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
-  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
-  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
-  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
-} /* allstat */
-
-/*---------------------------------
-
-  qh_allstatistics()
-    reset printed flag for all statistics
-*/
-void qh_allstatistics(void) {
-  int i;
-
-  for(i=ZEND; i--; )
-    qhstat printed[i]= False;
-} /* allstatistics */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_collectstatistics()
-    collect statistics for qh.facet_list
-
-*/
-void qh_collectstatistics(void) {
-  facetT *facet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  realT dotproduct, dist;
-  int sizneighbors, sizridges, sizvertices, i;
-
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  zval_(Zmempoints)= qh num_points * qh normal_size +
-                             sizeof(qhT) + sizeof(qhstatT);
-  zval_(Zmemfacets)= 0;
-  zval_(Zmemridges)= 0;
-  zval_(Zmemvertices)= 0;
-  zval_(Zangle)= 0;
-  wval_(Wangle)= 0.0;
-  zval_(Znumridges)= 0;
-  zval_(Znumfacets)= 0;
-  zval_(Znumneighbors)= 0;
-  zval_(Znumvertices)= 0;
-  zval_(Znumvneighbors)= 0;
-  zval_(Znummergetot)= 0;
-  zval_(Znummergemax)= 0;
-  zval_(Zvertices)= qh num_vertices - qh_setsize(qh del_vertices);
-  if (qh MERGING || qh APPROXhull || qh JOGGLEmax < REALmax/2)
-    wmax_(Wmaxoutside, qh max_outside);
-  if (qh MERGING)
-    wmin_(Wminvertex, qh min_vertex);
-  FORALLfacets
-    facet->seen= False;
-  if (qh DELAUNAY) {
-    FORALLfacets {
-      if (facet->upperdelaunay != qh UPPERdelaunay)
-        facet->seen= True; /* remove from angle statistics */
-    }
-  }
-  FORALLfacets {
-    if (facet->visible && qh NEWfacets)
-      continue;
-    sizvertices= qh_setsize(facet->vertices);
-    sizneighbors= qh_setsize(facet->neighbors);
-    sizridges= qh_setsize(facet->ridges);
-    zinc_(Znumfacets);
-    zadd_(Znumvertices, sizvertices);
-    zmax_(Zmaxvertices, sizvertices);
-    zadd_(Znumneighbors, sizneighbors);
-    zmax_(Zmaxneighbors, sizneighbors);
-    zadd_(Znummergetot, facet->nummerge);
-    i= facet->nummerge; /* avoid warnings */
-    zmax_(Znummergemax, i);
-    if (!facet->simplicial) {
-      if (sizvertices == qh hull_dim) {
-        zinc_(Znowsimplicial);
-      }else {
-        zinc_(Znonsimplicial);
-      }
-    }
-    if (sizridges) {
-      zadd_(Znumridges, sizridges);
-      zmax_(Zmaxridges, sizridges);
-    }
-    zadd_(Zmemfacets, sizeof(facetT) + qh normal_size + 2*sizeof(setT)
-       + SETelemsize * (sizneighbors + sizvertices));
-    if (facet->ridges) {
-      zadd_(Zmemridges,
-         sizeof(setT) + SETelemsize * sizridges + sizridges *
-         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh hull_dim-1))/2);
-    }
-    if (facet->outsideset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->outsideset));
-    if (facet->coplanarset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->coplanarset));
-    if (facet->seen) /* Delaunay upper envelope */
-      continue;
-    facet->seen= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
-          || neighbor->seen || !facet->normal || !neighbor->normal)
-        continue;
-      dotproduct= qh_getangle(facet->normal, neighbor->normal);
-      zinc_(Zangle);
-      wadd_(Wangle, dotproduct);
-      wmax_(Wanglemax, dotproduct)
-      wmin_(Wanglemin, dotproduct)
-    }
-    if (facet->normal) {
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdiststat);
-        qh_distplane(vertex->point, facet, &dist);
-        wmax_(Wvertexmax, dist);
-        wmin_(Wvertexmin, dist);
-      }
-    }
-  }
-  FORALLvertices {
-    if (vertex->deleted)
-      continue;
-    zadd_(Zmemvertices, sizeof(vertexT));
-    if (vertex->neighbors) {
-      sizneighbors= qh_setsize(vertex->neighbors);
-      zadd_(Znumvneighbors, sizneighbors);
-      zmax_(Zmaxvneighbors, sizneighbors);
-      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
-    }
-  }
-  qh RANDOMdist= qh old_randomdist;
-} /* collectstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_freestatistics(  )
-    free memory used for statistics
-*/
-void qh_freestatistics(void) {
-
-#if qh_QHpointer
-  qh_free(qh_qhstat);
-  qh_qhstat= NULL;
-#endif
-} /* freestatistics */
-
-/*---------------------------------
-
-  qh_initstatistics(  )
-    allocate and initialize statistics
-
-  notes:
-    uses qh_malloc() instead of qh_memalloc() since mem.c not set up yet
-    NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
-    On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
-    Also invoked by QhullQh().
-*/
-void qh_initstatistics(void) {
-  int i;
-  realT realx;
-  int intx;
-
-#if qh_QHpointer
-  if(qh_qhstat){  /* qh_initstatistics may be called from Qhull::resetStatistics() */
-      qh_free(qh_qhstat);
-      qh_qhstat= 0;
-  }
-  if (!(qh_qhstat= (qhstatT *)qh_malloc(sizeof(qhstatT)))) {
-    qh_fprintf_stderr(6183, "qhull error (qh_initstatistics): insufficient memory\n");
-    qh_exit(qh_ERRmem);  /* can not use qh_errexit() */
-  }
-#endif
-
-  qhstat next= 0;
-  qh_allstatA();
-  qh_allstatB();
-  qh_allstatC();
-  qh_allstatD();
-  qh_allstatE();
-  qh_allstatE2();
-  qh_allstatF();
-  qh_allstatG();
-  qh_allstatH();
-  qh_allstatI();
-  if (qhstat next > (int)sizeof(qhstat id)) {
-    qh_fprintf(qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
-      qhstat.next %d should be <= sizeof(qhstat id) %d\n", qhstat next, (int)sizeof(qhstat id));
-#if 0 /* for locating error, Znumridges should be duplicated */
-    for(i=0; i < ZEND; i++) {
-      int j;
-      for(j=i+1; j < ZEND; j++) {
-        if (qhstat id[i] == qhstat id[j]) {
-          qh_fprintf(qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
-              qhstat id[i], i, j);
-        }
-      }
-    }
-#endif
-    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qhstat init[zinc].i= 0;
-  qhstat init[zadd].i= 0;
-  qhstat init[zmin].i= INT_MAX;
-  qhstat init[zmax].i= INT_MIN;
-  qhstat init[wadd].r= 0;
-  qhstat init[wmin].r= REALmax;
-  qhstat init[wmax].r= -REALmax;
-  for(i=0; i < ZEND; i++) {
-    if (qhstat type[i] > ZTYPEreal) {
-      realx= qhstat init[(unsigned char)(qhstat type[i])].r;
-      qhstat stats[i].r= realx;
-    }else if (qhstat type[i] != zdoc) {
-      intx= qhstat init[(unsigned char)(qhstat type[i])].i;
-      qhstat stats[i].i= intx;
-    }
-  }
-} /* initstatistics */
-
-/*---------------------------------
-
-  qh_newstats(  )
-    returns True if statistics for zdoc
-
-  returns:
-    next zdoc
-*/
-boolT qh_newstats(int idx, int *nextindex) {
-  boolT isnew= False;
-  int start, i;
-
-  if (qhstat type[qhstat id[idx]] == zdoc)
-    start= idx+1;
-  else
-    start= idx;
-  for(i= start; i < qhstat next && qhstat type[qhstat id[i]] != zdoc; i++) {
-    if (!qh_nostatistic(qhstat id[i]) && !qhstat printed[qhstat id[i]])
-        isnew= True;
-  }
-  *nextindex= i;
-  return isnew;
-} /* newstats */
-
-/*---------------------------------
-
-  qh_nostatistic( index )
-    true if no statistic to print
-*/
-boolT qh_nostatistic(int i) {
-
-  if ((qhstat type[i] > ZTYPEreal
-       &&qhstat stats[i].r == qhstat init[(unsigned char)(qhstat type[i])].r)
-      || (qhstat type[i] < ZTYPEreal
-          &&qhstat stats[i].i == qhstat init[(unsigned char)(qhstat type[i])].i))
-    return True;
-  return False;
-} /* nostatistic */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_printallstatistics( fp, string )
-    print all statistics with header 'string'
-*/
-void qh_printallstatistics(FILE *fp, const char *string) {
-
-  qh_allstatistics();
-  qh_collectstatistics();
-  qh_printstatistics(fp, string);
-  qh_memstatistics(fp);
-}
-
-
-/*---------------------------------
-
-  qh_printstatistics( fp, string )
-    print statistics to a file with header 'string'
-    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
-
-  see:
-    qh_printallstatistics()
-*/
-void qh_printstatistics(FILE *fp, const char *string) {
-  int i, k;
-  realT ave;
-
-  if (qh num_points != qh num_vertices) {
-    wval_(Wpbalance)= 0;
-    wval_(Wpbalance2)= 0;
-  }else
-    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(fp, 9350, "\n\
-%s\n\
- qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh rbox_command,
-     qh qhull_command, qh_version, qh qhull_options);
-  qh_fprintf(fp, 9351, "\nprecision constants:\n\
- %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
- %6.2g max. roundoff error for distance computation('En')\n\
- %6.2g max. roundoff error for angle computations\n\
- %6.2g min. distance for outside points ('Wn')\n\
- %6.2g min. distance for visible facets ('Vn')\n\
- %6.2g max. distance for coplanar facets ('Un')\n\
- %6.2g max. facet width for recomputing centrum and area\n\
-",
-  qh MAXabs_coord, qh DISTround, qh ANGLEround, qh MINoutside,
-        qh MINvisible, qh MAXcoplanar, qh WIDEfacet);
-  if (qh KEEPnearinside)
-    qh_fprintf(fp, 9352, "\
- %6.2g max. distance for near-inside points\n", qh NEARinside);
-  if (qh premerge_cos < REALmax/2) qh_fprintf(fp, 9353, "\
- %6.2g max. cosine for pre-merge angle\n", qh premerge_cos);
-  if (qh PREmerge) qh_fprintf(fp, 9354, "\
- %6.2g radius of pre-merge centrum\n", qh premerge_centrum);
-  if (qh postmerge_cos < REALmax/2) qh_fprintf(fp, 9355, "\
- %6.2g max. cosine for post-merge angle\n", qh postmerge_cos);
-  if (qh POSTmerge) qh_fprintf(fp, 9356, "\
- %6.2g radius of post-merge centrum\n", qh postmerge_centrum);
-  qh_fprintf(fp, 9357, "\
- %6.2g max. distance for merging two simplicial facets\n\
- %6.2g max. roundoff error for arithmetic operations\n\
- %6.2g min. denominator for divisions\n\
-  zero diagonal for Gauss: ", qh ONEmerge, REALepsilon, qh MINdenom);
-  for(k=0; k < qh hull_dim; k++)
-    qh_fprintf(fp, 9358, "%6.2e ", qh NEARzero[k]);
-  qh_fprintf(fp, 9359, "\n\n");
-  for(i=0 ; i < qhstat next; )
-    qh_printstats(fp, i, &i);
-} /* printstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_printstatlevel( fp, id )
-    print level information for a statistic
-
-  notes:
-    nop if id >= ZEND, printed, or same as initial value
-*/
-void qh_printstatlevel(FILE *fp, int id) {
-#define NULLfield "       "
-
-  if (id >= ZEND || qhstat printed[id])
-    return;
-  if (qhstat type[id] == zdoc) {
-    qh_fprintf(fp, 9360, "%s\n", qhstat doc[id]);
-    return;
-  }
-  if (qh_nostatistic(id) || !qhstat doc[id])
-    return;
-  qhstat printed[id]= True;
-  if (qhstat count[id] != -1
-      && qhstat stats[(unsigned char)(qhstat count[id])].i == 0)
-    qh_fprintf(fp, 9361, " *0 cnt*");
-  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] == -1)
-    qh_fprintf(fp, 9362, "%7.2g", qhstat stats[id].r);
-  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] != -1)
-    qh_fprintf(fp, 9363, "%7.2g", qhstat stats[id].r/ qhstat stats[(unsigned char)(qhstat count[id])].i);
-  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] == -1)
-    qh_fprintf(fp, 9364, "%7d", qhstat stats[id].i);
-  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] != -1)
-    qh_fprintf(fp, 9365, "%7.3g", (realT) qhstat stats[id].i / qhstat stats[(unsigned char)(qhstat count[id])].i);
-  qh_fprintf(fp, 9366, " %s\n", qhstat doc[id]);
-} /* printstatlevel */
-
-
-/*---------------------------------
-
-  qh_printstats( fp, index, nextindex )
-    print statistics for a zdoc group
-
-  returns:
-    next zdoc if non-null
-*/
-void qh_printstats(FILE *fp, int idx, int *nextindex) {
-  int j, nexti;
-
-  if (qh_newstats(idx, &nexti)) {
-    qh_fprintf(fp, 9367, "\n");
-    for (j=idx; j--------------------------------
-
-  qh_stddev( num, tot, tot2, ave )
-    compute the standard deviation and average from statistics
-
-    tot2 is the sum of the squares
-  notes:
-    computes r.m.s.:
-      (x-ave)^2
-      == x^2 - 2x tot/num +   (tot/num)^2
-      == tot2 - 2 tot tot/num + tot tot/num
-      == tot2 - tot ave
-*/
-realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
-  realT stddev;
-
-  *ave= tot/num;
-  stddev= sqrt(tot2/num - *ave * *ave);
-  return stddev;
-} /* stddev */
-
-#endif /* qh_KEEPstatistics */
-
-#if !qh_KEEPstatistics
-void    qh_collectstatistics(void) {}
-void    qh_printallstatistics(FILE *fp, char *string) {};
-void    qh_printstatistics(FILE *fp, char *string) {}
-#endif
-
diff --git a/src/qhull/src/libqhull/stat.h b/src/qhull/src/libqhull/stat.h
deleted file mode 100644
index d86fc0a87..000000000
--- a/src/qhull/src/libqhull/stat.h
+++ /dev/null
@@ -1,543 +0,0 @@
-/*
      ---------------------------------
-
-   stat.h
-     contains all statistics that are collected for qhull
-
-   see qh-stat.htm and stat.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull/stat.h#4 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-
-   recompile qhull if you change this file
-
-   Integer statistics are Z* while real statistics are W*.
-
-   define maydebugx to call a routine at every statistic event
-
-*/
-
-#ifndef qhDEFstat
-#define qhDEFstat 1
-
-#include "libqhull.h"
-
-/*---------------------------------
-
-  qh_KEEPstatistics
-    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
-*/
-#ifndef qh_KEEPstatistics
-#define qh_KEEPstatistics 1
-#endif
-
-/*---------------------------------
-
-  Zxxx for integers, Wxxx for reals
-
-  notes:
-    be sure that all statistics are defined in stat.c
-      otherwise initialization may core dump
-    can pick up all statistics by:
-      grep '[zw].*_[(][ZW]' *.c >z.x
-    remove trailers with query">-
-    remove leaders with  query-replace-regexp [ ^I]+  (
-*/
-#if qh_KEEPstatistics
-enum qh_statistics {     /* alphabetical after Z/W */
-    Zacoplanar,
-    Wacoplanarmax,
-    Wacoplanartot,
-    Zangle,
-    Wangle,
-    Wanglemax,
-    Wanglemin,
-    Zangletests,
-    Wareatot,
-    Wareamax,
-    Wareamin,
-    Zavoidold,
-    Wavoidoldmax,
-    Wavoidoldtot,
-    Zback0,
-    Zbestcentrum,
-    Zbestdist,
-    Zbestlower,
-    Zbestlowerall,
-    Zbestloweralln,
-    Zbestlowerv,
-    Zcentrumtests,
-    Zcheckpart,
-    Zcomputefurthest,
-    Zconcave,
-    Wconcavemax,
-    Wconcavetot,
-    Zconcaveridges,
-    Zconcaveridge,
-    Zcoplanar,
-    Wcoplanarmax,
-    Wcoplanartot,
-    Zcoplanarangle,
-    Zcoplanarcentrum,
-    Zcoplanarhorizon,
-    Zcoplanarinside,
-    Zcoplanarpart,
-    Zcoplanarridges,
-    Wcpu,
-    Zcyclefacetmax,
-    Zcyclefacettot,
-    Zcyclehorizon,
-    Zcyclevertex,
-    Zdegen,
-    Wdegenmax,
-    Wdegentot,
-    Zdegenvertex,
-    Zdelfacetdup,
-    Zdelridge,
-    Zdelvertextot,
-    Zdelvertexmax,
-    Zdetsimplex,
-    Zdistcheck,
-    Zdistconvex,
-    Zdistgood,
-    Zdistio,
-    Zdistplane,
-    Zdiststat,
-    Zdistvertex,
-    Zdistzero,
-    Zdoc1,
-    Zdoc2,
-    Zdoc3,
-    Zdoc4,
-    Zdoc5,
-    Zdoc6,
-    Zdoc7,
-    Zdoc8,
-    Zdoc9,
-    Zdoc10,
-    Zdoc11,
-    Zdoc12,
-    Zdropdegen,
-    Zdropneighbor,
-    Zdupflip,
-    Zduplicate,
-    Wduplicatemax,
-    Wduplicatetot,
-    Zdupridge,
-    Zdupsame,
-    Zflipped,
-    Wflippedmax,
-    Wflippedtot,
-    Zflippedfacets,
-    Zfindbest,
-    Zfindbestmax,
-    Zfindbesttot,
-    Zfindcoplanar,
-    Zfindfail,
-    Zfindhorizon,
-    Zfindhorizonmax,
-    Zfindhorizontot,
-    Zfindjump,
-    Zfindnew,
-    Zfindnewmax,
-    Zfindnewtot,
-    Zfindnewjump,
-    Zfindnewsharp,
-    Zgauss0,
-    Zgoodfacet,
-    Zhashlookup,
-    Zhashridge,
-    Zhashridgetest,
-    Zhashtests,
-    Zinsidevisible,
-    Zintersect,
-    Zintersectfail,
-    Zintersectmax,
-    Zintersectnum,
-    Zintersecttot,
-    Zmaxneighbors,
-    Wmaxout,
-    Wmaxoutside,
-    Zmaxridges,
-    Zmaxvertex,
-    Zmaxvertices,
-    Zmaxvneighbors,
-    Zmemfacets,
-    Zmempoints,
-    Zmemridges,
-    Zmemvertices,
-    Zmergeflipdup,
-    Zmergehorizon,
-    Zmergeinittot,
-    Zmergeinitmax,
-    Zmergeinittot2,
-    Zmergeintohorizon,
-    Zmergenew,
-    Zmergesettot,
-    Zmergesetmax,
-    Zmergesettot2,
-    Zmergesimplex,
-    Zmergevertex,
-    Wmindenom,
-    Wminvertex,
-    Zminnorm,
-    Zmultiridge,
-    Znearlysingular,
-    Zneighbor,
-    Wnewbalance,
-    Wnewbalance2,
-    Znewfacettot,
-    Znewfacetmax,
-    Znewvertex,
-    Wnewvertex,
-    Wnewvertexmax,
-    Znoarea,
-    Znonsimplicial,
-    Znowsimplicial,
-    Znotgood,
-    Znotgoodnew,
-    Znotmax,
-    Znumfacets,
-    Znummergemax,
-    Znummergetot,
-    Znumneighbors,
-    Znumridges,
-    Znumvertices,
-    Znumvisibility,
-    Znumvneighbors,
-    Zonehorizon,
-    Zpartangle,
-    Zpartcoplanar,
-    Zpartflip,
-    Zparthorizon,
-    Zpartinside,
-    Zpartition,
-    Zpartitionall,
-    Zpartnear,
-    Zpbalance,
-    Wpbalance,
-    Wpbalance2,
-    Zpostfacets,
-    Zpremergetot,
-    Zprocessed,
-    Zremvertex,
-    Zremvertexdel,
-    Zrenameall,
-    Zrenamepinch,
-    Zrenameshare,
-    Zretry,
-    Wretrymax,
-    Zridge,
-    Wridge,
-    Wridgemax,
-    Zridge0,
-    Wridge0,
-    Wridge0max,
-    Zridgemid,
-    Wridgemid,
-    Wridgemidmax,
-    Zridgeok,
-    Wridgeok,
-    Wridgeokmax,
-    Zsearchpoints,
-    Zsetplane,
-    Ztestvneighbor,
-    Ztotcheck,
-    Ztothorizon,
-    Ztotmerge,
-    Ztotpartcoplanar,
-    Ztotpartition,
-    Ztotridges,
-    Ztotvertices,
-    Ztotvisible,
-    Ztricoplanar,
-    Ztricoplanarmax,
-    Ztricoplanartot,
-    Ztridegen,
-    Ztrimirror,
-    Ztrinull,
-    Wvertexmax,
-    Wvertexmin,
-    Zvertexridge,
-    Zvertexridgetot,
-    Zvertexridgemax,
-    Zvertices,
-    Zvisfacettot,
-    Zvisfacetmax,
-    Zvisit,
-    Zvisit2max,
-    Zvisvertextot,
-    Zvisvertexmax,
-    Zvvisit,
-    Zvvisit2max,
-    Zwidefacet,
-    Zwidevertices,
-    ZEND};
-
-/*---------------------------------
-
-  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
-
-  notes:
-    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
-*/
-#else
-enum qh_statistics {     /* for zzdef etc. macros */
-  Zback0,
-  Zbestdist,
-  Zcentrumtests,
-  Zcheckpart,
-  Zconcaveridges,
-  Zcoplanarhorizon,
-  Zcoplanarpart,
-  Zcoplanarridges,
-  Zcyclefacettot,
-  Zcyclehorizon,
-  Zdelvertextot,
-  Zdistcheck,
-  Zdistconvex,
-  Zdistzero,
-  Zdoc1,
-  Zdoc2,
-  Zdoc3,
-  Zdoc11,
-  Zflippedfacets,
-  Zgauss0,
-  Zminnorm,
-  Zmultiridge,
-  Znearlysingular,
-  Wnewvertexmax,
-  Znumvisibility,
-  Zpartcoplanar,
-  Zpartition,
-  Zpartitionall,
-  Zprocessed,
-  Zretry,
-  Zridge,
-  Wridge,
-  Wridgemax,
-  Zridge0,
-  Wridge0,
-  Wridge0max,
-  Zridgemid,
-  Wridgemid,
-  Wridgemidmax,
-  Zridgeok,
-  Wridgeok,
-  Wridgeokmax,
-  Zsetplane,
-  Ztotcheck,
-  Ztotmerge,
-    ZEND};
-#endif
-
-/*---------------------------------
-
-  ztype
-    the type of a statistic sets its initial value.
-
-  notes:
-    The type should be the same as the macro for collecting the statistic
-*/
-enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};
-
-/*========== macros and constants =============*/
-
-/*----------------------------------
-
-  MAYdebugx
-    define as maydebug() to be called frequently for error trapping
-*/
-#define MAYdebugx
-
-/*----------------------------------
-
-  zzdef_, zdef_( type, name, doc, -1)
-    define a statistic (assumes 'qhstat.next= 0;')
-
-  zdef_( type, name, doc, count)
-    define an averaged statistic
-    printed as name/count
-*/
-#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
-   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#if qh_KEEPstatistics
-#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
-   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#else
-#define zdef_(type,name,doc,count)
-#endif
-
-/*----------------------------------
-
-  zzinc_( name ), zinc_( name)
-    increment an integer statistic
-*/
-#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#if qh_KEEPstatistics
-#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#else
-#define zinc_(id) {}
-#endif
-
-/*----------------------------------
-
-  zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
-    add value to an integer or real statistic
-*/
-#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#if qh_KEEPstatistics
-#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#else
-#define zadd_(id, val) {}
-#define wadd_(id, val) {}
-#endif
-
-/*----------------------------------
-
-  zzval_( name ), zval_( name ), wwval_( name )
-    set or return value of a statistic
-*/
-#define zzval_(id) ((qhstat stats[id]).i)
-#define wwval_(id) ((qhstat stats[id]).r)
-#if qh_KEEPstatistics
-#define zval_(id) ((qhstat stats[id]).i)
-#define wval_(id) ((qhstat stats[id]).r)
-#else
-#define zval_(id) qhstat tempi
-#define wval_(id) qhstat tempr
-#endif
-
-/*----------------------------------
-
-  zmax_( id, val ), wmax_( id, value )
-    maximize id with val
-*/
-#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#if qh_KEEPstatistics
-#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
-#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#else
-#define zmax_(id, val) {}
-#define wmax_(id, val) {}
-#endif
-
-/*----------------------------------
-
-  zmin_( id, val ), wmin_( id, value )
-    minimize id with val
-*/
-#if qh_KEEPstatistics
-#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
-#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
-#else
-#define zmin_(id, val) {}
-#define wmin_(id, val) {}
-#endif
-
-/*================== stat.h types ==============*/
-
-
-/*----------------------------------
-
-  intrealT
-    union of integer and real, used for statistics
-*/
-typedef union intrealT intrealT;    /* union of int and realT */
-union intrealT {
-    int i;
-    realT r;
-};
-
-/*----------------------------------
-
-  qhstat
-    global data structure for statistics, similar to qh and qhrbox
-
-  notes:
-   access to qh_qhstat is via the "qhstat" macro.  There are two choices
-   qh_QHpointer = 1     access globals via a pointer
-                        enables qh_saveqhull() and qh_restoreqhull()
-                = 0     qh_qhstat is a static data structure
-                        only one instance of qhull() can be active at a time
-                        default value
-   qh_QHpointer is defined in libqhull.h
-   qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
-
-   allocated in stat.c using qh_malloc()
-*/
-#ifndef DEFqhstatT
-#define DEFqhstatT 1
-typedef struct qhstatT qhstatT;
-#endif
-
-#if qh_QHpointer_dllimport
-#define qhstat qh_qhstat->
-__declspec(dllimport) extern qhstatT *qh_qhstat;
-#elif qh_QHpointer
-#define qhstat qh_qhstat->
-extern qhstatT *qh_qhstat;
-#elif qh_dllimport
-#define qhstat qh_qhstat.
-__declspec(dllimport) extern qhstatT qh_qhstat;
-#else
-#define qhstat qh_qhstat.
-extern qhstatT qh_qhstat;
-#endif
-struct qhstatT {
-  intrealT   stats[ZEND];     /* integer and real statistics */
-  unsigned   char id[ZEND+10]; /* id's in print order */
-  const char *doc[ZEND];       /* array of documentation strings */
-  short int  count[ZEND];     /* -1 if none, else index of count to use */
-  char       type[ZEND];      /* type, see ztypes above */
-  char       printed[ZEND];   /* true, if statistic has been printed */
-  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
-
-  int        next;            /* next index for zdef_ */
-  int        precision;       /* index for precision problems */
-  int        vridges;         /* index for Voronoi ridges */
-  int        tempi;
-  realT      tempr;
-};
-
-/*========== function prototypes ===========*/
-
-void    qh_allstatA(void);
-void    qh_allstatB(void);
-void    qh_allstatC(void);
-void    qh_allstatD(void);
-void    qh_allstatE(void);
-void    qh_allstatE2(void);
-void    qh_allstatF(void);
-void    qh_allstatG(void);
-void    qh_allstatH(void);
-void    qh_allstatI(void);
-void    qh_allstatistics(void);
-void    qh_collectstatistics(void);
-void    qh_freestatistics(void);
-void    qh_initstatistics(void);
-boolT   qh_newstats(int idx, int *nextindex);
-boolT   qh_nostatistic(int i);
-void    qh_printallstatistics(FILE *fp, const char *string);
-void    qh_printstatistics(FILE *fp, const char *string);
-void    qh_printstatlevel(FILE *fp, int id);
-void    qh_printstats(FILE *fp, int idx, int *nextindex);
-realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);
-
-#endif   /* qhDEFstat */
diff --git a/src/qhull/src/libqhull/user.c b/src/qhull/src/libqhull/user.c
deleted file mode 100644
index d4726eaa3..000000000
--- a/src/qhull/src/libqhull/user.c
+++ /dev/null
@@ -1,538 +0,0 @@
-/*
      ---------------------------------
-
-   user.c
-   user redefinable functions
-
-   see user2.c for qh_fprintf, qh_malloc, qh_free
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   see libqhull.h for data structures, macros, and user-callable functions.
-
-   see user_eg.c, user_eg2.c, and unix.c for examples.
-
-   see user.h for user-definable constants
-
-      use qh_NOmem in mem.h to turn off memory management
-      use qh_NOmerge in user.h to turn off facet merging
-      set qh_KEEPstatistics in user.h to 0 to turn off statistics
-
-   This is unsupported software.  You're welcome to make changes,
-   but you're on your own if something goes wrong.  Use 'Tc' to
-   check frequently.  Usually qhull will report an error if
-   a data structure becomes inconsistent.  If so, it also reports
-   the last point added to the hull, e.g., 102.  You can then trace
-   the execution of qhull with "T4P102".
-
-   Please report any errors that you fix to qhull@qhull.org
-
-   Qhull-template is a template for calling qhull from within your application
-
-   if you recompile and load this module, then user.o will not be loaded
-   from qhull.a
-
-   you can add additional quick allocation sizes in qh_user_memsizes
-
-   if the other functions here are redefined to not use qh_print...,
-   then io.o will not be loaded from qhull.a.  See user_eg.c for an
-   example.  We recommend keeping io.o for the extra debugging
-   information it supplies.
-*/
-
-#include "qhull_a.h"
-
-#include 
-
-/*---------------------------------
-
-  Qhull-template
-    Template for calling qhull from inside your program
-
-  returns:
-    exit code(see qh_ERR... in libqhull.h)
-    all memory freed
-
-  notes:
-    This can be called any number of times.
-*/
-#if 0
-{
-  int dim;                  /* dimension of points */
-  int numpoints;            /* number of points */
-  coordT *points;           /* array of coordinates for each point */
-  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
-  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
-  FILE *outfile= stdout;    /* output from qh_produce_output()
-                               use NULL to skip qh_produce_output() */
-  FILE *errfile= stderr;    /* error messages from qhull code */
-  int exitcode;             /* 0 if no error from qhull */
-  facetT *facet;            /* set by FORALLfacets */
-  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-#if qh_QHpointer  /* see user.h */
-  if (qh_qh){ /* should be NULL */
-      qh_printf_stderr(6238, "Qhull link error.  The global variable qh_qh was not initialized\n\
-              to NULL by global.c.  Please compile this program with -Dqh_QHpointer_dllimport\n\
-              as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
-      exit(1);
-  }
-#endif
-
-  /* initialize dim, numpoints, points[], ismalloc here */
-  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh facet_list' contains the convex hull */
-    FORALLfacets {
-       /* ... your code ... */
-    }
-  }
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf(errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
-}
-#endif
-
-/*---------------------------------
-
-  qh_new_qhull( dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
-    build new qhull data structure and return exitcode (0 if no errors)
-    if numpoints=0 and points=NULL, initializes qhull
-
-  notes:
-    do not modify points until finished with results.
-      The qhull data structure contains pointers into the points array.
-    do not call qhull functions before qh_new_qhull().
-      The qhull data structure is not initialized until qh_new_qhull().
-
-    Default errfile is stderr, outfile may be null
-    qhull_cmd must start with "qhull "
-    projects points to a new point array for Delaunay triangulations ('d' and 'v')
-    transforms points into a new point array for halfspace intersection ('H')
-
-
-  To allow multiple, concurrent calls to qhull()
-    - set qh_QHpointer in user.h
-    - use qh_save_qhull and qh_restore_qhull to swap the global data structure between calls.
-    - use qh_freeqhull(qh_ALL) to free intermediate convex hulls
-
-  see:
-      Qhull-template at the beginning of this file.
-      An example of using qh_new_qhull is user_eg.c
-*/
-int qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
-                char *qhull_cmd, FILE *outfile, FILE *errfile) {
-  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
-     These parameters are not referenced after a longjmp() and hence not clobbered.
-     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
-  int exitcode, hulldim;
-  boolT new_ismalloc;
-  static boolT firstcall = True;
-  coordT *new_points;
-  if(!errfile){
-      errfile= stderr;
-  }
-  if (firstcall) {
-    qh_meminit(errfile);
-    firstcall= False;
-  } else {
-    qh_memcheck();
-  }
-  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
-    qh_fprintf(errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
-    return qh_ERRinput;
-  }
-  qh_initqhull_start(NULL, outfile, errfile);
-  if(numpoints==0 && points==NULL){
-      trace1((qh ferr, 1047, "qh_new_qhull: initialize Qhull\n"));
-      return 0;
-  }
-  trace1((qh ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
-  exitcode = setjmp(qh errexit);
-  if (!exitcode)
-  {
-    qh NOerrexit = False;
-    qh_initflags(qhull_cmd);
-    if (qh DELAUNAY)
-      qh PROJECTdelaunay= True;
-    if (qh HALFspace) {
-      /* points is an array of halfspaces,
-         the last coordinate of each halfspace is its offset */
-      hulldim= dim-1;
-      qh_setfeasible(hulldim);
-      new_points= qh_sethalfspace_all(dim, numpoints, points, qh feasible_point);
-      new_ismalloc= True;
-      if (ismalloc)
-        qh_free(points);
-    }else {
-      hulldim= dim;
-      new_points= points;
-      new_ismalloc= ismalloc;
-    }
-    qh_init_B(new_points, numpoints, hulldim, new_ismalloc);
-    qh_qhull();
-    qh_check_output();
-    if (outfile) {
-      qh_produce_output();
-    }else {
-      qh_prepare_output();
-    }
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-  }
-  qh NOerrexit = True;
-  return exitcode;
-} /* new_qhull */
-
-/*---------------------------------
-
-  qh_errexit( exitcode, facet, ridge )
-    report and exit from an error
-    report facet and ridge if non-NULL
-    reports useful information such as last point processed
-    set qh.FORCEoutput to print neighborhood of facet
-
-  see:
-    qh_errexit2() in libqhull.c for printing 2 facets
-
-  design:
-    check for error within error processing
-    compute qh.hulltime
-    print facet and ridge (if any)
-    report commandString, options, qh.furthest_id
-    print summary and statistics (including precision statistics)
-    if qh_ERRsingular
-      print help text for singular data set
-    exit program via long jump (if defined) or exit()
-*/
-void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
-
-  if (qh ERREXITcalled) {
-    qh_fprintf(qh ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh ERREXITcalled= True;
-  if (!qh QHULLfinished)
-    qh hulltime= qh_CPUclock - qh hulltime;
-  qh_errprint("ERRONEOUS", facet, NULL, ridge, NULL);
-  qh_fprintf(qh ferr, 8127, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
-  qh_fprintf(qh ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
-  if (qh furthest_id >= 0) {
-    qh_fprintf(qh ferr, 8129, "Last point added to hull was p%d.", qh furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
-    if (qh QHULLfinished)
-      qh_fprintf(qh ferr, 8131, "\nQhull has finished constructing the hull.");
-    else if (qh POSTmerging)
-      qh_fprintf(qh ferr, 8132, "\nQhull has started post-merging.");
-    qh_fprintf(qh ferr, 8133, "\n");
-  }
-  if (qh FORCEoutput && (qh QHULLfinished || (!facet && !ridge)))
-    qh_produce_output();
-  else if (exitcode != qh_ERRinput) {
-    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh hull_dim+1) {
-      qh_fprintf(qh ferr, 8134, "\nAt error exit:\n");
-      qh_printsummary(qh ferr);
-      if (qh PRINTstatistics) {
-        qh_collectstatistics();
-        qh_printstatistics(qh ferr, "at error exit");
-        qh_memstatistics(qh ferr);
-      }
-    }
-    if (qh PRINTprecision)
-      qh_printstats(qh ferr, qhstat precision, NULL);
-  }
-  if (!exitcode)
-    exitcode= qh_ERRqhull;
-  else if (exitcode == qh_ERRsingular)
-    qh_printhelp_singular(qh ferr);
-  else if (exitcode == qh_ERRprec && !qh PREmerge)
-    qh_printhelp_degenerate(qh ferr);
-  if (qh NOerrexit) {
-    qh_fprintf(qh ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh ERREXITcalled= False;
-  qh NOerrexit= True;
-  qh ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
-  longjmp(qh errexit, exitcode);
-} /* errexit */
-
-
-/*---------------------------------
-
-  qh_errprint( fp, string, atfacet, otherfacet, atridge, atvertex )
-    prints out the information of facets and ridges to fp
-    also prints neighbors and geomview output
-
-  notes:
-    except for string, any parameter may be NULL
-*/
-void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-  int i;
-
-  if (atfacet) {
-    qh_fprintf(qh ferr, 8135, "%s FACET:\n", string);
-    qh_printfacet(qh ferr, atfacet);
-  }
-  if (otherfacet) {
-    qh_fprintf(qh ferr, 8136, "%s OTHER FACET:\n", string);
-    qh_printfacet(qh ferr, otherfacet);
-  }
-  if (atridge) {
-    qh_fprintf(qh ferr, 8137, "%s RIDGE:\n", string);
-    qh_printridge(qh ferr, atridge);
-    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
-      qh_printfacet(qh ferr, atridge->top);
-    if (atridge->bottom
-        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
-      qh_printfacet(qh ferr, atridge->bottom);
-    if (!atfacet)
-      atfacet= atridge->top;
-    if (!otherfacet)
-      otherfacet= otherfacet_(atridge, atfacet);
-  }
-  if (atvertex) {
-    qh_fprintf(qh ferr, 8138, "%s VERTEX:\n", string);
-    qh_printvertex(qh ferr, atvertex);
-  }
-  if (qh fout && qh FORCEoutput && atfacet && !qh QHULLfinished && !qh IStracing) {
-    qh_fprintf(qh ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
-    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
-      qh_printneighborhood(qh fout, qh PRINTout[i], atfacet, otherfacet,
-                            !qh_ALL);
-  }
-} /* errprint */
-
-
-/*---------------------------------
-
-  qh_printfacetlist( fp, facetlist, facets, printall )
-    print all fields for a facet list and/or set of facets to fp
-    if !printall,
-      only prints good facets
-
-  notes:
-    also prints all vertices
-*/
-void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
-  facetT *facet, **facetp;
-
-  qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
-  FORALLfacet_(facetlist)
-    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
-  FOREACHfacet_(facets)
-    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
-  qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
-} /* printfacetlist */
-
-
-/*---------------------------------
-
-  qh_printhelp_degenerate( fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(FILE *fp) {
-
-  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
-    qh_fprintf(fp, 9368, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
-  else if (!qh_QUICKhelp) {
-    qh_fprintf(fp, 9369, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    qh_fprintf(fp, 9370, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
-      qh_fprintf(fp, 9371, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh DELAUNAY && !qh ATinfinity)
-      qh_fprintf(fp, 9372, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    qh_fprintf(fp, 9373, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh DISTround);
-    qh_fprintf(fp, 9374, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/*---------------------------------
-
-  qh_printhelp_narrowhull( minangle )
-    Warn about a narrow hull
-
-  notes:
-    Alternatively, reduce qh_WARNnarrow in user.h
-
-*/
-void qh_printhelp_narrowhull(FILE *fp, realT minangle) {
-
-    qh_fprintf(fp, 9375, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
-produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
-last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
-See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-} /* printhelp_narrowhull */
-
-/*---------------------------------
-
-  qh_printhelp_singular( fp )
-    prints descriptive message for singular input
-*/
-void qh_printhelp_singular(FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  qh_fprintf(fp, 9376, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh hull_dim);
-  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    qh_fprintf(fp, 9377, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh DISTround);
-  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, qh_IDunknown);
-  qh_fprintf(fp, 9378, "\n");
-  FORALLfacets {
-    qh_fprintf(fp, 9379, "facet");
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh interior_point, facet, &dist);
-    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh HALFspace)
-      qh_fprintf(fp, 9382, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    qh_fprintf(fp, 9383,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh hull_dim >= qh_INITIALmax)
-      qh_fprintf(fp, 9384, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    qh_fprintf(fp, 9387, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh DISTround);
-#if REALfloat
-    qh_fprintf(fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
-#endif
-    qh_fprintf(fp, 9389, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-  }
-} /* printhelp_singular */
-
-/*---------------------------------
-
-  qh_user_memsizes()
-    allocate up to 10 additional, quick allocation sizes
-
-  notes:
-    increase maximum number of allocations in qh_initqhull_mem()
-*/
-void qh_user_memsizes(void) {
-
-  /* qh_memsize(size); */
-} /* user_memsizes */
-
-
diff --git a/src/qhull/src/libqhull/user.h b/src/qhull/src/libqhull/user.h
deleted file mode 100644
index 523aa7b4e..000000000
--- a/src/qhull/src/libqhull/user.h
+++ /dev/null
@@ -1,909 +0,0 @@
-/*
      ---------------------------------
-
-   user.h
-   user redefinable constants
-
-   for each source file, user.h is included first
-   see qh-user.htm.  see COPYING for copyright information.
-
-   See user.c for sample code.
-
-   before reading any code, review libqhull.h for data structure definitions and
-   the "qh" macro.
-
-Sections:
-   ============= qhull library constants ======================
-   ============= data types and configuration macros ==========
-   ============= performance related constants ================
-   ============= memory constants =============================
-   ============= joggle constants =============================
-   ============= conditional compilation ======================
-   ============= -merge constants- ============================
-
-Code flags --
-  NOerrors -- the code does not call qh_errexit()
-  WARN64 -- the code may be incompatible with 64-bit pointers
-
-*/
-
-#include 
-
-#ifndef qhDEFuser
-#define qhDEFuser 1
-
-/* Derived from Qt's corelib/global/qglobal.h */
-#if !defined(SAG_COM) && !defined(__CYGWIN__) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
-#   define QHULL_OS_WIN
-#elif defined(__MWERKS__) && defined(__INTEL__) /* Metrowerks discontinued before the release of Intel Macs */
-#   define QHULL_OS_WIN
-#endif
-/*============================================================*/
-/*============= qhull library constants ======================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  FILENAMElen -- max length for TI and TO filenames
-
-*/
-
-#define qh_FILENAMElen 500
-
-/*----------------------------------
-
-  msgcode -- Unique message codes for qh_fprintf
-
-  If add new messages, assign these values and increment in user.h and user_r.h
-  See QhullError.h for 10000 errors.
-
-  def counters =  [27, 1048, 2059, 3026, 4068, 5003,
-     6273, 7081, 8147, 9411, 10000, 11029]
-
-  See: qh_ERR* [libqhull.h]
-*/
-
-#define MSG_TRACE0 0
-#define MSG_TRACE1 1000
-#define MSG_TRACE2 2000
-#define MSG_TRACE3 3000
-#define MSG_TRACE4 4000
-#define MSG_TRACE5 5000
-#define MSG_ERROR  6000   /* errors written to qh.ferr */
-#define MSG_WARNING 7000
-#define MSG_STDERR  8000  /* log messages Written to qh.ferr */
-#define MSG_OUTPUT  9000
-#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp (QHULLlastError is in QhullError.h) */
-#define MSG_FIXUP  11000  /* FIXUP QH11... */
-#define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
-
-
-/*----------------------------------
-
-  qh_OPTIONline -- max length of an option line 'FO'
-*/
-#define qh_OPTIONline 80
-
-/*============================================================*/
-/*============= data types and configuration macros ==========*/
-/*============================================================*/
-
-/*----------------------------------
-
-  realT
-    set the size of floating point numbers
-
-  qh_REALdigits
-    maximimum number of significant digits
-
-  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
-    format strings for printf
-
-  qh_REALmax, qh_REALmin
-    maximum and minimum (near zero) values
-
-  qh_REALepsilon
-    machine roundoff.  Maximum roundoff error for addition and multiplication.
-
-  notes:
-   Select whether to store floating point numbers in single precision (float)
-   or double precision (double).
-
-   Use 'float' to save about 8% in time and 25% in space.  This is particularly
-   helpful if high-d where convex hulls are space limited.  Using 'float' also
-   reduces the printed size of Qhull's output since numbers have 8 digits of
-   precision.
-
-   Use 'double' when greater arithmetic precision is needed.  This is needed
-   for Delaunay triangulations and Voronoi diagrams when you are not merging
-   facets.
-
-   If 'double' gives insufficient precision, your data probably includes
-   degeneracies.  If so you should use facet merging (done by default)
-   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
-   You may also use option 'Po' to force output despite precision errors.
-
-   You may use 'long double', but many format statements need to be changed
-   and you may need a 'long double' square root routine.  S. Grundmann
-   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
-   much slower with little gain in precision.
-
-   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
-      returns False.  Use (a > REALmax/2) instead of (a == REALmax).
-
-   REALfloat =   1      all numbers are 'float' type
-             =   0      all numbers are 'double' type
-*/
-#define REALfloat 0
-
-#if (REALfloat == 1)
-#define realT float
-#define REALmax FLT_MAX
-#define REALmin FLT_MIN
-#define REALepsilon FLT_EPSILON
-#define qh_REALdigits 8   /* maximum number of significant digits */
-#define qh_REAL_1 "%6.8g "
-#define qh_REAL_2n "%6.8g %6.8g\n"
-#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
-
-#elif (REALfloat == 0)
-#define realT double
-#define REALmax DBL_MAX
-#define REALmin DBL_MIN
-#define REALepsilon DBL_EPSILON
-#define qh_REALdigits 16    /* maximum number of significant digits */
-#define qh_REAL_1 "%6.16g "
-#define qh_REAL_2n "%6.16g %6.16g\n"
-#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
-
-#else
-#error unknown float option
-#endif
-
-/*----------------------------------
-
-  qh_CPUclock
-    define the clock() function for reporting the total time spent by Qhull
-    returns CPU ticks as a 'long int'
-    qh_CPUclock is only used for reporting the total time spent by Qhull
-
-  qh_SECticks
-    the number of clock ticks per second
-
-  notes:
-    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
-    to define a custom clock, set qh_CLOCKtype to 0
-
-    if your system does not use clock() to return CPU ticks, replace
-    qh_CPUclock with the corresponding function.  It is converted
-    to 'unsigned long' to prevent wrap-around during long runs.  By default,
-     defines clock_t as 'long'
-
-   Set qh_CLOCKtype to
-
-     1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
-                Note:  may fail if more than 1 hour elapsed time
-
-     2          use qh_clock() with POSIX times() (see global.c)
-*/
-#define qh_CLOCKtype 1  /* change to the desired number */
-
-#if (qh_CLOCKtype == 1)
-
-#if defined(CLOCKS_PER_SECOND)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SECOND
-
-#elif defined(CLOCKS_PER_SEC)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SEC
-
-#elif defined(CLK_TCK)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLK_TCK
-
-#else
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks 1E6
-#endif
-
-#elif (qh_CLOCKtype == 2)
-#define qh_CPUclock    qh_clock()  /* return CPU clock */
-#define qh_SECticks 100
-
-#else /* qh_CLOCKtype == ? */
-#error unknown clock option
-#endif
-
-/*----------------------------------
-
-  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
-    define random number generator
-
-    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
-    qh_RANDOMseed sets the random number seed for qh_RANDOMint
-
-  Set qh_RANDOMtype (default 5) to:
-    1       for random() with 31 bits (UCB)
-    2       for rand() with RAND_MAX or 15 bits (system 5)
-    3       for rand() with 31 bits (Sun)
-    4       for lrand48() with 31 bits (Solaris)
-    5       for qh_rand() with 31 bits (included with Qhull)
-
-  notes:
-    Random numbers are used by rbox to generate point sets.  Random
-    numbers are used by Qhull to rotate the input ('QRn' option),
-    simulate a randomized algorithm ('Qr' option), and to simulate
-    roundoff errors ('Rn' option).
-
-    Random number generators differ between systems.  Most systems provide
-    rand() but the period varies.  The period of rand() is not critical
-    since qhull does not normally use random numbers.
-
-    The default generator is Park & Miller's minimal standard random
-    number generator [CACM 31:1195 '88].  It is included with Qhull.
-
-    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
-    output will likely be invisible.
-*/
-#define qh_RANDOMtype 5   /* *** change to the desired number *** */
-
-#if (qh_RANDOMtype == 1)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
-#define qh_RANDOMint random()
-#define qh_RANDOMseed_(seed) srandom(seed);
-
-#elif (qh_RANDOMtype == 2)
-#ifdef RAND_MAX
-#define qh_RANDOMmax ((realT)RAND_MAX)
-#else
-#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
-#endif
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 3)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 4)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
-#define qh_RANDOMint lrand48()
-#define qh_RANDOMseed_(seed) srand48(seed);
-
-#elif (qh_RANDOMtype == 5)
-#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
-#define qh_RANDOMint qh_rand()
-#define qh_RANDOMseed_(seed) qh_srand(seed);
-/* unlike rand(), never returns 0 */
-
-#else
-#error: unknown random option
-#endif
-
-/*----------------------------------
-
-  qh_ORIENTclock
-    0 for inward pointing normals by Geomview convention
-*/
-#define qh_ORIENTclock 0
-
-
-/*============================================================*/
-/*============= joggle constants =============================*/
-/*============================================================*/
-
-/*----------------------------------
-
-qh_JOGGLEdefault
-default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
-
-notes:
-rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
-rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
-rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
-rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
-rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
-rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
-rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
-rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
-rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
-the later have about 20 points per facet, each of which may interfere
-
-pick a value large enough to avoid retries on most inputs
-*/
-#define qh_JOGGLEdefault 30000.0
-
-/*----------------------------------
-
-qh_JOGGLEincrease
-factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
-*/
-#define qh_JOGGLEincrease 10.0
-
-/*----------------------------------
-
-qh_JOGGLEretry
-if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
-
-notes:
-try twice at the original value in case of bad luck the first time
-*/
-#define qh_JOGGLEretry 2
-
-/*----------------------------------
-
-qh_JOGGLEagain
-every following qh_JOGGLEagain, increase qh.JOGGLEmax
-
-notes:
-1 is OK since it's already failed qh_JOGGLEretry times
-*/
-#define qh_JOGGLEagain 1
-
-/*----------------------------------
-
-qh_JOGGLEmaxincrease
-maximum qh.JOGGLEmax due to qh_JOGGLEincrease
-relative to qh.MAXwidth
-
-notes:
-qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
-*/
-#define qh_JOGGLEmaxincrease 1e-2
-
-/*----------------------------------
-
-qh_JOGGLEmaxretry
-stop after qh_JOGGLEmaxretry attempts
-*/
-#define qh_JOGGLEmaxretry 100
-
-/*============================================================*/
-/*============= performance related constants ================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  qh_HASHfactor
-    total hash slots / used hash slots.  Must be at least 1.1.
-
-  notes:
-    =2 for at worst 50% occupancy for qh.hash_table and normally 25% occupancy
-*/
-#define qh_HASHfactor 2
-
-/*----------------------------------
-
-  qh_VERIFYdirect
-    with 'Tv' verify all points against all facets if op count is smaller
-
-  notes:
-    if greater, calls qh_check_bestdist() instead
-*/
-#define qh_VERIFYdirect 1000000
-
-/*----------------------------------
-
-  qh_INITIALsearch
-     if qh_INITIALmax, search points up to this dimension
-*/
-#define qh_INITIALsearch 6
-
-/*----------------------------------
-
-  qh_INITIALmax
-    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
-
-  notes:
-    from points with non-zero determinants
-    use option 'Qs' to override (much slower)
-*/
-#define qh_INITIALmax 8
-
-/*============================================================*/
-/*============= memory constants =============================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  qh_MEMalign
-    memory alignment for qh_meminitbuffers() in global.c
-
-  notes:
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.
-
-    If using gcc, best alignment is  [fmax_() is defined in geom_r.h]
-              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
-*/
-#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
-
-/*----------------------------------
-
-  qh_MEMbufsize
-    size of additional memory buffers
-
-  notes:
-    used for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
-
-/*----------------------------------
-
-  qh_MEMinitbuf
-    size of initial memory buffer
-
-  notes:
-    use for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
-
-/*----------------------------------
-
-  qh_INFINITE
-    on output, indicates Voronoi center at infinity
-*/
-#define qh_INFINITE  -10.101
-
-/*----------------------------------
-
-  qh_DEFAULTbox
-    default box size (Geomview expects 0.5)
-
-  qh_DEFAULTbox
-    default box size for integer coorindate (rbox only)
-*/
-#define qh_DEFAULTbox 0.5
-#define qh_DEFAULTzbox 1e6
-
-/*============================================================*/
-/*============= conditional compilation ======================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  __cplusplus
-    defined by C++ compilers
-
-  __MSC_VER
-    defined by Microsoft Visual C++
-
-  __MWERKS__ && __INTEL__
-    defined by Metrowerks when compiling for Windows (not Intel-based Macintosh)
-
-  __MWERKS__ && __POWERPC__
-    defined by Metrowerks when compiling for PowerPC-based Macintosh
-  __STDC__
-    defined for strict ANSI C
-*/
-
-/*----------------------------------
-
-  qh_COMPUTEfurthest
-    compute furthest distance to an outside point instead of storing it with the facet
-    =1 to compute furthest
-
-  notes:
-    computing furthest saves memory but costs time
-      about 40% more distance tests for partitioning
-      removes facet->furthestdist
-*/
-#define qh_COMPUTEfurthest 0
-
-/*----------------------------------
-
-  qh_KEEPstatistics
-    =0 removes most of statistic gathering and reporting
-
-  notes:
-    if 0, code size is reduced by about 4%.
-*/
-#define qh_KEEPstatistics 1
-
-/*----------------------------------
-
-  qh_MAXoutside
-    record outer plane for each facet
-    =1 to record facet->maxoutside
-
-  notes:
-    this takes a realT per facet and slightly slows down qhull
-    it produces better outer planes for geomview output
-*/
-#define qh_MAXoutside 1
-
-/*----------------------------------
-
-  qh_NOmerge
-    disables facet merging if defined
-
-  notes:
-    This saves about 10% space.
-
-    Unless 'Q0'
-      qh_NOmerge sets 'QJ' to avoid precision errors
-
-    #define qh_NOmerge
-
-  see:
-    qh_NOmem in mem.c
-
-    see user.c/user_eg.c for removing io.o
-*/
-
-/*----------------------------------
-
-  qh_NOtrace
-    no tracing if defined
-
-  notes:
-    This saves about 5% space.
-
-    #define qh_NOtrace
-*/
-
-/*----------------------------------
-
-  qh_QHpointer
-    access global data with pointer or static structure
-
-  qh_QHpointer  = 1     access globals via a pointer to allocated memory
-                        enables qh_saveqhull() and qh_restoreqhull()
-                        [2010, gcc] costs about 4% in time and 4% in space
-                        [2003, msvc] costs about 8% in time and 2% in space
-
-                = 0     qh_qh and qh_qhstat are static data structures
-                        only one instance of qhull() can be active at a time
-                        default value
-
-  qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
-  It is required for msvc-2005.  It is not needed for gcc.
-
-  notes:
-    [jan'16] qh_QHpointer is deprecated for Qhull.  Use libqhull_r instead.
-    all global variables for qhull are in qh, qhmem, and qhstat
-    qh is defined in libqhull.h
-    qhmem is defined in mem.h
-    qhstat is defined in stat.h
-
-*/
-#ifdef qh_QHpointer
-#if qh_dllimport
-#error QH6207 Qhull error: Use qh_QHpointer_dllimport instead of qh_dllimport with qh_QHpointer
-#endif
-#else
-#define qh_QHpointer 0
-#if qh_QHpointer_dllimport
-#error QH6234 Qhull error: Use qh_dllimport instead of qh_QHpointer_dllimport when qh_QHpointer is not defined
-#endif
-#endif
-#if 0  /* sample code */
-    qhT *oldqhA, *oldqhB;
-
-    exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-    /* use results from first call to qh_new_qhull */
-    oldqhA= qh_save_qhull();
-    exitcode= qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
-                      flags, outfile, errfile);
-    /* use results from second call to qh_new_qhull */
-    oldqhB= qh_save_qhull();
-    qh_restore_qhull(&oldqhA);
-    /* use results from first call to qh_new_qhull */
-    qh_freeqhull(qh_ALL);  /* frees all memory used by first call */
-    qh_restore_qhull(&oldqhB);
-    /* use results from second call to qh_new_qhull */
-    qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
-    qh_memfreeshort(&curlong, &totlong);  /* frees short memory and memory allocator */
-#endif
-
-/*----------------------------------
-
-  qh_QUICKhelp
-    =1 to use abbreviated help messages, e.g., for degenerate inputs
-*/
-#define qh_QUICKhelp    0
-
-/*============================================================*/
-/*============= -merge constants- ============================*/
-/*============================================================*/
-/*
-   These constants effect facet merging.  You probably will not need
-   to modify them.  They effect the performance of facet merging.
-*/
-
-/*----------------------------------
-
-  qh_DIMmergeVertex
-    max dimension for vertex merging (it is not effective in high-d)
-*/
-#define qh_DIMmergeVertex 6
-
-/*----------------------------------
-
-  qh_DIMreduceBuild
-     max dimension for vertex reduction during build (slow in high-d)
-*/
-#define qh_DIMreduceBuild 5
-
-/*----------------------------------
-
-  qh_BESTcentrum
-     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
-     else, qh_findbestneighbor() tests all vertices (much better merges)
-
-  qh_BESTcentrum2
-     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
-*/
-#define qh_BESTcentrum 20
-#define qh_BESTcentrum2 2
-
-/*----------------------------------
-
-  qh_BESTnonconvex
-    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
-
-  notes:
-    It is needed because qh_findbestneighbor is slow for large facets
-*/
-#define qh_BESTnonconvex 15
-
-/*----------------------------------
-
-  qh_MAXnewmerges
-    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
-
-  notes:
-    It is needed because postmerge can merge many facets at once
-*/
-#define qh_MAXnewmerges 2
-
-/*----------------------------------
-
-  qh_MAXnewcentrum
-    if <= dim+n vertices (n approximates the number of merges),
-      reset the centrum in qh_updatetested() and qh_mergecycle_facets()
-
-  notes:
-    needed to reduce cost and because centrums may move too much if
-    many vertices in high-d
-*/
-#define qh_MAXnewcentrum 5
-
-/*----------------------------------
-
-  qh_COPLANARratio
-    for 3-d+ merging, qh.MINvisible is n*premerge_centrum
-
-  notes:
-    for non-merging, it's DISTround
-*/
-#define qh_COPLANARratio 3
-
-/*----------------------------------
-
-  qh_DISToutside
-    When is a point clearly outside of a facet?
-    Stops search in qh_findbestnew or qh_partitionall
-    qh_findbest uses qh.MINoutside since since it is only called if no merges.
-
-  notes:
-    'Qf' always searches for best facet
-    if !qh.MERGING, same as qh.MINoutside.
-    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
-      [Note: Zdelvertextot occurs normally with interior points]
-            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
-    When there is a sharp edge, need to move points to a
-    clearly good facet; otherwise may be lost in another partitioning.
-    if too big then O(n^2) behavior for partitioning in cone
-    if very small then important points not processed
-    Needed in qh_partitionall for
-      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
-    Needed in qh_findbestnew for many instances of
-      RBOX 1000 s Z1 G1e-13 t | QHULL Tv
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
-     fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
-
-/*----------------------------------
-
-  qh_RATIOnearinside
-    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
-    qh_check_maxout().
-
-  notes:
-    This is overkill since do not know the correct value.
-    It effects whether 'Qc' reports all coplanar points
-    Not used for 'd' since non-extreme points are coplanar
-*/
-#define qh_RATIOnearinside 5
-
-/*----------------------------------
-
-  qh_SEARCHdist
-    When is a facet coplanar with the best facet?
-    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
-      (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
-
-/*----------------------------------
-
-  qh_USEfindbestnew
-     Always use qh_findbestnew for qh_partitionpoint, otherwise use
-     qh_findbestnew if merged new facet or sharpnewfacets.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
-
-/*----------------------------------
-
-  qh_WIDEcoplanar
-    n*MAXcoplanar or n*MINvisible for a WIDEfacet
-
-    if vertex is further than qh.WIDEfacet from the hyperplane
-    then its ridges are not counted in computing the area, and
-    the facet's centrum is frozen.
-
-  notes:
-   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
-      qh_WIDEcoplanar * qh.MINvisible);
-*/
-#define qh_WIDEcoplanar 6
-
-/*----------------------------------
-
-  qh_WIDEduplicate
-    Merge ratio for errexit from qh_forcedmerges due to duplicate ridge
-    Override with option Q12 no-wide-duplicate
-
-    Notes:
-      Merging a duplicate ridge can lead to very wide facets.
-      A future release of qhull will avoid duplicate ridges by removing duplicate sub-ridges from the horizon
-*/
-#define qh_WIDEduplicate 100
-
-/*----------------------------------
-
-  qh_MAXnarrow
-    max. cosine in initial hull that sets qh.NARROWhull
-
-  notes:
-    If qh.NARROWhull, the initial partition does not make
-    coplanar points.  If narrow, a coplanar point can be
-    coplanar to two facets of opposite orientations and
-    distant from the exact convex hull.
-
-    Conservative estimate.  Don't actually see problems until it is -1.0
-*/
-#define qh_MAXnarrow -0.99999999
-
-/*----------------------------------
-
-  qh_WARNnarrow
-    max. cosine in initial hull to warn about qh.NARROWhull
-
-  notes:
-    this is a conservative estimate.
-    Don't actually see problems until it is -1.0.  See qh-impre.htm
-*/
-#define qh_WARNnarrow -0.999999999999999
-
-/*----------------------------------
-
-  qh_ZEROdelaunay
-    a zero Delaunay facet occurs for input sites coplanar with their convex hull
-    the last normal coefficient of a zero Delaunay facet is within
-        qh_ZEROdelaunay * qh.ANGLEround of 0
-
-  notes:
-    qh_ZEROdelaunay does not allow for joggled input ('QJ').
-
-    You can avoid zero Delaunay facets by surrounding the input with a box.
-
-    Use option 'PDk:-n' to explicitly define zero Delaunay facets
-      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
-      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
-*/
-#define qh_ZEROdelaunay 2
-
-/*============================================================*/
-/*============= Microsoft DevStudio ==========================*/
-/*============================================================*/
-
-/*
-   Finding Memory Leaks Using the CRT Library
-   https://msdn.microsoft.com/en-us/library/x98tx3cf(v=vs.100).aspx
-
-   Reports enabled in qh_lib_check for Debug window and stderr
-
-   From 2005=>msvcr80d, 2010=>msvcr100d, 2012=>msvcr110d
-
-   Watch: {,,msvcr80d.dll}_crtBreakAlloc  Value from {n} in the leak report
-   _CrtSetBreakAlloc(689); // qh_lib_check() [global_r.c]
-
-   Examples
-     http://free-cad.sourceforge.net/SrcDocu/d2/d7f/MemDebug_8cpp_source.html
-     https://github.com/illlust/Game/blob/master/library/MemoryLeak.cpp
-*/
-#if 0   /* off (0) by default for QHULL_CRTDBG */
-#define QHULL_CRTDBG
-#endif
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)
-#define _CRTDBG_MAP_ALLOC
-#include 
-#include 
-#endif
-#endif /* qh_DEFuser */
-
-
-
diff --git a/src/qhull/src/libqhull/usermem.c b/src/qhull/src/libqhull/usermem.c
deleted file mode 100644
index 0e99e8f66..000000000
--- a/src/qhull/src/libqhull/usermem.c
+++ /dev/null
@@ -1,94 +0,0 @@
-/*
      ---------------------------------
-
-   usermem.c
-   qh_exit(), qh_free(), and qh_malloc()
-
-   See README.txt.
-
-   If you redefine one of these functions you must redefine all of them.
-   If you recompile and load this file, then usermem.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See userprintf.c for qh_fprintf and userprintf_rbox.c for qh_fprintf_rbox
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull.h"
-
-#include 
-#include 
-
-/*---------------------------------
-
-  qh_exit( exitcode )
-    exit program
-
-  notes:
-    qh_exit() is called when qh_errexit() and longjmp() are not available.
-
-    This is the only use of exit() in Qhull
-    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
-*/
-void qh_exit(int exitcode) {
-    exit(exitcode);
-} /* exit */
-
-/*---------------------------------
-
-  qh_fprintf_stderr( msgcode, format, list of args )
-    fprintf to stderr with msgcode (non-zero)
-
-  notes:
-    qh_fprintf_stderr() is called when qh.ferr is not defined, usually due to an initialization error
-    
-    It is typically followed by qh_errexit().
-
-    Redefine this function to avoid using stderr
-
-    Use qh_fprintf [userprintf.c] for normal printing
-*/
-void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    va_start(args, fmt);
-    if(msgcode)
-      fprintf(stderr, "QH%.4d ", msgcode);
-    vfprintf(stderr, fmt, args);
-    va_end(args);
-} /* fprintf_stderr */
-
-/*---------------------------------
-
-  qh_free( mem )
-    free memory
-
-  notes:
-    same as free()
-    No calls to qh_errexit() 
-*/
-void qh_free(void *mem) {
-    free(mem);
-} /* free */
-
-/*---------------------------------
-
-    qh_malloc( mem )
-      allocate memory
-
-    notes:
-      same as malloc()
-*/
-void *qh_malloc(size_t size) {
-    return malloc(size);
-} /* malloc */
-
-
diff --git a/src/qhull/src/libqhull/userprintf.c b/src/qhull/src/libqhull/userprintf.c
deleted file mode 100644
index 190d7cd79..000000000
--- a/src/qhull/src/libqhull/userprintf.c
+++ /dev/null
@@ -1,66 +0,0 @@
-/*
      ---------------------------------
-
-   userprintf.c
-   qh_fprintf()
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   If you recompile and load this file, then userprintf.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
-   see Qhull.cpp and RboxPoints.cpp for examples.
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull.h"
-#include "mem.h"
-
-#include 
-#include 
-#include 
-
-/*---------------------------------
-
-   qh_fprintf(fp, msgcode, format, list of args )
-     print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib.c
-
-   notes:
-     same as fprintf()
-     fgets() is not trapped like fprintf()
-     exit qh_fprintf via qh_errexit()
-     may be called for errors in qh_initstatistics and qh_meminit
-*/
-
-void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    if (!fp) {
-        /* could use qhmem.ferr, but probably better to be cautious */
-        qh_fprintf_stderr(6232, "Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf called.\n");
-        qh_errexit(6232, NULL, NULL);
-    }
-    va_start(args, fmt);
-#if qh_QHpointer
-    if (qh_qh && qh ANNOTATEoutput) {
-#else
-    if (qh ANNOTATEoutput) {
-#endif
-      fprintf(fp, "[QH%.4d]", msgcode);
-    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
-      fprintf(fp, "QH%.4d ", msgcode);
-    }
-    vfprintf(fp, fmt, args);
-    va_end(args);
-
-    /* Place debugging traps here. Use with option 'Tn' */
-
-} /* qh_fprintf */
-
diff --git a/src/qhull/src/libqhull/userprintf_rbox.c b/src/qhull/src/libqhull/userprintf_rbox.c
deleted file mode 100644
index 8edd2001a..000000000
--- a/src/qhull/src/libqhull/userprintf_rbox.c
+++ /dev/null
@@ -1,53 +0,0 @@
-/*
      ---------------------------------
-
-   userprintf_rbox.c
-   qh_fprintf_rbox()
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   If you recompile and load this file, then userprintf_rbox.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
-   see Qhull.cpp and RboxPoints.cpp for examples.
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull.h"
-
-#include 
-#include 
-#include 
-
-/*---------------------------------
-
-   qh_fprintf_rbox(fp, msgcode, format, list of args )
-     print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib.c
-
-   notes:
-     same as fprintf()
-     fgets() is not trapped like fprintf()
-     exit qh_fprintf_rbox via qh_errexit_rbox()
-*/
-
-void qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    if (!fp) {
-        qh_fprintf_stderr(6231, "Qhull internal error (userprintf_rbox.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
-        qh_errexit_rbox(6231);
-    }
-    if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
-      fprintf(fp, "QH%.4d ", msgcode);
-    va_start(args, fmt);
-    vfprintf(fp, fmt, args);
-    va_end(args);
-} /* qh_fprintf_rbox */
-
diff --git a/src/qhull/src/libqhull_r/Makefile b/src/qhull/src/libqhull_r/Makefile
deleted file mode 100644
index 5c40969e0..000000000
--- a/src/qhull/src/libqhull_r/Makefile
+++ /dev/null
@@ -1,240 +0,0 @@
-# Simple gcc Makefile for reentrant qhull and rbox (default gcc/g++)
-#
-#   make help
-#   See README.txt and ../../Makefile
-#       
-# Variables
-#   BINDIR         directory where to copy executables
-#   DESTDIR        destination directory for 'make install'
-#   DOCDIR         directory where to copy html documentation
-#   INCDIR         directory where to copy headers
-#   LIBDIR         directory where to copy libraries
-#   MANDIR         directory where to copy manual pages
-#   PRINTMAN       command for printing manual pages
-#   PRINTC         command for printing C files
-#   CC             ANSI C or C++ compiler
-#   CC_OPTS1       options used to compile .c files
-#   CC_OPTS2       options used to link .o files
-#   CC_OPTS3       options to build shared libraries
-#
-#   LIBQHULL_OBJS  .o files for linking
-#   LIBQHULL_HDRS  .h files for printing
-#   CFILES         .c files for printing
-#   DOCFILES       documentation files
-#   FILES          miscellaneous files for printing
-#   TFILES         .txt versions of html files
-#   FILES          all other files
-#   LIBQHULL_OBJS  specifies the object files of libqhullstatic_r.a
-#
-# Results
-#   rbox           Generates points sets for qhull, qconvex, etc.
-#   qhull          Computes convex hulls and related structures
-#   qconvex, qdelaunay, qhalf, qvoronoi
-#                  Specializations of qhull for each geometric structure
-#   libqhullstatic_r.a Static library for reentrant qhull
-#   testqset_r     Standalone test of reentrant qset_r.c with mem_r.c
-#   user_eg        An example of using qhull (reentrant)
-#   user_eg2       An example of using qhull (reentrant)
-#
-# Make targets
-#   make           Build results using gcc or another compiler
-#   make clean     Remove object files
-#   make cleanall  Remove generated files
-#   make doc       Print documentation
-#   make help
-#   make install   Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
-#   make new       Rebuild qhull and rbox from source
-#   make printall  Print all files
-#   make qtest     Quick test of qset, rbox, and qhull
-#   make test      Quck test of qhull, qconvex, etc.
-#
-# Do not replace tabs with spaces.  Needed for build rules
-# Unix line endings (\n)
-# $Id: //main/2015/qhull/src/libqhull_r/Makefile#6 $
-
-DESTDIR = /usr/local
-BINDIR	= $(DESTDIR)/bin
-INCDIR	= $(DESTDIR)/include
-LIBDIR	= $(DESTDIR)/lib
-DOCDIR	= $(DESTDIR)/share/doc/qhull
-MANDIR	= $(DESTDIR)/share/man/man1
-
-# if you do not have enscript, try a2ps or just use lpr.  The files are text.
-PRINTMAN = enscript -2rl
-PRINTC = enscript -2r
-# PRINTMAN = lpr
-# PRINTC = lpr
-
-#for Gnu's gcc compiler, -O3 for optimization, -g for debugging, -pg for profiling
-# -fpic  needed for gcc x86_64-linux-gnu.  Not needed for mingw
-CC        = gcc
-CC_OPTS1  = -O3 -ansi -I../../src -fpic $(CC_WARNINGS)
-
-# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
-#CC       = cc
-#CC_OPTS1 = -Xc -v -fast -I../../src 
-
-# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
-#CC       = cc
-#CC_OPTS1 = -ansi -O2 -I../../src 
-
-# for Next cc compiler with fat executable
-#CC       = cc
-#CC_OPTS1 = -ansi -O2 -I../../src -arch m68k -arch i386 -arch hppa
-
-# For loader, ld, 
-CC_OPTS2 = $(CC_OPTS1)
-
-# Default targets for make
-
-all: qhull_links qhull_all qtest
-
-help:
-	head -n 50 Makefile
-
-clean:
-	rm -f *.o 
-	# Delete linked files from other directories [qhull_links]
-	rm -f qconvex_r.c unix_r.c qdelaun_r.c qhalf_r.c qvoronoi_r.c rbox_r.c
-	rm -f user_eg_r.c user_eg2_r.c testqset_r.c
-	
-cleanall: clean
-	rm -f qconvex qdelaunay qhalf qvoronoi qhull *.exe
-	rm -f core user_eg_r user_eg2_r testqset_r libqhullstatic_r.a
-
-doc: 
-	$(PRINTMAN) $(TXTFILES) $(DOCFILES)
-
-install:
-	mkdir -p $(BINDIR)
-	mkdir -p $(DOCDIR)
-	mkdir -p $(INCDIR)/libqhull
-	mkdir -p $(MANDIR)
-	cp -p qconvex qdelaunay qhalf qhull qvoronoi rbox $(BINDIR)
-	cp -p libqhullstatic_r.a $(LIBDIR)
-	cp -p ../../html/qhull.man $(MANDIR)/qhull.1
-	cp -p ../../html/rbox.man $(MANDIR)/rbox.1
-	cp -p ../../html/* $(DOCDIR)
-	cp *.h $(INCDIR)/libqhull_r
-
-new:	cleanall all
-
-printall: doc printh printc printf
-
-printh:
-	$(PRINTC) $(LIBQHULL_HDRS)
-
-printc:
-	$(PRINTC) $(CFILES)
-
-# LIBQHULL_OBJS_1 ordered by frequency of execution with small files at end.  Better locality.
-# Same definitions as ../../Makefile
-
-LIBQHULLS_OBJS_1= global_r.o stat_r.o geom2_r.o poly2_r.o merge_r.o \
-        libqhull_r.o geom_r.o poly_r.o qset_r.o mem_r.o random_r.o 
-
-LIBQHULLS_OBJS_2= $(LIBQHULLS_OBJS_1) usermem_r.o userprintf_r.o io_r.o user_r.o
-
-LIBQHULLS_OBJS= $(LIBQHULLS_OBJS_2)  rboxlib_r.o userprintf_rbox_r.o
-
-LIBQHULL_HDRS= user_r.h libqhull_r.h qhull_ra.h geom_r.h \
-        io_r.h mem_r.h merge_r.h poly_r.h random_r.h \
-        qset_r.h stat_r.h
-
-# CFILES ordered alphabetically after libqhull.c 
-CFILES= ../qhull/unix_r.c libqhull_r.c geom_r.c geom2_r.c global_r.c io_r.c \
-	mem_r.c merge_r.c poly_r.c poly2_r.c random_r.c rboxlib_r.c \
-	qset_r.c stat_r.c user_r.c usermem_r.c userprintf_r.c \
-	../qconvex/qconvex.c ../qdelaunay/qdelaun.c ../qhalf/qhalf.c ../qvoronoi/qvoronoi.c
-
-TXTFILES= ../../Announce.txt ../../REGISTER.txt ../../COPYING.txt ../../README.txt ../Changes.txt
-DOCFILES= ../../html/rbox.txt ../../html/qhull.txt
-
-.c.o:
-	$(CC) -c $(CC_OPTS1) -o $@ $<
-
-# Work around problems with ../ in Red Hat Linux
-qhull_links:
-	# On MINSYS, 'ln -s' may create a copy instead of a symbolic link
-	[ -f qconvex_r.c ]  || ln -s ../qconvex/qconvex_r.c
-	[ -f qdelaun_r.c ]  || ln -s ../qdelaunay/qdelaun_r.c
-	[ -f qhalf_r.c ]    || ln -s ../qhalf/qhalf_r.c
-	[ -f qvoronoi_r.c ] || ln -s ../qvoronoi/qvoronoi_r.c
-	[ -f rbox_r.c ]     || ln -s ../rbox/rbox_r.c
-	[ -f testqset_r.c ] || ln -s ../testqset_r/testqset_r.c
-	[ -f unix_r.c ]     || ln -s ../qhull/unix_r.c
-	[ -f user_eg_r.c ]  || ln -s ../user_eg/user_eg_r.c
-	[ -f user_eg2_r.c ] || ln -s ../user_eg2/user_eg2_r.c
-
-# compile qhull without using bin/libqhullstatic_r.a
-qhull_all: qconvex_r.o qdelaun_r.o qhalf_r.o qvoronoi_r.o unix_r.o user_eg_r.o user_eg2_r.o rbox_r.o testqset_r.o $(LIBQHULLS_OBJS)
-	$(CC) -o qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qconvex_r.o
-	$(CC) -o qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qdelaun_r.o
-	$(CC) -o qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qhalf_r.o
-	$(CC) -o qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qvoronoi_r.o
-	$(CC) -o qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) unix_r.o 
-	$(CC) -o rbox $(CC_OPTS2) -lm $(LIBQHULLS_OBJS) rbox_r.o
-	$(CC) -o user_eg $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) user_eg_r.o 
-	$(CC) -o user_eg2 $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_1) user_eg2_r.o  usermem_r.o userprintf_r.o io_r.o
-	$(CC) -o testqset_r $(CC_OPTS2) -lm mem_r.o qset_r.o usermem_r.o testqset_r.o
-	-ar -rs libqhullstatic_r.a $(LIBQHULLS_OBJS)
-	#libqhullstatic_r.a is not needed for qhull
-	#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
-	#ranlib libqhullstatic_r.a
-
-qtest:
-	@echo ============================================
-	@echo == make qtest ==============================
-	@echo ============================================
-	@echo -n "== "
-	@date
-	@echo
-	@echo Testing qset.c and mem.c with testqset
-	./testqset_r 10000
-	@echo Run the qhull smoketest
-	./rbox D4 | ./qhull
-	@echo ============================================
-	@echo == To smoketest qhull programs
-	@echo '==     make test'
-	@echo ============================================
-	@echo
-	@echo ============================================
-	@echo == For all make targets
-	@echo '==     make help'
-	@echo ============================================
-	@echo
-
-test: qtest
-	@echo ==============================
-	@echo ========= qconvex ============
-	@echo ==============================
-	-./rbox 10 | ./qconvex Tv 
-	@echo
-	@echo ==============================
-	@echo ========= qdelaunay ==========
-	@echo ==============================
-	-./rbox 10 | ./qdelaunay Tv 
-	@echo
-	@echo ==============================
-	@echo ========= qhalf ==============
-	@echo ==============================
-	-./rbox 10 | ./qconvex FQ FV n Tv | ./qhalf Tv
-	@echo
-	@echo ==============================
-	@echo ========= qvoronoi ===========
-	@echo ==============================
-	-./rbox 10 | ./qvoronoi Tv
-	@echo
-	@echo ==============================
-	@echo ========= user_eg ============
-	@echo == w/o shared library ========
-	@echo ==============================
-	-./user_eg
-	@echo
-	@echo ==============================
-	@echo ========= user_eg2 ===========
-	@echo ==============================
-	-./user_eg2
-	@echo
-
-# end of Makefile
diff --git a/src/qhull/src/libqhull_r/geom2_r.c b/src/qhull/src/libqhull_r/geom2_r.c
deleted file mode 100644
index 0345440be..000000000
--- a/src/qhull/src/libqhull_r/geom2_r.c
+++ /dev/null
@@ -1,2096 +0,0 @@
-/*
      ---------------------------------
-
-
-   geom2_r.c
-   infrequently used geometric routines of qhull
-
-   see qh-geom_r.htm and geom_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/geom2_r.c#6 $$Change: 2065 $
-   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-
-   frequently used code goes into geom_r.c
-*/
-
-#include "qhull_ra.h"
-
-/*================== functions in alphabetic order ============*/
-
-/*---------------------------------
-
-  qh_copypoints(qh, points, numpoints, dimension)
-    return qh_malloc'd copy of points
-  
-  notes:
-    qh_free the returned points to avoid a memory leak
-*/
-coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension) {
-  int size;
-  coordT *newpoints;
-
-  size= numpoints * dimension * (int)sizeof(coordT);
-  if (!(newpoints= (coordT*)qh_malloc((size_t)size))) {
-    qh_fprintf(qh, qh->ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
-        numpoints);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
-  return newpoints;
-} /* copypoints */
-
-/*---------------------------------
-
-  qh_crossproduct( dim, vecA, vecB, vecC )
-    crossproduct of 2 dim vectors
-    C= A x B
-
-  notes:
-    from Glasner, Graphics Gems I, p. 639
-    only defined for dim==3
-*/
-void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
-
-  if (dim == 3) {
-    vecC[0]=   det2_(vecA[1], vecA[2],
-                     vecB[1], vecB[2]);
-    vecC[1]= - det2_(vecA[0], vecA[2],
-                     vecB[0], vecB[2]);
-    vecC[2]=   det2_(vecA[0], vecA[1],
-                     vecB[0], vecB[1]);
-  }
-} /* vcross */
-
-/*---------------------------------
-
-  qh_determinant(qh, rows, dim, nearzero )
-    compute signed determinant of a square matrix
-    uses qh.NEARzero to test for degenerate matrices
-
-  returns:
-    determinant
-    overwrites rows and the matrix
-    if dim == 2 or 3
-      nearzero iff determinant < qh->NEARzero[dim-1]
-      (!quite correct, not critical)
-    if dim >= 4
-      nearzero iff diagonal[k] < qh->NEARzero[k]
-*/
-realT qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero) {
-  realT det=0;
-  int i;
-  boolT sign= False;
-
-  *nearzero= False;
-  if (dim < 2) {
-    qh_fprintf(qh, qh->ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }else if (dim == 2) {
-    det= det2_(rows[0][0], rows[0][1],
-                 rows[1][0], rows[1][1]);
-    if (fabs_(det) < 10*qh->NEARzero[1])  /* not really correct, what should this be? */
-      *nearzero= True;
-  }else if (dim == 3) {
-    det= det3_(rows[0][0], rows[0][1], rows[0][2],
-                 rows[1][0], rows[1][1], rows[1][2],
-                 rows[2][0], rows[2][1], rows[2][2]);
-    if (fabs_(det) < 10*qh->NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63 */
-      *nearzero= True;
-  }else {
-    qh_gausselim(qh, rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
-    det= 1.0;
-    for (i=dim; i--; )
-      det *= (rows[i])[i];
-    if (sign)
-      det= -det;
-  }
-  return det;
-} /* determinant */
-
-/*---------------------------------
-
-  qh_detjoggle(qh, points, numpoints, dimension )
-    determine default max joggle for point array
-      as qh_distround * qh_JOGGLEdefault
-
-  returns:
-    initial value for JOGGLEmax from points and REALepsilon
-
-  notes:
-    computes DISTround since qh_maxmin not called yet
-    if qh->SCALElast, last dimension will be scaled later to MAXwidth
-
-    loop duplicated from qh_maxmin
-*/
-realT qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension) {
-  realT abscoord, distround, joggle, maxcoord, mincoord;
-  pointT *point, *pointtemp;
-  realT maxabs= -REALmax;
-  realT sumabs= 0;
-  realT maxwidth= 0;
-  int k;
-
-  for (k=0; k < dimension; k++) {
-    if (qh->SCALElast && k == dimension-1)
-      abscoord= maxwidth;
-    else if (qh->DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
-      abscoord= 2 * maxabs * maxabs;  /* may be low by qh->hull_dim/2 */
-    else {
-      maxcoord= -REALmax;
-      mincoord= REALmax;
-      FORALLpoint_(qh, points, numpoints) {
-        maximize_(maxcoord, point[k]);
-        minimize_(mincoord, point[k]);
-      }
-      maximize_(maxwidth, maxcoord-mincoord);
-      abscoord= fmax_(maxcoord, -mincoord);
-    }
-    sumabs += abscoord;
-    maximize_(maxabs, abscoord);
-  } /* for k */
-  distround= qh_distround(qh, qh->hull_dim, maxabs, sumabs);
-  joggle= distround * qh_JOGGLEdefault;
-  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
-  trace2((qh, qh->ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
-  return joggle;
-} /* detjoggle */
-
-/*---------------------------------
-
-  qh_detroundoff(qh)
-    determine maximum roundoff errors from
-      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
-      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
-
-    accounts for qh.SETroundoff, qh.RANDOMdist, qh->MERGEexact
-      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
-      qh.postmerge_centrum, qh.MINoutside,
-      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
-
-  returns:
-    sets qh.DISTround, etc. (see below)
-    appends precision constants to qh.qhull_options
-
-  see:
-    qh_maxmin() for qh.NEARzero
-
-  design:
-    determine qh.DISTround for distance computations
-    determine minimum denominators for qh_divzero
-    determine qh.ANGLEround for angle computations
-    adjust qh.premerge_cos,... for roundoff error
-    determine qh.ONEmerge for maximum error due to a single merge
-    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
-      qh.MINoutside, qh.WIDEfacet
-    initialize qh.max_vertex and qh.minvertex
-*/
-void qh_detroundoff(qhT *qh) {
-
-  qh_option(qh, "_max-width", NULL, &qh->MAXwidth);
-  if (!qh->SETroundoff) {
-    qh->DISTround= qh_distround(qh, qh->hull_dim, qh->MAXabs_coord, qh->MAXsumcoord);
-    if (qh->RANDOMdist)
-      qh->DISTround += qh->RANDOMfactor * qh->MAXabs_coord;
-    qh_option(qh, "Error-roundoff", NULL, &qh->DISTround);
-  }
-  qh->MINdenom= qh->MINdenom_1 * qh->MAXabs_coord;
-  qh->MINdenom_1_2= sqrt(qh->MINdenom_1 * qh->hull_dim) ;  /* if will be normalized */
-  qh->MINdenom_2= qh->MINdenom_1_2 * qh->MAXabs_coord;
-                                              /* for inner product */
-  qh->ANGLEround= 1.01 * qh->hull_dim * REALepsilon;
-  if (qh->RANDOMdist)
-    qh->ANGLEround += qh->RANDOMfactor;
-  if (qh->premerge_cos < REALmax/2) {
-    qh->premerge_cos -= qh->ANGLEround;
-    if (qh->RANDOMdist)
-      qh_option(qh, "Angle-premerge-with-random", NULL, &qh->premerge_cos);
-  }
-  if (qh->postmerge_cos < REALmax/2) {
-    qh->postmerge_cos -= qh->ANGLEround;
-    if (qh->RANDOMdist)
-      qh_option(qh, "Angle-postmerge-with-random", NULL, &qh->postmerge_cos);
-  }
-  qh->premerge_centrum += 2 * qh->DISTround;    /*2 for centrum and distplane()*/
-  qh->postmerge_centrum += 2 * qh->DISTround;
-  if (qh->RANDOMdist && (qh->MERGEexact || qh->PREmerge))
-    qh_option(qh, "Centrum-premerge-with-random", NULL, &qh->premerge_centrum);
-  if (qh->RANDOMdist && qh->POSTmerge)
-    qh_option(qh, "Centrum-postmerge-with-random", NULL, &qh->postmerge_centrum);
-  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
-    realT maxangle= 1.0, maxrho;
-
-    minimize_(maxangle, qh->premerge_cos);
-    minimize_(maxangle, qh->postmerge_cos);
-    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
-    qh->ONEmerge= sqrt((realT)qh->hull_dim) * qh->MAXwidth *
-      sqrt(1.0 - maxangle * maxangle) + qh->DISTround;
-    maxrho= qh->hull_dim * qh->premerge_centrum + qh->DISTround;
-    maximize_(qh->ONEmerge, maxrho);
-    maxrho= qh->hull_dim * qh->postmerge_centrum + qh->DISTround;
-    maximize_(qh->ONEmerge, maxrho);
-    if (qh->MERGING)
-      qh_option(qh, "_one-merge", NULL, &qh->ONEmerge);
-  }
-  qh->NEARinside= qh->ONEmerge * qh_RATIOnearinside; /* only used if qh->KEEPnearinside */
-  if (qh->JOGGLEmax < REALmax/2 && (qh->KEEPcoplanar || qh->KEEPinside)) {
-    realT maxdist;             /* adjust qh.NEARinside for joggle */
-    qh->KEEPnearinside= True;
-    maxdist= sqrt((realT)qh->hull_dim) * qh->JOGGLEmax + qh->DISTround;
-    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
-    maximize_(qh->NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
-  }
-  if (qh->KEEPnearinside)
-    qh_option(qh, "_near-inside", NULL, &qh->NEARinside);
-  if (qh->JOGGLEmax < qh->DISTround) {
-    qh_fprintf(qh, qh->ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
-         qh->JOGGLEmax, qh->DISTround);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->MINvisible > REALmax/2) {
-    if (!qh->MERGING)
-      qh->MINvisible= qh->DISTround;
-    else if (qh->hull_dim <= 3)
-      qh->MINvisible= qh->premerge_centrum;
-    else
-      qh->MINvisible= qh_COPLANARratio * qh->premerge_centrum;
-    if (qh->APPROXhull && qh->MINvisible > qh->MINoutside)
-      qh->MINvisible= qh->MINoutside;
-    qh_option(qh, "Visible-distance", NULL, &qh->MINvisible);
-  }
-  if (qh->MAXcoplanar > REALmax/2) {
-    qh->MAXcoplanar= qh->MINvisible;
-    qh_option(qh, "U-coplanar-distance", NULL, &qh->MAXcoplanar);
-  }
-  if (!qh->APPROXhull) {             /* user may specify qh->MINoutside */
-    qh->MINoutside= 2 * qh->MINvisible;
-    if (qh->premerge_cos < REALmax/2)
-      maximize_(qh->MINoutside, (1- qh->premerge_cos) * qh->MAXabs_coord);
-    qh_option(qh, "Width-outside", NULL, &qh->MINoutside);
-  }
-  qh->WIDEfacet= qh->MINoutside;
-  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MAXcoplanar);
-  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MINvisible);
-  qh_option(qh, "_wide-facet", NULL, &qh->WIDEfacet);
-  if (qh->MINvisible > qh->MINoutside + 3 * REALepsilon
-  && !qh->BESToutside && !qh->FORCEoutput)
-    qh_fprintf(qh, qh->ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
-             qh->MINvisible, qh->MINoutside);
-  qh->max_vertex= qh->DISTround;
-  qh->min_vertex= -qh->DISTround;
-  /* numeric constants reported in printsummary */
-} /* detroundoff */
-
-/*---------------------------------
-
-  qh_detsimplex(qh, apex, points, dim, nearzero )
-    compute determinant of a simplex with point apex and base points
-
-  returns:
-     signed determinant and nearzero from qh_determinant
-
-  notes:
-     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
-
-  design:
-    construct qm_matrix by subtracting apex from points
-    compute determinate
-*/
-realT qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero) {
-  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
-  coordT **rows;
-  int k,  i=0;
-  realT det;
-
-  zinc_(Zdetsimplex);
-  gmcoord= qh->gm_matrix;
-  rows= qh->gm_row;
-  FOREACHpoint_(points) {
-    if (i == dim)
-      break;
-    rows[i++]= gmcoord;
-    coordp= point;
-    coorda= apex;
-    for (k=dim; k--; )
-      *(gmcoord++)= *coordp++ - *coorda++;
-  }
-  if (i < dim) {
-    qh_fprintf(qh, qh->ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
-               i, dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  det= qh_determinant(qh, rows, dim, nearzero);
-  trace2((qh, qh->ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
-          det, qh_pointid(qh, apex), dim, *nearzero));
-  return det;
-} /* detsimplex */
-
-/*---------------------------------
-
-  qh_distnorm( dim, point, normal, offset )
-    return distance from point to hyperplane at normal/offset
-
-  returns:
-    dist
-
-  notes:
-    dist > 0 if point is outside of hyperplane
-
-  see:
-    qh_distplane in geom_r.c
-*/
-realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
-  coordT *normalp= normal, *coordp= point;
-  realT dist;
-  int k;
-
-  dist= *offsetp;
-  for (k=dim; k--; )
-    dist += *(coordp++) * *(normalp++);
-  return dist;
-} /* distnorm */
-
-/*---------------------------------
-
-  qh_distround(qh, dimension, maxabs, maxsumabs )
-    compute maximum round-off error for a distance computation
-      to a normalized hyperplane
-    maxabs is the maximum absolute value of a coordinate
-    maxsumabs is the maximum possible sum of absolute coordinate values
-
-  returns:
-    max dist round for REALepsilon
-
-  notes:
-    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
-    use sqrt(dim) since one vector is normalized
-      or use maxsumabs since one vector is < 1
-*/
-realT qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs) {
-  realT maxdistsum, maxround;
-
-  maxdistsum= sqrt((realT)dimension) * maxabs;
-  minimize_( maxdistsum, maxsumabs);
-  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
-              /* adds maxabs for offset */
-  trace4((qh, qh->ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
-                 maxround, maxabs, maxsumabs, maxdistsum));
-  return maxround;
-} /* distround */
-
-/*---------------------------------
-
-  qh_divzero( numer, denom, mindenom1, zerodiv )
-    divide by a number that's nearly zero
-    mindenom1= minimum denominator for dividing into 1.0
-
-  returns:
-    quotient
-    sets zerodiv and returns 0.0 if it would overflow
-
-  design:
-    if numer is nearly zero and abs(numer) < abs(denom)
-      return numer/denom
-    else if numer is nearly zero
-      return 0 and zerodiv
-    else if denom/numer non-zero
-      return numer/denom
-    else
-      return 0 and zerodiv
-*/
-realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
-  realT temp, numerx, denomx;
-
-
-  if (numer < mindenom1 && numer > -mindenom1) {
-    numerx= fabs_(numer);
-    denomx= fabs_(denom);
-    if (numerx < denomx) {
-      *zerodiv= False;
-      return numer/denom;
-    }else {
-      *zerodiv= True;
-      return 0.0;
-    }
-  }
-  temp= denom/numer;
-  if (temp > mindenom1 || temp < -mindenom1) {
-    *zerodiv= False;
-    return numer/denom;
-  }else {
-    *zerodiv= True;
-    return 0.0;
-  }
-} /* divzero */
-
-
-/*---------------------------------
-
-  qh_facetarea(qh, facet )
-    return area for a facet
-
-  notes:
-    if non-simplicial,
-      uses centrum to triangulate facet and sums the projected areas.
-    if (qh->DELAUNAY),
-      computes projected area instead for last coordinate
-    assumes facet->normal exists
-    projecting tricoplanar facets to the hyperplane does not appear to make a difference
-
-  design:
-    if simplicial
-      compute area
-    else
-      for each ridge
-        compute area from centrum to ridge
-    negate area if upper Delaunay facet
-*/
-realT qh_facetarea(qhT *qh, facetT *facet) {
-  vertexT *apex;
-  pointT *centrum;
-  realT area= 0.0;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->simplicial) {
-    apex= SETfirstt_(facet->vertices, vertexT);
-    area= qh_facetarea_simplex(qh, qh->hull_dim, apex->point, facet->vertices,
-                    apex, facet->toporient, facet->normal, &facet->offset);
-  }else {
-    if (qh->CENTERtype == qh_AScentrum)
-      centrum= facet->center;
-    else
-      centrum= qh_getcentrum(qh, facet);
-    FOREACHridge_(facet->ridges)
-      area += qh_facetarea_simplex(qh, qh->hull_dim, centrum, ridge->vertices,
-                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
-    if (qh->CENTERtype != qh_AScentrum)
-      qh_memfree(qh, centrum, qh->normal_size);
-  }
-  if (facet->upperdelaunay && qh->DELAUNAY)
-    area= -area;  /* the normal should be [0,...,1] */
-  trace4((qh, qh->ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
-  return area;
-} /* facetarea */
-
-/*---------------------------------
-
-  qh_facetarea_simplex(qh, dim, apex, vertices, notvertex, toporient, normal, offset )
-    return area for a simplex defined by
-      an apex, a base of vertices, an orientation, and a unit normal
-    if simplicial or tricoplanar facet,
-      notvertex is defined and it is skipped in vertices
-
-  returns:
-    computes area of simplex projected to plane [normal,offset]
-    returns 0 if vertex too far below plane (qh->WIDEfacet)
-      vertex can't be apex of tricoplanar facet
-
-  notes:
-    if (qh->DELAUNAY),
-      computes projected area instead for last coordinate
-    uses qh->gm_matrix/gm_row and qh->hull_dim
-    helper function for qh_facetarea
-
-  design:
-    if Notvertex
-      translate simplex to apex
-    else
-      project simplex to normal/offset
-      translate simplex to apex
-    if Delaunay
-      set last row/column to 0 with -1 on diagonal
-    else
-      set last row to Normal
-    compute determinate
-    scale and flip sign for area
-*/
-realT qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
-        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
-  pointT *coorda, *coordp, *gmcoord;
-  coordT **rows, *normalp;
-  int k,  i=0;
-  realT area, dist;
-  vertexT *vertex, **vertexp;
-  boolT nearzero;
-
-  gmcoord= qh->gm_matrix;
-  rows= qh->gm_row;
-  FOREACHvertex_(vertices) {
-    if (vertex == notvertex)
-      continue;
-    rows[i++]= gmcoord;
-    coorda= apex;
-    coordp= vertex->point;
-    normalp= normal;
-    if (notvertex) {
-      for (k=dim; k--; )
-        *(gmcoord++)= *coordp++ - *coorda++;
-    }else {
-      dist= *offset;
-      for (k=dim; k--; )
-        dist += *coordp++ * *normalp++;
-      if (dist < -qh->WIDEfacet) {
-        zinc_(Znoarea);
-        return 0.0;
-      }
-      coordp= vertex->point;
-      normalp= normal;
-      for (k=dim; k--; )
-        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
-    }
-  }
-  if (i != dim-1) {
-    qh_fprintf(qh, qh->ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
-               i, dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  rows[i]= gmcoord;
-  if (qh->DELAUNAY) {
-    for (i=0; i < dim-1; i++)
-      rows[i][dim-1]= 0.0;
-    for (k=dim; k--; )
-      *(gmcoord++)= 0.0;
-    rows[dim-1][dim-1]= -1.0;
-  }else {
-    normalp= normal;
-    for (k=dim; k--; )
-      *(gmcoord++)= *normalp++;
-  }
-  zinc_(Zdetsimplex);
-  area= qh_determinant(qh, rows, dim, &nearzero);
-  if (toporient)
-    area= -area;
-  area *= qh->AREAfactor;
-  trace4((qh, qh->ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
-          area, qh_pointid(qh, apex), toporient, nearzero));
-  return area;
-} /* facetarea_simplex */
-
-/*---------------------------------
-
-  qh_facetcenter(qh, vertices )
-    return Voronoi center (Voronoi vertex) for a facet's vertices
-
-  returns:
-    return temporary point equal to the center
-
-  see:
-    qh_voronoi_center()
-*/
-pointT *qh_facetcenter(qhT *qh, setT *vertices) {
-  setT *points= qh_settemp(qh, qh_setsize(qh, vertices));
-  vertexT *vertex, **vertexp;
-  pointT *center;
-
-  FOREACHvertex_(vertices)
-    qh_setappend(qh, &points, vertex->point);
-  center= qh_voronoi_center(qh, qh->hull_dim-1, points);
-  qh_settempfree(qh, &points);
-  return center;
-} /* facetcenter */
-
-/*---------------------------------
-
-  qh_findgooddist(qh, point, facetA, dist, facetlist )
-    find best good facet visible for point from facetA
-    assumes facetA is visible from point
-
-  returns:
-    best facet, i.e., good facet that is furthest from point
-      distance to best facet
-      NULL if none
-
-    moves good, visible facets (and some other visible facets)
-      to end of qh->facet_list
-
-  notes:
-    uses qh->visit_id
-
-  design:
-    initialize bestfacet if facetA is good
-    move facetA to end of facetlist
-    for each facet on facetlist
-      for each unvisited neighbor of facet
-        move visible neighbors to end of facetlist
-        update best good neighbor
-        if no good neighbors, update best facet
-*/
-facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp,
-               facetT **facetlist) {
-  realT bestdist= -REALmax, dist;
-  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
-  boolT goodseen= False;
-
-  if (facetA->good) {
-    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
-    qh_distplane(qh, point, facetA, &bestdist);
-    bestfacet= facetA;
-    goodseen= True;
-  }
-  qh_removefacet(qh, facetA);
-  qh_appendfacet(qh, facetA);
-  *facetlist= facetA;
-  facetA->visitid= ++qh->visit_id;
-  FORALLfacet_(*facetlist) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      if (goodseen && !neighbor->good)
-        continue;
-      zzinc_(Zcheckpart);
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > 0) {
-        qh_removefacet(qh, neighbor);
-        qh_appendfacet(qh, neighbor);
-        if (neighbor->good) {
-          goodseen= True;
-          if (dist > bestdist) {
-            bestdist= dist;
-            bestfacet= neighbor;
-          }
-        }
-      }
-    }
-  }
-  if (bestfacet) {
-    *distp= bestdist;
-    trace2((qh, qh->ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
-      qh_pointid(qh, point), bestdist, bestfacet->id));
-    return bestfacet;
-  }
-  trace4((qh, qh->ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
-      qh_pointid(qh, point), facetA->id));
-  return NULL;
-}  /* findgooddist */
-
-/*---------------------------------
-
-  qh_getarea(qh, facetlist )
-    set area of all facets in facetlist
-    collect statistics
-    nop if hasAreaVolume
-
-  returns:
-    sets qh->totarea/totvol to total area and volume of convex hull
-    for Delaunay triangulation, computes projected area of the lower or upper hull
-      ignores upper hull if qh->ATinfinity
-
-  notes:
-    could compute outer volume by expanding facet area by rays from interior
-    the following attempt at perpendicular projection underestimated badly:
-      qh.totoutvol += (-dist + facet->maxoutside + qh->DISTround)
-                            * area/ qh->hull_dim;
-  design:
-    for each facet on facetlist
-      compute facet->area
-      update qh.totarea and qh.totvol
-*/
-void qh_getarea(qhT *qh, facetT *facetlist) {
-  realT area;
-  realT dist;
-  facetT *facet;
-
-  if (qh->hasAreaVolume)
-    return;
-  if (qh->REPORTfreq)
-    qh_fprintf(qh, qh->ferr, 8020, "computing area of each facet and volume of the convex hull\n");
-  else
-    trace1((qh, qh->ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
-  qh->totarea= qh->totvol= 0.0;
-  FORALLfacet_(facetlist) {
-    if (!facet->normal)
-      continue;
-    if (facet->upperdelaunay && qh->ATinfinity)
-      continue;
-    if (!facet->isarea) {
-      facet->f.area= qh_facetarea(qh, facet);
-      facet->isarea= True;
-    }
-    area= facet->f.area;
-    if (qh->DELAUNAY) {
-      if (facet->upperdelaunay == qh->UPPERdelaunay)
-        qh->totarea += area;
-    }else {
-      qh->totarea += area;
-      qh_distplane(qh, qh->interior_point, facet, &dist);
-      qh->totvol += -dist * area/ qh->hull_dim;
-    }
-    if (qh->PRINTstatistics) {
-      wadd_(Wareatot, area);
-      wmax_(Wareamax, area);
-      wmin_(Wareamin, area);
-    }
-  }
-  qh->hasAreaVolume= True;
-} /* getarea */
-
-/*---------------------------------
-
-  qh_gram_schmidt(qh, dim, row )
-    implements Gram-Schmidt orthogonalization by rows
-
-  returns:
-    false if zero norm
-    overwrites rows[dim][dim]
-
-  notes:
-    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
-    overflow due to small divisors not handled
-
-  design:
-    for each row
-      compute norm for row
-      if non-zero, normalize row
-      for each remaining rowA
-        compute inner product of row and rowA
-        reduce rowA by row * inner product
-*/
-boolT qh_gram_schmidt(qhT *qh, int dim, realT **row) {
-  realT *rowi, *rowj, norm;
-  int i, j, k;
-
-  for (i=0; i < dim; i++) {
-    rowi= row[i];
-    for (norm= 0.0, k= dim; k--; rowi++)
-      norm += *rowi * *rowi;
-    norm= sqrt(norm);
-    wmin_(Wmindenom, norm);
-    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
-      return False;
-    for (k=dim; k--; )
-      *(--rowi) /= norm;
-    for (j=i+1; j < dim; j++) {
-      rowj= row[j];
-      for (norm= 0.0, k=dim; k--; )
-        norm += *rowi++ * *rowj++;
-      for (k=dim; k--; )
-        *(--rowj) -= *(--rowi) * norm;
-    }
-  }
-  return True;
-} /* gram_schmidt */
-
-
-/*---------------------------------
-
-  qh_inthresholds(qh, normal, angle )
-    return True if normal within qh.lower_/upper_threshold
-
-  returns:
-    estimate of angle by summing of threshold diffs
-      angle may be NULL
-      smaller "angle" is better
-
-  notes:
-    invalid if qh.SPLITthresholds
-
-  see:
-    qh.lower_threshold in qh_initbuild()
-    qh_initthresholds()
-
-  design:
-    for each dimension
-      test threshold
-*/
-boolT qh_inthresholds(qhT *qh, coordT *normal, realT *angle) {
-  boolT within= True;
-  int k;
-  realT threshold;
-
-  if (angle)
-    *angle= 0.0;
-  for (k=0; k < qh->hull_dim; k++) {
-    threshold= qh->lower_threshold[k];
-    if (threshold > -REALmax/2) {
-      if (normal[k] < threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-    if (qh->upper_threshold[k] < REALmax/2) {
-      threshold= qh->upper_threshold[k];
-      if (normal[k] > threshold)
-        within= False;
-      if (angle) {
-        threshold -= normal[k];
-        *angle += fabs_(threshold);
-      }
-    }
-  }
-  return within;
-} /* inthresholds */
-
-
-/*---------------------------------
-
-  qh_joggleinput(qh)
-    randomly joggle input to Qhull by qh.JOGGLEmax
-    initial input is qh.first_point/qh.num_points of qh.hull_dim
-      repeated calls use qh.input_points/qh.num_points
-
-  returns:
-    joggles points at qh.first_point/qh.num_points
-    copies data to qh.input_points/qh.input_malloc if first time
-    determines qh.JOGGLEmax if it was zero
-    if qh.DELAUNAY
-      computes the Delaunay projection of the joggled points
-
-  notes:
-    if qh.DELAUNAY, unnecessarily joggles the last coordinate
-    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
-
-  design:
-    if qh.DELAUNAY
-      set qh.SCALElast for reduced precision errors
-    if first call
-      initialize qh.input_points to the original input points
-      if qh.JOGGLEmax == 0
-        determine default qh.JOGGLEmax
-    else
-      increase qh.JOGGLEmax according to qh.build_cnt
-    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
-    if qh.DELAUNAY
-      sets the Delaunay projection
-*/
-void qh_joggleinput(qhT *qh) {
-  int i, seed, size;
-  coordT *coordp, *inputp;
-  realT randr, randa, randb;
-
-  if (!qh->input_points) { /* first call */
-    qh->input_points= qh->first_point;
-    qh->input_malloc= qh->POINTSmalloc;
-    size= qh->num_points * qh->hull_dim * sizeof(coordT);
-    if (!(qh->first_point=(coordT*)qh_malloc((size_t)size))) {
-      qh_fprintf(qh, qh->ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
-          qh->num_points);
-      qh_errexit(qh, qh_ERRmem, NULL, NULL);
-    }
-    qh->POINTSmalloc= True;
-    if (qh->JOGGLEmax == 0.0) {
-      qh->JOGGLEmax= qh_detjoggle(qh, qh->input_points, qh->num_points, qh->hull_dim);
-      qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-    }
-  }else {                 /* repeated call */
-    if (!qh->RERUN && qh->build_cnt > qh_JOGGLEretry) {
-      if (((qh->build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
-        realT maxjoggle= qh->MAXwidth * qh_JOGGLEmaxincrease;
-        if (qh->JOGGLEmax < maxjoggle) {
-          qh->JOGGLEmax *= qh_JOGGLEincrease;
-          minimize_(qh->JOGGLEmax, maxjoggle);
-        }
-      }
-    }
-    qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-  }
-  if (qh->build_cnt > 1 && qh->JOGGLEmax > fmax_(qh->MAXwidth/4, 0.1)) {
-      qh_fprintf(qh, qh->ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
-                qh->JOGGLEmax);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  /* for some reason, using qh->ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
-  seed= qh_RANDOMint;
-  qh_option(qh, "_joggle-seed", &seed, NULL);
-  trace0((qh, qh->ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
-    qh->JOGGLEmax, seed));
-  inputp= qh->input_points;
-  coordp= qh->first_point;
-  randa= 2.0 * qh->JOGGLEmax/qh_RANDOMmax;
-  randb= -qh->JOGGLEmax;
-  size= qh->num_points * qh->hull_dim;
-  for (i=size; i--; ) {
-    randr= qh_RANDOMint;
-    *(coordp++)= *(inputp++) + (randr * randa + randb);
-  }
-  if (qh->DELAUNAY) {
-    qh->last_low= qh->last_high= qh->last_newhigh= REALmax;
-    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
-  }
-} /* joggleinput */
-
-/*---------------------------------
-
-  qh_maxabsval( normal, dim )
-    return pointer to maximum absolute value of a dim vector
-    returns NULL if dim=0
-*/
-realT *qh_maxabsval(realT *normal, int dim) {
-  realT maxval= -REALmax;
-  realT *maxp= NULL, *colp, absval;
-  int k;
-
-  for (k=dim, colp= normal; k--; colp++) {
-    absval= fabs_(*colp);
-    if (absval > maxval) {
-      maxval= absval;
-      maxp= colp;
-    }
-  }
-  return maxp;
-} /* maxabsval */
-
-
-/*---------------------------------
-
-  qh_maxmin(qh, points, numpoints, dimension )
-    return max/min points for each dimension
-    determine max and min coordinates
-
-  returns:
-    returns a temporary set of max and min points
-      may include duplicate points. Does not include qh.GOODpoint
-    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
-         qh.MAXlastcoord, qh.MINlastcoord
-    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
-
-  notes:
-    loop duplicated in qh_detjoggle()
-
-  design:
-    initialize global precision variables
-    checks definition of REAL...
-    for each dimension
-      for each point
-        collect maximum and minimum point
-      collect maximum of maximums and minimum of minimums
-      determine qh.NEARzero for Gaussian Elimination
-*/
-setT *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension) {
-  int k;
-  realT maxcoord, temp;
-  pointT *minimum, *maximum, *point, *pointtemp;
-  setT *set;
-
-  qh->max_outside= 0.0;
-  qh->MAXabs_coord= 0.0;
-  qh->MAXwidth= -REALmax;
-  qh->MAXsumcoord= 0.0;
-  qh->min_vertex= 0.0;
-  qh->WAScoplanar= False;
-  if (qh->ZEROcentrum)
-    qh->ZEROall_ok= True;
-  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
-  && REALmax > 0.0 && -REALmax < 0.0)
-    ; /* all ok */
-  else {
-    qh_fprintf(qh, qh->ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
-REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
-             REALepsilon, REALmin, REALmax, -REALmax);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  set= qh_settemp(qh, 2*dimension);
-  for (k=0; k < dimension; k++) {
-    if (points == qh->GOODpointp)
-      minimum= maximum= points + dimension;
-    else
-      minimum= maximum= points;
-    FORALLpoint_(qh, points, numpoints) {
-      if (point == qh->GOODpointp)
-        continue;
-      if (maximum[k] < point[k])
-        maximum= point;
-      else if (minimum[k] > point[k])
-        minimum= point;
-    }
-    if (k == dimension-1) {
-      qh->MINlastcoord= minimum[k];
-      qh->MAXlastcoord= maximum[k];
-    }
-    if (qh->SCALElast && k == dimension-1)
-      maxcoord= qh->MAXwidth;
-    else {
-      maxcoord= fmax_(maximum[k], -minimum[k]);
-      if (qh->GOODpointp) {
-        temp= fmax_(qh->GOODpointp[k], -qh->GOODpointp[k]);
-        maximize_(maxcoord, temp);
-      }
-      temp= maximum[k] - minimum[k];
-      maximize_(qh->MAXwidth, temp);
-    }
-    maximize_(qh->MAXabs_coord, maxcoord);
-    qh->MAXsumcoord += maxcoord;
-    qh_setappend(qh, &set, maximum);
-    qh_setappend(qh, &set, minimum);
-    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
-       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
-       Golub & van Loan say that n^3 can be ignored and 10 be used in
-       place of rho */
-    qh->NEARzero[k]= 80 * qh->MAXsumcoord * REALepsilon;
-  }
-  if (qh->IStracing >=1)
-    qh_printpoints(qh, qh->ferr, "qh_maxmin: found the max and min points(by dim):", set);
-  return(set);
-} /* maxmin */
-
-/*---------------------------------
-
-  qh_maxouter(qh)
-    return maximum distance from facet to outer plane
-    normally this is qh.max_outside+qh.DISTround
-    does not include qh.JOGGLEmax
-
-  see:
-    qh_outerinner()
-
-  notes:
-    need to add another qh.DISTround if testing actual point with computation
-
-  for joggle:
-    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
-    need to use Wnewvertexmax since could have a coplanar point for a high
-      facet that is replaced by a low facet
-    need to add qh.JOGGLEmax if testing input points
-*/
-realT qh_maxouter(qhT *qh) {
-  realT dist;
-
-  dist= fmax_(qh->max_outside, qh->DISTround);
-  dist += qh->DISTround;
-  trace4((qh, qh->ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh->max_outside));
-  return dist;
-} /* maxouter */
-
-/*---------------------------------
-
-  qh_maxsimplex(qh, dim, maxpoints, points, numpoints, simplex )
-    determines maximum simplex for a set of points
-    starts from points already in simplex
-    skips qh.GOODpointp (assumes that it isn't in maxpoints)
-
-  returns:
-    simplex with dim+1 points
-
-  notes:
-    assumes at least pointsneeded points in points
-    maximizes determinate for x,y,z,w, etc.
-    uses maxpoints as long as determinate is clearly non-zero
-
-  design:
-    initialize simplex with at least two points
-      (find points with max or min x coordinate)
-    for each remaining dimension
-      add point that maximizes the determinate
-        (use points from maxpoints first)
-*/
-void qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
-  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
-  boolT nearzero, maxnearzero= False;
-  int k, sizinit;
-  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
-
-  sizinit= qh_setsize(qh, *simplex);
-  if (sizinit < 2) {
-    if (qh_setsize(qh, maxpoints) >= 2) {
-      FOREACHpoint_(maxpoints) {
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }else {
-      FORALLpoint_(qh, points, numpoints) {
-        if (point == qh->GOODpointp)
-          continue;
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-        if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }
-    qh_setunique(qh, simplex, minx);
-    if (qh_setsize(qh, *simplex) < 2)
-      qh_setunique(qh, simplex, maxx);
-    sizinit= qh_setsize(qh, *simplex);
-    if (sizinit < 2) {
-      qh_precision(qh, "input has same x coordinate");
-      if (zzval_(Zsetplane) > qh->hull_dim+1) {
-        qh_fprintf(qh, qh->ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
-                 qh_setsize(qh, maxpoints)+numpoints);
-        qh_errexit(qh, qh_ERRprec, NULL, NULL);
-      }else {
-        qh_fprintf(qh, qh->ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh->hull_dim);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-    }
-  }
-  for (k=sizinit; k < dim+1; k++) {
-    maxpoint= NULL;
-    maxdet= -REALmax;
-    FOREACHpoint_(maxpoints) {
-      if (!qh_setin(*simplex, point)) {
-        det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
-        if ((det= fabs_(det)) > maxdet) {
-          maxdet= det;
-          maxpoint= point;
-          maxnearzero= nearzero;
-        }
-      }
-    }
-    if (!maxpoint || maxnearzero) {
-      zinc_(Zsearchpoints);
-      if (!maxpoint) {
-        trace0((qh, qh->ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
-      }else {
-        trace0((qh, qh->ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
-                k+1, qh_pointid(qh, maxpoint), maxdet));
-      }
-      FORALLpoint_(qh, points, numpoints) {
-        if (point == qh->GOODpointp)
-          continue;
-        if (!qh_setin(*simplex, point)) {
-          det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
-          if ((det= fabs_(det)) > maxdet) {
-            maxdet= det;
-            maxpoint= point;
-            maxnearzero= nearzero;
-          }
-        }
-      }
-    } /* !maxpoint */
-    if (!maxpoint) {
-      qh_fprintf(qh, qh->ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    qh_setappend(qh, simplex, maxpoint);
-    trace1((qh, qh->ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
-            qh_pointid(qh, maxpoint), k+1, maxdet));
-  } /* k */
-} /* maxsimplex */
-
-/*---------------------------------
-
-  qh_minabsval( normal, dim )
-    return minimum absolute value of a dim vector
-*/
-realT qh_minabsval(realT *normal, int dim) {
-  realT minval= 0;
-  realT maxval= 0;
-  realT *colp;
-  int k;
-
-  for (k=dim, colp=normal; k--; colp++) {
-    maximize_(maxval, *colp);
-    minimize_(minval, *colp);
-  }
-  return fmax_(maxval, -minval);
-} /* minabsval */
-
-
-/*---------------------------------
-
-  qh_mindif(qh, vecA, vecB, dim )
-    return index of min abs. difference of two vectors
-*/
-int qh_mindiff(realT *vecA, realT *vecB, int dim) {
-  realT mindiff= REALmax, diff;
-  realT *vecAp= vecA, *vecBp= vecB;
-  int k, mink= 0;
-
-  for (k=0; k < dim; k++) {
-    diff= *vecAp++ - *vecBp++;
-    diff= fabs_(diff);
-    if (diff < mindiff) {
-      mindiff= diff;
-      mink= k;
-    }
-  }
-  return mink;
-} /* mindiff */
-
-
-
-/*---------------------------------
-
-  qh_orientoutside(qh, facet  )
-    make facet outside oriented via qh.interior_point
-
-  returns:
-    True if facet reversed orientation.
-*/
-boolT qh_orientoutside(qhT *qh, facetT *facet) {
-  int k;
-  realT dist;
-
-  qh_distplane(qh, qh->interior_point, facet, &dist);
-  if (dist > 0) {
-    for (k=qh->hull_dim; k--; )
-      facet->normal[k]= -facet->normal[k];
-    facet->offset= -facet->offset;
-    return True;
-  }
-  return False;
-} /* orientoutside */
-
-/*---------------------------------
-
-  qh_outerinner(qh, facet, outerplane, innerplane  )
-    if facet and qh.maxoutdone (i.e., qh_check_maxout)
-      returns outer and inner plane for facet
-    else
-      returns maximum outer and inner plane
-    accounts for qh.JOGGLEmax
-
-  see:
-    qh_maxouter(qh), qh_check_bestdist(), qh_check_points()
-
-  notes:
-    outerplaner or innerplane may be NULL
-    facet is const
-    Does not error (QhullFacet)
-
-    includes qh.DISTround for actual points
-    adds another qh.DISTround if testing with floating point arithmetic
-*/
-void qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
-  realT dist, mindist;
-  vertexT *vertex, **vertexp;
-
-  if (outerplane) {
-    if (!qh_MAXoutside || !facet || !qh->maxoutdone) {
-      *outerplane= qh_maxouter(qh);       /* includes qh.DISTround */
-    }else { /* qh_MAXoutside ... */
-#if qh_MAXoutside
-      *outerplane= facet->maxoutside + qh->DISTround;
-#endif
-
-    }
-    if (qh->JOGGLEmax < REALmax/2)
-      *outerplane += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-  }
-  if (innerplane) {
-    if (facet) {
-      mindist= REALmax;
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        minimize_(mindist, dist);
-      }
-      *innerplane= mindist - qh->DISTround;
-    }else
-      *innerplane= qh->min_vertex - qh->DISTround;
-    if (qh->JOGGLEmax < REALmax/2)
-      *innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-  }
-} /* outerinner */
-
-/*---------------------------------
-
-  qh_pointdist( point1, point2, dim )
-    return distance between two points
-
-  notes:
-    returns distance squared if 'dim' is negative
-*/
-coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
-  coordT dist, diff;
-  int k;
-
-  dist= 0.0;
-  for (k= (dim > 0 ? dim : -dim); k--; ) {
-    diff= *point1++ - *point2++;
-    dist += diff * diff;
-  }
-  if (dim > 0)
-    return(sqrt(dist));
-  return dist;
-} /* pointdist */
-
-
-/*---------------------------------
-
-  qh_printmatrix(qh, fp, string, rows, numrow, numcol )
-    print matrix to fp given by row vectors
-    print string as header
-    qh may be NULL if fp is defined
-
-  notes:
-    print a vector by qh_printmatrix(qh, fp, "", &vect, 1, len)
-*/
-void qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
-  realT *rowp;
-  realT r; /*bug fix*/
-  int i,k;
-
-  qh_fprintf(qh, fp, 9001, "%s\n", string);
-  for (i=0; i < numrow; i++) {
-    rowp= rows[i];
-    for (k=0; k < numcol; k++) {
-      r= *rowp++;
-      qh_fprintf(qh, fp, 9002, "%6.3g ", r);
-    }
-    qh_fprintf(qh, fp, 9003, "\n");
-  }
-} /* printmatrix */
-
-
-/*---------------------------------
-
-  qh_printpoints(qh, fp, string, points )
-    print pointids to fp for a set of points
-    if string, prints string and 'p' point ids
-*/
-void qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points) {
-  pointT *point, **pointp;
-
-  if (string) {
-    qh_fprintf(qh, fp, 9004, "%s", string);
-    FOREACHpoint_(points)
-      qh_fprintf(qh, fp, 9005, " p%d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9006, "\n");
-  }else {
-    FOREACHpoint_(points)
-      qh_fprintf(qh, fp, 9007, " %d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9008, "\n");
-  }
-} /* printpoints */
-
-
-/*---------------------------------
-
-  qh_projectinput(qh)
-    project input points using qh.lower_bound/upper_bound and qh->DELAUNAY
-    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
-      removes dimension k
-    if halfspace intersection
-      removes dimension k from qh.feasible_point
-    input points in qh->first_point, num_points, input_dim
-
-  returns:
-    new point array in qh->first_point of qh->hull_dim coordinates
-    sets qh->POINTSmalloc
-    if qh->DELAUNAY
-      projects points to paraboloid
-      lowbound/highbound is also projected
-    if qh->ATinfinity
-      adds point "at-infinity"
-    if qh->POINTSmalloc
-      frees old point array
-
-  notes:
-    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
-
-
-  design:
-    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
-    determines newdim and newnum for qh->hull_dim and qh->num_points
-    projects points to newpoints
-    projects qh.lower_bound to itself
-    projects qh.upper_bound to itself
-    if qh->DELAUNAY
-      if qh->ATINFINITY
-        projects points to paraboloid
-        computes "infinity" point as vertex average and 10% above all points
-      else
-        uses qh_setdelaunay to project points to paraboloid
-*/
-void qh_projectinput(qhT *qh) {
-  int k,i;
-  int newdim= qh->input_dim, newnum= qh->num_points;
-  signed char *project;
-  int projectsize= (qh->input_dim+1)*sizeof(*project);
-  pointT *newpoints, *coord, *infinity;
-  realT paraboloid, maxboloid= 0;
-
-  project= (signed char*)qh_memalloc(qh, projectsize);
-  memset((char*)project, 0, (size_t)projectsize);
-  for (k=0; k < qh->input_dim; k++) {   /* skip Delaunay bound */
-    if (qh->lower_bound[k] == 0 && qh->upper_bound[k] == 0) {
-      project[k]= -1;
-      newdim--;
-    }
-  }
-  if (qh->DELAUNAY) {
-    project[k]= 1;
-    newdim++;
-    if (qh->ATinfinity)
-      newnum++;
-  }
-  if (newdim != qh->hull_dim) {
-    qh_memfree(qh, project, projectsize);
-    qh_fprintf(qh, qh->ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh->hull_dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (!(newpoints= qh->temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
-    qh_memfree(qh, project, projectsize);
-    qh_fprintf(qh, qh->ferr, 6016, "qhull error: insufficient memory to project %d points\n",
-           qh->num_points);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  /* qh_projectpoints throws error if mismatched dimensions */
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->first_point,
-                    qh->num_points, qh->input_dim, newpoints, newdim);
-  trace1((qh, qh->ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->lower_bound,
-                    1, qh->input_dim+1, qh->lower_bound, newdim+1);
-  qh_projectpoints(qh, project, qh->input_dim+1, qh->upper_bound,
-                    1, qh->input_dim+1, qh->upper_bound, newdim+1);
-  if (qh->HALFspace) {
-    if (!qh->feasible_point) {
-      qh_memfree(qh, project, projectsize);
-      qh_fprintf(qh, qh->ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    qh_projectpoints(qh, project, qh->input_dim, qh->feasible_point,
-                      1, qh->input_dim, qh->feasible_point, newdim);
-  }
-  qh_memfree(qh, project, projectsize);
-  if (qh->POINTSmalloc)
-    qh_free(qh->first_point);
-  qh->first_point= newpoints;
-  qh->POINTSmalloc= True;
-  qh->temp_malloc= NULL;
-  if (qh->DELAUNAY && qh->ATinfinity) {
-    coord= qh->first_point;
-    infinity= qh->first_point + qh->hull_dim * qh->num_points;
-    for (k=qh->hull_dim-1; k--; )
-      infinity[k]= 0.0;
-    for (i=qh->num_points; i--; ) {
-      paraboloid= 0.0;
-      for (k=0; k < qh->hull_dim-1; k++) {
-        paraboloid += *coord * *coord;
-        infinity[k] += *coord;
-        coord++;
-      }
-      *(coord++)= paraboloid;
-      maximize_(maxboloid, paraboloid);
-    }
-    /* coord == infinity */
-    for (k=qh->hull_dim-1; k--; )
-      *(coord++) /= qh->num_points;
-    *(coord++)= maxboloid * 1.1;
-    qh->num_points++;
-    trace0((qh, qh->ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
-  }else if (qh->DELAUNAY)  /* !qh->ATinfinity */
-    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
-} /* projectinput */
-
-
-/*---------------------------------
-
-  qh_projectpoints(qh, project, n, points, numpoints, dim, newpoints, newdim )
-    project points/numpoints/dim to newpoints/newdim
-    if project[k] == -1
-      delete dimension k
-    if project[k] == 1
-      add dimension k by duplicating previous column
-    n is size of project
-
-  notes:
-    newpoints may be points if only adding dimension at end
-
-  design:
-    check that 'project' and 'newdim' agree
-    for each dimension
-      if project == -1
-        skip dimension
-      else
-        determine start of column in newpoints
-        determine start of column in points
-          if project == +1, duplicate previous column
-        copy dimension (column) from points to newpoints
-*/
-void qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
-        int numpoints, int dim, realT *newpoints, int newdim) {
-  int testdim= dim, oldk=0, newk=0, i,j=0,k;
-  realT *newp, *oldp;
-
-  for (k=0; k < n; k++)
-    testdim += project[k];
-  if (testdim != newdim) {
-    qh_fprintf(qh, qh->ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
-      newdim, testdim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  for (j=0; j= dim)
-          continue;
-        oldp= points+oldk;
-      }else
-        oldp= points+oldk++;
-      for (i=numpoints; i--; ) {
-        *newp= *oldp;
-        newp += newdim;
-        oldp += dim;
-      }
-    }
-    if (oldk >= dim)
-      break;
-  }
-  trace1((qh, qh->ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
-    numpoints, dim, newdim));
-} /* projectpoints */
-
-
-/*---------------------------------
-
-  qh_rotateinput(qh, rows )
-    rotate input using row matrix
-    input points given by qh->first_point, num_points, hull_dim
-    assumes rows[dim] is a scratch buffer
-    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    rotated input
-    sets qh->POINTSmalloc
-
-  design:
-    see qh_rotatepoints
-*/
-void qh_rotateinput(qhT *qh, realT **rows) {
-
-  if (!qh->POINTSmalloc) {
-    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
-    qh->POINTSmalloc= True;
-  }
-  qh_rotatepoints(qh, qh->first_point, qh->num_points, qh->hull_dim, rows);
-}  /* rotateinput */
-
-/*---------------------------------
-
-  qh_rotatepoints(qh, points, numpoints, dim, row )
-    rotate numpoints points by a d-dim row matrix
-    assumes rows[dim] is a scratch buffer
-
-  returns:
-    rotated points in place
-
-  design:
-    for each point
-      for each coordinate
-        use row[dim] to compute partial inner product
-      for each coordinate
-        rotate by partial inner product
-*/
-void qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **row) {
-  realT *point, *rowi, *coord= NULL, sum, *newval;
-  int i,j,k;
-
-  if (qh->IStracing >= 1)
-    qh_printmatrix(qh, qh->ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
-  for (point= points, j= numpoints; j--; point += dim) {
-    newval= row[dim];
-    for (i=0; i < dim; i++) {
-      rowi= row[i];
-      coord= point;
-      for (sum= 0.0, k= dim; k--; )
-        sum += *rowi++ * *coord++;
-      *(newval++)= sum;
-    }
-    for (k=dim; k--; )
-      *(--coord)= *(--newval);
-  }
-} /* rotatepoints */
-
-
-/*---------------------------------
-
-  qh_scaleinput(qh)
-    scale input points using qh->low_bound/high_bound
-    input points given by qh->first_point, num_points, hull_dim
-    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    scales coordinates of points to low_bound[k], high_bound[k]
-    sets qh->POINTSmalloc
-
-  design:
-    see qh_scalepoints
-*/
-void qh_scaleinput(qhT *qh) {
-
-  if (!qh->POINTSmalloc) {
-    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
-    qh->POINTSmalloc= True;
-  }
-  qh_scalepoints(qh, qh->first_point, qh->num_points, qh->hull_dim,
-       qh->lower_bound, qh->upper_bound);
-}  /* scaleinput */
-
-/*---------------------------------
-
-  qh_scalelast(qh, points, numpoints, dim, low, high, newhigh )
-    scale last coordinate to [0,m] for Delaunay triangulations
-    input points given by points, numpoints, dim
-
-  returns:
-    changes scale of last coordinate from [low, high] to [0, newhigh]
-    overwrites last coordinate of each point
-    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
-
-  notes:
-    when called by qh_setdelaunay, low/high may not match actual data
-
-  design:
-    compute scale and shift factors
-    apply to last coordinate of each point
-*/
-void qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
-                   coordT high, coordT newhigh) {
-  realT scale, shift;
-  coordT *coord;
-  int i;
-  boolT nearzero= False;
-
-  trace4((qh, qh->ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
-    low, high, newhigh));
-  qh->last_low= low;
-  qh->last_high= high;
-  qh->last_newhigh= newhigh;
-  scale= qh_divzero(newhigh, high - low,
-                  qh->MINdenom_1, &nearzero);
-  if (nearzero) {
-    if (qh->DELAUNAY)
-      qh_fprintf(qh, qh->ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
-    else
-      qh_fprintf(qh, qh->ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
-                newhigh, low, high, high-low);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  shift= - low * newhigh / (high-low);
-  coord= points + dim - 1;
-  for (i=numpoints; i--; coord += dim)
-    *coord= *coord * scale + shift;
-} /* scalelast */
-
-/*---------------------------------
-
-  qh_scalepoints(qh, points, numpoints, dim, newlows, newhighs )
-    scale points to new lowbound and highbound
-    retains old bound when newlow= -REALmax or newhigh= +REALmax
-
-  returns:
-    scaled points
-    overwrites old points
-
-  design:
-    for each coordinate
-      compute current low and high bound
-      compute scale and shift factors
-      scale all points
-      enforce new low and high bound for all points
-*/
-void qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
-        realT *newlows, realT *newhighs) {
-  int i,k;
-  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
-  boolT nearzero= False;
-
-  for (k=0; k < dim; k++) {
-    newhigh= newhighs[k];
-    newlow= newlows[k];
-    if (newhigh > REALmax/2 && newlow < -REALmax/2)
-      continue;
-    low= REALmax;
-    high= -REALmax;
-    for (i=numpoints, coord=points+k; i--; coord += dim) {
-      minimize_(low, *coord);
-      maximize_(high, *coord);
-    }
-    if (newhigh > REALmax/2)
-      newhigh= high;
-    if (newlow < -REALmax/2)
-      newlow= low;
-    if (qh->DELAUNAY && k == dim-1 && newhigh < newlow) {
-      qh_fprintf(qh, qh->ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
-               k, k, newhigh, newlow);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    scale= qh_divzero(newhigh - newlow, high - low,
-                  qh->MINdenom_1, &nearzero);
-    if (nearzero) {
-      qh_fprintf(qh, qh->ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
-              k, newlow, newhigh, low, high);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    shift= (newlow * high - low * newhigh)/(high-low);
-    coord= points+k;
-    for (i=numpoints; i--; coord += dim)
-      *coord= *coord * scale + shift;
-    coord= points+k;
-    if (newlow < newhigh) {
-      mincoord= newlow;
-      maxcoord= newhigh;
-    }else {
-      mincoord= newhigh;
-      maxcoord= newlow;
-    }
-    for (i=numpoints; i--; coord += dim) {
-      minimize_(*coord, maxcoord);  /* because of roundoff error */
-      maximize_(*coord, mincoord);
-    }
-    trace0((qh, qh->ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
-      k, low, high, newlow, newhigh, numpoints, scale, shift));
-  }
-} /* scalepoints */
-
-
-/*---------------------------------
-
-  qh_setdelaunay(qh, dim, count, points )
-    project count points to dim-d paraboloid for Delaunay triangulation
-
-    dim is one more than the dimension of the input set
-    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
-
-    points is a dim*count realT array.  The first dim-1 coordinates
-    are the coordinates of the first input point.  array[dim] is
-    the first coordinate of the second input point.  array[2*dim] is
-    the first coordinate of the third input point.
-
-    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
-      calls qh_scalelast to scale the last coordinate the same as the other points
-
-  returns:
-    for each point
-      sets point[dim-1] to sum of squares of coordinates
-    scale points to 'Qbb' if needed
-
-  notes:
-    to project one point, use
-      qh_setdelaunay(qh, qh->hull_dim, 1, point)
-
-    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
-    the coordinates after the original projection.
-
-*/
-void qh_setdelaunay(qhT *qh, int dim, int count, pointT *points) {
-  int i, k;
-  coordT *coordp, coord;
-  realT paraboloid;
-
-  trace0((qh, qh->ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
-  coordp= points;
-  for (i=0; i < count; i++) {
-    coord= *coordp++;
-    paraboloid= coord*coord;
-    for (k=dim-2; k--; ) {
-      coord= *coordp++;
-      paraboloid += coord*coord;
-    }
-    *coordp++ = paraboloid;
-  }
-  if (qh->last_low < REALmax/2)
-    qh_scalelast(qh, points, count, dim, qh->last_low, qh->last_high, qh->last_newhigh);
-} /* setdelaunay */
-
-
-/*---------------------------------
-
-  qh_sethalfspace(qh, dim, coords, nextp, normal, offset, feasible )
-    set point to dual of halfspace relative to feasible point
-    halfspace is normal coefficients and offset.
-
-  returns:
-    false and prints error if feasible point is outside of hull
-    overwrites coordinates for point at dim coords
-    nextp= next point (coords)
-    does not call qh_errexit
-
-  design:
-    compute distance from feasible point to halfspace
-    divide each normal coefficient by -dist
-*/
-boolT qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
-         coordT *normal, coordT *offset, coordT *feasible) {
-  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
-  realT dist;
-  realT r; /*bug fix*/
-  int k;
-  boolT zerodiv;
-
-  dist= *offset;
-  for (k=dim; k--; )
-    dist += *(normp++) * *(feasiblep++);
-  if (dist > 0)
-    goto LABELerroroutside;
-  normp= normal;
-  if (dist < -qh->MINdenom) {
-    for (k=dim; k--; )
-      *(coordp++)= *(normp++) / -dist;
-  }else {
-    for (k=dim; k--; ) {
-      *(coordp++)= qh_divzero(*(normp++), -dist, qh->MINdenom_1, &zerodiv);
-      if (zerodiv)
-        goto LABELerroroutside;
-    }
-  }
-  *nextp= coordp;
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
-    for (k=dim, coordp=coords; k--; ) {
-      r= *coordp++;
-      qh_fprintf(qh, qh->ferr, 8022, " %6.2g", r);
-    }
-    qh_fprintf(qh, qh->ferr, 8023, "\n");
-  }
-  return True;
-LABELerroroutside:
-  feasiblep= feasible;
-  normp= normal;
-  qh_fprintf(qh, qh->ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh, qh->ferr, 8024, qh_REAL_1, r=*(feasiblep++));
-  qh_fprintf(qh, qh->ferr, 8025, "\n     halfspace: ");
-  for (k=dim; k--; )
-    qh_fprintf(qh, qh->ferr, 8026, qh_REAL_1, r=*(normp++));
-  qh_fprintf(qh, qh->ferr, 8027, "\n     at offset: ");
-  qh_fprintf(qh, qh->ferr, 8028, qh_REAL_1, *offset);
-  qh_fprintf(qh, qh->ferr, 8029, " and distance: ");
-  qh_fprintf(qh, qh->ferr, 8030, qh_REAL_1, dist);
-  qh_fprintf(qh, qh->ferr, 8031, "\n");
-  return False;
-} /* sethalfspace */
-
-/*---------------------------------
-
-  qh_sethalfspace_all(qh, dim, count, halfspaces, feasible )
-    generate dual for halfspace intersection with feasible point
-    array of count halfspaces
-      each halfspace is normal coefficients followed by offset
-      the origin is inside the halfspace if the offset is negative
-    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
-
-  returns:
-    malloc'd array of count X dim-1 points
-
-  notes:
-    call before qh_init_B or qh_initqhull_globals
-    free memory when done
-    unused/untested code: please email bradb@shore.net if this works ok for you
-    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
-    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
-
-  design:
-    see qh_sethalfspace
-*/
-coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible) {
-  int i, newdim;
-  pointT *newpoints;
-  coordT *coordp, *normalp, *offsetp;
-
-  trace0((qh, qh->ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
-  newdim= dim - 1;
-  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
-    qh_fprintf(qh, qh->ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
-          count);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coordp= newpoints;
-  normalp= halfspaces;
-  for (i=0; i < count; i++) {
-    offsetp= normalp + newdim;
-    if (!qh_sethalfspace(qh, newdim, coordp, &coordp, normalp, offsetp, feasible)) {
-      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
-      qh_fprintf(qh, qh->ferr, 8032, "The halfspace was at index %d\n", i);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    normalp= offsetp + 1;
-  }
-  return newpoints;
-} /* sethalfspace_all */
-
-
-/*---------------------------------
-
-  qh_sharpnewfacets(qh)
-
-  returns:
-    true if could be an acute angle (facets in different quadrants)
-
-  notes:
-    for qh_findbest
-
-  design:
-    for all facets on qh.newfacet_list
-      if two facets are in different quadrants
-        set issharp
-*/
-boolT qh_sharpnewfacets(qhT *qh) {
-  facetT *facet;
-  boolT issharp = False;
-  int *quadrant, k;
-
-  quadrant= (int*)qh_memalloc(qh, qh->hull_dim * sizeof(int));
-  FORALLfacet_(qh->newfacet_list) {
-    if (facet == qh->newfacet_list) {
-      for (k=qh->hull_dim; k--; )
-        quadrant[ k]= (facet->normal[ k] > 0);
-    }else {
-      for (k=qh->hull_dim; k--; ) {
-        if (quadrant[ k] != (facet->normal[ k] > 0)) {
-          issharp= True;
-          break;
-        }
-      }
-    }
-    if (issharp)
-      break;
-  }
-  qh_memfree(qh, quadrant, qh->hull_dim * sizeof(int));
-  trace3((qh, qh->ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
-  return issharp;
-} /* sharpnewfacets */
-
-/*---------------------------------
-
-  qh_voronoi_center(qh, dim, points )
-    return Voronoi center for a set of points
-    dim is the orginal dimension of the points
-    gh.gm_matrix/qh.gm_row are scratch buffers
-
-  returns:
-    center as a temporary point (qh_memalloc)
-    if non-simplicial,
-      returns center for max simplex of points
-
-  notes:
-    only called by qh_facetcenter
-    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
-
-  design:
-    if non-simplicial
-      determine max simplex for points
-    translate point0 of simplex to origin
-    compute sum of squares of diagonal
-    compute determinate
-    compute Voronoi center (see Bowyer & Woodwark)
-*/
-pointT *qh_voronoi_center(qhT *qh, int dim, setT *points) {
-  pointT *point, **pointp, *point0;
-  pointT *center= (pointT*)qh_memalloc(qh, qh->center_size);
-  setT *simplex;
-  int i, j, k, size= qh_setsize(qh, points);
-  coordT *gmcoord;
-  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
-  boolT nearzero, infinite;
-
-  if (size == dim+1)
-    simplex= points;
-  else if (size < dim+1) {
-    qh_memfree(qh, center, qh->center_size);
-    qh_fprintf(qh, qh->ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
-             dim+1);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    simplex= points;  /* never executed -- avoids warning */
-  }else {
-    simplex= qh_settemp(qh, dim+1);
-    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
-  }
-  point0= SETfirstt_(simplex, pointT);
-  gmcoord= qh->gm_matrix;
-  for (k=0; k < dim; k++) {
-    qh->gm_row[k]= gmcoord;
-    FOREACHpoint_(simplex) {
-      if (point != point0)
-        *(gmcoord++)= point[k] - point0[k];
-    }
-  }
-  sum2row= gmcoord;
-  for (i=0; i < dim; i++) {
-    sum2= 0.0;
-    for (k=0; k < dim; k++) {
-      diffp= qh->gm_row[k] + i;
-      sum2 += *diffp * *diffp;
-    }
-    *(gmcoord++)= sum2;
-  }
-  det= qh_determinant(qh, qh->gm_row, dim, &nearzero);
-  factor= qh_divzero(0.5, det, qh->MINdenom, &infinite);
-  if (infinite) {
-    for (k=dim; k--; )
-      center[k]= (float)qh_INFINITE;
-    if (qh->IStracing)
-      qh_printpoints(qh, qh->ferr, "qh_voronoi_center: at infinity for ", simplex);
-  }else {
-    for (i=0; i < dim; i++) {
-      gmcoord= qh->gm_matrix;
-      sum2p= sum2row;
-      for (k=0; k < dim; k++) {
-        qh->gm_row[k]= gmcoord;
-        if (k == i) {
-          for (j=dim; j--; )
-            *(gmcoord++)= *sum2p++;
-        }else {
-          FOREACHpoint_(simplex) {
-            if (point != point0)
-              *(gmcoord++)= point[k] - point0[k];
-          }
-        }
-      }
-      center[i]= qh_determinant(qh, qh->gm_row, dim, &nearzero)*factor + point0[i];
-    }
-#ifndef qh_NOtrace
-    if (qh->IStracing >= 3) {
-      qh_fprintf(qh, qh->ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
-      qh_printmatrix(qh, qh->ferr, "center:", ¢er, 1, dim);
-      if (qh->IStracing >= 5) {
-        qh_printpoints(qh, qh->ferr, "points", simplex);
-        FOREACHpoint_(simplex)
-          qh_fprintf(qh, qh->ferr, 8034, "p%d dist %.2g, ", qh_pointid(qh, point),
-                   qh_pointdist(point, center, dim));
-        qh_fprintf(qh, qh->ferr, 8035, "\n");
-      }
-    }
-#endif
-  }
-  if (simplex != points)
-    qh_settempfree(qh, &simplex);
-  return center;
-} /* voronoi_center */
-
diff --git a/src/qhull/src/libqhull_r/geom_r.c b/src/qhull/src/libqhull_r/geom_r.c
deleted file mode 100644
index 8104813ca..000000000
--- a/src/qhull/src/libqhull_r/geom_r.c
+++ /dev/null
@@ -1,1234 +0,0 @@
-/*
      ---------------------------------
-
-   geom_r.c
-   geometric routines of qhull
-
-   see qh-geom_r.htm and geom_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/geom_r.c#2 $$Change: 1995 $
-   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
-
-   infrequent code goes into geom2_r.c
-*/
-
-#include "qhull_ra.h"
-
-/*---------------------------------
-
-  qh_distplane(qh, point, facet, dist )
-    return distance from point to facet
-
-  returns:
-    dist
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    dist > 0 if point is above facet (i.e., outside)
-    does not error (for qh_sortfacets, qh_outerinner)
-
-  see:
-    qh_distnorm in geom2_r.c
-    qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
-*/
-void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
-  coordT *normal= facet->normal, *coordp, randr;
-  int k;
-
-  switch (qh->hull_dim){
-  case 2:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
-    break;
-  case 3:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
-    break;
-  case 4:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
-    break;
-  case 5:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
-    break;
-  case 6:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
-    break;
-  case 7:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
-    break;
-  case 8:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
-    break;
-  default:
-    *dist= facet->offset;
-    coordp= point;
-    for (k=qh->hull_dim; k--; )
-      *dist += *coordp++ * *normal++;
-    break;
-  }
-  zinc_(Zdistplane);
-  if (!qh->RANDOMdist && qh->IStracing < 4)
-    return;
-  if (qh->RANDOMdist) {
-    randr= qh_RANDOMint;
-    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh->RANDOMfactor * qh->MAXabs_coord;
-  }
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
-    qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
-    qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
-  }
-  return;
-} /* distplane */
-
-
-/*---------------------------------
-
-  qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
-    find facet that is furthest below a point
-    for upperDelaunay facets
-      returns facet only if !qh_NOupper and clearly above
-
-  input:
-    starts search at 'startfacet' (can not be flipped)
-    if !bestoutside(qh_ALL), stops at qh.MINoutside
-
-  returns:
-    best facet (reports error if NULL)
-    early out if isoutside defined and bestdist > qh.MINoutside
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart counts the number of distance tests
-
-  see also:
-    qh_findbestnew()
-
-  notes:
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
-      avoid calls to distplane, function calls, and real number operations.
-    caller traces result
-    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
-    Made code more complicated.
-
-  when called by qh_partitionvisible():
-    indicated by qh_ISnewfacets
-    qh.newfacet_list is list of simplicial, new facets
-    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
-    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
-
-  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
-                 qh_check_bestdist(), qh_addpoint()
-    indicated by !qh_ISnewfacets
-    returns best facet in neighborhood of given facet
-      this is best facet overall if dist > -   qh.MAXcoplanar
-        or hull has at least a "spherical" curvature
-
-  design:
-    initialize and test for early exit
-    repeat while there are better facets
-      for each neighbor of facet
-        exit if outside facet found
-        test for better facet
-    if point is inside and partitioning
-      test for new facets with a "sharp" intersection
-      if so, future calls go to qh_findbestnew()
-    test horizon facets
-*/
-facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT isnewfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  facetT *facet, *neighbor, **neighborp;
-  facetT *bestfacet= NULL, *lastfacet= NULL;
-  int oldtrace= qh->IStracing;
-  unsigned int visitid= ++qh->visit_id;
-  int numpartnew=0;
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  zinc_(Zfindbest);
-  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
-    if (qh->TRACElevel > qh->IStracing)
-      qh->IStracing= qh->TRACElevel;
-    qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
-             qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
-    qh_fprintf(qh, qh->ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
-    qh_fprintf(qh, qh->ferr, 8006, "  Last point added was p%d.", qh->furthest_id);
-    qh_fprintf(qh, qh->ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
-  }
-  if (isoutside)
-    *isoutside= True;
-  if (!startfacet->flipped) {  /* test startfacet */
-    *numpart= 1;
-    qh_distplane(qh, point, startfacet, dist);  /* this code is duplicated below */
-    if (!bestoutside && *dist >= qh->MINoutside
-    && (!startfacet->upperdelaunay || !noupper)) {
-      bestfacet= startfacet;
-      goto LABELreturn_best;
-    }
-    bestdist= *dist;
-    if (!startfacet->upperdelaunay) {
-      bestfacet= startfacet;
-    }
-  }else
-    *numpart= 0;
-  startfacet->visitid= visitid;
-  facet= startfacet;
-  while (facet) {
-    trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
-                facet->id, bestdist, getid_(bestfacet)));
-    lastfacet= facet;
-    FOREACHneighbor_(facet) {
-      if (!neighbor->newfacet && isnewfacets)
-        continue;
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {  /* code duplicated above */
-        (*numpart)++;
-        qh_distplane(qh, point, neighbor, dist);
-        if (*dist > bestdist) {
-          if (!bestoutside && *dist >= qh->MINoutside
-          && (!neighbor->upperdelaunay || !noupper)) {
-            bestfacet= neighbor;
-            goto LABELreturn_best;
-          }
-          if (!neighbor->upperdelaunay) {
-            bestfacet= neighbor;
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }else if (!bestfacet) {
-            bestdist= *dist;
-            break; /* switch to neighbor */
-          }
-        } /* end of *dist>bestdist */
-      } /* end of !flipped */
-    } /* end of FOREACHneighbor */
-    facet= neighbor;  /* non-NULL only if *dist>bestdist */
-  } /* end of while facet (directed search) */
-  if (isnewfacets) {
-    if (!bestfacet) {
-      bestdist= -REALmax/2;
-      bestfacet= qh_findbestnew(qh, point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
-      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-    }else if (!qh->findbest_notsharp && bestdist < - qh->DISTround) {
-      if (qh_sharpnewfacets(qh)) {
-        /* seldom used, qh_findbestnew will retest all facets */
-        zinc_(Zfindnewsharp);
-        bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
-        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-        qh->findbestnew= True;
-      }else
-        qh->findbest_notsharp= True;
-    }
-  }
-  if (!bestfacet)
-    bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart);
-  if (testhorizon)
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
-  *dist= bestdist;
-  if (isoutside && bestdist < qh->MINoutside)
-    *isoutside= False;
-LABELreturn_best:
-  zadd_(Zfindbesttot, *numpart);
-  zmax_(Zfindbestmax, *numpart);
-  (*numpart) += numpartnew;
-  qh->IStracing= oldtrace;
-  return bestfacet;
-}  /* findbest */
-
-
-/*---------------------------------
-
-  qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
-    search coplanar and better horizon facets from startfacet/bestdist
-    ischeckmax turns off statistics and minsearch update
-    all arguments must be initialized
-  returns(ischeckmax):
-    best facet
-  returns(!ischeckmax):
-    best facet that is not upperdelaunay
-    allows upperdelaunay that is clearly outside
-  returns:
-    bestdist is distance to bestfacet
-    numpart -- updates number of distance tests
-
-  notes:
-    no early out -- use qh_findbest() or qh_findbestnew()
-    Searches coplanar or better horizon facets
-
-  when called by qh_check_maxout() (qh_IScheckmax)
-    startfacet must be closest to the point
-      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
-      even though other facets are below the point.
-    updates facet->maxoutside for good, visited facets
-    may return NULL
-
-    searchdist is qh.max_outside + 2 * DISTround
-      + max( MINvisible('Vn'), MAXcoplanar('Un'));
-    This setting is a guess.  It must be at least max_outside + 2*DISTround
-    because a facet may have a geometric neighbor across a vertex
-
-  design:
-    for each horizon facet of coplanar best facets
-      continue if clearly inside
-      unless upperdelaunay or clearly outside
-         update best facet
-*/
-facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
-  facetT *bestfacet= startfacet;
-  realT dist;
-  facetT *neighbor, **neighborp, *facet;
-  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
-  int numpartinit= *numpart, coplanarfacetset_size;
-  unsigned int visitid= ++qh->visit_id;
-  boolT newbest= False; /* for tracing */
-  realT minsearch, searchdist;  /* skip facets that are too far from point */
-
-  if (!ischeckmax) {
-    zinc_(Zfindhorizon);
-  }else {
-#if qh_MAXoutside
-    if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
-      startfacet->maxoutside= *bestdist;
-#endif
-  }
-  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
-  minsearch= *bestdist - searchdist;
-  if (ischeckmax) {
-    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
-    minimize_(minsearch, -searchdist);
-  }
-  coplanarfacetset_size= 0;
-  facet= startfacet;
-  while (True) {
-    trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
-                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
-                minsearch, searchdist));
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == visitid)
-        continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {
-        qh_distplane(qh, point, neighbor, &dist);
-        (*numpart)++;
-        if (dist > *bestdist) {
-          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
-            bestfacet= neighbor;
-            *bestdist= dist;
-            newbest= True;
-            if (!ischeckmax) {
-              minsearch= dist - searchdist;
-              if (dist > *bestdist + searchdist) {
-                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
-                coplanarfacetset_size= 0;
-              }
-            }
-          }
-        }else if (dist < minsearch)
-          continue;  /* if ischeckmax, dist can't be positive */
-#if qh_MAXoutside
-        if (ischeckmax && dist > neighbor->maxoutside)
-          neighbor->maxoutside= dist;
-#endif
-      } /* end of !flipped */
-      if (nextfacet) {
-        if (!coplanarfacetset_size++) {
-          SETfirst_(qh->coplanarfacetset)= nextfacet;
-          SETtruncate_(qh->coplanarfacetset, 1);
-        }else
-          qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
-                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
-      }
-      nextfacet= neighbor;
-    } /* end of EACHneighbor */
-    facet= nextfacet;
-    if (facet)
-      nextfacet= NULL;
-    else if (!coplanarfacetset_size)
-      break;
-    else if (!--coplanarfacetset_size) {
-      facet= SETfirstt_(qh->coplanarfacetset, facetT);
-      SETtruncate_(qh->coplanarfacetset, 0);
-    }else
-      facet= (facetT*)qh_setdellast(qh->coplanarfacetset);
-  } /* while True, for each facet in qh.coplanarfacetset */
-  if (!ischeckmax) {
-    zadd_(Zfindhorizontot, *numpart - numpartinit);
-    zmax_(Zfindhorizonmax, *numpart - numpartinit);
-    if (newbest)
-      zinc_(Zparthorizon);
-  }
-  trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
-  return bestfacet;
-}  /* findbesthorizon */
-
-/*---------------------------------
-
-  qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
-    find best newfacet for point
-    searches all of qh.newfacet_list starting at startfacet
-    searches horizon facets of coplanar best newfacets
-    searches all facets if startfacet == qh.facet_list
-  returns:
-    best new or horizon facet that is not upperdelaunay
-    early out if isoutside and not 'Qf'
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart is number of distance tests
-
-  notes:
-    Always used for merged new facets (see qh_USEfindbestnew)
-    Avoids upperdelaunay facet unless (isoutside and outside)
-
-    Uses qh.visit_id, qh.coplanarfacetset.
-    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
-
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    a point maybe coplanar to the bestfacet, below its horizon facet,
-    and above a horizon facet of a coplanar newfacet.  For example,
-      rbox 1000 s Z1 G1e-13 | qhull
-      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
-
-    qh_findbestnew() used if
-       qh_sharpnewfacets -- newfacets contains a sharp angle
-       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
-
-  see also:
-    qh_partitionall() and qh_findbest()
-
-  design:
-    for each new facet starting from startfacet
-      test distance from point to facet
-      return facet if clearly outside
-      unless upperdelaunay and a lowerdelaunay exists
-         update best facet
-    test horizon facets
-*/
-facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
-           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2;
-  facetT *bestfacet= NULL, *facet;
-  int oldtrace= qh->IStracing, i;
-  unsigned int visitid= ++qh->visit_id;
-  realT distoutside= 0.0;
-  boolT isdistoutside; /* True if distoutside is defined */
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  if (!startfacet) {
-    if (qh->MERGING)
-      qh_fprintf(qh, qh->ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
-    else
-      qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
-              qh->furthest_id);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  zinc_(Zfindnew);
-  if (qh->BESToutside || bestoutside)
-    isdistoutside= False;
-  else {
-    isdistoutside= True;
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-  }
-  if (isoutside)
-    *isoutside= True;
-  *numpart= 0;
-  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
-    if (qh->TRACElevel > qh->IStracing)
-      qh->IStracing= qh->TRACElevel;
-    qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
-             qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
-    qh_fprintf(qh, qh->ferr, 8009, "  Last point added p%d visitid %d.",  qh->furthest_id, visitid);
-    qh_fprintf(qh, qh->ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
-  }
-  /* visit all new facets starting with startfacet, maybe qh->facet_list */
-  for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
-    FORALLfacet_(facet) {
-      if (facet == startfacet && i)
-        break;
-      facet->visitid= visitid;
-      if (!facet->flipped) {
-        qh_distplane(qh, point, facet, dist);
-        (*numpart)++;
-        if (*dist > bestdist) {
-          if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
-            bestfacet= facet;
-            if (isdistoutside && *dist >= distoutside)
-              goto LABELreturn_bestnew;
-            bestdist= *dist;
-          }
-        }
-      } /* end of !flipped */
-    } /* FORALLfacet from startfacet or qh->newfacet_list */
-  }
-  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
-                                        !qh_NOupper, &bestdist, numpart);
-  *dist= bestdist;
-  if (isoutside && *dist < qh->MINoutside)
-    *isoutside= False;
-LABELreturn_bestnew:
-  zadd_(Zfindnewtot, *numpart);
-  zmax_(Zfindnewmax, *numpart);
-  trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
-  qh->IStracing= oldtrace;
-  return bestfacet;
-}  /* findbestnew */
-
-/* ============ hyperplane functions -- keep code together [?] ============ */
-
-/*---------------------------------
-
-  qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
-    given an upper-triangular rows array and a sign,
-    solve for normal equation x using back substitution over rows U
-
-  returns:
-     normal= x
-
-     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
-       if fails on last row
-         this means that the hyperplane intersects [0,..,1]
-         sets last coordinate of normal to sign
-       otherwise
-         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
-         sets nearzero
-
-  notes:
-     assumes numrow == numcol-1
-
-     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
-
-     solves Ux=b where Ax=b and PA=LU
-     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
-     last row of A= [0,...,0,1]
-
-     1) Ly=Pb == y=b since P only permutes the 0's of   b
-
-  design:
-    for each row from end
-      perform back substitution
-      if near zero
-        use qh_divzero for division
-        if zero divide and not last row
-          set tail of normal to 0
-*/
-void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
-        coordT *normal, boolT *nearzero) {
-  int i, j;
-  coordT *normalp, *normal_tail, *ai, *ak;
-  realT diagonal;
-  boolT waszero;
-  int zerocol= -1;
-
-  normalp= normal + numcol - 1;
-  *normalp--= (sign ? -1.0 : 1.0);
-  for (i=numrow; i--; ) {
-    *normalp= 0.0;
-    ai= rows[i] + i + 1;
-    ak= normalp+1;
-    for (j=i+1; j < numcol; j++)
-      *normalp -= *ai++ * *ak++;
-    diagonal= (rows[i])[i];
-    if (fabs_(diagonal) > qh->MINdenom_2)
-      *(normalp--) /= diagonal;
-    else {
-      waszero= False;
-      *normalp= qh_divzero(*normalp, diagonal, qh->MINdenom_1_2, &waszero);
-      if (waszero) {
-        zerocol= i;
-        *(normalp--)= (sign ? -1.0 : 1.0);
-        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
-          *normal_tail= 0.0;
-      }else
-        normalp--;
-    }
-  }
-  if (zerocol != -1) {
-    zzinc_(Zback0);
-    *nearzero= True;
-    trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
-    qh_precision(qh, "zero diagonal on back substitution");
-  }
-} /* backnormal */
-
-/*---------------------------------
-
-  qh_gausselim(qh, rows, numrow, numcol, sign )
-    Gaussian elimination with partial pivoting
-
-  returns:
-    rows is upper triangular (includes row exchanges)
-    flips sign for each row exchange
-    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
-
-  notes:
-    if nearzero, the determinant's sign may be incorrect.
-    assumes numrow <= numcol
-
-  design:
-    for each row
-      determine pivot and exchange rows if necessary
-      test for near zero
-      perform gaussian elimination step
-*/
-void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
-  realT *ai, *ak, *rowp, *pivotrow;
-  realT n, pivot, pivot_abs= 0.0, temp;
-  int i, j, k, pivoti, flip=0;
-
-  *nearzero= False;
-  for (k=0; k < numrow; k++) {
-    pivot_abs= fabs_((rows[k])[k]);
-    pivoti= k;
-    for (i=k+1; i < numrow; i++) {
-      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
-        pivot_abs= temp;
-        pivoti= i;
-      }
-    }
-    if (pivoti != k) {
-      rowp= rows[pivoti];
-      rows[pivoti]= rows[k];
-      rows[k]= rowp;
-      *sign ^= 1;
-      flip ^= 1;
-    }
-    if (pivot_abs <= qh->NEARzero[k]) {
-      *nearzero= True;
-      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
-        if (qh->IStracing >= 4) {
-          qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
-          qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
-        }
-        zzinc_(Zgauss0);
-        qh_precision(qh, "zero pivot for Gaussian elimination");
-        goto LABELnextcol;
-      }
-    }
-    pivotrow= rows[k] + k;
-    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
-    for (i=k+1; i < numrow; i++) {
-      ai= rows[i] + k;
-      ak= pivotrow;
-      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
-      for (j= numcol - (k+1); j--; )
-        *ai++ -= n * *ak++;
-    }
-  LABELnextcol:
-    ;
-  }
-  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
-  if (qh->IStracing >= 5)
-    qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
-} /* gausselim */
-
-
-/*---------------------------------
-
-  qh_getangle(qh, vect1, vect2 )
-    returns the dot product of two vectors
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    the angle may be > 1.0 or < -1.0 because of roundoff errors
-
-*/
-realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
-  realT angle= 0, randr;
-  int k;
-
-  for (k=qh->hull_dim; k--; )
-    angle += *vect1++ * *vect2++;
-  if (qh->RANDOMdist) {
-    randr= qh_RANDOMint;
-    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh->RANDOMfactor;
-  }
-  trace4((qh, qh->ferr, 4006, "qh_getangle: %2.2g\n", angle));
-  return(angle);
-} /* getangle */
-
-
-/*---------------------------------
-
-  qh_getcenter(qh, vertices )
-    returns arithmetic center of a set of vertices as a new point
-
-  notes:
-    allocates point array for center
-*/
-pointT *qh_getcenter(qhT *qh, setT *vertices) {
-  int k;
-  pointT *center, *coord;
-  vertexT *vertex, **vertexp;
-  int count= qh_setsize(qh, vertices);
-
-  if (count < 2) {
-    qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  center= (pointT *)qh_memalloc(qh, qh->normal_size);
-  for (k=0; k < qh->hull_dim; k++) {
-    coord= center+k;
-    *coord= 0.0;
-    FOREACHvertex_(vertices)
-      *coord += vertex->point[k];
-    *coord /= count;  /* count>=2 by QH6003 */
-  }
-  return(center);
-} /* getcenter */
-
-
-/*---------------------------------
-
-  qh_getcentrum(qh, facet )
-    returns the centrum for a facet as a new point
-
-  notes:
-    allocates the centrum
-*/
-pointT *qh_getcentrum(qhT *qh, facetT *facet) {
-  realT dist;
-  pointT *centrum, *point;
-
-  point= qh_getcenter(qh, facet->vertices);
-  zzinc_(Zcentrumtests);
-  qh_distplane(qh, point, facet, &dist);
-  centrum= qh_projectpoint(qh, point, facet, dist);
-  qh_memfree(qh, point, qh->normal_size);
-  trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
-          facet->id, qh_setsize(qh, facet->vertices), dist));
-  return centrum;
-} /* getcentrum */
-
-
-/*---------------------------------
-
-  qh_getdistance(qh, facet, neighbor, mindist, maxdist )
-    returns the maxdist and mindist distance of any vertex from neighbor
-
-  returns:
-    the max absolute value
-
-  design:
-    for each vertex of facet that is not in neighbor
-      test the distance from vertex to neighbor
-*/
-realT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
-  vertexT *vertex, **vertexp;
-  realT dist, maxd, mind;
-
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHvertex_(neighbor->vertices)
-    vertex->seen= True;
-  mind= 0.0;
-  maxd= 0.0;
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      zzinc_(Zbestdist);
-      qh_distplane(qh, vertex->point, neighbor, &dist);
-      if (dist < mind)
-        mind= dist;
-      else if (dist > maxd)
-        maxd= dist;
-    }
-  }
-  *mindist= mind;
-  *maxdist= maxd;
-  mind= -mind;
-  if (maxd > mind)
-    return maxd;
-  else
-    return mind;
-} /* getdistance */
-
-
-/*---------------------------------
-
-  qh_normalize(qh, normal, dim, toporient )
-    normalize a vector and report if too small
-    does not use min norm
-
-  see:
-    qh_normalize2
-*/
-void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
-  qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-} /* normalize */
-
-/*---------------------------------
-
-  qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
-    normalize a vector and report if too small
-    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
-
-  returns:
-    normalized vector
-    flips sign if !toporient
-    if minnorm non-NULL,
-      sets ismin if normal < minnorm
-
-  notes:
-    if zero norm
-       sets all elements to sqrt(1.0/dim)
-    if divide by zero (divzero())
-       sets largest element to   +/-1
-       bumps Znearlysingular
-
-  design:
-    computes norm
-    test for minnorm
-    if not near zero
-      normalizes normal
-    else if zero norm
-      sets normal to standard value
-    else
-      uses qh_divzero to normalize
-      if nearzero
-        sets norm to direction of maximum value
-*/
-void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin) {
-  int k;
-  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
-  boolT zerodiv;
-
-  norm1= normal+1;
-  norm2= normal+2;
-  norm3= normal+3;
-  if (dim == 2)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
-  else if (dim == 3)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
-  else if (dim == 4) {
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3));
-  }else if (dim > 4) {
-    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3);
-    for (k=dim-4, colp=normal+4; k--; colp++)
-      norm += (*colp) * (*colp);
-    norm= sqrt(norm);
-  }
-  if (minnorm) {
-    if (norm < *minnorm)
-      *ismin= True;
-    else
-      *ismin= False;
-  }
-  wmin_(Wmindenom, norm);
-  if (norm > qh->MINdenom) {
-    if (!toporient)
-      norm= -norm;
-    *normal /= norm;
-    *norm1 /= norm;
-    if (dim == 2)
-      ; /* all done */
-    else if (dim == 3)
-      *norm2 /= norm;
-    else if (dim == 4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-    }else if (dim >4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-      for (k=dim-4, colp=normal+4; k--; )
-        *colp++ /= norm;
-    }
-  }else if (norm == 0.0) {
-    temp= sqrt(1.0/dim);
-    for (k=dim, colp=normal; k--; )
-      *colp++ = temp;
-  }else {
-    if (!toporient)
-      norm= -norm;
-    for (k=dim, colp=normal; k--; colp++) { /* k used below */
-      temp= qh_divzero(*colp, norm, qh->MINdenom_1, &zerodiv);
-      if (!zerodiv)
-        *colp= temp;
-      else {
-        maxp= qh_maxabsval(normal, dim);
-        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
-        for (k=dim, colp=normal; k--; colp++)
-          *colp= 0.0;
-        *maxp= temp;
-        zzinc_(Znearlysingular);
-        trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
-               norm, qh->furthest_id));
-        return;
-      }
-    }
-  }
-} /* normalize */
-
-
-/*---------------------------------
-
-  qh_projectpoint(qh, point, facet, dist )
-    project point onto a facet by dist
-
-  returns:
-    returns a new point
-
-  notes:
-    if dist= distplane(point,facet)
-      this projects point to hyperplane
-    assumes qh_memfree_() is valid for normal_size
-*/
-pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
-  pointT *newpoint, *np, *normal;
-  int normsize= qh->normal_size;
-  int k;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
-  np= newpoint;
-  normal= facet->normal;
-  for (k=qh->hull_dim; k--; )
-    *(np++)= *point++ - dist * *normal++;
-  return(newpoint);
-} /* projectpoint */
-
-
-/*---------------------------------
-
-  qh_setfacetplane(qh, facet )
-    sets the hyperplane for a facet
-    if qh.RANDOMdist, joggles hyperplane
-
-  notes:
-    uses global buffers qh.gm_matrix and qh.gm_row
-    overwrites facet->normal if already defined
-    updates Wnewvertex if PRINTstatistics
-    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
-
-  design:
-    copy vertex coordinates to qh.gm_matrix/gm_row
-    compute determinate
-    if nearzero
-      recompute determinate with gaussian elimination
-      if nearzero
-        force outside orientation by testing interior point
-*/
-void qh_setfacetplane(qhT *qh, facetT *facet) {
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int normsize= qh->normal_size;
-  int k,i, oldtrace= 0;
-  realT dist;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-  coordT *coord, *gmcoord;
-  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
-  boolT nearzero= False;
-
-  zzinc_(Zsetplane);
-  if (!facet->normal)
-    qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
-  if (facet == qh->tracefacet) {
-    oldtrace= qh->IStracing;
-    qh->IStracing= 5;
-    qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
-    qh_fprintf(qh, qh->ferr, 8013, "  Last point added to hull was p%d.", qh->furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh, qh->ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
-    qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
-      qh_printsummary(qh, qh->ferr);
-  }
-  if (qh->hull_dim <= 4) {
-    i= 0;
-    if (qh->RANDOMdist) {
-      gmcoord= qh->gm_matrix;
-      FOREACHvertex_(facet->vertices) {
-        qh->gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++)= *coord++ * qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
-      }
-    }else {
-      FOREACHvertex_(facet->vertices)
-       qh->gm_row[i++]= vertex->point;
-    }
-    qh_sethyperplane_det(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-  }
-  if (qh->hull_dim > 4 || nearzero) {
-    i= 0;
-    gmcoord= qh->gm_matrix;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        qh->gm_row[i++]= gmcoord;
-        coord= vertex->point;
-        point= point0;
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++)= *coord++ - *point++;
-      }
-    }
-    qh->gm_row[i]= gmcoord;  /* for areasimplex */
-    if (qh->RANDOMdist) {
-      gmcoord= qh->gm_matrix;
-      for (i=qh->hull_dim-1; i--; ) {
-        for (k=qh->hull_dim; k--; )
-          *(gmcoord++) *= qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
-      }
-    }
-    qh_sethyperplane_gauss(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-    if (nearzero) {
-      if (qh_orientoutside(qh, facet)) {
-        trace0((qh, qh->ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh->furthest_id));
-      /* this is part of using Gaussian Elimination.  For example in 5-d
-           1 1 1 1 0
-           1 1 1 1 1
-           0 0 0 1 0
-           0 1 0 0 0
-           1 0 0 0 0
-           norm= 0.38 0.38 -0.76 0.38 0
-         has a determinate of 1, but g.e. after subtracting pt. 0 has
-         0's in the diagonal, even with full pivoting.  It does work
-         if you subtract pt. 4 instead. */
-      }
-    }
-  }
-  facet->upperdelaunay= False;
-  if (qh->DELAUNAY) {
-    if (qh->UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
-      if (facet->normal[qh->hull_dim -1] >= qh->ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }else {
-      if (facet->normal[qh->hull_dim -1] > -qh->ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }
-  }
-  if (qh->PRINTstatistics || qh->IStracing || qh->TRACElevel || qh->JOGGLEmax < REALmax) {
-    qh->old_randomdist= qh->RANDOMdist;
-    qh->RANDOMdist= False;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-        boolT istrace= False;
-        zinc_(Zdiststat);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        dist= fabs_(dist);
-        zinc_(Znewvertex);
-        wadd_(Wnewvertex, dist);
-        if (dist > wwval_(Wnewvertexmax)) {
-          wwval_(Wnewvertexmax)= dist;
-          if (dist > qh->max_outside) {
-            qh->max_outside= dist;  /* used by qh_maxouter(qh) */
-            if (dist > qh->TRACEdist)
-              istrace= True;
-          }
-        }else if (-dist > qh->TRACEdist)
-          istrace= True;
-        if (istrace) {
-          qh_fprintf(qh, qh->ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
-                qh_pointid(qh, vertex->point), vertex->id, dist, facet->id, qh->furthest_id);
-          qh_errprint(qh, "DISTANT", facet, NULL, NULL, NULL);
-        }
-      }
-    }
-    qh->RANDOMdist= qh->old_randomdist;
-  }
-  if (qh->IStracing >= 3) {
-    qh_fprintf(qh, qh->ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
-             facet->id, facet->offset);
-    for (k=0; k < qh->hull_dim; k++)
-      qh_fprintf(qh, qh->ferr, 8018, "%2.2g ", facet->normal[k]);
-    qh_fprintf(qh, qh->ferr, 8019, "\n");
-  }
-  if (facet == qh->tracefacet)
-    qh->IStracing= oldtrace;
-} /* setfacetplane */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_det(qh, dim, rows, point0, toporient, normal, offset, nearzero )
-    given dim X dim array indexed by rows[], one row per point,
-        toporient(flips all signs),
-        and point0 (any row)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-    sets nearzero if hyperplane not through points
-
-  notes:
-    only defined for dim == 2..4
-    rows[] is not modified
-    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
-    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
-
-  derivation of 3-d minnorm
-    Goal: all vertices V_i within qh.one_merge of hyperplane
-    Plan: exactly translate the facet so that V_0 is the origin
-          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
-          exactly rotate the effective perturbation to only effect n_0
-             this introduces a factor of sqrt(3)
-    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
-    Let M_d be the max coordinate difference
-    Let M_a be the greater of M_d and the max abs. coordinate
-    Let u be machine roundoff and distround be max error for distance computation
-    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
-    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
-    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
-
-  derivation of 4-d minnorm
-    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
-     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
-    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
-     [all other terms contain at least two factors nearly zero.]
-    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
-    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
-*/
-void qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
-          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
-  realT maxround, dist;
-  int i;
-  pointT *point;
-
-
-  if (dim == 2) {
-    normal[0]= dY(1,0);
-    normal[1]= dX(0,1);
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
-    *nearzero= False;  /* since nearzero norm => incident points */
-  }else if (dim == 3) {
-    normal[0]= det2_(dY(2,0), dZ(2,0),
-                     dY(1,0), dZ(1,0));
-    normal[1]= det2_(dX(1,0), dZ(1,0),
-                     dX(2,0), dZ(2,0));
-    normal[2]= det2_(dX(2,0), dY(2,0),
-                     dX(1,0), dY(1,0));
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2]);
-    maxround= qh->DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }else if (dim == 4) {
-    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
-                        dY(1,0), dZ(1,0), dW(1,0),
-                        dY(3,0), dZ(3,0), dW(3,0));
-    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
-                        dX(1,0), dZ(1,0), dW(1,0),
-                        dX(3,0), dZ(3,0), dW(3,0));
-    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
-                        dX(1,0), dY(1,0), dW(1,0),
-                        dX(3,0), dY(3,0), dW(3,0));
-    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
-                        dX(1,0), dY(1,0), dZ(1,0),
-                        dX(3,0), dY(3,0), dZ(3,0));
-    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-               + point0[2]*normal[2] + point0[3]*normal[3]);
-    maxround= qh->DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-               + point[2]*normal[2] + point[3]*normal[3]);
-        if (dist > maxround || dist < -maxround) {
-          *nearzero= True;
-          break;
-        }
-      }
-    }
-  }
-  if (*nearzero) {
-    zzinc_(Zminnorm);
-    trace0((qh, qh->ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh->furthest_id));
-    zzinc_(Znearlysingular);
-  }
-} /* sethyperplane_det */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_gauss(qh, dim, rows, point0, toporient, normal, offset, nearzero )
-    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-
-  notes:
-    if nearzero
-      orientation may be incorrect because of incorrect sign flips in gausselim
-    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
-        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
-    i.e., N is normal to the hyperplane, and the unnormalized
-        distance to [0 .. 1] is either 1 or   0
-
-  design:
-    perform gaussian elimination
-    flip sign for negative values
-    perform back substitution
-    normalize result
-    compute offset
-*/
-void qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
-                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
-  coordT *pointcoord, *normalcoef;
-  int k;
-  boolT sign= toporient, nearzero2= False;
-
-  qh_gausselim(qh, rows, dim-1, dim, &sign, nearzero);
-  for (k=dim-1; k--; ) {
-    if ((rows[k])[k] < 0)
-      sign ^= 1;
-  }
-  if (*nearzero) {
-    zzinc_(Znearlysingular);
-    trace0((qh, qh->ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh->furthest_id));
-    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
-  }else {
-    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
-    if (nearzero2) {
-      zzinc_(Znearlysingular);
-      trace0((qh, qh->ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh->furthest_id));
-    }
-  }
-  if (nearzero2)
-    *nearzero= True;
-  qh_normalize2(qh, normal, dim, True, NULL, NULL);
-  pointcoord= point0;
-  normalcoef= normal;
-  *offset= -(*pointcoord++ * *normalcoef++);
-  for (k=dim-1; k--; )
-    *offset -= *pointcoord++ * *normalcoef++;
-} /* sethyperplane_gauss */
-
-
-
diff --git a/src/qhull/src/libqhull_r/geom_r.h b/src/qhull/src/libqhull_r/geom_r.h
deleted file mode 100644
index d73e95345..000000000
--- a/src/qhull/src/libqhull_r/geom_r.h
+++ /dev/null
@@ -1,184 +0,0 @@
-/*
      ---------------------------------
-
-  geom_r.h
-    header file for geometric routines
-
-   see qh-geom_r.htm and geom_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/geom_r.h#3 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-#include "libqhull_r.h"
-
-/* ============ -macros- ======================== */
-
-/*----------------------------------
-
-  fabs_(a)
-    returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*----------------------------------
-
-  fmax_(a,b)
-    returns the maximum value of a and b
-*/
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  fmin_(a,b)
-    returns the minimum value of a and b
-*/
-#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  maximize_(maxval, val)
-    set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
-
-/*----------------------------------
-
-  minimize_(minval, val)
-    set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
-
-/*----------------------------------
-
-  det2_(a1, a2,
-        b1, b2)
-
-    compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*----------------------------------
-
-  det3_(a1, a2, a3,
-       b1, b2, b3,
-       c1, c2, c3)
-
-    compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
-                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*----------------------------------
-
-  dX( p1, p2 )
-  dY( p1, p2 )
-  dZ( p1, p2 )
-
-    given two indices into rows[],
-
-    compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void    qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
-void    qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist);
-facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT isnewfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT *point,
-                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
-facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet, realT *dist,
-                     boolT bestoutside, boolT *isoutside, int *numpart);
-void    qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
-realT   qh_getangle(qhT *qh, pointT *vect1, pointT *vect2);
-pointT *qh_getcenter(qhT *qh, setT *vertices);
-pointT *qh_getcentrum(qhT *qh, facetT *facet);
-realT   qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
-void    qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient);
-void    qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin);
-pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist);
-
-void    qh_setfacetplane(qhT *qh, facetT *newfacets);
-void    qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
-              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
-void    qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
-             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
-boolT   qh_sharpnewfacets(qhT *qh);
-
-/*========= infrequently used code in geom2_r.c =============*/
-
-coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension);
-void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT   qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero);
-realT   qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension);
-void    qh_detroundoff(qhT *qh);
-realT   qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero);
-realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
-realT   qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs);
-realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
-realT   qh_facetarea(qhT *qh, facetT *facet);
-realT   qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
-          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
-pointT *qh_facetcenter(qhT *qh, setT *vertices);
-facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
-void    qh_getarea(qhT *qh, facetT *facetlist);
-boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
-boolT   qh_inthresholds(qhT *qh, coordT *normal, realT *angle);
-void    qh_joggleinput(qhT *qh);
-realT  *qh_maxabsval(realT *normal, int dim);
-setT   *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension);
-realT   qh_maxouter(qhT *qh);
-void    qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
-realT   qh_minabsval(realT *normal, int dim);
-int     qh_mindiff(realT *vecA, realT *vecB, int dim);
-boolT   qh_orientoutside(qhT *qh, facetT *facet);
-void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
-coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
-void    qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol);
-void    qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points);
-void    qh_projectinput(qhT *qh);
-void    qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
-             int numpoints, int dim, realT *newpoints, int newdim);
-void    qh_rotateinput(qhT *qh, realT **rows);
-void    qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **rows);
-void    qh_scaleinput(qhT *qh);
-void    qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
-                   coordT high, coordT newhigh);
-void    qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
-                realT *newlows, realT *newhighs);
-boolT   qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
-              coordT *normal, coordT *offset, coordT *feasible);
-coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
-pointT *qh_voronoi_center(qhT *qh, int dim, setT *points);
-
-#ifdef __cplusplus
-} /* extern "C"*/
-#endif
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/src/qhull/src/libqhull_r/global_r.c b/src/qhull/src/libqhull_r/global_r.c
deleted file mode 100644
index eef465ca1..000000000
--- a/src/qhull/src/libqhull_r/global_r.c
+++ /dev/null
@@ -1,2100 +0,0 @@
-
-/*
      ---------------------------------
-
-   global_r.c
-   initializes all the globals of the qhull application
-
-   see README
-
-   see libqhull_r.h for qh.globals and function prototypes
-
-   see qhull_ra.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/global_r.c#16 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
- */
-
-#include "qhull_ra.h"
-
-/*========= qh->definition -- globals defined in libqhull_r.h =======================*/
-
-/*----------------------------------
-
-  qh_version
-    version string by year and date
-    qh_version2 for Unix users and -V
-
-    the revision increases on code changes only
-
-  notes:
-    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
-                    qhull-news.html, Eudora signatures, CMakeLists.txt
-    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
-    check that CmakeLists @version is the same as qh_version2
-    change year:    Copying.txt
-    check download size
-    recompile user_eg_r.c, rbox_r.c, libqhull_r.c, qconvex_r.c, qdelaun_r.c qvoronoi_r.c, qhalf_r.c, testqset_r.c
-*/
-
-const char qh_version[]= "2015.2.r 2016/01/18";
-const char qh_version2[]= "qhull_r 7.2.0 (2015.2.r 2016/01/18)";
-
-/*---------------------------------
-
-  qh_appendprint(qh, printFormat )
-    append printFormat to qh.PRINTout unless already defined
-*/
-void qh_appendprint(qhT *qh, qh_PRINT format) {
-  int i;
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    if (qh->PRINTout[i] == format && format != qh_PRINTqhull)
-      break;
-    if (!qh->PRINTout[i]) {
-      qh->PRINTout[i]= format;
-      break;
-    }
-  }
-} /* appendprint */
-
-/*---------------------------------
-
-  qh_checkflags(qh, commandStr, hiddenFlags )
-    errors if commandStr contains hiddenFlags
-    hiddenFlags starts and ends with a space and is space delimited (checked)
-
-  notes:
-    ignores first word (e.g., "qconvex i")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initflags() initializes Qhull according to commandStr
-*/
-void qh_checkflags(qhT *qh, char *command, char *hiddenflags) {
-  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
-  char key, opt, prevopt;
-  char chkkey[]= "   ";
-  char chkopt[]=  "    ";
-  char chkopt2[]= "     ";
-  boolT waserr= False;
-
-  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
-    qh_fprintf(qh, qh->ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (strpbrk(hiddenflags, ",\n\r\t")) {
-    qh_fprintf(qh, qh->ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    key = *s++;
-    chkerr = NULL;
-    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
-      s= qh_skipfilename(qh, ++s);
-      continue;
-    }
-    chkkey[1]= key;
-    if (strstr(hiddenflags, chkkey)) {
-      chkerr= chkkey;
-    }else if (isupper(key)) {
-      opt= ' ';
-      prevopt= ' ';
-      chkopt[1]= key;
-      chkopt2[1]= key;
-      while (!chkerr && *s && !isspace(*s)) {
-        opt= *s++;
-        if (isalpha(opt)) {
-          chkopt[2]= opt;
-          if (strstr(hiddenflags, chkopt))
-            chkerr= chkopt;
-          if (prevopt != ' ') {
-            chkopt2[2]= prevopt;
-            chkopt2[3]= opt;
-            if (strstr(hiddenflags, chkopt2))
-              chkerr= chkopt2;
-          }
-        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
-              && (prevopt == ' ' || islower(prevopt))) {
-            chkopt[2]= opt;
-            if (strstr(hiddenflags, chkopt))
-              chkerr= chkopt;
-        }else {
-          qh_strtod(s-1, &t);
-          if (s < t)
-            s= t;
-        }
-        prevopt= opt;
-      }
-    }
-    if (chkerr) {
-      *chkerr= '\'';
-      chkerr[strlen(chkerr)-1]=  '\'';
-      qh_fprintf(qh, qh->ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
-      waserr= True;
-    }
-  }
-  if (waserr)
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-} /* checkflags */
-
-/*---------------------------------
-
-  qh_clear_outputflags(qh)
-    Clear output flags for QhullPoints
-*/
-void qh_clear_outputflags(qhT *qh) {
-  int i,k;
-
-  qh->ANNOTATEoutput= False;
-  qh->DOintersections= False;
-  qh->DROPdim= -1;
-  qh->FORCEoutput= False;
-  qh->GETarea= False;
-  qh->GOODpoint= 0;
-  qh->GOODpointp= NULL;
-  qh->GOODthreshold= False;
-  qh->GOODvertex= 0;
-  qh->GOODvertexp= NULL;
-  qh->IStracing= 0;
-  qh->KEEParea= False;
-  qh->KEEPmerge= False;
-  qh->KEEPminArea= REALmax;
-  qh->PRINTcentrums= False;
-  qh->PRINTcoplanar= False;
-  qh->PRINTdots= False;
-  qh->PRINTgood= False;
-  qh->PRINTinner= False;
-  qh->PRINTneighbors= False;
-  qh->PRINTnoplanes= False;
-  qh->PRINToptions1st= False;
-  qh->PRINTouter= False;
-  qh->PRINTprecision= True;
-  qh->PRINTridges= False;
-  qh->PRINTspheres= False;
-  qh->PRINTstatistics= False;
-  qh->PRINTsummary= False;
-  qh->PRINTtransparent= False;
-  qh->SPLITthresholds= False;
-  qh->TRACElevel= 0;
-  qh->TRInormals= False;
-  qh->USEstdout= False;
-  qh->VERIFYoutput= False;
-  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh->lower_threshold[k]= -REALmax;
-    qh->upper_threshold[k]= REALmax;
-    qh->lower_bound[k]= -REALmax;
-    qh->upper_bound[k]= REALmax;
-  }
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    qh->PRINTout[i]= qh_PRINTnone;
-  }
-
-  if (!qh->qhull_commandsiz2)
-      qh->qhull_commandsiz2= (int)strlen(qh->qhull_command); /* WARN64 */
-  else {
-      qh->qhull_command[qh->qhull_commandsiz2]= '\0';
-  }
-  if (!qh->qhull_optionsiz2)
-    qh->qhull_optionsiz2= (int)strlen(qh->qhull_options);  /* WARN64 */
-  else {
-    qh->qhull_options[qh->qhull_optionsiz2]= '\0';
-    qh->qhull_optionlen= qh_OPTIONline;  /* start a new line */
-  }
-} /* clear_outputflags */
-
-/*---------------------------------
-
-  qh_clock()
-    return user CPU time in 100ths (qh_SECtick)
-    only defined for qh_CLOCKtype == 2
-
-  notes:
-    use first value to determine time 0
-    from Stevens '92 8.15
-*/
-unsigned long qh_clock(qhT *qh) {
-
-#if (qh_CLOCKtype == 2)
-  struct tms time;
-  static long clktck;  /* initialized first call and never updated */
-  double ratio, cpu;
-  unsigned long ticks;
-
-  if (!clktck) {
-    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
-      qh_fprintf(qh, qh->ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-  }
-  if (times(&time) == -1) {
-    qh_fprintf(qh, qh->ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  ratio= qh_SECticks / (double)clktck;
-  ticks= time.tms_utime * ratio;
-  return ticks;
-#else
-  qh_fprintf(qh, qh->ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
-  qh_errexit(qh, qh_ERRqhull, NULL, NULL); /* never returns */
-  return 0;
-#endif
-} /* clock */
-
-/*---------------------------------
-
-  qh_freebuffers()
-    free up global memory buffers
-
-  notes:
-    must match qh_initbuffers()
-*/
-void qh_freebuffers(qhT *qh) {
-
-  trace5((qh, qh->ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
-  /* allocated by qh_initqhull_buffers */
-  qh_memfree(qh, qh->NEARzero, qh->hull_dim * sizeof(realT));
-  qh_memfree(qh, qh->lower_threshold, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->upper_threshold, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->lower_bound, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->upper_bound, (qh->input_dim+1) * sizeof(realT));
-  qh_memfree(qh, qh->gm_matrix, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
-  qh_memfree(qh, qh->gm_row, (qh->hull_dim+1) * sizeof(coordT *));
-  qh->NEARzero= qh->lower_threshold= qh->upper_threshold= NULL;
-  qh->lower_bound= qh->upper_bound= NULL;
-  qh->gm_matrix= NULL;
-  qh->gm_row= NULL;
-  qh_setfree(qh, &qh->other_points);
-  qh_setfree(qh, &qh->del_vertices);
-  qh_setfree(qh, &qh->coplanarfacetset);
-  if (qh->line)                /* allocated by qh_readinput, freed if no error */
-    qh_free(qh->line);
-  if (qh->half_space)
-    qh_free(qh->half_space);
-  if (qh->temp_malloc)
-    qh_free(qh->temp_malloc);
-  if (qh->feasible_point)      /* allocated by qh_readfeasible */
-    qh_free(qh->feasible_point);
-  if (qh->feasible_string)     /* allocated by qh_initflags */
-    qh_free(qh->feasible_string);
-  qh->line= qh->feasible_string= NULL;
-  qh->half_space= qh->feasible_point= qh->temp_malloc= NULL;
-  /* usually allocated by qh_readinput */
-  if (qh->first_point && qh->POINTSmalloc) {
-    qh_free(qh->first_point);
-    qh->first_point= NULL;
-  }
-  if (qh->input_points && qh->input_malloc) { /* set by qh_joggleinput */
-    qh_free(qh->input_points);
-    qh->input_points= NULL;
-  }
-  trace5((qh, qh->ferr, 5002, "qh_freebuffers: finished\n"));
-} /* freebuffers */
-
-
-/*---------------------------------
-
-  qh_freebuild(qh, allmem )
-    free global memory used by qh_initbuild and qh_buildhull
-    if !allmem,
-      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
-
-  design:
-    free centrums
-    free each vertex
-    mark unattached ridges
-    for each facet
-      free ridges
-      free outside set, coplanar set, neighbor set, ridge set, vertex set
-      free facet
-    free hash table
-    free interior point
-    free merge set
-    free temporary sets
-*/
-void qh_freebuild(qhT *qh, boolT allmem) {
-  facetT *facet;
-  vertexT *vertex;
-  ridgeT *ridge, **ridgep;
-  mergeT *merge, **mergep;
-
-  trace1((qh, qh->ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
-  if (qh->del_vertices)
-    qh_settruncate(qh, qh->del_vertices, 0);
-  if (allmem) {
-    while ((vertex= qh->vertex_list)) {
-      if (vertex->next)
-        qh_delvertex(qh, vertex);
-      else {
-        qh_memfree(qh, vertex, (int)sizeof(vertexT));
-        qh->newvertex_list= qh->vertex_list= NULL;
-      }
-    }
-  }else if (qh->VERTEXneighbors) {
-    FORALLvertices
-      qh_setfreelong(qh, &(vertex->neighbors));
-  }
-  qh->VERTEXneighbors= False;
-  qh->GOODclosest= NULL;
-  if (allmem) {
-    FORALLfacets {
-      FOREACHridge_(facet->ridges)
-        ridge->seen= False;
-    }
-    FORALLfacets {
-      if (facet->visible) {
-        FOREACHridge_(facet->ridges) {
-          if (!otherfacet_(ridge, facet)->visible)
-            ridge->seen= True;  /* an unattached ridge */
-        }
-      }
-    }
-    while ((facet= qh->facet_list)) {
-      FOREACHridge_(facet->ridges) {
-        if (ridge->seen) {
-          qh_setfree(qh, &(ridge->vertices));
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }else
-          ridge->seen= True;
-      }
-      qh_setfree(qh, &(facet->outsideset));
-      qh_setfree(qh, &(facet->coplanarset));
-      qh_setfree(qh, &(facet->neighbors));
-      qh_setfree(qh, &(facet->ridges));
-      qh_setfree(qh, &(facet->vertices));
-      if (facet->next)
-        qh_delfacet(qh, facet);
-      else {
-        qh_memfree(qh, facet, (int)sizeof(facetT));
-        qh->visible_list= qh->newfacet_list= qh->facet_list= NULL;
-      }
-    }
-  }else {
-    FORALLfacets {
-      qh_setfreelong(qh, &(facet->outsideset));
-      qh_setfreelong(qh, &(facet->coplanarset));
-      if (!facet->simplicial) {
-        qh_setfreelong(qh, &(facet->neighbors));
-        qh_setfreelong(qh, &(facet->ridges));
-        qh_setfreelong(qh, &(facet->vertices));
-      }
-    }
-  }
-  qh_setfree(qh, &(qh->hash_table));
-  qh_memfree(qh, qh->interior_point, qh->normal_size);
-  qh->interior_point= NULL;
-  FOREACHmerge_(qh->facet_mergeset)  /* usually empty */
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-  qh->facet_mergeset= NULL;  /* temp set */
-  qh->degen_mergeset= NULL;  /* temp set */
-  qh_settempfree_all(qh);
-} /* freebuild */
-
-/*---------------------------------
-
-  qh_freeqhull(qh, allmem )
-
-  free global memory and set qhT to 0
-  if !allmem,
-    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
-
-notes:
-  sets qh.NOerrexit in case caller forgets to
-  Does not throw errors
-
-see:
-  see qh_initqhull_start2()
-  For libqhull_r, qhstatT is part of qhT
-
-design:
-  free global and temporary memory from qh_initbuild and qh_buildhull
-  free buffers
-*/
-void qh_freeqhull(qhT *qh, boolT allmem) {
-
-  qh->NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
-  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
-  qh_freebuild(qh, allmem);
-  qh_freebuffers(qh);
-  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
-  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));
-  qh->NOerrexit= True;
-} /* freeqhull2 */
-
-/*---------------------------------
-
-  qh_init_A(qh, infile, outfile, errfile, argc, argv )
-    initialize memory and stdio files
-    convert input options to option string (qh.qhull_command)
-
-  notes:
-    infile may be NULL if qh_readpoints() is not called
-
-    errfile should always be defined.  It is used for reporting
-    errors.  outfile is used for output and format options.
-
-    argc/argv may be 0/NULL
-
-    called before error handling initialized
-    qh_errexit() may not be used
-*/
-void qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
-  qh_meminit(qh, errfile);
-  qh_initqhull_start(qh, infile, outfile, errfile);
-  qh_init_qhull_command(qh, argc, argv);
-} /* init_A */
-
-/*---------------------------------
-
-  qh_init_B(qh, points, numpoints, dim, ismalloc )
-    initialize globals for points array
-
-    points has numpoints dim-dimensional points
-      points[0] is the first coordinate of the first point
-      points[1] is the second coordinate of the first point
-      points[dim] is the first coordinate of the second point
-
-    ismalloc=True
-      Qhull will call qh_free(points) on exit or input transformation
-    ismalloc=False
-      Qhull will allocate a new point array if needed for input transformation
-
-    qh.qhull_command
-      is the option string.
-      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
-
-  returns:
-    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
-      projects the input to a new point array
-
-        if qh.DELAUNAY,
-          qh.hull_dim is increased by one
-        if qh.ATinfinity,
-          qh_projectinput adds point-at-infinity for Delaunay tri.
-
-    if qh.SCALEinput
-      changes the upper and lower bounds of the input, see qh_scaleinput(qh)
-
-    if qh.ROTATEinput
-      rotates the input by a random rotation, see qh_rotateinput()
-      if qh.DELAUNAY
-        rotates about the last coordinate
-
-  notes:
-    called after points are defined
-    qh_errexit() may be used
-*/
-void qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
-  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc);
-  if (qh->qhmem.LASTsize == 0)
-    qh_initqhull_mem(qh);
-  /* mem_r.c and qset_r.c are initialized */
-  qh_initqhull_buffers(qh);
-  qh_initthresholds(qh, qh->qhull_command);
-  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay))
-    qh_projectinput(qh);
-  if (qh->SCALEinput)
-    qh_scaleinput(qh);
-  if (qh->ROTATErandom >= 0) {
-    qh_randommatrix(qh, qh->gm_matrix, qh->hull_dim, qh->gm_row);
-    if (qh->DELAUNAY) {
-      int k, lastk= qh->hull_dim-1;
-      for (k=0; k < lastk; k++) {
-        qh->gm_row[k][lastk]= 0.0;
-        qh->gm_row[lastk][k]= 0.0;
-      }
-      qh->gm_row[lastk][lastk]= 1.0;
-    }
-    qh_gram_schmidt(qh, qh->hull_dim, qh->gm_row);
-    qh_rotateinput(qh, qh->gm_row);
-  }
-} /* init_B */
-
-/*---------------------------------
-
-  qh_init_qhull_command(qh, argc, argv )
-    build qh.qhull_command from argc/argv
-    Calls qh_exit if qhull_command is too short
-
-  returns:
-    a space-delimited string of options (just as typed)
-
-  notes:
-    makes option string easy to input and output
-
-    argc/argv may be 0/NULL
-*/
-void qh_init_qhull_command(qhT *qh, int argc, char *argv[]) {
-
-  if (!qh_argv_to_command(argc, argv, qh->qhull_command, (int)sizeof(qh->qhull_command))){
-    /* Assumes qh.ferr is defined. */
-    qh_fprintf(qh, qh->ferr, 6033, "qhull input error: more than %d characters in command line.\n",
-          (int)sizeof(qh->qhull_command));
-    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
-  }
-} /* init_qhull_command */
-
-/*---------------------------------
-
-  qh_initflags(qh, commandStr )
-    set flags and initialized constants from commandStr
-    calls qh_exit() if qh->NOerrexit
-
-  returns:
-    sets qh.qhull_command to command if needed
-
-  notes:
-    ignores first word (e.g., "qhull d")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
-    'prompt' in unix_r.c for documentation
-
-  design:
-    for each space-delimited option group
-      if top-level option
-        check syntax
-        append appropriate option to option string
-        set appropriate global variable or append printFormat to print options
-      else
-        for each sub-option
-          check syntax
-          append appropriate option to option string
-          set appropriate global variable or append printFormat to print options
-*/
-void qh_initflags(qhT *qh, char *command) {
-  int k, i, lastproject;
-  char *s= command, *t, *prev_s, *start, key;
-  boolT isgeom= False, wasproject;
-  realT r;
-
-  if(qh->NOerrexit){
-    qh_fprintf(qh, qh->ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
-    qh_exit(6245);
-  }
-  if (command <= &qh->qhull_command[0] || command > &qh->qhull_command[0] + sizeof(qh->qhull_command)) {
-    if (command != &qh->qhull_command[0]) {
-      *qh->qhull_command= '\0';
-      strncat(qh->qhull_command, command, sizeof(qh->qhull_command)-strlen(qh->qhull_command)-1);
-    }
-    while (*s && !isspace(*s))  /* skip program name */
-      s++;
-  }
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    prev_s= s;
-    switch (*s++) {
-    case 'd':
-      qh_option(qh, "delaunay", NULL, NULL);
-      qh->DELAUNAY= True;
-      break;
-    case 'f':
-      qh_option(qh, "facets", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTfacets);
-      break;
-    case 'i':
-      qh_option(qh, "incidence", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTincidences);
-      break;
-    case 'm':
-      qh_option(qh, "mathematica", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTmathematica);
-      break;
-    case 'n':
-      qh_option(qh, "normals", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTnormals);
-      break;
-    case 'o':
-      qh_option(qh, "offFile", NULL, NULL);
-      qh_appendprint(qh, qh_PRINToff);
-      break;
-    case 'p':
-      qh_option(qh, "points", NULL, NULL);
-      qh_appendprint(qh, qh_PRINTpoints);
-      break;
-    case 's':
-      qh_option(qh, "summary", NULL, NULL);
-      qh->PRINTsummary= True;
-      break;
-    case 'v':
-      qh_option(qh, "voronoi", NULL, NULL);
-      qh->VORONOI= True;
-      qh->DELAUNAY= True;
-      break;
-    case 'A':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh->premerge_cos= -qh_strtod(s, &s);
-          qh_option(qh, "Angle-premerge-", NULL, &qh->premerge_cos);
-          qh->PREmerge= True;
-        }else {
-          qh->postmerge_cos= qh_strtod(s, &s);
-          qh_option(qh, "Angle-postmerge", NULL, &qh->postmerge_cos);
-          qh->POSTmerge= True;
-        }
-        qh->MERGING= True;
-      }
-      break;
-    case 'C':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
-      else {
-        if (*s == '-') {
-          qh->premerge_centrum= -qh_strtod(s, &s);
-          qh_option(qh, "Centrum-premerge-", NULL, &qh->premerge_centrum);
-          qh->PREmerge= True;
-        }else {
-          qh->postmerge_centrum= qh_strtod(s, &s);
-          qh_option(qh, "Centrum-postmerge", NULL, &qh->postmerge_centrum);
-          qh->POSTmerge= True;
-        }
-        qh->MERGING= True;
-      }
-      break;
-    case 'E':
-      if (*s == '-')
-        qh_fprintf(qh, qh->ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
-      else {
-        qh->DISTround= qh_strtod(s, &s);
-        qh_option(qh, "Distance-roundoff", NULL, &qh->DISTround);
-        qh->SETroundoff= True;
-      }
-      break;
-    case 'H':
-      start= s;
-      qh->HALFspace= True;
-      qh_strtod(s, &t);
-      while (t > s)  {
-        if (*t && !isspace(*t)) {
-          if (*t == ',')
-            t++;
-          else
-            qh_fprintf(qh, qh->ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
-        }
-        s= t;
-        qh_strtod(s, &t);
-      }
-      if (start < t) {
-        if (!(qh->feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
-          qh_fprintf(qh, qh->ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
-          qh_errexit(qh, qh_ERRmem, NULL, NULL);
-        }
-        strncpy(qh->feasible_string, start, (size_t)(t-start));
-        qh_option(qh, "Halfspace-about", NULL, NULL);
-        qh_option(qh, qh->feasible_string, NULL, NULL);
-      }else
-        qh_option(qh, "Halfspace", NULL, NULL);
-      break;
-    case 'R':
-      if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
-      else {
-        qh->RANDOMfactor= qh_strtod(s, &s);
-        qh_option(qh, "Random_perturb", NULL, &qh->RANDOMfactor);
-        qh->RANDOMdist= True;
-      }
-      break;
-    case 'V':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
-      else {
-        qh->MINvisible= qh_strtod(s, &s);
-        qh_option(qh, "Visible", NULL, &qh->MINvisible);
-      }
-      break;
-    case 'U':
-      if (!isdigit(*s) && *s != '-')
-        qh_fprintf(qh, qh->ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
-      else {
-        qh->MAXcoplanar= qh_strtod(s, &s);
-        qh_option(qh, "U-coplanar", NULL, &qh->MAXcoplanar);
-      }
-      break;
-    case 'W':
-      if (*s == '-')
-        qh_fprintf(qh, qh->ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
-      else if (!isdigit(*s))
-        qh_fprintf(qh, qh->ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
-      else {
-        qh->MINoutside= qh_strtod(s, &s);
-        qh_option(qh, "W-outside", NULL, &qh->MINoutside);
-        qh->APPROXhull= True;
-      }
-      break;
-    /************  sub menus ***************/
-    case 'F':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option(qh, "Farea", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTarea);
-          qh->GETarea= True;
-          break;
-        case 'A':
-          qh_option(qh, "FArea-total", NULL, NULL);
-          qh->GETarea= True;
-          break;
-        case 'c':
-          qh_option(qh, "Fcoplanars", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTcoplanars);
-          break;
-        case 'C':
-          qh_option(qh, "FCentrums", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTcentrums);
-          break;
-        case 'd':
-          qh_option(qh, "Fd-cdd-in", NULL, NULL);
-          qh->CDDinput= True;
-          break;
-        case 'D':
-          qh_option(qh, "FD-cdd-out", NULL, NULL);
-          qh->CDDoutput= True;
-          break;
-        case 'F':
-          qh_option(qh, "FFacets-xridge", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTfacets_xridge);
-          break;
-        case 'i':
-          qh_option(qh, "Finner", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTinner);
-          break;
-        case 'I':
-          qh_option(qh, "FIDs", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTids);
-          break;
-        case 'm':
-          qh_option(qh, "Fmerges", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTmerges);
-          break;
-        case 'M':
-          qh_option(qh, "FMaple", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTmaple);
-          break;
-        case 'n':
-          qh_option(qh, "Fneighbors", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTneighbors);
-          break;
-        case 'N':
-          qh_option(qh, "FNeighbors-vertex", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTvneighbors);
-          break;
-        case 'o':
-          qh_option(qh, "Fouter", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTouter);
-          break;
-        case 'O':
-          if (qh->PRINToptions1st) {
-            qh_option(qh, "FOptions", NULL, NULL);
-            qh_appendprint(qh, qh_PRINToptions);
-          }else
-            qh->PRINToptions1st= True;
-          break;
-        case 'p':
-          qh_option(qh, "Fpoint-intersect", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTpointintersect);
-          break;
-        case 'P':
-          qh_option(qh, "FPoint-nearest", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTpointnearest);
-          break;
-        case 'Q':
-          qh_option(qh, "FQhull", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTqhull);
-          break;
-        case 's':
-          qh_option(qh, "Fsummary", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTsummary);
-          break;
-        case 'S':
-          qh_option(qh, "FSize", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTsize);
-          qh->GETarea= True;
-          break;
-        case 't':
-          qh_option(qh, "Ftriangles", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTtriangles);
-          break;
-        case 'v':
-          /* option set in qh_initqhull_globals */
-          qh_appendprint(qh, qh_PRINTvertices);
-          break;
-        case 'V':
-          qh_option(qh, "FVertex-average", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTaverage);
-          break;
-        case 'x':
-          qh_option(qh, "Fxtremes", NULL, NULL);
-          qh_appendprint(qh, qh_PRINTextremes);
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'G':
-      isgeom= True;
-      qh_appendprint(qh, qh_PRINTgeom);
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'a':
-          qh_option(qh, "Gall-points", NULL, NULL);
-          qh->PRINTdots= True;
-          break;
-        case 'c':
-          qh_option(qh, "Gcentrums", NULL, NULL);
-          qh->PRINTcentrums= True;
-          break;
-        case 'h':
-          qh_option(qh, "Gintersections", NULL, NULL);
-          qh->DOintersections= True;
-          break;
-        case 'i':
-          qh_option(qh, "Ginner", NULL, NULL);
-          qh->PRINTinner= True;
-          break;
-        case 'n':
-          qh_option(qh, "Gno-planes", NULL, NULL);
-          qh->PRINTnoplanes= True;
-          break;
-        case 'o':
-          qh_option(qh, "Gouter", NULL, NULL);
-          qh->PRINTouter= True;
-          break;
-        case 'p':
-          qh_option(qh, "Gpoints", NULL, NULL);
-          qh->PRINTcoplanar= True;
-          break;
-        case 'r':
-          qh_option(qh, "Gridges", NULL, NULL);
-          qh->PRINTridges= True;
-          break;
-        case 't':
-          qh_option(qh, "Gtransparent", NULL, NULL);
-          qh->PRINTtransparent= True;
-          break;
-        case 'v':
-          qh_option(qh, "Gvertices", NULL, NULL);
-          qh->PRINTspheres= True;
-          break;
-        case 'D':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
-          else {
-            if (qh->DROPdim >= 0)
-              qh_fprintf(qh, qh->ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
-                   qh->DROPdim);
-            qh->DROPdim= qh_strtol(s, &s);
-            qh_option(qh, "GDrop-dim", &qh->DROPdim, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'P':
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'd': case 'D':  /* see qh_initthresholds() */
-          key= s[-1];
-          i= qh_strtol(s, &s);
-          r= 0;
-          if (*s == ':') {
-            s++;
-            r= qh_strtod(s, &s);
-          }
-          if (key == 'd')
-            qh_option(qh, "Pdrop-facets-dim-less", &i, &r);
-          else
-            qh_option(qh, "PDrop-facets-dim-more", &i, &r);
-          break;
-        case 'g':
-          qh_option(qh, "Pgood-facets", NULL, NULL);
-          qh->PRINTgood= True;
-          break;
-        case 'G':
-          qh_option(qh, "PGood-facet-neighbors", NULL, NULL);
-          qh->PRINTneighbors= True;
-          break;
-        case 'o':
-          qh_option(qh, "Poutput-forced", NULL, NULL);
-          qh->FORCEoutput= True;
-          break;
-        case 'p':
-          qh_option(qh, "Pprecision-ignore", NULL, NULL);
-          qh->PRINTprecision= False;
-          break;
-        case 'A':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
-          else {
-            qh->KEEParea= qh_strtol(s, &s);
-            qh_option(qh, "PArea-keep", &qh->KEEParea, NULL);
-            qh->GETarea= True;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
-          else {
-            qh->KEEPminArea= qh_strtod(s, &s);
-            qh_option(qh, "PFacet-area-keep", NULL, &qh->KEEPminArea);
-            qh->GETarea= True;
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
-          else {
-            qh->KEEPmerge= qh_strtol(s, &s);
-            qh_option(qh, "PMerge-keep", &qh->KEEPmerge, NULL);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'Q':
-      lastproject= -1;
-      while (*s && !isspace(*s)) {
-        switch (*s++) {
-        case 'b': case 'B':  /* handled by qh_initthresholds */
-          key= s[-1];
-          if (key == 'b' && *s == 'B') {
-            s++;
-            r= qh_DEFAULTbox;
-            qh->SCALEinput= True;
-            qh_option(qh, "QbBound-unit-box", NULL, &r);
-            break;
-          }
-          if (key == 'b' && *s == 'b') {
-            s++;
-            qh->SCALElast= True;
-            qh_option(qh, "Qbbound-last", NULL, NULL);
-            break;
-          }
-          k= qh_strtol(s, &s);
-          r= 0.0;
-          wasproject= False;
-          if (*s == ':') {
-            s++;
-            if ((r= qh_strtod(s, &s)) == 0.0) {
-              t= s;            /* need true dimension for memory allocation */
-              while (*t && !isspace(*t)) {
-                if (toupper(*t++) == 'B'
-                 && k == qh_strtol(t, &t)
-                 && *t++ == ':'
-                 && qh_strtod(t, &t) == 0.0) {
-                  qh->PROJECTinput++;
-                  trace2((qh, qh->ferr, 2004, "qh_initflags: project dimension %d\n", k));
-                  qh_option(qh, "Qb-project-dim", &k, NULL);
-                  wasproject= True;
-                  lastproject= k;
-                  break;
-                }
-              }
-            }
-          }
-          if (!wasproject) {
-            if (lastproject == k && r == 0.0)
-              lastproject= -1;  /* doesn't catch all possible sequences */
-            else if (key == 'b') {
-              qh->SCALEinput= True;
-              if (r == 0.0)
-                r= -qh_DEFAULTbox;
-              qh_option(qh, "Qbound-dim-low", &k, &r);
-            }else {
-              qh->SCALEinput= True;
-              if (r == 0.0)
-                r= qh_DEFAULTbox;
-              qh_option(qh, "QBound-dim-high", &k, &r);
-            }
-          }
-          break;
-        case 'c':
-          qh_option(qh, "Qcoplanar-keep", NULL, NULL);
-          qh->KEEPcoplanar= True;
-          break;
-        case 'f':
-          qh_option(qh, "Qfurthest-outside", NULL, NULL);
-          qh->BESToutside= True;
-          break;
-        case 'g':
-          qh_option(qh, "Qgood-facets-only", NULL, NULL);
-          qh->ONLYgood= True;
-          break;
-        case 'i':
-          qh_option(qh, "Qinterior-keep", NULL, NULL);
-          qh->KEEPinside= True;
-          break;
-        case 'm':
-          qh_option(qh, "Qmax-outside-only", NULL, NULL);
-          qh->ONLYmax= True;
-          break;
-        case 'r':
-          qh_option(qh, "Qrandom-outside", NULL, NULL);
-          qh->RANDOMoutside= True;
-          break;
-        case 's':
-          qh_option(qh, "Qsearch-initial-simplex", NULL, NULL);
-          qh->ALLpoints= True;
-          break;
-        case 't':
-          qh_option(qh, "Qtriangulate", NULL, NULL);
-          qh->TRIangulate= True;
-          break;
-        case 'T':
-          qh_option(qh, "QTestPoints", NULL, NULL);
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
-          else {
-            qh->TESTpoints= qh_strtol(s, &s);
-            qh_option(qh, "QTestPoints", &qh->TESTpoints, NULL);
-          }
-          break;
-        case 'u':
-          qh_option(qh, "QupperDelaunay", NULL, NULL);
-          qh->UPPERdelaunay= True;
-          break;
-        case 'v':
-          qh_option(qh, "Qvertex-neighbors-convex", NULL, NULL);
-          qh->TESTvneighbors= True;
-          break;
-        case 'x':
-          qh_option(qh, "Qxact-merge", NULL, NULL);
-          qh->MERGEexact= True;
-          break;
-        case 'z':
-          qh_option(qh, "Qz-infinity-point", NULL, NULL);
-          qh->ATinfinity= True;
-          break;
-        case '0':
-          qh_option(qh, "Q0-no-premerge", NULL, NULL);
-          qh->NOpremerge= True;
-          break;
-        case '1':
-          if (!isdigit(*s)) {
-            qh_option(qh, "Q1-no-angle-sort", NULL, NULL);
-            qh->ANGLEmerge= False;
-            break;
-          }
-          switch (*s++) {
-          case '0':
-            qh_option(qh, "Q10-no-narrow", NULL, NULL);
-            qh->NOnarrow= True;
-            break;
-          case '1':
-            qh_option(qh, "Q11-trinormals Qtriangulate", NULL, NULL);
-            qh->TRInormals= True;
-            qh->TRIangulate= True;
-            break;
-          case '2':
-              qh_option(qh, "Q12-no-wide-dup", NULL, NULL);
-              qh->NOwide= True;
-            break;
-          default:
-            s--;
-            qh_fprintf(qh, qh->ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
-            while (*++s && !isspace(*s));
-            break;
-          }
-          break;
-        case '2':
-          qh_option(qh, "Q2-no-merge-independent", NULL, NULL);
-          qh->MERGEindependent= False;
-          goto LABELcheckdigit;
-          break; /* no warnings */
-        case '3':
-          qh_option(qh, "Q3-no-merge-vertices", NULL, NULL);
-          qh->MERGEvertices= False;
-        LABELcheckdigit:
-          if (isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
-                     *s++);
-          break;
-        case '4':
-          qh_option(qh, "Q4-avoid-old-into-new", NULL, NULL);
-          qh->AVOIDold= True;
-          break;
-        case '5':
-          qh_option(qh, "Q5-no-check-outer", NULL, NULL);
-          qh->SKIPcheckmax= True;
-          break;
-        case '6':
-          qh_option(qh, "Q6-no-concave-merge", NULL, NULL);
-          qh->SKIPconvex= True;
-          break;
-        case '7':
-          qh_option(qh, "Q7-no-breadth-first", NULL, NULL);
-          qh->VIRTUALmemory= True;
-          break;
-        case '8':
-          qh_option(qh, "Q8-no-near-inside", NULL, NULL);
-          qh->NOnearinside= True;
-          break;
-        case '9':
-          qh_option(qh, "Q9-pick-furthest", NULL, NULL);
-          qh->PICKfurthest= True;
-          break;
-        case 'G':
-          i= qh_strtol(s, &t);
-          if (qh->GOODpoint)
-            qh_fprintf(qh, qh->ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh, qh->ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
-          else if (i < 0 || *s == '-') {
-            qh->GOODpoint= i-1;
-            qh_option(qh, "QGood-if-dont-see-point", &i, NULL);
-          }else {
-            qh->GOODpoint= i+1;
-            qh_option(qh, "QGood-if-see-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'J':
-          if (!isdigit(*s) && *s != '-')
-            qh->JOGGLEmax= 0.0;
-          else {
-            qh->JOGGLEmax= (realT) qh_strtod(s, &s);
-            qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s) && *s != '-')
-            qh_fprintf(qh, qh->ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
-          else {
-            qh->ROTATErandom= i= qh_strtol(s, &s);
-            if (i > 0)
-              qh_option(qh, "QRotate-id", &i, NULL );
-            else if (i < -1)
-              qh_option(qh, "QRandom-seed", &i, NULL );
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (qh->GOODvertex)
-            qh_fprintf(qh, qh->ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
-          else if (s == t)
-            qh_fprintf(qh, qh->ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
-          else if (i < 0) {
-            qh->GOODvertex= i - 1;
-            qh_option(qh, "QV-good-facets-not-point", &i, NULL);
-          }else {
-            qh_option(qh, "QV-good-facets-point", &i, NULL);
-            qh->GOODvertex= i + 1;
-          }
-          s= t;
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    case 'T':
-      while (*s && !isspace(*s)) {
-        if (isdigit(*s) || *s == '-')
-          qh->IStracing= qh_strtol(s, &s);
-        else switch (*s++) {
-        case 'a':
-          qh_option(qh, "Tannotate-output", NULL, NULL);
-          qh->ANNOTATEoutput= True;
-          break;
-        case 'c':
-          qh_option(qh, "Tcheck-frequently", NULL, NULL);
-          qh->CHECKfrequently= True;
-          break;
-        case 's':
-          qh_option(qh, "Tstatistics", NULL, NULL);
-          qh->PRINTstatistics= True;
-          break;
-        case 'v':
-          qh_option(qh, "Tverify", NULL, NULL);
-          qh->VERIFYoutput= True;
-          break;
-        case 'z':
-          if (qh->ferr == qh_FILEstderr) {
-            /* The C++ interface captures the output in qh_fprint_qhull() */
-            qh_option(qh, "Tz-stdout", NULL, NULL);
-            qh->USEstdout= True;
-          }else if (!qh->fout)
-            qh_fprintf(qh, qh->ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
-          else {
-            qh_option(qh, "Tz-stdout", NULL, NULL);
-            qh->USEstdout= True;
-            qh->ferr= qh->fout;
-            qh->qhmem.ferr= qh->fout;
-          }
-          break;
-        case 'C':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
-          else {
-            i= qh_strtol(s, &s);
-            qh_option(qh, "TCone-stop", &i, NULL);
-            qh->STOPcone= i + 1;
-          }
-          break;
-        case 'F':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
-          else {
-            qh->REPORTfreq= qh_strtol(s, &s);
-            qh_option(qh, "TFacet-log", &qh->REPORTfreq, NULL);
-            qh->REPORTfreq2= qh->REPORTfreq/2;  /* for tracemerging() */
-          }
-          break;
-        case 'I':
-          if (!isspace(*s))
-            qh_fprintf(qh, qh->ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
-          while (isspace(*s))
-            s++;
-          t= qh_skipfilename(qh, s);
-          {
-            char filename[qh_FILENAMElen];
-
-            qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
-            s= t;
-            if (!freopen(filename, "r", stdin)) {
-              qh_fprintf(qh, qh->ferr, 6041, "qhull error: could not open file \"%s\".", filename);
-              qh_errexit(qh, qh_ERRinput, NULL, NULL);
-            }else {
-              qh_option(qh, "TInput-file", NULL, NULL);
-              qh_option(qh, filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'O':
-            if (!isspace(*s))
-                qh_fprintf(qh, qh->ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
-            while (isspace(*s))
-                s++;
-            t= qh_skipfilename(qh, s);
-            {
-              char filename[qh_FILENAMElen];
-
-              qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
-              s= t;
-              if (!qh->fout) {
-                qh_fprintf(qh, qh->ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
-              }else if (!freopen(filename, "w", qh->fout)) {
-                qh_fprintf(qh, qh->ferr, 6044, "qhull error: could not open file \"%s\".", filename);
-                qh_errexit(qh, qh_ERRinput, NULL, NULL);
-              }else {
-                qh_option(qh, "TOutput-file", NULL, NULL);
-              qh_option(qh, filename, NULL, NULL);
-            }
-          }
-          break;
-        case 'P':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
-          else {
-            qh->TRACEpoint= qh_strtol(s, &s);
-            qh_option(qh, "Trace-point", &qh->TRACEpoint, NULL);
-          }
-          break;
-        case 'M':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
-          else {
-            qh->TRACEmerge= qh_strtol(s, &s);
-            qh_option(qh, "Trace-merge", &qh->TRACEmerge, NULL);
-          }
-          break;
-        case 'R':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
-          else {
-            qh->RERUN= qh_strtol(s, &s);
-            qh_option(qh, "TRerun", &qh->RERUN, NULL);
-          }
-          break;
-        case 'V':
-          i= qh_strtol(s, &t);
-          if (s == t)
-            qh_fprintf(qh, qh->ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
-          else if (i < 0) {
-            qh->STOPpoint= i - 1;
-            qh_option(qh, "TV-stop-before-point", &i, NULL);
-          }else {
-            qh->STOPpoint= i + 1;
-            qh_option(qh, "TV-stop-after-point", &i, NULL);
-          }
-          s= t;
-          break;
-        case 'W':
-          if (!isdigit(*s))
-            qh_fprintf(qh, qh->ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
-          else {
-            qh->TRACEdist= (realT) qh_strtod(s, &s);
-            qh_option(qh, "TWide-trace", NULL, &qh->TRACEdist);
-          }
-          break;
-        default:
-          s--;
-          qh_fprintf(qh, qh->ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
-          while (*++s && !isspace(*s));
-          break;
-        }
-      }
-      break;
-    default:
-      qh_fprintf(qh, qh->ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
-               (int)s[-1]);
-      break;
-    }
-    if (s-1 == prev_s && *s && !isspace(*s)) {
-      qh_fprintf(qh, qh->ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
-               (int)*prev_s, (int)*prev_s);
-      while (*s && !isspace(*s))
-        s++;
-    }
-  }
-  if (qh->STOPcone && qh->JOGGLEmax < REALmax/2)
-    qh_fprintf(qh, qh->ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
-  if (isgeom && !qh->FORCEoutput && qh->PRINTout[1])
-    qh_fprintf(qh, qh->ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
-  /* set derived values in qh_initqhull_globals */
-} /* initflags */
-
-
-/*---------------------------------
-
-  qh_initqhull_buffers(qh)
-    initialize global memory buffers
-
-  notes:
-    must match qh_freebuffers()
-*/
-void qh_initqhull_buffers(qhT *qh) {
-  int k;
-
-  qh->TEMPsize= (qh->qhmem.LASTsize - sizeof(setT))/SETelemsize;
-  if (qh->TEMPsize <= 0 || qh->TEMPsize > qh->qhmem.LASTsize)
-    qh->TEMPsize= 8;  /* e.g., if qh_NOmem */
-  qh->other_points= qh_setnew(qh, qh->TEMPsize);
-  qh->del_vertices= qh_setnew(qh, qh->TEMPsize);
-  qh->coplanarfacetset= qh_setnew(qh, qh->TEMPsize);
-  qh->NEARzero= (realT *)qh_memalloc(qh, qh->hull_dim * sizeof(realT));
-  qh->lower_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->upper_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->lower_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  qh->upper_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
-  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
-    qh->lower_threshold[k]= -REALmax;
-    qh->upper_threshold[k]= REALmax;
-    qh->lower_bound[k]= -REALmax;
-    qh->upper_bound[k]= REALmax;
-  }
-  qh->gm_matrix= (coordT *)qh_memalloc(qh, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
-  qh->gm_row= (coordT **)qh_memalloc(qh, (qh->hull_dim+1) * sizeof(coordT *));
-} /* initqhull_buffers */
-
-/*---------------------------------
-
-  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc )
-    initialize globals
-    if ismalloc
-      points were malloc'd and qhull should free at end
-
-  returns:
-    sets qh.first_point, num_points, input_dim, hull_dim and others
-    seeds random number generator (seed=1 if tracing)
-    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
-    adjust user flags as needed
-    also checks DIM3 dependencies and constants
-
-  notes:
-    do not use qh_point() since an input transformation may move them elsewhere
-
-  see:
-    qh_initqhull_start() sets default values for non-zero globals
-
-  design:
-    initialize points array from input arguments
-    test for qh.ZEROcentrum
-      (i.e., use opposite vertex instead of cetrum for convexity testing)
-    initialize qh.CENTERtype, qh.normal_size,
-      qh.center_size, qh.TRACEpoint/level,
-    initialize and test random numbers
-    qh_initqhull_outputflags() -- adjust and test output flags
-*/
-void qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
-  int seed, pointsneeded, extra= 0, i, randi, k;
-  realT randr;
-  realT factorial;
-
-  time_t timedata;
-
-  trace0((qh, qh->ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh->rbox_command,
-      qh->qhull_command));
-  qh->POINTSmalloc= ismalloc;
-  qh->first_point= points;
-  qh->num_points= numpoints;
-  qh->hull_dim= qh->input_dim= dim;
-  if (!qh->NOpremerge && !qh->MERGEexact && !qh->PREmerge && qh->JOGGLEmax > REALmax/2) {
-    qh->MERGING= True;
-    if (qh->hull_dim <= 4) {
-      qh->PREmerge= True;
-      qh_option(qh, "_pre-merge", NULL, NULL);
-    }else {
-      qh->MERGEexact= True;
-      qh_option(qh, "Qxact_merge", NULL, NULL);
-    }
-  }else if (qh->MERGEexact)
-    qh->MERGING= True;
-  if (!qh->NOpremerge && qh->JOGGLEmax > REALmax/2) {
-#ifdef qh_NOmerge
-    qh->JOGGLEmax= 0.0;
-#endif
-  }
-  if (qh->TRIangulate && qh->JOGGLEmax < REALmax/2 && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
-  if (qh->JOGGLEmax < REALmax/2 && qh->DELAUNAY && !qh->SCALEinput && !qh->SCALElast) {
-    qh->SCALElast= True;
-    qh_option(qh, "Qbbound-last-qj", NULL, NULL);
-  }
-  if (qh->MERGING && !qh->POSTmerge && qh->premerge_cos > REALmax/2
-  && qh->premerge_centrum == 0) {
-    qh->ZEROcentrum= True;
-    qh->ZEROall_ok= True;
-    qh_option(qh, "_zero-centrum", NULL, NULL);
-  }
-  if (qh->JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
-          REALepsilon);
-#ifdef qh_NOmerge
-  if (qh->MERGING) {
-    qh_fprintf(qh, qh->ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-#endif
-  if (qh->DELAUNAY && qh->KEEPcoplanar && !qh->KEEPinside) {
-    qh->KEEPinside= True;
-    qh_option(qh, "Qinterior-keep", NULL, NULL);
-  }
-  if (qh->DELAUNAY && qh->HALFspace) {
-    qh_fprintf(qh, qh->ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (!qh->DELAUNAY && (qh->UPPERdelaunay || qh->ATinfinity)) {
-    qh_fprintf(qh, qh->ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->UPPERdelaunay && qh->ATinfinity) {
-    qh_fprintf(qh, qh->ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->SCALElast && !qh->DELAUNAY && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
-  qh->DOcheckmax= (!qh->SKIPcheckmax && qh->MERGING );
-  qh->KEEPnearinside= (qh->DOcheckmax && !(qh->KEEPinside && qh->KEEPcoplanar)
-                          && !qh->NOnearinside);
-  if (qh->MERGING)
-    qh->CENTERtype= qh_AScentrum;
-  else if (qh->VORONOI)
-    qh->CENTERtype= qh_ASvoronoi;
-  if (qh->TESTvneighbors && !qh->MERGING) {
-    qh_fprintf(qh, qh->ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
-    qh_errexit(qh, qh_ERRinput, NULL ,NULL);
-  }
-  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay)) {
-    qh->hull_dim -= qh->PROJECTinput;
-    if (qh->DELAUNAY) {
-      qh->hull_dim++;
-      if (qh->ATinfinity)
-        extra= 1;
-    }
-  }
-  if (qh->hull_dim <= 1) {
-    qh_fprintf(qh, qh->ferr, 6050, "qhull error: dimension %d must be > 1\n", qh->hull_dim);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  for (k=2, factorial=1.0; k < qh->hull_dim; k++)
-    factorial *= k;
-  qh->AREAfactor= 1.0 / factorial;
-  trace2((qh, qh->ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
-        dim, numpoints, ismalloc, qh->PROJECTinput, qh->hull_dim));
-  qh->normal_size= qh->hull_dim * sizeof(coordT);
-  qh->center_size= qh->normal_size - sizeof(coordT);
-  pointsneeded= qh->hull_dim+1;
-  if (qh->hull_dim > qh_DIMmergeVertex) {
-    qh->MERGEvertices= False;
-    qh_option(qh, "Q3-no-merge-vertices-dim-high", NULL, NULL);
-  }
-  if (qh->GOODpoint)
-    pointsneeded++;
-#ifdef qh_NOtrace
-  if (qh->IStracing) {
-    qh_fprintf(qh, qh->ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-#endif
-  if (qh->RERUN > 1) {
-    qh->TRACElastrun= qh->IStracing; /* qh_build_withrestart duplicates next conditional */
-    if (qh->IStracing != -1)
-      qh->IStracing= 0;
-  }else if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
-    qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
-    qh->IStracing= 0;
-  }
-  if (qh->ROTATErandom == 0 || qh->ROTATErandom == -1) {
-    seed= (int)time(&timedata);
-    if (qh->ROTATErandom  == -1) {
-      seed= -seed;
-      qh_option(qh, "QRandom-seed", &seed, NULL );
-    }else
-      qh_option(qh, "QRotate-random", &seed, NULL);
-    qh->ROTATErandom= seed;
-  }
-  seed= qh->ROTATErandom;
-  if (seed == INT_MIN)    /* default value */
-    seed= 1;
-  else if (seed < 0)
-    seed= -seed;
-  qh_RANDOMseed_(qh, seed);
-  randr= 0.0;
-  for (i=1000; i--; ) {
-    randi= qh_RANDOMint;
-    randr += randi;
-    if (randi > qh_RANDOMmax) {
-      qh_fprintf(qh, qh->ferr, 8036, "\
-qhull configuration error (qh_RANDOMmax in user.h):\n\
-   random integer %d > qh_RANDOMmax(qh, %.8g)\n",
-               randi, qh_RANDOMmax);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-  }
-  qh_RANDOMseed_(qh, seed);
-  randr = randr/1000;
-  if (randr < qh_RANDOMmax * 0.1
-  || randr > qh_RANDOMmax * 0.9)
-    qh_fprintf(qh, qh->ferr, 8037, "\
-qhull configuration warning (qh_RANDOMmax in user.h):\n\
-   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
-   Is qh_RANDOMmax (%.2g) wrong?\n",
-             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
-  qh->RANDOMa= 2.0 * qh->RANDOMfactor/qh_RANDOMmax;
-  qh->RANDOMb= 1.0 - qh->RANDOMfactor;
-  if (qh_HASHfactor < 1.1) {
-    qh_fprintf(qh, qh->ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
-      qh_HASHfactor);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (numpoints+extra < pointsneeded) {
-    qh_fprintf(qh, qh->ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
-            numpoints, pointsneeded);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  qh_initqhull_outputflags(qh);
-} /* initqhull_globals */
-
-/*---------------------------------
-
-  qh_initqhull_mem(qh, )
-    initialize mem_r.c for qhull
-    qh.hull_dim and qh.normal_size determine some of the allocation sizes
-    if qh.MERGING,
-      includes ridgeT
-    calls qh_user_memsizes(qh) to add up to 10 additional sizes for quick allocation
-      (see numsizes below)
-
-  returns:
-    mem_r.c already for qh_memalloc/qh_memfree (errors if called beforehand)
-
-  notes:
-    qh_produceoutput() prints memsizes
-
-*/
-void qh_initqhull_mem(qhT *qh) {
-  int numsizes;
-  int i;
-
-  numsizes= 8+10;
-  qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, numsizes,
-                     qh_MEMbufsize, qh_MEMinitbuf);
-  qh_memsize(qh, (int)sizeof(vertexT));
-  if (qh->MERGING) {
-    qh_memsize(qh, (int)sizeof(ridgeT));
-    qh_memsize(qh, (int)sizeof(mergeT));
-  }
-  qh_memsize(qh, (int)sizeof(facetT));
-  i= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;  /* ridge.vertices */
-  qh_memsize(qh, i);
-  qh_memsize(qh, qh->normal_size);        /* normal */
-  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
-  qh_memsize(qh, i);
-  qh_user_memsizes(qh);
-  qh_memsetup(qh);
-} /* initqhull_mem */
-
-/*---------------------------------
-
-  qh_initqhull_outputflags
-    initialize flags concerned with output
-
-  returns:
-    adjust user flags as needed
-
-  see:
-    qh_clear_outputflags() resets the flags
-
-  design:
-    test for qh.PRINTgood (i.e., only print 'good' facets)
-    check for conflicting print output options
-*/
-void qh_initqhull_outputflags(qhT *qh) {
-  boolT printgeom= False, printmath= False, printcoplanar= False;
-  int i;
-
-  trace3((qh, qh->ferr, 3024, "qh_initqhull_outputflags: %s\n", qh->qhull_command));
-  if (!(qh->PRINTgood || qh->PRINTneighbors)) {
-    if (qh->KEEParea || qh->KEEPminArea < REALmax/2 || qh->KEEPmerge || qh->DELAUNAY
-        || (!qh->ONLYgood && (qh->GOODvertex || qh->GOODpoint))) {
-      qh->PRINTgood= True;
-      qh_option(qh, "Pgood", NULL, NULL);
-    }
-  }
-  if (qh->PRINTtransparent) {
-    if (qh->hull_dim != 4 || !qh->DELAUNAY || qh->VORONOI || qh->DROPdim >= 0) {
-      qh_fprintf(qh, qh->ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    qh->DROPdim = 3;
-    qh->PRINTridges = True;
-  }
-  for (i=qh_PRINTEND; i--; ) {
-    if (qh->PRINTout[i] == qh_PRINTgeom)
-      printgeom= True;
-    else if (qh->PRINTout[i] == qh_PRINTmathematica || qh->PRINTout[i] == qh_PRINTmaple)
-      printmath= True;
-    else if (qh->PRINTout[i] == qh_PRINTcoplanars)
-      printcoplanar= True;
-    else if (qh->PRINTout[i] == qh_PRINTpointnearest)
-      printcoplanar= True;
-    else if (qh->PRINTout[i] == qh_PRINTpointintersect && !qh->HALFspace) {
-      qh_fprintf(qh, qh->ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTtriangles && (qh->HALFspace || qh->VORONOI)) {
-      qh_fprintf(qh, qh->ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTcentrums && qh->VORONOI) {
-      qh_fprintf(qh, qh->ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }else if (qh->PRINTout[i] == qh_PRINTvertices) {
-      if (qh->VORONOI)
-        qh_option(qh, "Fvoronoi", NULL, NULL);
-      else
-        qh_option(qh, "Fvertices", NULL, NULL);
-    }
-  }
-  if (printcoplanar && qh->DELAUNAY && qh->JOGGLEmax < REALmax/2) {
-    if (qh->PRINTprecision)
-      qh_fprintf(qh, qh->ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
-  }
-  if (printmath && (qh->hull_dim > 3 || qh->VORONOI)) {
-    qh_fprintf(qh, qh->ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (printgeom) {
-    if (qh->hull_dim > 4) {
-      qh_fprintf(qh, qh->ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->PRINTnoplanes && !(qh->PRINTcoplanar + qh->PRINTcentrums
-     + qh->PRINTdots + qh->PRINTspheres + qh->DOintersections + qh->PRINTridges)) {
-      qh_fprintf(qh, qh->ferr, 6058, "qhull input error: no output specified for Geomview\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->VORONOI && (qh->hull_dim > 3 || qh->DROPdim >= 0)) {
-      qh_fprintf(qh, qh->ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    /* can not warn about furthest-site Geomview output: no lower_threshold */
-    if (qh->hull_dim == 4 && qh->DROPdim == -1 &&
-        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
-      qh_fprintf(qh, qh->ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
-available for 4-d output(ignored).  Could use 'GDn' instead.\n");
-      qh->PRINTcoplanar= qh->PRINTspheres= qh->PRINTcentrums= False;
-    }
-  }
-  if (!qh->KEEPcoplanar && !qh->KEEPinside && !qh->ONLYgood) {
-    if ((qh->PRINTcoplanar && qh->PRINTspheres) || printcoplanar) {
-      if (qh->QHULLfinished) {
-        qh_fprintf(qh, qh->ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
-      }else {
-        qh->KEEPcoplanar = True;
-        qh_option(qh, "Qcoplanar", NULL, NULL);
-      }
-    }
-  }
-  qh->PRINTdim= qh->hull_dim;
-  if (qh->DROPdim >=0) {    /* after Geomview checks */
-    if (qh->DROPdim < qh->hull_dim) {
-      qh->PRINTdim--;
-      if (!printgeom || qh->hull_dim < 3)
-        qh_fprintf(qh, qh->ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh->DROPdim);
-    }else
-      qh->DROPdim= -1;
-  }else if (qh->VORONOI) {
-    qh->DROPdim= qh->hull_dim-1;
-    qh->PRINTdim= qh->hull_dim-1;
-  }
-} /* qh_initqhull_outputflags */
-
-/*---------------------------------
-
-  qh_initqhull_start(qh, infile, outfile, errfile )
-    allocate memory if needed and call qh_initqhull_start2()
-*/
-void qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
-
-  qh_initstatistics(qh);
-  qh_initqhull_start2(qh, infile, outfile, errfile);
-} /* initqhull_start */
-
-/*---------------------------------
-
-  qh_initqhull_start2(qh, infile, outfile, errfile )
-    start initialization of qhull
-    initialize statistics, stdio, default values for global variables
-    assumes qh is allocated
-  notes:
-    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
-  see:
-    qh_maxmin() determines the precision constants
-    qh_freeqhull()
-*/
-void qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
-  time_t timedata;
-  int seed;
-
-  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
-  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
-  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));   /* every field is 0, FALSE, NULL */
-  qh->NOerrexit= True;
-  qh->ANGLEmerge= True;
-  qh->DROPdim= -1;
-  qh->ferr= errfile;
-  qh->fin= infile;
-  qh->fout= outfile;
-  qh->furthest_id= qh_IDunknown;
-  qh->JOGGLEmax= REALmax;
-  qh->KEEPminArea = REALmax;
-  qh->last_low= REALmax;
-  qh->last_high= REALmax;
-  qh->last_newhigh= REALmax;
-  qh->last_random= 1;
-  qh->max_outside= 0.0;
-  qh->max_vertex= 0.0;
-  qh->MAXabs_coord= 0.0;
-  qh->MAXsumcoord= 0.0;
-  qh->MAXwidth= -REALmax;
-  qh->MERGEindependent= True;
-  qh->MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
-  qh->MINoutside= 0.0;
-  qh->MINvisible= REALmax;
-  qh->MAXcoplanar= REALmax;
-  qh->outside_err= REALmax;
-  qh->premerge_centrum= 0.0;
-  qh->premerge_cos= REALmax;
-  qh->PRINTprecision= True;
-  qh->PRINTradius= 0.0;
-  qh->postmerge_cos= REALmax;
-  qh->postmerge_centrum= 0.0;
-  qh->ROTATErandom= INT_MIN;
-  qh->MERGEvertices= True;
-  qh->totarea= 0.0;
-  qh->totvol= 0.0;
-  qh->TRACEdist= REALmax;
-  qh->TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
-  qh->tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
-  qh->tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
-  seed= (int)time(&timedata);
-  qh_RANDOMseed_(qh, seed);
-  qh->run_id= qh_RANDOMint;
-  if(!qh->run_id)
-      qh->run_id++;  /* guarantee non-zero */
-  qh_option(qh, "run-id", &qh->run_id, NULL);
-  strcat(qh->qhull, "qhull");
-} /* initqhull_start2 */
-
-/*---------------------------------
-
-  qh_initthresholds(qh, commandString )
-    set thresholds for printing and scaling from commandString
-
-  returns:
-    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
-
-  see:
-    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
-    qh_inthresholds()
-
-  design:
-    for each 'Pdn' or 'PDn' option
-      check syntax
-      set qh.lower_threshold or qh.upper_threshold
-    set qh.GOODthreshold if an unbounded threshold is used
-    set qh.SPLITthreshold if a bounded threshold is used
-*/
-void qh_initthresholds(qhT *qh, char *command) {
-  realT value;
-  int idx, maxdim, k;
-  char *s= command; /* non-const due to strtol */
-  char key;
-
-  maxdim= qh->input_dim;
-  if (qh->DELAUNAY && (qh->PROJECTdelaunay || qh->PROJECTinput))
-    maxdim++;
-  while (*s) {
-    if (*s == '-')
-      s++;
-    if (*s == 'P') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'd' || key == 'D') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh, qh->ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
-                    key, s-1);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= qh->hull_dim) {
-            qh_fprintf(qh, qh->ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
-                idx, key, qh->hull_dim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-            if (fabs((double)value) > 1.0) {
-              qh_fprintf(qh, qh->ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
-                      value, key);
-              continue;
-            }
-          }else
-            value= 0.0;
-          if (key == 'd')
-            qh->lower_threshold[idx]= value;
-          else
-            qh->upper_threshold[idx]= value;
-        }
-      }
-    }else if (*s == 'Q') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-        if (key == 'b' && *s == 'B') {
-          s++;
-          for (k=maxdim; k--; ) {
-            qh->lower_bound[k]= -qh_DEFAULTbox;
-            qh->upper_bound[k]= qh_DEFAULTbox;
-          }
-        }else if (key == 'b' && *s == 'b')
-          s++;
-        else if (key == 'b' || key == 'B') {
-          if (!isdigit(*s)) {
-            qh_fprintf(qh, qh->ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
-                    key);
-            continue;
-          }
-          idx= qh_strtol(s, &s);
-          if (idx >= maxdim) {
-            qh_fprintf(qh, qh->ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
-                idx, key, maxdim);
-            continue;
-          }
-          if (*s == ':') {
-            s++;
-            value= qh_strtod(s, &s);
-          }else if (key == 'b')
-            value= -qh_DEFAULTbox;
-          else
-            value= qh_DEFAULTbox;
-          if (key == 'b')
-            qh->lower_bound[idx]= value;
-          else
-            qh->upper_bound[idx]= value;
-        }
-      }
-    }else {
-      while (*s && !isspace(*s))
-        s++;
-    }
-    while (isspace(*s))
-      s++;
-  }
-  for (k=qh->hull_dim; k--; ) {
-    if (qh->lower_threshold[k] > -REALmax/2) {
-      qh->GOODthreshold= True;
-      if (qh->upper_threshold[k] < REALmax/2) {
-        qh->SPLITthresholds= True;
-        qh->GOODthreshold= False;
-        break;
-      }
-    }else if (qh->upper_threshold[k] < REALmax/2)
-      qh->GOODthreshold= True;
-  }
-} /* initthresholds */
-
-/*---------------------------------
-
-  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
-    Report error if library does not agree with caller
-
-  notes:
-    NOerrors -- qh_lib_check can not call qh_errexit()
-*/
-void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
-    boolT iserror= False;
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
-    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
-    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
-    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
-    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
-#endif
-
-    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
-        qh_fprintf_stderr(6257, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a static qhT.  Library is reentrant.\n");
-        iserror= True;
-    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
-        qh_fprintf_stderr(6258, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a dynamic qhT via qh_QHpointer.  Library is reentrant.\n");
-        iserror= True;
-    }else if (qhullLibraryType!=QHULL_REENTRANT) { /* 2 */
-        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
-        iserror= True;
-    }
-    if (qhTsize != sizeof(qhT)) {
-        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
-        iserror= True;
-    }
-    if (vertexTsize != sizeof(vertexT)) {
-        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
-        iserror= True;
-    }
-    if (ridgeTsize != sizeof(ridgeT)) {
-        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
-        iserror= True;
-    }
-    if (facetTsize != sizeof(facetT)) {
-        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
-        iserror= True;
-    }
-    if (setTsize && setTsize != sizeof(setT)) {
-        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
-        iserror= True;
-    }
-    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
-        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
-        iserror= True;
-    }
-    if (iserror) {
-        qh_fprintf_stderr(6259, "qh_lib_check: Cannot continue.  Library '%s' is reentrant (e.g., qhull_r.so)\n", qh_version2);
-        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-    }
-} /* lib_check */
-
-/*---------------------------------
-
-  qh_option(qh, option, intVal, realVal )
-    add an option description to qh.qhull_options
-
-  notes:
-    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
-    will be printed with statistics ('Ts') and errors
-    strlen(option) < 40
-*/
-void qh_option(qhT *qh, const char *option, int *i, realT *r) {
-  char buf[200];
-  int len, maxlen;
-
-  sprintf(buf, "  %s", option);
-  if (i)
-    sprintf(buf+strlen(buf), " %d", *i);
-  if (r)
-    sprintf(buf+strlen(buf), " %2.2g", *r);
-  len= (int)strlen(buf);  /* WARN64 */
-  qh->qhull_optionlen += len;
-  maxlen= sizeof(qh->qhull_options) - len -1;
-  maximize_(maxlen, 0);
-  if (qh->qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
-    qh->qhull_optionlen= len;
-    strncat(qh->qhull_options, "\n", (size_t)(maxlen--));
-  }
-  strncat(qh->qhull_options, buf, (size_t)maxlen);
-} /* option */
-
-/*---------------------------------
-
-  qh_zero( qh, errfile )
-    Initialize and zero Qhull's memory for qh_new_qhull()
-
-  notes:
-    Not needed in global.c because static variables are initialized to zero
-*/
-void qh_zero(qhT *qh, FILE *errfile) {
-    memset((char *)qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
-    qh->NOerrexit= True;
-    qh_meminit(qh, errfile);
-} /* zero */
-
diff --git a/src/qhull/src/libqhull_r/index.htm b/src/qhull/src/libqhull_r/index.htm
deleted file mode 100644
index c62030e06..000000000
--- a/src/qhull/src/libqhull_r/index.htm
+++ /dev/null
@@ -1,266 +0,0 @@
-
-
-
-
-Reentrant Qhull functions, macros, and data structures
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code
    
-To: Qhull files
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
-
    
-
-
-
    Reentrant Qhull functions, macros, and data structures
    
-
    
-
    The following sections provide an overview and index to
-reentrant Qhull's functions, macros, and data structures.
-Each section starts with an introduction.
-See also Calling
-Qhull from C programs and Calling Qhull from C++ programs.
    
-
-
    Qhull uses the following conventions:
    
-
    
-
-
      
-
    • in code, global variables start with "qh "
-
    • in documentation, global variables start with 'qh.'
-
    • constants start with an upper case word
-
    • important globals include an '_'
-
    • functions, macros, and constants start with "qh_"
      • 
-
    • data types end in "T"
      • 
-
    • macros with arguments end in "_"
      • 
-
    • iterators are macros that use local variables
      • 
-
    • iterators for sets start with "FOREACH"
      • 
-
    • iterators for lists start with "FORALL"
      • 
-
    • qhull options are in single quotes (e.g., 'Pdn')
      • 
-
    • lists are sorted alphabetically
      • 
-
    • preprocessor directives on left margin for older compilers
      • 
-
    
-
    
-
    
-Reentrant Qhull is nearly the same as non-reentrant Qhull.  In reentrant
-Qhull, the qhT data structure is the first parameter to most functions. Qhull accesses
-this data structure with 'qh->...'.
-In non-reentrant Qhull, the global data structure is either a struct (qh_QHpointer==0)
-or a pointer (qh_QHpointer==1).  The non-reentrant code looks different because this data
-structure is accessed via the 'qh' macro.   This macro expands to 'qh_qh.' or 'qh_qh->' (resp.).
-
    
-When reading code with an editor, a search for
-'"function'
-will locate the header of qh_function.  A search for '* function'
-will locate the tail of qh_function.
-
-
    A useful starting point is libqhull_r.h.  It defines most
-of Qhull data structures and top-level functions.  Search for 'PFn' to
-determine the corresponding constant in Qhull.  Search for 'Fp' to
-determine the corresponding qh_PRINT... constant.
-Search io_r.c to learn how the print function is implemented.
    
-
-
    If your web browser is configured for .c and .h files, the function, macro, and data type links
-go to the corresponding source location.  To configure your web browser for .c and .h files.
-
      
-
    • In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
-
    • Opera 12.10
-
        
-
      1. In Tools > Preferences > Advanced > Downloads
-
      2. Uncheck 'Hide file types opened with Opera'
-
      3. Quick find 'html'
-
      4. Select 'text/html' > Edit
-
      5. Add File extensions 'c,h,'
-
      6. Click 'OK'
-
      
-
    • Internet Explorer -- Mime types are not available from 'Internet Options'.    Is there a registry key for these settings?
-
    • Firefox -- Mime types are not available from 'Preferences'.  Is there an add-on to change the file extensions for a mime type?
-
    • Chrome -- Can Chrome be configured?
-
    
-
-
    
-Please report documentation and link errors
-to qhull-bug@qhull.org.
-
    
-
-
    Copyright © 1997-2015 C.B. Barber
    
-
-
    
-
-
    »Qhull files 
    
-
    
-
-
    This sections lists the .c and .h files for Qhull. Please
-refer to these files for detailed information.
    
-
    
-
-
    
-
    Makefile, CMakeLists.txt
    
-
    Makefile is preconfigured for gcc.  CMakeLists.txt supports multiple
-platforms with CMake.
-Qhull includes project files for Visual Studio and Qt.
-
    
-
-
     
    
-
    libqhull_r.h 
    
-
    Include file for the Qhull library (libqhull.so, qhull.dll, libqhullstatic.a).
-Data structures are documented under Poly.
-Global variables are documented under Global.
-Other data structures and variables are documented under
-Qhull or Geom.
    
-
-
     
    
-
    Geom, 
-geom_r.h, 
-geom_r.c, 
-geom2_r.c, 
-random_r.c, 
-random_r.h
    
-
    Geometric routines. These routines implement mathematical
-functions such as Gaussian elimination and geometric
-routines needed for Qhull. Frequently used routines are
-in geom_r.c while infrequent ones are in geom2_r.c.
-
    
-
-
     
    
-
    Global, 
-global_r.c, 
-libqhull_r.h 
    
-
    Global routines. Qhull uses a global data structure, qh,
-to store globally defined constants, lists, sets, and
-variables.
-global_r.c initializes and frees these
-structures. 
    
-
-
     
    
-
    Io, io_r.h,
-io_r.c 
    
-
    Input and output routines. Qhull provides a wide range of
-input and output options.
    
-
-
     
    
-
    Mem, 
-mem_r.h, 
-mem_r.c 
    
-
    Memory routines. Qhull provides memory allocation and
-deallocation. It uses quick-fit allocation.
    
-
-
     
    
-
    Merge, 
-merge_r.h, 
-merge_r.c 
    
-
    Merge routines. Qhull handles precision problems by
-merged facets or joggled input. These routines merge simplicial facets,
-merge non-simplicial facets, merge cycles of facets, and
-rename redundant vertices.
    
-
-
     
    
-
    Poly, 
-poly_r.h, 
-poly_r.c, 
-poly2_r.c, 
-libqhull_r.h 
    
-
    Polyhedral routines. Qhull produces a polyhedron as a
-list of facets with vertices, neighbors, ridges, and
-geometric information. libqhull_r.h defines the main
-data structures. Frequently used routines are in poly_r.c
-while infrequent ones are in poly2_r.c.
    
-
-
     
    
-
    Qhull, 
-libqhull_r.c, 
-libqhull_r.h, 
-qhull_ra.h, 
-unix_r.c , 
-qconvex_r.c , 
-qdelaun_r.c , 
-qhalf_r.c , 
-qvoronoi_r.c 
    
-
    Top-level routines. The Quickhull algorithm is
-implemented by libqhull_r.c. qhull_ra.h
-includes all header files. 
    
-
-
     
    
-
    Set, 
-qset_r.h, 
-qset_r.c 
    
-
    Set routines. Qhull implements its data structures as
-sets. A set is an array of pointers that is expanded as
-needed. This is a separate package that may be used in
-other applications. 
    
-
-
     
    
-
    Stat, 
-stat_r.h, 
-stat_r.c 
    
-
    Statistical routines. Qhull maintains statistics about
-its implementation. 
    
-
-
     
    
-
    User, 
-user_r.h, 
-user_r.c, 
-user_eg_r.c, 
-user_eg2_r.c, 
-user_eg3_r.cpp, 
-
    
-
    User-defined routines. Qhull allows the user to configure
-the code with defined constants and specialized routines.
-
    
-
    
-
    
-
-
    
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull files
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/io_r.c b/src/qhull/src/libqhull_r/io_r.c
deleted file mode 100644
index 9721a000d..000000000
--- a/src/qhull/src/libqhull_r/io_r.c
+++ /dev/null
@@ -1,4062 +0,0 @@
-/*
      ---------------------------------
-
-   io_r.c
-   Input/Output routines of qhull application
-
-   see qh-io_r.htm and io_r.h
-
-   see user_r.c for qh_errprint and qh_printfacetlist
-
-   unix_r.c calls qh_readpoints and qh_produce_output
-
-   unix_r.c and user_r.c are the only callers of io_r.c functions
-   This allows the user to avoid loading io_r.o from qhull.a
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/io_r.c#4 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*========= -functions in alphabetical order after qh_produce_output(qh)  =====*/
-
-/*---------------------------------
-
-  qh_produce_output(qh)
-  qh_produce_output2(qh)
-    prints out the result of qhull in desired format
-    qh_produce_output2(qh) does not call qh_prepare_output(qh)
-    if qh.GETarea
-      computes and prints area and volume
-    qh.PRINTout[] is an array of output formats
-
-  notes:
-    prints output in qh.PRINTout order
-*/
-void qh_produce_output(qhT *qh) {
-    int tempsize= qh_setsize(qh, qh->qhmem.tempstack);
-
-    qh_prepare_output(qh);
-    qh_produce_output2(qh);
-    if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
-        qh_fprintf(qh, qh->ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
-            qh_setsize(qh, qh->qhmem.tempstack));
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-} /* produce_output */
-
-
-void qh_produce_output2(qhT *qh) {
-  int i, tempsize= qh_setsize(qh, qh->qhmem.tempstack), d_1;
-
-  if (qh->PRINTsummary)
-    qh_printsummary(qh, qh->ferr);
-  else if (qh->PRINTout[0] == qh_PRINTnone)
-    qh_printsummary(qh, qh->fout);
-  for (i=0; i < qh_PRINTEND; i++)
-    qh_printfacets(qh, qh->fout, qh->PRINTout[i], qh->facet_list, NULL, !qh_ALL);
-  qh_allstatistics(qh);
-  if (qh->PRINTprecision && !qh->MERGING && (qh->JOGGLEmax > REALmax/2 || qh->RERUN))
-    qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
-  if (qh->VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
-    qh_printstats(qh, qh->ferr, qh->qhstat.vridges, NULL);
-  if (qh->PRINTstatistics) {
-    qh_printstatistics(qh, qh->ferr, "");
-    qh_memstatistics(qh, qh->ferr);
-    d_1= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;
-    qh_fprintf(qh, qh->ferr, 8040, "\
-    size in bytes: merge %d ridge %d vertex %d facet %d\n\
-         normal %d ridge vertices %d facet vertices or neighbors %d\n",
-            (int)sizeof(mergeT), (int)sizeof(ridgeT),
-            (int)sizeof(vertexT), (int)sizeof(facetT),
-            qh->normal_size, d_1, d_1 + SETelemsize);
-  }
-  if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
-    qh_fprintf(qh, qh->ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
-             qh_setsize(qh, qh->qhmem.tempstack));
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* produce_output2 */
-
-/*---------------------------------
-
-  qh_dfacet(qh, id )
-    print facet by id, for debugging
-
-*/
-void qh_dfacet(qhT *qh, unsigned id) {
-  facetT *facet;
-
-  FORALLfacets {
-    if (facet->id == id) {
-      qh_printfacet(qh, qh->fout, facet);
-      break;
-    }
-  }
-} /* dfacet */
-
-
-/*---------------------------------
-
-  qh_dvertex(qh, id )
-    print vertex by id, for debugging
-*/
-void qh_dvertex(qhT *qh, unsigned id) {
-  vertexT *vertex;
-
-  FORALLvertices {
-    if (vertex->id == id) {
-      qh_printvertex(qh, qh->fout, vertex);
-      break;
-    }
-  }
-} /* dvertex */
-
-
-/*---------------------------------
-
-  qh_compare_facetarea(p1, p2 )
-    used by qsort() to order facets by area
-*/
-int qh_compare_facetarea(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  if (!a->isarea)
-    return -1;
-  if (!b->isarea)
-    return 1;
-  if (a->f.area > b->f.area)
-    return 1;
-  else if (a->f.area == b->f.area)
-    return 0;
-  return -1;
-} /* compare_facetarea */
-
-/*---------------------------------
-
-  qh_compare_facetmerge(p1, p2 )
-    used by qsort() to order facets by number of merges
-*/
-int qh_compare_facetmerge(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-
-  return(a->nummerge - b->nummerge);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_facetvisit(p1, p2 )
-    used by qsort() to order facets by visit id or id
-*/
-int qh_compare_facetvisit(const void *p1, const void *p2) {
-  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
-  int i,j;
-
-  if (!(i= a->visitid))
-    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
-  if (!(j= b->visitid))
-    j= 0 - b->id;
-  return(i - j);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_vertexpoint( p1, p2 )
-    used by qsort() to order vertices by point id
-
-  Not usable in qhulllib_r since qh_pointid depends on qh
-
-  int qh_compare_vertexpoint(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return((qh_pointid(qh, a->point) > qh_pointid(qh, b->point)?1:-1));
-}*/
-
-/*---------------------------------
-
-  qh_copyfilename(qh, dest, size, source, length )
-    copy filename identified by qh_skipfilename()
-
-  notes:
-    see qh_skipfilename() for syntax
-*/
-void qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length) {
-  char c= *source;
-
-  if (length > size + 1) {
-      qh_fprintf(qh, qh->ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  strncpy(filename, source, length);
-  filename[length]= '\0';
-  if (c == '\'' || c == '"') {
-    char *s= filename + 1;
-    char *t= filename;
-    while (*s) {
-      if (*s == c) {
-          if (s[-1] == '\\')
-              t[-1]= c;
-      }else
-          *t++= *s;
-      s++;
-    }
-    *t= '\0';
-  }
-} /* copyfilename */
-
-/*---------------------------------
-
-  qh_countfacets(qh, facetlist, facets, printall,
-          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
-    count good facets for printing and set visitid
-    if allfacets, ignores qh_skipfacet()
-
-  notes:
-    qh_printsummary and qh_countfacets must match counts
-
-  returns:
-    numfacets, numsimplicial, total neighbors, numridges, coplanars
-    each facet with ->visitid indicating 1-relative position
-      ->visitid==0 indicates not good
-
-  notes
-    numfacets >= numsimplicial
-    if qh.NEWfacets,
-      does not count visible facets (matches qh_printafacet)
-
-  design:
-    for all facets on facetlist and in facets set
-      unless facet is skipped or visible (i.e., will be deleted)
-        mark facet->visitid
-        update counts
-*/
-void qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
-    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
-  facetT *facet, **facetp;
-  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
-
-  FORALLfacet_(facetlist) {
-    if ((facet->visible && qh->NEWfacets)
-    || (!printall && qh_skipfacet(qh, facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(qh, facet->neighbors);
-      if (facet->simplicial) {
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(qh, facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(qh, facet->coplanarset);
-    }
-  }
-
-  FOREACHfacet_(facets) {
-    if ((facet->visible && qh->NEWfacets)
-    || (!printall && qh_skipfacet(qh, facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize(qh, facet->neighbors);
-      if (facet->simplicial){
-        numsimplicial++;
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else
-        numridges += qh_setsize(qh, facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize(qh, facet->coplanarset);
-    }
-  }
-  qh->visit_id += numfacets+1;
-  *numfacetsp= numfacets;
-  *numsimplicialp= numsimplicial;
-  *totneighborsp= totneighbors;
-  *numridgesp= numridges;
-  *numcoplanarsp= numcoplanars;
-  *numtricoplanarsp= numtricoplanars;
-} /* countfacets */
-
-/*---------------------------------
-
-  qh_detvnorm(qh, vertex, vertexA, centers, offset )
-    compute separating plane of the Voronoi diagram for a pair of input sites
-    centers= set of facets (i.e., Voronoi vertices)
-      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  returns:
-    norm
-      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
-      copy the data before reusing qh.gm_matrix
-    offset
-      if 'QVn'
-        sign adjusted so that qh.GOODvertexp is inside
-      else
-        sign adjusted so that vertex is inside
-
-    qh.gm_matrix= simplex of points from centers relative to first center
-
-  notes:
-    in io_r.c so that code for 'v Tv' can be removed by removing io_r.c
-    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
-
-  design:
-    determine midpoint of input sites
-    build points as the set of Voronoi vertices
-    select a simplex from points (if necessary)
-      include midpoint if the Voronoi region is unbounded
-    relocate the first vertex of the simplex to the origin
-    compute the normalized hyperplane through the simplex
-    orient the hyperplane toward 'QVn' or 'vertex'
-    if 'Tv' or 'Ts'
-      if bounded
-        test that hyperplane is the perpendicular bisector of the input sites
-      test that Voronoi vertices not in the simplex are still on the hyperplane
-    free up temporary memory
-*/
-pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
-  facetT *facet, **facetp;
-  int  i, k, pointid, pointidA, point_i, point_n;
-  setT *simplex= NULL;
-  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
-  coordT *coord, *gmcoord, *normalp;
-  setT *points= qh_settemp(qh, qh->TEMPsize);
-  boolT nearzero= False;
-  boolT unbounded= False;
-  int numcenters= 0;
-  int dim= qh->hull_dim - 1;
-  realT dist, offset, angle, zero= 0.0;
-
-  midpoint= qh->gm_matrix + qh->hull_dim * qh->hull_dim;  /* last row */
-  for (k=0; k < dim; k++)
-    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
-  FOREACHfacet_(centers) {
-    numcenters++;
-    if (!facet->visitid)
-      unbounded= True;
-    else {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-      qh_setappend(qh, &points, facet->center);
-    }
-  }
-  if (numcenters > dim) {
-    simplex= qh_settemp(qh, qh->TEMPsize);
-    qh_setappend(qh, &simplex, vertex->point);
-    if (unbounded)
-      qh_setappend(qh, &simplex, midpoint);
-    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
-    qh_setdelnth(qh, simplex, 0);
-  }else if (numcenters == dim) {
-    if (unbounded)
-      qh_setappend(qh, &points, midpoint);
-    simplex= points;
-  }else {
-    qh_fprintf(qh, qh->ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  i= 0;
-  gmcoord= qh->gm_matrix;
-  point0= SETfirstt_(simplex, pointT);
-  FOREACHpoint_(simplex) {
-    if (qh->IStracing >= 4)
-      qh_printmatrix(qh, qh->ferr, "qh_detvnorm: Voronoi vertex or midpoint",
-                              &point, 1, dim);
-    if (point != point0) {
-      qh->gm_row[i++]= gmcoord;
-      coord= point0;
-      for (k=dim; k--; )
-        *(gmcoord++)= *point++ - *coord++;
-    }
-  }
-  qh->gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
-  normal= gmcoord;
-  qh_sethyperplane_gauss(qh, dim, qh->gm_row, point0, True,
-                normal, &offset, &nearzero);
-  if (qh->GOODvertexp == vertexA->point)
-    inpoint= vertexA->point;
-  else
-    inpoint= vertex->point;
-  zinc_(Zdistio);
-  dist= qh_distnorm(dim, inpoint, normal, &offset);
-  if (dist > 0) {
-    offset= -offset;
-    normalp= normal;
-    for (k=dim; k--; ) {
-      *normalp= -(*normalp);
-      normalp++;
-    }
-  }
-  if (qh->VERIFYoutput || qh->PRINTstatistics) {
-    pointid= qh_pointid(qh, vertex->point);
-    pointidA= qh_pointid(qh, vertexA->point);
-    if (!unbounded) {
-      zinc_(Zdiststat);
-      dist= qh_distnorm(dim, midpoint, normal, &offset);
-      if (dist < 0)
-        dist= -dist;
-      zzinc_(Zridgemid);
-      wwmax_(Wridgemidmax, dist);
-      wwadd_(Wridgemid, dist);
-      trace4((qh, qh->ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
-                 pointid, pointidA, dist));
-      for (k=0; k < dim; k++)
-        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
-      qh_normalize(qh, midpoint, dim, False);
-      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
-      if (angle < 0.0)
-        angle= angle + 1.0;
-      else
-        angle= angle - 1.0;
-      if (angle < 0.0)
-        angle -= angle;
-      trace4((qh, qh->ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
-                 pointid, pointidA, angle, nearzero));
-      if (nearzero) {
-        zzinc_(Zridge0);
-        wwmax_(Wridge0max, angle);
-        wwadd_(Wridge0, angle);
-      }else {
-        zzinc_(Zridgeok)
-        wwmax_(Wridgeokmax, angle);
-        wwadd_(Wridgeok, angle);
-      }
-    }
-    if (simplex != points) {
-      FOREACHpoint_i_(qh, points) {
-        if (!qh_setin(simplex, point)) {
-          facet= SETelemt_(centers, point_i, facetT);
-          zinc_(Zdiststat);
-          dist= qh_distnorm(dim, point, normal, &offset);
-          if (dist < 0)
-            dist= -dist;
-          zzinc_(Zridge);
-          wwmax_(Wridgemax, dist);
-          wwadd_(Wridge, dist);
-          trace4((qh, qh->ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
-                             pointid, pointidA, facet->visitid, dist));
-        }
-      }
-    }
-  }
-  *offsetp= offset;
-  if (simplex != points)
-    qh_settempfree(qh, &simplex);
-  qh_settempfree(qh, &points);
-  return normal;
-} /* detvnorm */
-
-/*---------------------------------
-
-  qh_detvridge(qh, vertexA )
-    determine Voronoi ridge from 'seen' neighbors of vertexA
-    include one vertex-at-infinite if an !neighbor->visitid
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    sorted by center id
-*/
-setT *qh_detvridge(qhT *qh, vertexT *vertex) {
-  setT *centers= qh_settemp(qh, qh->TEMPsize);
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-  facetT *neighbor, **neighborp;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->seen) {
-      if (neighbor->visitid) {
-        if (!neighbor->tricoplanar || qh_setunique(qh, &tricenters, neighbor->center))
-          qh_setappend(qh, ¢ers, neighbor);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(qh, ¢ers, neighbor);
-      }
-    }
-  }
-  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(qh, centers),
-             sizeof(facetT *), qh_compare_facetvisit);
-  qh_settempfree(qh, &tricenters);
-  return centers;
-} /* detvridge */
-
-/*---------------------------------
-
-  qh_detvridge3(qh, atvertex, vertex )
-    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
-    include one vertex-at-infinite for !neighbor->visitid
-    assumes all facet->seen2= True
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    listed in adjacency order (!oriented)
-    all facet->seen2= True
-
-  design:
-    mark all neighbors of atvertex
-    for each adjacent neighbor of both atvertex and vertex
-      if neighbor selected
-        add neighbor to set of Voronoi vertices
-*/
-setT *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex) {
-  setT *centers= qh_settemp(qh, qh->TEMPsize);
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-  facetT *neighbor, **neighborp, *facet= NULL;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= False;
-  FOREACHneighbor_(vertex) {
-    if (!neighbor->seen2) {
-      facet= neighbor;
-      break;
-    }
-  }
-  while (facet) {
-    facet->seen2= True;
-    if (neighbor->seen) {
-      if (facet->visitid) {
-        if (!facet->tricoplanar || qh_setunique(qh, &tricenters, facet->center))
-          qh_setappend(qh, ¢ers, facet);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend(qh, ¢ers, facet);
-      }
-    }
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen2) {
-        if (qh_setin(vertex->neighbors, neighbor))
-          break;
-        else
-          neighbor->seen2= True;
-      }
-    }
-    facet= neighbor;
-  }
-  if (qh->CHECKfrequently) {
-    FOREACHneighbor_(vertex) {
-      if (!neighbor->seen2) {
-          qh_fprintf(qh, qh->ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
-                 qh_pointid(qh, vertex->point), neighbor->id);
-        qh_errexit(qh, qh_ERRqhull, neighbor, NULL);
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= True;
-  qh_settempfree(qh, &tricenters);
-  return centers;
-} /* detvridge3 */
-
-/*---------------------------------
-
-  qh_eachvoronoi(qh, fp, printvridge, vertex, visitall, innerouter, inorder )
-    if visitall,
-      visit all Voronoi ridges for vertex (i.e., an input site)
-    else
-      visit all unvisited Voronoi ridges for vertex
-      all vertex->seen= False if unvisited
-    assumes
-      all facet->seen= False
-      all facet->seen2= True (for qh_detvridge3)
-      all facet->visitid == 0 if vertex_at_infinity
-                         == index of Voronoi vertex
-                         >= qh.num_facets if ignored
-    innerouter:
-      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
-      qh_RIDGEinner- only inner
-      qh_RIDGEouter- only outer
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns:
-    number of visited ridges (does not include previously visited ridges)
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-        fp== any pointer (assumes FILE*)
-        vertex,vertexA= pair of input sites that define a Voronoi ridge
-        centers= set of facets (i.e., Voronoi vertices)
-                 ->visitid == index or 0 if vertex_at_infinity
-                 ordered for 3-d Voronoi diagram
-  notes:
-    uses qh.vertex_visit
-
-  see:
-    qh_eachvoronoi_all()
-
-  design:
-    mark selected neighbors of atvertex
-    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
-      for each unvisited vertex
-        if atvertex and vertex share more than d-1 neighbors
-          bump totalcount
-          if printvridge defined
-            build the set of shared neighbors (i.e., Voronoi vertices)
-            call printvridge
-*/
-int qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
-  boolT unbounded;
-  int count;
-  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
-  setT *centers;
-  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
-
-  vertexT *vertex, **vertexp;
-  boolT firstinf;
-  unsigned int numfacets= (unsigned int)qh->num_facets;
-  int totridges= 0;
-
-  qh->vertex_visit++;
-  atvertex->seen= True;
-  if (visitall) {
-    FORALLvertices
-      vertex->seen= False;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->visitid < numfacets)
-      neighbor->seen= True;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->seen) {
-      FOREACHvertex_(neighbor->vertices) {
-        if (vertex->visitid != qh->vertex_visit && !vertex->seen) {
-          vertex->visitid= qh->vertex_visit;
-          count= 0;
-          firstinf= True;
-          qh_settruncate(qh, tricenters, 0);
-          FOREACHneighborA_(vertex) {
-            if (neighborA->seen) {
-              if (neighborA->visitid) {
-                if (!neighborA->tricoplanar || qh_setunique(qh, &tricenters, neighborA->center))
-                  count++;
-              }else if (firstinf) {
-                count++;
-                firstinf= False;
-              }
-            }
-          }
-          if (count >= qh->hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
-            if (firstinf) {
-              if (innerouter == qh_RIDGEouter)
-                continue;
-              unbounded= False;
-            }else {
-              if (innerouter == qh_RIDGEinner)
-                continue;
-              unbounded= True;
-            }
-            totridges++;
-            trace4((qh, qh->ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
-                  count, qh_pointid(qh, atvertex->point), qh_pointid(qh, vertex->point)));
-            if (printvridge && fp) {
-              if (inorder && qh->hull_dim == 3+1) /* 3-d Voronoi diagram */
-                centers= qh_detvridge3(qh, atvertex, vertex);
-              else
-                centers= qh_detvridge(qh, vertex);
-              (*printvridge)(qh, fp, atvertex, vertex, centers, unbounded);
-              qh_settempfree(qh, ¢ers);
-            }
-          }
-        }
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen= False;
-  qh_settempfree(qh, &tricenters);
-  return totridges;
-} /* eachvoronoi */
-
-
-/*---------------------------------
-
-  qh_eachvoronoi_all(qh, fp, printvridge, isUpper, innerouter, inorder )
-    visit all Voronoi ridges
-
-    innerouter:
-      see qh_eachvoronoi()
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns
-    total number of ridges
-
-    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
-      facet->visitid= Voronoi vertex index(same as 'o' format)
-    else
-      facet->visitid= 0
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-      [see qh_eachvoronoi]
-
-  notes:
-    Not used for qhull.exe
-    same effect as qh_printvdiagram but ridges not sorted by point id
-*/
-int qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
-  facetT *facet;
-  vertexT *vertex;
-  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
-  int totridges= 0;
-
-  qh_clearcenters(qh, qh_ASvoronoi);
-  qh_vertexneighbors(qh);
-  maximize_(qh->visit_id, (unsigned) qh->num_facets);
-  FORALLfacets {
-    facet->visitid= 0;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  FORALLfacets {
-    if (facet->upperdelaunay == isUpper)
-      facet->visitid= numcenters++;
-  }
-  FORALLvertices
-    vertex->seen= False;
-  FORALLvertices {
-    if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
-      continue;
-    totridges += qh_eachvoronoi(qh, fp, printvridge, vertex,
-                   !qh_ALL, innerouter, inorder);
-  }
-  return totridges;
-} /* eachvoronoi_all */
-
-/*---------------------------------
-
-  qh_facet2point(qh, facet, point0, point1, mindist )
-    return two projected temporary vertices for a 2-d facet
-    may be non-simplicial
-
-  returns:
-    point0 and point1 oriented and projected to the facet
-    returns mindist (maximum distance below plane)
-*/
-void qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
-  vertexT *vertex0, *vertex1;
-  realT dist;
-
-  if (facet->toporient ^ qh_ORIENTclock) {
-    vertex0= SETfirstt_(facet->vertices, vertexT);
-    vertex1= SETsecondt_(facet->vertices, vertexT);
-  }else {
-    vertex1= SETfirstt_(facet->vertices, vertexT);
-    vertex0= SETsecondt_(facet->vertices, vertexT);
-  }
-  zadd_(Zdistio, 2);
-  qh_distplane(qh, vertex0->point, facet, &dist);
-  *mindist= dist;
-  *point0= qh_projectpoint(qh, vertex0->point, facet, dist);
-  qh_distplane(qh, vertex1->point, facet, &dist);
-  minimize_(*mindist, dist);
-  *point1= qh_projectpoint(qh, vertex1->point, facet, dist);
-} /* facet2point */
-
-
-/*---------------------------------
-
-  qh_facetvertices(qh, facetlist, facets, allfacets )
-    returns temporary set of vertices in a set and/or list of facets
-    if allfacets, ignores qh_skipfacet()
-
-  returns:
-    vertices with qh.vertex_visit
-
-  notes:
-    optimized for allfacets of facet_list
-
-  design:
-    if allfacets of facet_list
-      create vertex set from vertex_list
-    else
-      for each selected facet in facets or facetlist
-        append unvisited vertices to vertex set
-*/
-setT *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets) {
-  setT *vertices;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-
-  qh->vertex_visit++;
-  if (facetlist == qh->facet_list && allfacets && !facets) {
-    vertices= qh_settemp(qh, qh->num_vertices);
-    FORALLvertices {
-      vertex->visitid= qh->vertex_visit;
-      qh_setappend(qh, &vertices, vertex);
-    }
-  }else {
-    vertices= qh_settemp(qh, qh->TEMPsize);
-    FORALLfacet_(facetlist) {
-      if (!allfacets && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHvertex_(facet->vertices) {
-        if (vertex->visitid != qh->vertex_visit) {
-          vertex->visitid= qh->vertex_visit;
-          qh_setappend(qh, &vertices, vertex);
-        }
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (!allfacets && qh_skipfacet(qh, facet))
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        qh_setappend(qh, &vertices, vertex);
-      }
-    }
-  }
-  return vertices;
-} /* facetvertices */
-
-/*---------------------------------
-
-  qh_geomplanes(qh, facet, outerplane, innerplane )
-    return outer and inner planes for Geomview
-    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
-
-  notes:
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-*/
-void qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
-  realT radius;
-
-  if (qh->MERGING || qh->JOGGLEmax < REALmax/2) {
-    qh_outerinner(qh, facet, outerplane, innerplane);
-    radius= qh->PRINTradius;
-    if (qh->JOGGLEmax < REALmax/2)
-      radius -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);  /* already accounted for in qh_outerinner() */
-    *outerplane += radius;
-    *innerplane -= radius;
-    if (qh->PRINTcoplanar || qh->PRINTspheres) {
-      *outerplane += qh->MAXabs_coord * qh_GEOMepsilon;
-      *innerplane -= qh->MAXabs_coord * qh_GEOMepsilon;
-    }
-  }else
-    *innerplane= *outerplane= 0;
-} /* geomplanes */
-
-
-/*---------------------------------
-
-  qh_markkeep(qh, facetlist )
-    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
-    ignores visible facets (!part of convex hull)
-
-  returns:
-    may clear facet->good
-    recomputes qh.num_good
-
-  design:
-    get set of good facets
-    if qh.KEEParea
-      sort facets by area
-      clear facet->good for all but n largest facets
-    if qh.KEEPmerge
-      sort facets by merge count
-      clear facet->good for all but n most merged facets
-    if qh.KEEPminarea
-      clear facet->good if area too small
-    update qh.num_good
-*/
-void qh_markkeep(qhT *qh, facetT *facetlist) {
-  facetT *facet, **facetp;
-  setT *facets= qh_settemp(qh, qh->num_facets);
-  int size, count;
-
-  trace2((qh, qh->ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
-          qh->KEEParea, qh->KEEPmerge, qh->KEEPminArea));
-  FORALLfacet_(facetlist) {
-    if (!facet->visible && facet->good)
-      qh_setappend(qh, &facets, facet);
-  }
-  size= qh_setsize(qh, facets);
-  if (qh->KEEParea) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetarea);
-    if ((count= size - qh->KEEParea) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh->KEEPmerge) {
-    qsort(SETaddr_(facets, facetT), (size_t)size,
-             sizeof(facetT *), qh_compare_facetmerge);
-    if ((count= size - qh->KEEPmerge) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh->KEEPminArea < REALmax/2) {
-    FOREACHfacet_(facets) {
-      if (!facet->isarea || facet->f.area < qh->KEEPminArea)
-        facet->good= False;
-    }
-  }
-  qh_settempfree(qh, &facets);
-  count= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      count++;
-  }
-  qh->num_good= count;
-} /* markkeep */
-
-
-/*---------------------------------
-
-  qh_markvoronoi(qh, facetlist, facets, printall, isLower, numcenters )
-    mark voronoi vertices for printing by site pairs
-
-  returns:
-    temporary set of vertices indexed by pointid
-    isLower set if printing lower hull (i.e., at least one facet is lower hull)
-    numcenters= total number of Voronoi vertices
-    bumps qh.printoutnum for vertex-at-infinity
-    clears all facet->seen and sets facet->seen2
-
-    if selected
-      facet->visitid= Voronoi vertex id
-    else if upper hull (or 'Qu' and lower hull)
-      facet->visitid= 0
-    else
-      facet->visitid >= qh->num_facets
-
-  notes:
-    ignores qh.ATinfinity, if defined
-*/
-setT *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
-  int numcenters=0;
-  facetT *facet, **facetp;
-  setT *vertices;
-  boolT isLower= False;
-
-  qh->printoutnum++;
-  qh_clearcenters(qh, qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
-  qh_vertexneighbors(qh);
-  vertices= qh_pointvertex(qh);
-  if (qh->ATinfinity)
-    SETelem_(vertices, qh->num_points-1)= NULL;
-  qh->visit_id++;
-  maximize_(qh->visit_id, (unsigned) qh->num_facets);
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(qh, facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(qh, facet)) {
-      if (!facet->upperdelaunay) {
-        isLower= True;
-        break;
-      }
-    }
-  }
-  FORALLfacets {
-    if (facet->normal && (facet->upperdelaunay == isLower))
-      facet->visitid= 0;  /* facetlist or facets may overwrite */
-    else
-      facet->visitid= qh->visit_id;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  numcenters++;  /* qh_INFINITE */
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet(qh, facet))
-      facet->visitid= numcenters++;
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet(qh, facet))
-      facet->visitid= numcenters++;
-  }
-  *isLowerp= isLower;
-  *numcentersp= numcenters;
-  trace2((qh, qh->ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
-  return vertices;
-} /* markvoronoi */
-
-/*---------------------------------
-
-  qh_order_vertexneighbors(qh, vertex )
-    order facet neighbors of a 2-d or 3-d vertex by adjacency
-
-  notes:
-    does not orient the neighbors
-
-  design:
-    initialize a new neighbor set with the first facet in vertex->neighbors
-    while vertex->neighbors non-empty
-      select next neighbor in the previous facet's neighbor set
-    set vertex->neighbors to the new neighbor set
-*/
-void qh_order_vertexneighbors(qhT *qh, vertexT *vertex) {
-  setT *newset;
-  facetT *facet, *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
-  newset= qh_settemp(qh, qh_setsize(qh, vertex->neighbors));
-  facet= (facetT*)qh_setdellast(vertex->neighbors);
-  qh_setappend(qh, &newset, facet);
-  while (qh_setsize(qh, vertex->neighbors)) {
-    FOREACHneighbor_(vertex) {
-      if (qh_setin(facet->neighbors, neighbor)) {
-        qh_setdel(vertex->neighbors, neighbor);
-        qh_setappend(qh, &newset, neighbor);
-        facet= neighbor;
-        break;
-      }
-    }
-    if (!neighbor) {
-      qh_fprintf(qh, qh->ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
-        vertex->id, facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-  }
-  qh_setfree(qh, &vertex->neighbors);
-  qh_settemppop(qh);
-  vertex->neighbors= newset;
-} /* order_vertexneighbors */
-
-/*---------------------------------
-
-  qh_prepare_output(qh, )
-    prepare for qh_produce_output2(qh) according to
-      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
-    does not reset facet->good
-
-  notes
-    except for PRINTstatistics, no-op if previously called with same options
-*/
-void qh_prepare_output(qhT *qh) {
-  if (qh->VORONOI) {
-    qh_clearcenters(qh, qh_ASvoronoi);  /* must be before qh_triangulate */
-    qh_vertexneighbors(qh);
-  }
-  if (qh->TRIangulate && !qh->hasTriangulation) {
-    qh_triangulate(qh);
-    if (qh->VERIFYoutput && !qh->CHECKfrequently)
-      qh_checkpolygon(qh, qh->facet_list);
-  }
-  qh_findgood_all(qh, qh->facet_list);
-  if (qh->GETarea)
-    qh_getarea(qh, qh->facet_list);
-  if (qh->KEEParea || qh->KEEPmerge || qh->KEEPminArea < REALmax/2)
-    qh_markkeep(qh, qh->facet_list);
-  if (qh->PRINTstatistics)
-    qh_collectstatistics(qh);
-}
-
-/*---------------------------------
-
-  qh_printafacet(qh, fp, format, facet, printall )
-    print facet to fp in given output format (see qh.PRINTout)
-
-  returns:
-    nop if !printall and qh_skipfacet()
-    nop if visible facet and NEWfacets and format != PRINTfacets
-    must match qh_countfacets
-
-  notes
-    preserves qh.visit_id
-    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
-
-  see
-    qh_printbegin() and qh_printend()
-
-  design:
-    test for printing facet
-    call appropriate routine for format
-    or output results directly
-*/
-void qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
-  realT color[4], offset, dist, outerplane, innerplane;
-  boolT zerodiv;
-  coordT *point, *normp, *coordp, **pointp, *feasiblep;
-  int k;
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  if (!printall && qh_skipfacet(qh, facet))
-    return;
-  if (facet->visible && qh->NEWfacets && format != qh_PRINTfacets)
-    return;
-  qh->printoutnum++;
-  switch (format) {
-  case qh_PRINTarea:
-    if (facet->isarea) {
-      qh_fprintf(qh, fp, 9009, qh_REAL_1, facet->f.area);
-      qh_fprintf(qh, fp, 9010, "\n");
-    }else
-      qh_fprintf(qh, fp, 9011, "0\n");
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(qh, fp, 9012, "%d", qh_setsize(qh, facet->coplanarset));
-    FOREACHpoint_(facet->coplanarset)
-      qh_fprintf(qh, fp, 9013, " %d", qh_pointid(qh, point));
-    qh_fprintf(qh, fp, 9014, "\n");
-    break;
-  case qh_PRINTcentrums:
-    qh_printcenter(qh, fp, format, NULL, facet);
-    break;
-  case qh_PRINTfacets:
-    qh_printfacet(qh, fp, facet);
-    break;
-  case qh_PRINTfacets_xridge:
-    qh_printfacetheader(qh, fp, facet);
-    break;
-  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
-    if (!facet->normal)
-      break;
-    for (k=qh->hull_dim; k--; ) {
-      color[k]= (facet->normal[k]+1.0)/2.0;
-      maximize_(color[k], -1.0);
-      minimize_(color[k], +1.0);
-    }
-    qh_projectdim3(qh, color, color);
-    if (qh->PRINTdim != qh->hull_dim)
-      qh_normalize2(qh, color, 3, True, NULL, NULL);
-    if (qh->hull_dim <= 2)
-      qh_printfacet2geom(qh, fp, facet, color);
-    else if (qh->hull_dim == 3) {
-      if (facet->simplicial)
-        qh_printfacet3geom_simplicial(qh, fp, facet, color);
-      else
-        qh_printfacet3geom_nonsimplicial(qh, fp, facet, color);
-    }else {
-      if (facet->simplicial)
-        qh_printfacet4geom_simplicial(qh, fp, facet, color);
-      else
-        qh_printfacet4geom_nonsimplicial(qh, fp, facet, color);
-    }
-    break;
-  case qh_PRINTids:
-    qh_fprintf(qh, fp, 9015, "%d\n", facet->id);
-    break;
-  case qh_PRINTincidences:
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh->hull_dim == 3 && format != qh_PRINTtriangles)
-      qh_printfacet3vertex(qh, fp, facet, format);
-    else if (facet->simplicial || qh->hull_dim == 2 || format == qh_PRINToff)
-      qh_printfacetNvertex_simplicial(qh, fp, facet, format);
-    else
-      qh_printfacetNvertex_nonsimplicial(qh, fp, facet, qh->printoutvar++, format);
-    break;
-  case qh_PRINTinner:
-    qh_outerinner(qh, facet, NULL, &innerplane);
-    offset= facet->offset - innerplane;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTmerges:
-    qh_fprintf(qh, fp, 9016, "%d\n", facet->nummerge);
-    break;
-  case qh_PRINTnormals:
-    offset= facet->offset;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTouter:
-    qh_outerinner(qh, facet, &outerplane, NULL);
-    offset= facet->offset - outerplane;
-  LABELprintnorm:
-    if (!facet->normal) {
-      qh_fprintf(qh, fp, 9017, "no normal for facet f%d\n", facet->id);
-      break;
-    }
-    if (qh->CDDoutput) {
-      qh_fprintf(qh, fp, 9018, qh_REAL_1, -offset);
-      for (k=0; k < qh->hull_dim; k++)
-        qh_fprintf(qh, fp, 9019, qh_REAL_1, -facet->normal[k]);
-    }else {
-      for (k=0; k < qh->hull_dim; k++)
-        qh_fprintf(qh, fp, 9020, qh_REAL_1, facet->normal[k]);
-      qh_fprintf(qh, fp, 9021, qh_REAL_1, offset);
-    }
-    qh_fprintf(qh, fp, 9022, "\n");
-    break;
-  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
-  case qh_PRINTmaple:
-    if (qh->hull_dim == 2)
-      qh_printfacet2math(qh, fp, facet, format, qh->printoutvar++);
-    else
-      qh_printfacet3math(qh, fp, facet, format, qh->printoutvar++);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(qh, fp, 9023, "%d", qh_setsize(qh, facet->neighbors));
-    FOREACHneighbor_(facet)
-      qh_fprintf(qh, fp, 9024, " %d",
-               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
-    qh_fprintf(qh, fp, 9025, "\n");
-    break;
-  case qh_PRINTpointintersect:
-    if (!qh->feasible_point) {
-      qh_fprintf(qh, qh->ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (facet->offset > 0)
-      goto LABELprintinfinite;
-    point= coordp= (coordT*)qh_memalloc(qh, qh->normal_size);
-    normp= facet->normal;
-    feasiblep= qh->feasible_point;
-    if (facet->offset < -qh->MINdenom) {
-      for (k=qh->hull_dim; k--; )
-        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
-    }else {
-      for (k=qh->hull_dim; k--; ) {
-        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh->MINdenom_1,
-                                 &zerodiv) + *(feasiblep++);
-        if (zerodiv) {
-          qh_memfree(qh, point, qh->normal_size);
-          goto LABELprintinfinite;
-        }
-      }
-    }
-    qh_printpoint(qh, fp, NULL, point);
-    qh_memfree(qh, point, qh->normal_size);
-    break;
-  LABELprintinfinite:
-    for (k=qh->hull_dim; k--; )
-      qh_fprintf(qh, fp, 9026, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(qh, fp, 9027, "\n");
-    break;
-  case qh_PRINTpointnearest:
-    FOREACHpoint_(facet->coplanarset) {
-      int id, id2;
-      vertex= qh_nearvertex(qh, facet, point, &dist);
-      id= qh_pointid(qh, vertex->point);
-      id2= qh_pointid(qh, point);
-      qh_fprintf(qh, fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
-    }
-    break;
-  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9029, "1 ");
-    qh_printcenter(qh, fp, format, NULL, facet);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(qh, fp, 9030, "%d", qh_setsize(qh, facet->vertices));
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9031, " %d", qh_pointid(qh, vertex->point));
-    qh_fprintf(qh, fp, 9032, "\n");
-    break;
-  default:
-    break;
-  }
-} /* printafacet */
-
-/*---------------------------------
-
-  qh_printbegin(qh, )
-    prints header for all output formats
-
-  returns:
-    checks for valid format
-
-  notes:
-    uses qh.visit_id for 3/4off
-    changes qh.interior_point if printing centrums
-    qh_countfacets clears facet->visitid for non-good facets
-
-  see
-    qh_printend() and qh_printafacet()
-
-  design:
-    count facets and related statistics
-    print header for format
-*/
-void qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  int i, num;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-  pointT *point, **pointp, *pointtemp;
-
-  qh->printoutnum= 0;
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-  switch (format) {
-  case qh_PRINTnone:
-    break;
-  case qh_PRINTarea:
-    qh_fprintf(qh, fp, 9033, "%d\n", numfacets);
-    break;
-  case qh_PRINTcoplanars:
-    qh_fprintf(qh, fp, 9034, "%d\n", numfacets);
-    break;
-  case qh_PRINTcentrums:
-    if (qh->CENTERtype == qh_ASnone)
-      qh_clearcenters(qh, qh_AScentrum);
-    qh_fprintf(qh, fp, 9035, "%d\n%d\n", qh->hull_dim, numfacets);
-    break;
-  case qh_PRINTfacets:
-  case qh_PRINTfacets_xridge:
-    if (facetlist)
-      qh_printvertexlist(qh, fp, "Vertices and facets:\n", facetlist, facets, printall);
-    break;
-  case qh_PRINTgeom:
-    if (qh->hull_dim > 4)  /* qh_initqhull_globals also checks */
-      goto LABELnoformat;
-    if (qh->VORONOI && qh->hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
-      goto LABELnoformat;
-    if (qh->hull_dim == 2 && (qh->PRINTridges || qh->DOintersections))
-      qh_fprintf(qh, qh->ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
-    if (qh->hull_dim == 4 && (qh->PRINTinner || qh->PRINTouter ||
-                             (qh->PRINTdim == 4 && qh->PRINTcentrums)))
-      qh_fprintf(qh, qh->ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
-    if (qh->PRINTdim == 4 && (qh->PRINTspheres))
-      qh_fprintf(qh, qh->ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
-    if (qh->PRINTdim == 4 && qh->DOintersections && qh->PRINTnoplanes)
-      qh_fprintf(qh, qh->ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
-    if (qh->PRINTdim == 2) {
-      qh_fprintf(qh, fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
-              qh->rbox_command, qh->qhull_command);
-    }else if (qh->PRINTdim == 3) {
-      qh_fprintf(qh, fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
-              qh->rbox_command, qh->qhull_command);
-    }else if (qh->PRINTdim == 4) {
-      qh->visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
-        qh_printend4geom(qh, NULL, facet, &num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(qh, NULL, facet, &num, printall);
-      qh->ridgeoutnum= num;
-      qh->printoutvar= 0;  /* counts number of ridges in output */
-      qh_fprintf(qh, fp, 9038, "LIST # %s | %s\n", qh->rbox_command, qh->qhull_command);
-    }
-
-    if (qh->PRINTdots) {
-      qh->printoutnum++;
-      num= qh->num_points + qh_setsize(qh, qh->other_points);
-      if (qh->DELAUNAY && qh->ATinfinity)
-        num--;
-      if (qh->PRINTdim == 4)
-        qh_fprintf(qh, fp, 9039, "4VECT %d %d 1\n", num, num);
-      else
-        qh_fprintf(qh, fp, 9040, "VECT %d %d 1\n", num, num);
-
-      for (i=num; i--; ) {
-        if (i % 20 == 0)
-          qh_fprintf(qh, fp, 9041, "\n");
-        qh_fprintf(qh, fp, 9042, "1 ");
-      }
-      qh_fprintf(qh, fp, 9043, "# 1 point per line\n1 ");
-      for (i=num-1; i--; ) { /* num at least 3 for D2 */
-        if (i % 20 == 0)
-          qh_fprintf(qh, fp, 9044, "\n");
-        qh_fprintf(qh, fp, 9045, "0 ");
-      }
-      qh_fprintf(qh, fp, 9046, "# 1 color for all\n");
-      FORALLpoints {
-        if (!qh->DELAUNAY || !qh->ATinfinity || qh_pointid(qh, point) != qh->num_points-1) {
-          if (qh->PRINTdim == 4)
-            qh_printpoint(qh, fp, NULL, point);
-            else
-              qh_printpoint3(qh, fp, point);
-        }
-      }
-      FOREACHpoint_(qh->other_points) {
-        if (qh->PRINTdim == 4)
-          qh_printpoint(qh, fp, NULL, point);
-        else
-          qh_printpoint3(qh, fp, point);
-      }
-      qh_fprintf(qh, fp, 9047, "0 1 1 1  # color of points\n");
-    }
-
-    if (qh->PRINTdim == 4  && !qh->PRINTnoplanes)
-      /* 4dview loads up multiple 4OFF objects slowly */
-      qh_fprintf(qh, fp, 9048, "4OFF %d %d 1\n", 3*qh->ridgeoutnum, qh->ridgeoutnum);
-    qh->PRINTcradius= 2 * qh->DISTround;  /* include test DISTround */
-    if (qh->PREmerge) {
-      maximize_(qh->PRINTcradius, qh->premerge_centrum + qh->DISTround);
-    }else if (qh->POSTmerge)
-      maximize_(qh->PRINTcradius, qh->postmerge_centrum + qh->DISTround);
-    qh->PRINTradius= qh->PRINTcradius;
-    if (qh->PRINTspheres + qh->PRINTcoplanar)
-      maximize_(qh->PRINTradius, qh->MAXabs_coord * qh_MINradius);
-    if (qh->premerge_cos < REALmax/2) {
-      maximize_(qh->PRINTradius, (1- qh->premerge_cos) * qh->MAXabs_coord);
-    }else if (!qh->PREmerge && qh->POSTmerge && qh->postmerge_cos < REALmax/2) {
-      maximize_(qh->PRINTradius, (1- qh->postmerge_cos) * qh->MAXabs_coord);
-    }
-    maximize_(qh->PRINTradius, qh->MINvisible);
-    if (qh->JOGGLEmax < REALmax/2)
-      qh->PRINTradius += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-    if (qh->PRINTdim != 4 &&
-        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
-      vertices= qh_facetvertices(qh, facetlist, facets, printall);
-      if (qh->PRINTspheres && qh->PRINTdim <= 3)
-        qh_printspheres(qh, fp, vertices, qh->PRINTradius);
-      if (qh->PRINTcoplanar || qh->PRINTcentrums) {
-        qh->firstcentrum= True;
-        if (qh->PRINTcoplanar&& !qh->PRINTspheres) {
-          FOREACHvertex_(vertices)
-            qh_printpointvect2(qh, fp, vertex->point, NULL, qh->interior_point, qh->PRINTradius);
-        }
-        FORALLfacet_(facetlist) {
-          if (!printall && qh_skipfacet(qh, facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
-            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
-          if (!qh->PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-        }
-        FOREACHfacet_(facets) {
-          if (!printall && qh_skipfacet(qh, facet))
-            continue;
-          if (!facet->normal)
-            continue;
-          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
-            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
-          if (!qh->PRINTcoplanar)
-            continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
-        }
-      }
-      qh_settempfree(qh, &vertices);
-    }
-    qh->visit_id++; /* for printing hyperplane intersections */
-    break;
-  case qh_PRINTids:
-    qh_fprintf(qh, fp, 9049, "%d\n", numfacets);
-    break;
-  case qh_PRINTincidences:
-    if (qh->VORONOI && qh->PRINTprecision)
-      qh_fprintf(qh, qh->ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
-    qh->printoutvar= qh->vertex_id;  /* centrum id for non-simplicial facets */
-    if (qh->hull_dim <= 3)
-      qh_fprintf(qh, fp, 9050, "%d\n", numfacets);
-    else
-      qh_fprintf(qh, fp, 9051, "%d\n", numsimplicial+numridges);
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh->rbox_command,
-            qh->qhull_command, numfacets, qh->hull_dim+1);
-    else
-      qh_fprintf(qh, fp, 9053, "%d\n%d\n", qh->hull_dim+1, numfacets);
-    break;
-  case qh_PRINTmathematica:
-  case qh_PRINTmaple:
-    if (qh->hull_dim > 3)  /* qh_initbuffers also checks */
-      goto LABELnoformat;
-    if (qh->VORONOI)
-      qh_fprintf(qh, qh->ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
-    if (format == qh_PRINTmaple) {
-      if (qh->hull_dim == 2)
-        qh_fprintf(qh, fp, 9054, "PLOT(CURVES(\n");
-      else
-        qh_fprintf(qh, fp, 9055, "PLOT3D(POLYGONS(\n");
-    }else
-      qh_fprintf(qh, fp, 9056, "{\n");
-    qh->printoutvar= 0;   /* counts number of facets for notfirst */
-    break;
-  case qh_PRINTmerges:
-    qh_fprintf(qh, fp, 9057, "%d\n", numfacets);
-    break;
-  case qh_PRINTpointintersect:
-    qh_fprintf(qh, fp, 9058, "%d\n%d\n", qh->hull_dim, numfacets);
-    break;
-  case qh_PRINTneighbors:
-    qh_fprintf(qh, fp, 9059, "%d\n", numfacets);
-    break;
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh->VORONOI)
-      goto LABELnoformat;
-    num = qh->hull_dim;
-    if (format == qh_PRINToff || qh->hull_dim == 2)
-      qh_fprintf(qh, fp, 9060, "%d\n%d %d %d\n", num,
-        qh->num_points+qh_setsize(qh, qh->other_points), numfacets, totneighbors/2);
-    else { /* qh_PRINTtriangles */
-      qh->printoutvar= qh->num_points+qh_setsize(qh, qh->other_points); /* first centrum */
-      if (qh->DELAUNAY)
-        num--;  /* drop last dimension */
-      qh_fprintf(qh, fp, 9061, "%d\n%d %d %d\n", num, qh->printoutvar
-        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
-    }
-    FORALLpoints
-      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
-    FOREACHpoint_(qh->other_points)
-      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
-    if (format == qh_PRINTtriangles && qh->hull_dim > 2) {
-      FORALLfacets {
-        if (!facet->simplicial && facet->visitid)
-          qh_printcenter(qh, qh->fout, format, NULL, facet);
-      }
-    }
-    break;
-  case qh_PRINTpointnearest:
-    qh_fprintf(qh, fp, 9062, "%d\n", numcoplanars);
-    break;
-  case qh_PRINTpoints:
-    if (!qh->VORONOI)
-      goto LABELnoformat;
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
-           qh->qhull_command, numfacets, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9064, "%d\n%d\n", qh->hull_dim-1, numfacets);
-    break;
-  case qh_PRINTvertices:
-    qh_fprintf(qh, fp, 9065, "%d\n", numfacets);
-    break;
-  case qh_PRINTsummary:
-  default:
-  LABELnoformat:
-    qh_fprintf(qh, qh->ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
-         qh->hull_dim);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* printbegin */
-
-/*---------------------------------
-
-  qh_printcenter(qh, fp, string, facet )
-    print facet->center as centrum or Voronoi center
-    string may be NULL.  Don't include '%' codes.
-    nop if qh->CENTERtype neither CENTERvoronoi nor CENTERcentrum
-    if upper envelope of Delaunay triangulation and point at-infinity
-      prints qh_INFINITE instead;
-
-  notes:
-    defines facet->center if needed
-    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
-    Same as QhullFacet::printCenter
-*/
-void qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
-  int k, num;
-
-  if (qh->CENTERtype != qh_ASvoronoi && qh->CENTERtype != qh_AScentrum)
-    return;
-  if (string)
-    qh_fprintf(qh, fp, 9066, string);
-  if (qh->CENTERtype == qh_ASvoronoi) {
-    num= qh->hull_dim-1;
-    if (!facet->normal || !facet->upperdelaunay || !qh->ATinfinity) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-      for (k=0; k < num; k++)
-        qh_fprintf(qh, fp, 9067, qh_REAL_1, facet->center[k]);
-    }else {
-      for (k=0; k < num; k++)
-        qh_fprintf(qh, fp, 9068, qh_REAL_1, qh_INFINITE);
-    }
-  }else /* qh->CENTERtype == qh_AScentrum */ {
-    num= qh->hull_dim;
-    if (format == qh_PRINTtriangles && qh->DELAUNAY)
-      num--;
-    if (!facet->center)
-      facet->center= qh_getcentrum(qh, facet);
-    for (k=0; k < num; k++)
-      qh_fprintf(qh, fp, 9069, qh_REAL_1, facet->center[k]);
-  }
-  if (format == qh_PRINTgeom && num == 2)
-    qh_fprintf(qh, fp, 9070, " 0\n");
-  else
-    qh_fprintf(qh, fp, 9071, "\n");
-} /* printcenter */
-
-/*---------------------------------
-
-  qh_printcentrum(qh, fp, facet, radius )
-    print centrum for a facet in OOGL format
-    radius defines size of centrum
-    2-d or 3-d only
-
-  returns:
-    defines facet->center if needed
-*/
-void qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius) {
-  pointT *centrum, *projpt;
-  boolT tempcentrum= False;
-  realT xaxis[4], yaxis[4], normal[4], dist;
-  realT green[3]={0, 1, 0};
-  vertexT *apex;
-  int k;
-
-  if (qh->CENTERtype == qh_AScentrum) {
-    if (!facet->center)
-      facet->center= qh_getcentrum(qh, facet);
-    centrum= facet->center;
-  }else {
-    centrum= qh_getcentrum(qh, facet);
-    tempcentrum= True;
-  }
-  qh_fprintf(qh, fp, 9072, "{appearance {-normal -edge normscale 0} ");
-  if (qh->firstcentrum) {
-    qh->firstcentrum= False;
-    qh_fprintf(qh, fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
--0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3  0.3 0.0001     0 0 1 1\n\
--0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
-  }else
-    qh_fprintf(qh, fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
-  apex= SETfirstt_(facet->vertices, vertexT);
-  qh_distplane(qh, apex->point, facet, &dist);
-  projpt= qh_projectpoint(qh, apex->point, facet, dist);
-  for (k=qh->hull_dim; k--; ) {
-    xaxis[k]= projpt[k] - centrum[k];
-    normal[k]= facet->normal[k];
-  }
-  if (qh->hull_dim == 2) {
-    xaxis[2]= 0;
-    normal[2]= 0;
-  }else if (qh->hull_dim == 4) {
-    qh_projectdim3(qh, xaxis, xaxis);
-    qh_projectdim3(qh, normal, normal);
-    qh_normalize2(qh, normal, qh->PRINTdim, True, NULL, NULL);
-  }
-  qh_crossproduct(3, xaxis, normal, yaxis);
-  qh_fprintf(qh, fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
-  qh_fprintf(qh, fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
-  qh_fprintf(qh, fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
-  qh_printpoint3(qh, fp, centrum);
-  qh_fprintf(qh, fp, 9078, "1 }}}\n");
-  qh_memfree(qh, projpt, qh->normal_size);
-  qh_printpointvect(qh, fp, centrum, facet->normal, NULL, radius, green);
-  if (tempcentrum)
-    qh_memfree(qh, centrum, qh->normal_size);
-} /* printcentrum */
-
-/*---------------------------------
-
-  qh_printend(qh, fp, format )
-    prints trailer for all output formats
-
-  see:
-    qh_printbegin() and qh_printafacet()
-
-*/
-void qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int num;
-  facetT *facet, **facetp;
-
-  if (!qh->printoutnum)
-    qh_fprintf(qh, qh->ferr, 7055, "qhull warning: no facets printed\n");
-  switch (format) {
-  case qh_PRINTgeom:
-    if (qh->hull_dim == 4 && qh->DROPdim < 0  && !qh->PRINTnoplanes) {
-      qh->visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)
-        qh_printend4geom(qh, fp, facet,&num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom(qh, fp, facet, &num, printall);
-      if (num != qh->ridgeoutnum || qh->printoutvar != qh->ridgeoutnum) {
-        qh_fprintf(qh, qh->ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh->ridgeoutnum, qh->printoutvar, num);
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-      }
-    }else
-      qh_fprintf(qh, fp, 9079, "}\n");
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9080, "end\n");
-    break;
-  case qh_PRINTmaple:
-    qh_fprintf(qh, fp, 9081, "));\n");
-    break;
-  case qh_PRINTmathematica:
-    qh_fprintf(qh, fp, 9082, "}\n");
-    break;
-  case qh_PRINTpoints:
-    if (qh->CDDoutput)
-      qh_fprintf(qh, fp, 9083, "end\n");
-    break;
-  default:
-    break;
-  }
-} /* printend */
-
-/*---------------------------------
-
-  qh_printend4geom(qh, fp, facet, numridges, printall )
-    helper function for qh_printbegin/printend
-
-  returns:
-    number of printed ridges
-
-  notes:
-    just counts printed ridges if fp=NULL
-    uses facet->visitid
-    must agree with qh_printfacet4geom...
-
-  design:
-    computes color for facet from its normal
-    prints each ridge of facet
-*/
-void qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *nump, boolT printall) {
-  realT color[3];
-  int i, num= *nump;
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-
-  if (!printall && qh_skipfacet(qh, facet))
-    return;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  if (!facet->normal)
-    return;
-  if (fp) {
-    for (i=0; i < 3; i++) {
-      color[i]= (facet->normal[i]+1.0)/2.0;
-      maximize_(color[i], -1.0);
-      minimize_(color[i], +1.0);
-    }
-  }
-  facet->visitid= qh->visit_id;
-  if (facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        if (fp)
-          qh_fprintf(qh, fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }else {
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh->visit_id) {
-        if (fp)
-          qh_fprintf(qh, fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
-                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-                 ridge->id, facet->id, neighbor->id);
-        num++;
-      }
-    }
-  }
-  *nump= num;
-} /* printend4geom */
-
-/*---------------------------------
-
-  qh_printextremes(qh, fp, facetlist, facets, printall )
-    print extreme points for convex hulls or halfspace intersections
-
-  notes:
-    #points, followed by ids, one per line
-
-    sorted by id
-    same order as qh_printpoints_out if no coplanar/interior points
-*/
-void qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices, *points;
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int id;
-  int numpoints=0, point_i, point_n;
-  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-
-  points= qh_settemp(qh, allpoints);
-  qh_setzero(qh, points, 0, allpoints);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(qh, vertex->point);
-    if (id >= 0) {
-      SETelem_(points, id)= vertex->point;
-      numpoints++;
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  qh_fprintf(qh, fp, 9086, "%d\n", numpoints);
-  FOREACHpoint_i_(qh, points) {
-    if (point)
-      qh_fprintf(qh, fp, 9087, "%d\n", point_i);
-  }
-  qh_settempfree(qh, &points);
-} /* printextremes */
-
-/*---------------------------------
-
-  qh_printextremes_2d(qh, fp, facetlist, facets, printall )
-    prints point ids for facets in qh_ORIENTclock order
-
-  notes:
-    #points, followed by ids, one per line
-    if facetlist/facets are disjoint than the output includes skips
-    errors if facets form a loop
-    does not print coplanar points
-*/
-void qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
-  setT *vertices;
-  facetT *facet, *startfacet, *nextfacet;
-  vertexT *vertexA, *vertexB;
-
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh->visit_id */
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_fprintf(qh, fp, 9088, "%d\n", qh_setsize(qh, vertices));
-  qh_settempfree(qh, &vertices);
-  if (!numfacets)
-    return;
-  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
-  qh->vertex_visit++;
-  qh->visit_id++;
-  do {
-    if (facet->toporient ^ qh_ORIENTclock) {
-      vertexA= SETfirstt_(facet->vertices, vertexT);
-      vertexB= SETsecondt_(facet->vertices, vertexT);
-      nextfacet= SETfirstt_(facet->neighbors, facetT);
-    }else {
-      vertexA= SETsecondt_(facet->vertices, vertexT);
-      vertexB= SETfirstt_(facet->vertices, vertexT);
-      nextfacet= SETsecondt_(facet->neighbors, facetT);
-    }
-    if (facet->visitid == qh->visit_id) {
-      qh_fprintf(qh, qh->ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
-                 facet->id, nextfacet->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, nextfacet);
-    }
-    if (facet->visitid) {
-      if (vertexA->visitid != qh->vertex_visit) {
-        vertexA->visitid= qh->vertex_visit;
-        qh_fprintf(qh, fp, 9089, "%d\n", qh_pointid(qh, vertexA->point));
-      }
-      if (vertexB->visitid != qh->vertex_visit) {
-        vertexB->visitid= qh->vertex_visit;
-        qh_fprintf(qh, fp, 9090, "%d\n", qh_pointid(qh, vertexB->point));
-      }
-    }
-    facet->visitid= qh->visit_id;
-    facet= nextfacet;
-  }while (facet && facet != startfacet);
-} /* printextremes_2d */
-
-/*---------------------------------
-
-  qh_printextremes_d(qh, fp, facetlist, facets, printall )
-    print extreme points of input sites for Delaunay triangulations
-
-  notes:
-    #points, followed by ids, one per line
-
-    unordered
-*/
-void qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  vertexT *vertex, **vertexp;
-  boolT upperseen, lowerseen;
-  facetT *neighbor, **neighborp;
-  int numpoints=0;
-
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_vertexneighbors(qh);
-  FOREACHvertex_(vertices) {
-    upperseen= lowerseen= False;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay)
-        upperseen= True;
-      else
-        lowerseen= True;
-    }
-    if (upperseen && lowerseen) {
-      vertex->seen= True;
-      numpoints++;
-    }else
-      vertex->seen= False;
-  }
-  qh_fprintf(qh, fp, 9091, "%d\n", numpoints);
-  FOREACHvertex_(vertices) {
-    if (vertex->seen)
-      qh_fprintf(qh, fp, 9092, "%d\n", qh_pointid(qh, vertex->point));
-  }
-  qh_settempfree(qh, &vertices);
-} /* printextremes_d */
-
-/*---------------------------------
-
-  qh_printfacet(qh, fp, facet )
-    prints all fields of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-*/
-void qh_printfacet(qhT *qh, FILE *fp, facetT *facet) {
-
-  qh_printfacetheader(qh, fp, facet);
-  if (facet->ridges)
-    qh_printfacetridges(qh, fp, facet);
-} /* printfacet */
-
-
-/*---------------------------------
-
-  qh_printfacet2geom(qh, fp, facet, color )
-    print facet as part of a 2-d VECT for Geomview
-
-    notes:
-      assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
-      mindist is calculated within io_r.c.  maxoutside is calculated elsewhere
-      so a DISTround error may have occurred.
-*/
-void qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  pointT *point0, *point1;
-  realT mindist, innerplane, outerplane;
-  int k;
-
-  qh_facet2point(qh, facet, &point0, &point1, &mindist);
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet2geom_points(qh, fp, point0, point1, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet2geom_points(qh, fp, point0, point1, facet, innerplane, color);
-  }
-  qh_memfree(qh, point1, qh->normal_size);
-  qh_memfree(qh, point0, qh->normal_size);
-} /* printfacet2geom */
-
-/*---------------------------------
-
-  qh_printfacet2geom_points(qh, fp, point1, point2, facet, offset, color )
-    prints a 2-d facet as a VECT with 2 points at some offset.
-    The points are on the facet's plane.
-*/
-void qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
-                               facetT *facet, realT offset, realT color[3]) {
-  pointT *p1= point1, *p2= point2;
-
-  qh_fprintf(qh, fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
-  if (offset != 0.0) {
-    p1= qh_projectpoint(qh, p1, facet, -offset);
-    p2= qh_projectpoint(qh, p2, facet, -offset);
-  }
-  qh_fprintf(qh, fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
-           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
-  if (offset != 0.0) {
-    qh_memfree(qh, p1, qh->normal_size);
-    qh_memfree(qh, p2, qh->normal_size);
-  }
-  qh_fprintf(qh, fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printfacet2geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet2math(qh, fp, facet, format, notfirst )
-    print 2-d Maple or Mathematica output for a facet
-    may be non-simplicial
-
-  notes:
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet3math
-*/
-void qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  pointT *point0, *point1;
-  realT mindist;
-  const char *pointfmt;
-
-  qh_facet2point(qh, facet, &point0, &point1, &mindist);
-  if (notfirst)
-    qh_fprintf(qh, fp, 9096, ",");
-  if (format == qh_PRINTmaple)
-    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
-  else
-    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
-  qh_fprintf(qh, fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
-  qh_memfree(qh, point1, qh->normal_size);
-  qh_memfree(qh, point0, qh->normal_size);
-} /* printfacet2math */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_nonsimplicial(qh, fp, facet, color )
-    print Geomview OFF for a 3-d nonsimplicial facet.
-    if DOintersections, prints ridges to unvisited neighbors(qh->visit_id)
-
-  notes
-    uses facet->visitid for intersections and ridges
-*/
-void qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  ridgeT *ridge, **ridgep;
-  setT *projectedpoints, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  pointT *projpt, *point, **pointp;
-  facetT *neighbor;
-  realT dist, outerplane, innerplane;
-  int cntvertices, k;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(qh, facet); /* oriented */
-  cntvertices= qh_setsize(qh, vertices);
-  projectedpoints= qh_settemp(qh, cntvertices);
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(qh, vertex->point, facet, &dist);
-    projpt= qh_projectpoint(qh, vertex->point, facet, dist);
-    qh_setappend(qh, &projectedpoints, projpt);
-  }
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, innerplane, color);
-  }
-  FOREACHpoint_(projectedpoints)
-    qh_memfree(qh, point, qh->normal_size);
-  qh_settempfree(qh, &projectedpoints);
-  qh_settempfree(qh, &vertices);
-  if ((qh->DOintersections || qh->PRINTridges)
-  && (!facet->visible || !qh->NEWfacets)) {
-    facet->visitid= qh->visit_id;
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh->visit_id) {
-        if (qh->DOintersections)
-          qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, black);
-        if (qh->PRINTridges) {
-          vertexA= SETfirstt_(ridge->vertices, vertexT);
-          vertexB= SETsecondt_(ridge->vertices, vertexT);
-          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
-        }
-      }
-    }
-  }
-} /* printfacet3geom_nonsimplicial */
-
-/*---------------------------------
-
-  qh_printfacet3geom_points(qh, fp, points, facet, offset )
-    prints a 3-d facet as OFF Geomview object.
-    offset is relative to the facet's hyperplane
-    Facet is determined as a list of points
-*/
-void qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
-  int k, n= qh_setsize(qh, points), i;
-  pointT *point, **pointp;
-  setT *printpoints;
-
-  qh_fprintf(qh, fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
-  if (offset != 0.0) {
-    printpoints= qh_settemp(qh, n);
-    FOREACHpoint_(points)
-      qh_setappend(qh, &printpoints, qh_projectpoint(qh, point, facet, -offset));
-  }else
-    printpoints= points;
-  FOREACHpoint_(printpoints) {
-    for (k=0; k < qh->hull_dim; k++) {
-      if (k == qh->DROPdim)
-        qh_fprintf(qh, fp, 9099, "0 ");
-      else
-        qh_fprintf(qh, fp, 9100, "%8.4g ", point[k]);
-    }
-    if (printpoints != points)
-      qh_memfree(qh, point, qh->normal_size);
-    qh_fprintf(qh, fp, 9101, "\n");
-  }
-  if (printpoints != points)
-    qh_settempfree(qh, &printpoints);
-  qh_fprintf(qh, fp, 9102, "%d ", n);
-  for (i=0; i < n; i++)
-    qh_fprintf(qh, fp, 9103, "%d ", i);
-  qh_fprintf(qh, fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
-} /* printfacet3geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_simplicial(qh, )
-    print Geomview OFF for a 3-d simplicial facet.
-
-  notes:
-    may flip color
-    uses facet->visitid for intersections and ridges
-
-    assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
-    innerplane may be off by qh->DISTround.  Maxoutside is calculated elsewhere
-    so a DISTround error may have occurred.
-*/
-void qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  setT *points, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  facetT *neighbor, **neighborp;
-  realT outerplane, innerplane;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-  int k;
-
-  qh_geomplanes(qh, facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex(qh, facet);
-  points= qh_settemp(qh, qh->TEMPsize);
-  FOREACHvertex_(vertices)
-    qh_setappend(qh, &points, vertex->point);
-  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
-    qh_printfacet3geom_points(qh, fp, points, facet, outerplane, color);
-  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
-              outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(qh, fp, points, facet, innerplane, color);
-  }
-  qh_settempfree(qh, &points);
-  qh_settempfree(qh, &vertices);
-  if ((qh->DOintersections || qh->PRINTridges)
-  && (!facet->visible || !qh->NEWfacets)) {
-    facet->visitid= qh->visit_id;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-        if (qh->DOintersections)
-           qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, black);
-        if (qh->PRINTridges) {
-          vertexA= SETfirstt_(vertices, vertexT);
-          vertexB= SETsecondt_(vertices, vertexT);
-          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
-        }
-        qh_setfree(qh, &vertices);
-      }
-    }
-  }
-} /* printfacet3geom_simplicial */
-
-/*---------------------------------
-
-  qh_printfacet3math(qh, fp, facet, notfirst )
-    print 3-d Maple or Mathematica output for a facet
-
-  notes:
-    may be non-simplicial
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-    see qh_printfacet2math
-*/
-void qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
-  vertexT *vertex, **vertexp;
-  setT *points, *vertices;
-  pointT *point, **pointp;
-  boolT firstpoint= True;
-  realT dist;
-  const char *pointfmt, *endfmt;
-
-  if (notfirst)
-    qh_fprintf(qh, fp, 9105, ",\n");
-  vertices= qh_facet3vertex(qh, facet);
-  points= qh_settemp(qh, qh_setsize(qh, vertices));
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(qh, vertex->point, facet, &dist);
-    point= qh_projectpoint(qh, vertex->point, facet, dist);
-    qh_setappend(qh, &points, point);
-  }
-  if (format == qh_PRINTmaple) {
-    qh_fprintf(qh, fp, 9106, "[");
-    pointfmt= "[%16.8f, %16.8f, %16.8f]";
-    endfmt= "]";
-  }else {
-    qh_fprintf(qh, fp, 9107, "Polygon[{");
-    pointfmt= "{%16.8f, %16.8f, %16.8f}";
-    endfmt= "}]";
-  }
-  FOREACHpoint_(points) {
-    if (firstpoint)
-      firstpoint= False;
-    else
-      qh_fprintf(qh, fp, 9108, ",\n");
-    qh_fprintf(qh, fp, 9109, pointfmt, point[0], point[1], point[2]);
-  }
-  FOREACHpoint_(points)
-    qh_memfree(qh, point, qh->normal_size);
-  qh_settempfree(qh, &points);
-  qh_settempfree(qh, &vertices);
-  qh_fprintf(qh, fp, 9110, "%s", endfmt);
-} /* printfacet3math */
-
-
-/*---------------------------------
-
-  qh_printfacet3vertex(qh, fp, facet, format )
-    print vertices in a 3-d facet as point ids
-
-  notes:
-    prints number of vertices first if format == qh_PRINToff
-    the facet may be non-simplicial
-*/
-void qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facet3vertex(qh, facet);
-  if (format == qh_PRINToff)
-    qh_fprintf(qh, fp, 9111, "%d ", qh_setsize(qh, vertices));
-  FOREACHvertex_(vertices)
-    qh_fprintf(qh, fp, 9112, "%d ", qh_pointid(qh, vertex->point));
-  qh_fprintf(qh, fp, 9113, "\n");
-  qh_settempfree(qh, &vertices);
-} /* printfacet3vertex */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_nonsimplicial(qh, )
-    print Geomview 4OFF file for a 4d nonsimplicial facet
-    prints all ridges to unvisited neighbors (qh.visit_id)
-    if qh.DROPdim
-      prints in OFF format
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  facetT *neighbor;
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  pointT *point;
-  int k;
-  realT dist;
-
-  facet->visitid= qh->visit_id;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh->visit_id)
-      continue;
-    if (qh->PRINTtransparent && !neighbor->good)
-      continue;
-    if (qh->DOintersections)
-      qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, color);
-    else {
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
-      else {
-        qh->printoutvar++;
-        qh_fprintf(qh, fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
-      }
-      FOREACHvertex_(ridge->vertices) {
-        zinc_(Zdistio);
-        qh_distplane(qh, vertex->point,facet, &dist);
-        point=qh_projectpoint(qh, vertex->point,facet, dist);
-        for (k=0; k < qh->hull_dim; k++) {
-          if (k != qh->DROPdim)
-            qh_fprintf(qh, fp, 9116, "%8.4g ", point[k]);
-        }
-        qh_fprintf(qh, fp, 9117, "\n");
-        qh_memfree(qh, point, qh->normal_size);
-      }
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-  }
-} /* printfacet4geom_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_simplicial(qh, fp, facet, color )
-    print Geomview 4OFF file for a 4d simplicial facet
-    prints triangles for unvisited neighbors (qh.visit_id)
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
-  setT *vertices;
-  facetT *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int k;
-
-  facet->visitid= qh->visit_id;
-  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
-    return;
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid == qh->visit_id)
-      continue;
-    if (qh->PRINTtransparent && !neighbor->good)
-      continue;
-    vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                          SETindex_(facet->neighbors, neighbor), 0);
-    if (qh->DOintersections)
-      qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, color);
-    else {
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
-                facet->id, neighbor->id);
-      else {
-        qh->printoutvar++;
-        qh_fprintf(qh, fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
-      }
-      FOREACHvertex_(vertices) {
-        for (k=0; k < qh->hull_dim; k++) {
-          if (k != qh->DROPdim)
-            qh_fprintf(qh, fp, 9121, "%8.4g ", vertex->point[k]);
-        }
-        qh_fprintf(qh, fp, 9122, "\n");
-      }
-      if (qh->DROPdim >= 0)
-        qh_fprintf(qh, fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-    qh_setfree(qh, &vertices);
-  }
-} /* printfacet4geom_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_nonsimplicial(qh, fp, facet, id, format )
-    print vertices for an N-d non-simplicial facet
-    triangulates each ridge to the id
-*/
-void qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->visible && qh->NEWfacets)
-    return;
-  FOREACHridge_(facet->ridges) {
-    if (format == qh_PRINTtriangles)
-      qh_fprintf(qh, fp, 9124, "%d ", qh->hull_dim);
-    qh_fprintf(qh, fp, 9125, "%d ", id);
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      FOREACHvertex_(ridge->vertices)
-        qh_fprintf(qh, fp, 9126, "%d ", qh_pointid(qh, vertex->point));
-    }else {
-      FOREACHvertexreverse12_(ridge->vertices)
-        qh_fprintf(qh, fp, 9127, "%d ", qh_pointid(qh, vertex->point));
-    }
-    qh_fprintf(qh, fp, 9128, "\n");
-  }
-} /* printfacetNvertex_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_simplicial(qh, fp, facet, format )
-    print vertices for an N-d simplicial facet
-    prints vertices for non-simplicial facets
-      2-d facets (orientation preserved by qh_mergefacet2d)
-      PRINToff ('o') for 4-d and higher
-*/
-void qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
-  vertexT *vertex, **vertexp;
-
-  if (format == qh_PRINToff || format == qh_PRINTtriangles)
-    qh_fprintf(qh, fp, 9129, "%d ", qh_setsize(qh, facet->vertices));
-  if ((facet->toporient ^ qh_ORIENTclock)
-  || (qh->hull_dim > 2 && !facet->simplicial)) {
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9130, "%d ", qh_pointid(qh, vertex->point));
-  }else {
-    FOREACHvertexreverse12_(facet->vertices)
-      qh_fprintf(qh, fp, 9131, "%d ", qh_pointid(qh, vertex->point));
-  }
-  qh_fprintf(qh, fp, 9132, "\n");
-} /* printfacetNvertex_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetheader(qh, fp, facet )
-    prints header fields of a facet to fp
-
-  notes:
-    for 'f' output and debugging
-    Same as QhullFacet::printHeader()
-*/
-void qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet) {
-  pointT *point, **pointp, *furthest;
-  facetT *neighbor, **neighborp;
-  realT dist;
-
-  if (facet == qh_MERGEridge) {
-    qh_fprintf(qh, fp, 9133, " MERGEridge\n");
-    return;
-  }else if (facet == qh_DUPLICATEridge) {
-    qh_fprintf(qh, fp, 9134, " DUPLICATEridge\n");
-    return;
-  }else if (!facet) {
-    qh_fprintf(qh, fp, 9135, " NULLfacet\n");
-    return;
-  }
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  qh_fprintf(qh, fp, 9136, "- f%d\n", facet->id);
-  qh_fprintf(qh, fp, 9137, "    - flags:");
-  if (facet->toporient)
-    qh_fprintf(qh, fp, 9138, " top");
-  else
-    qh_fprintf(qh, fp, 9139, " bottom");
-  if (facet->simplicial)
-    qh_fprintf(qh, fp, 9140, " simplicial");
-  if (facet->tricoplanar)
-    qh_fprintf(qh, fp, 9141, " tricoplanar");
-  if (facet->upperdelaunay)
-    qh_fprintf(qh, fp, 9142, " upperDelaunay");
-  if (facet->visible)
-    qh_fprintf(qh, fp, 9143, " visible");
-  if (facet->newfacet)
-    qh_fprintf(qh, fp, 9144, " new");
-  if (facet->tested)
-    qh_fprintf(qh, fp, 9145, " tested");
-  if (!facet->good)
-    qh_fprintf(qh, fp, 9146, " notG");
-  if (facet->seen)
-    qh_fprintf(qh, fp, 9147, " seen");
-  if (facet->coplanar)
-    qh_fprintf(qh, fp, 9148, " coplanar");
-  if (facet->mergehorizon)
-    qh_fprintf(qh, fp, 9149, " mergehorizon");
-  if (facet->keepcentrum)
-    qh_fprintf(qh, fp, 9150, " keepcentrum");
-  if (facet->dupridge)
-    qh_fprintf(qh, fp, 9151, " dupridge");
-  if (facet->mergeridge && !facet->mergeridge2)
-    qh_fprintf(qh, fp, 9152, " mergeridge1");
-  if (facet->mergeridge2)
-    qh_fprintf(qh, fp, 9153, " mergeridge2");
-  if (facet->newmerge)
-    qh_fprintf(qh, fp, 9154, " newmerge");
-  if (facet->flipped)
-    qh_fprintf(qh, fp, 9155, " flipped");
-  if (facet->notfurthest)
-    qh_fprintf(qh, fp, 9156, " notfurthest");
-  if (facet->degenerate)
-    qh_fprintf(qh, fp, 9157, " degenerate");
-  if (facet->redundant)
-    qh_fprintf(qh, fp, 9158, " redundant");
-  qh_fprintf(qh, fp, 9159, "\n");
-  if (facet->isarea)
-    qh_fprintf(qh, fp, 9160, "    - area: %2.2g\n", facet->f.area);
-  else if (qh->NEWfacets && facet->visible && facet->f.replace)
-    qh_fprintf(qh, fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
-  else if (facet->newfacet) {
-    if (facet->f.samecycle && facet->f.samecycle != facet)
-      qh_fprintf(qh, fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
-  }else if (facet->tricoplanar /* !isarea */) {
-    if (facet->f.triowner)
-      qh_fprintf(qh, fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
-  }else if (facet->f.newcycle)
-    qh_fprintf(qh, fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
-  if (facet->nummerge)
-    qh_fprintf(qh, fp, 9165, "    - merges: %d\n", facet->nummerge);
-  qh_printpointid(qh, fp, "    - normal: ", qh->hull_dim, facet->normal, qh_IDunknown);
-  qh_fprintf(qh, fp, 9166, "    - offset: %10.7g\n", facet->offset);
-  if (qh->CENTERtype == qh_ASvoronoi || facet->center)
-    qh_printcenter(qh, fp, qh_PRINTfacets, "    - center: ", facet);
-#if qh_MAXoutside
-  if (facet->maxoutside > qh->DISTround)
-    qh_fprintf(qh, fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
-#endif
-  if (!SETempty_(facet->outsideset)) {
-    furthest= (pointT*)qh_setlast(facet->outsideset);
-    if (qh_setsize(qh, facet->outsideset) < 6) {
-      qh_fprintf(qh, fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(qh, furthest));
-      FOREACHpoint_(facet->outsideset)
-        qh_printpoint(qh, fp, "     ", point);
-    }else if (qh_setsize(qh, facet->outsideset) < 21) {
-      qh_printpoints(qh, fp, "    - outside set:", facet->outsideset);
-    }else {
-      qh_fprintf(qh, fp, 9169, "    - outside set:  %d points.", qh_setsize(qh, facet->outsideset));
-      qh_printpoint(qh, fp, "  Furthest", furthest);
-    }
-#if !qh_COMPUTEfurthest
-    qh_fprintf(qh, fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
-#endif
-  }
-  if (!SETempty_(facet->coplanarset)) {
-    furthest= (pointT*)qh_setlast(facet->coplanarset);
-    if (qh_setsize(qh, facet->coplanarset) < 6) {
-      qh_fprintf(qh, fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(qh, furthest));
-      FOREACHpoint_(facet->coplanarset)
-        qh_printpoint(qh, fp, "     ", point);
-    }else if (qh_setsize(qh, facet->coplanarset) < 21) {
-      qh_printpoints(qh, fp, "    - coplanar set:", facet->coplanarset);
-    }else {
-      qh_fprintf(qh, fp, 9172, "    - coplanar set:  %d points.", qh_setsize(qh, facet->coplanarset));
-      qh_printpoint(qh, fp, "  Furthest", furthest);
-    }
-    zinc_(Zdistio);
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, fp, 9173, "      furthest distance= %2.2g\n", dist);
-  }
-  qh_printvertices(qh, fp, "    - vertices:", facet->vertices);
-  qh_fprintf(qh, fp, 9174, "    - neighboring facets:");
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      qh_fprintf(qh, fp, 9175, " MERGE");
-    else if (neighbor == qh_DUPLICATEridge)
-      qh_fprintf(qh, fp, 9176, " DUP");
-    else
-      qh_fprintf(qh, fp, 9177, " f%d", neighbor->id);
-  }
-  qh_fprintf(qh, fp, 9178, "\n");
-  qh->RANDOMdist= qh->old_randomdist;
-} /* printfacetheader */
-
-
-/*---------------------------------
-
-  qh_printfacetridges(qh, fp, facet )
-    prints ridges of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-    assumes the ridges exist
-    for 'f' output
-    same as QhullFacet::printRidges
-*/
-void qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int numridges= 0;
-
-
-  if (facet->visible && qh->NEWfacets) {
-    qh_fprintf(qh, fp, 9179, "    - ridges(ids may be garbage):");
-    FOREACHridge_(facet->ridges)
-      qh_fprintf(qh, fp, 9180, " r%d", ridge->id);
-    qh_fprintf(qh, fp, 9181, "\n");
-  }else {
-    qh_fprintf(qh, fp, 9182, "    - ridges:\n");
-    FOREACHridge_(facet->ridges)
-      ridge->seen= False;
-    if (qh->hull_dim == 3) {
-      ridge= SETfirstt_(facet->ridges, ridgeT);
-      while (ridge && !ridge->seen) {
-        ridge->seen= True;
-        qh_printridge(qh, fp, ridge);
-        numridges++;
-        ridge= qh_nextridge3d(ridge, facet, NULL);
-        }
-    }else {
-      FOREACHneighbor_(facet) {
-        FOREACHridge_(facet->ridges) {
-          if (otherfacet_(ridge,facet) == neighbor) {
-            ridge->seen= True;
-            qh_printridge(qh, fp, ridge);
-            numridges++;
-          }
-        }
-      }
-    }
-    if (numridges != qh_setsize(qh, facet->ridges)) {
-      qh_fprintf(qh, fp, 9183, "     - all ridges:");
-      FOREACHridge_(facet->ridges)
-        qh_fprintf(qh, fp, 9184, " r%d", ridge->id);
-        qh_fprintf(qh, fp, 9185, "\n");
-    }
-    FOREACHridge_(facet->ridges) {
-      if (!ridge->seen)
-        qh_printridge(qh, fp, ridge);
-    }
-  }
-} /* printfacetridges */
-
-/*---------------------------------
-
-  qh_printfacets(qh, fp, format, facetlist, facets, printall )
-    prints facetlist and/or facet set in output format
-
-  notes:
-    also used for specialized formats ('FO' and summary)
-    turns off 'Rn' option since want actual numbers
-*/
-void qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  facetT *facet, **facetp;
-  setT *vertices;
-  coordT *center;
-  realT outerplane, innerplane;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  if (qh->CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
-    qh_fprintf(qh, qh->ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
-  if (format == qh_PRINTnone)
-    ; /* print nothing */
-  else if (format == qh_PRINTaverage) {
-    vertices= qh_facetvertices(qh, facetlist, facets, printall);
-    center= qh_getcenter(qh, vertices);
-    qh_fprintf(qh, fp, 9186, "%d 1\n", qh->hull_dim);
-    qh_printpointid(qh, fp, NULL, qh->hull_dim, center, qh_IDunknown);
-    qh_memfree(qh, center, qh->normal_size);
-    qh_settempfree(qh, &vertices);
-  }else if (format == qh_PRINTextremes) {
-    if (qh->DELAUNAY)
-      qh_printextremes_d(qh, fp, facetlist, facets, printall);
-    else if (qh->hull_dim == 2)
-      qh_printextremes_2d(qh, fp, facetlist, facets, printall);
-    else
-      qh_printextremes(qh, fp, facetlist, facets, printall);
-  }else if (format == qh_PRINToptions)
-    qh_fprintf(qh, fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  else if (format == qh_PRINTpoints && !qh->VORONOI)
-    qh_printpoints_out(qh, fp, facetlist, facets, printall);
-  else if (format == qh_PRINTqhull)
-    qh_fprintf(qh, fp, 9188, "%s | %s\n", qh->rbox_command, qh->qhull_command);
-  else if (format == qh_PRINTsize) {
-    qh_fprintf(qh, fp, 9189, "0\n2 ");
-    qh_fprintf(qh, fp, 9190, qh_REAL_1, qh->totarea);
-    qh_fprintf(qh, fp, 9191, qh_REAL_1, qh->totvol);
-    qh_fprintf(qh, fp, 9192, "\n");
-  }else if (format == qh_PRINTsummary) {
-    qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-    vertices= qh_facetvertices(qh, facetlist, facets, printall);
-    qh_fprintf(qh, fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh->hull_dim,
-                qh->num_points + qh_setsize(qh, qh->other_points),
-                qh->num_vertices, qh->num_facets - qh->num_visible,
-                qh_setsize(qh, vertices), numfacets, numcoplanars,
-                numfacets - numsimplicial, zzval_(Zdelvertextot),
-                numtricoplanars);
-    qh_settempfree(qh, &vertices);
-    qh_outerinner(qh, NULL, &outerplane, &innerplane);
-    qh_fprintf(qh, fp, 9194, qh_REAL_2n, outerplane, innerplane);
-  }else if (format == qh_PRINTvneighbors)
-    qh_printvneighbors(qh, fp, facetlist, facets, printall);
-  else if (qh->VORONOI && format == qh_PRINToff)
-    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
-  else if (qh->VORONOI && format == qh_PRINTgeom) {
-    qh_printbegin(qh, fp, format, facetlist, facets, printall);
-    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
-    qh_printend(qh, fp, format, facetlist, facets, printall);
-  }else if (qh->VORONOI
-  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
-    qh_printvdiagram(qh, fp, format, facetlist, facets, printall);
-  else {
-    qh_printbegin(qh, fp, format, facetlist, facets, printall);
-    FORALLfacet_(facetlist)
-      qh_printafacet(qh, fp, format, facet, printall);
-    FOREACHfacet_(facets)
-      qh_printafacet(qh, fp, format, facet, printall);
-    qh_printend(qh, fp, format, facetlist, facets, printall);
-  }
-  qh->RANDOMdist= qh->old_randomdist;
-} /* printfacets */
-
-
-/*---------------------------------
-
-  qh_printhyperplaneintersection(qh, fp, facet1, facet2, vertices, color )
-    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
-*/
-void qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
-                   setT *vertices, realT color[3]) {
-  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
-  vertexT *vertex, **vertexp;
-  int i, k;
-  boolT nearzero1, nearzero2;
-
-  costheta= qh_getangle(qh, facet1->normal, facet2->normal);
-  denominator= 1 - costheta * costheta;
-  i= qh_setsize(qh, vertices);
-  if (qh->hull_dim == 3)
-    qh_fprintf(qh, fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
-  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
-    qh_fprintf(qh, fp, 9196, "OFF 3 1 1 ");
-  else
-    qh->printoutvar++;
-  qh_fprintf(qh, fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
-  mindenom= 1 / (10.0 * qh->MAXabs_coord);
-  FOREACHvertex_(vertices) {
-    zadd_(Zdistio, 2);
-    qh_distplane(qh, vertex->point, facet1, &dist1);
-    qh_distplane(qh, vertex->point, facet2, &dist2);
-    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
-    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
-    if (nearzero1 || nearzero2)
-      s= t= 0.0;
-    for (k=qh->hull_dim; k--; )
-      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
-    if (qh->PRINTdim <= 3) {
-      qh_projectdim3(qh, p, p);
-      qh_fprintf(qh, fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
-    }else
-      qh_fprintf(qh, fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
-    if (nearzero1+nearzero2)
-      qh_fprintf(qh, fp, 9200, "p%d(coplanar facets)\n", qh_pointid(qh, vertex->point));
-    else
-      qh_fprintf(qh, fp, 9201, "projected p%d\n", qh_pointid(qh, vertex->point));
-  }
-  if (qh->hull_dim == 3)
-    qh_fprintf(qh, fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
-    qh_fprintf(qh, fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printhyperplaneintersection */
-
-/*---------------------------------
-
-  qh_printline3geom(qh, fp, pointA, pointB, color )
-    prints a line as a VECT
-    prints 0's for qh.DROPdim
-
-  notes:
-    if pointA == pointB,
-      it's a 1 point VECT
-*/
-void qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
-  int k;
-  realT pA[4], pB[4];
-
-  qh_projectdim3(qh, pointA, pA);
-  qh_projectdim3(qh, pointB, pB);
-  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
-      (fabs(pA[1] - pB[1]) > 1e-3) ||
-      (fabs(pA[2] - pB[2]) > 1e-3)) {
-    qh_fprintf(qh, fp, 9204, "VECT 1 2 1 2 1\n");
-    for (k=0; k < 3; k++)
-       qh_fprintf(qh, fp, 9205, "%8.4g ", pB[k]);
-    qh_fprintf(qh, fp, 9206, " # p%d\n", qh_pointid(qh, pointB));
-  }else
-    qh_fprintf(qh, fp, 9207, "VECT 1 1 1 1 1\n");
-  for (k=0; k < 3; k++)
-    qh_fprintf(qh, fp, 9208, "%8.4g ", pA[k]);
-  qh_fprintf(qh, fp, 9209, " # p%d\n", qh_pointid(qh, pointA));
-  qh_fprintf(qh, fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
-}
-
-/*---------------------------------
-
-  qh_printneighborhood(qh, fp, format, facetA, facetB, printall )
-    print neighborhood of one or two facets
-
-  notes:
-    calls qh_findgood_all()
-    bumps qh.visit_id
-*/
-void qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
-  facetT *neighbor, **neighborp, *facet;
-  setT *facets;
-
-  if (format == qh_PRINTnone)
-    return;
-  qh_findgood_all(qh, qh->facet_list);
-  if (facetA == facetB)
-    facetB= NULL;
-  facets= qh_settemp(qh, 2*(qh_setsize(qh, facetA->neighbors)+1));
-  qh->visit_id++;
-  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
-    if (facet->visitid != qh->visit_id) {
-      facet->visitid= qh->visit_id;
-      qh_setappend(qh, &facets, facet);
-    }
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      if (printall || !qh_skipfacet(qh, neighbor))
-        qh_setappend(qh, &facets, neighbor);
-    }
-  }
-  qh_printfacets(qh, fp, format, NULL, facets, printall);
-  qh_settempfree(qh, &facets);
-} /* printneighborhood */
-
-/*---------------------------------
-
-  qh_printpoint(qh, fp, string, point )
-  qh_printpointid(qh, fp, string, dim, point, id )
-    prints the coordinates of a point
-
-  returns:
-    if string is defined
-      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
-
-  notes:
-    nop if point is NULL
-    Same as QhullPoint's printPoint
-*/
-void qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point) {
-  int id= qh_pointid(qh, point);
-
-  qh_printpointid(qh, fp, string, qh->hull_dim, point, id);
-} /* printpoint */
-
-void qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id) {
-  int k;
-  realT r; /*bug fix*/
-
-  if (!point)
-    return;
-  if (string) {
-    qh_fprintf(qh, fp, 9211, "%s", string);
-    if (id != qh_IDunknown && id != qh_IDnone)
-      qh_fprintf(qh, fp, 9212, " p%d: ", id);
-  }
-  for (k=dim; k--; ) {
-    r= *point++;
-    if (string)
-      qh_fprintf(qh, fp, 9213, " %8.4g", r);
-    else
-      qh_fprintf(qh, fp, 9214, qh_REAL_1, r);
-  }
-  qh_fprintf(qh, fp, 9215, "\n");
-} /* printpointid */
-
-/*---------------------------------
-
-  qh_printpoint3(qh, fp, point )
-    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
-*/
-void qh_printpoint3(qhT *qh, FILE *fp, pointT *point) {
-  int k;
-  realT p[4];
-
-  qh_projectdim3(qh, point, p);
-  for (k=0; k < 3; k++)
-    qh_fprintf(qh, fp, 9216, "%8.4g ", p[k]);
-  qh_fprintf(qh, fp, 9217, " # p%d\n", qh_pointid(qh, point));
-} /* printpoint3 */
-
-/*----------------------------------------
--printpoints- print pointids for a set of points starting at index
-   see geom_r.c
-*/
-
-/*---------------------------------
-
-  qh_printpoints_out(qh, fp, facetlist, facets, printall )
-    prints vertices, coplanar/inside points, for facets by their point coordinates
-    allows qh.CDDoutput
-
-  notes:
-    same format as qhull input
-    if no coplanar/interior points,
-      same order as qh_printextremes
-*/
-void qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
-  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  int numpoints=0, point_i, point_n;
-  setT *vertices, *points;
-  facetT *facet, **facetp;
-  pointT *point, **pointp;
-  vertexT *vertex, **vertexp;
-  int id;
-
-  points= qh_settemp(qh, allpoints);
-  qh_setzero(qh, points, 0, allpoints);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid(qh, vertex->point);
-    if (id >= 0)
-      SETelem_(points, id)= vertex->point;
-  }
-  if (qh->KEEPinside || qh->KEEPcoplanar || qh->KEEPnearinside) {
-    FORALLfacet_(facetlist) {
-      if (!printall && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(qh, point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-    FOREACHfacet_(facets) {
-      if (!printall && qh_skipfacet(qh, facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid(qh, point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  FOREACHpoint_i_(qh, points) {
-    if (point)
-      numpoints++;
-  }
-  if (qh->CDDoutput)
-    qh_fprintf(qh, fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
-             qh->qhull_command, numpoints, qh->hull_dim + 1);
-  else
-    qh_fprintf(qh, fp, 9219, "%d\n%d\n", qh->hull_dim, numpoints);
-  FOREACHpoint_i_(qh, points) {
-    if (point) {
-      if (qh->CDDoutput)
-        qh_fprintf(qh, fp, 9220, "1 ");
-      qh_printpoint(qh, fp, NULL, point);
-    }
-  }
-  if (qh->CDDoutput)
-    qh_fprintf(qh, fp, 9221, "end\n");
-  qh_settempfree(qh, &points);
-} /* printpoints_out */
-
-
-/*---------------------------------
-
-  qh_printpointvect(qh, fp, point, normal, center, radius, color )
-    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
-*/
-void qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
-  realT diff[4], pointA[4];
-  int k;
-
-  for (k=qh->hull_dim; k--; ) {
-    if (center)
-      diff[k]= point[k]-center[k];
-    else if (normal)
-      diff[k]= normal[k];
-    else
-      diff[k]= 0;
-  }
-  if (center)
-    qh_normalize2(qh, diff, qh->hull_dim, True, NULL, NULL);
-  for (k=qh->hull_dim; k--; )
-    pointA[k]= point[k]+diff[k] * radius;
-  qh_printline3geom(qh, fp, point, pointA, color);
-} /* printpointvect */
-
-/*---------------------------------
-
-  qh_printpointvect2(qh, fp, point, normal, center, radius )
-    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
-*/
-void qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
-  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
-
-  qh_printpointvect(qh, fp, point, normal, center, radius, red);
-  qh_printpointvect(qh, fp, point, normal, center, -radius, yellow);
-} /* printpointvect2 */
-
-/*---------------------------------
-
-  qh_printridge(qh, fp, ridge )
-    prints the information in a ridge
-
-  notes:
-    for qh_printfacetridges()
-    same as operator<< [QhullRidge.cpp]
-*/
-void qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge) {
-
-  qh_fprintf(qh, fp, 9222, "     - r%d", ridge->id);
-  if (ridge->tested)
-    qh_fprintf(qh, fp, 9223, " tested");
-  if (ridge->nonconvex)
-    qh_fprintf(qh, fp, 9224, " nonconvex");
-  qh_fprintf(qh, fp, 9225, "\n");
-  qh_printvertices(qh, fp, "           vertices:", ridge->vertices);
-  if (ridge->top && ridge->bottom)
-    qh_fprintf(qh, fp, 9226, "           between f%d and f%d\n",
-            ridge->top->id, ridge->bottom->id);
-} /* printridge */
-
-/*---------------------------------
-
-  qh_printspheres(qh, fp, vertices, radius )
-    prints 3-d vertices as OFF spheres
-
-  notes:
-    inflated octahedron from Stuart Levy earth/mksphere2
-*/
-void qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius) {
-  vertexT *vertex, **vertexp;
-
-  qh->printoutnum++;
-  qh_fprintf(qh, fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
-INST geom {define vsphere OFF\n\
-18 32 48\n\
-\n\
-0 0 1\n\
-1 0 0\n\
-0 1 0\n\
--1 0 0\n\
-0 -1 0\n\
-0 0 -1\n\
-0.707107 0 0.707107\n\
-0 -0.707107 0.707107\n\
-0.707107 -0.707107 0\n\
--0.707107 0 0.707107\n\
--0.707107 -0.707107 0\n\
-0 0.707107 0.707107\n\
--0.707107 0.707107 0\n\
-0.707107 0.707107 0\n\
-0.707107 0 -0.707107\n\
-0 0.707107 -0.707107\n\
--0.707107 0 -0.707107\n\
-0 -0.707107 -0.707107\n\
-\n\
-3 0 6 11\n\
-3 0 7 6 \n\
-3 0 9 7 \n\
-3 0 11 9\n\
-3 1 6 8 \n\
-3 1 8 14\n\
-3 1 13 6\n\
-3 1 14 13\n\
-3 2 11 13\n\
-3 2 12 11\n\
-3 2 13 15\n\
-3 2 15 12\n\
-3 3 9 12\n\
-3 3 10 9\n\
-3 3 12 16\n\
-3 3 16 10\n\
-3 4 7 10\n\
-3 4 8 7\n\
-3 4 10 17\n\
-3 4 17 8\n\
-3 5 14 17\n\
-3 5 15 14\n\
-3 5 16 15\n\
-3 5 17 16\n\
-3 6 13 11\n\
-3 7 8 6\n\
-3 9 10 7\n\
-3 11 12 9\n\
-3 14 8 17\n\
-3 15 13 14\n\
-3 16 12 15\n\
-3 17 10 16\n} transforms { TLIST\n");
-  FOREACHvertex_(vertices) {
-    qh_fprintf(qh, fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
-      radius, vertex->id, radius, radius);
-    qh_printpoint3(qh, fp, vertex->point);
-    qh_fprintf(qh, fp, 9229, "1\n");
-  }
-  qh_fprintf(qh, fp, 9230, "}}}\n");
-} /* printspheres */
-
-
-/*----------------------------------------------
--printsummary-
-                see libqhull_r.c
-*/
-
-/*---------------------------------
-
-  qh_printvdiagram(qh, fp, format, facetlist, facets, printall )
-    print voronoi diagram
-      # of pairs of input sites
-      #indices site1 site2 vertex1 ...
-
-    sites indexed by input point id
-      point 0 is the first input point
-    vertices indexed by 'o' and 'p' order
-      vertex 0 is the 'vertex-at-infinity'
-      vertex 1 is the first Voronoi vertex
-
-  see:
-    qh_printvoronoi()
-    qh_eachvoronoi_all()
-
-  notes:
-    if all facets are upperdelaunay,
-      prints upper hull (furthest-site Voronoi diagram)
-*/
-void qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  int totcount, numcenters;
-  boolT isLower;
-  qh_RIDGE innerouter= qh_RIDGEall;
-  printvridgeT printvridge= NULL;
-
-  if (format == qh_PRINTvertices) {
-    innerouter= qh_RIDGEall;
-    printvridge= qh_printvridge;
-  }else if (format == qh_PRINTinner) {
-    innerouter= qh_RIDGEinner;
-    printvridge= qh_printvnorm;
-  }else if (format == qh_PRINTouter) {
-    innerouter= qh_RIDGEouter;
-    printvridge= qh_printvnorm;
-  }else {
-    qh_fprintf(qh, qh->ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
-  totcount= qh_printvdiagram2(qh, NULL, NULL, vertices, innerouter, False);
-  qh_fprintf(qh, fp, 9231, "%d\n", totcount);
-  totcount= qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, True /* inorder*/);
-  qh_settempfree(qh, &vertices);
-#if 0  /* for testing qh_eachvoronoi_all */
-  qh_fprintf(qh, fp, 9232, "\n");
-  totcount= qh_eachvoronoi_all(qh, fp, printvridge, qh->UPPERdelaunay, innerouter, True /* inorder*/);
-  qh_fprintf(qh, fp, 9233, "%d\n", totcount);
-#endif
-} /* printvdiagram */
-
-/*---------------------------------
-
-  qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, inorder )
-    visit all pairs of input sites (vertices) for selected Voronoi vertices
-    vertices may include NULLs
-
-  innerouter:
-    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
-    qh_RIDGEinner print only inner ridges
-    qh_RIDGEouter print only outer ridges
-
-  inorder:
-    print 3-d Voronoi vertices in order
-
-  assumes:
-    qh_markvoronoi marked facet->visitid for Voronoi vertices
-    all facet->seen= False
-    all facet->seen2= True
-
-  returns:
-    total number of Voronoi ridges
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers) for each ridge
-      [see qh_eachvoronoi()]
-
-  see:
-    qh_eachvoronoi_all()
-*/
-int qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
-  int totcount= 0;
-  int vertex_i, vertex_n;
-  vertexT *vertex;
-
-  FORALLvertices
-    vertex->seen= False;
-  FOREACHvertex_i_(qh, vertices) {
-    if (vertex) {
-      if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
-        continue;
-      totcount += qh_eachvoronoi(qh, fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
-    }
-  }
-  return totcount;
-} /* printvdiagram2 */
-
-/*---------------------------------
-
-  qh_printvertex(qh, fp, vertex )
-    prints the information in a vertex
-    Duplicated as operator<< [QhullVertex.cpp]
-*/
-void qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex) {
-  pointT *point;
-  int k, count= 0;
-  facetT *neighbor, **neighborp;
-  realT r; /*bug fix*/
-
-  if (!vertex) {
-    qh_fprintf(qh, fp, 9234, "  NULLvertex\n");
-    return;
-  }
-  qh_fprintf(qh, fp, 9235, "- p%d(v%d):", qh_pointid(qh, vertex->point), vertex->id);
-  point= vertex->point;
-  if (point) {
-    for (k=qh->hull_dim; k--; ) {
-      r= *point++;
-      qh_fprintf(qh, fp, 9236, " %5.2g", r);
-    }
-  }
-  if (vertex->deleted)
-    qh_fprintf(qh, fp, 9237, " deleted");
-  if (vertex->delridge)
-    qh_fprintf(qh, fp, 9238, " ridgedeleted");
-  qh_fprintf(qh, fp, 9239, "\n");
-  if (vertex->neighbors) {
-    qh_fprintf(qh, fp, 9240, "  neighbors:");
-    FOREACHneighbor_(vertex) {
-      if (++count % 100 == 0)
-        qh_fprintf(qh, fp, 9241, "\n     ");
-      qh_fprintf(qh, fp, 9242, " f%d", neighbor->id);
-    }
-    qh_fprintf(qh, fp, 9243, "\n");
-  }
-} /* printvertex */
-
-
-/*---------------------------------
-
-  qh_printvertexlist(qh, fp, string, facetlist, facets, printall )
-    prints vertices used by a facetlist or facet set
-    tests qh_skipfacet() if !printall
-*/
-void qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
-                         setT *facets, boolT printall) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  qh_fprintf(qh, fp, 9244, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_printvertex(qh, fp, vertex);
-  qh_settempfree(qh, &vertices);
-} /* printvertexlist */
-
-
-/*---------------------------------
-
-  qh_printvertices(qh, fp, string, vertices )
-    prints vertices in a set
-    duplicated as printVertexSet [QhullVertex.cpp]
-*/
-void qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  qh_fprintf(qh, fp, 9245, "%s", string);
-  FOREACHvertex_(vertices)
-    qh_fprintf(qh, fp, 9246, " p%d(v%d)", qh_pointid(qh, vertex->point), vertex->id);
-  qh_fprintf(qh, fp, 9247, "\n");
-} /* printvertices */
-
-/*---------------------------------
-
-  qh_printvneighbors(qh, fp, facetlist, facets, printall )
-    print vertex neighbors of vertices in facetlist and facets ('FN')
-
-  notes:
-    qh_countfacets clears facet->visitid for non-printed facets
-
-  design:
-    collect facet count and related statistics
-    if necessary, build neighbor sets for each vertex
-    collect vertices in facetlist and facets
-    build a point array for point->vertex and point->coplanar facet
-    for each point
-      list vertex neighbors or coplanar facet
-*/
-void qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
-  setT *vertices, *vertex_points, *coplanar_points;
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  vertexT *vertex, **vertexp;
-  int vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  pointT *point, **pointp;
-
-  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
-  qh_fprintf(qh, fp, 9248, "%d\n", numpoints);
-  qh_vertexneighbors(qh);
-  vertices= qh_facetvertices(qh, facetlist, facets, printall);
-  vertex_points= qh_settemp(qh, numpoints);
-  coplanar_points= qh_settemp(qh, numpoints);
-  qh_setzero(qh, vertex_points, 0, numpoints);
-  qh_setzero(qh, coplanar_points, 0, numpoints);
-  FOREACHvertex_(vertices)
-    qh_point_add(qh, vertex_points, vertex->point, vertex);
-  FORALLfacet_(facetlist) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, coplanar_points, point, facet);
-  }
-  FOREACHfacet_(facets) {
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, coplanar_points, point, facet);
-  }
-  FOREACHvertex_i_(qh, vertex_points) {
-    if (vertex) {
-      numneighbors= qh_setsize(qh, vertex->neighbors);
-      qh_fprintf(qh, fp, 9249, "%d", numneighbors);
-      if (qh->hull_dim == 3)
-        qh_order_vertexneighbors(qh, vertex);
-      else if (qh->hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex)
-        qh_fprintf(qh, fp, 9250, " %d",
-                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
-      qh_fprintf(qh, fp, 9251, "\n");
-    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
-      qh_fprintf(qh, fp, 9252, "1 %d\n",
-                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
-    else
-      qh_fprintf(qh, fp, 9253, "0\n");
-  }
-  qh_settempfree(qh, &coplanar_points);
-  qh_settempfree(qh, &vertex_points);
-  qh_settempfree(qh, &vertices);
-} /* printvneighbors */
-
-/*---------------------------------
-
-  qh_printvoronoi(qh, fp, format, facetlist, facets, printall )
-    print voronoi diagram in 'o' or 'G' format
-    for 'o' format
-      prints voronoi centers for each facet and for infinity
-      for each vertex, lists ids of printed facets or infinity
-      assumes facetlist and facets are disjoint
-    for 'G' format
-      prints an OFF object
-      adds a 0 coordinate to center
-      prints infinity but does not list in vertices
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    if 'o',
-      prints a line for each point except "at-infinity"
-    if all facets are upperdelaunay,
-      reverses lower and upper hull
-*/
-void qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
-  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  setT *vertices;
-  vertexT *vertex;
-  boolT isLower;
-  unsigned int numfacets= (unsigned int) qh->num_facets;
-
-  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
-  FOREACHvertex_i_(qh, vertices) {
-    if (vertex) {
-      numvertices++;
-      numneighbors = numinf = 0;
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-      if (numinf && !numneighbors) {
-        SETelem_(vertices, vertex_i)= NULL;
-        numvertices--;
-      }
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(qh, fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
-                numcenters, numvertices);
-  else
-    qh_fprintf(qh, fp, 9255, "%d\n%d %d 1\n", qh->hull_dim-1, numcenters, qh_setsize(qh, vertices));
-  if (format == qh_PRINTgeom) {
-    for (k=qh->hull_dim-1; k--; )
-      qh_fprintf(qh, fp, 9256, qh_REAL_1, 0.0);
-    qh_fprintf(qh, fp, 9257, " 0 # infinity not used\n");
-  }else {
-    for (k=qh->hull_dim-1; k--; )
-      qh_fprintf(qh, fp, 9258, qh_REAL_1, qh_INFINITE);
-    qh_fprintf(qh, fp, 9259, "\n");
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(qh, fp, 9260, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(qh, fp, format, NULL, facet);
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        qh_fprintf(qh, fp, 9261, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter(qh, fp, format, NULL, facet);
-    }
-  }
-  FOREACHvertex_i_(qh, vertices) {
-    numneighbors= 0;
-    numinf=0;
-    if (vertex) {
-      if (qh->hull_dim == 3)
-        qh_order_vertexneighbors(qh, vertex);
-      else if (qh->hull_dim >= 4)
-        qsort(SETaddr_(vertex->neighbors, facetT),
-             (size_t)qh_setsize(qh, vertex->neighbors),
-             sizeof(facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-          numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-    }
-    if (format == qh_PRINTgeom) {
-      if (vertex) {
-        qh_fprintf(qh, fp, 9262, "%d", numneighbors);
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid && neighbor->visitid < numfacets)
-            qh_fprintf(qh, fp, 9263, " %d", neighbor->visitid);
-        }
-        qh_fprintf(qh, fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
-      }else
-        qh_fprintf(qh, fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
-    }else {
-      if (numinf)
-        numneighbors++;
-      qh_fprintf(qh, fp, 9266, "%d", numneighbors);
-      if (vertex) {
-        FOREACHneighbor_(vertex) {
-          if (neighbor->visitid == 0) {
-            if (numinf) {
-              numinf= 0;
-              qh_fprintf(qh, fp, 9267, " %d", neighbor->visitid);
-            }
-          }else if (neighbor->visitid < numfacets)
-            qh_fprintf(qh, fp, 9268, " %d", neighbor->visitid);
-        }
-      }
-      qh_fprintf(qh, fp, 9269, "\n");
-    }
-  }
-  if (format == qh_PRINTgeom)
-    qh_fprintf(qh, fp, 9270, "}\n");
-  qh_settempfree(qh, &vertices);
-} /* printvoronoi */
-
-/*---------------------------------
-
-  qh_printvnorm(qh, fp, vertex, vertexA, centers, unbounded )
-    print one separating plane of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  note:
-    parameter unbounded is UNUSED by this callback
-
-  see:
-    qh_printvdiagram()
-    qh_eachvoronoi()
-*/
-void qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  pointT *normal;
-  realT offset;
-  int k;
-  QHULL_UNUSED(unbounded);
-
-  normal= qh_detvnorm(qh, vertex, vertexA, centers, &offset);
-  qh_fprintf(qh, fp, 9271, "%d %d %d ",
-      2+qh->hull_dim, qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
-  for (k=0; k< qh->hull_dim-1; k++)
-    qh_fprintf(qh, fp, 9272, qh_REAL_1, normal[k]);
-  qh_fprintf(qh, fp, 9273, qh_REAL_1, offset);
-  qh_fprintf(qh, fp, 9274, "\n");
-} /* printvnorm */
-
-/*---------------------------------
-
-  qh_printvridge(qh, fp, vertex, vertexA, centers, unbounded )
-    print one ridge of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    the user may use a different function
-    parameter unbounded is UNUSED
-*/
-void qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  facetT *facet, **facetp;
-  QHULL_UNUSED(unbounded);
-
-  qh_fprintf(qh, fp, 9275, "%d %d %d", qh_setsize(qh, centers)+2,
-       qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
-  FOREACHfacet_(centers)
-    qh_fprintf(qh, fp, 9276, " %d", facet->visitid);
-  qh_fprintf(qh, fp, 9277, "\n");
-} /* printvridge */
-
-/*---------------------------------
-
-  qh_projectdim3(qh, source, destination )
-    project 2-d 3-d or 4-d point to a 3-d point
-    uses qh.DROPdim and qh.hull_dim
-    source and destination may be the same
-
-  notes:
-    allocate 4 elements to destination just in case
-*/
-void qh_projectdim3(qhT *qh, pointT *source, pointT *destination) {
-  int i,k;
-
-  for (k=0, i=0; k < qh->hull_dim; k++) {
-    if (qh->hull_dim == 4) {
-      if (k != qh->DROPdim)
-        destination[i++]= source[k];
-    }else if (k == qh->DROPdim)
-      destination[i++]= 0;
-    else
-      destination[i++]= source[k];
-  }
-  while (i < 3)
-    destination[i++]= 0.0;
-} /* projectdim3 */
-
-/*---------------------------------
-
-  qh_readfeasible(qh, dim, curline )
-    read feasible point from current line and qh.fin
-
-  returns:
-    number of lines read from qh.fin
-    sets qh.feasible_point with malloc'd coordinates
-
-  notes:
-    checks for qh.HALFspace
-    assumes dim > 1
-
-  see:
-    qh_setfeasible
-*/
-int qh_readfeasible(qhT *qh, int dim, const char *curline) {
-  boolT isfirst= True;
-  int linecount= 0, tokcount= 0;
-  const char *s;
-  char *t, firstline[qh_MAXfirst+1];
-  coordT *coords, value;
-
-  if (!qh->HALFspace) {
-    qh_fprintf(qh, qh->ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (qh->feasible_string)
-    qh_fprintf(qh, qh->ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
-  if (!(qh->feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
-    qh_fprintf(qh, qh->ferr, 6071, "qhull error: insufficient memory for feasible point\n");
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coords= qh->feasible_point;
-  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh->fin)))) {
-    if (isfirst)
-      isfirst= False;
-    else
-      linecount++;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t)
-        break;
-      s= t;
-      *(coords++)= value;
-      if (++tokcount == dim) {
-        while (isspace(*s))
-          s++;
-        qh_strtod(s, &t);
-        if (s != t) {
-          qh_fprintf(qh, qh->ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
-               s);
-          qh_errexit(qh, qh_ERRinput, NULL, NULL);
-        }
-        return linecount;
-      }
-    }
-  }
-  qh_fprintf(qh, qh->ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
-           tokcount, dim);
-  qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  return 0;
-} /* readfeasible */
-
-/*---------------------------------
-
-  qh_readpoints(qh, numpoints, dimension, ismalloc )
-    read points from qh.fin into qh.first_point, qh.num_points
-    qh.fin is lines of coordinates, one per vertex, first line number of points
-    if 'rbox D4',
-      gives message
-    if qh.ATinfinity,
-      adds point-at-infinity for Delaunay triangulations
-
-  returns:
-    number of points, array of point coordinates, dimension, ismalloc True
-    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
-        and clears qh.PROJECTdelaunay
-    if qh.HALFspace, reads optional feasible point, reads halfspaces,
-        converts to dual.
-
-  for feasible point in "cdd format" in 3-d:
-    3 1
-    coordinates
-    comments
-    begin
-    n 4 real/integer
-    ...
-    end
-
-  notes:
-    dimension will change in qh_initqhull_globals if qh.PROJECTinput
-    uses malloc() since qh_mem not initialized
-    FIXUP QH11012: qh_readpoints needs rewriting, too long
-*/
-coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc) {
-  coordT *points, *coords, *infinity= NULL;
-  realT paraboloid, maxboloid= -REALmax, value;
-  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
-  char *s= 0, *t, firstline[qh_MAXfirst+1];
-  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
-  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
-  int tokcount= 0, linecount=0, maxcount, coordcount=0;
-  boolT islong, isfirst= True, wasbegin= False;
-  boolT isdelaunay= qh->DELAUNAY && !qh->PROJECTinput;
-
-  if (qh->CDDinput) {
-    while ((s= fgets(firstline, qh_MAXfirst, qh->fin))) {
-      linecount++;
-      if (qh->HALFspace && linecount == 1 && isdigit(*s)) {
-        dimfeasible= qh_strtol(s, &s);
-        while (isspace(*s))
-          s++;
-        if (qh_strtol(s, &s) == 1)
-          linecount += qh_readfeasible(qh, dimfeasible, s);
-        else
-          dimfeasible= 0;
-      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
-        break;
-      else if (!*qh->rbox_command)
-        strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-    }
-    if (!s) {
-      qh_fprintf(qh, qh->ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-  }
-  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh->fin))) {
-    linecount++;
-    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
-      wasbegin= True;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      if (!*s)
-        break;
-      if (!isdigit(*s)) {
-        if (!*qh->rbox_command) {
-          strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-          firsttext= linecount;
-        }
-        break;
-      }
-      if (!diminput)
-        diminput= qh_strtol(s, &s);
-      else {
-        numinput= qh_strtol(s, &s);
-        if (numinput == 1 && diminput >= 2 && qh->HALFspace && !qh->CDDinput) {
-          linecount += qh_readfeasible(qh, diminput, s); /* checks if ok */
-          dimfeasible= diminput;
-          diminput= numinput= 0;
-        }else
-          break;
-      }
-    }
-  }
-  if (!s) {
-    qh_fprintf(qh, qh->ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (diminput > numinput) {
-    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
-    diminput= numinput;
-    numinput= tempi;
-  }
-  if (diminput < 2) {
-    qh_fprintf(qh, qh->ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
-            diminput);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (isdelaunay) {
-    qh->PROJECTdelaunay= False;
-    if (qh->CDDinput)
-      *dimension= diminput;
-    else
-      *dimension= diminput+1;
-    *numpoints= numinput;
-    if (qh->ATinfinity)
-      (*numpoints)++;
-  }else if (qh->HALFspace) {
-    *dimension= diminput - 1;
-    *numpoints= numinput;
-    if (diminput < 3) {
-      qh_fprintf(qh, qh->ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
-            diminput);
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (dimfeasible) {
-      if (dimfeasible != *dimension) {
-        qh_fprintf(qh, qh->ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
-          dimfeasible, diminput);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-    }else
-      qh_setfeasible(qh, *dimension);
-  }else {
-    if (qh->CDDinput)
-      *dimension= diminput-1;
-    else
-      *dimension= diminput;
-    *numpoints= numinput;
-  }
-  qh->normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
-  if (qh->HALFspace) {
-    qh->half_space= coordp= (coordT*)qh_malloc(qh->normal_size + sizeof(coordT));
-    if (qh->CDDinput) {
-      offsetp= qh->half_space;
-      normalp= offsetp + 1;
-    }else {
-      normalp= qh->half_space;
-      offsetp= normalp + *dimension;
-    }
-  }
-  qh->maxline= diminput * (qh_REALdigits + 5);
-  maximize_(qh->maxline, 500);
-  qh->line= (char*)qh_malloc((qh->maxline+1) * sizeof(char));
-  *ismalloc= True;  /* use malloc since memory not setup */
-  coords= points= qh->temp_malloc=  /* numinput and diminput >=2 by QH6220 */
-        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
-  if (!coords || !qh->line || (qh->HALFspace && !qh->half_space)) {
-    qh_fprintf(qh, qh->ferr, 6076, "qhull error: insufficient memory to read %d points\n",
-            numinput);
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  if (isdelaunay && qh->ATinfinity) {
-    infinity= points + numinput * (*dimension);
-    for (k= (*dimension) - 1; k--; )
-      infinity[k]= 0.0;
-  }
-  maxcount= numinput * diminput;
-  paraboloid= 0.0;
-  while ((s= (isfirst ?  s : fgets(qh->line, qh->maxline, qh->fin)))) {
-    if (!isfirst) {
-      linecount++;
-      if (*s == 'e' || *s == 'E') {
-        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
-          if (qh->CDDinput )
-            break;
-          else if (wasbegin)
-            qh_fprintf(qh, qh->ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
-        }
-      }
-    }
-    islong= False;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod(s, &t);
-      if (s == t) {
-        if (!*qh->rbox_command)
-         strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
-        if (*s && !firsttext)
-          firsttext= linecount;
-        if (!islong && !firstshort && coordcount)
-          firstshort= linecount;
-        break;
-      }
-      if (!firstpoint)
-        firstpoint= linecount;
-      s= t;
-      if (++tokcount > maxcount)
-        continue;
-      if (qh->HALFspace) {
-        if (qh->CDDinput)
-          *(coordp++)= -value; /* both coefficients and offset */
-        else
-          *(coordp++)= value;
-      }else {
-        *(coords++)= value;
-        if (qh->CDDinput && !coordcount) {
-          if (value != 1.0) {
-            qh_fprintf(qh, qh->ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
-                   linecount);
-            qh_errexit(qh, qh_ERRinput, NULL, NULL);
-          }
-          coords--;
-        }else if (isdelaunay) {
-          paraboloid += value * value;
-          if (qh->ATinfinity) {
-            if (qh->CDDinput)
-              infinity[coordcount-1] += value;
-            else
-              infinity[coordcount] += value;
-          }
-        }
-      }
-      if (++coordcount == diminput) {
-        coordcount= 0;
-        if (isdelaunay) {
-          *(coords++)= paraboloid;
-          maximize_(maxboloid, paraboloid);
-          paraboloid= 0.0;
-        }else if (qh->HALFspace) {
-          if (!qh_sethalfspace(qh, *dimension, coords, &coords, normalp, offsetp, qh->feasible_point)) {
-            qh_fprintf(qh, qh->ferr, 8048, "The halfspace was on line %d\n", linecount);
-            if (wasbegin)
-              qh_fprintf(qh, qh->ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
-            qh_errexit(qh, qh_ERRinput, NULL, NULL);
-          }
-          coordp= qh->half_space;
-        }
-        while (isspace(*s))
-          s++;
-        if (*s) {
-          islong= True;
-          if (!firstlong)
-            firstlong= linecount;
-        }
-      }
-    }
-    if (!islong && !firstshort && coordcount)
-      firstshort= linecount;
-    if (!isfirst && s - qh->line >= qh->maxline) {
-      qh_fprintf(qh, qh->ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
-              linecount, (int) (s - qh->line));   /* WARN64 */
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    isfirst= False;
-  }
-  if (tokcount != maxcount) {
-    newnum= fmin_(numinput, tokcount/diminput);
-    qh_fprintf(qh, qh->ferr, 7073,"\
-qhull warning: instead of %d %d-dimensional points, input contains\n\
-%d points and %d extra coordinates.  Line %d is the first\npoint",
-       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
-    if (firsttext)
-      qh_fprintf(qh, qh->ferr, 8051, ", line %d is the first comment", firsttext);
-    if (firstshort)
-      qh_fprintf(qh, qh->ferr, 8052, ", line %d is the first short\nline", firstshort);
-    if (firstlong)
-      qh_fprintf(qh, qh->ferr, 8053, ", line %d is the first long line", firstlong);
-    qh_fprintf(qh, qh->ferr, 8054, ".  Continue with %d points.\n", newnum);
-    numinput= newnum;
-    if (isdelaunay && qh->ATinfinity) {
-      for (k= tokcount % diminput; k--; )
-        infinity[k] -= *(--coords);
-      *numpoints= newnum+1;
-    }else {
-      coords -= tokcount % diminput;
-      *numpoints= newnum;
-    }
-  }
-  if (isdelaunay && qh->ATinfinity) {
-    for (k= (*dimension) -1; k--; )
-      infinity[k] /= numinput;
-    if (coords == infinity)
-      coords += (*dimension) -1;
-    else {
-      for (k=0; k < (*dimension) -1; k++)
-        *(coords++)= infinity[k];
-    }
-    *(coords++)= maxboloid * 1.1;
-  }
-  if (qh->rbox_command[0]) {
-    qh->rbox_command[strlen(qh->rbox_command)-1]= '\0';
-    if (!strcmp(qh->rbox_command, "./rbox D4"))
-      qh_fprintf(qh, qh->ferr, 8055, "\n\
-This is the qhull test case.  If any errors or core dumps occur,\n\
-recompile qhull with 'make new'.  If errors still occur, there is\n\
-an incompatibility.  You should try a different compiler.  You can also\n\
-change the choices in user.h.  If you discover the source of the problem,\n\
-please send mail to qhull_bug@qhull.org.\n\
-\n\
-Type 'qhull' for a short list of options.\n");
-  }
-  qh_free(qh->line);
-  qh->line= NULL;
-  if (qh->half_space) {
-    qh_free(qh->half_space);
-    qh->half_space= NULL;
-  }
-  qh->temp_malloc= NULL;
-  trace1((qh, qh->ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
-          numinput, diminput));
-  return(points);
-} /* readpoints */
-
-
-/*---------------------------------
-
-  qh_setfeasible(qh, dim )
-    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
-
-  notes:
-    "n,n,n" already checked by qh_initflags()
-    see qh_readfeasible()
-    called only once from qh_new_qhull, otherwise leaks memory
-*/
-void qh_setfeasible(qhT *qh, int dim) {
-  int tokcount= 0;
-  char *s;
-  coordT *coords, value;
-
-  if (!(s= qh->feasible_string)) {
-    qh_fprintf(qh, qh->ferr, 6223, "\
-qhull input error: halfspace intersection needs a feasible point.\n\
-Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (!(qh->feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
-    qh_fprintf(qh, qh->ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
-    qh_errexit(qh, qh_ERRmem, NULL, NULL);
-  }
-  coords= qh->feasible_point;
-  while (*s) {
-    value= qh_strtod(s, &s);
-    if (++tokcount > dim) {
-      qh_fprintf(qh, qh->ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
-          qh->feasible_string, dim);
-      break;
-    }
-    *(coords++)= value;
-    if (*s)
-      s++;
-  }
-  while (++tokcount <= dim)
-    *(coords++)= 0.0;
-} /* setfeasible */
-
-/*---------------------------------
-
-  qh_skipfacet(qh, facet )
-    returns 'True' if this facet is not to be printed
-
-  notes:
-    based on the user provided slice thresholds and 'good' specifications
-*/
-boolT qh_skipfacet(qhT *qh, facetT *facet) {
-  facetT *neighbor, **neighborp;
-
-  if (qh->PRINTneighbors) {
-    if (facet->good)
-      return !qh->PRINTgood;
-    FOREACHneighbor_(facet) {
-      if (neighbor->good)
-        return False;
-    }
-    return True;
-  }else if (qh->PRINTgood)
-    return !facet->good;
-  else if (!facet->normal)
-    return True;
-  return(!qh_inthresholds(qh, facet->normal, NULL));
-} /* skipfacet */
-
-/*---------------------------------
-
-  qh_skipfilename(qh, string )
-    returns pointer to character after filename
-
-  notes:
-    skips leading spaces
-    ends with spacing or eol
-    if starts with ' or " ends with the same, skipping \' or \"
-    For qhull, qh_argv_to_command() only uses double quotes
-*/
-char *qh_skipfilename(qhT *qh, char *filename) {
-  char *s= filename;  /* non-const due to return */
-  char c;
-
-  while (*s && isspace(*s))
-    s++;
-  c= *s++;
-  if (c == '\0') {
-    qh_fprintf(qh, qh->ferr, 6204, "qhull input error: filename expected, none found.\n");
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  if (c == '\'' || c == '"') {
-    while (*s !=c || s[-1] == '\\') {
-      if (!*s) {
-        qh_fprintf(qh, qh->ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      s++;
-    }
-    s++;
-  }
-  else while (*s && !isspace(*s))
-      s++;
-  return s;
-} /* skipfilename */
-
diff --git a/src/qhull/src/libqhull_r/io_r.h b/src/qhull/src/libqhull_r/io_r.h
deleted file mode 100644
index 12e05ae7a..000000000
--- a/src/qhull/src/libqhull_r/io_r.h
+++ /dev/null
@@ -1,167 +0,0 @@
-/*
      ---------------------------------
-
-   io_r.h
-   declarations of Input/Output functions
-
-   see README, libqhull_r.h and io_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/io_r.h#3 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-#include "libqhull_r.h"
-
-/*============ constants and flags ==================*/
-
-/*----------------------------------
-
-  qh_MAXfirst
-    maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst  200
-
-/*----------------------------------
-
-  qh_MINradius
-    min radius for Gp and Gv, fraction of maxcoord
-*/
-#define qh_MINradius 0.02
-
-/*----------------------------------
-
-  qh_GEOMepsilon
-    adjust outer planes for 'lines closer' and geomview roundoff.
-    This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*----------------------------------
-
-  qh_WHITESPACE
-    possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*----------------------------------
-
-  qh_RIDGE
-    to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
-    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*----------------------------------
-
-  printvridgeT
-    prints results of qh_printvdiagram
-
-  see:
-    qh_printvridge for an example
-*/
-typedef void (*printvridgeT)(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void    qh_dfacet(qhT *qh, unsigned id);
-void    qh_dvertex(qhT *qh, unsigned id);
-int     qh_compare_facetarea(const void *p1, const void *p2);
-int     qh_compare_facetmerge(const void *p1, const void *p2);
-int     qh_compare_facetvisit(const void *p1, const void *p2);
-/* int  qh_compare_vertexpoint(const void *p1, const void *p2); Not useable since it depends on qh */
-void    qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length);
-void    qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
-              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
-              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
-pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
-setT   *qh_detvridge(qhT *qh, vertexT *vertex);
-setT   *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex);
-int     qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int     qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
-void    qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist);
-setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
-void    qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_markkeep(qhT *qh, facetT *facetlist);
-setT   *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
-void    qh_order_vertexneighbors(qhT *qh, vertexT *vertex);
-void    qh_prepare_output(qhT *qh);
-void    qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
-void    qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet);
-void    qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius);
-void    qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *num, boolT printall);
-void    qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printfacet(qhT *qh, FILE *fp, facetT *facet);
-void    qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
-void    qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
-                               facetT *facet, realT offset, realT color[3]);
-void    qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
-void    qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
-void    qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
-void    qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format);
-void    qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
-void    qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet);
-void    qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet);
-void    qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
-                   setT *vertices, realT color[3]);
-void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
-void    qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point);
-void    qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id);
-void    qh_printpoint3(qhT *qh, FILE *fp, pointT *point);
-void    qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
-void    qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
-void    qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge);
-void    qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius);
-void    qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-int     qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
-void    qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex);
-void    qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
-                         setT *facets, boolT printall);
-void    qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices);
-void    qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall);
-void    qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_produce_output(qhT *qh);
-void    qh_produce_output2(qhT *qh);
-void    qh_projectdim3(qhT *qh, pointT *source, pointT *destination);
-int     qh_readfeasible(qhT *qh, int dim, const char *curline);
-coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
-void    qh_setfeasible(qhT *qh, int dim);
-boolT   qh_skipfacet(qhT *qh, facetT *facet);
-char   *qh_skipfilename(qhT *qh, char *filename);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFio */
diff --git a/src/qhull/src/libqhull_r/libqhull_r.c b/src/qhull/src/libqhull_r/libqhull_r.c
deleted file mode 100644
index 0fe0c980d..000000000
--- a/src/qhull/src/libqhull_r/libqhull_r.c
+++ /dev/null
@@ -1,1403 +0,0 @@
-/*
      ---------------------------------
-
-   libqhull_r.c
-   Quickhull algorithm for convex hulls
-
-   qhull() and top-level routines
-
-   see qh-qhull_r.htm, libqhull.h, unix_r.c
-
-   see qhull_ra.h for internal functions
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.c#2 $$Change: 2047 $
-   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*============= functions in alphabetic order after qhull() =======*/
-
-/*---------------------------------
-
-  qh_qhull(qh)
-    compute DIM3 convex hull of qh.num_points starting at qh.first_point
-    qh->contains all global options and variables
-
-  returns:
-    returns polyhedron
-      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
-
-    returns global variables
-      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
-
-    returns precision constants
-      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
-
-  notes:
-    unless needed for output
-      qh.max_vertex and qh.min_vertex are max/min due to merges
-
-  see:
-    to add individual points to either qh.num_points
-      use qh_addpoint()
-
-    if qh.GETarea
-      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
-
-  design:
-    record starting time
-    initialize hull and partition points
-    build convex hull
-    unless early termination
-      update facet->maxoutside for vertices, coplanar, and near-inside points
-    error if temporary sets exist
-    record end time
-*/
-
-void qh_qhull(qhT *qh) {
-  int numoutside;
-
-  qh->hulltime= qh_CPUclock;
-  if (qh->RERUN || qh->JOGGLEmax < REALmax/2)
-    qh_build_withrestart(qh);
-  else {
-    qh_initbuild(qh);
-    qh_buildhull(qh);
-  }
-  if (!qh->STOPpoint && !qh->STOPcone) {
-    if (qh->ZEROall_ok && !qh->TESTvneighbors && qh->MERGEexact)
-      qh_checkzero(qh, qh_ALL);
-    if (qh->ZEROall_ok && !qh->TESTvneighbors && !qh->WAScoplanar) {
-      trace2((qh, qh->ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
-      qh->DOcheckmax= False;
-    }else {
-      if (qh->MERGEexact || (qh->hull_dim > qh_DIMreduceBuild && qh->PREmerge))
-        qh_postmerge(qh, "First post-merge", qh->premerge_centrum, qh->premerge_cos,
-             (qh->POSTmerge ? False : qh->TESTvneighbors));
-      else if (!qh->POSTmerge && qh->TESTvneighbors)
-        qh_postmerge(qh, "For testing vertex neighbors", qh->premerge_centrum,
-             qh->premerge_cos, True);
-      if (qh->POSTmerge)
-        qh_postmerge(qh, "For post-merging", qh->postmerge_centrum,
-             qh->postmerge_cos, qh->TESTvneighbors);
-      if (qh->visible_list == qh->facet_list) { /* i.e., merging done */
-        qh->findbestnew= True;
-        qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numoutside);
-        qh->findbestnew= False;
-        qh_deletevisible(qh /*qh.visible_list*/);
-        qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-      }
-    }
-    if (qh->DOcheckmax){
-      if (qh->REPORTfreq) {
-        qh_buildtracing(qh, NULL, NULL);
-        qh_fprintf(qh, qh->ferr, 8115, "\nTesting all coplanar points.\n");
-      }
-      qh_check_maxout(qh);
-    }
-    if (qh->KEEPnearinside && !qh->maxoutdone)
-      qh_nearcoplanar(qh);
-  }
-  if (qh_setsize(qh, qh->qhmem.tempstack) != 0) {
-    qh_fprintf(qh, qh->ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
-             qh_setsize(qh, qh->qhmem.tempstack));
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh->hulltime= qh_CPUclock - qh->hulltime;
-  qh->QHULLfinished= True;
-  trace1((qh, qh->ferr, 1036, "Qhull: algorithm completed\n"));
-} /* qhull */
-
-/*---------------------------------
-
-  qh_addpoint(qh, furthest, facet, checkdist )
-    add point (usually furthest point) above facet to hull
-    if checkdist,
-      check that point is above facet.
-      if point is not outside of the hull, uses qh_partitioncoplanar()
-      assumes that facet is defined by qh_findbestfacet()
-    else if facet specified,
-      assumes that point is above facet (major damage if below)
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns False if user requested an early termination
-     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
-    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
-    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
-    if unknown point, adds a pointer to qh.other_points
-      do not deallocate the point's coordinates
-
-  notes:
-    assumes point is near its best facet and not at a local minimum of a lens
-      distributions.  Use qh_findbestfacet to avoid this case.
-    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
-
-  see also:
-    qh_triangulate() -- triangulate non-simplicial facets
-
-  design:
-    add point to other_points if needed
-    if checkdist
-      if point not above facet
-        partition coplanar point
-        exit
-    exit if pre STOPpoint requested
-    find horizon and visible facets for point
-    make new facets for point to horizon
-    make hyperplanes for point
-    compute balance statistics
-    match neighboring new facets
-    update vertex neighbors and delete interior vertices
-    exit if STOPcone requested
-    merge non-convex new facets
-    if merge found, many merges, or 'Qf'
-       use qh_findbestnew() instead of qh_findbest()
-    partition outside points from visible facets
-    delete visible facets
-    check polyhedron if requested
-    exit if post STOPpoint requested
-    reset working lists of facets and vertices
-*/
-boolT qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist) {
-  int goodvisible, goodhorizon;
-  vertexT *vertex;
-  facetT *newfacet;
-  realT dist, newbalance, pbalance;
-  boolT isoutside= False;
-  int numpart, numpoints, numnew, firstnew;
-
-  qh->maxoutdone= False;
-  if (qh_pointid(qh, furthest) == qh_IDunknown)
-    qh_setappend(qh, &qh->other_points, furthest);
-  if (!facet) {
-    qh_fprintf(qh, qh->ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (checkdist) {
-    facet= qh_findbest(qh, furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
-                        &dist, &isoutside, &numpart);
-    zzadd_(Zpartition, numpart);
-    if (!isoutside) {
-      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
-      facet->notfurthest= True;
-      qh_partitioncoplanar(qh, furthest, facet, &dist);
-      return True;
-    }
-  }
-  qh_buildtracing(qh, furthest, facet);
-  if (qh->STOPpoint < 0 && qh->furthest_id == -qh->STOPpoint-1) {
-    facet->notfurthest= True;
-    return False;
-  }
-  qh_findhorizon(qh, furthest, facet, &goodvisible, &goodhorizon);
-  if (qh->ONLYgood && !(goodvisible+goodhorizon) && !qh->GOODclosest) {
-    zinc_(Znotgood);
-    facet->notfurthest= True;
-    /* last point of outsideset is no longer furthest.  This is ok
-       since all points of the outside are likely to be bad */
-    qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    return True;
-  }
-  zzinc_(Zprocessed);
-  firstnew= qh->facet_id;
-  vertex= qh_makenewfacets(qh, furthest /*visible_list, attaches if !ONLYgood */);
-  qh_makenewplanes(qh /* newfacet_list */);
-  numnew= qh->facet_id - firstnew;
-  newbalance= numnew - (realT) (qh->num_facets-qh->num_visible)
-                         * qh->hull_dim/qh->num_vertices;
-  wadd_(Wnewbalance, newbalance);
-  wadd_(Wnewbalance2, newbalance * newbalance);
-  if (qh->ONLYgood
-  && !qh_findgood(qh, qh->newfacet_list, goodhorizon) && !qh->GOODclosest) {
-    FORALLnew_facets
-      qh_delfacet(qh, newfacet);
-    qh_delvertex(qh, vertex);
-    qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-    zinc_(Znotgoodnew);
-    facet->notfurthest= True;
-    return True;
-  }
-  if (qh->ONLYgood)
-    qh_attachnewfacets(qh /*visible_list*/);
-  qh_matchnewfacets(qh);
-  qh_updatevertices(qh);
-  if (qh->STOPcone && qh->furthest_id == qh->STOPcone-1) {
-    facet->notfurthest= True;
-    return False;  /* visible_list etc. still defined */
-  }
-  qh->findbestnew= False;
-  if (qh->PREmerge || qh->MERGEexact) {
-    qh_premerge(qh, vertex, qh->premerge_centrum, qh->premerge_cos);
-    if (qh_USEfindbestnew)
-      qh->findbestnew= True;
-    else {
-      FORALLnew_facets {
-        if (!newfacet->simplicial) {
-          qh->findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
-          break;
-        }
-      }
-    }
-  }else if (qh->BESToutside)
-    qh->findbestnew= True;
-  qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numpoints);
-  qh->findbestnew= False;
-  qh->findbest_notsharp= False;
-  zinc_(Zpbalance);
-  pbalance= numpoints - (realT) qh->hull_dim /* assumes all points extreme */
-                * (qh->num_points - qh->num_vertices)/qh->num_vertices;
-  wadd_(Wpbalance, pbalance);
-  wadd_(Wpbalance2, pbalance * pbalance);
-  qh_deletevisible(qh /*qh.visible_list*/);
-  zmax_(Zmaxvertex, qh->num_vertices);
-  qh->NEWfacets= False;
-  if (qh->IStracing >= 4) {
-    if (qh->num_facets < 2000)
-      qh_printlists(qh);
-    qh_printfacetlist(qh, qh->newfacet_list, NULL, True);
-    qh_checkpolygon(qh, qh->facet_list);
-  }else if (qh->CHECKfrequently) {
-    if (qh->num_facets < 50)
-      qh_checkpolygon(qh, qh->facet_list);
-    else
-      qh_checkpolygon(qh, qh->newfacet_list);
-  }
-  if (qh->STOPpoint > 0 && qh->furthest_id == qh->STOPpoint-1)
-    return False;
-  qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  /* qh_triangulate(qh); to test qh.TRInormals */
-  trace2((qh, qh->ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
-    qh_pointid(qh, furthest), numnew, newbalance, pbalance));
-  return True;
-} /* addpoint */
-
-/*---------------------------------
-
-  qh_build_withrestart(qh)
-    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
-       qh_errexit always undoes qh_build_withrestart()
-    qh.FIRSTpoint/qh.NUMpoints is point array
-       it may be moved by qh_joggleinput(qh)
-*/
-void qh_build_withrestart(qhT *qh) {
-  int restart;
-
-  qh->ALLOWrestart= True;
-  while (True) {
-    restart= setjmp(qh->restartexit); /* simple statement for CRAY J916 */
-    if (restart) {       /* only from qh_precision() */
-      zzinc_(Zretry);
-      wmax_(Wretrymax, qh->JOGGLEmax);
-      /* QH7078 warns about using 'TCn' with 'QJn' */
-      qh->STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
-    }
-    if (!qh->RERUN && qh->JOGGLEmax < REALmax/2) {
-      if (qh->build_cnt > qh_JOGGLEmaxretry) {
-        qh_fprintf(qh, qh->ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
-        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
-        or modify qh_JOGGLE... parameters in user.h\n",
-           qh->build_cnt, qh->JOGGLEmax);
-        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-      }
-      if (qh->build_cnt && !restart)
-        break;
-    }else if (qh->build_cnt && qh->build_cnt >= qh->RERUN)
-      break;
-    qh->STOPcone= 0;
-    qh_freebuild(qh, True);  /* first call is a nop */
-    qh->build_cnt++;
-    if (!qh->qhull_optionsiz)
-      qh->qhull_optionsiz= (int)strlen(qh->qhull_options);   /* WARN64 */
-    else {
-      qh->qhull_options [qh->qhull_optionsiz]= '\0';
-      qh->qhull_optionlen= qh_OPTIONline;  /* starts a new line */
-    }
-    qh_option(qh, "_run", &qh->build_cnt, NULL);
-    if (qh->build_cnt == qh->RERUN) {
-      qh->IStracing= qh->TRACElastrun;  /* duplicated from qh_initqhull_globals */
-      if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
-        qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
-        qh->IStracing= 0;
-      }
-      qh->qhmem.IStracing= qh->IStracing;
-    }
-    if (qh->JOGGLEmax < REALmax/2)
-      qh_joggleinput(qh);
-    qh_initbuild(qh);
-    qh_buildhull(qh);
-    if (qh->JOGGLEmax < REALmax/2 && !qh->MERGING)
-      qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }
-  qh->ALLOWrestart= False;
-} /* qh_build_withrestart */
-
-/*---------------------------------
-
-  qh_buildhull(qh)
-    construct a convex hull by adding outside points one at a time
-
-  returns:
-
-  notes:
-    may be called multiple times
-    checks facet and vertex lists for incorrect flags
-    to recover from STOPcone, call qh_deletevisible and qh_resetlists
-
-  design:
-    check visible facet and newfacet flags
-    check newlist vertex flags and qh.STOPcone/STOPpoint
-    for each facet with a furthest outside point
-      add point to facet
-      exit if qh.STOPcone or qh.STOPpoint requested
-    if qh.NARROWhull for initial simplex
-      partition remaining outside points to coplanar sets
-*/
-void qh_buildhull(qhT *qh) {
-  facetT *facet;
-  pointT *furthest;
-  vertexT *vertex;
-  int id;
-
-  trace1((qh, qh->ferr, 1037, "qh_buildhull: start build hull\n"));
-  FORALLfacets {
-    if (facet->visible || facet->newfacet) {
-      qh_fprintf(qh, qh->ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
-                   facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-  }
-  FORALLvertices {
-    if (vertex->newlist) {
-      qh_fprintf(qh, qh->ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
-                   vertex->id);
-      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-    id= qh_pointid(qh, vertex->point);
-    if ((qh->STOPpoint>0 && id == qh->STOPpoint-1) ||
-        (qh->STOPpoint<0 && id == -qh->STOPpoint-1) ||
-        (qh->STOPcone>0 && id == qh->STOPcone-1)) {
-      trace1((qh, qh->ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
-      return;
-    }
-  }
-  qh->facet_next= qh->facet_list;      /* advance facet when processed */
-  while ((furthest= qh_nextfurthest(qh, &facet))) {
-    qh->num_outside--;  /* if ONLYmax, furthest may not be outside */
-    if (!qh_addpoint(qh, furthest, facet, qh->ONLYmax))
-      break;
-  }
-  if (qh->NARROWhull) /* move points from outsideset to coplanarset */
-    qh_outcoplanar(qh /* facet_list */ );
-  if (qh->num_outside && !furthest) {
-    qh_fprintf(qh, qh->ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh->num_outside);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  trace1((qh, qh->ferr, 1039, "qh_buildhull: completed the hull construction\n"));
-} /* buildhull */
-
-
-/*---------------------------------
-
-  qh_buildtracing(qh, furthest, facet )
-    trace an iteration of qh_buildhull() for furthest point and facet
-    if !furthest, prints progress message
-
-  returns:
-    tracks progress with qh.lastreport
-    updates qh.furthest_id (-3 if furthest is NULL)
-    also resets visit_id, vertext_visit on wrap around
-
-  see:
-    qh_tracemerging()
-
-  design:
-    if !furthest
-      print progress message
-      exit
-    if 'TFn' iteration
-      print progress message
-    else if tracing
-      trace furthest point and facet
-    reset qh.visit_id and qh.vertex_visit if overflow may occur
-    set qh.furthest_id for tracing
-*/
-void qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet) {
-  realT dist= 0;
-  float cpu;
-  int total, furthestid;
-  time_t timedata;
-  struct tm *tp;
-  vertexT *vertex;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  if (!furthest) {
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    qh_fprintf(qh, qh->ferr, 8118, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  Last point was p%d\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
-      total, qh->num_facets, qh->num_vertices, qh->furthest_id);
-    return;
-  }
-  furthestid= qh_pointid(qh, furthest);
-  if (qh->TRACEpoint == furthestid) {
-    qh->IStracing= qh->TRACElevel;
-    qh->qhmem.IStracing= qh->TRACElevel;
-  }else if (qh->TRACEpoint != qh_IDunknown && qh->TRACEdist < REALmax/2) {
-    qh->IStracing= 0;
-    qh->qhmem.IStracing= 0;
-  }
-  if (qh->REPORTfreq && (qh->facet_id-1 > qh->lastreport+qh->REPORTfreq)) {
-    qh->lastreport= qh->facet_id-1;
-    time(&timedata);
-    tp= localtime(&timedata);
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    zinc_(Zdistio);
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, qh->ferr, 8119, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  There are %d\n\
- outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
-      total, qh->num_facets, qh->num_vertices, qh->num_outside+1,
-      furthestid, qh->vertex_id, dist, getid_(facet));
-  }else if (qh->IStracing >=1) {
-    cpu= (float)qh_CPUclock - (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    qh_distplane(qh, furthest, facet, &dist);
-    qh_fprintf(qh, qh->ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
-      furthestid, qh->vertex_id, qh->num_facets, dist,
-      getid_(facet), qh->num_outside+1, cpu, qh->furthest_id);
-  }
-  zmax_(Zvisit2max, (int)qh->visit_id/2);
-  if (qh->visit_id > (unsigned) INT_MAX) { /* 31 bits */
-    zinc_(Zvisit);
-    qh->visit_id= 0;
-    FORALLfacets
-      facet->visitid= 0;
-  }
-  zmax_(Zvvisit2max, (int)qh->vertex_visit/2);
-  if (qh->vertex_visit > (unsigned) INT_MAX) { /* 31 bits */ 
-    zinc_(Zvvisit);
-    qh->vertex_visit= 0;
-    FORALLvertices
-      vertex->visitid= 0;
-  }
-  qh->furthest_id= furthestid;
-  qh->RANDOMdist= qh->old_randomdist;
-} /* buildtracing */
-
-/*---------------------------------
-
-  qh_errexit2(qh, exitcode, facet, otherfacet )
-    return exitcode to system after an error
-    report two facets
-
-  returns:
-    assumes exitcode non-zero
-
-  see:
-    normally use qh_errexit() in user.c(reports a facet and a ridge)
-*/
-void qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet) {
-
-  qh_errprint(qh, "ERRONEOUS", facet, otherfacet, NULL, NULL);
-  qh_errexit(qh, exitcode, NULL, NULL);
-} /* errexit2 */
-
-
-/*---------------------------------
-
-  qh_findhorizon(qh, point, facet, goodvisible, goodhorizon )
-    given a visible facet, find the point's horizon and visible facets
-    for all facets, !facet-visible
-
-  returns:
-    returns qh.visible_list/num_visible with all visible facets
-      marks visible facets with ->visible
-    updates count of good visible and good horizon facets
-    updates qh.max_outside, qh.max_vertex, facet->maxoutside
-
-  see:
-    similar to qh_delpoint()
-
-  design:
-    move facet to qh.visible_list at end of qh.facet_list
-    for all visible facets
-     for each unvisited neighbor of a visible facet
-       compute distance of point to neighbor
-       if point above neighbor
-         move neighbor to end of qh.visible_list
-       else if point is coplanar with neighbor
-         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
-         mark neighbor coplanar (will create a samecycle later)
-         update horizon statistics
-*/
-void qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
-  facetT *neighbor, **neighborp, *visible;
-  int numhorizon= 0, coplanar= 0;
-  realT dist;
-
-  trace1((qh, qh->ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(qh, point),facet->id));
-  *goodvisible= *goodhorizon= 0;
-  zinc_(Ztotvisible);
-  qh_removefacet(qh, facet);  /* visible_list at end of qh->facet_list */
-  qh_appendfacet(qh, facet);
-  qh->num_visible= 1;
-  if (facet->good)
-    (*goodvisible)++;
-  qh->visible_list= facet;
-  facet->visible= True;
-  facet->f.replace= NULL;
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "visible", facet, NULL, NULL, NULL);
-  qh->visit_id++;
-  FORALLvisible_facets {
-    if (visible->tricoplanar && !qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh, qh_ERRqhull, visible, NULL);
-    }
-    visible->visitid= qh->visit_id;
-    FOREACHneighbor_(visible) {
-      if (neighbor->visitid == qh->visit_id)
-        continue;
-      neighbor->visitid= qh->visit_id;
-      zzinc_(Znumvisibility);
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > qh->MINvisible) {
-        zinc_(Ztotvisible);
-        qh_removefacet(qh, neighbor);  /* append to end of qh->visible_list */
-        qh_appendfacet(qh, neighbor);
-        neighbor->visible= True;
-        neighbor->f.replace= NULL;
-        qh->num_visible++;
-        if (neighbor->good)
-          (*goodvisible)++;
-        if (qh->IStracing >=4)
-          qh_errprint(qh, "visible", neighbor, NULL, NULL, NULL);
-      }else {
-        if (dist > - qh->MAXcoplanar) {
-          neighbor->coplanar= True;
-          zzinc_(Zcoplanarhorizon);
-          qh_precision(qh, "coplanar horizon");
-          coplanar++;
-          if (qh->MERGING) {
-            if (dist > 0) {
-              maximize_(qh->max_outside, dist);
-              maximize_(qh->max_vertex, dist);
-#if qh_MAXoutside
-              maximize_(neighbor->maxoutside, dist);
-#endif
-            }else
-              minimize_(qh->min_vertex, dist);  /* due to merge later */
-          }
-          trace2((qh, qh->ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)\n",
-              qh_pointid(qh, point), neighbor->id, dist, qh->MINvisible));
-        }else
-          neighbor->coplanar= False;
-        zinc_(Ztothorizon);
-        numhorizon++;
-        if (neighbor->good)
-          (*goodhorizon)++;
-        if (qh->IStracing >=4)
-          qh_errprint(qh, "horizon", neighbor, NULL, NULL, NULL);
-      }
-    }
-  }
-  if (!numhorizon) {
-    qh_precision(qh, "empty horizon");
-    qh_fprintf(qh, qh->ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
-QhullPoint p%d was above all facets.\n", qh_pointid(qh, point));
-    qh_printfacetlist(qh, qh->facet_list, NULL, True);
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-  trace1((qh, qh->ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
-       numhorizon, *goodhorizon, qh->num_visible, *goodvisible, coplanar));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-} /* findhorizon */
-
-/*---------------------------------
-
-  qh_nextfurthest(qh, visible )
-    returns next furthest point and visible facet for qh_addpoint()
-    starts search at qh.facet_next
-
-  returns:
-    removes furthest point from outside set
-    NULL if none available
-    advances qh.facet_next over facets with empty outside sets
-
-  design:
-    for each facet from qh.facet_next
-      if empty outside set
-        advance qh.facet_next
-      else if qh.NARROWhull
-        determine furthest outside point
-        if furthest point is not outside
-          advance qh.facet_next(point will be coplanar)
-    remove furthest point from outside set
-*/
-pointT *qh_nextfurthest(qhT *qh, facetT **visible) {
-  facetT *facet;
-  int size, idx;
-  realT randr, dist;
-  pointT *furthest;
-
-  while ((facet= qh->facet_next) != qh->facet_tail) {
-    if (!facet->outsideset) {
-      qh->facet_next= facet->next;
-      continue;
-    }
-    SETreturnsize_(facet->outsideset, size);
-    if (!size) {
-      qh_setfree(qh, &facet->outsideset);
-      qh->facet_next= facet->next;
-      continue;
-    }
-    if (qh->NARROWhull) {
-      if (facet->notfurthest)
-        qh_furthestout(qh, facet);
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-#if qh_COMPUTEfurthest
-      qh_distplane(qh, furthest, facet, &dist);
-      zinc_(Zcomputefurthest);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist < qh->MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
-        qh->facet_next= facet->next;
-        continue;
-      }
-    }
-    if (!qh->RANDOMoutside && !qh->VIRTUALmemory) {
-      if (qh->PICKfurthest) {
-        qh_furthestnext(qh /* qh->facet_list */);
-        facet= qh->facet_next;
-      }
-      *visible= facet;
-      return((pointT*)qh_setdellast(facet->outsideset));
-    }
-    if (qh->RANDOMoutside) {
-      int outcoplanar = 0;
-      if (qh->NARROWhull) {
-        FORALLfacets {
-          if (facet == qh->facet_next)
-            break;
-          if (facet->outsideset)
-            outcoplanar += qh_setsize(qh, facet->outsideset);
-        }
-      }
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor((qh->num_outside - outcoplanar) * randr);
-      FORALLfacet_(qh->facet_next) {
-        if (facet->outsideset) {
-          SETreturnsize_(facet->outsideset, size);
-          if (!size)
-            qh_setfree(qh, &facet->outsideset);
-          else if (size > idx) {
-            *visible= facet;
-            return((pointT*)qh_setdelnth(qh, facet->outsideset, idx));
-          }else
-            idx -= size;
-        }
-      }
-      qh_fprintf(qh, qh->ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
-              qh->num_outside, idx+1, randr);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }else { /* VIRTUALmemory */
-      facet= qh->facet_tail->previous;
-      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
-        if (facet->outsideset)
-          qh_setfree(qh, &facet->outsideset);
-        qh_removefacet(qh, facet);
-        qh_prependfacet(qh, facet, &qh->facet_list);
-        continue;
-      }
-      *visible= facet;
-      return furthest;
-    }
-  }
-  return NULL;
-} /* nextfurthest */
-
-/*---------------------------------
-
-  qh_partitionall(qh, vertices, points, numpoints )
-    partitions all points in points/numpoints to the outsidesets of facets
-    vertices= vertices in qh.facet_list(!partitioned)
-
-  returns:
-    builds facet->outsideset
-    does not partition qh.GOODpoint
-    if qh.ONLYgood && !qh.MERGING,
-      does not partition qh.GOODvertex
-
-  notes:
-    faster if qh.facet_list sorted by anticipated size of outside set
-
-  design:
-    initialize pointset with all points
-    remove vertices from pointset
-    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
-    for all facets
-      for all remaining points in pointset
-        compute distance from point to facet
-        if point is outside facet
-          remove point from pointset (by not reappending)
-          update bestpoint
-          append point or old bestpoint to facet's outside set
-      append bestpoint to facet's outside set (furthest)
-    for all points remaining in pointset
-      partition point into facets' outside sets and coplanar sets
-*/
-void qh_partitionall(qhT *qh, setT *vertices, pointT *points, int numpoints){
-  setT *pointset;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp, *bestpoint;
-  int size, point_i, point_n, point_end, remaining, i, id;
-  facetT *facet;
-  realT bestdist= -REALmax, dist, distoutside;
-
-  trace1((qh, qh->ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
-  pointset= qh_settemp(qh, numpoints);
-  qh->num_outside= 0;
-  pointp= SETaddr_(pointset, pointT);
-  for (i=numpoints, point= points; i--; point += qh->hull_dim)
-    *(pointp++)= point;
-  qh_settruncate(qh, pointset, numpoints);
-  FOREACHvertex_(vertices) {
-    if ((id= qh_pointid(qh, vertex->point)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  id= qh_pointid(qh, qh->GOODpointp);
-  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
-    SETelem_(pointset, id)= NULL;
-  if (qh->GOODvertexp && qh->ONLYgood && !qh->MERGING) { /* matches qhull()*/
-    if ((id= qh_pointid(qh, qh->GOODvertexp)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  if (!qh->BESToutside) {  /* matches conditional for qh_partitionpoint below */
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-    zval_(Ztotpartition)= qh->num_points - qh->hull_dim - 1; /*misses GOOD... */
-    remaining= qh->num_facets;
-    point_end= numpoints;
-    FORALLfacets {
-      size= point_end/(remaining--) + 100;
-      facet->outsideset= qh_setnew(qh, size);
-      bestpoint= NULL;
-      point_end= 0;
-      FOREACHpoint_i_(qh, pointset) {
-        if (point) {
-          zzinc_(Zpartitionall);
-          qh_distplane(qh, point, facet, &dist);
-          if (dist < distoutside)
-            SETelem_(pointset, point_end++)= point;
-          else {
-            qh->num_outside++;
-            if (!bestpoint) {
-              bestpoint= point;
-              bestdist= dist;
-            }else if (dist > bestdist) {
-              qh_setappend(qh, &facet->outsideset, bestpoint);
-              bestpoint= point;
-              bestdist= dist;
-            }else
-              qh_setappend(qh, &facet->outsideset, point);
-          }
-        }
-      }
-      if (bestpoint) {
-        qh_setappend(qh, &facet->outsideset, bestpoint);
-#if !qh_COMPUTEfurthest
-        facet->furthestdist= bestdist;
-#endif
-      }else
-        qh_setfree(qh, &facet->outsideset);
-      qh_settruncate(qh, pointset, point_end);
-    }
-  }
-  /* if !qh->BESToutside, pointset contains points not assigned to outsideset */
-  if (qh->BESToutside || qh->MERGING || qh->KEEPcoplanar || qh->KEEPinside) {
-    qh->findbestnew= True;
-    FOREACHpoint_i_(qh, pointset) {
-      if (point)
-        qh_partitionpoint(qh, point, qh->facet_list);
-    }
-    qh->findbestnew= False;
-  }
-  zzadd_(Zpartitionall, zzval_(Zpartition));
-  zzval_(Zpartition)= 0;
-  qh_settempfree(qh, &pointset);
-  if (qh->IStracing >= 4)
-    qh_printfacetlist(qh, qh->facet_list, NULL, True);
-} /* partitionall */
-
-
-/*---------------------------------
-
-  qh_partitioncoplanar(qh, point, facet, dist )
-    partition coplanar point to a facet
-    dist is distance from point to facet
-    if dist NULL,
-      searches for bestfacet and does nothing if inside
-    if qh.findbestnew set,
-      searches new facets instead of using qh_findbest()
-
-  returns:
-    qh.max_ouside updated
-    if qh.KEEPcoplanar or qh.KEEPinside
-      point assigned to best coplanarset
-
-  notes:
-    facet->maxoutside is updated at end by qh_check_maxout
-
-  design:
-    if dist undefined
-      find best facet for point
-      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
-        exit
-    if keeping coplanar/nearinside/inside points
-      if point is above furthest coplanar point
-        append point to coplanar set (it is the new furthest)
-        update qh.max_outside
-      else
-        append point one before end of coplanar set
-    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
-    and bestfacet is more than perpendicular to facet
-      repartition the point using qh_findbest() -- it may be put on an outsideset
-    else
-      update qh.max_outside
-*/
-void qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist) {
-  facetT *bestfacet;
-  pointT *oldfurthest;
-  realT bestdist, dist2= 0, angle;
-  int numpart= 0, oldfindbest;
-  boolT isoutside;
-
-  qh->WAScoplanar= True;
-  if (!dist) {
-    if (qh->findbestnew)
-      bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
-    else
-      bestfacet= qh_findbest(qh, point, facet, qh_ALL, !qh_ISnewfacets, qh->DELAUNAY,
-                          &bestdist, &isoutside, &numpart);
-    zinc_(Ztotpartcoplanar);
-    zzadd_(Zpartcoplanar, numpart);
-    if (!qh->DELAUNAY && !qh->KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
-      if (qh->KEEPnearinside) {
-        if (bestdist < -qh->NEARinside) {
-          zinc_(Zcoplanarinside);
-          trace4((qh, qh->ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
-          return;
-        }
-      }else if (bestdist < -qh->MAXcoplanar) {
-          trace4((qh, qh->ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
-                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
-        zinc_(Zcoplanarinside);
-        return;
-      }
-    }
-  }else {
-    bestfacet= facet;
-    bestdist= *dist;
-  }
-  if (bestdist > qh->max_outside) {
-    if (!dist && facet != bestfacet) {
-      zinc_(Zpartangle);
-      angle= qh_getangle(qh, facet->normal, bestfacet->normal);
-      if (angle < 0) {
-        /* typically due to deleted vertex and coplanar facets, e.g.,
-             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
-        zinc_(Zpartflip);
-        trace2((qh, qh->ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
-                qh_pointid(qh, point), facet->id, bestfacet->id, bestdist));
-        oldfindbest= qh->findbestnew;
-        qh->findbestnew= False;
-        qh_partitionpoint(qh, point, bestfacet);
-        qh->findbestnew= oldfindbest;
-        return;
-      }
-    }
-    qh->max_outside= bestdist;
-    if (bestdist > qh->TRACEdist) {
-      qh_fprintf(qh, qh->ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
-                     qh_pointid(qh, point), facet->id, bestdist, bestfacet->id, qh->furthest_id);
-      qh_errprint(qh, "DISTANT", facet, bestfacet, NULL, NULL);
-    }
-  }
-  if (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside) {
-    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
-    if (oldfurthest) {
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, oldfurthest, bestfacet, &dist2);
-    }
-    if (!oldfurthest || dist2 < bestdist)
-      qh_setappend(qh, &bestfacet->coplanarset, point);
-    else
-      qh_setappend2ndlast(qh, &bestfacet->coplanarset, point);
-  }
-  trace4((qh, qh->ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
-          qh_pointid(qh, point), bestfacet->id, bestdist));
-} /* partitioncoplanar */
-
-/*---------------------------------
-
-  qh_partitionpoint(qh, point, facet )
-    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
-    if qh.findbestnew
-      uses qh_findbestnew() to search all new facets
-    else
-      uses qh_findbest()
-
-  notes:
-    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
-
-  design:
-    find best facet for point
-      (either exhaustive search of new facets or directed search from facet)
-    if qh.NARROWhull
-      retain coplanar and nearinside points as outside points
-    if point is outside bestfacet
-      if point above furthest point for bestfacet
-        append point to outside set (it becomes the new furthest)
-        if outside set was empty
-          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
-        update bestfacet->furthestdist
-      else
-        append point one before end of outside set
-    else if point is coplanar to bestfacet
-      if keeping coplanar points or need to update qh.max_outside
-        partition coplanar point into bestfacet
-    else if near-inside point
-      partition as coplanar point into bestfacet
-    else is an inside point
-      if keeping inside points
-        partition as coplanar point into bestfacet
-*/
-void qh_partitionpoint(qhT *qh, pointT *point, facetT *facet) {
-  realT bestdist;
-  boolT isoutside;
-  facetT *bestfacet;
-  int numpart;
-#if qh_COMPUTEfurthest
-  realT dist;
-#endif
-
-  if (qh->findbestnew)
-    bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh->BESToutside, &isoutside, &numpart);
-  else
-    bestfacet= qh_findbest(qh, point, facet, qh->BESToutside, qh_ISnewfacets, !qh_NOupper,
-                          &bestdist, &isoutside, &numpart);
-  zinc_(Ztotpartition);
-  zzadd_(Zpartition, numpart);
-  if (qh->NARROWhull) {
-    if (qh->DELAUNAY && !isoutside && bestdist >= -qh->MAXcoplanar)
-      qh_precision(qh, "nearly incident point(narrow hull)");
-    if (qh->KEEPnearinside) {
-      if (bestdist >= -qh->NEARinside)
-        isoutside= True;
-    }else if (bestdist >= -qh->MAXcoplanar)
-      isoutside= True;
-  }
-
-  if (isoutside) {
-    if (!bestfacet->outsideset
-    || !qh_setlast(bestfacet->outsideset)) {
-      qh_setappend(qh, &(bestfacet->outsideset), point);
-      if (!bestfacet->newfacet) {
-        qh_removefacet(qh, bestfacet);  /* make sure it's after qh->facet_next */
-        qh_appendfacet(qh, bestfacet);
-      }
-#if !qh_COMPUTEfurthest
-      bestfacet->furthestdist= bestdist;
-#endif
-    }else {
-#if qh_COMPUTEfurthest
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, oldfurthest, bestfacet, &dist);
-      if (dist < bestdist)
-        qh_setappend(qh, &(bestfacet->outsideset), point);
-      else
-        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
-#else
-      if (bestfacet->furthestdist < bestdist) {
-        qh_setappend(qh, &(bestfacet->outsideset), point);
-        bestfacet->furthestdist= bestdist;
-      }else
-        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
-#endif
-    }
-    qh->num_outside++;
-    trace4((qh, qh->ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
-          qh_pointid(qh, point), bestfacet->id, bestfacet->newfacet));
-  }else if (qh->DELAUNAY || bestdist >= -qh->MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
-    zzinc_(Zcoplanarpart);
-    if (qh->DELAUNAY)
-      qh_precision(qh, "nearly incident point");
-    if ((qh->KEEPcoplanar + qh->KEEPnearinside) || bestdist > qh->max_outside)
-      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-    else {
-      trace4((qh, qh->ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
-          qh_pointid(qh, point), bestfacet->id));
-    }
-  }else if (qh->KEEPnearinside && bestdist > -qh->NEARinside) {
-    zinc_(Zpartnear);
-    qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-  }else {
-    zinc_(Zpartinside);
-    trace4((qh, qh->ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
-          qh_pointid(qh, point), bestfacet->id, bestdist));
-    if (qh->KEEPinside)
-      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
-  }
-} /* partitionpoint */
-
-/*---------------------------------
-
-  qh_partitionvisible(qh, allpoints, numoutside )
-    partitions points in visible facets to qh.newfacet_list
-    qh.visible_list= visible facets
-    for visible facets
-      1st neighbor (if any) points to a horizon facet or a new facet
-    if allpoints(!used),
-      repartitions coplanar points
-
-  returns:
-    updates outside sets and coplanar sets of qh.newfacet_list
-    updates qh.num_outside (count of outside points)
-
-  notes:
-    qh.findbest_notsharp should be clear (extra work if set)
-
-  design:
-    for all visible facets with outside set or coplanar set
-      select a newfacet for visible facet
-      if outside set
-        partition outside set into new facets
-      if coplanar set and keeping coplanar/near-inside/inside points
-        if allpoints
-          partition coplanar set into new facets, may be assigned outside
-        else
-          partition coplanar set into coplanar sets of new facets
-    for each deleted vertex
-      if allpoints
-        partition vertex into new facets, may be assigned outside
-      else
-        partition vertex into coplanar sets of new facets
-*/
-void qh_partitionvisible(qhT *qh /*qh.visible_list*/, boolT allpoints, int *numoutside) {
-  facetT *visible, *newfacet;
-  pointT *point, **pointp;
-  int coplanar=0, size;
-  unsigned count;
-  vertexT *vertex, **vertexp;
-
-  if (qh->ONLYmax)
-    maximize_(qh->MINoutside, qh->max_vertex);
-  *numoutside= 0;
-  FORALLvisible_facets {
-    if (!visible->outsideset && !visible->coplanarset)
-      continue;
-    newfacet= visible->f.replace;
-    count= 0;
-    while (newfacet && newfacet->visible) {
-      newfacet= newfacet->f.replace;
-      if (count++ > qh->facet_id)
-        qh_infiniteloop(qh, visible);
-    }
-    if (!newfacet)
-      newfacet= qh->newfacet_list;
-    if (newfacet == qh->facet_tail) {
-      qh_fprintf(qh, qh->ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
-      qh_errexit(qh, qh_ERRprec, NULL, NULL);
-    }
-    if (visible->outsideset) {
-      size= qh_setsize(qh, visible->outsideset);
-      *numoutside += size;
-      qh->num_outside -= size;
-      FOREACHpoint_(visible->outsideset)
-        qh_partitionpoint(qh, point, newfacet);
-    }
-    if (visible->coplanarset && (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside)) {
-      size= qh_setsize(qh, visible->coplanarset);
-      coplanar += size;
-      FOREACHpoint_(visible->coplanarset) {
-        if (allpoints) /* not used */
-          qh_partitionpoint(qh, point, newfacet);
-        else
-          qh_partitioncoplanar(qh, point, newfacet, NULL);
-      }
-    }
-  }
-  FOREACHvertex_(qh->del_vertices) {
-    if (vertex->point) {
-      if (allpoints) /* not used */
-        qh_partitionpoint(qh, vertex->point, qh->newfacet_list);
-      else
-        qh_partitioncoplanar(qh, vertex->point, qh->newfacet_list, NULL);
-    }
-  }
-  trace1((qh, qh->ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
-} /* partitionvisible */
-
-
-
-/*---------------------------------
-
-  qh_precision(qh, reason )
-    restart on precision errors if not merging and if 'QJn'
-*/
-void qh_precision(qhT *qh, const char *reason) {
-
-  if (qh->ALLOWrestart && !qh->PREmerge && !qh->MERGEexact) {
-    if (qh->JOGGLEmax < REALmax/2) {
-      trace0((qh, qh->ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
-      /* May be called repeatedly if qh->ALLOWrestart */
-      longjmp(qh->restartexit, qh_ERRprec);
-    }
-  }
-} /* qh_precision */
-
-/*---------------------------------
-
-  qh_printsummary(qh, fp )
-    prints summary to fp
-
-  notes:
-    not in io_r.c so that user_eg.c can prevent io_r.c from loading
-    qh_printsummary and qh_countfacets must match counts
-
-  design:
-    determine number of points, vertices, and coplanar points
-    print summary
-*/
-void qh_printsummary(qhT *qh, FILE *fp) {
-  realT ratio, outerplane, innerplane;
-  float cpu;
-  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
-  int goodused;
-  facetT *facet;
-  const char *s;
-  int numdel= zzval_(Zdelvertextot);
-  int numtricoplanars= 0;
-
-  size= qh->num_points + qh_setsize(qh, qh->other_points);
-  numvertices= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
-  id= qh_pointid(qh, qh->GOODpointp);
-  FORALLfacets {
-    if (facet->coplanarset)
-      numcoplanars += qh_setsize(qh, facet->coplanarset);
-    if (facet->good) {
-      if (facet->simplicial) {
-        if (facet->keepcentrum && facet->tricoplanar)
-          numtricoplanars++;
-      }else if (qh_setsize(qh, facet->vertices) != qh->hull_dim)
-        nonsimplicial++;
-    }
-  }
-  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
-    size--;
-  if (qh->STOPcone || qh->STOPpoint)
-      qh_fprintf(qh, fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
-  if (qh->UPPERdelaunay)
-    goodused= qh->GOODvertex + qh->GOODpoint + qh->SPLITthresholds;
-  else if (qh->DELAUNAY)
-    goodused= qh->GOODvertex + qh->GOODpoint + qh->GOODthreshold;
-  else
-    goodused= qh->num_good;
-  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  if (qh->VORONOI) {
-    if (qh->UPPERdelaunay)
-      qh_fprintf(qh, fp, 9289, "\n\
-Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9290, "\n\
-Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9291, "  Number of Voronoi regions%s: %d\n",
-              qh->ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(qh, fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(qh, fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(qh, fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(qh, fp, 9295, "  Number of%s Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh->DELAUNAY) {
-    if (qh->UPPERdelaunay)
-      qh_fprintf(qh, fp, 9297, "\n\
-Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    else
-      qh_fprintf(qh, fp, 9298, "\n\
-Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9299, "  Number of input sites%s: %d\n",
-              qh->ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      qh_fprintf(qh, fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      qh_fprintf(qh, fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      qh_fprintf(qh, fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    qh_fprintf(qh, fp, 9303, "  Number of%s Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh->HALFspace) {
-    qh_fprintf(qh, fp, 9305, "\n\
-Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9306, "  Number of halfspaces: %d\n", size);
-    qh_fprintf(qh, fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh->KEEPinside && qh->KEEPcoplanar)
-        s= "similar and redundant";
-      else if (qh->KEEPinside)
-        s= "redundant";
-      else
-        s= "similar";
-      qh_fprintf(qh, fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(qh, fp, 9309, "  Number of intersection points: %d\n", qh->num_facets - qh->num_visible);
-    if (goodused)
-      qh_fprintf(qh, fp, 9310, "  Number of 'good' intersection points: %d\n", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else {
-    qh_fprintf(qh, fp, 9312, "\n\
-Convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
-    qh_fprintf(qh, fp, 9313, "  Number of vertices: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh->KEEPinside && qh->KEEPcoplanar)
-        s= "coplanar and interior";
-      else if (qh->KEEPinside)
-        s= "interior";
-      else
-        s= "coplanar";
-      qh_fprintf(qh, fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
-    }
-    qh_fprintf(qh, fp, 9315, "  Number of facets: %d\n", qh->num_facets - qh->num_visible);
-    if (goodused)
-      qh_fprintf(qh, fp, 9316, "  Number of 'good' facets: %d\n", qh->num_good);
-    if (nonsimplicial)
-      qh_fprintf(qh, fp, 9317, "  Number of%s non-simplicial facets: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }
-  if (numtricoplanars)
-      qh_fprintf(qh, fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
-  qh_fprintf(qh, fp, 9319, "\nStatistics for: %s | %s",
-                      qh->rbox_command, qh->qhull_command);
-  if (qh->ROTATErandom != INT_MIN)
-    qh_fprintf(qh, fp, 9320, " QR%d\n\n", qh->ROTATErandom);
-  else
-    qh_fprintf(qh, fp, 9321, "\n\n");
-  qh_fprintf(qh, fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
-  qh_fprintf(qh, fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
-  if (qh->DELAUNAY)
-    qh_fprintf(qh, fp, 9324, "  Number of facets in hull: %d\n", qh->num_facets - qh->num_visible);
-  qh_fprintf(qh, fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
-      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
-#if 0  /* NOTE: must print before printstatistics() */
-  {realT stddev, ave;
-  qh_fprintf(qh, fp, 9326, "  average new facet balance: %2.2g\n",
-          wval_(Wnewbalance)/zval_(Zprocessed));
-  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(qh, fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
-  qh_fprintf(qh, fp, 9328, "  average partition balance: %2.2g\n",
-          wval_(Wpbalance)/zval_(Zpbalance));
-  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  qh_fprintf(qh, fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
-  }
-#endif
-  if (nummerged) {
-    qh_fprintf(qh, fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
-          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
-          zzval_(Zdistzero));
-    qh_fprintf(qh, fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
-    qh_fprintf(qh, fp, 9332,"  Number of merged facets: %d\n", nummerged);
-  }
-  if (!qh->RANDOMoutside && qh->QHULLfinished) {
-    cpu= (float)qh->hulltime;
-    cpu /= (float)qh_SECticks;
-    wval_(Wcpu)= cpu;
-    qh_fprintf(qh, fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
-  }
-  if (qh->RERUN) {
-    if (!qh->PREmerge && !qh->MERGEexact)
-      qh_fprintf(qh, fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
-           zzval_(Zretry)*100.0/qh->build_cnt);  /* careful of order */
-  }else if (qh->JOGGLEmax < REALmax/2) {
-    if (zzval_(Zretry))
-      qh_fprintf(qh, fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
-         zzval_(Zretry), qh->JOGGLEmax);
-    else
-      qh_fprintf(qh, fp, 9336, "  Input joggled by: %2.2g\n", qh->JOGGLEmax);
-  }
-  if (qh->totarea != 0.0)
-    qh_fprintf(qh, fp, 9337, "  %s facet area:   %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totarea);
-  if (qh->totvol != 0.0)
-    qh_fprintf(qh, fp, 9338, "  %s volume:       %2.8g\n",
-            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totvol);
-  if (qh->MERGING) {
-    qh_outerinner(qh, NULL, &outerplane, &innerplane);
-    if (outerplane > 2 * qh->DISTround) {
-      qh_fprintf(qh, fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
-            (qh->QHULLfinished ? "" : "merged "), outerplane);
-      ratio= outerplane/(qh->ONEmerge + qh->DISTround);
-      /* don't report ratio if MINoutside is large */
-      if (ratio > 0.05 && 2* qh->ONEmerge > qh->MINoutside && qh->JOGGLEmax > REALmax/2)
-        qh_fprintf(qh, fp, 9340, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(qh, fp, 9341, "\n");
-    }
-    if (innerplane < -2 * qh->DISTround) {
-      qh_fprintf(qh, fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
-            (qh->QHULLfinished ? "" : "merged "), innerplane);
-      ratio= -innerplane/(qh->ONEmerge+qh->DISTround);
-      if (ratio > 0.05 && qh->JOGGLEmax > REALmax/2)
-        qh_fprintf(qh, fp, 9343, " (%.1fx)\n", ratio);
-      else
-        qh_fprintf(qh, fp, 9344, "\n");
-    }
-  }
-  qh_fprintf(qh, fp, 9345, "\n");
-} /* printsummary */
-
-
diff --git a/src/qhull/src/libqhull_r/libqhull_r.h b/src/qhull/src/libqhull_r/libqhull_r.h
deleted file mode 100644
index 363e6da6a..000000000
--- a/src/qhull/src/libqhull_r/libqhull_r.h
+++ /dev/null
@@ -1,1134 +0,0 @@
-/*
      ---------------------------------
-
-   libqhull_r.h
-   user-level header file for using qhull.a library
-
-   see qh-qhull_r.htm, qhull_ra.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.h#8 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-
-   includes function prototypes for libqhull_r.c, geom_r.c, global_r.c, io_r.c, user.c
-
-   use mem_r.h for mem_r.c
-   use qset_r.h for qset_r.c
-
-   see unix_r.c for an example of using libqhull_r.h
-
-   recompile qhull if you change this file
-*/
-
-#ifndef qhDEFlibqhull
-#define qhDEFlibqhull 1
-
-/*=========================== -included files ==============*/
-
-/* user_r.h first for QHULL_CRTDBG */
-#include "user_r.h"      /* user definable constants (e.g., realT). */
-
-#include "mem_r.h"   /* Needed for qhT in libqhull_r.h */
-#include "qset_r.h"   /* Needed for QHULL_LIB_CHECK */
-/* include stat_r.h after defining boolT.  statT needed for qhT in libqhull_r.h */
-
-#include 
-#include 
-#include 
-#include 
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if     !_MSC_VER
-#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
-#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
-#error  your compiler is a standard C compiler, you can delete this warning from libqhull_r.h
-#endif
-#endif
-#endif
-
-/*============ constants and basic types ====================*/
-
-extern const char qh_version[]; /* defined in global_r.c */
-extern const char qh_version2[]; /* defined in global_r.c */
-
-/*----------------------------------
-
-  coordT
-    coordinates and coefficients are stored as realT (i.e., double)
-
-  notes:
-    Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
-
-    Could use 'float' for data and 'double' for calculations (realT vs. coordT)
-      This requires many type casts, and adjusted error bounds.
-      Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*----------------------------------
-
-  pointT
-    a point is an array of coordinates, usually qh.hull_dim
-    qh_pointid returns
-      qh_IDnone if point==0 or qh is undefined
-      qh_IDinterior for qh.interior_point
-      qh_IDunknown if point is neither in qh.first_point... nor qh.other_points
-
-  notes:
-    qh.STOPcone and qh.STOPpoint assume that qh_IDunknown==-1 (other negative numbers indicate points)
-    qh_IDunknown is also returned by getid_() for unknown facet, ridge, or vertex
-*/
-#define pointT coordT
-typedef enum
-{
-    qh_IDnone = -3, qh_IDinterior = -2, qh_IDunknown = -1
-}
-qh_pointT;
-
-/*----------------------------------
-
-  flagT
-    Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*----------------------------------
-
-  boolT
-    boolean value, either True or False
-
-  notes:
-    needed for portability
-    Use qh_False/qh_True as synonyms
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-#define qh_False 0
-#define qh_True 1
-
-#include "stat_r.h"  /* needs boolT */
-
-/*----------------------------------
-
-  qh_CENTER
-    to distinguish facet->center
-*/
-typedef enum
-{
-    qh_ASnone = 0,   /* If not MERGING and not VORONOI */
-    qh_ASvoronoi,    /* Set by qh_clearcenters on qh_prepare_output, or if not MERGING and VORONOI */
-    qh_AScentrum     /* If MERGING (assumed during merging) */
-}
-qh_CENTER;
-
-/*----------------------------------
-
-  qh_PRINT
-    output formats for printing (qh.PRINTout).
-    'Fa' 'FV' 'Fc' 'FC'
-
-
-   notes:
-   some of these names are similar to qhT names.  The similar names are only
-   used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone= 0,
-  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
-  qh_PRINTcoplanars, qh_PRINTcentrums,
-  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
-  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
-  qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
-  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
-  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
-  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
-  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
-  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
-  qh_PRINTEND} qh_PRINT;
-
-/*----------------------------------
-
-  qh_ALL
-    argument flag for selecting everything
-*/
-#define qh_ALL      True
-#define qh_NOupper  True     /* argument for qh_findbest */
-#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets  True     /* argument for qh_findbest */
-#define qh_RESETvisible  True     /* argument for qh_resetlists */
-
-/*----------------------------------
-
-  qh_ERR
-    Qhull exit codes, for indicating errors
-    See: MSG_ERROR and MSG_WARNING [user.h]
-*/
-#define qh_ERRnone  0    /* no error occurred during qhull */
-#define qh_ERRinput 1    /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec  3    /* precision error */
-#define qh_ERRmem   4    /* insufficient memory, matches mem_r.h */
-#define qh_ERRqhull 5    /* internal error detected, matches mem_r.h */
-
-/*----------------------------------
-
-qh_FILEstderr
-Fake stderr to distinguish error output from normal output
-For C++ interface.  Must redefine qh_fprintf_qhull
-*/
-#define qh_FILEstderr ((FILE*)1)
-
-/* ============ -structures- ====================
-   each of the following structures is defined by a typedef
-   all realT and coordT fields occur at the beginning of a structure
-        (otherwise space may be wasted due to alignment)
-   define all flags together and pack into 32-bit number
-
-   DEFqhT and DEFsetT are likewise defined in
-   mem_r.h, qset_r.h, and stat_r.h.
-
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-
-#ifndef DEFqhT
-#define DEFqhT 1
-typedef struct qhT qhT;          /* defined below */
-#endif
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset_r.h */
-#endif
-
-/*----------------------------------
-
-  facetT
-    defines a facet
-
-  notes:
-   qhull() generates the hull as a list of facets.
-
-  topological information:
-    f.previous,next     doubly-linked list of facets
-    f.vertices          set of vertices
-    f.ridges            set of ridges
-    f.neighbors         set of neighbors
-    f.toporient         True if facet has top-orientation (else bottom)
-
-  geometric information:
-    f.offset,normal     hyperplane equation
-    f.maxoutside        offset to outer plane -- all points inside
-    f.center            centrum for testing convexity or Voronoi center for output
-    f.simplicial        True if facet is simplicial
-    f.flipped           True if facet does not include qh.interior_point
-
-  for constructing hull:
-    f.visible           True if facet on list of visible facets (will be deleted)
-    f.newfacet          True if facet on list of newly created facets
-    f.coplanarset       set of points coplanar with this facet
-                        (includes near-inside points for later testing)
-    f.outsideset        set of points outside of this facet
-    f.furthestdist      distance to furthest point of outside set
-    f.visitid           marks visited facets during a loop
-    f.replace           replacement facet for to-be-deleted, visible facets
-    f.samecycle,newcycle cycle of facets for merging into horizon facet
-
-  see below for other flags and fields
-*/
-struct facetT {
-#if !qh_COMPUTEfurthest
-  coordT   furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
-  coordT   maxoutside;  /* max computed distance of point to facet
-                        Before QHULLfinished this is an approximation
-                        since maxdist not always set for mergefacet
-                        Actual outer plane is +DISTround and
-                        computed outer plane is +2*DISTround */
-#endif
-  coordT   offset;      /* exact offset of hyperplane from origin */
-  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
-                        /*   if ->tricoplanar, shared with a neighbor */
-  union {               /* in order of testing */
-   realT   area;        /* area of facet, only in io_r.c if  ->isarea */
-   facetT *replace;     /*  replacement facet if ->visible and NEWfacets
-                             is NULL only if qh_mergedegen_redundant or interior */
-   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
-                             if ->newfacet */
-   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
-   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
-   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
-  }f;
-  coordT  *center;      /* set according to qh.CENTERtype */
-                        /*   qh_ASnone:    no center (not MERGING) */
-                        /*   qh_AScentrum: centrum for testing convexity (qh_getcentrum) */
-                        /*                 assumed qh_AScentrum while merging */
-                        /*   qh_ASvoronoi: Voronoi center (qh_facetcenter) */
-                        /* after constructing the hull, it may be changed (qh_clearcenter) */
-                        /* if tricoplanar and !keepcentrum, shared with a neighbor */
-  facetT  *previous;    /* previous facet in the facet_list */
-  facetT  *next;        /* next facet in the facet_list */
-  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
-                           if simplicial, 1st vertex was apex/furthest */
-  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
-                           for simplicial facets, neighbors define the ridges */
-  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
-                           neighbor is opposite the kth vertex, and the first
-                           neighbor is the horizon facet for the first vertex*/
-  setT    *outsideset;  /* set of points outside this facet
-                           if non-empty, last point is furthest
-                           if NARROWhull, includes coplanars for partitioning*/
-  setT    *coplanarset; /* set of points coplanar with this facet
-                           > qh.min_vertex and <= facet->max_outside
-                           a point is assigned to the furthest facet
-                           if non-empty, last point is furthest away */
-  unsigned visitid;     /* visit_id, for visiting all neighbors,
-                           all uses are independent */
-  unsigned id;          /* unique identifier from qh.facet_id */
-  unsigned nummerge:9;  /* number of merges */
-#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io_r.c */
-  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
-                          /*   all tricoplanars share the same apex */
-                          /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
-                          /*     ->keepcentrum is true for the owner.  It has the ->coplanareset */
-                          /*   if ->degenerate, does not span facet (one logical ridge) */
-                          /*   during qh_triangulate, f.trivisible points to original facet */
-  flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
-  flagT    visible:1;   /* True if visible facet (will be deleted) */
-  flagT    toporient:1; /* True if created with top orientation
-                           after merging, use ridge orientation */
-  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
-  flagT    seen:1;      /* used to perform operations only once, like visitid */
-  flagT    seen2:1;     /* used to perform operations only once, like visitid */
-  flagT    flipped:1;   /* True if facet is flipped */
-  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
-  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
-
-/*-------- flags primarily for output ---------*/
-  flagT    good:1;      /* True if a facet marked good for output */
-  flagT    isarea:1;    /* True if facet->f.area is defined */
-
-/*-------- flags for merging ------------------*/
-  flagT    dupridge:1;  /* True if duplicate ridge in facet */
-  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
-                            ->normal defined (also defined for mergeridge2) */
-  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (qhT *qh, mark_dupridges */
-  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
-  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
-  flagT     cycledone:1;/* True if mergecycle_all already done */
-  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
-  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
-  flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
-  flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
-  flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*----------------------------------
-
-  ridgeT
-    defines a ridge
-
-  notes:
-  a ridge is hull_dim-1 simplex between two neighboring facets.  If the
-  facets are non-simplicial, there may be more than one ridge between
-  two facets.  E.G. a 4-d hypercube has two triangles between each pair
-  of neighboring facets.
-
-  topological information:
-    vertices            a set of vertices
-    top,bottom          neighboring facets with orientation
-
-  geometric information:
-    tested              True if ridge is clearly convex
-    nonconvex           True if ridge is non-convex
-*/
-struct ridgeT {
-  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
-                           NULL if a degen ridge (matchsame) */
-  facetT  *top;         /* top facet this ridge is part of */
-  facetT  *bottom;      /* bottom facet this ridge is part of */
-  unsigned id;          /* unique identifier.  Same size as vertex_id and ridge_id */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    tested:1;    /* True when ridge is tested for convexity */
-  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
-                           only one ridge between neighbors may have nonconvex */
-};
-
-/*----------------------------------
-
-  vertexT
-     defines a vertex
-
-  topological information:
-    next,previous       doubly-linked list of all vertices
-    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
-
-  geometric information:
-    point               array of DIM3 coordinates
-*/
-struct vertexT {
-  vertexT *next;        /* next vertex in vertex_list */
-  vertexT *previous;    /* previous vertex in vertex_list */
-  pointT  *point;       /* hull_dim coordinates (coordT) */
-  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
-                           inits in io_r.c or after first merge */
-  unsigned id;          /* unique identifier.  Same size as qh.vertex_id and qh.ridge_id */
-  unsigned visitid;    /* for use with qh.vertex_visit, size must match */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    seen2:1;     /* another seen flag */
-  flagT    delridge:1;  /* vertex was part of a deleted ridge */
-  flagT    deleted:1;   /* true if vertex on qh.del_vertices */
-  flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*----------------------------------
-
-  qhT
-   All global variables for qhull are in qhT.  It includes qhmemT, qhstatT, and rbox globals
-
-   This version of Qhull is reentrant, but it is not thread-safe.
-
-   Do not run separate threads on the same instance of qhT.
-
-   QHULL_LIB_CHECK checks that a program and the corresponding
-   qhull library were built with the same type of header files.
-*/
-
-#define QHULL_NON_REENTRANT 0
-#define QHULL_QH_POINTER 1
-#define QHULL_REENTRANT 2
-
-#define QHULL_LIB_TYPE QHULL_REENTRANT
-
-#define QHULL_LIB_CHECK qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), sizeof(setT), sizeof(qhmemT));
-#define QHULL_LIB_CHECK_RBOX qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), 0, 0);
-
-struct qhT {
-
-/*----------------------------------
-
-  qh constants
-    configuration flags and constants for Qhull
-
-  notes:
-    The user configures Qhull by defining flags.  They are
-    copied into qh by qh_setflags().  qh-quick_r.htm#options defines the flags.
-*/
-  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
-  boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
-  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
-  realT   MINoutside;     /*   'Wn' min. distance for an outside point */
-  boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
-  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
-                             for improving precision in Delaunay triangulations */
-  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
-  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
-  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
-  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
-  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
-  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
-  realT postmerge_cos;    /*   'An'    cos_max when post merging */
-  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
-  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
-  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
-  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
-  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
-  pointT *GOODpointp;     /*   the actual point */
-  boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
-                             false if qh.SPLITthreshold */
-  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
-  pointT *GOODvertexp;     /*   the actual point */
-  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
-  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
-  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
-  int   KEEParea;         /* 'PAn' number of largest facets to keep */
-  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
-  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
-                              set automatically if 'd Qc' */
-  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
-  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
-  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
-  boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
-  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
-  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
-  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
-  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
-  boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
-  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
-  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
-  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
-  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
-  boolT NOwide;           /* true 'Q12' if no error on wide merge due to duplicate ridge */
-  boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
-  boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
-  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
-  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
-  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
-                        /* NOTE: some of these names are similar to qh_PRINT names */
-  boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
-  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
-  int   PRINTdim;         /* print dimension for Geomview output */
-  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
-  boolT PRINTgood;        /* true 'Pg' if printing good facets */
-  boolT PRINTinner;       /* true 'Gi' if printing inner planes */
-  boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
-  boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
-  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
-  boolT PRINTouter;       /* true 'Go' if printing outer planes */
-  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
-  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
-  boolT PRINTridges;      /* true 'Gr' if print ridges */
-  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
-  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
-  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
-  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
-  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
-                             need projectinput() for Delaunay in qh_init_B */
-  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
-  boolT QUICKhelp;        /* true if quick help message for degen input */
-  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
-  realT RANDOMfactor;     /*    maximum random perturbation */
-  realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
-  realT RANDOMb;
-  boolT RANDOMoutside;    /* true if select a random outside point */
-  int   REPORTfreq;       /* buildtracing reports every n facets */
-  int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
-  int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
-  int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
-  boolT SCALEinput;       /* true 'Qbk' if scaling input */
-  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
-  boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
-  boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
-  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
-  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
-                               used only for printing (!for qh.ONLYgood) */
-  int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
-                          /*       also used by qh_build_withresart for err exit*/
-  int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
-                                        adding point n */
-  int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
-  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
-  int   TRACElevel;       /* 'Tn' conditional IStracing level */
-  int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
-  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
-  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
-  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
-  boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
-  boolT TRInormals;       /* true 'Q11' if triangulate duplicates ->normal and ->center (sets Qt) */
-  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
-  boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
-  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
-  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
-  boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
-
-  /*--------input constants ---------*/
-  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
-  boolT DOcheckmax;       /* true if calling qh_check_maxout (qhT *qh, qh_initqhull_globals) */
-  char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
-  coordT *feasible_point;  /*    as coordinates, both malloc'd */
-  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io_r.c */
-  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
-  int   hull_dim;         /* dimension of hull, set by initbuffers */
-  int   input_dim;        /* dimension of input, set by initbuffers */
-  int   num_points;       /* number of input points */
-  pointT *first_point;    /* array of input points, see POINTSmalloc */
-  boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
-  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
-  boolT input_malloc;     /* true if qh.input_points malloc'd */
-  char  qhull_command[256];/* command line that invoked this program */
-  int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
-  char  rbox_command[256]; /* command line that produced the input points */
-  char  qhull_options[512];/* descriptive list of options */
-  int   qhull_optionlen;  /*    length of last line */
-  int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
-  int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
-  int   run_id;           /* non-zero, random identifier for this instance of qhull */
-  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
-  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
-  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
-                             must set either GOODthreshold or SPLITthreshold
-                             if Delaunay, default is 0.0 for upper envelope */
-  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
-  realT *upper_bound;     /* scale point[k] to new upper bound */
-  realT *lower_bound;     /* scale point[k] to new lower bound
-                             project if both upper_ and lower_bound == 0 */
-
-/*----------------------------------
-
-  qh precision constants
-    precision constants for Qhull
-
-  notes:
-    qh_detroundoff(qh) computes the maximum roundoff error for distance
-    and other computations.  It also sets default values for the
-    qh constants above.
-*/
-  realT ANGLEround;       /* max round off error for angles */
-  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
-  realT cos_max;          /* max cosine for convexity (roundoff added) */
-  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
-  realT MAXabs_coord;     /* max absolute coordinate */
-  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
-  realT MAXsumcoord;      /* max sum of coordinates */
-  realT MAXwidth;         /* max rectilinear width of point coordinates */
-  realT MINdenom_1;       /* min. abs. value for 1/x */
-  realT MINdenom;         /*    use divzero if denominator < MINdenom */
-  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
-  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
-  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
-  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
-  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
-  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
-  realT ONEmerge;         /* max distance for merging simplicial facets */
-  realT outside_err;      /* application's epsilon for coplanar points
-                             qh_check_bestdist() qh_check_points() reports error if point outside */
-  realT WIDEfacet;        /* size of wide facet for skipping ridge in
-                             area computation and locking centrum */
-
-/*----------------------------------
-
-  qh internal constants
-    internal constants for Qhull
-*/
-  char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
-  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
-  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
-  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
-  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
-  FILE *fin;              /* pointer to input file, init by qh_initqhull_start */
-  FILE *fout;             /* pointer to output file */
-  FILE *ferr;             /* pointer to error file */
-  pointT *interior_point; /* center point of the initial simplex*/
-  int normal_size;     /* size in bytes for facet normals and point coords*/
-  int center_size;     /* size in bytes for Voronoi centers */
-  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
-
-/*----------------------------------
-
-  qh facet and vertex lists
-    defines lists of facets, new facets, visible facets, vertices, and
-    new vertices.  Includes counts, next ids, and trace ids.
-  see:
-    qh_resetlists()
-*/
-  facetT *facet_list;     /* first facet */
-  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
-  facetT *facet_next;     /* next facet for buildhull()
-                             previous facets do not have outside sets
-                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
-  facetT *newfacet_list;  /* list of new facets to end of facet_list */
-  facetT *visible_list;   /* list of visible facets preceding newfacet_list,
-                             facet->visible set */
-  int       num_visible;  /* current number of visible facets */
-  unsigned tracefacet_id;  /* set at init, then can print whenever */
-  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
-  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
-  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
-  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
-  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
-  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
-                             all vertices have 'newlist' set */
-  int   num_facets;       /* number of facets in facet_list
-                             includes visible faces (num_visible) */
-  int   num_vertices;     /* number of vertices in facet_list */
-  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
-                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
-  int   num_good;         /* number of good facets (after findgood_all) */
-  unsigned facet_id;      /* ID of next, new facet from newfacet() */
-  unsigned ridge_id;      /* ID of next, new ridge from newridge() */
-  unsigned vertex_id;     /* ID of next, new vertex from newvertex() */
-
-/*----------------------------------
-
-  qh global variables
-    defines minimum and maximum distances, next visit ids, several flags,
-    and other global variables.
-    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
-*/
-  unsigned long hulltime; /* ignore time to set up input and randomize */
-                          /*   use unsigned to avoid wrap-around errors */
-  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
-  int   build_cnt;        /* number of calls to qh_initbuild */
-  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
-  int   furthest_id;      /* pointid of furthest point, for tracing */
-  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
-  boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
-  boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
-  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
-  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
-  realT max_outside;      /* maximum distance from a point to a facet,
-                               before roundoff, not simplicial vertices
-                               actual outer plane is +DISTround and
-                               computed outer plane is +2*DISTround */
-  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
-                               before roundoff, due to a merge */
-  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
-                               before roundoff, due to a merge
-                               if qh.JOGGLEmax, qh_makenewplanes sets it
-                               recomputed if qh.DOcheckmax, default -qh.DISTround */
-  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
-                              from makecone/attachnewfacets to deletevisible */
-  boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
-  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
-  boolT NOerrexit;        /* true if qh.errexit is not available, cleared after setjmp */
-  realT PRINTcradius;     /* radius for printing centrums */
-  realT PRINTradius;      /* radius for printing vertex spheres and points */
-  boolT POSTmerging;      /* true when post merging */
-  int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
-  int   printoutnum;      /* number of facets printed */
-  boolT QHULLfinished;    /* True after qhull() is finished */
-  realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
-  realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
-  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
-  unsigned int vertex_visit; /* unique ID for searching vertices, reset with qh_buildtracing */
-  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
-  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qhT *qh, qh_check_maxout) */
-
-/*----------------------------------
-
-  qh global sets
-    defines sets for merging, initial simplex, hashing, extra input points,
-    and deleted vertices
-*/
-  setT *facet_mergeset;   /* temporary set of merges to be done */
-  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
-  setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
-                             size is setsize() */
-  setT *other_points;     /* additional points */
-  setT *del_vertices;     /* vertices to partition and delete with visible
-                             facets.  Have deleted set for checkfacet */
-
-/*----------------------------------
-
-  qh global buffers
-    defines buffers for maxtrix operations, input, and error messages
-*/
-  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom_r.c */
-  coordT **gm_row;        /* array of gm_matrix rows */
-  char* line;             /* malloc'd input line of maxline+1 chars */
-  int maxline;
-  coordT *half_space;     /* malloc'd input array for halfspace (qh.normal_size+coordT) */
-  coordT *temp_malloc;    /* malloc'd input array for points */
-
-/*----------------------------------
-
-  qh static variables
-    defines static variables for individual functions
-
-  notes:
-    do not use 'static' within a function.  Multiple instances of qhull
-    may exist.
-
-    do not assume zero initialization, 'QPn' may cause a restart
-*/
-  boolT ERREXITcalled;    /* true during qh_errexit (qhT *qh, prevents duplicate calls */
-  boolT firstcentrum;     /* for qh_printcentrum */
-  boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
-  setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
-  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
-  realT last_high;
-  realT last_newhigh;
-  unsigned lastreport;    /* for qh_buildtracing */
-  int mergereport;        /* for qh_tracemerging */
-  setT *old_tempstack;    /* for saving qh->qhmem.tempstack in save_qhull */
-  int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
-
-/*----------------------------------
-
-  qh memory management, rbox globals, and statistics
-
-  Replaces global data structures defined for libqhull
-*/
-  int     last_random;    /* Last random number from qh_rand (random_r.c) */
-  jmp_buf rbox_errexit;   /* errexit from rboxlib_r.c, defined by qh_rboxpoints() only */
-  char    jmpXtra3[40];   /* extra bytes in case jmp_buf is defined wrong by compiler */
-  int     rbox_isinteger;
-  double  rbox_out_offset;
-  void *  cpp_object;     /* C++ pointer.  Currently used by RboxPoints.qh_fprintf_rbox */
-
-  /* Last, otherwise zero'd by qh_initqhull_start2 (global_r.c */
-  qhmemT  qhmem;          /* Qhull managed memory (mem_r.h) */
-  /* After qhmem because its size depends on the number of statistics */
-  qhstatT qhstat;         /* Qhull statistics (stat_r.h) */
-};
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  otherfacet_(ridge, facet)
-    return neighboring facet for a ridge in facet
-*/
-#define otherfacet_(ridge, facet) \
-                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
-
-/*----------------------------------
-
-  getid_(p)
-    return int ID for facet, ridge, or vertex
-    return qh_IDunknown(-1) if NULL
-*/
-#define getid_(p)       ((p) ? (int)((p)->id) : qh_IDunknown)
-
-/*============== FORALL macros ===================*/
-
-/*----------------------------------
-
-  FORALLfacets { ... }
-    assign 'facet' to each facet in qh.facet_list
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-    assumes qh defined
-
-  see:
-    FORALLfacet_( facetlist )
-*/
-#define FORALLfacets for (facet=qh->facet_list;facet && facet->next;facet=facet->next)
-
-/*----------------------------------
-
-  FORALLpoints { ... }
-    assign 'point' to each point in qh.first_point, qh.num_points
-
-  notes:
-    assumes qh defined
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoints FORALLpoint_(qh, qh->first_point, qh->num_points)
-
-/*----------------------------------
-
-  FORALLpoint_( qh, points, num) { ... }
-    assign 'point' to each point in points array of num points
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoint_(qh, points, num) for (point= (points), \
-      pointtemp= (points)+qh->hull_dim*(num); point < pointtemp; point += qh->hull_dim)
-
-/*----------------------------------
-
-  FORALLvertices { ... }
-    assign 'vertex' to each vertex in qh.vertex_list
-
-  declare:
-    vertexT *vertex;
-
-  notes:
-    assumes qh.vertex_list terminated with a sentinel
-    assumes qh defined
-*/
-#define FORALLvertices for (vertex=qh->vertex_list;vertex && vertex->next;vertex= vertex->next)
-
-/*----------------------------------
-
-  FOREACHfacet_( facets ) { ... }
-    assign 'facet' to each facet in facets
-
-  declare:
-    facetT *facet, **facetp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_( facet ) { ... }
-    assign 'neighbor' to each neighbor in facet->neighbors
-
-  FOREACHneighbor_( vertex ) { ... }
-    assign 'neighbor' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor, **neighborp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_( points ) { ... }
-    assign 'point' to each point in points set
-
-  declare:
-    pointT *point, **pointp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_( ridges ) { ... }
-    assign 'ridge' to each ridge in ridges set
-
-  declare:
-    ridgeT *ridge, **ridgep;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices set
-
-  declare:
-    vertexT *vertex, **vertexp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
-
-/*----------------------------------
-
-  FOREACHfacet_i_( qh, facets ) { ... }
-    assign 'facet' and 'facet_i' for each facet in facets set
-
-  declare:
-    facetT *facet;
-    int     facet_n, facet_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHfacet_i_(qh, facets)    FOREACHsetelement_i_(qh, facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_i_( qh, facet ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
-
-  FOREACHneighbor_i_( qh, vertex ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor;
-    int     neighbor_n, neighbor_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHneighbor_i_(qh, facet)  FOREACHsetelement_i_(qh, facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_i_( qh, points ) { ... }
-    assign 'point' and 'point_i' for each point in points set
-
-  declare:
-    pointT *point;
-    int     point_n, point_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHpoint_i_(qh, points)    FOREACHsetelement_i_(qh, pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_i_( qh, ridges ) { ... }
-    assign 'ridge' and 'ridge_i' for each ridge in ridges set
-
-  declare:
-    ridgeT *ridge;
-    int     ridge_n, ridge_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHridge_i_(qh, ridges)    FOREACHsetelement_i_(qh, ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_i_( qh, vertices ) { ... }
-    assign 'vertex' and 'vertex_i' for each vertex in vertices set
-
-  declare:
-    vertexT *vertex;
-    int     vertex_n, vertex_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHvertex_i_(qh, vertices) FOREACHsetelement_i_(qh, vertexT, vertices,vertex)
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/********* -libqhull_r.c prototypes (duplicated from qhull_ra.h) **********************/
-
-void    qh_qhull(qhT *qh);
-boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
-void    qh_printsummary(qhT *qh, FILE *fp);
-
-/********* -user.c prototypes (alphabetical) **********************/
-
-void    qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge);
-void    qh_errprint(qhT *qh, const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
-int     qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
-                char *qhull_cmd, FILE *outfile, FILE *errfile);
-void    qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printhelp_degenerate(qhT *qh, FILE *fp);
-void    qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle);
-void    qh_printhelp_singular(qhT *qh, FILE *fp);
-void    qh_user_memsizes(qhT *qh);
-
-/********* -usermem_r.c prototypes (alphabetical) **********************/
-void    qh_exit(int exitcode);
-void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-
-/********* -userprintf_r.c and userprintf_rbox_r.c prototypes **********************/
-void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-
-/***** -geom_r.c/geom2_r.c/random_r.c prototypes (duplicated from geom_r.h, random_r.h) ****************/
-
-facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
-                     boolT bestoutside, boolT newfacets, boolT noupper,
-                     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
-                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
-boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
-void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_printsummary(qhT *qh, FILE *fp);
-void    qh_projectinput(qhT *qh);
-void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
-void    qh_rotateinput(qhT *qh, realT **rows);
-void    qh_scaleinput(qhT *qh);
-void    qh_setdelaunay(qhT *qh, int dim, int count, pointT *points);
-coordT  *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
-
-/***** -global_r.c prototypes (alphabetical) ***********************/
-
-unsigned long qh_clock(qhT *qh);
-void    qh_checkflags(qhT *qh, char *command, char *hiddenflags);
-void    qh_clear_outputflags(qhT *qh);
-void    qh_freebuffers(qhT *qh);
-void    qh_freeqhull(qhT *qh, boolT allmem);
-void    qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
-void    qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_init_qhull_command(qhT *qh, int argc, char *argv[]);
-void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_initflags(qhT *qh, char *command);
-void    qh_initqhull_buffers(qhT *qh);
-void    qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_initqhull_mem(qhT *qh);
-void    qh_initqhull_outputflags(qhT *qh);
-void    qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
-void    qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
-void    qh_initthresholds(qhT *qh, char *command);
-void    qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize);
-void    qh_option(qhT *qh, const char *option, int *i, realT *r);
-void    qh_zero(qhT *qh, FILE *errfile);
-
-/***** -io_r.c prototypes (duplicated from io_r.h) ***********************/
-
-void    qh_dfacet(qhT *qh, unsigned id);
-void    qh_dvertex(qhT *qh, unsigned id);
-void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_produce_output(qhT *qh);
-coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
-
-
-/********* -mem_r.c prototypes (duplicated from mem_r.h) **********************/
-
-void qh_meminit(qhT *qh, FILE *ferr);
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
-
-/********* -poly_r.c/poly2_r.c prototypes (duplicated from poly_r.h) **********************/
-
-void    qh_check_output(qhT *qh);
-void    qh_check_points(qhT *qh);
-setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
-facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
-pointT *qh_point(qhT *qh, int id);
-setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
-int     qh_pointid(qhT *qh, pointT *point);
-setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
-void    qh_setvoronoi_all(qhT *qh);
-void    qh_triangulate(qhT *qh /*qh.facet_list*/);
-
-/********* -rboxpoints_r.c prototypes **********************/
-int     qh_rboxpoints(qhT *qh, char* rbox_command);
-void    qh_errexit_rbox(qhT *qh, int exitcode);
-
-/********* -stat_r.c prototypes (duplicated from stat_r.h) **********************/
-
-void    qh_collectstatistics(qhT *qh);
-void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFlibqhull */
diff --git a/src/qhull/src/libqhull_r/libqhull_r.pro b/src/qhull/src/libqhull_r/libqhull_r.pro
deleted file mode 100644
index 6b8db44b7..000000000
--- a/src/qhull/src/libqhull_r/libqhull_r.pro
+++ /dev/null
@@ -1,67 +0,0 @@
-# -------------------------------------------------
-# libqhull_r.pro -- Qt project for Qhull shared library
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-DESTDIR = ../../lib
-DLLDESTDIR = ../../bin
-TEMPLATE = lib
-CONFIG += shared warn_on
-CONFIG -= qt
-
-build_pass:CONFIG(debug, debug|release):{
-    TARGET = qhull_rd
-    OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release):{
-    TARGET = qhull_r
-    OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-win32-msvc* : DEF_FILE += ../../src/libqhull_r/qhull_r-exports.def
-
-# libqhull_r/libqhull_r.pro and ../qhull-libqhull-src_r.pri have the same SOURCES and HEADERS
-
-SOURCES += ../libqhull_r/global_r.c
-SOURCES += ../libqhull_r/stat_r.c
-SOURCES += ../libqhull_r/geom2_r.c
-SOURCES += ../libqhull_r/poly2_r.c
-SOURCES += ../libqhull_r/merge_r.c
-SOURCES += ../libqhull_r/libqhull_r.c
-SOURCES += ../libqhull_r/geom_r.c
-SOURCES += ../libqhull_r/poly_r.c
-SOURCES += ../libqhull_r/qset_r.c
-SOURCES += ../libqhull_r/mem_r.c
-SOURCES += ../libqhull_r/random_r.c
-SOURCES += ../libqhull_r/usermem_r.c
-SOURCES += ../libqhull_r/userprintf_r.c
-SOURCES += ../libqhull_r/io_r.c
-SOURCES += ../libqhull_r/user_r.c
-SOURCES += ../libqhull_r/rboxlib_r.c
-SOURCES += ../libqhull_r/userprintf_rbox_r.c
-
-HEADERS += ../libqhull_r/geom_r.h
-HEADERS += ../libqhull_r/io_r.h
-HEADERS += ../libqhull_r/libqhull_r.h
-HEADERS += ../libqhull_r/mem_r.h
-HEADERS += ../libqhull_r/merge_r.h
-HEADERS += ../libqhull_r/poly_r.h
-HEADERS += ../libqhull_r/random_r.h
-HEADERS += ../libqhull_r/qhull_ra.h
-HEADERS += ../libqhull_r/qset_r.h
-HEADERS += ../libqhull_r/stat_r.h
-HEADERS += ../libqhull_r/user_r.h
-
-OTHER_FILES += qh-geom_r.htm
-OTHER_FILES += qh-globa_r.htm
-OTHER_FILES += qh-io_r.htm
-OTHER_FILES += qh-mem_r.htm
-OTHER_FILES += qh-merge_r.htm
-OTHER_FILES += qh-poly_r.htm
-OTHER_FILES += qh-qhull_r.htm
-OTHER_FILES += qh-set_r.htm
-OTHER_FILES += qh-stat_r.htm
-OTHER_FILES += qh-user_r.htm
diff --git a/src/qhull/src/libqhull_r/mem_r.c b/src/qhull/src/libqhull_r/mem_r.c
deleted file mode 100644
index 801a8c76a..000000000
--- a/src/qhull/src/libqhull_r/mem_r.c
+++ /dev/null
@@ -1,562 +0,0 @@
-/*
      ---------------------------------
-
-  mem_r.c
-    memory management routines for qhull
-
-  See libqhull/mem_r.c for a standalone program.
-
-  To initialize memory:
-
-    qh_meminit(qh, stderr);
-    qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
-    qh_memsize(qh, (int)sizeof(facetT));
-    qh_memsize(qh, (int)sizeof(facetT));
-    ...
-    qh_memsetup(qh);
-
-  To free up all memory buffers:
-    qh_memfreeshort(qh, &curlong, &totlong);
-
-  if qh_NOmem,
-    malloc/free is used instead of mem.c
-
-  notes:
-    uses Quickfit algorithm (freelists for commonly allocated sizes)
-    assumes small sizes for freelists (it discards the tail of memory buffers)
-
-  see:
-    qh-mem_r.htm and mem_r.h
-    global_r.c (qh_initbuffers) for an example of using mem_r.c
-
-  Copyright (c) 1993-2015 The Geometry Center.
-  $Id: //main/2015/qhull/src/libqhull_r/mem_r.c#5 $$Change: 2065 $
-  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
-*/
-
-#include "libqhull_r.h"  /* includes user_r.h and mem_r.h */
-
-#include 
-#include 
-#include 
-
-#ifndef qh_NOmem
-
-/*============= internal functions ==============*/
-
-static int qh_intcompare(const void *i, const void *j);
-
-/*========== functions in alphabetical order ======== */
-
-/*---------------------------------
-
-  qh_intcompare( i, j )
-    used by qsort and bsearch to compare two integers
-*/
-static int qh_intcompare(const void *i, const void *j) {
-  return(*((const int *)i) - *((const int *)j));
-} /* intcompare */
-
-
-/*----------------------------------
-
-  qh_memalloc( qh, insize )
-    returns object of insize bytes
-    qhmem is the global memory structure
-
-  returns:
-    pointer to allocated memory
-    errors if insufficient memory
-
-  notes:
-    use explicit type conversion to avoid type warnings on some compilers
-    actual object may be larger than insize
-    use qh_memalloc_() for inline code for quick allocations
-    logs allocations if 'T5'
-    caller is responsible for freeing the memory.
-    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
-
-  design:
-    if size < qh->qhmem.LASTsize
-      if qh->qhmem.freelists[size] non-empty
-        return first object on freelist
-      else
-        round up request to size of qh->qhmem.freelists[size]
-        allocate new allocation buffer if necessary
-        allocate object from allocation buffer
-    else
-      allocate object with qh_malloc() in user.c
-*/
-void *qh_memalloc(qhT *qh, int insize) {
-  void **freelistp, *newbuffer;
-  int idx, size, n;
-  int outsize, bufsize;
-  void *object;
-
-  if (insize<0) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
-      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (insize>=0 && insize <= qh->qhmem.LASTsize) {
-    idx= qh->qhmem.indextable[insize];
-    outsize= qh->qhmem.sizetable[idx];
-    qh->qhmem.totshort += outsize;
-    freelistp= qh->qhmem.freelists+idx;
-    if ((object= *freelistp)) {
-      qh->qhmem.cntquick++;
-      qh->qhmem.totfree -= outsize;
-      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
-#ifdef qh_TRACEshort
-      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-      if (qh->qhmem.IStracing >= 5)
-          qh_fprintf(qh, qh->qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-      return(object);
-    }else {
-      qh->qhmem.cntshort++;
-      if (outsize > qh->qhmem.freesize) {
-        qh->qhmem.totdropped += qh->qhmem.freesize;
-        if (!qh->qhmem.curbuffer)
-          bufsize= qh->qhmem.BUFinit;
-        else
-          bufsize= qh->qhmem.BUFsize;
-        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
-          qh_fprintf(qh, qh->qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
-          qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-        }
-        *((void **)newbuffer)= qh->qhmem.curbuffer;  /* prepend newbuffer to curbuffer
-                                                    list.  newbuffer!=0 by QH6080 */
-        qh->qhmem.curbuffer= newbuffer;
-        size= (sizeof(void **) + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
-        qh->qhmem.freemem= (void *)((char *)newbuffer+size);
-        qh->qhmem.freesize= bufsize - size;
-        qh->qhmem.totbuffer += bufsize - size; /* easier to check */
-        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
-        n = qh->qhmem.totshort + qh->qhmem.totfree + qh->qhmem.totdropped + qh->qhmem.freesize - outsize;
-        if (qh->qhmem.totbuffer != n) {
-            qh_fprintf(qh, qh->qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qh->qhmem.totbuffer, n);
-            qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-        }
-      }
-      object= qh->qhmem.freemem;
-      qh->qhmem.freemem= (void *)((char *)qh->qhmem.freemem + outsize);
-      qh->qhmem.freesize -= outsize;
-      qh->qhmem.totunused += outsize - insize;
-#ifdef qh_TRACEshort
-      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-      if (qh->qhmem.IStracing >= 5)
-          qh_fprintf(qh, qh->qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-      return object;
-    }
-  }else {                     /* long allocation */
-    if (!qh->qhmem.indextable) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
-      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-    }
-    outsize= insize;
-    qh->qhmem.cntlong++;
-    qh->qhmem.totlong += outsize;
-    if (qh->qhmem.maxlong < qh->qhmem.totlong)
-      qh->qhmem.maxlong= qh->qhmem.totlong;
-    if (!(object= qh_malloc((size_t)outsize))) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
-      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-    }
-    if (qh->qhmem.IStracing >= 5)
-      qh_fprintf(qh, qh->qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, outsize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-  }
-  return(object);
-} /* memalloc */
-
-
-/*----------------------------------
-
-  qh_memcheck(qh)
-*/
-void qh_memcheck(qhT *qh) {
-  int i, count, totfree= 0;
-  void *object;
-
-  if (!qh) {
-    qh_fprintf_stderr(6243, "qh_memcheck(qh) error: qh is 0.  It does not point to a qhT");
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (qh->qhmem.ferr == 0 || qh->qhmem.IStracing < 0 || qh->qhmem.IStracing > 10 || (((qh->qhmem.ALIGNmask+1) & qh->qhmem.ALIGNmask) != 0)) {
-    qh_fprintf_stderr(6244, "qh_memcheck error: either qh->qhmem is overwritten or qh->qhmem is not initialized.  Call qh_mem_new() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qh->qhmem.ferr, qh->qhmem.IStracing, qh->qhmem.ALIGNmask);
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (qh->qhmem.IStracing != 0)
-    qh_fprintf(qh, qh->qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qh->qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem\n");
-  for (i=0; i < qh->qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    totfree += qh->qhmem.sizetable[i] * count;
-  }
-  if (totfree != qh->qhmem.totfree) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qh->qhmem.totfree, totfree);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing != 0)
-    qh_fprintf(qh, qh->qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree\n", totfree);
-} /* memcheck */
-
-/*----------------------------------
-
-  qh_memfree(qh, object, insize )
-    free up an object of size bytes
-    size is insize from qh_memalloc
-
-  notes:
-    object may be NULL
-    type checking warns if using (void **)object
-    use qh_memfree_() for quick free's of small objects
-
-  design:
-    if size <= qh->qhmem.LASTsize
-      append object to corresponding freelist
-    else
-      call qh_free(object)
-*/
-void qh_memfree(qhT *qh, void *object, int insize) {
-  void **freelistp;
-  int idx, outsize;
-
-  if (!object)
-    return;
-  if (insize <= qh->qhmem.LASTsize) {
-    qh->qhmem.freeshort++;
-    idx= qh->qhmem.indextable[insize];
-    outsize= qh->qhmem.sizetable[idx];
-    qh->qhmem.totfree += outsize;
-    qh->qhmem.totshort -= outsize;
-    freelistp= qh->qhmem.freelists + idx;
-    *((void **)object)= *freelistp;
-    *freelistp= object;
-#ifdef qh_TRACEshort
-    idx= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
-    if (qh->qhmem.IStracing >= 5)
-        qh_fprintf(qh, qh->qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
-#endif
-  }else {
-    qh->qhmem.freelong++;
-    qh->qhmem.totlong -= insize;
-    if (qh->qhmem.IStracing >= 5)
-      qh_fprintf(qh, qh->qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-    qh_free(object);
-  }
-} /* memfree */
-
-
-/*---------------------------------
-
-  qh_memfreeshort(qh, curlong, totlong )
-    frees up all short and qhmem memory allocations
-
-  returns:
-    number and size of current long allocations
-  
-  notes:
-    if qh_NOmem (qh_malloc() for all allocations), 
-       short objects (e.g., facetT) are not recovered.
-       use qh_freeqhull(qh, qh_ALL) instead.
- 
-  see:
-    qh_freeqhull(qh, allMem)
-    qh_memtotal(qh, curlong, totlong, curshort, totshort, maxlong, totbuffer);
-*/
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
-  void *buffer, *nextbuffer;
-  FILE *ferr;
-
-  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-  *totlong= qh->qhmem.totlong;
-  for (buffer= qh->qhmem.curbuffer; buffer; buffer= nextbuffer) {
-    nextbuffer= *((void **) buffer);
-    qh_free(buffer);
-  }
-  qh->qhmem.curbuffer= NULL;
-  if (qh->qhmem.LASTsize) {
-    qh_free(qh->qhmem.indextable);
-    qh_free(qh->qhmem.freelists);
-    qh_free(qh->qhmem.sizetable);
-  }
-  ferr= qh->qhmem.ferr;
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  qh->qhmem.ferr= ferr;
-} /* memfreeshort */
-
-
-/*----------------------------------
-
-  qh_meminit(qh, ferr )
-    initialize qhmem and test sizeof( void*)
-    Does not throw errors.  qh_exit on failure
-*/
-void qh_meminit(qhT *qh, FILE *ferr) {
-
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-      qh->qhmem.ferr= ferr;
-  else
-      qh->qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  if (sizeof(void*) > sizeof(ptr_intT)) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
-      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qh_memcheck(qh);
-} /* meminit */
-
-/*---------------------------------
-
-  qh_meminitbuffers(qh, tracelevel, alignment, numsizes, bufsize, bufinit )
-    initialize qhmem
-    if tracelevel >= 5, trace memory allocations
-    alignment= desired address alignment for memory allocations
-    numsizes= number of freelists
-    bufsize=  size of additional memory buffers for short allocations
-    bufinit=  size of initial memory buffer for short allocations
-*/
-void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qh->qhmem.IStracing= tracelevel;
-  qh->qhmem.NUMsizes= numsizes;
-  qh->qhmem.BUFsize= bufsize;
-  qh->qhmem.BUFinit= bufinit;
-  qh->qhmem.ALIGNmask= alignment-1;
-  if (qh->qhmem.ALIGNmask & ~qh->qhmem.ALIGNmask) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh->qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
-  qh->qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
-  if (!qh->qhmem.sizetable || !qh->qhmem.freelists) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing >= 1)
-    qh_fprintf(qh, qh->qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
-} /* meminitbuffers */
-
-/*---------------------------------
-
-  qh_memsetup(qh)
-    set up memory after running memsize()
-*/
-void qh_memsetup(qhT *qh) {
-  int k,i;
-
-  qsort(qh->qhmem.sizetable, (size_t)qh->qhmem.TABLEsize, sizeof(int), qh_intcompare);
-  qh->qhmem.LASTsize= qh->qhmem.sizetable[qh->qhmem.TABLEsize-1];
-  if(qh->qhmem.LASTsize >= qh->qhmem.BUFsize || qh->qhmem.LASTsize >= qh->qhmem.BUFinit) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
-            qh->qhmem.LASTsize, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  if (!(qh->qhmem.indextable= (int *)qh_malloc((qh->qhmem.LASTsize+1) * sizeof(int)))) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  for (k=qh->qhmem.LASTsize+1; k--; )
-    qh->qhmem.indextable[k]= k;
-  i= 0;
-  for (k=0; k <= qh->qhmem.LASTsize; k++) {
-    if (qh->qhmem.indextable[k] <= qh->qhmem.sizetable[i])
-      qh->qhmem.indextable[k]= i;
-    else
-      qh->qhmem.indextable[k]= ++i;
-  }
-} /* memsetup */
-
-/*---------------------------------
-
-  qh_memsize(qh, size )
-    define a free list for this size
-*/
-void qh_memsize(qhT *qh, int size) {
-  int k;
-
-  if(qh->qhmem.LASTsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  size= (size + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
-  for (k=qh->qhmem.TABLEsize; k--; ) {
-    if (qh->qhmem.sizetable[k] == size)
-      return;
-  }
-  if (qh->qhmem.TABLEsize < qh->qhmem.NUMsizes)
-    qh->qhmem.sizetable[qh->qhmem.TABLEsize++]= size;
-  else
-    qh_fprintf(qh, qh->qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qh->qhmem.NUMsizes);
-} /* memsize */
-
-
-/*---------------------------------
-
-  qh_memstatistics(qh, fp )
-    print out memory statistics
-
-    Verifies that qh->qhmem.totfree == sum of freelists
-*/
-void qh_memstatistics(qhT *qh, FILE *fp) {
-  int i;
-  int count;
-  void *object;
-
-  qh_memcheck(qh);
-  qh_fprintf(qh, fp, 9278, "\nmemory statistics:\n\
-%7d quick allocations\n\
-%7d short allocations\n\
-%7d long allocations\n\
-%7d short frees\n\
-%7d long frees\n\
-%7d bytes of short memory in use\n\
-%7d bytes of short memory in freelists\n\
-%7d bytes of dropped short memory\n\
-%7d bytes of unused short memory (estimated)\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n\
-%7d bytes of short memory buffers (minus links)\n\
-%7d bytes per short memory buffer (initially %d bytes)\n",
-           qh->qhmem.cntquick, qh->qhmem.cntshort, qh->qhmem.cntlong,
-           qh->qhmem.freeshort, qh->qhmem.freelong,
-           qh->qhmem.totshort, qh->qhmem.totfree,
-           qh->qhmem.totdropped + qh->qhmem.freesize, qh->qhmem.totunused,
-           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong,
-           qh->qhmem.totbuffer, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
-  if (qh->qhmem.cntlarger) {
-    qh_fprintf(qh, fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
-           qh->qhmem.cntlarger, ((float)qh->qhmem.totlarger)/(float)qh->qhmem.cntlarger);
-    qh_fprintf(qh, fp, 9280, "  freelists(bytes->count):");
-  }
-  for (i=0; i < qh->qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
-      count++;
-    qh_fprintf(qh, fp, 9281, " %d->%d", qh->qhmem.sizetable[i], count);
-  }
-  qh_fprintf(qh, fp, 9282, "\n\n");
-} /* memstatistics */
-
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    uses qh_malloc() and qh_free() instead
-*/
-#else /* qh_NOmem */
-
-void *qh_memalloc(qhT *qh, int insize) {
-  void *object;
-
-  if (!(object= qh_malloc((size_t)insize))) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
-    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-  }
-  qh->qhmem.cntlong++;
-  qh->qhmem.totlong += insize;
-  if (qh->qhmem.maxlong < qh->qhmem.totlong)
-      qh->qhmem.maxlong= qh->qhmem.totlong;
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-  return object;
-}
-
-void qh_memfree(qhT *qh, void *object, int insize) {
-
-  if (!object)
-    return;
-  qh_free(object);
-  qh->qhmem.freelong++;
-  qh->qhmem.totlong -= insize;
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
-}
-
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
-  *totlong= qh->qhmem.totlong;
-  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-}
-
-void qh_meminit(qhT *qh, FILE *ferr) {
-
-  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
-  if (ferr)
-      qh->qhmem.ferr= ferr;
-  else
-      qh->qhmem.ferr= stderr;
-  if (sizeof(void*) < sizeof(int)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-}
-
-void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qh->qhmem.IStracing= tracelevel;
-}
-
-void qh_memsetup(qhT *qh) {
-
-}
-
-void qh_memsize(qhT *qh, int size) {
-
-}
-
-void qh_memstatistics(qhT *qh, FILE *fp) {
-
-  qh_fprintf(qh, fp, 9409, "\nmemory statistics:\n\
-%7d long allocations\n\
-%7d long frees\n\
-%7d bytes of long memory allocated (max, except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n",
-           qh->qhmem.cntlong,
-           qh->qhmem.freelong,
-           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong);
-}
-
-#endif /* qh_NOmem */
-
-/*---------------------------------
-
-  qh_memtotal(qh, totlong, curlong, totshort, curshort, maxlong, totbuffer )
-    Return the total, allocated long and short memory
-
-  returns:
-    Returns the total current bytes of long and short allocations
-    Returns the current count of long and short allocations
-    Returns the maximum long memory and total short buffer (minus one link per buffer)
-    Does not error (for deprecated UsingLibQhull.cpp (libqhullpcpp))
-*/
-void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
-    *totlong= qh->qhmem.totlong;
-    *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
-    *totshort= qh->qhmem.totshort;
-    *curshort= qh->qhmem.cntshort + qh->qhmem.cntquick - qh->qhmem.freeshort;
-    *maxlong= qh->qhmem.maxlong;
-    *totbuffer= qh->qhmem.totbuffer;
-} /* memtotlong */
-
diff --git a/src/qhull/src/libqhull_r/mem_r.h b/src/qhull/src/libqhull_r/mem_r.h
deleted file mode 100644
index 25b551333..000000000
--- a/src/qhull/src/libqhull_r/mem_r.h
+++ /dev/null
@@ -1,234 +0,0 @@
-/*
      ---------------------------------
-
-   mem_r.h
-     prototypes for memory management functions
-
-   see qh-mem_r.htm, mem_r.c and qset_r.h
-
-   for error handling, writes message and calls
-     qh_errexit(qhT *qh, qhmem_ERRmem, NULL, NULL) if insufficient memory
-       and
-     qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL) otherwise
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/mem_r.h#4 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFmem
-#define qhDEFmem 1
-
-#include 
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset_r.h */
-#endif
-
-#ifndef DEFqhT
-#define DEFqhT 1
-typedef struct qhT qhT;          /* defined in libqhull_r.h */
-#endif
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    mem_r.c implements Quickfit memory allocation for about 20% time
-    savings.  If it fails on your machine, try to locate the
-    problem, and send the answer to qhull@qhull.org.  If this can
-    not be done, define qh_NOmem to use malloc/free instead.
-
-   #define qh_NOmem
-*/
-
-/*---------------------------------
-
-qh_TRACEshort
-Trace short and quick memory allocations at T5
-
-*/
-#define qh_TRACEshort
-
-/*-------------------------------------------
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem_r.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
-    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
-   see qh_MEMalign in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull_r.h */
-#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull_r.h */
-
-/*----------------------------------
-
-  ptr_intT
-    for casting a void * to an integer-type that holds a pointer
-    Used for integer expressions (e.g., computing qh_gethash() in poly_r.c)
-
-  notes:
-    WARN64 -- these notes indicate 64-bit issues
-    On 64-bit machines, a pointer may be larger than an 'int'.
-    qh_meminit()/mem_r.c checks that 'ptr_intT' holds a 'void*'
-    ptr_intT is typically a signed value, but not necessarily so
-    size_t is typically unsigned, but should match the parameter type
-    Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
-    This matches Qt convention and is easier to work with.
-*/
-#if (defined(__MINGW64__)) && defined(_WIN64)
-typedef long long ptr_intT;
-#elif (_MSC_VER) && defined(_WIN64)
-typedef long long ptr_intT;
-#else
-typedef long ptr_intT;
-#endif
-
-/*----------------------------------
-
-  qhmemT
-    global memory structure for mem_r.c
-
- notes:
-   users should ignore qhmem except for writing extensions
-   qhmem is allocated in mem_r.c
-
-   qhmem could be swapable like qh and qhstat, but then
-   multiple qh's and qhmem's would need to keep in synch.
-   A swapable qhmem would also waste memory buffers.  As long
-   as memory operations are atomic, there is no problem with
-   multiple qh structures being active at the same time.
-   If you need separate address spaces, you can swap the
-   contents of qh->qhmem.
-*/
-typedef struct qhmemT qhmemT;
-
-/* Update qhmem in mem_r.c if add or remove fields */
-struct qhmemT {               /* global memory management variables */
-  int      BUFsize;           /* size of memory allocation buffer */
-  int      BUFinit;           /* initial size of memory allocation buffer */
-  int      TABLEsize;         /* actual number of sizes in free list table */
-  int      NUMsizes;          /* maximum number of sizes in free list table */
-  int      LASTsize;          /* last size in free list table */
-  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
-  void   **freelists;          /* free list table, linked by offset 0 */
-  int     *sizetable;         /* size of each freelist */
-  int     *indextable;        /* size->index table */
-  void    *curbuffer;         /* current buffer, linked by offset 0 */
-  void    *freemem;           /*   free memory in curbuffer */
-  int      freesize;          /*   size of freemem in bytes */
-  setT    *tempstack;         /* stack of temporary memory, managed by users */
-  FILE    *ferr;              /* file for reporting errors when 'qh' may be undefined */
-  int      IStracing;         /* =5 if tracing memory allocations */
-  int      cntquick;          /* count of quick allocations */
-                              /* Note: removing statistics doesn't effect speed */
-  int      cntshort;          /* count of short allocations */
-  int      cntlong;           /* count of long allocations */
-  int      freeshort;         /* count of short memfrees */
-  int      freelong;          /* count of long memfrees */
-  int      totbuffer;         /* total short memory buffers minus buffer links */
-  int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
-  int      totfree;           /* total size of free, short memory on freelists */
-  int      totlong;           /* total size of long memory in use */
-  int      maxlong;           /*   maximum totlong */
-  int      totshort;          /* total size of short memory in use */
-  int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
-  int      cntlarger;         /* count of setlarger's */
-  int      totlarger;         /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*----------------------------------
-
-  qh_memalloc_(qh, insize, freelistp, object, type)
-    returns object of size bytes
-        assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#if defined qh_NOmem
-#define qh_memalloc_(qh, insize, freelistp, object, type) {\
-  object= (type*)qh_memalloc(qh, insize); }
-#elif defined qh_TRACEshort
-#define qh_memalloc_(qh, insize, freelistp, object, type) {\
-    freelistp= NULL; /* Avoid warnings */ \
-    object= (type*)qh_memalloc(qh, insize); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(qh, insize, freelistp, object, type) {\
-  freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
-  if ((object= (type*)*freelistp)) {\
-    qh->qhmem.totshort += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
-    qh->qhmem.totfree -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
-    qh->qhmem.cntquick++;  \
-    *freelistp= *((void **)*freelistp);\
-  }else object= (type*)qh_memalloc(qh, insize);}
-#endif
-
-/*----------------------------------
-
-  qh_memfree_(qh, object, insize, freelistp)
-    free up an object
-
-  notes:
-    object may be NULL
-    assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
-*/
-#if defined qh_NOmem
-#define qh_memfree_(qh, object, insize, freelistp) {\
-  qh_memfree(qh, object, insize); }
-#elif defined qh_TRACEshort
-#define qh_memfree_(qh, object, insize, freelistp) {\
-    freelistp= NULL; /* Avoid warnings */ \
-    qh_memfree(qh, object, insize); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(qh, object, insize, freelistp) {\
-  if (object) { \
-    qh->qhmem.freeshort++;\
-    freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
-    qh->qhmem.totshort -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
-    qh->qhmem.totfree += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
-    *((void **)object)= *freelistp;\
-    *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void *qh_memalloc(qhT *qh, int insize);
-void qh_memcheck(qhT *qh);
-void qh_memfree(qhT *qh, void *object, int insize);
-void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
-void qh_meminit(qhT *qh, FILE *ferr);
-void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes,
-                        int bufsize, int bufinit);
-void qh_memsetup(qhT *qh);
-void qh_memsize(qhT *qh, int size);
-void qh_memstatistics(qhT *qh, FILE *fp);
-void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFmem */
diff --git a/src/qhull/src/libqhull_r/merge_r.c b/src/qhull/src/libqhull_r/merge_r.c
deleted file mode 100644
index e5823de8d..000000000
--- a/src/qhull/src/libqhull_r/merge_r.c
+++ /dev/null
@@ -1,3627 +0,0 @@
-/*
      ---------------------------------
-
-   merge_r.c
-   merges non-convex facets
-
-   see qh-merge_r.htm and merge_r.h
-
-   other modules call qh_premerge() and qh_postmerge()
-
-   the user may call qh_postmerge() to perform additional merges.
-
-   To remove deleted facets and vertices (qhull() in libqhull_r.c):
-     qh_partitionvisible(qh, !qh_ALL, &numoutside);  // visible_list, newfacet_list
-     qh_deletevisible();         // qh.visible_list
-     qh_resetlists(qh, False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
-
-   assumes qh.CENTERtype= centrum
-
-   merges occur in qh_mergefacet and in qh_mergecycle
-   vertex->neighbors not set until the first merge occurs
-
-   Copyright (c) 1993-2015 C.B. Barber.
-   $Id: //main/2015/qhull/src/libqhull_r/merge_r.c#5 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-#ifndef qh_NOmerge
-
-/*===== functions(alphabetical after premerge and postmerge) ======*/
-
-/*---------------------------------
-
-  qh_premerge(qh, apex, maxcentrum )
-    pre-merge nonconvex facets in qh.newfacet_list for apex
-    maxcentrum defines coplanar and concave (qh_test_appendmerge)
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible set
-
-  notes:
-    uses globals, qh.MERGEexact, qh.PREmerge
-
-  design:
-    mark duplicate ridges in qh.newfacet_list
-    merge facet cycles in qh.newfacet_list
-    merge duplicate ridges and concave facets in qh.newfacet_list
-    check merged facet cycles for degenerate and redundant facets
-    merge degenerate and redundant facets
-    collect coplanar and concave facets
-    merge concave, coplanar, degenerate, and redundant facets
-*/
-void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
-  boolT othermerge= False;
-  facetT *newfacet;
-
-  if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
-    return;
-  trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
-            maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-  qh->centrum_radius= maxcentrum;
-  qh->cos_max= maxangle;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  if (qh->hull_dim >=3) {
-    qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
-    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
-    qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
-    FORALLnew_facets {  /* test samecycle merges */
-      if (!newfacet->simplicial && !newfacet->mergeridge)
-        qh_degen_redundant_neighbors(qh, newfacet, NULL);
-    }
-    if (qh_merge_degenredundant(qh))
-      othermerge= True;
-  }else /* qh->hull_dim == 2 */
-    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
-  qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
-  if (!qh->MERGEexact || zzval_(Ztotmerge)) {
-    zinc_(Zpremergetot);
-    qh->POSTmerging= False;
-    qh_getmergeset_initial(qh, qh->newfacet_list);
-    qh_all_merges(qh, othermerge, False);
-  }
-  qh_settempfree(qh, &qh->facet_mergeset);
-  qh_settempfree(qh, &qh->degen_mergeset);
-} /* premerge */
-
-/*---------------------------------
-
-  qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
-    post-merge nonconvex facets as defined by maxcentrum and maxangle
-    'reason' is for reporting progress
-    if vneighbors,
-      calls qh_test_vneighbors at end of qh_all_merge
-    if firstmerge,
-      calls qh_reducevertices before qh_getmergeset
-
-  returns:
-    if first call (qh.visible_list != qh.facet_list),
-      builds qh.facet_newlist, qh.newvertex_list
-    deleted facets added to qh.visible_list with facet->visible
-    qh.visible_list == qh.facet_list
-
-  notes:
-
-
-  design:
-    if first call
-      set qh.visible_list and qh.newfacet_list to qh.facet_list
-      add all facets to qh.newfacet_list
-      mark non-simplicial facets, facet->newmerge
-      set qh.newvertext_list to qh.vertex_list
-      add all vertices to qh.newvertex_list
-      if a pre-merge occured
-        set vertex->delridge {will retest the ridge}
-        if qh.MERGEexact
-          call qh_reducevertices()
-      if no pre-merging
-        merge flipped facets
-    determine non-convex facets
-    merge all non-convex facets
-*/
-void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-  facetT *newfacet;
-  boolT othermerges= False;
-  vertexT *vertex;
-
-  if (qh->REPORTfreq || qh->IStracing) {
-    qh_buildtracing(qh, NULL, NULL);
-    qh_printsummary(qh, qh->ferr);
-    if (qh->PRINTstatistics)
-      qh_printallstatistics(qh, qh->ferr, "reason");
-    qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
-        reason, maxcentrum, maxangle);
-  }
-  trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
-            vneighbors));
-  qh->centrum_radius= maxcentrum;
-  qh->cos_max= maxangle;
-  qh->POSTmerging= True;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  if (qh->visible_list != qh->facet_list) {  /* first call */
-    qh->NEWfacets= True;
-    qh->visible_list= qh->newfacet_list= qh->facet_list;
-    FORALLnew_facets {
-      newfacet->newfacet= True;
-       if (!newfacet->simplicial)
-        newfacet->newmerge= True;
-     zinc_(Zpostfacets);
-    }
-    qh->newvertex_list= qh->vertex_list;
-    FORALLvertices
-      vertex->newlist= True;
-    if (qh->VERTEXneighbors) { /* a merge has occurred */
-      FORALLvertices
-        vertex->delridge= True; /* test for redundant, needed? */
-      if (qh->MERGEexact) {
-        if (qh->hull_dim <= qh_DIMreduceBuild)
-          qh_reducevertices(qh); /* was skipped during pre-merging */
-      }
-    }
-    if (!qh->PREmerge && !qh->MERGEexact)
-      qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
-  }
-  qh_getmergeset_initial(qh, qh->newfacet_list);
-  qh_all_merges(qh, False, vneighbors);
-  qh_settempfree(qh, &qh->facet_mergeset);
-  qh_settempfree(qh, &qh->degen_mergeset);
-} /* post_merge */
-
-/*---------------------------------
-
-  qh_all_merges(qh, othermerge, vneighbors )
-    merge all non-convex facets
-
-    set othermerge if already merged facets (for qh_reducevertices)
-    if vneighbors
-      tests vertex neighbors for convexity at end
-    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
-    qh.degen_mergeset is defined
-    if qh.MERGEexact && !qh.POSTmerging,
-      does not merge coplanar facets
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible
-    deleted vertices added qh.delvertex_list with vertex->delvertex
-
-  notes:
-    unless !qh.MERGEindependent,
-      merges facets in independent sets
-    uses qh.newfacet_list as argument since merges call qh_removefacet()
-
-  design:
-    while merges occur
-      for each merge in qh.facet_mergeset
-        unless one of the facets was already merged in this pass
-          merge the facets
-        test merged facets for additional merges
-        add merges to qh.facet_mergeset
-      if vertices record neighboring facets
-        rename redundant vertices
-          update qh.facet_mergeset
-    if vneighbors ??
-      tests vertex neighbors for convexity at end
-*/
-void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
-  facetT *facet1, *facet2;
-  mergeT *merge;
-  boolT wasmerge= True, isreduce;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-  vertexT *vertex;
-  mergeType mergetype;
-  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
-
-  trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
-            getid_(qh->newfacet_list)));
-  while (True) {
-    wasmerge= False;
-    while (qh_setsize(qh, qh->facet_mergeset)) {
-      while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
-        facet1= merge->facet1;
-        facet2= merge->facet2;
-        mergetype= merge->type;
-        qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
-        if (facet1->visible || facet2->visible) /*deleted facet*/
-          continue;
-        if ((facet1->newfacet && !facet1->tested)
-                || (facet2->newfacet && !facet2->tested)) {
-          if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
-            continue;      /* perform independent sets of merges */
-        }
-        qh_merge_nonconvex(qh, facet1, facet2, mergetype);
-        numdegenredun += qh_merge_degenredundant(qh);
-        numnewmerges++;
-        wasmerge= True;
-        if (mergetype == MRGconcave)
-          numconcave++;
-        else /* MRGcoplanar or MRGanglecoplanar */
-          numcoplanar++;
-      } /* while setdellast */
-      if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
-      && numnewmerges > qh_MAXnewmerges) {
-        numnewmerges= 0;
-        qh_reducevertices(qh);  /* otherwise large post merges too slow */
-      }
-      qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
-    } /* while mergeset */
-    if (qh->VERTEXneighbors) {
-      isreduce= False;
-      if (qh->hull_dim >=4 && qh->POSTmerging) {
-        FORALLvertices
-          vertex->delridge= True;
-        isreduce= True;
-      }
-      if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
-          && qh->hull_dim <= qh_DIMreduceBuild) {
-        othermerge= False;
-        isreduce= True;
-      }
-      if (isreduce) {
-        if (qh_reducevertices(qh)) {
-          qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
-          continue;
-        }
-      }
-    }
-    if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
-      continue;
-    break;
-  } /* while (True) */
-  if (qh->CHECKfrequently && !qh->MERGEexact) {
-    qh->old_randomdist= qh->RANDOMdist;
-    qh->RANDOMdist= False;
-    qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
-    /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
-    qh->RANDOMdist= qh->old_randomdist;
-  }
-  trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
-    numcoplanar, numconcave, numdegenredun));
-  if (qh->IStracing >= 4 && qh->num_facets < 50)
-    qh_printlists(qh);
-} /* all_merges */
-
-
-/*---------------------------------
-
-  qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
-    appends an entry to qh.facet_mergeset or qh.degen_mergeset
-
-    angle ignored if NULL or !qh.ANGLEmerge
-
-  returns:
-    merge appended to facet_mergeset or degen_mergeset
-      sets ->degenerate or ->redundant if degen_mergeset
-
-  see:
-    qh_test_appendmerge()
-
-  design:
-    allocate merge entry
-    if regular merge
-      append to qh.facet_mergeset
-    else if degenerate merge and qh.facet_mergeset is all degenerate
-      append to qh.degen_mergeset
-    else if degenerate merge
-      prepend to qh.degen_mergeset
-    else if redundant merge
-      append to qh.degen_mergeset
-*/
-void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
-  mergeT *merge, *lastmerge;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (facet->redundant)
-    return;
-  if (facet->degenerate && mergetype == MRGdegen)
-    return;
-  qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
-  merge->facet1= facet;
-  merge->facet2= neighbor;
-  merge->type= mergetype;
-  if (angle && qh->ANGLEmerge)
-    merge->angle= *angle;
-  if (mergetype < MRGdegen)
-    qh_setappend(qh, &(qh->facet_mergeset), merge);
-  else if (mergetype == MRGdegen) {
-    facet->degenerate= True;
-    if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
-    || lastmerge->type == MRGdegen)
-      qh_setappend(qh, &(qh->degen_mergeset), merge);
-    else
-      qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
-  }else if (mergetype == MRGredundant) {
-    facet->redundant= True;
-    qh_setappend(qh, &(qh->degen_mergeset), merge);
-  }else /* mergetype == MRGmirror */ {
-    if (facet->redundant || neighbor->redundant) {
-      qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
-    }
-    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
-      qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
-           facet->id, neighbor->id);
-      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
-    }
-    facet->redundant= True;
-    neighbor->redundant= True;
-    qh_setappend(qh, &(qh->degen_mergeset), merge);
-  }
-} /* appendmergeset */
-
-
-/*---------------------------------
-
-  qh_basevertices(qh, samecycle )
-    return temporary set of base vertices for samecycle
-    samecycle is first facet in the cycle
-    assumes apex is SETfirst_( samecycle->vertices )
-
-  returns:
-    vertices(settemp)
-    all ->seen are cleared
-
-  notes:
-    uses qh_vertex_visit;
-
-  design:
-    for each facet in samecycle
-      for each unseen vertex in facet->vertices
-        append to result
-*/
-setT *qh_basevertices(qhT *qh, facetT *samecycle) {
-  facetT *same;
-  vertexT *apex, *vertex, **vertexp;
-  setT *vertices= qh_settemp(qh, qh->TEMPsize);
-
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  apex->visitid= ++qh->vertex_visit;
-  FORALLsame_cycle_(samecycle) {
-    if (same->mergeridge)
-      continue;
-    FOREACHvertex_(same->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        qh_setappend(qh, &vertices, vertex);
-        vertex->visitid= qh->vertex_visit;
-        vertex->seen= False;
-      }
-    }
-  }
-  trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
-         qh_setsize(qh, vertices)));
-  return vertices;
-} /* basevertices */
-
-/*---------------------------------
-
-  qh_checkconnect(qh)
-    check that new facets are connected
-    new facets are on qh.newfacet_list
-
-  notes:
-    this is slow and it changes the order of the facets
-    uses qh.visit_id
-
-  design:
-    move first new facet to end of qh.facet_list
-    for all newly appended facets
-      append unvisited neighbors to end of qh.facet_list
-    for all new facets
-      report error if unvisited
-*/
-void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
-  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
-
-  facet= qh->newfacet_list;
-  qh_removefacet(qh, facet);
-  qh_appendfacet(qh, facet);
-  facet->visitid= ++qh->visit_id;
-  FORALLfacet_(facet) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        qh_removefacet(qh, neighbor);
-        qh_appendfacet(qh, neighbor);
-        neighbor->visitid= qh->visit_id;
-      }
-    }
-  }
-  FORALLnew_facets {
-    if (newfacet->visitid == qh->visit_id)
-      break;
-    qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
-         newfacet->id);
-    errfacet= newfacet;
-  }
-  if (errfacet)
-    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
-} /* checkconnect */
-
-/*---------------------------------
-
-  qh_checkzero(qh, testall )
-    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
-
-    if testall,
-      test all facets for qh.MERGEexact post-merging
-    else
-      test qh.newfacet_list
-
-    if qh.MERGEexact,
-      allows coplanar ridges
-      skips convexity test while qh.ZEROall_ok
-
-  returns:
-    True if all facets !flipped, !dupridge, normal
-         if all horizon facets are simplicial
-         if all vertices are clearly below neighbor
-         if all opposite vertices of horizon are below
-    clears qh.ZEROall_ok if any problems or coplanar facets
-
-  notes:
-    uses qh.vertex_visit
-    horizon facets may define multiple new facets
-
-  design:
-    for all facets in qh.newfacet_list or qh.facet_list
-      check for flagged faults (flipped, etc.)
-    for all facets in qh.newfacet_list or qh.facet_list
-      for each neighbor of facet
-        skip horizon facets for qh.newfacet_list
-        test the opposite vertex
-      if qh.newfacet_list
-        test the other vertices in the facet's horizon facet
-*/
-boolT qh_checkzero(qhT *qh, boolT testall) {
-  facetT *facet, *neighbor, **neighborp;
-  facetT *horizon, *facetlist;
-  int neighbor_i;
-  vertexT *vertex, **vertexp;
-  realT dist;
-
-  if (testall)
-    facetlist= qh->facet_list;
-  else {
-    facetlist= qh->newfacet_list;
-    FORALLfacet_(facetlist) {
-      horizon= SETfirstt_(facet->neighbors, facetT);
-      if (!horizon->simplicial)
-        goto LABELproblem;
-      if (facet->flipped || facet->dupridge || !facet->normal)
-        goto LABELproblem;
-    }
-    if (qh->MERGEexact && qh->ZEROall_ok) {
-      trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
-      return True;
-    }
-  }
-  FORALLfacet_(facetlist) {
-    qh->vertex_visit++;
-    neighbor_i= 0;
-    horizon= NULL;
-    FOREACHneighbor_(facet) {
-      if (!neighbor_i && !testall) {
-        horizon= neighbor;
-        neighbor_i++;
-        continue; /* horizon facet tested in qh_findhorizon */
-      }
-      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-      vertex->visitid= qh->vertex_visit;
-      zzinc_(Zdistzero);
-      qh_distplane(qh, vertex->point, neighbor, &dist);
-      if (dist >= -qh->DISTround) {
-        qh->ZEROall_ok= False;
-        if (!qh->MERGEexact || testall || dist > qh->DISTround)
-          goto LABELnonconvex;
-      }
-    }
-    if (!testall && horizon) {
-      FOREACHvertex_(horizon->vertices) {
-        if (vertex->visitid != qh->vertex_visit) {
-          zzinc_(Zdistzero);
-          qh_distplane(qh, vertex->point, facet, &dist);
-          if (dist >= -qh->DISTround) {
-            qh->ZEROall_ok= False;
-            if (!qh->MERGEexact || dist > qh->DISTround)
-              goto LABELnonconvex;
-          }
-          break;
-        }
-      }
-    }
-  }
-  trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
-        (qh->MERGEexact && !testall) ?
-           "not concave, flipped, or duplicate ridged" : "clearly convex"));
-  return True;
-
- LABELproblem:
-  qh->ZEROall_ok= False;
-  trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
-       facet->id));
-  return False;
-
- LABELnonconvex:
-  trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
-         facet->id, neighbor->id, vertex->id, dist));
-  return False;
-} /* checkzero */
-
-/*---------------------------------
-
-  qh_compareangle(angle1, angle2 )
-    used by qsort() to order merges by angle
-*/
-int qh_compareangle(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return((a->angle > b->angle) ? 1 : -1);
-} /* compareangle */
-
-/*---------------------------------
-
-  qh_comparemerge(merge1, merge2 )
-    used by qsort() to order merges
-*/
-int qh_comparemerge(const void *p1, const void *p2) {
-  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
-
-  return(a->type - b->type);
-} /* comparemerge */
-
-/*---------------------------------
-
-  qh_comparevisit(vertex1, vertex2 )
-    used by qsort() to order vertices by their visitid
-*/
-int qh_comparevisit(const void *p1, const void *p2) {
-  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
-
-  return(a->visitid - b->visitid);
-} /* comparevisit */
-
-/*---------------------------------
-
-  qh_copynonconvex(qh, atridge )
-    set non-convex flag on other ridges (if any) between same neighbors
-
-  notes:
-    may be faster if use smaller ridge set
-
-  design:
-    for each ridge of atridge's top facet
-      if ridge shares the same neighbor
-        set nonconvex flag
-*/
-void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
-  facetT *facet, *otherfacet;
-  ridgeT *ridge, **ridgep;
-
-  facet= atridge->top;
-  otherfacet= atridge->bottom;
-  FOREACHridge_(facet->ridges) {
-    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
-      ridge->nonconvex= True;
-      trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
-              atridge->id, ridge->id));
-      break;
-    }
-  }
-} /* copynonconvex */
-
-/*---------------------------------
-
-  qh_degen_redundant_facet(qh, facet )
-    check facet for degen. or redundancy
-
-  notes:
-    bumps vertex_visit
-    called if a facet was redundant but no longer is (qh_merge_degenredundant)
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-
-  see:
-    qh_degen_redundant_neighbors()
-
-  design:
-    test for redundant neighbor
-    test for degenerate facet
-*/
-void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
-          facet->id));
-  FOREACHneighbor_(facet) {
-    qh->vertex_visit++;
-    FOREACHvertex_(neighbor->vertices)
-      vertex->visitid= qh->vertex_visit;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
-      trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
-      return;
-    }
-  }
-  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
-    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
-    trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* degen_redundant_facet */
-
-
-/*---------------------------------
-
-  qh_degen_redundant_neighbors(qh, facet, delfacet,  )
-    append degenerate and redundant neighbors to facet_mergeset
-    if delfacet,
-      only checks neighbors of both delfacet and facet
-    also checks current facet for degeneracy
-
-  notes:
-    bumps vertex_visit
-    called for each qh_mergefacet() and qh_mergecycle()
-    merge and statistics occur in merge_nonconvex
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-      it appends redundant facets after degenerate ones
-
-    a degenerate facet has fewer than hull_dim neighbors
-    a redundant facet's vertices is a subset of its neighbor's vertices
-    tests for redundant merges first (appendmergeset is nop for others)
-    in a merge, only needs to test neighbors of merged facet
-
-  see:
-    qh_merge_degenredundant() and qh_degen_redundant_facet()
-
-  design:
-    test for degenerate facet
-    test for redundant neighbor
-    test for degenerate neighbor
-*/
-void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-  int size;
-
-  trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
-          facet->id, getid_(delfacet)));
-  if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
-    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
-    trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
-  }
-  if (!delfacet)
-    delfacet= facet;
-  qh->vertex_visit++;
-  FOREACHvertex_(facet->vertices)
-    vertex->visitid= qh->vertex_visit;
-  FOREACHneighbor_(delfacet) {
-    /* uses early out instead of checking vertex count */
-    if (neighbor == facet)
-      continue;
-    FOREACHvertex_(neighbor->vertices) {
-      if (vertex->visitid != qh->vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
-      trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
-    }
-  }
-  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
-    if (neighbor == facet)
-      continue;
-    if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
-      qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
-      trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
-    }
-  }
-} /* degen_redundant_neighbors */
-
-
-/*---------------------------------
-
-  qh_find_newvertex(qh, oldvertex, vertices, ridges )
-    locate new vertex for renaming old vertex
-    vertices is a set of possible new vertices
-      vertices sorted by number of deleted ridges
-
-  returns:
-    newvertex or NULL
-      each ridge includes both vertex and oldvertex
-    vertices sorted by number of deleted ridges
-
-  notes:
-    modifies vertex->visitid
-    new vertex is in one of the ridges
-    renaming will not cause a duplicate ridge
-    renaming will minimize the number of deleted ridges
-    newvertex may not be adjacent in the dual (though unlikely)
-
-  design:
-    for each vertex in vertices
-      set vertex->visitid to number of references in ridges
-    remove unvisited vertices
-    set qh.vertex_visit above all possible values
-    sort vertices by number of references in ridges
-    add each ridge to qh.hash_table
-    for each vertex in vertices
-      look for a vertex that would not cause a duplicate ridge after a rename
-*/
-vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
-  vertexT *vertex, **vertexp;
-  setT *newridges;
-  ridgeT *ridge, **ridgep;
-  int size, hashsize;
-  int hash;
-
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 4) {
-    qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
-             oldvertex->id);
-    FOREACHvertex_(vertices)
-      qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
-    FOREACHridge_(ridges)
-      qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
-    qh_fprintf(qh, qh->ferr, 8066, "\n");
-  }
-#endif
-  FOREACHvertex_(vertices)
-    vertex->visitid= 0;
-  FOREACHridge_(ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->visitid++;
-  }
-  FOREACHvertex_(vertices) {
-    if (!vertex->visitid) {
-      qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
-      vertexp--; /* repeat since deleted this vertex */
-    }
-  }
-  qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
-  if (!qh_setsize(qh, vertices)) {
-    trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
-            oldvertex->id));
-    return NULL;
-  }
-  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
-                sizeof(vertexT *), qh_comparevisit);
-  /* can now use qh->vertex_visit */
-  if (qh->PRINTstatistics) {
-    size= qh_setsize(qh, vertices);
-    zinc_(Zintersect);
-    zadd_(Zintersecttot, size);
-    zmax_(Zintersectmax, size);
-  }
-  hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
-  FOREACHridge_(ridges)
-    qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
-  FOREACHvertex_(vertices) {
-    newridges= qh_vertexridges(qh, vertex);
-    FOREACHridge_(newridges) {
-      if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
-        zinc_(Zdupridge);
-        break;
-      }
-    }
-    qh_settempfree(qh, &newridges);
-    if (!ridge)
-      break;  /* found a rename */
-  }
-  if (vertex) {
-    /* counted in qh_renamevertex */
-    trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
-      vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
-  }else {
-    zinc_(Zfindfail);
-    trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
-      oldvertex->id, qh->furthest_id));
-  }
-  qh_setfree(qh, &qh->hash_table);
-  return vertex;
-} /* find_newvertex */
-
-/*---------------------------------
-
-  qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
-    test neighbor of facet for qh_findbestneighbor()
-    if testcentrum,
-      tests centrum (assumes it is defined)
-    else
-      tests vertices
-
-  returns:
-    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
-      updates bestfacet, dist, mindist, and maxdist
-*/
-void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
-      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
-  realT dist, mindist, maxdist;
-
-  if (testcentrum) {
-    zzinc_(Zbestdist);
-    qh_distplane(qh, facet->center, neighbor, &dist);
-    dist *= qh->hull_dim; /* estimate furthest vertex */
-    if (dist < 0) {
-      maxdist= 0;
-      mindist= dist;
-      dist= -dist;
-    }else {
-      mindist= 0;
-      maxdist= dist;
-    }
-  }else
-    dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
-  if (dist < *distp) {
-    *bestfacet= neighbor;
-    *mindistp= mindist;
-    *maxdistp= maxdist;
-    *distp= dist;
-  }
-} /* findbest_test */
-
-/*---------------------------------
-
-  qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
-    finds best neighbor (least dist) of a facet for merging
-
-  returns:
-    returns min and max distances and their max absolute value
-
-  notes:
-    error if qh_ASvoronoi
-    avoids merging old into new
-    assumes ridge->nonconvex only set on one ridge between a pair of facets
-    could use an early out predicate but not worth it
-
-  design:
-    if a large facet
-      will test centrum
-    else
-      will test vertices
-    if a large facet
-      test nonconvex neighbors for best merge
-    else
-      test all neighbors for the best merge
-    if testing centrum
-      get distance information
-*/
-facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  ridgeT *ridge, **ridgep;
-  boolT nonconvex= True, testcentrum= False;
-  int size= qh_setsize(qh, facet->vertices);
-
-  if(qh->CENTERtype==qh_ASvoronoi){
-    qh_fprintf(qh, qh->ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  *distp= REALmax;
-  if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
-    testcentrum= True;
-    zinc_(Zbestcentrum);
-    if (!facet->center)
-       facet->center= qh_getcentrum(qh, facet);
-  }
-  if (size > qh->hull_dim + qh_BESTnonconvex) {
-    FOREACHridge_(facet->ridges) {
-      if (ridge->nonconvex) {
-        neighbor= otherfacet_(ridge, facet);
-        qh_findbest_test(qh, testcentrum, facet, neighbor,
-                          &bestfacet, distp, mindistp, maxdistp);
-      }
-    }
-  }
-  if (!bestfacet) {
-    nonconvex= False;
-    FOREACHneighbor_(facet)
-      qh_findbest_test(qh, testcentrum, facet, neighbor,
-                        &bestfacet, distp, mindistp, maxdistp);
-  }
-  if (!bestfacet) {
-    qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  if (testcentrum)
-    qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
-  trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
-     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
-  return(bestfacet);
-} /* findbestneighbor */
-
-
-/*---------------------------------
-
-  qh_flippedmerges(qh, facetlist, wasmerge )
-    merge flipped facets into best neighbor
-    assumes qh.facet_mergeset at top of temporary stack
-
-  returns:
-    no flipped facets on facetlist
-    sets wasmerge if merge occurred
-    degen/redundant merges passed through
-
-  notes:
-    othermerges not needed since qh.facet_mergeset is empty before & after
-      keep it in case of change
-
-  design:
-    append flipped facets to qh.facetmergeset
-    for each flipped merge
-      find best neighbor
-      merge facet into neighbor
-      merge degenerate and redundant facets
-    remove flipped merges from qh.facet_mergeset
-*/
-void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *neighbor, *facet1;
-  realT dist, mindist, maxdist;
-  mergeT *merge, **mergep;
-  setT *othermerges;
-  int nummerge=0;
-
-  trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->flipped && !facet->visible)
-      qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
-  }
-  othermerges= qh_settemppop(qh); /* was facet_mergeset */
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh_settemppush(qh, othermerges);
-  FOREACHmerge_(othermerges) {
-    facet1= merge->facet1;
-    if (merge->type != MRGflip || facet1->visible)
-      continue;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
-    trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
-      facet1->id, neighbor->id, dist, qh->furthest_id));
-    qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
-    nummerge++;
-    if (qh->PRINTstatistics) {
-      zinc_(Zflipped);
-      wadd_(Wflippedtot, dist);
-      wmax_(Wflippedmax, dist);
-    }
-    qh_merge_degenredundant(qh);
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->facet1->visible || merge->facet2->visible)
-      qh_memfree(qh, merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(qh, &qh->facet_mergeset, merge);
-  }
-  qh_settempfree(qh, &othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
-} /* flippedmerges */
-
-
-/*---------------------------------
-
-  qh_forcedmerges(qh, wasmerge )
-    merge duplicated ridges
-
-  returns:
-    removes all duplicate ridges on facet_mergeset
-    wasmerge set if merge
-    qh.facet_mergeset may include non-forced merges(none for now)
-    qh.degen_mergeset includes degen/redun merges
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-     could rename vertices that pinch the horizon
-    assumes qh_merge_degenredundant() has not be called
-    othermerges isn't needed since facet_mergeset is empty afterwards
-      keep it in case of change
-
-  design:
-    for each duplicate ridge
-      find current facets by chasing f.replace links
-      check for wide merge due to duplicate ridge
-      determine best direction for facet
-      merge one facet into the other
-      remove duplicate ridges from qh.facet_mergeset
-*/
-void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
-  facetT *facet1, *facet2;
-  mergeT *merge, **mergep;
-  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
-  setT *othermerges;
-  int nummerge=0, numflip=0;
-
-  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
-  othermerges= qh_settemppop(qh); /* was facet_mergeset */
-  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh_settemppush(qh, othermerges);
-  FOREACHmerge_(othermerges) {
-    if (merge->type != MRGridge)
-        continue;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-        qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
-      facet1= facet1->f.replace; /* previously merged facet */
-    while (facet2->visible)
-      facet2= facet2->f.replace; /* previously merged facet */
-    if (facet1 == facet2)
-      continue;
-    if (!qh_setin(facet2->neighbors, facet1)) {
-      qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
-               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-    }
-    dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
-    dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
-    qh_check_dupridge(qh, facet1, dist1, facet2, dist2);
-    if (dist1 < dist2)
-      qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
-    else {
-      qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
-      dist1= dist2;
-      facet1= facet2;
-    }
-    if (facet1->flipped) {
-      zinc_(Zmergeflipdup);
-      numflip++;
-    }else
-      nummerge++;
-    if (qh->PRINTstatistics) {
-      zinc_(Zduplicate);
-      wadd_(Wduplicatetot, dist1);
-      wmax_(Wduplicatemax, dist1);
-    }
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->type == MRGridge)
-      qh_memfree(qh, merge, (int)sizeof(mergeT));
-    else
-      qh_setappend(qh, &qh->facet_mergeset, merge);
-  }
-  qh_settempfree(qh, &othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
-                nummerge, numflip));
-} /* forcedmerges */
-
-
-/*---------------------------------
-
-  qh_getmergeset(qh, facetlist )
-    determines nonconvex facets on facetlist
-    tests !tested ridges and nonconvex ridges of !tested facets
-
-  returns:
-    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
-    all ridges tested
-
-  notes:
-    assumes no nonconvex ridges with both facets tested
-    uses facet->tested/ridge->tested to prevent duplicate tests
-    can not limit tests to modified ridges since the centrum changed
-    uses qh.visit_id
-
-  see:
-    qh_getmergeset_initial()
-
-  design:
-    for each facet on facetlist
-      for each ridge of facet
-        if untested ridge
-          test ridge for convexity
-          if non-convex
-            append ridge to qh.facet_mergeset
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
-  qh->visit_id++;
-  FORALLfacet_(facetlist) {
-    if (facet->tested)
-      continue;
-    facet->visitid= qh->visit_id;
-    facet->tested= True;  /* must be non-simplicial due to merge */
-    FOREACHneighbor_(facet)
-      neighbor->seen= False;
-    FOREACHridge_(facet->ridges) {
-      if (ridge->tested && !ridge->nonconvex)
-        continue;
-      /* if tested & nonconvex, need to append merge */
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->seen) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-      }else if (neighbor->visitid != qh->visit_id) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-        neighbor->seen= True;      /* only one ridge is marked nonconvex */
-        if (qh_test_appendmerge(qh, facet, neighbor))
-          ridge->nonconvex= True;
-      }
-    }
-  }
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  if (qh->ANGLEmerge)
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh->POSTmerging) {
-    zadd_(Zmergesettot2, nummerges);
-  }else {
-    zadd_(Zmergesettot, nummerges);
-    zmax_(Zmergesetmax, nummerges);
-  }
-  trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
-} /* getmergeset */
-
-
-/*---------------------------------
-
-  qh_getmergeset_initial(qh, facetlist )
-    determine initial qh.facet_mergeset for facets
-    tests all facet/neighbor pairs on facetlist
-
-  returns:
-    sorted qh.facet_mergeset with nonconvex ridges
-    sets facet->tested, ridge->tested, and ridge->nonconvex
-
-  notes:
-    uses visit_id, assumes ridge->nonconvex is False
-
-  see:
-    qh_getmergeset()
-
-  design:
-    for each facet on facetlist
-      for each untested neighbor of facet
-        test facet and neighbor for convexity
-        if non-convex
-          append merge to qh.facet_mergeset
-          mark one of the ridges as nonconvex
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  qh->visit_id++;
-  FORALLfacet_(facetlist) {
-    facet->visitid= qh->visit_id;
-    facet->tested= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh->visit_id) {
-        if (qh_test_appendmerge(qh, facet, neighbor)) {
-          FOREACHridge_(neighbor->ridges) {
-            if (facet == otherfacet_(ridge, neighbor)) {
-              ridge->nonconvex= True;
-              break;    /* only one ridge is marked nonconvex */
-            }
-          }
-        }
-      }
-    }
-    FOREACHridge_(facet->ridges)
-      ridge->tested= True;
-  }
-  nummerges= qh_setsize(qh, qh->facet_mergeset);
-  if (qh->ANGLEmerge)
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
-  else
-    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
-  if (qh->POSTmerging) {
-    zadd_(Zmergeinittot2, nummerges);
-  }else {
-    zadd_(Zmergeinittot, nummerges);
-    zmax_(Zmergeinitmax, nummerges);
-  }
-  trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
-} /* getmergeset_initial */
-
-
-/*---------------------------------
-
-  qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
-    add ridge to hashtable without oldvertex
-
-  notes:
-    assumes hashtable is large enough
-
-  design:
-    determine hash value for ridge without oldvertex
-    find next empty slot for ridge
-*/
-void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
-  int hash;
-  ridgeT *ridgeA;
-
-  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
-  while (True) {
-    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-      SETelem_(hashtable, hash)= ridge;
-      break;
-    }else if (ridgeA == ridge)
-      break;
-    if (++hash == hashsize)
-      hash= 0;
-  }
-} /* hashridge */
-
-
-/*---------------------------------
-
-  qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
-    returns matching ridge without oldvertex in hashtable
-      for ridge without vertex
-    if oldvertex is NULL
-      matches with any one skip
-
-  returns:
-    matching ridge or NULL
-    if no match,
-      if ridge already in   table
-        hashslot= -1
-      else
-        hashslot= next NULL index
-
-  notes:
-    assumes hashtable is large enough
-    can't match ridge to itself
-
-  design:
-    get hash value for ridge without vertex
-    for each hashslot
-      return match if ridge matches ridgeA without oldvertex
-*/
-ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
-  int hash;
-  ridgeT *ridgeA;
-
-  *hashslot= 0;
-  zinc_(Zhashridge);
-  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
-  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-    if (ridgeA == ridge)
-      *hashslot= -1;
-    else {
-      zinc_(Zhashridgetest);
-      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
-        return ridgeA;
-    }
-    if (++hash == hashsize)
-      hash= 0;
-  }
-  if (!*hashslot)
-    *hashslot= hash;
-  return NULL;
-} /* hashridge_find */
-
-
-/*---------------------------------
-
-  qh_makeridges(qh, facet )
-    creates explicit ridges between simplicial facets
-
-  returns:
-    facet with ridges and without qh_MERGEridge
-    ->simplicial is False
-
-  notes:
-    allows qh_MERGEridge flag
-    uses existing ridges
-    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    look for qh_MERGEridge neighbors
-    mark neighbors that already have ridges
-    for each unprocessed neighbor of facet
-      create a ridge for neighbor and facet
-    if any qh_MERGEridge neighbors
-      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
-*/
-void qh_makeridges(qhT *qh, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int neighbor_i, neighbor_n;
-  boolT toporient, mergeridge= False;
-
-  if (!facet->simplicial)
-    return;
-  trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
-  facet->simplicial= False;
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      mergeridge= True;
-    else
-      neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges)
-    otherfacet_(ridge, facet)->seen= True;
-  FOREACHneighbor_i_(qh, facet) {
-    if (neighbor == qh_MERGEridge)
-      continue;  /* fixed by qh_mark_dupridges */
-    else if (!neighbor->seen) {  /* no current ridges */
-      ridge= qh_newridge(qh);
-      ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
-                                                          neighbor_i, 0);
-      toporient= facet->toporient ^ (neighbor_i & 0x1);
-      if (toporient) {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }else {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }
-#if 0 /* this also works */
-      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
-      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }else {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }
-#endif
-      qh_setappend(qh, &(facet->ridges), ridge);
-      qh_setappend(qh, &(neighbor->ridges), ridge);
-    }
-  }
-  if (mergeridge) {
-    while (qh_setdel(facet->neighbors, qh_MERGEridge))
-      ; /* delete each one */
-  }
-} /* makeridges */
-
-
-/*---------------------------------
-
-  qh_mark_dupridges(qh, facetlist )
-    add duplicated ridges to qh.facet_mergeset
-    facet->dupridge is true
-
-  returns:
-    duplicate ridges on qh.facet_mergeset
-    ->mergeridge/->mergeridge2 set
-    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
-    no MERGEridges in neighbor sets
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-    could rename vertices that pinch the horizon (thus removing subridge)
-    uses qh.visit_id
-
-  design:
-    for all facets on facetlist
-      if facet contains a duplicate ridge
-        for each neighbor of facet
-          if neighbor marked qh_MERGEridge (one side of the merge)
-            set facet->mergeridge
-          else
-            if neighbor contains a duplicate ridge
-            and the back link is qh_MERGEridge
-              append duplicate ridge to qh.facet_mergeset
-   for each duplicate ridge
-     make ridge sets in preparation for merging
-     remove qh_MERGEridge from neighbor set
-   for each duplicate ridge
-     restore the missing neighbor from the neighbor set that was qh_MERGEridge
-     add the missing ridge for this neighbor
-*/
-void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  int nummerge=0;
-  mergeT *merge, **mergep;
-
-
-  trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->dupridge) {
-      FOREACHneighbor_(facet) {
-        if (neighbor == qh_MERGEridge) {
-          facet->mergeridge= True;
-          continue;
-        }
-        if (neighbor->dupridge
-        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
-          qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
-          facet->mergeridge2= True;
-          facet->mergeridge= True;
-          nummerge++;
-        }
-      }
-    }
-  }
-  if (!nummerge)
-    return;
-  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
-    if (facet->mergeridge && !facet->mergeridge2)
-      qh_makeridges(qh, facet);
-  }
-  FOREACHmerge_(qh->facet_mergeset) {   /* restore the missing neighbors */
-    if (merge->type == MRGridge) {
-      qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
-      qh_makeridges(qh, merge->facet1);   /* and the missing ridges */
-    }
-  }
-  trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
-                nummerge));
-} /* mark_dupridges */
-
-/*---------------------------------
-
-  qh_maydropneighbor(qh, facet )
-    drop neighbor relationship if no ridge between facet and neighbor
-
-  returns:
-    neighbor sets updated
-    appends degenerate facets to qh.facet_mergeset
-
-  notes:
-    won't cause redundant facets since vertex inclusion is the same
-    may drop vertex and neighbor if no ridge
-    uses qh.visit_id
-
-  design:
-    visit all neighbors with ridges
-    for each unvisited neighbor of facet
-      delete neighbor and facet from the neighbor sets
-      if neighbor becomes degenerate
-        append neighbor to qh.degen_mergeset
-    if facet is degenerate
-      append facet to qh.degen_mergeset
-*/
-void qh_maydropneighbor(qhT *qh, facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  realT angledegen= qh_ANGLEdegen;
-  facetT *neighbor, **neighborp;
-
-  qh->visit_id++;
-  trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
-          facet->id));
-  FOREACHridge_(facet->ridges) {
-    ridge->top->visitid= qh->visit_id;
-    ridge->bottom->visitid= qh->visit_id;
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid != qh->visit_id) {
-      trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
-            facet->id, neighbor->id, qh->furthest_id));
-      zinc_(Zdropneighbor);
-      qh_setdel(facet->neighbors, neighbor);
-      neighborp--;  /* repeat, deleted a neighbor */
-      qh_setdel(neighbor->neighbors, facet);
-      if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
-        zinc_(Zdropdegen);
-        qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
-        trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
-      }
-    }
-  }
-  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
-    zinc_(Zdropdegen);
-    qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
-    trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* maydropneighbor */
-
-
-/*---------------------------------
-
-  qh_merge_degenredundant(qh)
-    merge all degenerate and redundant facets
-    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
-
-  returns:
-    number of merges performed
-    resets facet->degenerate/redundant
-    if deleted (visible) facet has no neighbors
-      sets ->f.replace to NULL
-
-  notes:
-    redundant merges happen before degenerate ones
-    merging and renaming vertices can result in degen/redundant facets
-
-  design:
-    for each merge on qh.degen_mergeset
-      if redundant merge
-        if non-redundant facet merged into redundant facet
-          recheck facet for redundancy
-        else
-          merge redundant facet into other facet
-*/
-int qh_merge_degenredundant(qhT *qh) {
-  int size;
-  mergeT *merge;
-  facetT *bestneighbor, *facet1, *facet2;
-  realT dist, mindist, maxdist;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-  mergeType mergetype;
-
-  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-    if (facet1->visible)
-      continue;
-    facet1->degenerate= False;
-    facet1->redundant= False;
-    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-    if (mergetype == MRGredundant) {
-      zinc_(Zneighbor);
-      while (facet2->visible) {
-        if (!facet2->f.replace) {
-          qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
-               facet1->id, facet2->id);
-          qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-        }
-        facet2= facet2->f.replace;
-      }
-      if (facet1 == facet2) {
-        qh_degen_redundant_facet(qh, facet1); /* in case of others */
-        continue;
-      }
-      trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
-            facet1->id, facet2->id));
-      qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
-      /* merge distance is already accounted for */
-      nummerges++;
-    }else {  /* mergetype == MRGdegen, other merges may have fixed */
-      if (!(size= qh_setsize(qh, facet1->neighbors))) {
-        zinc_(Zdelfacetdup);
-        trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
-        qh_willdelete(qh, facet1, NULL);
-        FOREACHvertex_(facet1->vertices) {
-          qh_setdel(vertex->neighbors, facet1);
-          if (!SETfirst_(vertex->neighbors)) {
-            zinc_(Zdegenvertex);
-            trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
-                 vertex->id, facet1->id));
-            vertex->deleted= True;
-            qh_setappend(qh, &qh->del_vertices, vertex);
-          }
-        }
-        nummerges++;
-      }else if (size < qh->hull_dim) {
-        bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
-        trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
-              facet1->id, size, bestneighbor->id, dist));
-        qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-        nummerges++;
-        if (qh->PRINTstatistics) {
-          zinc_(Zdegen);
-          wadd_(Wdegentot, dist);
-          wmax_(Wdegenmax, dist);
-        }
-      } /* else, another merge fixed the degeneracy and redundancy tested */
-    }
-  }
-  return nummerges;
-} /* merge_degenredundant */
-
-/*---------------------------------
-
-  qh_merge_nonconvex(qh, facet1, facet2, mergetype )
-    remove non-convex ridge between facet1 into facet2
-    mergetype gives why the facet's are non-convex
-
-  returns:
-    merges one of the facets into the best neighbor
-
-  design:
-    if one of the facets is a new facet
-      prefer merging new facet into old facet
-    find best neighbors for both facets
-    merge the nearest facet into its best neighbor
-    update the statistics
-*/
-void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
-  facetT *bestfacet, *bestneighbor, *neighbor;
-  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
-
-  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
-      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
-  /* concave or coplanar */
-  if (!facet1->newfacet) {
-    bestfacet= facet2;   /* avoid merging old facet if new is ok */
-    facet2= facet1;
-    facet1= bestfacet;
-  }else
-    bestfacet= facet1;
-  bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
-  neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
-  if (dist < dist2) {
-    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else if (qh->AVOIDold && !facet2->newfacet
-  && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
-       || dist * 1.5 < dist2)) {
-    zinc_(Zavoidold);
-    wadd_(Wavoidoldtot, dist);
-    wmax_(Wavoidoldmax, dist);
-    trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
-           facet2->id, dist2, facet1->id, dist2));
-    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else {
-    qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
-    dist= dist2;
-  }
-  if (qh->PRINTstatistics) {
-    if (mergetype == MRGanglecoplanar) {
-      zinc_(Zacoplanar);
-      wadd_(Wacoplanartot, dist);
-      wmax_(Wacoplanarmax, dist);
-    }else if (mergetype == MRGconcave) {
-      zinc_(Zconcave);
-      wadd_(Wconcavetot, dist);
-      wmax_(Wconcavemax, dist);
-    }else { /* MRGcoplanar */
-      zinc_(Zcoplanar);
-      wadd_(Wcoplanartot, dist);
-      wmax_(Wcoplanarmax, dist);
-    }
-  }
-} /* merge_nonconvex */
-
-/*---------------------------------
-
-  qh_mergecycle(qh, samecycle, newfacet )
-    merge a cycle of facets starting at samecycle into a newfacet
-    newfacet is a horizon facet with ->normal
-    samecycle facets are simplicial from an apex
-
-  returns:
-    initializes vertex neighbors on first merge
-    samecycle deleted (placed on qh.visible_list)
-    newfacet at end of qh.facet_list
-    deleted vertices on qh.del_vertices
-
-  see:
-    qh_mergefacet()
-    called by qh_mergecycle_all() for multiple, same cycle facets
-
-  design:
-    make vertex neighbors if necessary
-    make ridges for newfacet
-    merge neighbor sets of samecycle into newfacet
-    merge ridges of samecycle into newfacet
-    merge vertex neighbors of samecycle into newfacet
-    make apex of samecycle the apex of newfacet
-    if newfacet wasn't a new facet
-      add its vertices to qh.newvertex_list
-    delete samecycle facets a make newfacet a newfacet
-*/
-void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  int traceonce= False, tracerestore= 0;
-  vertexT *apex;
-#ifndef qh_NOtrace
-  facetT *same;
-#endif
-
-  if (newfacet->tricoplanar) {
-    if (!qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-    }
-    newfacet->tricoplanar= False;
-    newfacet->keepcentrum= False;
-  }
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  zzinc_(Ztotmerge);
-  if (qh->REPORTfreq2 && qh->POSTmerging) {
-    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
-      qh_tracemerging(qh);
-  }
-#ifndef qh_NOtrace
-  if (qh->TRACEmerge == zzval_(Ztotmerge))
-    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
-  trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
-        zzval_(Ztotmerge), samecycle->id, newfacet->id));
-  if (newfacet == qh->tracefacet) {
-    tracerestore= qh->IStracing;
-    qh->IStracing= 4;
-    qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
-               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh->furthest_id);
-    traceonce= True;
-  }
-  if (qh->IStracing >=4) {
-    qh_fprintf(qh, qh->ferr, 8069, "  same cycle:");
-    FORALLsame_cycle_(samecycle)
-      qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
-    qh_fprintf(qh, qh->ferr, 8071, "\n");
-  }
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
-#endif /* !qh_NOtrace */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_makeridges(qh, newfacet);
-  qh_mergecycle_neighbors(qh, samecycle, newfacet);
-  qh_mergecycle_ridges(qh, samecycle, newfacet);
-  qh_mergecycle_vneighbors(qh, samecycle, newfacet);
-  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
-    qh_setaddnth(qh, &newfacet->vertices, 0, apex);  /* apex has last id */
-  if (!newfacet->newfacet)
-    qh_newvertices(qh, newfacet->vertices);
-  qh_mergecycle_facets(qh, samecycle, newfacet);
-  qh_tracemerge(qh, samecycle, newfacet);
-  /* check for degen_redundant_neighbors after qh_forcedmerges() */
-  if (traceonce) {
-    qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
-    qh->IStracing= tracerestore;
-  }
-} /* mergecycle */
-
-/*---------------------------------
-
-  qh_mergecycle_all(qh, facetlist, wasmerge )
-    merge all samecycles of coplanar facets into horizon
-    don't merge facets with ->mergeridge (these already have ->normal)
-    all facets are simplicial from apex
-    all facet->cycledone == False
-
-  returns:
-    all newfacets merged into coplanar horizon facets
-    deleted vertices on  qh.del_vertices
-    sets wasmerge if any merge
-
-  see:
-    calls qh_mergecycle for multiple, same cycle facets
-
-  design:
-    for each facet on facetlist
-      skip facets with duplicate ridges and normals
-      check that facet is in a samecycle (->mergehorizon)
-      if facet only member of samecycle
-        sets vertex->delridge for all vertices except apex
-        merge facet into horizon
-      else
-        mark all facets in samecycle
-        remove facets with duplicate ridges from samecycle
-        merge samecycle into horizon (deletes facets from facetlist)
-*/
-void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *same, *prev, *horizon;
-  facetT *samecycle= NULL, *nextfacet, *nextsame;
-  vertexT *apex, *vertex, **vertexp;
-  int cycles=0, total=0, facets, nummerge;
-
-  trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
-  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
-    if (facet->normal)
-      continue;
-    if (!facet->mergehorizon) {
-      qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    horizon= SETfirstt_(facet->neighbors, facetT);
-    if (facet->f.samecycle == facet) {
-      zinc_(Zonehorizon);
-      /* merge distance done in qh_findhorizon */
-      apex= SETfirstt_(facet->vertices, vertexT);
-      FOREACHvertex_(facet->vertices) {
-        if (vertex != apex)
-          vertex->delridge= True;
-      }
-      horizon->f.newcycle= NULL;
-      qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
-    }else {
-      samecycle= facet;
-      facets= 0;
-      prev= facet;
-      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
-           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
-        nextsame= same->f.samecycle;
-        if (same->cycledone || same->visible)
-          qh_infiniteloop(qh, same);
-        same->cycledone= True;
-        if (same->normal) {
-          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
-          same->f.samecycle= NULL;
-        }else {
-          prev= same;
-          facets++;
-        }
-      }
-      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
-        nextfacet= nextfacet->next;
-      horizon->f.newcycle= NULL;
-      qh_mergecycle(qh, samecycle, horizon);
-      nummerge= horizon->nummerge + facets;
-      if (nummerge > qh_MAXnummerge)
-        horizon->nummerge= qh_MAXnummerge;
-      else
-        horizon->nummerge= (short unsigned int)nummerge;
-      zzinc_(Zcyclehorizon);
-      total += facets;
-      zzadd_(Zcyclefacettot, facets);
-      zmax_(Zcyclefacetmax, facets);
-    }
-    cycles++;
-  }
-  if (cycles)
-    *wasmerge= True;
-  trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
-} /* mergecycle_all */
-
-/*---------------------------------
-
-  qh_mergecycle_facets(qh, samecycle, newfacet )
-    finish merge of samecycle into newfacet
-
-  returns:
-    samecycle prepended to visible_list for later deletion and partitioning
-      each facet->f.replace == newfacet
-
-    newfacet moved to end of qh.facet_list
-      makes newfacet a newfacet (get's facet1->id if it was old)
-      sets newfacet->newmerge
-      clears newfacet->center (unless merging into a large facet)
-      clears newfacet->tested and ridge->tested for facet1
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  design:
-    make newfacet a new facet and set its flags
-    move samecycle facets to qh.visible_list for later deletion
-    unless newfacet is large
-      remove its centrum
-*/
-void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *next;
-
-  trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
-  qh_removefacet(qh, newfacet);  /* append as a newfacet to end of qh->facet_list */
-  qh_appendfacet(qh, newfacet);
-  newfacet->newfacet= True;
-  newfacet->simplicial= False;
-  newfacet->newmerge= True;
-
-  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
-    next= same->f.samecycle;  /* reused by willdelete */
-    qh_willdelete(qh, same, newfacet);
-  }
-  if (newfacet->center
-      && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
-    qh_memfree(qh, newfacet->center, qh->normal_size);
-    newfacet->center= NULL;
-  }
-  trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_facets */
-
-/*---------------------------------
-
-  qh_mergecycle_neighbors(qh, samecycle, newfacet )
-    add neighbors for samecycle facets to newfacet
-
-  returns:
-    newfacet with updated neighbors and vice-versa
-    newfacet has ridges
-    all neighbors of newfacet marked with qh.visit_id
-    samecycle facets marked with qh.visit_id-1
-    ridges updated for simplicial neighbors of samecycle with a ridge
-
-  notes:
-    assumes newfacet not in samecycle
-    usually, samecycle facets are new, simplicial facets without internal ridges
-      not so if horizon facet is coplanar to two different samecycles
-
-  see:
-    qh_mergeneighbors()
-
-  design:
-    check samecycle
-    delete neighbors from newfacet that are also in samecycle
-    for each neighbor of a facet in samecycle
-      if neighbor is simplicial
-        if first visit
-          move the neighbor relation to newfacet
-          update facet links for its ridges
-        else
-          make ridges for neighbor
-          remove samecycle reference
-      else
-        update neighbor sets
-*/
-void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor, **neighborp;
-  int delneighbors= 0, newneighbors= 0;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-
-  samevisitid= ++qh->visit_id;
-  FORALLsame_cycle_(samecycle) {
-    if (same->visitid == samevisitid || same->visible)
-      qh_infiniteloop(qh, samecycle);
-    same->visitid= samevisitid;
-  }
-  newfacet->visitid= ++qh->visit_id;
-  trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
-  FOREACHneighbor_(newfacet) {
-    if (neighbor->visitid == samevisitid) {
-      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
-      delneighbors++;
-    }else
-      neighbor->visitid= qh->visit_id;
-  }
-  qh_setcompact(qh, newfacet->neighbors);
-
-  trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHneighbor_(same) {
-      if (neighbor->visitid == samevisitid)
-        continue;
-      if (neighbor->simplicial) {
-        if (neighbor->visitid != qh->visit_id) {
-          qh_setappend(qh, &newfacet->neighbors, neighbor);
-          qh_setreplace(qh, neighbor->neighbors, same, newfacet);
-          newneighbors++;
-          neighbor->visitid= qh->visit_id;
-          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
-            if (ridge->top == same) {
-              ridge->top= newfacet;
-              break;
-            }else if (ridge->bottom == same) {
-              ridge->bottom= newfacet;
-              break;
-            }
-          }
-        }else {
-          qh_makeridges(qh, neighbor);
-          qh_setdel(neighbor->neighbors, same);
-          /* same can't be horizon facet for neighbor */
-        }
-      }else { /* non-simplicial neighbor */
-        qh_setdel(neighbor->neighbors, same);
-        if (neighbor->visitid != qh->visit_id) {
-          qh_setappend(qh, &neighbor->neighbors, newfacet);
-          qh_setappend(qh, &newfacet->neighbors, neighbor);
-          neighbor->visitid= qh->visit_id;
-          newneighbors++;
-        }
-      }
-    }
-  }
-  trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
-             delneighbors, newneighbors));
-} /* mergecycle_neighbors */
-
-/*---------------------------------
-
-  qh_mergecycle_ridges(qh, samecycle, newfacet )
-    add ridges/neighbors for facets in samecycle to newfacet
-    all new/old neighbors of newfacet marked with qh.visit_id
-    facets in samecycle marked with qh.visit_id-1
-    newfacet marked with qh.visit_id
-
-  returns:
-    newfacet has merged ridges
-
-  notes:
-    ridge already updated for simplicial neighbors of samecycle with a ridge
-
-  see:
-    qh_mergeridges()
-    qh_makeridges()
-
-  design:
-    remove ridges between newfacet and samecycle
-    for each facet in samecycle
-      for each ridge in facet
-        update facet pointers in ridge
-        skip ridges processed in qh_mergecycle_neighors
-        free ridges between newfacet and samecycle
-        free ridges between facets of samecycle (on 2nd visit)
-        append remaining ridges to newfacet
-      if simpilicial facet
-        for each neighbor of facet
-          if simplicial facet
-          and not samecycle facet or newfacet
-            make ridge between neighbor and newfacet
-*/
-void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor= NULL;
-  int numold=0, numnew=0;
-  int neighbor_i, neighbor_n;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-  boolT toporient;
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
-  samevisitid= qh->visit_id -1;
-  FOREACHridge_(newfacet->ridges) {
-    neighbor= otherfacet_(ridge, newfacet);
-    if (neighbor->visitid == samevisitid)
-      SETref_(ridge)= NULL; /* ridge free'd below */
-  }
-  qh_setcompact(qh, newfacet->ridges);
-
-  trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHridge_(same->ridges) {
-      if (ridge->top == same) {
-        ridge->top= newfacet;
-        neighbor= ridge->bottom;
-      }else if (ridge->bottom == same) {
-        ridge->bottom= newfacet;
-        neighbor= ridge->top;
-      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
-        qh_setappend(qh, &newfacet->ridges, ridge);
-        numold++;  /* already set by qh_mergecycle_neighbors */
-        continue;
-      }else {
-        qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
-        qh_errexit(qh, qh_ERRqhull, NULL, ridge);
-      }
-      if (neighbor == newfacet) {
-        qh_setfree(qh, &(ridge->vertices));
-        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else if (neighbor->visitid == samevisitid) {
-        qh_setdel(neighbor->ridges, ridge);
-        qh_setfree(qh, &(ridge->vertices));
-        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        numold++;
-      }else {
-        qh_setappend(qh, &newfacet->ridges, ridge);
-        numold++;
-      }
-    }
-    if (same->ridges)
-      qh_settruncate(qh, same->ridges, 0);
-    if (!same->simplicial)
-      continue;
-    FOREACHneighbor_i_(qh, same) {       /* note: !newfact->simplicial */
-      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
-        ridge= qh_newridge(qh);
-        ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
-                                                          neighbor_i, 0);
-        toporient= same->toporient ^ (neighbor_i & 0x1);
-        if (toporient) {
-          ridge->top= newfacet;
-          ridge->bottom= neighbor;
-        }else {
-          ridge->top= neighbor;
-          ridge->bottom= newfacet;
-        }
-        qh_setappend(qh, &(newfacet->ridges), ridge);
-        qh_setappend(qh, &(neighbor->ridges), ridge);
-        numnew++;
-      }
-    }
-  }
-
-  trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
-             numold, numnew));
-} /* mergecycle_ridges */
-
-/*---------------------------------
-
-  qh_mergecycle_vneighbors(qh, samecycle, newfacet )
-    create vertex neighbors for newfacet from vertices of facets in samecycle
-    samecycle marked with visitid == qh.visit_id - 1
-
-  returns:
-    newfacet vertices with updated neighbors
-    marks newfacet with qh.visit_id-1
-    deletes vertices that are merged away
-    sets delridge on all vertices (faster here than in mergecycle_ridges)
-
-  see:
-    qh_mergevertex_neighbors()
-
-  design:
-    for each vertex of samecycle facet
-      set vertex->delridge
-      delete samecycle facets from vertex neighbors
-      append newfacet to vertex neighbors
-      if vertex only in newfacet
-        delete it from newfacet
-        add it to qh.del_vertices for later deletion
-*/
-void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
-  facetT *neighbor, **neighborp;
-  unsigned int mergeid;
-  vertexT *vertex, **vertexp, *apex;
-  setT *vertices;
-
-  trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
-  mergeid= qh->visit_id - 1;
-  newfacet->visitid= mergeid;
-  vertices= qh_basevertices(qh, samecycle); /* temp */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_setappend(qh, &vertices, apex);
-  FOREACHvertex_(vertices) {
-    vertex->delridge= True;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == mergeid)
-        SETref_(neighbor)= NULL;
-    }
-    qh_setcompact(qh, vertex->neighbors);
-    qh_setappend(qh, &vertex->neighbors, newfacet);
-    if (!SETsecond_(vertex->neighbors)) {
-      zinc_(Zcyclevertex);
-      trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
-        vertex->id, samecycle->id, newfacet->id));
-      qh_setdelsorted(newfacet->vertices, vertex);
-      vertex->deleted= True;
-      qh_setappend(qh, &qh->del_vertices, vertex);
-    }
-  }
-  qh_settempfree(qh, &vertices);
-  trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_vneighbors */
-
-/*---------------------------------
-
-  qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
-    merges facet1 into facet2
-    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
-
-  returns:
-    qh.max_outside and qh.min_vertex updated
-    initializes vertex neighbors on first merge
-
-  returns:
-    facet2 contains facet1's vertices, neighbors, and ridges
-      facet2 moved to end of qh.facet_list
-      makes facet2 a newfacet
-      sets facet2->newmerge set
-      clears facet2->center (unless merging into a large facet)
-      clears facet2->tested and ridge->tested for facet1
-
-    facet1 prepended to visible_list for later deletion and partitioning
-      facet1->f.replace == facet2
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  notes:
-    mindist/maxdist may be NULL (only if both NULL)
-    traces merge if fmax_(maxdist,-mindist) > TRACEdist
-
-  see:
-    qh_mergecycle()
-
-  design:
-    trace merge and check for degenerate simplex
-    make ridges for both facets
-    update qh.max_outside, qh.max_vertex, qh.min_vertex
-    update facet2->maxoutside and keepcentrum
-    update facet2->nummerge
-    update tested flags for facet2
-    if facet1 is simplicial
-      merge facet1 into facet2
-    else
-      merge facet1's neighbors into facet2
-      merge facet1's ridges into facet2
-      merge facet1's vertices into facet2
-      merge facet1's vertex neighbors into facet2
-      add facet2's vertices to qh.new_vertexlist
-      unless qh_MERGEapex
-        test facet2 for degenerate or redundant neighbors
-      move facet1 to qh.visible_list for later deletion
-      move facet2 to end of qh.newfacet_list
-*/
-void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
-  boolT traceonce= False;
-  vertexT *vertex, **vertexp;
-  int tracerestore=0, nummerge;
-
-  if (facet1->tricoplanar || facet2->tricoplanar) {
-    if (!qh->TRInormals) {
-      qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-    }
-    if (facet2->tricoplanar) {
-      facet2->tricoplanar= False;
-      facet2->keepcentrum= False;
-    }
-  }
-  zzinc_(Ztotmerge);
-  if (qh->REPORTfreq2 && qh->POSTmerging) {
-    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
-      qh_tracemerging(qh);
-  }
-#ifndef qh_NOtrace
-  if (qh->build_cnt >= qh->RERUN) {
-    if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
-      tracerestore= 0;
-      qh->IStracing= qh->TRACElevel;
-      traceonce= True;
-      qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
-             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
-    }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
-      tracerestore= qh->IStracing;
-      qh->IStracing= 4;
-      traceonce= True;
-      qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
-                 zzval_(Ztotmerge), qh->tracefacet_id,  qh->furthest_id);
-    }
-  }
-  if (qh->IStracing >= 2) {
-    realT mergemin= -2;
-    realT mergemax= -2;
-
-    if (mindist) {
-      mergemin= *mindist;
-      mergemax= *maxdist;
-    }
-    qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
-    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
-  }
-#endif /* !qh_NOtrace */
-  if (facet1 == facet2 || facet1->visible || facet2->visible) {
-    qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
-             facet1->id, facet2->id);
-    qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-  }
-  if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
-    qh_fprintf(qh, qh->ferr, 6227, "\n\
-qhull precision error: Only %d facets remain.  Can not merge another\n\
-pair.  The input is too degenerate or the convexity constraints are\n\
-too strong.\n", qh->hull_dim+1);
-    if (qh->hull_dim >= 5 && !qh->MERGEexact)
-      qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  qh_makeridges(qh, facet1);
-  qh_makeridges(qh, facet2);
-  if (qh->IStracing >=4)
-    qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
-  if (mindist) {
-    maximize_(qh->max_outside, *maxdist);
-    maximize_(qh->max_vertex, *maxdist);
-#if qh_MAXoutside
-    maximize_(facet2->maxoutside, *maxdist);
-#endif
-    minimize_(qh->min_vertex, *mindist);
-    if (!facet2->keepcentrum
-    && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidefacet);
-    }
-  }
-  nummerge= facet1->nummerge + facet2->nummerge + 1;
-  if (nummerge >= qh_MAXnummerge)
-    facet2->nummerge= qh_MAXnummerge;
-  else
-    facet2->nummerge= (short unsigned int)nummerge;
-  facet2->newmerge= True;
-  facet2->dupridge= False;
-  qh_updatetested(qh, facet1, facet2);
-  if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
-    qh_mergesimplex(qh, facet1, facet2, mergeapex);
-  else {
-    qh->vertex_visit++;
-    FOREACHvertex_(facet2->vertices)
-      vertex->visitid= qh->vertex_visit;
-    if (qh->hull_dim == 2)
-      qh_mergefacet2d(qh, facet1, facet2);
-    else {
-      qh_mergeneighbors(qh, facet1, facet2);
-      qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
-    }
-    qh_mergeridges(qh, facet1, facet2);
-    qh_mergevertex_neighbors(qh, facet1, facet2);
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);
-  }
-  if (!mergeapex)
-    qh_degen_redundant_neighbors(qh, facet2, facet1);
-  if (facet2->coplanar || !facet2->newfacet) {
-    zinc_(Zmergeintohorizon);
-  }else if (!facet1->newfacet && facet2->newfacet) {
-    zinc_(Zmergehorizon);
-  }else {
-    zinc_(Zmergenew);
-  }
-  qh_willdelete(qh, facet1, facet2);
-  qh_removefacet(qh, facet2);  /* append as a newfacet to end of qh->facet_list */
-  qh_appendfacet(qh, facet2);
-  facet2->newfacet= True;
-  facet2->tested= False;
-  qh_tracemerge(qh, facet1, facet2);
-  if (traceonce) {
-    qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
-    qh->IStracing= tracerestore;
-  }
-} /* mergefacet */
-
-
-/*---------------------------------
-
-  qh_mergefacet2d(qh, facet1, facet2 )
-    in 2d, merges neighbors and vertices of facet1 into facet2
-
-  returns:
-    build ridges for neighbors if necessary
-    facet2 looks like a simplicial facet except for centrum, ridges
-      neighbors are opposite the corresponding vertex
-      maintains orientation of facet2
-
-  notes:
-    qh_mergefacet() retains non-simplicial structures
-      they are not needed in 2d, but later routines may use them
-    preserves qh.vertex_visit for qh_mergevertex_neighbors()
-
-  design:
-    get vertices and neighbors
-    determine new vertices and neighbors
-    set new vertices and neighbors and adjust orientation
-    make ridges for new neighbor if needed
-*/
-void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
-  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
-  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
-
-  vertex1A= SETfirstt_(facet1->vertices, vertexT);
-  vertex1B= SETsecondt_(facet1->vertices, vertexT);
-  vertex2A= SETfirstt_(facet2->vertices, vertexT);
-  vertex2B= SETsecondt_(facet2->vertices, vertexT);
-  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
-  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
-  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
-  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
-  if (vertex1A == vertex2A) {
-    vertexA= vertex1B;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1A;
-  }else if (vertex1A == vertex2B) {
-    vertexA= vertex1B;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1A;
-  }else if (vertex1B == vertex2A) {
-    vertexA= vertex1A;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1B;
-  }else { /* 1B == 2B */
-    vertexA= vertex1A;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1B;
-  }
-  /* vertexB always from facet2, neighborB always from facet1 */
-  if (vertexA->id > vertexB->id) {
-    SETfirst_(facet2->vertices)= vertexA;
-    SETsecond_(facet2->vertices)= vertexB;
-    if (vertexB == vertex2A)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborA;
-    SETsecond_(facet2->neighbors)= neighborB;
-  }else {
-    SETfirst_(facet2->vertices)= vertexB;
-    SETsecond_(facet2->vertices)= vertexA;
-    if (vertexB == vertex2B)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborB;
-    SETsecond_(facet2->neighbors)= neighborA;
-  }
-  qh_makeridges(qh, neighborB);
-  qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
-  trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
-       vertexA->id, neighborB->id, facet1->id, facet2->id));
-} /* mergefacet2d */
-
-
-/*---------------------------------
-
-  qh_mergeneighbors(qh, facet1, facet2 )
-    merges the neighbors of facet1 into facet2
-
-  see:
-    qh_mergecycle_neighbors()
-
-  design:
-    for each neighbor of facet1
-      if neighbor is also a neighbor of facet2
-        if neighbor is simpilicial
-          make ridges for later deletion as a degenerate facet
-        update its neighbor set
-      else
-        move the neighbor relation to facet2
-    remove the neighbor relation for facet1 and facet2
-*/
-void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
-  facetT *neighbor, **neighborp;
-
-  trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  qh->visit_id++;
-  FOREACHneighbor_(facet2) {
-    neighbor->visitid= qh->visit_id;
-  }
-  FOREACHneighbor_(facet1) {
-    if (neighbor->visitid == qh->visit_id) {
-      if (neighbor->simplicial)    /* is degen, needs ridges */
-        qh_makeridges(qh, neighbor);
-      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
-        qh_setdel(neighbor->neighbors, facet1);
-      else {
-        qh_setdel(neighbor->neighbors, facet2);
-        qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
-      }
-    }else if (neighbor != facet2) {
-      qh_setappend(qh, &(facet2->neighbors), neighbor);
-      qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
-    }
-  }
-  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
-  qh_setdel(facet2->neighbors, facet1);
-} /* mergeneighbors */
-
-
-/*---------------------------------
-
-  qh_mergeridges(qh, facet1, facet2 )
-    merges the ridge set of facet1 into facet2
-
-  returns:
-    may delete all ridges for a vertex
-    sets vertex->delridge on deleted ridges
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    delete ridges between facet1 and facet2
-      mark (delridge) vertices on these ridges for later testing
-    for each remaining ridge
-      rename facet1 to facet2
-*/
-void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-
-  trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
-          facet1->id, facet2->id));
-  FOREACHridge_(facet2->ridges) {
-    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
-      FOREACHvertex_(ridge->vertices)
-        vertex->delridge= True;
-      qh_delridge(qh, ridge);  /* expensive in high-d, could rebuild */
-      ridgep--; /*repeat*/
-    }
-  }
-  FOREACHridge_(facet1->ridges) {
-    if (ridge->top == facet1)
-      ridge->top= facet2;
-    else
-      ridge->bottom= facet2;
-    qh_setappend(qh, &(facet2->ridges), ridge);
-  }
-} /* mergeridges */
-
-
-/*---------------------------------
-
-  qh_mergesimplex(qh, facet1, facet2, mergeapex )
-    merge simplicial facet1 into facet2
-    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
-      vertex id is latest (most recently created)
-    facet1 may be contained in facet2
-    ridges exist for both facets
-
-  returns:
-    facet2 with updated vertices, ridges, neighbors
-    updated neighbors for facet1's vertices
-    facet1 not deleted
-    sets vertex->delridge on deleted ridges
-
-  notes:
-    special case code since this is the most common merge
-    called from qh_mergefacet()
-
-  design:
-    if qh_MERGEapex
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to facet2
-    else
-      for each ridge between facet1 and facet2
-        set vertex->delridge
-      determine the apex for facet1 (i.e., vertex to be merged)
-      unless apex already in facet2
-        insert apex into vertices for facet2
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to qh.new_vertexlist if necessary
-      for each vertex of facet1
-        if apex
-          rename facet1 to facet2 in its vertex neighbors
-        else
-          delete facet1 from vertex neighors
-          if only in facet2
-            add vertex to qh.del_vertices for later deletion
-      for each ridge of facet1
-        delete ridges between facet1 and facet2
-        append other ridges to facet2 after renaming facet to facet2
-*/
-void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
-  vertexT *vertex, **vertexp, *apex;
-  ridgeT *ridge, **ridgep;
-  boolT issubset= False;
-  int vertex_i= -1, vertex_n;
-  facetT *neighbor, **neighborp, *otherfacet;
-
-  if (mergeapex) {
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);  /* apex is new */
-    apex= SETfirstt_(facet1->vertices, vertexT);
-    if (SETfirstt_(facet2->vertices, vertexT) != apex)
-      qh_setaddnth(qh, &facet2->vertices, 0, apex);  /* apex has last id */
-    else
-      issubset= True;
-  }else {
-    zinc_(Zmergesimplex);
-    FOREACHvertex_(facet1->vertices)
-      vertex->seen= False;
-    FOREACHridge_(facet1->ridges) {
-      if (otherfacet_(ridge, facet1) == facet2) {
-        FOREACHvertex_(ridge->vertices) {
-          vertex->seen= True;
-          vertex->delridge= True;
-        }
-        break;
-      }
-    }
-    FOREACHvertex_(facet1->vertices) {
-      if (!vertex->seen)
-        break;  /* must occur */
-    }
-    apex= vertex;
-    trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
-          apex->id, facet1->id, facet2->id));
-    FOREACHvertex_i_(qh, facet2->vertices) {
-      if (vertex->id < apex->id) {
-        break;
-      }else if (vertex->id == apex->id) {
-        issubset= True;
-        break;
-      }
-    }
-    if (!issubset)
-      qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
-    if (!facet2->newfacet)
-      qh_newvertices(qh, facet2->vertices);
-    else if (!apex->newlist) {
-      qh_removevertex(qh, apex);
-      qh_appendvertex(qh, apex);
-    }
-  }
-  trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
-          facet1->id));
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex == apex && !issubset)
-      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(qh, vertex, facet1, facet2);
-    }
-  }
-  trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
-          facet1->id, facet2->id));
-  qh->visit_id++;
-  FOREACHneighbor_(facet2)
-    neighbor->visitid= qh->visit_id;
-  FOREACHridge_(facet1->ridges) {
-    otherfacet= otherfacet_(ridge, facet1);
-    if (otherfacet == facet2) {
-      qh_setdel(facet2->ridges, ridge);
-      qh_setfree(qh, &(ridge->vertices));
-      qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-      qh_setdel(facet2->neighbors, facet1);
-    }else {
-      qh_setappend(qh, &facet2->ridges, ridge);
-      if (otherfacet->visitid != qh->visit_id) {
-        qh_setappend(qh, &facet2->neighbors, otherfacet);
-        qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
-        otherfacet->visitid= qh->visit_id;
-      }else {
-        if (otherfacet->simplicial)    /* is degen, needs ridges */
-          qh_makeridges(qh, otherfacet);
-        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
-          qh_setdel(otherfacet->neighbors, facet1);
-        else {   /*keep newfacet->neighbors->horizon*/
-          qh_setdel(otherfacet->neighbors, facet2);
-          qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
-        }
-      }
-      if (ridge->top == facet1) /* wait until after qh_makeridges */
-        ridge->top= facet2;
-      else
-        ridge->bottom= facet2;
-    }
-  }
-  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
-  trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
-          facet1->id, getid_(apex), facet2->id));
-} /* mergesimplex */
-
-/*---------------------------------
-
-  qh_mergevertex_del(qh, vertex, facet1, facet2 )
-    delete a vertex because of merging facet1 into facet2
-
-  returns:
-    deletes vertex from facet2
-    adds vertex to qh.del_vertices for later deletion
-*/
-void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
-
-  zinc_(Zmergevertex);
-  trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
-          vertex->id, facet1->id, facet2->id));
-  qh_setdelsorted(facet2->vertices, vertex);
-  vertex->deleted= True;
-  qh_setappend(qh, &qh->del_vertices, vertex);
-} /* mergevertex_del */
-
-/*---------------------------------
-
-  qh_mergevertex_neighbors(qh, facet1, facet2 )
-    merge the vertex neighbors of facet1 to facet2
-
-  returns:
-    if vertex is current qh.vertex_visit
-      deletes facet1 from vertex->neighbors
-    else
-      renames facet1 to facet2 in vertex->neighbors
-    deletes vertices if only one neighbor
-
-  notes:
-    assumes vertex neighbor sets are good
-*/
-void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
-  vertexT *vertex, **vertexp;
-
-  trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
-          facet1->id, facet2->id));
-  if (qh->tracevertex) {
-    qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
-             facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
-    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
-  }
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex->visitid != qh->vertex_visit)
-      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-        qh_mergevertex_del(qh, vertex, facet1, facet2);
-    }
-  }
-  if (qh->tracevertex)
-    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
-} /* mergevertex_neighbors */
-
-
-/*---------------------------------
-
-  qh_mergevertices(qh, vertices1, vertices2 )
-    merges the vertex set of facet1 into facet2
-
-  returns:
-    replaces vertices2 with merged set
-    preserves vertex_visit for qh_mergevertex_neighbors
-    updates qh.newvertex_list
-
-  design:
-    create a merged set of both vertices (in inverse id order)
-*/
-void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
-  int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
-  setT *mergedvertices;
-  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
-
-  mergedvertices= qh_settemp(qh, newsize);
-  FOREACHvertex_(vertices1) {
-    if (!*vertex2 || vertex->id > (*vertex2)->id)
-      qh_setappend(qh, &mergedvertices, vertex);
-    else {
-      while (*vertex2 && (*vertex2)->id > vertex->id)
-        qh_setappend(qh, &mergedvertices, *vertex2++);
-      if (!*vertex2 || (*vertex2)->id < vertex->id)
-        qh_setappend(qh, &mergedvertices, vertex);
-      else
-        qh_setappend(qh, &mergedvertices, *vertex2++);
-    }
-  }
-  while (*vertex2)
-    qh_setappend(qh, &mergedvertices, *vertex2++);
-  if (newsize < qh_setsize(qh, mergedvertices)) {
-    qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(qh, vertices2);
-  *vertices2= mergedvertices;
-  qh_settemppop(qh);
-} /* mergevertices */
-
-
-/*---------------------------------
-
-  qh_neighbor_intersections(qh, vertex )
-    return intersection of all vertices in vertex->neighbors except for vertex
-
-  returns:
-    returns temporary set of vertices
-    does not include vertex
-    NULL if a neighbor is simplicial
-    NULL if empty set
-
-  notes:
-    used for renaming vertices
-
-  design:
-    initialize the intersection set with vertices of the first two neighbors
-    delete vertex from the intersection
-    for each remaining neighbor
-      intersect its vertex set with the intersection set
-      return NULL if empty
-    return the intersection set
-*/
-setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
-  facetT *neighbor, **neighborp, *neighborA, *neighborB;
-  setT *intersect;
-  int neighbor_i, neighbor_n;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->simplicial)
-      return NULL;
-  }
-  neighborA= SETfirstt_(vertex->neighbors, facetT);
-  neighborB= SETsecondt_(vertex->neighbors, facetT);
-  zinc_(Zintersectnum);
-  if (!neighborA)
-    return NULL;
-  if (!neighborB)
-    intersect= qh_setcopy(qh, neighborA->vertices, 0);
-  else
-    intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
-  qh_settemppush(qh, intersect);
-  qh_setdelsorted(intersect, vertex);
-  FOREACHneighbor_i_(qh, vertex) {
-    if (neighbor_i >= 2) {
-      zinc_(Zintersectnum);
-      qh_vertexintersect(qh, &intersect, neighbor->vertices);
-      if (!SETfirst_(intersect)) {
-        zinc_(Zintersectfail);
-        qh_settempfree(qh, &intersect);
-        return NULL;
-      }
-    }
-  }
-  trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
-          qh_setsize(qh, intersect), vertex->id));
-  return intersect;
-} /* neighbor_intersections */
-
-/*---------------------------------
-
-  qh_newvertices(qh, vertices )
-    add vertices to end of qh.vertex_list (marks as new vertices)
-
-  returns:
-    vertices on qh.newvertex_list
-    vertex->newlist set
-*/
-void qh_newvertices(qhT *qh, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(qh, vertex);
-      qh_appendvertex(qh, vertex);
-    }
-  }
-} /* newvertices */
-
-/*---------------------------------
-
-  qh_reducevertices(qh)
-    reduce extra vertices, shared vertices, and redundant vertices
-    facet->newmerge is set if merged since last call
-    if !qh.MERGEvertices, only removes extra vertices
-
-  returns:
-    True if also merged degen_redundant facets
-    vertices are renamed if possible
-    clears facet->newmerge and vertex->delridge
-
-  notes:
-    ignored if 2-d
-
-  design:
-    merge any degenerate or redundant facets
-    for each newly merged facet
-      remove extra vertices
-    if qh.MERGEvertices
-      for each newly merged facet
-        for each vertex
-          if vertex was on a deleted ridge
-            rename vertex if it is shared
-      remove delridge flag from new vertices
-*/
-boolT qh_reducevertices(qhT *qh) {
-  int numshare=0, numrename= 0;
-  boolT degenredun= False;
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  if (qh->hull_dim == 2)
-    return False;
-  if (qh_merge_degenredundant(qh))
-    degenredun= True;
- LABELrestart:
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      if (!qh->MERGEvertices)
-        newfacet->newmerge= False;
-      qh_remove_extravertices(qh, newfacet);
-    }
-  }
-  if (!qh->MERGEvertices)
-    return False;
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      newfacet->newmerge= False;
-      FOREACHvertex_(newfacet->vertices) {
-        if (vertex->delridge) {
-          if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
-            numshare++;
-            vertexp--; /* repeat since deleted vertex */
-          }
-        }
-      }
-    }
-  }
-  FORALLvertex_(qh->newvertex_list) {
-    if (vertex->delridge && !vertex->deleted) {
-      vertex->delridge= False;
-      if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
-        numrename++;
-        if (qh_merge_degenredundant(qh)) {
-          degenredun= True;
-          goto LABELrestart;
-        }
-      }
-    }
-  }
-  trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
-          numshare, numrename, degenredun));
-  return degenredun;
-} /* reducevertices */
-
-/*---------------------------------
-
-  qh_redundant_vertex(qh, vertex )
-    detect and rename a redundant vertex
-    vertices have full vertex->neighbors
-
-  returns:
-    returns true if find a redundant vertex
-      deletes vertex(vertex->deleted)
-
-  notes:
-    only needed if vertex->delridge and hull_dim >= 4
-    may add degenerate facets to qh.facet_mergeset
-    doesn't change vertex->neighbors or create redundant facets
-
-  design:
-    intersect vertices of all facet neighbors of vertex
-    determine ridges for these vertices
-    if find a new vertex for vertex amoung these ridges and vertices
-      rename vertex to the new vertex
-*/
-vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
-  vertexT *newvertex= NULL;
-  setT *vertices, *ridges;
-
-  trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
-  if ((vertices= qh_neighbor_intersections(qh, vertex))) {
-    ridges= qh_vertexridges(qh, vertex);
-    if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
-      qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
-    qh_settempfree(qh, &ridges);
-    qh_settempfree(qh, &vertices);
-  }
-  return newvertex;
-} /* redundant_vertex */
-
-/*---------------------------------
-
-  qh_remove_extravertices(qh, facet )
-    remove extra vertices from non-simplicial facets
-
-  returns:
-    returns True if it finds them
-
-  design:
-    for each vertex in facet
-      if vertex not in a ridge (i.e., no longer used)
-        delete vertex from facet
-        delete facet from vertice's neighbors
-        unless vertex in another facet
-          add vertex to qh.del_vertices for later deletion
-*/
-boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  boolT foundrem= False;
-
-  trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
-          facet->id));
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHridge_(facet->ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->seen= True;
-  }
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      foundrem= True;
-      zinc_(Zremvertex);
-      qh_setdelsorted(facet->vertices, vertex);
-      qh_setdel(vertex->neighbors, facet);
-      if (!qh_setsize(qh, vertex->neighbors)) {
-        vertex->deleted= True;
-        qh_setappend(qh, &qh->del_vertices, vertex);
-        zinc_(Zremvertexdel);
-        trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
-      }else
-        trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
-      vertexp--; /*repeat*/
-    }
-  }
-  return foundrem;
-} /* remove_extravertices */
-
-/*---------------------------------
-
-  qh_rename_sharedvertex(qh, vertex, facet )
-    detect and rename if shared vertex in facet
-    vertices have full ->neighbors
-
-  returns:
-    newvertex or NULL
-    the vertex may still exist in other facets (i.e., a neighbor was pinched)
-    does not change facet->neighbors
-    updates vertex->neighbors
-
-  notes:
-    a shared vertex for a facet is only in ridges to one neighbor
-    this may undo a pinched facet
-
-    it does not catch pinches involving multiple facets.  These appear
-      to be difficult to detect, since an exhaustive search is too expensive.
-
-  design:
-    if vertex only has two neighbors
-      determine the ridges that contain the vertex
-      determine the vertices shared by both neighbors
-      if can find a new vertex in this set
-        rename the vertex to the new vertex
-*/
-vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
-  facetT *neighbor, **neighborp, *neighborA= NULL;
-  setT *vertices, *ridges;
-  vertexT *newvertex;
-
-  if (qh_setsize(qh, vertex->neighbors) == 2) {
-    neighborA= SETfirstt_(vertex->neighbors, facetT);
-    if (neighborA == facet)
-      neighborA= SETsecondt_(vertex->neighbors, facetT);
-  }else if (qh->hull_dim == 3)
-    return NULL;
-  else {
-    qh->visit_id++;
-    FOREACHneighbor_(facet)
-      neighbor->visitid= qh->visit_id;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == qh->visit_id) {
-        if (neighborA)
-          return NULL;
-        neighborA= neighbor;
-      }
-    }
-    if (!neighborA) {
-      qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
-        vertex->id, facet->id);
-      qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-    }
-  }
-  /* the vertex is shared by facet and neighborA */
-  ridges= qh_settemp(qh, qh->TEMPsize);
-  neighborA->visitid= ++qh->visit_id;
-  qh_vertexridges_facet(qh, vertex, facet, &ridges);
-  trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
-    qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
-  zinc_(Zintersectnum);
-  vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
-  qh_setdel(vertices, vertex);
-  qh_settemppush(qh, vertices);
-  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
-    qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
-  qh_settempfree(qh, &vertices);
-  qh_settempfree(qh, &ridges);
-  return newvertex;
-} /* rename_sharedvertex */
-
-/*---------------------------------
-
-  qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
-    renames oldvertex as newvertex in ridge
-
-  returns:
-
-  design:
-    delete oldvertex from ridge
-    if newvertex already in ridge
-      copy ridge->noconvex to another ridge if possible
-      delete the ridge
-    else
-      insert newvertex into the ridge
-      adjust the ridge's orientation
-*/
-void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
-  int nth= 0, oldnth;
-  facetT *temp;
-  vertexT *vertex, **vertexp;
-
-  oldnth= qh_setindex(ridge->vertices, oldvertex);
-  qh_setdelnthsorted(qh, ridge->vertices, oldnth);
-  FOREACHvertex_(ridge->vertices) {
-    if (vertex == newvertex) {
-      zinc_(Zdelridge);
-      if (ridge->nonconvex) /* only one ridge has nonconvex set */
-        qh_copynonconvex(qh, ridge);
-      trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
-        ridge->id, oldvertex->id, newvertex->id));
-      qh_delridge(qh, ridge);
-      return;
-    }
-    if (vertex->id < newvertex->id)
-      break;
-    nth++;
-  }
-  qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
-  if (abs(oldnth - nth)%2) {
-    trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
-            ridge->id));
-    temp= ridge->top;
-    ridge->top= ridge->bottom;
-    ridge->bottom= temp;
-  }
-} /* renameridgevertex */
-
-
-/*---------------------------------
-
-  qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
-    renames oldvertex as newvertex in ridges
-    gives oldfacet/neighborA if oldvertex is shared between two facets
-
-  returns:
-    oldvertex may still exist afterwards
-
-
-  notes:
-    can not change neighbors of newvertex (since it's a subset)
-
-  design:
-    for each ridge in ridges
-      rename oldvertex to newvertex and delete degenerate ridges
-    if oldfacet not defined
-      for each neighbor of oldvertex
-        delete oldvertex from neighbor's vertices
-        remove extra vertices from neighbor
-      add oldvertex to qh.del_vertices
-    else if oldvertex only between oldfacet and neighborA
-      delete oldvertex from oldfacet and neighborA
-      add oldvertex to qh.del_vertices
-    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
-      delete oldvertex from oldfacet
-      delete oldfacet from oldvertice's neighbors
-      remove extra vertices (e.g., oldvertex) from neighborA
-*/
-void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  boolT istrace= False;
-
-  if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
-        newvertex->id == qh->tracevertex_id)
-    istrace= True;
-  FOREACHridge_(ridges)
-    qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
-  if (!oldfacet) {
-    zinc_(Zrenameall);
-    if (istrace)
-      qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
-               oldvertex->id, newvertex->id);
-    FOREACHneighbor_(oldvertex) {
-      qh_maydropneighbor(qh, neighbor);
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-      if (qh_remove_extravertices(qh, neighbor))
-        neighborp--; /* neighbor may be deleted */
-    }
-    if (!oldvertex->deleted) {
-      oldvertex->deleted= True;
-      qh_setappend(qh, &qh->del_vertices, oldvertex);
-    }
-  }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
-    zinc_(Zrenameshare);
-    if (istrace)
-      qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id);
-    FOREACHneighbor_(oldvertex)
-      qh_setdelsorted(neighbor->vertices, oldvertex);
-    oldvertex->deleted= True;
-    qh_setappend(qh, &qh->del_vertices, oldvertex);
-  }else {
-    zinc_(Zrenamepinch);
-    if (istrace || qh->IStracing)
-      qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
-    qh_setdelsorted(oldfacet->vertices, oldvertex);
-    qh_setdel(oldvertex->neighbors, oldfacet);
-    qh_remove_extravertices(qh, neighborA);
-  }
-} /* renamevertex */
-
-
-/*---------------------------------
-
-  qh_test_appendmerge(qh, facet, neighbor )
-    tests facet/neighbor for convexity
-    appends to mergeset if non-convex
-    if pre-merging,
-      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
-
-  returns:
-    true if appends facet/neighbor to mergeset
-    sets facet->center as needed
-    does not change facet->seen
-
-  design:
-    if qh.cos_max is defined
-      if the angle between facet normals is too shallow
-        append an angle-coplanar merge to qh.mergeset
-        return True
-    make facet's centrum if needed
-    if facet's centrum is above the neighbor
-      set isconcave
-    else
-      if facet's centrum is not below the neighbor
-        set iscoplanar
-      make neighbor's centrum if needed
-      if neighbor's centrum is above the facet
-        set isconcave
-      else if neighbor's centrum is not below the facet
-        set iscoplanar
-   if isconcave or iscoplanar
-     get angle if needed
-     append concave or coplanar merge to qh.mergeset
-*/
-boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
-  realT dist, dist2= -REALmax, angle= -REALmax;
-  boolT isconcave= False, iscoplanar= False, okangle= False;
-
-  if (qh->SKIPconvex && !qh->POSTmerging)
-    return False;
-  if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
-    angle= qh_getangle(qh, facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-    if (angle > qh->cos_max) {
-      zinc_(Zcoplanarangle);
-      qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
-      trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
-         angle, facet->id, neighbor->id));
-      return True;
-    }else
-      okangle= True;
-  }
-  if (!facet->center)
-    facet->center= qh_getcentrum(qh, facet);
-  zzinc_(Zcentrumtests);
-  qh_distplane(qh, facet->center, neighbor, &dist);
-  if (dist > qh->centrum_radius)
-    isconcave= True;
-  else {
-    if (dist > -qh->centrum_radius)
-      iscoplanar= True;
-    if (!neighbor->center)
-      neighbor->center= qh_getcentrum(qh, neighbor);
-    zzinc_(Zcentrumtests);
-    qh_distplane(qh, neighbor->center, facet, &dist2);
-    if (dist2 > qh->centrum_radius)
-      isconcave= True;
-    else if (!iscoplanar && dist2 > -qh->centrum_radius)
-      iscoplanar= True;
-  }
-  if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
-    return False;
-  if (!okangle && qh->ANGLEmerge) {
-    angle= qh_getangle(qh, facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-  }
-  if (isconcave) {
-    zinc_(Zconcaveridge);
-    if (qh->ANGLEmerge)
-      angle += qh_ANGLEconcave + 0.5;
-    qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
-    trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
-           facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
-  }else /* iscoplanar */ {
-    zinc_(Zcoplanarcentrum);
-    qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
-    trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
-              facet->id, neighbor->id, dist, dist2, angle));
-  }
-  return True;
-} /* test_appendmerge */
-
-/*---------------------------------
-
-  qh_test_vneighbors(qh)
-    test vertex neighbors for convexity
-    tests all facets on qh.newfacet_list
-
-  returns:
-    true if non-convex vneighbors appended to qh.facet_mergeset
-    initializes vertex neighbors if needed
-
-  notes:
-    assumes all facet neighbors have been tested
-    this can be expensive
-    this does not guarantee that a centrum is below all facets
-      but it is unlikely
-    uses qh.visit_id
-
-  design:
-    build vertex neighbors if necessary
-    for all new facets
-      for all vertices
-        for each unvisited facet neighbor of the vertex
-          test new facet and neighbor for convexity
-*/
-boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
-  facetT *newfacet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-
-  trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
-  if (!qh->VERTEXneighbors)
-    qh_vertexneighbors(qh);
-  FORALLnew_facets
-    newfacet->seen= False;
-  FORALLnew_facets {
-    newfacet->seen= True;
-    newfacet->visitid= qh->visit_id++;
-    FOREACHneighbor_(newfacet)
-      newfacet->visitid= qh->visit_id;
-    FOREACHvertex_(newfacet->vertices) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->seen || neighbor->visitid == qh->visit_id)
-          continue;
-        if (qh_test_appendmerge(qh, newfacet, neighbor))
-          nummerges++;
-      }
-    }
-  }
-  zadd_(Ztestvneighbor, nummerges);
-  trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
-           nummerges));
-  return (nummerges > 0);
-} /* test_vneighbors */
-
-/*---------------------------------
-
-  qh_tracemerge(qh, facet1, facet2 )
-    print trace message after merge
-*/
-void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
-  boolT waserror= False;
-
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 4)
-    qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
-  if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
-    qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
-    if (facet2 != qh->tracefacet)
-      qh_errprint(qh, "TRACE", qh->tracefacet,
-        (qh->tracevertex && qh->tracevertex->neighbors) ?
-           SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
-        NULL, qh->tracevertex);
-  }
-  if (qh->tracevertex) {
-    if (qh->tracevertex->deleted)
-      qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
-            qh->furthest_id);
-    else
-      qh_checkvertex(qh, qh->tracevertex);
-  }
-  if (qh->tracefacet) {
-    qh_checkfacet(qh, qh->tracefacet, True, &waserror);
-    if (waserror)
-      qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
-  }
-#endif /* !qh_NOtrace */
-  if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
-    qh_checkfacet(qh, facet2, True, &waserror);
-    if (waserror)
-      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-} /* tracemerge */
-
-/*---------------------------------
-
-  qh_tracemerging(qh)
-    print trace message during POSTmerging
-
-  returns:
-    updates qh.mergereport
-
-  notes:
-    called from qh_mergecycle() and qh_mergefacet()
-
-  see:
-    qh_buildtracing()
-*/
-void qh_tracemerging(qhT *qh) {
-  realT cpu;
-  int total;
-  time_t timedata;
-  struct tm *tp;
-
-  qh->mergereport= zzval_(Ztotmerge);
-  time(&timedata);
-  tp= localtime(&timedata);
-  cpu= qh_CPUclock;
-  cpu /= qh_SECticks;
-  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  qh_fprintf(qh, qh->ferr, 8087, "\n\
-At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
-  contains %d facets and %d vertices.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
-      total, qh->num_facets - qh->num_visible,
-      qh->num_vertices-qh_setsize(qh, qh->del_vertices));
-} /* tracemerging */
-
-/*---------------------------------
-
-  qh_updatetested(qh, facet1, facet2 )
-    clear facet2->tested and facet1->ridge->tested for merge
-
-  returns:
-    deletes facet2->center unless it's already large
-      if so, clears facet2->ridge->tested
-
-  design:
-    clear facet2->tested
-    clear ridge->tested for facet1's ridges
-    if facet2 has a centrum
-      if facet2 is large
-        set facet2->keepcentrum
-      else if facet2 has 3 vertices due to many merges, or not large and post merging
-        clear facet2->keepcentrum
-      unless facet2->keepcentrum
-        clear facet2->center to recompute centrum later
-        clear ridge->tested for facet2's ridges
-*/
-void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  int size;
-
-  facet2->tested= False;
-  FOREACHridge_(facet1->ridges)
-    ridge->tested= False;
-  if (!facet2->center)
-    return;
-  size= qh_setsize(qh, facet2->vertices);
-  if (!facet2->keepcentrum) {
-    if (size > qh->hull_dim + qh_MAXnewcentrum) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidevertices);
-    }
-  }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
-    /* center and keepcentrum was set */
-    if (size == qh->hull_dim || qh->POSTmerging)
-      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
-  }
-  if (!facet2->keepcentrum) {
-    qh_memfree(qh, facet2->center, qh->normal_size);
-    facet2->center= NULL;
-    FOREACHridge_(facet2->ridges)
-      ridge->tested= False;
-  }
-} /* updatetested */
-
-/*---------------------------------
-
-  qh_vertexridges(qh, vertex )
-    return temporary set of ridges adjacent to a vertex
-    vertex->neighbors defined
-
-  ntoes:
-    uses qh.visit_id
-    does not include implicit ridges for simplicial facets
-
-  design:
-    for each neighbor of vertex
-      add ridges that include the vertex to ridges
-*/
-setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
-  facetT *neighbor, **neighborp;
-  setT *ridges= qh_settemp(qh, qh->TEMPsize);
-  int size;
-
-  qh->visit_id++;
-  FOREACHneighbor_(vertex)
-    neighbor->visitid= qh->visit_id;
-  FOREACHneighbor_(vertex) {
-    if (*neighborp)   /* no new ridges in last neighbor */
-      qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
-  }
-  if (qh->PRINTstatistics || qh->IStracing) {
-    size= qh_setsize(qh, ridges);
-    zinc_(Zvertexridge);
-    zadd_(Zvertexridgetot, size);
-    zmax_(Zvertexridgemax, size);
-    trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
-             size, vertex->id));
-  }
-  return ridges;
-} /* vertexridges */
-
-/*---------------------------------
-
-  qh_vertexridges_facet(qh, vertex, facet, ridges )
-    add adjacent ridges for vertex in facet
-    neighbor->visitid==qh.visit_id if it hasn't been visited
-
-  returns:
-    ridges updated
-    sets facet->visitid to qh.visit_id-1
-
-  design:
-    for each ridge of facet
-      if ridge of visited neighbor (i.e., unprocessed)
-        if vertex in ridge
-          append ridge to vertex
-    mark facet processed
-*/
-void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor;
-
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh->visit_id
-    && qh_setin(ridge->vertices, vertex))
-      qh_setappend(qh, ridges, ridge);
-  }
-  facet->visitid= qh->visit_id-1;
-} /* vertexridges_facet */
-
-/*---------------------------------
-
-  qh_willdelete(qh, facet, replace )
-    moves facet to visible list
-    sets facet->f.replace to replace (may be NULL)
-
-  returns:
-    bumps qh.num_visible
-*/
-void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
-
-  qh_removefacet(qh, facet);
-  qh_prependfacet(qh, facet, &qh->visible_list);
-  qh->num_visible++;
-  facet->visible= True;
-  facet->f.replace= replace;
-} /* willdelete */
-
-#else /* qh_NOmerge */
-void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
-}
-void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-}
-boolT qh_checkzero(qhT *qh, boolT testall) {
-   }
-#endif /* qh_NOmerge */
-
diff --git a/src/qhull/src/libqhull_r/merge_r.h b/src/qhull/src/libqhull_r/merge_r.h
deleted file mode 100644
index 30a51815d..000000000
--- a/src/qhull/src/libqhull_r/merge_r.h
+++ /dev/null
@@ -1,186 +0,0 @@
-/*
      ---------------------------------
-
-   merge_r.h
-   header file for merge_r.c
-
-   see qh-merge_r.htm and merge_r.c
-
-   Copyright (c) 1993-2015 C.B. Barber.
-   $Id: //main/2015/qhull/src/libqhull_r/merge_r.h#3 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-#include "libqhull_r.h"
-
-
-/*============ -constants- ==============*/
-
-/*----------------------------------
-
-  qh_ANGLEredundant
-    indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*----------------------------------
-
-  qh_ANGLEdegen
-    indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen     5.0
-
-/*----------------------------------
-
-  qh_ANGLEconcave
-    offset to indicate concave facets in mergeT->angle
-
-  notes:
-    concave facets are assigned the range of [2,4] in mergeT->angle
-    roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave  1.5
-
-/*----------------------------------
-
-  MRG... (mergeType)
-    indicates the type of a merge (mergeT->type)
-*/
-typedef enum {  /* in sort order for facet_mergeset */
-  MRGnone= 0,
-  MRGcoplanar,          /* centrum coplanar */
-  MRGanglecoplanar,     /* angle coplanar */
-                        /* could detect half concave ridges */
-  MRGconcave,           /* concave ridge */
-  MRGflip,              /* flipped facet. facet1 == facet2 */
-  MRGridge,             /* duplicate ridge (qh_MERGEridge) */
-                        /* degen and redundant go onto degen_mergeset */
-  MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
-  MRGredundant,         /* redundant facet (vertex subset) */
-                        /* merge_degenredundant assumes degen < redundant */
-  MRGmirror,            /* mirror facet from qh_triangulate */
-  ENDmrg
-} mergeType;
-
-/*----------------------------------
-
-  qh_MERGEapex
-    flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex     True
-
-/*============ -structures- ====================*/
-
-/*----------------------------------
-
-  mergeT
-    structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT {         /* initialize in qh_appendmergeset */
-  realT   angle;        /* angle between normals of facet1 and facet2 */
-  facetT *facet1;       /* will merge facet1 into facet2 */
-  facetT *facet2;
-  mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FOREACHmerge_( merges ) {...}
-    assign 'merge' to each merge in merges
-
-  notes:
-    uses 'mergeT *merge, **mergep;'
-    if qh_mergefacet(),
-      restart since qh.facet_mergeset may change
-    see FOREACHsetelement_
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void    qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle);
-void    qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
-             boolT vneighbors);
-void    qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors);
-void    qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
-setT   *qh_basevertices(qhT *qh, facetT *samecycle);
-void    qh_checkconnect(qhT *qh /* qh.new_facets */);
-boolT   qh_checkzero(qhT *qh, boolT testall);
-int     qh_compareangle(const void *p1, const void *p2);
-int     qh_comparemerge(const void *p1, const void *p2);
-int     qh_comparevisit(const void *p1, const void *p2);
-void    qh_copynonconvex(qhT *qh, ridgeT *atridge);
-void    qh_degen_redundant_facet(qhT *qh, facetT *facet);
-void    qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet);
-vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges);
-void    qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
-           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
-facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
-void    qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge);
-void    qh_forcedmerges(qhT *qh, boolT *wasmerge);
-void    qh_getmergeset(qhT *qh, facetT *facetlist);
-void    qh_getmergeset_initial(qhT *qh, facetT *facetlist);
-void    qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
-ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot);
-void    qh_makeridges(qhT *qh, facetT *facet);
-void    qh_mark_dupridges(qhT *qh, facetT *facetlist);
-void    qh_maydropneighbor(qhT *qh, facetT *facet);
-int     qh_merge_degenredundant(qhT *qh);
-void    qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype);
-void    qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge);
-void    qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
-void    qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
-void    qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2);
-void    qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2);
-void    qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2);
-void    qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex);
-void    qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2);
-void    qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2);
-void    qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices);
-setT   *qh_neighbor_intersections(qhT *qh, vertexT *vertex);
-void    qh_newvertices(qhT *qh, setT *vertices);
-boolT   qh_reducevertices(qhT *qh);
-vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex);
-boolT   qh_remove_extravertices(qhT *qh, facetT *facet);
-vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet);
-void    qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
-void    qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges,
-                        facetT *oldfacet, facetT *neighborA);
-boolT   qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor);
-boolT   qh_test_vneighbors(qhT *qh /* qh.newfacet_list */);
-void    qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2);
-void    qh_tracemerging(qhT *qh);
-void    qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2);
-setT   *qh_vertexridges(qhT *qh, vertexT *vertex);
-void    qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges);
-void    qh_willdelete(qhT *qh, facetT *facet, facetT *replace);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFmerge */
diff --git a/src/qhull/src/libqhull_r/poly2_r.c b/src/qhull/src/libqhull_r/poly2_r.c
deleted file mode 100644
index b8ae9af9f..000000000
--- a/src/qhull/src/libqhull_r/poly2_r.c
+++ /dev/null
@@ -1,3222 +0,0 @@
-/*
      ---------------------------------
-
-   poly2_r.c
-   implements polygons and simplicies
-
-   see qh-poly_r.htm, poly_r.h and libqhull_r.h
-
-   frequently used code is in poly_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/poly2_r.c#10 $$Change: 2069 $
-   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_addhash( newelem, hashtable, hashsize, hash )
-    add newelem to linear hash table at hash if not already there
-*/
-void qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash) {
-  int scan;
-  void *elem;
-
-  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (elem == newelem)
-      break;
-  }
-  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
-  if (!elem)
-    SETelem_(hashtable, scan)= newelem;
-} /* addhash */
-
-/*---------------------------------
-
-  qh_check_bestdist(qh)
-    check that all points are within max_outside of the nearest facet
-    if qh.ONLYgood,
-      ignores !good facets
-
-  see:
-    qh_check_maxout(), qh_outerinner()
-
-  notes:
-    only called from qh_check_points()
-      seldom used since qh.MERGING is almost always set
-    if notverified>0 at end of routine
-      some points were well inside the hull.  If the hull contains
-      a lens-shaped component, these points were not verified.  Use
-      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
-
-  design:
-    determine facet for each point (if any)
-    for each point
-      start with the assigned facet or with the first facet
-      find the best facet for the point and check all coplanar facets
-      error if point is outside of facet
-*/
-void qh_check_bestdist(qhT *qh) {
-  boolT waserror= False, unassigned;
-  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
-  facetT *facetlist;
-  realT dist, maxoutside, maxdist= -REALmax;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
-  setT *facets;
-
-  trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
-      qh->facet_list->id));
-  maxoutside= qh_maxouter(qh);
-  maxoutside += qh->DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
-  facets= qh_pointfacet(qh /*qh.facet_list*/);
-  if (!qh_QUICKhelp && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 8091, "\n\
-qhull output completed.  Verifying that %d points are\n\
-below %2.2g of the nearest %sfacet.\n",
-             qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ?  "good " : ""));
-  FOREACHfacet_i_(qh, facets) {  /* for each point with facet assignment */
-    if (facet)
-      unassigned= False;
-    else {
-      unassigned= True;
-      facet= qh->facet_list;
-    }
-    point= qh_point(qh, facet_i);
-    if (point == qh->GOODpointp)
-      continue;
-    qh_distplane(qh, point, facet, &dist);
-    numpart++;
-    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
-    /* occurs after statistics reported */
-    maximize_(maxdist, dist);
-    if (dist > maxoutside) {
-      if (qh->ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-        notgood++;
-      else {
-        waserror= True;
-        qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-                facet_i, bestfacet->id, dist, maxoutside);
-        if (errfacet1 != bestfacet) {
-          errfacet2= errfacet1;
-          errfacet1= bestfacet;
-        }
-      }
-    }else if (unassigned && dist < -qh->MAXcoplanar)
-      notverified++;
-  }
-  qh_settempfree(qh, &facets);
-  if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
-    qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
-a lens-shaped component, these points were not verified.  Use\n\
-options 'Qci Tv' to verify all points.\n", notverified);
-  if (maxdist > qh->outside_err) {
-    qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-              maxdist, qh->outside_err);
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-  }else if (waserror && qh->outside_err > REALmax/2)
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
-  trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
-} /* check_bestdist */
-
-/*---------------------------------
-
-  qh_check_dupridge(qh, facet1, dist1, facet2, dist2)
-    Check duplicate ridge between facet1 and facet2 for wide merge
-    dist1 is the maximum distance of facet1's vertices to facet2
-    dist2 is the maximum distance of facet2's vertices to facet1
-
-  Returns
-    Level 1 log of the duplicate ridge with the minimum distance between vertices
-    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
-
-  called from:
-    qh_forcedmerges()
-*/
-#ifndef qh_NOmerge
-void qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
-  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
-  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
-  realT minvertex= REALmax;
-
-  mergedist= fmin_(dist1, dist2);
-  qh_outerinner(qh, NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
-  prevdist= fmax_(outerplane, innerplane);
-  maximize_(prevdist, qh->ONEmerge + qh->DISTround);
-  maximize_(prevdist, qh->MINoutside + qh->DISTround);
-  ratio= mergedist/prevdist;
-  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
-    FOREACHvertexA_(facet1->vertices) {
-      if (vertex > vertexA){   /* Test each pair once */
-        dist= qh_pointdist(vertex->point, vertexA->point, qh->hull_dim);
-        minimize_(minvertex, dist);
-      }
-    }
-  }
-  trace0((qh, qh->ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
-        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh->furthest_id));
-  if (ratio > qh_WIDEduplicate) {
-    qh_fprintf(qh, qh->ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
-          ratio, minvertex, facet1->id, facet2->id, mergedist, qh->furthest_id);
-    if (qh->DELAUNAY)
-      qh_fprintf(qh, qh->ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
-    if(minvertex > qh_WIDEduplicate*prevdist)
-      qh_fprintf(qh, qh->ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
-          minvertex, qh_WIDEduplicate, prevdist);
-    if (!qh->NOwide)
-      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
-  }
-} /* check_dupridge */
-#endif
-
-/*---------------------------------
-
-  qh_check_maxout(qh)
-    updates qh.max_outside by checking all points against bestfacet
-    if qh.ONLYgood, ignores !good facets
-
-  returns:
-    updates facet->maxoutside via qh_findbesthorizon()
-    sets qh.maxoutdone
-    if printing qh.min_vertex (qh_outerinner),
-      it is updated to the current vertices
-    removes inside/coplanar points from coplanarset as needed
-
-  notes:
-    defines coplanar as min_vertex instead of MAXcoplanar
-    may not need to check near-inside points because of qh.MAXcoplanar
-      and qh.KEEPnearinside (before it was -DISTround)
-
-  see also:
-    qh_check_bestdist()
-
-  design:
-    if qh.min_vertex is needed
-      for all neighbors of all vertices
-        test distance from vertex to neighbor
-    determine facet for each point (if any)
-    for each point with an assigned facet
-      find the best facet for the point and check all coplanar facets
-        (updates outer planes)
-    remove near-inside points from coplanar sets
-*/
-#ifndef qh_NOmerge
-void qh_check_maxout(qhT *qh) {
-  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
-  realT dist, maxoutside, minvertex, old_maxoutside;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0;
-  setT *facets, *vertices;
-  vertexT *vertex;
-
-  trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
-  maxoutside= minvertex= 0;
-  if (qh->VERTEXneighbors
-  && (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
-        || qh->TRACElevel || qh->PRINTstatistics
-        || qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
-    trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
-    vertices= qh_pointvertex(qh /*qh.facet_list*/);
-    FORALLvertices {
-      FOREACHneighbor_(vertex) {
-        zinc_(Zdistvertex);  /* distance also computed by main loop below */
-        qh_distplane(qh, vertex->point, neighbor, &dist);
-        minimize_(minvertex, dist);
-        if (-dist > qh->TRACEdist || dist > qh->TRACEdist
-        || neighbor == qh->tracefacet || vertex == qh->tracevertex)
-          qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
-                    qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
-      }
-    }
-    if (qh->MERGING) {
-      wmin_(Wminvertex, qh->min_vertex);
-    }
-    qh->min_vertex= minvertex;
-    qh_settempfree(qh, &vertices);
-  }
-  facets= qh_pointfacet(qh /*qh.facet_list*/);
-  do {
-    old_maxoutside= fmax_(qh->max_outside, maxoutside);
-    FOREACHfacet_i_(qh, facets) {     /* for each point with facet assignment */
-      if (facet) {
-        point= qh_point(qh, facet_i);
-        if (point == qh->GOODpointp)
-          continue;
-        zzinc_(Ztotcheck);
-        qh_distplane(qh, point, facet, &dist);
-        numpart++;
-        bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
-        if (bestfacet && dist > maxoutside) {
-          if (qh->ONLYgood && !bestfacet->good
-          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
-               && dist > maxoutside))
-            notgood++;
-          else
-            maxoutside= dist;
-        }
-        if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
-          qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
-          qh_pointid(qh, point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
-      }
-    }
-  }while
-    (maxoutside > 2*old_maxoutside);
-    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
-          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
-  zzadd_(Zcheckpart, numpart);
-  qh_settempfree(qh, &facets);
-  wval_(Wmaxout)= maxoutside - qh->max_outside;
-  wmax_(Wmaxoutside, qh->max_outside);
-  qh->max_outside= maxoutside;
-  qh_nearcoplanar(qh /*qh.facet_list*/);
-  qh->maxoutdone= True;
-  trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
-       maxoutside, qh->min_vertex, notgood));
-} /* check_maxout */
-#else /* qh_NOmerge */
-void qh_check_maxout(qhT *qh) {
-}
-#endif
-
-/*---------------------------------
-
-  qh_check_output(qh)
-    performs the checks at the end of qhull algorithm
-    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
-*/
-void qh_check_output(qhT *qh) {
-  int i;
-
-  if (qh->STOPcone)
-    return;
-  if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
-    qh_checkpolygon(qh, qh->facet_list);
-    qh_checkflipped_all(qh, qh->facet_list);
-    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
-    qh_checkflipped_all(qh, qh->facet_list);
-    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
-  }
-} /* check_output */
-
-
-
-/*---------------------------------
-
-  qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
-    check that point is less than maxoutside from facet
-*/
-void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
-  realT dist;
-
-  /* occurs after statistics reported */
-  qh_distplane(qh, point, facet, &dist);
-  if (dist > *maxoutside) {
-    if (*errfacet1 != facet) {
-      *errfacet2= *errfacet1;
-      *errfacet1= facet;
-    }
-    qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-              qh_pointid(qh, point), facet->id, dist, *maxoutside);
-  }
-  maximize_(*maxdist, dist);
-} /* qh_check_point */
-
-
-/*---------------------------------
-
-  qh_check_points(qh)
-    checks that all points are inside all facets
-
-  notes:
-    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
-       calls qh_findbesthorizon (seldom done).
-    ignores flipped facets
-    maxoutside includes 2 qh.DISTrounds
-      one qh.DISTround for the computed distances in qh_check_points
-    qh_printafacet and qh_printsummary needs only one qh.DISTround
-    the computation for qh.VERIFYdirect does not account for qh.other_points
-
-  design:
-    if many points
-      use qh_check_bestdist()
-    else
-      for all facets
-        for all points
-          check that point is inside facet
-*/
-void qh_check_points(qhT *qh) {
-  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
-  realT total, maxoutside, maxdist= -REALmax;
-  pointT *point, **pointp, *pointtemp;
-  boolT testouter;
-
-  maxoutside= qh_maxouter(qh);
-  maxoutside += qh->DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
-          maxoutside));
-  if (qh->num_good)   /* miss counts other_points and !good facets */
-     total= (float)qh->num_good * (float)qh->num_points;
-  else
-     total= (float)qh->num_facets * (float)qh->num_points;
-  if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
-    if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
-      qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
-Verify may report that a point is outside of a facet.\n");
-    qh_check_bestdist(qh);
-  }else {
-    if (qh_MAXoutside && qh->maxoutdone)
-      testouter= True;
-    else
-      testouter= False;
-    if (!qh_QUICKhelp) {
-      if (qh->MERGEexact)
-        qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
-is outside of a facet.  See qh-optq.htm#Qx\n");
-      else if (qh->SKIPcheckmax || qh->NOnearinside)
-        qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
-near-inside points ('Q8').  Verify may report that a point is outside\n\
-of a facet.\n");
-    }
-    if (qh->PRINTprecision) {
-      if (testouter)
-        qh_fprintf(qh, qh->ferr, 8098, "\n\
-Output completed.  Verifying that all points are below outer planes of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              (qh->ONLYgood ?  "good " : ""), total);
-      else
-        qh_fprintf(qh, qh->ferr, 8099, "\n\
-Output completed.  Verifying that all points are below %2.2g of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-              maxoutside, (qh->ONLYgood ?  "good " : ""), total);
-    }
-    FORALLfacets {
-      if (!facet->good && qh->ONLYgood)
-        continue;
-      if (facet->flipped)
-        continue;
-      if (!facet->normal) {
-        qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
-        continue;
-      }
-      if (testouter) {
-#if qh_MAXoutside
-        maxoutside= facet->maxoutside + 2* qh->DISTround;
-        /* one DISTround to actual point and another to computed point */
-#endif
-      }
-      FORALLpoints {
-        if (point != qh->GOODpointp)
-          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-      FOREACHpoint_(qh->other_points) {
-        if (point != qh->GOODpointp)
-          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-    }
-    if (maxdist > qh->outside_err) {
-      qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
-                maxdist, qh->outside_err );
-      qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
-    }else if (errfacet1 && qh->outside_err > REALmax/2)
-        qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
-    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
-    trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
-  }
-} /* check_points */
-
-
-/*---------------------------------
-
-  qh_checkconvex(qh, facetlist, fault )
-    check that each ridge in facetlist is convex
-    fault = qh_DATAfault if reporting errors
-          = qh_ALGORITHMfault otherwise
-
-  returns:
-    counts Zconcaveridges and Zcoplanarridges
-    errors if concaveridge or if merging an coplanar ridge
-
-  note:
-    if not merging,
-      tests vertices for neighboring simplicial facets
-    else if ZEROcentrum,
-      tests vertices for neighboring simplicial   facets
-    else
-      tests centrums of neighboring facets
-
-  design:
-    for all facets
-      report flipped facets
-      if ZEROcentrum and simplicial neighbors
-        test vertices for neighboring simplicial facets
-      else
-        test centrum against all neighbors
-*/
-void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
-  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
-  vertexT *vertex;
-  realT dist;
-  pointT *centrum;
-  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
-  int neighbor_i;
-
-  trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
-  if (!qh->RERUN) {
-    zzval_(Zconcaveridges)= 0;
-    zzval_(Zcoplanarridges)= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->flipped) {
-      qh_precision(qh, "flipped facet");
-      qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
-               facet->id);
-      errfacet1= facet;
-      waserror= True;
-      continue;
-    }
-    if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
-      allsimplicial= False;
-    else {
-      allsimplicial= True;
-      neighbor_i= 0;
-      FOREACHneighbor_(facet) {
-        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-        if (!neighbor->simplicial || neighbor->tricoplanar) {
-          allsimplicial= False;
-          continue;
-        }
-        qh_distplane(qh, vertex->point, neighbor, &dist);
-        if (dist > -qh->DISTround) {
-          if (fault == qh_DATAfault) {
-            qh_precision(qh, "coplanar or concave ridge");
-            qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
-            qh_errexit(qh, qh_ERRsingular, NULL, NULL);
-          }
-          if (dist > qh->DISTround) {
-            zzinc_(Zconcaveridges);
-            qh_precision(qh, "concave ridge");
-            qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
-              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
-            errfacet1= facet;
-            errfacet2= neighbor;
-            waserror= True;
-          }else if (qh->ZEROcentrum) {
-            if (dist > 0) {     /* qh_checkzero checks that dist < - qh->DISTround */
-              zzinc_(Zcoplanarridges);
-              qh_precision(qh, "coplanar ridge");
-              qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
-                facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
-              errfacet1= facet;
-              errfacet2= neighbor;
-              waserror= True;
-            }
-          }else {
-            zzinc_(Zcoplanarridges);
-            qh_precision(qh, "coplanar ridge");
-            trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
-              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
-          }
-        }
-      }
-    }
-    if (!allsimplicial) {
-      if (qh->CENTERtype == qh_AScentrum) {
-        if (!facet->center)
-          facet->center= qh_getcentrum(qh, facet);
-        centrum= facet->center;
-      }else {
-        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
-           centrum_warning= True;
-           qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
-        }
-        centrum= qh_getcentrum(qh, facet);
-        tempcentrum= True;
-      }
-      FOREACHneighbor_(facet) {
-        if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
-          continue;
-        if (facet->tricoplanar || neighbor->tricoplanar)
-          continue;
-        zzinc_(Zdistconvex);
-        qh_distplane(qh, centrum, neighbor, &dist);
-        if (dist > qh->DISTround) {
-          zzinc_(Zconcaveridges);
-          qh_precision(qh, "concave ridge");
-          qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
-                                     can test against centrum radius instead */
-          zzinc_(Zcoplanarridges);
-          qh_precision(qh, "coplanar ridge");
-          qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-        }
-      }
-      if (tempcentrum)
-        qh_memfree(qh, centrum, qh->normal_size);
-    }
-  }
-  if (waserror && !qh->FORCEoutput)
-    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
-} /* checkconvex */
-
-
-/*---------------------------------
-
-  qh_checkfacet(qh, facet, newmerge, waserror )
-    checks for consistency errors in facet
-    newmerge set if from merge_r.c
-
-  returns:
-    sets waserror if any error occurs
-
-  checks:
-    vertex ids are inverse sorted
-    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
-    if non-simplicial, at least as many ridges as neighbors
-    neighbors are not duplicated
-    ridges are not duplicated
-    in 3-d, ridges=verticies
-    (qh.hull_dim-1) ridge vertices
-    neighbors are reciprocated
-    ridge neighbors are facet neighbors and a ridge for every neighbor
-    simplicial neighbors match facetintersect
-    vertex intersection matches vertices of common ridges
-    vertex neighbors and facet vertices agree
-    all ridges have distinct vertex sets
-
-  notes:
-    uses neighbor->seen
-
-  design:
-    check sets
-    check vertices
-    check sizes of neighbors and vertices
-    check for qh_MERGEridge and qh_DUPLICATEridge flags
-    check neighbor set
-    check ridge set
-    check ridges, neighbors, and vertices
-*/
-void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
-  facetT *neighbor, **neighborp, *errother=NULL;
-  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
-  vertexT *vertex, **vertexp;
-  unsigned previousid= INT_MAX;
-  int numneighbors, numvertices, numridges=0, numRvertices=0;
-  boolT waserror= False;
-  int skipA, skipB, ridge_i, ridge_n, i;
-  setT *intersection;
-
-  if (facet->visible) {
-    qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
-      facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  if (!facet->normal) {
-    qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
-      facet->id);
-    waserror= True;
-  }
-  qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
-  qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
-  qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
-  qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
-  qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
-  FOREACHvertex_(facet->vertices) {
-    if (vertex->deleted) {
-      qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
-      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-      waserror= True;
-    }
-    if (vertex->id >= previousid) {
-      qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
-      waserror= True;
-      break;
-    }
-    previousid= vertex->id;
-  }
-  numneighbors= qh_setsize(qh, facet->neighbors);
-  numvertices= qh_setsize(qh, facet->vertices);
-  numridges= qh_setsize(qh, facet->ridges);
-  if (facet->simplicial) {
-    if (numvertices+numneighbors != 2*qh->hull_dim
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
-                facet->id, numvertices, numneighbors);
-      qh_setprint(qh, qh->ferr, "", facet->neighbors);
-      waserror= True;
-    }
-  }else { /* non-simplicial */
-    if (!newmerge
-    &&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
-    && !facet->degenerate && !facet->redundant) {
-      qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
-         facet->id, numvertices, numneighbors);
-       waserror= True;
-    }
-    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
-    if (numridges < numneighbors
-    ||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
-    ||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
-      if (!facet->degenerate && !facet->redundant) {
-        qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
-            facet->id, numridges, numneighbors, numvertices);
-        waserror= True;
-      }
-    }
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
-      qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    neighbor->seen= True;
-  }
-  FOREACHneighbor_(facet) {
-    if (!qh_setin(neighbor->neighbors, facet)) {
-      qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
-              facet->id, neighbor->id, neighbor->id, facet->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    if (!neighbor->seen) {
-      qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
-              facet->id, neighbor->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
-    ridge->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    if (ridge->seen) {
-      qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
-              facet->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-    ridge->seen= True;
-    numRvertices= qh_setsize(qh, ridge->vertices);
-    if (numRvertices != qh->hull_dim - 1) {
-      qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
-                ridge->top->id, ridge->bottom->id, numRvertices);
-      errridge= ridge;
-      waserror= True;
-    }
-    neighbor= otherfacet_(ridge, facet);
-    neighbor->seen= True;
-    if (!qh_setin(facet->neighbors, neighbor)) {
-      qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
-           facet->id, neighbor->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-  }
-  if (!facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen) {
-        qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
-              facet->id, neighbor->id);
-        errother= neighbor;
-        waserror= True;
-      }
-      intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
-      qh_settemppush(qh, intersection);
-      FOREACHvertex_(facet->vertices) {
-        vertex->seen= False;
-        vertex->seen2= False;
-      }
-      FOREACHvertex_(intersection)
-        vertex->seen= True;
-      FOREACHridge_(facet->ridges) {
-        if (neighbor != otherfacet_(ridge, facet))
-            continue;
-        FOREACHvertex_(ridge->vertices) {
-          if (!vertex->seen) {
-            qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
-                  vertex->id, ridge->id, facet->id, neighbor->id);
-            qh_errexit(qh, qh_ERRqhull, facet, ridge);
-          }
-          vertex->seen2= True;
-        }
-      }
-      if (!newmerge) {
-        FOREACHvertex_(intersection) {
-          if (!vertex->seen2) {
-            if (qh->IStracing >=3 || !qh->MERGING) {
-              qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
- not in a ridge.  This is ok under merging.  Last point was p%d\n",
-                     vertex->id, facet->id, neighbor->id, qh->furthest_id);
-              if (!qh->FORCEoutput && !qh->MERGING) {
-                qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
-                if (!qh->MERGING)
-                  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-              }
-            }
-          }
-        }
-      }
-      qh_settempfree(qh, &intersection);
-    }
-  }else { /* simplicial */
-    FOREACHneighbor_(facet) {
-      if (neighbor->simplicial) {
-        skipA= SETindex_(facet->neighbors, neighbor);
-        skipB= qh_setindex(neighbor->neighbors, facet);
-        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
-          qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
-                   facet->id, skipA, neighbor->id, skipB);
-          errother= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
-    FOREACHridge_i_(qh, facet->ridges) {           /* expensive */
-      for (i=ridge_i+1; i < ridge_n; i++) {
-        ridge2= SETelemt_(facet->ridges, i, ridgeT);
-        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
-          qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
-                  ridge->id, ridge2->id);
-          errridge= ridge;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
-    *waserrorp= True;
-  }
-} /* checkfacet */
-
-
-/*---------------------------------
-
-  qh_checkflipped_all(qh, facetlist )
-    checks orientation of facets in list against interior point
-*/
-void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
-  facetT *facet;
-  boolT waserror= False;
-  realT dist;
-
-  if (facetlist == qh->facet_list)
-    zzval_(Zflippedfacets)= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
-      qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
-              facet->id, dist);
-      if (!qh->FORCEoutput) {
-        qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
-        waserror= True;
-      }
-    }
-  }
-  if (waserror) {
-    qh_fprintf(qh, qh->ferr, 8101, "\n\
-A flipped facet occurs when its distance to the interior point is\n\
-greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
-    qh_errexit(qh, qh_ERRprec, NULL, NULL);
-  }
-} /* checkflipped_all */
-
-/*---------------------------------
-
-  qh_checkpolygon(qh, facetlist )
-    checks the correctness of the structure
-
-  notes:
-    call with either qh.facet_list or qh.newfacet_list
-    checks num_facets and num_vertices if qh.facet_list
-
-  design:
-    for each facet
-      checks facet and outside set
-    initializes vertexlist
-    for each facet
-      checks vertex set
-    if checking all facets(qh.facetlist)
-      check facet count
-      if qh.VERTEXneighbors
-        check vertex neighbors and count
-      check vertex count
-*/
-void qh_checkpolygon(qhT *qh, facetT *facetlist) {
-  facetT *facet;
-  vertexT *vertex, **vertexp, *vertexlist;
-  int numfacets= 0, numvertices= 0, numridges= 0;
-  int totvneighbors= 0, totvertices= 0;
-  boolT waserror= False, nextseen= False, visibleseen= False;
-
-  trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
-  if (facetlist != qh->facet_list || qh->ONLYgood)
-    nextseen= True;
-  FORALLfacet_(facetlist) {
-    if (facet == qh->visible_list)
-      visibleseen= True;
-    if (!facet->visible) {
-      if (!nextseen) {
-        if (facet == qh->facet_next)
-          nextseen= True;
-        else if (qh_setsize(qh, facet->outsideset)) {
-          if (!qh->NARROWhull
-#if !qh_COMPUTEfurthest
-               || facet->furthestdist >= qh->MINoutside
-#endif
-                        ) {
-            qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
-                     facet->id);
-            qh_errexit(qh, qh_ERRqhull, facet, NULL);
-          }
-        }
-      }
-      numfacets++;
-      qh_checkfacet(qh, facet, False, &waserror);
-    }
-  }
-  if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
-    qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
-    qh_printlists(qh);
-    qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
-  }
-  if (facetlist == qh->facet_list)
-    vertexlist= qh->vertex_list;
-  else if (facetlist == qh->newfacet_list)
-    vertexlist= qh->newvertex_list;
-  else
-    vertexlist= NULL;
-  FORALLvertex_(vertexlist) {
-    vertex->seen= False;
-    vertex->visitid= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visible)
-      continue;
-    if (facet->simplicial)
-      numridges += qh->hull_dim;
-    else
-      numridges += qh_setsize(qh, facet->ridges);
-    FOREACHvertex_(facet->vertices) {
-      vertex->visitid++;
-      if (!vertex->seen) {
-        vertex->seen= True;
-        numvertices++;
-        if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
-          qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
-                   vertex->point, vertex->id, qh->first_point);
-          waserror= True;
-        }
-      }
-    }
-  }
-  qh->vertex_visit += (unsigned int)numfacets;
-  if (facetlist == qh->facet_list) {
-    if (numfacets != qh->num_facets - qh->num_visible) {
-      qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
-              numfacets, qh->num_facets, qh->num_visible);
-      waserror= True;
-    }
-    qh->vertex_visit++;
-    if (qh->VERTEXneighbors) {
-      FORALLvertices {
-        qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
-        if (vertex->deleted)
-          continue;
-        totvneighbors += qh_setsize(qh, vertex->neighbors);
-      }
-      FORALLfacet_(facetlist)
-        totvertices += qh_setsize(qh, facet->vertices);
-      if (totvneighbors != totvertices) {
-        qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
-                totvneighbors, totvertices);
-        waserror= True;
-      }
-    }
-    if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
-      qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
-              numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
-      waserror= True;
-    }
-    if (qh->hull_dim == 2 && numvertices != numfacets) {
-      qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
-        numvertices, numfacets);
-      waserror= True;
-    }
-    if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
-      qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
-        A vertex appears twice in a edge list.  May occur during merging.",
-        numvertices, numfacets, numridges/2);
-      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
-    }
-  }
-  if (waserror)
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-} /* checkpolygon */
-
-
-/*---------------------------------
-
-  qh_checkvertex(qh, vertex )
-    check vertex for consistency
-    checks vertex->neighbors
-
-  notes:
-    neighbors checked efficiently in checkpolygon
-*/
-void qh_checkvertex(qhT *qh, vertexT *vertex) {
-  boolT waserror= False;
-  facetT *neighbor, **neighborp, *errfacet=NULL;
-
-  if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
-    qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
-    waserror= True;
-  }
-  if (vertex->id >= qh->vertex_id) {
-    qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
-    waserror= True;
-  }
-  if (!waserror && !vertex->deleted) {
-    if (qh_setsize(qh, vertex->neighbors)) {
-      FOREACHneighbor_(vertex) {
-        if (!qh_setin(neighbor->vertices, vertex)) {
-          qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
-          errfacet= neighbor;
-          waserror= True;
-        }
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
-    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
-  }
-} /* checkvertex */
-
-/*---------------------------------
-
-  qh_clearcenters(qh, type )
-    clear old data from facet->center
-
-  notes:
-    sets new centertype
-    nop if CENTERtype is the same
-*/
-void qh_clearcenters(qhT *qh, qh_CENTER type) {
-  facetT *facet;
-
-  if (qh->CENTERtype != type) {
-    FORALLfacets {
-      if (facet->tricoplanar && !facet->keepcentrum)
-          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
-      else if (qh->CENTERtype == qh_ASvoronoi){
-        if (facet->center) {
-          qh_memfree(qh, facet->center, qh->center_size);
-          facet->center= NULL;
-        }
-      }else /* qh->CENTERtype == qh_AScentrum */ {
-        if (facet->center) {
-          qh_memfree(qh, facet->center, qh->normal_size);
-          facet->center= NULL;
-        }
-      }
-    }
-    qh->CENTERtype= type;
-  }
-  trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
-} /* clearcenters */
-
-/*---------------------------------
-
-  qh_createsimplex(qh, vertices )
-    creates a simplex from a set of vertices
-
-  returns:
-    initializes qh.facet_list to the simplex
-    initializes qh.newfacet_list, .facet_tail
-    initializes qh.vertex_list, .newvertex_list, .vertex_tail
-
-  design:
-    initializes lists
-    for each vertex
-      create a new facet
-    for each new facet
-      create its neighbor set
-*/
-void qh_createsimplex(qhT *qh, setT *vertices) {
-  facetT *facet= NULL, *newfacet;
-  boolT toporient= True;
-  int vertex_i, vertex_n, nth;
-  setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
-  vertexT *vertex;
-
-  qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
-  qh->num_facets= qh->num_vertices= qh->num_visible= 0;
-  qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
-  FOREACHvertex_i_(qh, vertices) {
-    newfacet= qh_newfacet(qh);
-    newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
-                                                vertex_i, 0);
-    newfacet->toporient= (unsigned char)toporient;
-    qh_appendfacet(qh, newfacet);
-    newfacet->newfacet= True;
-    qh_appendvertex(qh, vertex);
-    qh_setappend(qh, &newfacets, newfacet);
-    toporient ^= True;
-  }
-  FORALLnew_facets {
-    nth= 0;
-    FORALLfacet_(qh->newfacet_list) {
-      if (facet != newfacet)
-        SETelem_(newfacet->neighbors, nth++)= facet;
-    }
-    qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
-  }
-  qh_settempfree(qh, &newfacets);
-  trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
-} /* createsimplex */
-
-/*---------------------------------
-
-  qh_delridge(qh, ridge )
-    deletes ridge from data structures it belongs to
-    frees up its memory
-
-  notes:
-    in merge_r.c, caller sets vertex->delridge for each vertex
-    ridges also freed in qh_freeqhull
-*/
-void qh_delridge(qhT *qh, ridgeT *ridge) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  qh_setdel(ridge->top->ridges, ridge);
-  qh_setdel(ridge->bottom->ridges, ridge);
-  qh_setfree(qh, &(ridge->vertices));
-  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-} /* delridge */
-
-
-/*---------------------------------
-
-  qh_delvertex(qh, vertex )
-    deletes a vertex and frees its memory
-
-  notes:
-    assumes vertex->adjacencies have been updated if needed
-    unlinks from vertex_list
-*/
-void qh_delvertex(qhT *qh, vertexT *vertex) {
-
-  if (vertex == qh->tracevertex)
-    qh->tracevertex= NULL;
-  qh_removevertex(qh, vertex);
-  qh_setfree(qh, &vertex->neighbors);
-  qh_memfree(qh, vertex, (int)sizeof(vertexT));
-} /* delvertex */
-
-
-/*---------------------------------
-
-  qh_facet3vertex(qh, )
-    return temporary set of 3-d vertices in qh_ORIENTclock order
-
-  design:
-    if simplicial facet
-      build set from facet->vertices with facet->toporient
-    else
-      for each ridge in order
-        build set from ridge's vertices
-*/
-setT *qh_facet3vertex(qhT *qh, facetT *facet) {
-  ridgeT *ridge, *firstridge;
-  vertexT *vertex;
-  int cntvertices, cntprojected=0;
-  setT *vertices;
-
-  cntvertices= qh_setsize(qh, facet->vertices);
-  vertices= qh_settemp(qh, cntvertices);
-  if (facet->simplicial) {
-    if (cntvertices != 3) {
-      qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
-                  cntvertices, facet->id);
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
-    if (facet->toporient ^ qh_ORIENTclock)
-      qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
-    else
-      qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
-    qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
-  }else {
-    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
-    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
-      qh_setappend(qh, &vertices, vertex);
-      if (++cntprojected > cntvertices || ridge == firstridge)
-        break;
-    }
-    if (!ridge || cntprojected != cntvertices) {
-      qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
-                  facet->id, cntprojected);
-      qh_errexit(qh, qh_ERRqhull, facet, ridge);
-    }
-  }
-  return vertices;
-} /* facet3vertex */
-
-/*---------------------------------
-
-  qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
-    find facet that is furthest below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    if bestoutside is set (e.g., qh_ALL)
-      returns best facet that is not upperdelaunay
-      if Delaunay and inside, point is outside circumsphere of bestfacet
-    else
-      returns first facet below point
-      if point is inside, returns nearest, !upperdelaunay facet
-    distance to facet
-    isoutside set if outside of facet
-
-  notes:
-    For tricoplanar facets, this finds one of the tricoplanar facets closest
-    to the point.  For Delaunay triangulations, the point may be inside a
-    different tricoplanar facet. See locate a facet with qh_findbestfacet()
-
-    If inside, qh_findbestfacet performs an exhaustive search
-       this may be too conservative.  Sometimes it is clearly required.
-
-    qh_findbestfacet is not used by qhull.
-    uses qh.visit_id and qh.coplanarset
-
-  see:
-    qh_findbest
-*/
-facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside) {
-  facetT *bestfacet= NULL;
-  int numpart, totpart= 0;
-
-  bestfacet= qh_findbest(qh, point, qh->facet_list,
-                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
-                            bestdist, isoutside, &totpart);
-  if (*bestdist < -qh->DISTround) {
-    bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
-    totpart += numpart;
-    if ((isoutside && *isoutside && bestoutside)
-    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
-      bestfacet= qh_findbest(qh, point, bestfacet,
-                            bestoutside, False, bestoutside,
-                            bestdist, isoutside, &totpart);
-      totpart += numpart;
-    }
-  }
-  trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
-          bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
-  return bestfacet;
-} /* findbestfacet */
-
-/*---------------------------------
-
-  qh_findbestlower(qh, facet, point, bestdist, numpart )
-    returns best non-upper, non-flipped neighbor of facet for point
-    if needed, searches vertex neighbors
-
-  returns:
-    returns bestdist and updates numpart
-
-  notes:
-    if Delaunay and inside, point is outside of circumsphere of bestfacet
-    called by qh_findbest() for points above an upperdelaunay facet
-
-*/
-facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  realT dist;
-  vertexT *vertex;
-  boolT isoutside= False;  /* not used */
-
-  zinc_(Zbestlower);
-  FOREACHneighbor_(upperfacet) {
-    if (neighbor->upperdelaunay || neighbor->flipped)
-      continue;
-    (*numpart)++;
-    qh_distplane(qh, point, neighbor, &dist);
-    if (dist > bestdist) {
-      bestfacet= neighbor;
-      bestdist= dist;
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerv);
-    /* rarely called, numpart does not count nearvertex computations */
-    vertex= qh_nearvertex(qh, upperfacet, point, &dist);
-    qh_vertexneighbors(qh);
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay || neighbor->flipped)
-        continue;
-      (*numpart)++;
-      qh_distplane(qh, point, neighbor, &dist);
-      if (dist > bestdist) {
-        bestfacet= neighbor;
-        bestdist= dist;
-      }
-    }
-  }
-  if (!bestfacet) {
-    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
-    zmax_(Zbestloweralln, qh->num_facets);
-    /* [dec'15] Previously reported as QH6228 */
-    trace3((qh, qh->ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
-       upperfacet->id));
-    /* rarely called */
-    bestfacet= qh_findfacet_all(qh, point, &bestdist, &isoutside, numpart);
-  }
-  *bestdistp= bestdist;
-  trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
-          bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
-  return bestfacet;
-} /* findbestlower */
-
-/*---------------------------------
-
-  qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
-    exhaustive search for facet below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns first facet below point
-    if point is inside,
-      returns nearest facet
-    distance to facet
-    isoutside if point is outside of the hull
-    number of distance tests
-
-  notes:
-    primarily for library users, rarely used by Qhull
-*/
-facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
-                          int *numpart) {
-  facetT *bestfacet= NULL, *facet;
-  realT dist;
-  int totpart= 0;
-
-  *bestdist= -REALmax;
-  *isoutside= False;
-  FORALLfacets {
-    if (facet->flipped || !facet->normal)
-      continue;
-    totpart++;
-    qh_distplane(qh, point, facet, &dist);
-    if (dist > *bestdist) {
-      *bestdist= dist;
-      bestfacet= facet;
-      if (dist > qh->MINoutside) {
-        *isoutside= True;
-        break;
-      }
-    }
-  }
-  *numpart= totpart;
-  trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
-          getid_(bestfacet), *bestdist, *isoutside, totpart));
-  return bestfacet;
-} /* findfacet_all */
-
-/*---------------------------------
-
-  qh_findgood(qh, facetlist, goodhorizon )
-    identify good facets for qh.PRINTgood
-    if qh.GOODvertex>0
-      facet includes point as vertex
-      if !match, returns goodhorizon
-      inactive if qh.MERGING
-    if qh.GOODpoint
-      facet is visible or coplanar (>0) or not visible (<0)
-    if qh.GOODthreshold
-      facet->normal matches threshold
-    if !goodhorizon and !match,
-      selects facet with closest angle
-      sets GOODclosest
-
-  returns:
-    number of new, good facets found
-    determines facet->good
-    may update qh.GOODclosest
-
-  notes:
-    qh_findgood_all further reduces the good region
-
-  design:
-    count good facets
-    mark good facets for qh.GOODpoint
-    mark good facets for qh.GOODthreshold
-    if necessary
-      update qh.GOODclosest
-*/
-int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
-  facetT *facet, *bestfacet= NULL;
-  realT angle, bestangle= REALmax, dist;
-  int  numgood=0;
-
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh->GOODvertex>0 && !qh->MERGING) {
-    FORALLfacet_(facetlist) {
-      if (!qh_isvertex(qh->GOODvertexp, facet->vertices)) {
-        facet->good= False;
-        numgood--;
-      }
-    }
-  }
-  if (qh->GOODpoint && numgood) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        zinc_(Zdistgood);
-        qh_distplane(qh, qh->GOODpointp, facet, &dist);
-        if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
-          facet->good= False;
-          numgood--;
-        }
-      }
-    }
-  }
-  if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        if (!qh_inthresholds(qh, facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && (!goodhorizon || qh->GOODclosest)) {
-      if (qh->GOODclosest) {
-        if (qh->GOODclosest->visible)
-          qh->GOODclosest= NULL;
-        else {
-          qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
-          if (angle < bestangle)
-            bestfacet= qh->GOODclosest;
-        }
-      }
-      if (bestfacet && bestfacet != qh->GOODclosest) {
-        if (qh->GOODclosest)
-          qh->GOODclosest->good= False;
-        qh->GOODclosest= bestfacet;
-        bestfacet->good= True;
-        numgood++;
-        trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-        return numgood;
-      }
-    }else if (qh->GOODclosest) { /* numgood > 0 */
-      qh->GOODclosest->good= False;
-      qh->GOODclosest= NULL;
-    }
-  }
-  zadd_(Zgoodfacet, numgood);
-  trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
-               numgood, goodhorizon));
-  if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
-    return goodhorizon;
-  return numgood;
-} /* findgood */
-
-/*---------------------------------
-
-  qh_findgood_all(qh, facetlist )
-    apply other constraints for good facets (used by qh.PRINTgood)
-    if qh.GOODvertex
-      facet includes (>0) or doesn't include (<0) point as vertex
-      if last good facet and ONLYgood, prints warning and continues
-    if qh.SPLITthresholds
-      facet->normal matches threshold, or if none, the closest one
-    calls qh_findgood
-    nop if good not used
-
-  returns:
-    clears facet->good if not good
-    sets qh.num_good
-
-  notes:
-    this is like qh_findgood but more restrictive
-
-  design:
-    uses qh_findgood to mark good facets
-    marks facets for qh.GOODvertex
-    marks facets for qh.SPLITthreholds
-*/
-void qh_findgood_all(qhT *qh, facetT *facetlist) {
-  facetT *facet, *bestfacet=NULL;
-  realT angle, bestangle= REALmax;
-  int  numgood=0, startgood;
-
-  if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
-  && !qh->SPLITthresholds)
-    return;
-  if (!qh->ONLYgood)
-    qh_findgood(qh, qh->facet_list, 0);
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh->GOODvertexp, facet->vertices))) {
-        if (!--numgood) {
-          if (qh->ONLYgood) {
-            qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
-               qh_pointid(qh, qh->GOODvertexp), facet->id);
-            return;
-          }else if (qh->GOODvertex > 0)
-            qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
-                qh->GOODvertex-1, qh->GOODvertex-1);
-          else
-            qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
-                -qh->GOODvertex - 1, -qh->GOODvertex - 1);
-        }
-        facet->good= False;
-      }
-    }
-  }
-  startgood= numgood;
-  if (qh->SPLITthresholds) {
-    FORALLfacet_(facetlist) {
-      if (facet->good) {
-        if (!qh_inthresholds(qh, facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && bestfacet) {
-      bestfacet->good= True;
-      numgood++;
-      trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-      return;
-    }
-  }
-  qh->num_good= numgood;
-  trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
-        numgood, startgood));
-} /* findgood_all */
-
-/*---------------------------------
-
-  qh_furthestnext()
-    set qh.facet_next to facet with furthest of all furthest points
-    searches all facets on qh.facet_list
-
-  notes:
-    this may help avoid precision problems
-*/
-void qh_furthestnext(qhT *qh /* qh->facet_list */) {
-  facetT *facet, *bestfacet= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FORALLfacets {
-    if (facet->outsideset) {
-#if qh_COMPUTEfurthest
-      pointT *furthest;
-      furthest= (pointT*)qh_setlast(facet->outsideset);
-      zinc_(Zcomputefurthest);
-      qh_distplane(qh, furthest, facet, &dist);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist > bestdist) {
-        bestfacet= facet;
-        bestdist= dist;
-      }
-    }
-  }
-  if (bestfacet) {
-    qh_removefacet(qh, bestfacet);
-    qh_prependfacet(qh, bestfacet, &qh->facet_next);
-    trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
-            bestfacet->id, bestdist));
-  }
-} /* furthestnext */
-
-/*---------------------------------
-
-  qh_furthestout(qh, facet )
-    make furthest outside point the last point of outsideset
-
-  returns:
-    updates facet->outsideset
-    clears facet->notfurthest
-    sets facet->furthestdist
-
-  design:
-    determine best point of outsideset
-    make it the last point of outsideset
-*/
-void qh_furthestout(qhT *qh, facetT *facet) {
-  pointT *point, **pointp, *bestpoint= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FOREACHpoint_(facet->outsideset) {
-    qh_distplane(qh, point, facet, &dist);
-    zinc_(Zcomputefurthest);
-    if (dist > bestdist) {
-      bestpoint= point;
-      bestdist= dist;
-    }
-  }
-  if (bestpoint) {
-    qh_setdel(facet->outsideset, point);
-    qh_setappend(qh, &facet->outsideset, point);
-#if !qh_COMPUTEfurthest
-    facet->furthestdist= bestdist;
-#endif
-  }
-  facet->notfurthest= False;
-  trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
-          qh_pointid(qh, point), facet->id));
-} /* furthestout */
-
-
-/*---------------------------------
-
-  qh_infiniteloop(qh, facet )
-    report infinite loop error due to facet
-*/
-void qh_infiniteloop(qhT *qh, facetT *facet) {
-
-  qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
-  qh_errexit(qh, qh_ERRqhull, facet, NULL);
-} /* qh_infiniteloop */
-
-/*---------------------------------
-
-  qh_initbuild()
-    initialize hull and outside sets with point array
-    qh.FIRSTpoint/qh.NUMpoints is point array
-    if qh.GOODpoint
-      adds qh.GOODpoint to initial hull
-
-  returns:
-    qh_facetlist with initial hull
-    points partioned into outside sets, coplanar sets, or inside
-    initializes qh.GOODpointp, qh.GOODvertexp,
-
-  design:
-    initialize global variables used during qh_buildhull
-    determine precision constants and points with max/min coordinate values
-      if qh.SCALElast, scale last coordinate(for 'd')
-    build initial simplex
-    partition input points into facets of initial simplex
-    set up lists
-    if qh.ONLYgood
-      check consistency
-      add qh.GOODvertex if defined
-*/
-void qh_initbuild(qhT *qh) {
-  setT *maxpoints, *vertices;
-  facetT *facet;
-  int i, numpart;
-  realT dist;
-  boolT isoutside;
-
-  qh->furthest_id= qh_IDunknown;
-  qh->lastreport= 0;
-  qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
-  qh->visit_id= qh->vertex_visit= 0;
-  qh->maxoutdone= False;
-
-  if (qh->GOODpoint > 0)
-    qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
-  else if (qh->GOODpoint < 0)
-    qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
-  if (qh->GOODvertex > 0)
-    qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
-  else if (qh->GOODvertex < 0)
-    qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
-  if ((qh->GOODpoint
-       && (qh->GOODpointp < qh->first_point  /* also catches !GOODpointp */
-           || qh->GOODpointp > qh_point(qh, qh->num_points-1)))
-    || (qh->GOODvertex
-        && (qh->GOODvertexp < qh->first_point  /* also catches !GOODvertexp */
-            || qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
-    qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
-             qh->num_points-1);
-    qh_errexit(qh, qh_ERRinput, NULL, NULL);
-  }
-  maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
-  if (qh->SCALElast)
-    qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
-               qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
-  qh_detroundoff(qh);
-  if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
-                  && qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
-    for (i=qh_PRINTEND; i--; ) {
-      if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
-          && !qh->GOODthreshold && !qh->SPLITthresholds)
-        break;  /* in this case, don't set upper_threshold */
-    }
-    if (i < 0) {
-      if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
-        qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
-        qh->GOODthreshold= True;
-      }else {
-        qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
-        if (!qh->GOODthreshold)
-          qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
-          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
-      }
-    }
-  }
-  vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
-  qh_initialhull(qh, vertices);  /* initial qh->facet_list */
-  qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
-  if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
-    if (qh->TRACElevel || qh->IStracing)
-      qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
-         qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
-    qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  }
-  qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
-  qh->facet_next= qh->facet_list;
-  qh_furthestnext(qh /* qh->facet_list */);
-  if (qh->PREmerge) {
-    qh->cos_max= qh->premerge_cos;
-    qh->centrum_radius= qh->premerge_centrum;
-  }
-  if (qh->ONLYgood) {
-    if (qh->GOODvertex > 0 && qh->MERGING) {
-      qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (!(qh->GOODthreshold || qh->GOODpoint
-         || (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
-      qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
-good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    if (qh->GOODvertex > 0  && !qh->MERGING  /* matches qh_partitionall */
-        && !qh_isvertex(qh->GOODvertexp, vertices)) {
-      facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
-                          &dist, !qh_ALL, &isoutside, &numpart);
-      zadd_(Zdistgood, numpart);
-      if (!isoutside) {
-        qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
-               qh_pointid(qh, qh->GOODvertexp));
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
-        qh_settempfree(qh, &vertices);
-        qh_settempfree(qh, &maxpoints);
-        return;
-      }
-    }
-    qh_findgood(qh, qh->facet_list, 0);
-  }
-  qh_settempfree(qh, &vertices);
-  qh_settempfree(qh, &maxpoints);
-  trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
-} /* initbuild */
-
-/*---------------------------------
-
-  qh_initialhull(qh, vertices )
-    constructs the initial hull as a DIM3 simplex of vertices
-
-  design:
-    creates a simplex (initializes lists)
-    determines orientation of simplex
-    sets hyperplanes for facets
-    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
-    checks for flipped facets and qh.NARROWhull
-    checks the result
-*/
-void qh_initialhull(qhT *qh, setT *vertices) {
-  facetT *facet, *firstfacet, *neighbor, **neighborp;
-  realT dist, angle, minangle= REALmax;
-#ifndef qh_NOtrace
-  int k;
-#endif
-
-  qh_createsimplex(qh, vertices);  /* qh->facet_list */
-  qh_resetlists(qh, False, qh_RESETvisible);
-  qh->facet_next= qh->facet_list;      /* advance facet when processed */
-  qh->interior_point= qh_getcenter(qh, vertices);
-  firstfacet= qh->facet_list;
-  qh_setfacetplane(qh, firstfacet);
-  zinc_(Znumvisibility); /* needs to be in printsummary */
-  qh_distplane(qh, qh->interior_point, firstfacet, &dist);
-  if (dist > 0) {
-    FORALLfacets
-      facet->toporient ^= (unsigned char)True;
-  }
-  FORALLfacets
-    qh_setfacetplane(qh, facet);
-  FORALLfacets {
-    if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
-      trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
-      facet->flipped= False;
-      FORALLfacets {
-        facet->toporient ^= (unsigned char)True;
-        qh_orientoutside(qh, facet);
-      }
-      break;
-    }
-  }
-  FORALLfacets {
-    if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
-      if (qh->DELAUNAY && ! qh->ATinfinity) {
-        if (qh->UPPERdelaunay)
-          qh_fprintf(qh, qh->ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
-        else
-          qh_fprintf(qh, qh->ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".  Use option 'Qs' to search all points for the initial simplex.\n");
-        qh_errexit(qh, qh_ERRinput, NULL, NULL);
-      }
-      qh_precision(qh, "initial simplex is flat");
-      qh_fprintf(qh, qh->ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
-                   facet->id);
-      qh_errexit(qh, qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
-    }
-    FOREACHneighbor_(facet) {
-      angle= qh_getangle(qh, facet->normal, neighbor->normal);
-      minimize_( minangle, angle);
-    }
-  }
-  if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
-    realT diff= 1.0 + minangle;
-
-    qh->NARROWhull= True;
-    qh_option(qh, "_narrow-hull", NULL, &diff);
-    if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
-      qh_printhelp_narrowhull(qh, qh->ferr, minangle);
-  }
-  zzval_(Zprocessed)= qh->hull_dim+1;
-  qh_checkpolygon(qh, qh->facet_list);
-  qh_checkconvex(qh, qh->facet_list,   qh_DATAfault);
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 1) {
-    qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
-    for (k=0; k < qh->hull_dim; k++)
-      qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
-    qh_fprintf(qh, qh->ferr, 8107, "\n");
-  }
-#endif
-} /* initialhull */
-
-/*---------------------------------
-
-  qh_initialvertices(qh, dim, maxpoints, points, numpoints )
-    determines a non-singular set of initial vertices
-    maxpoints may include duplicate points
-
-  returns:
-    temporary set of dim+1 vertices in descending order by vertex id
-    if qh.RANDOMoutside && !qh.ALLpoints
-      picks random points
-    if dim >= qh_INITIALmax,
-      uses min/max x and max points with non-zero determinants
-
-  notes:
-    unless qh.ALLpoints,
-      uses maxpoints as long as determinate is non-zero
-*/
-setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
-  pointT *point, **pointp;
-  setT *vertices, *simplex, *tested;
-  realT randr;
-  int idx, point_i, point_n, k;
-  boolT nearzero= False;
-
-  vertices= qh_settemp(qh, dim + 1);
-  simplex= qh_settemp(qh, dim+1);
-  if (qh->ALLpoints)
-    qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
-  else if (qh->RANDOMoutside) {
-    while (qh_setsize(qh, simplex) != dim+1) {
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      idx= (int)floor(qh->num_points * randr);
-      while (qh_setin(simplex, qh_point(qh, idx))) {
-            idx++; /* in case qh_RANDOMint always returns the same value */
-        idx= idx < qh->num_points ? idx : 0;
-      }
-      qh_setappend(qh, &simplex, qh_point(qh, idx));
-    }
-  }else if (qh->hull_dim >= qh_INITIALmax) {
-    tested= qh_settemp(qh, dim+1);
-    qh_setappend(qh, &simplex, SETfirst_(maxpoints));   /* max and min X coord */
-    qh_setappend(qh, &simplex, SETsecond_(maxpoints));
-    qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
-    k= qh_setsize(qh, simplex);
-    FOREACHpoint_i_(qh, maxpoints) {
-      if (point_i & 0x1) {     /* first pick up max. coord. points */
-        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-          qh_detsimplex(qh, point, simplex, k, &nearzero);
-          if (nearzero)
-            qh_setappend(qh, &tested, point);
-          else {
-            qh_setappend(qh, &simplex, point);
-            if (++k == dim)  /* use search for last point */
-              break;
-          }
-        }
-      }
-    }
-    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(qh, point, simplex, k, &nearzero);
-        if (nearzero)
-          qh_setappend(qh, &tested, point);
-        else {
-          qh_setappend(qh, &simplex, point);
-          k++;
-        }
-      }
-    }
-    idx= 0;
-    while (k != dim && (point= qh_point(qh, idx++))) {
-      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
-        qh_detsimplex(qh, point, simplex, k, &nearzero);
-        if (!nearzero){
-          qh_setappend(qh, &simplex, point);
-          k++;
-        }
-      }
-    }
-    qh_settempfree(qh, &tested);
-    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
-  }else
-    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
-  FOREACHpoint_(simplex)
-    qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
-  qh_settempfree(qh, &simplex);
-  return vertices;
-} /* initialvertices */
-
-
-/*---------------------------------
-
-  qh_isvertex( point, vertices )
-    returns vertex if point is in vertex set, else returns NULL
-
-  notes:
-    for qh.GOODvertex
-*/
-vertexT *qh_isvertex(pointT *point, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (vertex->point == point)
-      return vertex;
-  }
-  return NULL;
-} /* isvertex */
-
-/*---------------------------------
-
-  qh_makenewfacets(qh, point )
-    make new facets from point and qh.visible_list
-
-  returns:
-    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
-    qh.newvertex_list= list of vertices in new facets with ->newlist set
-
-    if (qh.ONLYgood)
-      newfacets reference horizon facets, but not vice versa
-      ridges reference non-simplicial horizon ridges, but not vice versa
-      does not change existing facets
-    else
-      sets qh.NEWfacets
-      new facets attached to horizon facets and ridges
-      for visible facets,
-        visible->r.replace is corresponding new facet
-
-  see also:
-    qh_makenewplanes() -- make hyperplanes for facets
-    qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
-    qh_matchnewfacets() -- match up neighbors
-    qh_updatevertices() -- update vertex neighbors and delvertices
-    qh_deletevisible() -- delete visible facets
-    qh_checkpolygon() --check the result
-    qh_triangulate() -- triangulate a non-simplicial facet
-
-  design:
-    for each visible facet
-      make new facets to its horizon facets
-      update its f.replace
-      clear its neighbor set
-*/
-vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
-  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  qh->newfacet_list= qh->facet_tail;
-  qh->newvertex_list= qh->vertex_tail;
-  apex= qh_newvertex(qh, point);
-  qh_appendvertex(qh, apex);
-  qh->visit_id++;
-  if (!qh->ONLYgood)
-    qh->NEWfacets= True;
-  FORALLvisible_facets {
-    FOREACHneighbor_(visible)
-      neighbor->seen= False;
-    if (visible->ridges) {
-      visible->visitid= qh->visit_id;
-      newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
-    }
-    if (visible->simplicial)
-      newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
-    if (!qh->ONLYgood) {
-      if (newfacet2)  /* newfacet is null if all ridges defined */
-        newfacet= newfacet2;
-      if (newfacet)
-        visible->f.replace= newfacet;
-      else
-        zinc_(Zinsidevisible);
-      SETfirst_(visible->neighbors)= NULL;
-    }
-  }
-  trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
-          numnew, qh_pointid(qh, point)));
-  if (qh->IStracing >= 4)
-    qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
-  return apex;
-} /* makenewfacets */
-
-/*---------------------------------
-
-  qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
-    match duplicate ridges in qh.hash_table for atfacet/atskip
-    duplicates marked with ->dupridge and qh_DUPLICATEridge
-
-  returns:
-    picks match with worst merge (min distance apart)
-    updates hashcount
-
-  see also:
-    qh_matchneighbor
-
-  notes:
-
-  design:
-    compute hash value for atfacet and atskip
-    repeat twice -- once to make best matches, once to match the rest
-      for each possible facet in qh.hash_table
-        if it is a matching facet and pass 2
-          make match
-          unless tricoplanar, mark match for merging (qh_MERGEridge)
-          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
-        if it is a matching facet and pass 1
-          test if this is a better match
-      if pass 1,
-        make best match (it will not be merged)
-*/
-#ifndef qh_NOmerge
-void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
-  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
-  realT maxdist= -REALmax, mindist, dist2, low, high;
-
-  hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
-                     SETelem_(atfacet->vertices, atskip));
-  trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
-          atfacet->id, atskip, hash, *hashcount));
-  for (makematch= 0; makematch < 2; makematch++) {
-    qh->visit_id++;
-    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
-      zinc_(Zhashlookup);
-      nextfacet= NULL;
-      newfacet->visitid= qh->visit_id;
-      for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
-           scan= (++scan >= hashsize ? 0 : scan)) {
-        if (!facet->dupridge || facet->visitid == qh->visit_id)
-          continue;
-        zinc_(Zhashtests);
-        if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
-          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
-            if (!makematch) {
-              qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
-                     facet->id, skip, newfacet->id, newskip, hash);
-              qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
-            }
-          }else if (ismatch && makematch) {
-            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
-              SETelem_(facet->neighbors, skip)= newfacet;
-              if (newfacet->tricoplanar)
-                SETelem_(newfacet->neighbors, newskip)= facet;
-              else
-                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
-              *hashcount -= 2; /* removed two unmatched facets */
-              trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
-                    facet->id, skip, newfacet->id, newskip));
-            }
-          }else if (ismatch) {
-            mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
-            dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
-            minimize_(mindist, dist2);
-            if (mindist > maxdist) {
-              maxdist= mindist;
-              maxmatch= facet;
-              maxskip= skip;
-              maxmatch2= newfacet;
-              maxskip2= newskip;
-            }
-            trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
-                    facet->id, skip, newfacet->id, newskip, mindist,
-                    maxmatch->id, maxmatch2->id));
-          }else { /* !ismatch */
-            nextfacet= facet;
-            nextskip= skip;
-          }
-        }
-        if (makematch && !facet
-        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
-          qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
-                     newfacet->id, newskip, hash);
-          qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-        }
-      }
-    } /* end of for each new facet at hash */
-    if (!makematch) {
-      if (!maxmatch) {
-        qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
-                     atfacet->id, atskip, hash);
-        qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
-      }
-      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
-      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
-      *hashcount -= 2; /* removed two unmatched facets */
-      zzinc_(Zmultiridge);
-      trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
-              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
-      qh_precision(qh, "ridge with multiple neighbors");
-      if (qh->IStracing >= 4)
-        qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
-    }
-  }
-} /* matchduplicates */
-
-/*---------------------------------
-
-  qh_nearcoplanar()
-    for all facets, remove near-inside points from facet->coplanarset
-    coplanar points defined by innerplane from qh_outerinner()
-
-  returns:
-    if qh->KEEPcoplanar && !qh->KEEPinside
-      facet->coplanarset only contains coplanar points
-    if qh.JOGGLEmax
-      drops inner plane by another qh.JOGGLEmax diagonal since a
-        vertex could shift out while a coplanar point shifts in
-
-  notes:
-    used for qh.PREmerge and qh.JOGGLEmax
-    must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
-  design:
-    if not keeping coplanar or inside points
-      free all coplanar sets
-    else if not keeping both coplanar and inside points
-      remove !coplanar or !inside points from coplanar sets
-*/
-void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
-  facetT *facet;
-  pointT *point, **pointp;
-  int numpart;
-  realT dist, innerplane;
-
-  if (!qh->KEEPcoplanar && !qh->KEEPinside) {
-    FORALLfacets {
-      if (facet->coplanarset)
-        qh_setfree(qh, &facet->coplanarset);
-    }
-  }else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
-    qh_outerinner(qh, NULL, NULL, &innerplane);
-    if (qh->JOGGLEmax < REALmax/2)
-      innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
-    numpart= 0;
-    FORALLfacets {
-      if (facet->coplanarset) {
-        FOREACHpoint_(facet->coplanarset) {
-          numpart++;
-          qh_distplane(qh, point, facet, &dist);
-          if (dist < innerplane) {
-            if (!qh->KEEPinside)
-              SETref_(point)= NULL;
-          }else if (!qh->KEEPcoplanar)
-            SETref_(point)= NULL;
-        }
-        qh_setcompact(qh, facet->coplanarset);
-      }
-    }
-    zzadd_(Zcheckpart, numpart);
-  }
-} /* nearcoplanar */
-
-/*---------------------------------
-
-  qh_nearvertex(qh, facet, point, bestdist )
-    return nearest vertex in facet to point
-
-  returns:
-    vertex and its distance
-
-  notes:
-    if qh.DELAUNAY
-      distance is measured in the input set
-    searches neighboring tricoplanar facets (requires vertexneighbors)
-      Slow implementation.  Recomputes vertex set for each point.
-    The vertex set could be stored in the qh.keepcentrum facet.
-*/
-vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
-  realT bestdist= REALmax, dist;
-  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
-  coordT *center;
-  facetT *neighbor, **neighborp;
-  setT *vertices;
-  int dim= qh->hull_dim;
-
-  if (qh->DELAUNAY)
-    dim--;
-  if (facet->tricoplanar) {
-    if (!qh->VERTEXneighbors || !facet->center) {
-      qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-    }
-    vertices= qh_settemp(qh, qh->TEMPsize);
-    apex= SETfirstt_(facet->vertices, vertexT);
-    center= facet->center;
-    FOREACHneighbor_(apex) {
-      if (neighbor->center == center) {
-        FOREACHvertex_(neighbor->vertices)
-          qh_setappend(qh, &vertices, vertex);
-      }
-    }
-  }else
-    vertices= facet->vertices;
-  FOREACHvertex_(vertices) {
-    dist= qh_pointdist(vertex->point, point, -dim);
-    if (dist < bestdist) {
-      bestdist= dist;
-      bestvertex= vertex;
-    }
-  }
-  if (facet->tricoplanar)
-    qh_settempfree(qh, &vertices);
-  *bestdistp= sqrt(bestdist);
-  if (!bestvertex) {
-      qh_fprintf(qh, qh->ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(qh, point));
-      qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
-        bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point))); /* bestvertex!=0 by QH2161 */
-  return bestvertex;
-} /* nearvertex */
-
-/*---------------------------------
-
-  qh_newhashtable(qh, newsize )
-    returns size of qh.hash_table of at least newsize slots
-
-  notes:
-    assumes qh.hash_table is NULL
-    qh_HASHfactor determines the number of extra slots
-    size is not divisible by 2, 3, or 5
-*/
-int qh_newhashtable(qhT *qh, int newsize) {
-  int size;
-
-  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
-  while (True) {
-    if (newsize<0 || size<0) {
-        qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
-        qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
-    }
-    if ((size%3) && (size%5))
-      break;
-    size += 2;
-    /* loop terminates because there is an infinite number of primes */
-  }
-  qh->hash_table= qh_setnew(qh, size);
-  qh_setzero(qh, qh->hash_table, 0, size);
-  return size;
-} /* newhashtable */
-
-/*---------------------------------
-
-  qh_newvertex(qh, point )
-    returns a new vertex for point
-*/
-vertexT *qh_newvertex(qhT *qh, pointT *point) {
-  vertexT *vertex;
-
-  zinc_(Ztotvertices);
-  vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
-  memset((char *) vertex, (size_t)0, sizeof(vertexT));
-  if (qh->vertex_id == UINT_MAX) {
-    qh_memfree(qh, vertex, (int)sizeof(vertexT));
-    qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  if (qh->vertex_id == qh->tracevertex_id)
-    qh->tracevertex= vertex;
-  vertex->id= qh->vertex_id++;
-  vertex->point= point;
-  trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
-          vertex->id));
-  return(vertex);
-} /* newvertex */
-
-/*---------------------------------
-
-  qh_nextridge3d( atridge, facet, vertex )
-    return next ridge and vertex for a 3d facet
-    returns NULL on error
-    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
-
-  notes:
-    in qh_ORIENTclock order
-    this is a O(n^2) implementation to trace all ridges
-    be sure to stop on any 2nd visit
-    same as QhullRidge::nextRidge3d
-    does not use qhT or qh_errexit [QhullFacet.cpp]
-
-  design:
-    for each ridge
-      exit if it is the ridge after atridge
-*/
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-  vertexT *atvertex, *vertex, *othervertex;
-  ridgeT *ridge, **ridgep;
-
-  if ((atridge->top == facet) ^ qh_ORIENTclock)
-    atvertex= SETsecondt_(atridge->vertices, vertexT);
-  else
-    atvertex= SETfirstt_(atridge->vertices, vertexT);
-  FOREACHridge_(facet->ridges) {
-    if (ridge == atridge)
-      continue;
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      othervertex= SETsecondt_(ridge->vertices, vertexT);
-      vertex= SETfirstt_(ridge->vertices, vertexT);
-    }else {
-      vertex= SETsecondt_(ridge->vertices, vertexT);
-      othervertex= SETfirstt_(ridge->vertices, vertexT);
-    }
-    if (vertex == atvertex) {
-      if (vertexp)
-        *vertexp= othervertex;
-      return ridge;
-    }
-  }
-  return NULL;
-} /* nextridge3d */
-#else /* qh_NOmerge */
-void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-}
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_outcoplanar()
-    move points from all facets' outsidesets to their coplanarsets
-
-  notes:
-    for post-processing under qh.NARROWhull
-
-  design:
-    for each facet
-      for each outside point for facet
-        partition point into coplanar set
-*/
-void qh_outcoplanar(qhT *qh /* facet_list */) {
-  pointT *point, **pointp;
-  facetT *facet;
-  realT dist;
-
-  trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
-  FORALLfacets {
-    FOREACHpoint_(facet->outsideset) {
-      qh->num_outside--;
-      if (qh->KEEPcoplanar || qh->KEEPnearinside) {
-        qh_distplane(qh, point, facet, &dist);
-        zinc_(Zpartition);
-        qh_partitioncoplanar(qh, point, facet, &dist);
-      }
-    }
-    qh_setfree(qh, &facet->outsideset);
-  }
-} /* outcoplanar */
-
-/*---------------------------------
-
-  qh_point(qh, id )
-    return point for a point id, or NULL if unknown
-
-  alternative code:
-    return((pointT *)((unsigned   long)qh.first_point
-           + (unsigned long)((id)*qh.normal_size)));
-*/
-pointT *qh_point(qhT *qh, int id) {
-
-  if (id < 0)
-    return NULL;
-  if (id < qh->num_points)
-    return qh->first_point + id * qh->hull_dim;
-  id -= qh->num_points;
-  if (id < qh_setsize(qh, qh->other_points))
-    return SETelemt_(qh->other_points, id, pointT);
-  return NULL;
-} /* point */
-
-/*---------------------------------
-
-  qh_point_add(qh, set, point, elem )
-    stores elem at set[point.id]
-
-  returns:
-    access function for qh_pointfacet and qh_pointvertex
-
-  notes:
-    checks point.id
-*/
-void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
-  int id, size;
-
-  SETreturnsize_(set, size);
-  if ((id= qh_pointid(qh, point)) < 0)
-    qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
-      point, id);
-  else if (id >= size) {
-    qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
-             id, size);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }else
-    SETelem_(set, id)= elem;
-} /* point_add */
-
-
-/*---------------------------------
-
-  qh_pointfacet()
-    return temporary set of facet for each point
-    the set is indexed by point id
-
-  notes:
-    vertices assigned to one of the facets
-    coplanarset assigned to the facet
-    outside set assigned to the facet
-    NULL if no facet for point (inside)
-      includes qh.GOODpointp
-
-  access:
-    FOREACHfacet_i_(qh, facets) { ... }
-    SETelem_(facets, i)
-
-  design:
-    for each facet
-      add each vertex
-      add each coplanar point
-      add each outside point
-*/
-setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  setT *facets;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp;
-
-  facets= qh_settemp(qh, numpoints);
-  qh_setzero(qh, facets, 0, numpoints);
-  qh->vertex_visit++;
-  FORALLfacets {
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        qh_point_add(qh, facets, vertex->point, facet);
-      }
-    }
-    FOREACHpoint_(facet->coplanarset)
-      qh_point_add(qh, facets, point, facet);
-    FOREACHpoint_(facet->outsideset)
-      qh_point_add(qh, facets, point, facet);
-  }
-  return facets;
-} /* pointfacet */
-
-/*---------------------------------
-
-  qh_pointvertex(qh, )
-    return temporary set of vertices indexed by point id
-    entry is NULL if no vertex for a point
-      this will include qh.GOODpointp
-
-  access:
-    FOREACHvertex_i_(qh, vertices) { ... }
-    SETelem_(vertices, i)
-*/
-setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
-  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
-  setT *vertices;
-  vertexT *vertex;
-
-  vertices= qh_settemp(qh, numpoints);
-  qh_setzero(qh, vertices, 0, numpoints);
-  FORALLvertices
-    qh_point_add(qh, vertices, vertex->point, vertex);
-  return vertices;
-} /* pointvertex */
-
-
-/*---------------------------------
-
-  qh_prependfacet(qh, facet, facetlist )
-    prepend facet to the start of a facetlist
-
-  returns:
-    increments qh.numfacets
-    updates facetlist, qh.facet_list, facet_next
-
-  notes:
-    be careful of prepending since it can lose a pointer.
-      e.g., can lose _next by deleting and then prepending before _next
-*/
-void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
-  facetT *prevfacet, *list;
-
-
-  trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
-          facet->id, getid_(*facetlist)));
-  if (!*facetlist)
-    (*facetlist)= qh->facet_tail;
-  list= *facetlist;
-  prevfacet= list->previous;
-  facet->previous= prevfacet;
-  if (prevfacet)
-    prevfacet->next= facet;
-  list->previous= facet;
-  facet->next= *facetlist;
-  if (qh->facet_list == list)  /* this may change *facetlist */
-    qh->facet_list= facet;
-  if (qh->facet_next == list)
-    qh->facet_next= facet;
-  *facetlist= facet;
-  qh->num_facets++;
-} /* prependfacet */
-
-
-/*---------------------------------
-
-  qh_printhashtable(qh, fp )
-    print hash table to fp
-
-  notes:
-    not in I/O to avoid bringing io_r.c in
-
-  design:
-    for each hash entry
-      if defined
-        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
-          print entry and neighbors
-*/
-void qh_printhashtable(qhT *qh, FILE *fp) {
-  facetT *facet, *neighbor;
-  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
-  vertexT *vertex, **vertexp;
-
-  FOREACHfacet_i_(qh, qh->hash_table) {
-    if (facet) {
-      FOREACHneighbor_i_(qh, facet) {
-        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
-          break;
-      }
-      if (neighbor_i == neighbor_n)
-        continue;
-      qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
-      FOREACHvertex_(facet->vertices)
-        qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
-      qh_fprintf(qh, fp, 9285, "\n neighbors:");
-      FOREACHneighbor_i_(qh, facet) {
-        if (neighbor == qh_MERGEridge)
-          id= -3;
-        else if (neighbor == qh_DUPLICATEridge)
-          id= -2;
-        else
-          id= getid_(neighbor);
-        qh_fprintf(qh, fp, 9286, " %d", id);
-      }
-      qh_fprintf(qh, fp, 9287, "\n");
-    }
-  }
-} /* printhashtable */
-
-
-/*---------------------------------
-
-  qh_printlists(qh, fp )
-    print out facet and vertex list for debugging (without 'f/v' tags)
-*/
-void qh_printlists(qhT *qh) {
-  facetT *facet;
-  vertexT *vertex;
-  int count= 0;
-
-  qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
-  FORALLfacets {
-    if (++count % 100 == 0)
-      qh_fprintf(qh, qh->ferr, 8109, "\n     ");
-    qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
-  }
-  qh_fprintf(qh, qh->ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
-     getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
-     getid_(qh->newvertex_list));
-  count = 0;
-  FORALLvertices {
-    if (++count % 100 == 0)
-      qh_fprintf(qh, qh->ferr, 8112, "\n     ");
-    qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
-  }
-  qh_fprintf(qh, qh->ferr, 8114, "\n");
-} /* printlists */
-
-/*---------------------------------
-
-  qh_resetlists(qh, stats, qh_RESETvisible )
-    reset newvertex_list, newfacet_list, visible_list
-    if stats,
-      maintains statistics
-
-  returns:
-    visible_list is empty if qh_deletevisible was called
-*/
-void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
-  vertexT *vertex;
-  facetT *newfacet, *visible;
-  int totnew=0, totver=0;
-
-  if (stats) {
-    FORALLvertex_(qh->newvertex_list)
-      totver++;
-    FORALLnew_facets
-      totnew++;
-    zadd_(Zvisvertextot, totver);
-    zmax_(Zvisvertexmax, totver);
-    zadd_(Znewfacettot, totnew);
-    zmax_(Znewfacetmax, totnew);
-  }
-  FORALLvertex_(qh->newvertex_list)
-    vertex->newlist= False;
-  qh->newvertex_list= NULL;
-  FORALLnew_facets
-    newfacet->newfacet= False;
-  qh->newfacet_list= NULL;
-  if (resetVisible) {
-    FORALLvisible_facets {
-      visible->f.replace= NULL;
-      visible->visible= False;
-    }
-    qh->num_visible= 0;
-  }
-  qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
-  qh->NEWfacets= False;
-} /* resetlists */
-
-/*---------------------------------
-
-  qh_setvoronoi_all(qh)
-    compute Voronoi centers for all facets
-    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
-
-  returns:
-    facet->center is the Voronoi center
-
-  notes:
-    this is unused/untested code
-      please email bradb@shore.net if this works ok for you
-
-  use:
-    FORALLvertices {...} to locate the vertex for a point.
-    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
-*/
-void qh_setvoronoi_all(qhT *qh) {
-  facetT *facet;
-
-  qh_clearcenters(qh, qh_ASvoronoi);
-  qh_vertexneighbors(qh);
-
-  FORALLfacets {
-    if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
-      if (!facet->center)
-        facet->center= qh_facetcenter(qh, facet->vertices);
-    }
-  }
-} /* setvoronoi_all */
-
-#ifndef qh_NOmerge
-
-/*---------------------------------
-
-  qh_triangulate()
-    triangulate non-simplicial facets on qh.facet_list,
-    if qh->VORONOI, sets Voronoi centers of non-simplicial facets
-    nop if hasTriangulation
-
-  returns:
-    all facets simplicial
-    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
-
-  notes:
-    call after qh_check_output since may switch to Voronoi centers
-    Output may overwrite ->f.triowner with ->f.area
-*/
-void qh_triangulate(qhT *qh /*qh.facet_list*/) {
-  facetT *facet, *nextfacet, *owner;
-  int onlygood= qh->ONLYgood;
-  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
-  facetT *orig_neighbor= NULL, *otherfacet;
-  vertexT *new_vertex_list= NULL;
-  mergeT *merge;
-  mergeType mergetype;
-  int neighbor_i, neighbor_n;
-
-  if (qh->hasTriangulation)
-      return;
-  trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
-  if (qh->hull_dim == 2)
-    return;
-  if (qh->VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
-    qh_clearcenters(qh, qh_ASvoronoi);
-    qh_vertexneighbors(qh);
-  }
-  qh->ONLYgood= False; /* for makenew_nonsimplicial */
-  qh->visit_id++;
-  qh->NEWfacets= True;
-  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
-  qh->newvertex_list= qh->vertex_tail;
-  for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible || facet->simplicial)
-      continue;
-    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
-    if (!new_facet_list)
-      new_facet_list= facet;  /* will be moved to end */
-    qh_triangulate_facet(qh, facet, &new_vertex_list);
-  }
-  trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible)
-      continue;
-    if (facet->ridges) {
-      if (qh_setsize(qh, facet->ridges) > 0) {
-        qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
-        qh_errexit(qh, qh_ERRqhull, facet, NULL);
-      }
-      qh_setfree(qh, &facet->ridges);
-    }
-    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
-      zinc_(Ztrinull);
-      qh_triangulate_null(qh, facet);
-    }
-  }
-  trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
-  qh->visible_list= qh->facet_tail;
-  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree(qh, merge, (int)sizeof(mergeT));
-    if (mergetype == MRGmirror) {
-      zinc_(Ztrimirror);
-      qh_triangulate_mirror(qh, facet1, facet2);
-    }
-  }
-  qh_settempfree(qh, &qh->degen_mergeset);
-  trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
-  qh->newvertex_list= new_vertex_list;  /* all vertices of new facets */
-  qh->visible_list= NULL;
-  qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
-  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
-
-  trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
-  trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
-  FORALLfacet_(new_facet_list) {
-    if (facet->tricoplanar && !facet->visible) {
-      FOREACHneighbor_i_(qh, facet) {
-        if (neighbor_i == 0) {  /* first iteration */
-          if (neighbor->tricoplanar)
-            orig_neighbor= neighbor->f.triowner;
-          else
-            orig_neighbor= neighbor;
-        }else {
-          if (neighbor->tricoplanar)
-            otherfacet= neighbor->f.triowner;
-          else
-            otherfacet= neighbor;
-          if (orig_neighbor == otherfacet) {
-            zinc_(Ztridegen);
-            facet->degenerate= True;
-            break;
-          }
-        }
-      }
-    }
-  }
-
-  trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
-  owner= NULL;
-  visible= NULL;
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
-    nextfacet= facet->next;
-    if (facet->visible) {
-      if (facet->tricoplanar) { /* a null or mirrored facet */
-        qh_delfacet(qh, facet);
-        qh->num_visible--;
-      }else {  /* a non-simplicial facet followed by its tricoplanars */
-        if (visible && !owner) {
-          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
-          trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
-                       visible->id));
-          qh_delfacet(qh, visible);
-          qh->num_visible--;
-        }
-        visible= facet;
-        owner= NULL;
-      }
-    }else if (facet->tricoplanar) {
-      if (facet->f.triowner != visible || visible==NULL) {
-        qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
-        qh_errexit2(qh, qh_ERRqhull, facet, visible);
-      }
-      if (owner)
-        facet->f.triowner= owner;
-      else if (!facet->degenerate) {
-        owner= facet;
-        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
-        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
-        facet->coplanarset= visible->coplanarset;
-        facet->outsideset= visible->outsideset;
-        visible->coplanarset= NULL;
-        visible->outsideset= NULL;
-        if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
-          visible->center= NULL;
-          visible->normal= NULL;
-        }
-        qh_delfacet(qh, visible);
-        qh->num_visible--;
-      }
-    }
-  }
-  if (visible && !owner) {
-    trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
-                 visible->id));
-    qh_delfacet(qh, visible);
-    qh->num_visible--;
-  }
-  qh->NEWfacets= False;
-  qh->ONLYgood= onlygood; /* restore value */
-  if (qh->CHECKfrequently)
-    qh_checkpolygon(qh, qh->facet_list);
-  qh->hasTriangulation= True;
-} /* triangulate */
-
-
-/*---------------------------------
-
-  qh_triangulate_facet(qh, facetA, &firstVertex )
-    triangulate a non-simplicial facet
-      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
-  returns:
-    qh.newfacet_list == simplicial facets
-      facet->tricoplanar set and ->keepcentrum false
-      facet->degenerate set if duplicated apex
-      facet->f.trivisible set to facetA
-      facet->center copied from facetA (created if qh_ASvoronoi)
-        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
-      facet->normal,offset,maxoutside copied from facetA
-
-  notes:
-      only called by qh_triangulate
-      qh_makenew_nonsimplicial uses neighbor->seen for the same
-      if qh.TRInormals, newfacet->normal will need qh_free
-        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
-        keepcentrum is also set on Zwidefacet in qh_mergefacet
-        freed by qh_clearcenters
-
-  see also:
-      qh_addpoint() -- add a point
-      qh_makenewfacets() -- construct a cone of facets for a new vertex
-
-  design:
-      if qh_ASvoronoi,
-         compute Voronoi center (facet->center)
-      select first vertex (highest ID to preserve ID ordering of ->vertices)
-      triangulate from vertex to ridges
-      copy facet->center, normal, offset
-      update vertex neighbors
-*/
-void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
-  facetT *newfacet;
-  facetT *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
-
-  if (qh->IStracing >= 4)
-    qh_printfacet(qh, qh->ferr, facetA);
-  FOREACHneighbor_(facetA) {
-    neighbor->seen= False;
-    neighbor->coplanar= False;
-  }
-  if (qh->CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
-        && fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
-    facetA->center= qh_facetcenter(qh, facetA->vertices);
-  }
-  qh_willdelete(qh, facetA, NULL);
-  qh->newfacet_list= qh->facet_tail;
-  facetA->visitid= qh->visit_id;
-  apex= SETfirstt_(facetA->vertices, vertexT);
-  qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
-  SETfirst_(facetA->neighbors)= NULL;
-  FORALLnew_facets {
-    newfacet->tricoplanar= True;
-    newfacet->f.trivisible= facetA;
-    newfacet->degenerate= False;
-    newfacet->upperdelaunay= facetA->upperdelaunay;
-    newfacet->good= facetA->good;
-    if (qh->TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
-      newfacet->keepcentrum= True;
-      if(facetA->normal){
-        newfacet->normal= qh_memalloc(qh, qh->normal_size);
-        memcpy((char *)newfacet->normal, facetA->normal, qh->normal_size);
-      }
-      if (qh->CENTERtype == qh_AScentrum)
-        newfacet->center= qh_getcentrum(qh, newfacet);
-      else if (qh->CENTERtype == qh_ASvoronoi && facetA->center){
-        newfacet->center= qh_memalloc(qh, qh->center_size);
-        memcpy((char *)newfacet->center, facetA->center, qh->center_size);
-      }
-    }else {
-      newfacet->keepcentrum= False;
-      /* one facet will have keepcentrum=True at end of qh_triangulate */
-      newfacet->normal= facetA->normal;
-      newfacet->center= facetA->center;
-    }
-    newfacet->offset= facetA->offset;
-#if qh_MAXoutside
-    newfacet->maxoutside= facetA->maxoutside;
-#endif
-  }
-  qh_matchnewfacets(qh /*qh.newfacet_list*/);
-  zinc_(Ztricoplanar);
-  zadd_(Ztricoplanartot, numnew);
-  zmax_(Ztricoplanarmax, numnew);
-  qh->visible_list= NULL;
-  if (!(*first_vertex))
-    (*first_vertex)= qh->newvertex_list;
-  qh->newvertex_list= NULL;
-  qh_updatevertices(qh /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
-} /* triangulate_facet */
-
-/*---------------------------------
-
-  qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
-    relink facetA to facetB via oldfacets
-  returns:
-    adds mirror facets to qh->degen_mergeset (4-d and up only)
-  design:
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
-  int errmirror= False;
-
-  trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
-         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
-  if (qh_setin(facetA->neighbors, facetB)) {
-    if (!qh_setin(facetB->neighbors, facetA))
-      errmirror= True;
-    else
-      qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
-  }else if (qh_setin(facetB->neighbors, facetA))
-    errmirror= True;
-  if (errmirror) {
-    qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
-       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
-    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
-  }
-  qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
-  qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
-} /* triangulate_link */
-
-/*---------------------------------
-
-  qh_triangulate_mirror(qh, facetA, facetB)
-    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
-      a mirrored facet shares the same vertices of a logical ridge
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
-  facetT *neighbor, *neighborB;
-  int neighbor_i, neighbor_n;
-
-  trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
-         facetA->id, facetB->id));
-  FOREACHneighbor_i_(qh, facetA) {
-    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
-    if (neighbor == neighborB)
-      continue; /* occurs twice */
-    qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
-  }
-  qh_willdelete(qh, facetA, NULL);
-  qh_willdelete(qh, facetB, NULL);
-} /* triangulate_mirror */
-
-/*---------------------------------
-
-  qh_triangulate_null(qh, facetA)
-    remove null facetA from qh_triangulate_facet()
-      a null facet has vertex #1 (apex) == vertex #2
-  returns:
-    adds facetA to ->visible for deletion after qh_updatevertices
-    qh->degen_mergeset contains mirror facets (4-d and up only)
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_null(qhT *qh, facetT *facetA) {
-  facetT *neighbor, *otherfacet;
-
-  trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
-  neighbor= SETfirstt_(facetA->neighbors, facetT);
-  otherfacet= SETsecondt_(facetA->neighbors, facetT);
-  qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
-  qh_willdelete(qh, facetA, NULL);
-} /* triangulate_null */
-
-#else /* qh_NOmerge */
-void qh_triangulate(qhT *qh) {
-}
-#endif /* qh_NOmerge */
-
-   /*---------------------------------
-
-  qh_vertexintersect(qh, vertexsetA, vertexsetB )
-    intersects two vertex sets (inverse id ordered)
-    vertexsetA is a temporary set at the top of qh->qhmem.tempstack
-
-  returns:
-    replaces vertexsetA with the intersection
-
-  notes:
-    could overwrite vertexsetA if currently too slow
-*/
-void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
-  setT *intersection;
-
-  intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
-  qh_settempfree(qh, vertexsetA);
-  *vertexsetA= intersection;
-  qh_settemppush(qh, intersection);
-} /* vertexintersect */
-
-/*---------------------------------
-
-  qh_vertexintersect_new(qh, )
-    intersects two vertex sets (inverse id ordered)
-
-  returns:
-    a new set
-*/
-setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
-  setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
-  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
-
-  while (*vertexA && *vertexB) {
-    if (*vertexA  == *vertexB) {
-      qh_setappend(qh, &intersection, *vertexA);
-      vertexA++; vertexB++;
-    }else {
-      if ((*vertexA)->id > (*vertexB)->id)
-        vertexA++;
-      else
-        vertexB++;
-    }
-  }
-  return intersection;
-} /* vertexintersect_new */
-
-/*---------------------------------
-
-  qh_vertexneighbors(qh)
-    for each vertex in qh.facet_list,
-      determine its neighboring facets
-
-  returns:
-    sets qh.VERTEXneighbors
-      nop if qh.VERTEXneighbors already set
-      qh_addpoint() will maintain them
-
-  notes:
-    assumes all vertex->neighbors are NULL
-
-  design:
-    for each facet
-      for each vertex
-        append facet to vertex->neighbors
-*/
-void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  if (qh->VERTEXneighbors)
-    return;
-  trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
-  qh->vertex_visit++;
-  FORALLfacets {
-    if (facet->visible)
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh->vertex_visit) {
-        vertex->visitid= qh->vertex_visit;
-        vertex->neighbors= qh_setnew(qh, qh->hull_dim);
-      }
-      qh_setappend(qh, &vertex->neighbors, facet);
-    }
-  }
-  qh->VERTEXneighbors= True;
-} /* vertexneighbors */
-
-/*---------------------------------
-
-  qh_vertexsubset( vertexsetA, vertexsetB )
-    returns True if vertexsetA is a subset of vertexsetB
-    assumes vertexsets are sorted
-
-  note:
-    empty set is a subset of any other set
-*/
-boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
-  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
-
-  while (True) {
-    if (!*vertexA)
-      return True;
-    if (!*vertexB)
-      return False;
-    if ((*vertexA)->id > (*vertexB)->id)
-      return False;
-    if (*vertexA  == *vertexB)
-      vertexA++;
-    vertexB++;
-  }
-  return False; /* avoid warnings */
-} /* vertexsubset */
diff --git a/src/qhull/src/libqhull_r/poly_r.c b/src/qhull/src/libqhull_r/poly_r.c
deleted file mode 100644
index e5b479743..000000000
--- a/src/qhull/src/libqhull_r/poly_r.c
+++ /dev/null
@@ -1,1205 +0,0 @@
-/*
      ---------------------------------
-
-   poly_r.c
-   implements polygons and simplices
-
-   see qh-poly_r.htm, poly_r.h and libqhull_r.h
-
-   infrequent code is in poly2_r.c
-   (all but top 50 and their callers 12/3/95)
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/poly_r.c#3 $$Change: 2064 $
-   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_appendfacet(qh, facet )
-    appends facet to end of qh.facet_list,
-
-  returns:
-    updates qh.newfacet_list, facet_next, facet_list
-    increments qh.numfacets
-
-  notes:
-    assumes qh.facet_list/facet_tail is defined (createsimplex)
-
-  see:
-    qh_removefacet()
-
-*/
-void qh_appendfacet(qhT *qh, facetT *facet) {
-  facetT *tail= qh->facet_tail;
-
-  if (tail == qh->newfacet_list)
-    qh->newfacet_list= facet;
-  if (tail == qh->facet_next)
-    qh->facet_next= facet;
-  facet->previous= tail->previous;
-  facet->next= tail;
-  if (tail->previous)
-    tail->previous->next= facet;
-  else
-    qh->facet_list= facet;
-  tail->previous= facet;
-  qh->num_facets++;
-  trace4((qh, qh->ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
-} /* appendfacet */
-
-
-/*---------------------------------
-
-  qh_appendvertex(qh, vertex )
-    appends vertex to end of qh.vertex_list,
-
-  returns:
-    sets vertex->newlist
-    updates qh.vertex_list, newvertex_list
-    increments qh.num_vertices
-
-  notes:
-    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
-
-*/
-void qh_appendvertex(qhT *qh, vertexT *vertex) {
-  vertexT *tail= qh->vertex_tail;
-
-  if (tail == qh->newvertex_list)
-    qh->newvertex_list= vertex;
-  vertex->newlist= True;
-  vertex->previous= tail->previous;
-  vertex->next= tail;
-  if (tail->previous)
-    tail->previous->next= vertex;
-  else
-    qh->vertex_list= vertex;
-  tail->previous= vertex;
-  qh->num_vertices++;
-  trace4((qh, qh->ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
-} /* appendvertex */
-
-
-/*---------------------------------
-
-  qh_attachnewfacets(qh, )
-    attach horizon facets to new facets in qh.newfacet_list
-    newfacets have neighbor and ridge links to horizon but not vice versa
-    only needed for qh.ONLYgood
-
-  returns:
-    set qh.NEWfacets
-    horizon facets linked to new facets
-      ridges changed from visible facets to new facets
-      simplicial ridges deleted
-    qh.visible_list, no ridges valid
-    facet->f.replace is a newfacet (if any)
-
-  design:
-    delete interior ridges and neighbor sets by
-      for each visible, non-simplicial facet
-        for each ridge
-          if last visit or if neighbor is simplicial
-            if horizon neighbor
-              delete ridge for horizon's ridge set
-            delete ridge
-        erase neighbor set
-    attach horizon facets and new facets by
-      for all new facets
-        if corresponding horizon facet is simplicial
-          locate corresponding visible facet {may be more than one}
-          link visible facet to new facet
-          replace visible facet with new facet in horizon
-        else it's non-simplicial
-          for all visible neighbors of the horizon facet
-            link visible neighbor to new facet
-            delete visible neighbor from horizon facet
-          append new facet to horizon's neighbors
-          the first ridge of the new facet is the horizon ridge
-          link the new facet into the horizon ridge
-*/
-void qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
-  ridgeT *ridge, **ridgep;
-
-  qh->NEWfacets= True;
-  trace3((qh, qh->ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
-  qh->visit_id++;
-  FORALLvisible_facets {
-    visible->visitid= qh->visit_id;
-    if (visible->ridges) {
-      FOREACHridge_(visible->ridges) {
-        neighbor= otherfacet_(ridge, visible);
-        if (neighbor->visitid == qh->visit_id
-            || (!neighbor->visible && neighbor->simplicial)) {
-          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
-            qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(qh, &(ridge->vertices)); /* delete on 2nd visit */
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }
-      }
-      SETfirst_(visible->ridges)= NULL;
-    }
-    SETfirst_(visible->neighbors)= NULL;
-  }
-  trace1((qh, qh->ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
-  FORALLnew_facets {
-    horizon= SETfirstt_(newfacet->neighbors, facetT);
-    if (horizon->simplicial) {
-      visible= NULL;
-      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
-        if (neighbor->visible) {
-          if (visible) {
-            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
-                                  SETindex_(horizon->neighbors, neighbor))) {
-              visible= neighbor;
-              break;
-            }
-          }else
-            visible= neighbor;
-        }
-      }
-      if (visible) {
-        visible->f.replace= newfacet;
-        qh_setreplace(qh, horizon->neighbors, visible, newfacet);
-      }else {
-        qh_fprintf(qh, qh->ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
-                 horizon->id, newfacet->id);
-        qh_errexit2(qh, qh_ERRqhull, horizon, newfacet);
-      }
-    }else { /* non-simplicial, with a ridge for newfacet */
-      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
-        if (neighbor->visible) {
-          neighbor->f.replace= newfacet;
-          qh_setdelnth(qh, horizon->neighbors,
-                        SETindex_(horizon->neighbors, neighbor));
-          neighborp--; /* repeat */
-        }
-      }
-      qh_setappend(qh, &horizon->neighbors, newfacet);
-      ridge= SETfirstt_(newfacet->ridges, ridgeT);
-      if (ridge->top == horizon)
-        ridge->bottom= newfacet;
-      else
-        ridge->top= newfacet;
-      }
-  } /* newfacets */
-  if (qh->PRINTstatistics) {
-    FORALLvisible_facets {
-      if (!visible->f.replace)
-        zinc_(Zinsidevisible);
-    }
-  }
-} /* attachnewfacets */
-
-/*---------------------------------
-
-  qh_checkflipped(qh, facet, dist, allerror )
-    checks facet orientation to interior point
-
-    if allerror set,
-      tests against qh.DISTround
-    else
-      tests against 0 since tested against DISTround before
-
-  returns:
-    False if it flipped orientation (sets facet->flipped)
-    distance if non-NULL
-*/
-boolT qh_checkflipped(qhT *qh, facetT *facet, realT *distp, boolT allerror) {
-  realT dist;
-
-  if (facet->flipped && !distp)
-    return False;
-  zzinc_(Zdistcheck);
-  qh_distplane(qh, qh->interior_point, facet, &dist);
-  if (distp)
-    *distp= dist;
-  if ((allerror && dist > -qh->DISTround)|| (!allerror && dist >= 0.0)) {
-    facet->flipped= True;
-    zzinc_(Zflippedfacets);
-    trace0((qh, qh->ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
-              facet->id, dist, qh->furthest_id));
-    qh_precision(qh, "flipped facet");
-    return False;
-  }
-  return True;
-} /* checkflipped */
-
-/*---------------------------------
-
-  qh_delfacet(qh, facet )
-    removes facet from facet_list and frees up its memory
-
-  notes:
-    assumes vertices and ridges already freed
-*/
-void qh_delfacet(qhT *qh, facetT *facet) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-
-  trace4((qh, qh->ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
-  if (facet == qh->tracefacet)
-    qh->tracefacet= NULL;
-  if (facet == qh->GOODclosest)
-    qh->GOODclosest= NULL;
-  qh_removefacet(qh, facet);
-  if (!facet->tricoplanar || facet->keepcentrum) {
-    qh_memfree_(qh, facet->normal, qh->normal_size, freelistp);
-    if (qh->CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
-      qh_memfree_(qh, facet->center, qh->center_size, freelistp);
-    }else /* AScentrum */ {
-      qh_memfree_(qh, facet->center, qh->normal_size, freelistp);
-    }
-  }
-  qh_setfree(qh, &(facet->neighbors));
-  if (facet->ridges)
-    qh_setfree(qh, &(facet->ridges));
-  qh_setfree(qh, &(facet->vertices));
-  if (facet->outsideset)
-    qh_setfree(qh, &(facet->outsideset));
-  if (facet->coplanarset)
-    qh_setfree(qh, &(facet->coplanarset));
-  qh_memfree_(qh, facet, (int)sizeof(facetT), freelistp);
-} /* delfacet */
-
-
-/*---------------------------------
-
-  qh_deletevisible()
-    delete visible facets and vertices
-
-  returns:
-    deletes each facet and removes from facetlist
-    at exit, qh.visible_list empty (== qh.newfacet_list)
-
-  notes:
-    ridges already deleted
-    horizon facets do not reference facets on qh.visible_list
-    new facets in qh.newfacet_list
-    uses   qh.visit_id;
-*/
-void qh_deletevisible(qhT *qh /*qh.visible_list*/) {
-  facetT *visible, *nextfacet;
-  vertexT *vertex, **vertexp;
-  int numvisible= 0, numdel= qh_setsize(qh, qh->del_vertices);
-
-  trace1((qh, qh->ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
-         qh->num_visible, numdel));
-  for (visible= qh->visible_list; visible && visible->visible;
-                visible= nextfacet) { /* deleting current */
-    nextfacet= visible->next;
-    numvisible++;
-    qh_delfacet(qh, visible);
-  }
-  if (numvisible != qh->num_visible) {
-    qh_fprintf(qh, qh->ferr, 6103, "qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d\n",
-             qh->num_visible, numvisible);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-  qh->num_visible= 0;
-  zadd_(Zvisfacettot, numvisible);
-  zmax_(Zvisfacetmax, numvisible);
-  zzadd_(Zdelvertextot, numdel);
-  zmax_(Zdelvertexmax, numdel);
-  FOREACHvertex_(qh->del_vertices)
-    qh_delvertex(qh, vertex);
-  qh_settruncate(qh, qh->del_vertices, 0);
-} /* deletevisible */
-
-/*---------------------------------
-
-  qh_facetintersect(qh, facetA, facetB, skipa, skipB, prepend )
-    return vertices for intersection of two simplicial facets
-    may include 1 prepended entry (if more, need to settemppush)
-
-  returns:
-    returns set of qh.hull_dim-1 + prepend vertices
-    returns skipped index for each test and checks for exactly one
-
-  notes:
-    does not need settemp since set in quick memory
-
-  see also:
-    qh_vertexintersect and qh_vertexintersect_new
-    use qh_setnew_delnthsorted to get nth ridge (no skip information)
-
-  design:
-    locate skipped vertex by scanning facet A's neighbors
-    locate skipped vertex by scanning facet B's neighbors
-    intersect the vertex sets
-*/
-setT *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB,
-                         int *skipA,int *skipB, int prepend) {
-  setT *intersect;
-  int dim= qh->hull_dim, i, j;
-  facetT **neighborsA, **neighborsB;
-
-  neighborsA= SETaddr_(facetA->neighbors, facetT);
-  neighborsB= SETaddr_(facetB->neighbors, facetT);
-  i= j= 0;
-  if (facetB == *neighborsA++)
-    *skipA= 0;
-  else if (facetB == *neighborsA++)
-    *skipA= 1;
-  else if (facetB == *neighborsA++)
-    *skipA= 2;
-  else {
-    for (i=3; i < dim; i++) {
-      if (facetB == *neighborsA++) {
-        *skipA= i;
-        break;
-      }
-    }
-  }
-  if (facetA == *neighborsB++)
-    *skipB= 0;
-  else if (facetA == *neighborsB++)
-    *skipB= 1;
-  else if (facetA == *neighborsB++)
-    *skipB= 2;
-  else {
-    for (j=3; j < dim; j++) {
-      if (facetA == *neighborsB++) {
-        *skipB= j;
-        break;
-      }
-    }
-  }
-  if (i >= dim || j >= dim) {
-    qh_fprintf(qh, qh->ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
-            facetA->id, facetB->id);
-    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
-  }
-  intersect= qh_setnew_delnthsorted(qh, facetA->vertices, qh->hull_dim, *skipA, prepend);
-  trace4((qh, qh->ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
-          facetA->id, *skipA, facetB->id, *skipB));
-  return(intersect);
-} /* facetintersect */
-
-/*---------------------------------
-
-  qh_gethash(qh, hashsize, set, size, firstindex, skipelem )
-    return hashvalue for a set with firstindex and skipelem
-
-  notes:
-    returned hash is in [0,hashsize)
-    assumes at least firstindex+1 elements
-    assumes skipelem is NULL, in set, or part of hash
-
-    hashes memory addresses which may change over different runs of the same data
-    using sum for hash does badly in high d
-*/
-int qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem) {
-  void **elemp= SETelemaddr_(set, firstindex, void);
-  ptr_intT hash = 0, elem;
-  unsigned result;
-  int i;
-#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
-#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
-#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
-#endif
-
-  switch (size-firstindex) {
-  case 1:
-    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
-    break;
-  case 2:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
-    break;
-  case 3:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      - (ptr_intT) skipelem;
-    break;
-  case 4:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
-    break;
-  case 5:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
-    break;
-  case 6:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
-      - (ptr_intT) skipelem;
-    break;
-  default:
-    hash= 0;
-    i= 3;
-    do {     /* this is about 10% in 10-d */
-      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
-        hash ^= (elem << i) + (elem >> (32-i));
-        i += 3;
-        if (i >= 32)
-          i -= 32;
-      }
-    }while (*elemp);
-    break;
-  }
-  if (hashsize<0) {
-    qh_fprintf(qh, qh->ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
-    qh_errexit2(qh, qh_ERRqhull, NULL, NULL);
-  }
-  result= (unsigned)hash;
-  result %= (unsigned)hashsize;
-  /* result= 0; for debugging */
-  return result;
-#ifdef _MSC_VER
-#pragma warning( pop)
-#endif
-} /* gethash */
-
-/*---------------------------------
-
-  qh_makenewfacet(qh, vertices, toporient, horizon )
-    creates a toporient? facet from vertices
-
-  returns:
-    returns newfacet
-      adds newfacet to qh.facet_list
-      newfacet->vertices= vertices
-      if horizon
-        newfacet->neighbor= horizon, but not vice versa
-    newvertex_list updated with vertices
-*/
-facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient,facetT *horizon) {
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex(qh, vertex);
-      qh_appendvertex(qh, vertex);
-    }
-  }
-  newfacet= qh_newfacet(qh);
-  newfacet->vertices= vertices;
-  newfacet->toporient= (unsigned char)toporient;
-  if (horizon)
-    qh_setappend(qh, &(newfacet->neighbors), horizon);
-  qh_appendfacet(qh, newfacet);
-  return(newfacet);
-} /* makenewfacet */
-
-
-/*---------------------------------
-
-  qh_makenewplanes()
-    make new hyperplanes for facets on qh.newfacet_list
-
-  returns:
-    all facets have hyperplanes or are marked for   merging
-    doesn't create hyperplane if horizon is coplanar (will merge)
-    updates qh.min_vertex if qh.JOGGLEmax
-
-  notes:
-    facet->f.samecycle is defined for facet->mergehorizon facets
-*/
-void qh_makenewplanes(qhT *qh /* qh.newfacet_list */) {
-  facetT *newfacet;
-
-  FORALLnew_facets {
-    if (!newfacet->mergehorizon)
-      qh_setfacetplane(qh, newfacet);
-  }
-  if (qh->JOGGLEmax < REALmax/2)
-    minimize_(qh->min_vertex, -wwval_(Wnewvertexmax));
-} /* makenewplanes */
-
-/*---------------------------------
-
-  qh_makenew_nonsimplicial(qh, visible, apex, numnew )
-    make new facets for ridges of a visible facet
-
-  returns:
-    first newfacet, bumps numnew as needed
-    attaches new facets if !qh.ONLYgood
-    marks ridge neighbors for simplicial visible
-    if (qh.ONLYgood)
-      ridges on newfacet, horizon, and visible
-    else
-      ridge and neighbors between newfacet and   horizon
-      visible facet's ridges are deleted
-
-  notes:
-    qh.visit_id if visible has already been processed
-    sets neighbor->seen for building f.samecycle
-      assumes all 'seen' flags initially false
-
-  design:
-    for each ridge of visible facet
-      get neighbor of visible facet
-      if neighbor was already processed
-        delete the ridge (will delete all visible facets later)
-      if neighbor is a horizon facet
-        create a new facet
-        if neighbor coplanar
-          adds newfacet to f.samecycle for later merging
-        else
-          updates neighbor's neighbor set
-          (checks for non-simplicial facet with multiple ridges to visible facet)
-        updates neighbor's ridge set
-        (checks for simplicial neighbor to non-simplicial visible facet)
-        (deletes ridge if neighbor is simplicial)
-
-*/
-#ifndef qh_NOmerge
-facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor, *newfacet= NULL, *samecycle;
-  setT *vertices;
-  boolT toporient;
-  int ridgeid;
-
-  FOREACHridge_(visible->ridges) {
-    ridgeid= ridge->id;
-    neighbor= otherfacet_(ridge, visible);
-    if (neighbor->visible) {
-      if (!qh->ONLYgood) {
-        if (neighbor->visitid == qh->visit_id) {
-          qh_setfree(qh, &(ridge->vertices));  /* delete on 2nd visit */
-          qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
-        }
-      }
-    }else {  /* neighbor is an horizon facet */
-      toporient= (ridge->top == visible);
-      vertices= qh_setnew(qh, qh->hull_dim); /* makes sure this is quick */
-      qh_setappend(qh, &vertices, apex);
-      qh_setappend_set(qh, &vertices, ridge->vertices);
-      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar) {
-        newfacet->mergehorizon= True;
-        if (!neighbor->seen) {
-          newfacet->f.samecycle= newfacet;
-          neighbor->f.newcycle= newfacet;
-        }else {
-          samecycle= neighbor->f.newcycle;
-          newfacet->f.samecycle= samecycle->f.samecycle;
-          samecycle->f.samecycle= newfacet;
-        }
-      }
-      if (qh->ONLYgood) {
-        if (!neighbor->simplicial)
-          qh_setappend(qh, &(newfacet->ridges), ridge);
-      }else {  /* qh_attachnewfacets */
-        if (neighbor->seen) {
-          if (neighbor->simplicial) {
-            qh_fprintf(qh, qh->ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
-                   neighbor->id, visible->id);
-            qh_errexit2(qh, qh_ERRqhull, neighbor, visible);
-          }
-          qh_setappend(qh, &(neighbor->neighbors), newfacet);
-        }else
-          qh_setreplace(qh, neighbor->neighbors, visible, newfacet);
-        if (neighbor->simplicial) {
-          qh_setdel(neighbor->ridges, ridge);
-          qh_setfree(qh, &(ridge->vertices));
-          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
-        }else {
-          qh_setappend(qh, &(newfacet->ridges), ridge);
-          if (toporient)
-            ridge->top= newfacet;
-          else
-            ridge->bottom= newfacet;
-        }
-      trace4((qh, qh->ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
-            newfacet->id, apex->id, ridgeid, neighbor->id));
-      }
-    }
-    neighbor->seen= True;
-  } /* for each ridge */
-  if (!qh->ONLYgood)
-    SETfirst_(visible->ridges)= NULL;
-  return newfacet;
-} /* makenew_nonsimplicial */
-#else /* qh_NOmerge */
-facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_makenew_simplicial(qh, visible, apex, numnew )
-    make new facets for simplicial visible facet and apex
-
-  returns:
-    attaches new facets if (!qh.ONLYgood)
-      neighbors between newfacet and horizon
-
-  notes:
-    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
-
-  design:
-    locate neighboring horizon facet for visible facet
-    determine vertices and orientation
-    create new facet
-    if coplanar,
-      add new facet to f.samecycle
-    update horizon facet's neighbor list
-*/
-facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
-  facetT *neighbor, **neighborp, *newfacet= NULL;
-  setT *vertices;
-  boolT flip, toporient;
-  int horizonskip= 0, visibleskip= 0;
-
-  FOREACHneighbor_(visible) {
-    if (!neighbor->seen && !neighbor->visible) {
-      vertices= qh_facetintersect(qh, neighbor,visible, &horizonskip, &visibleskip, 1);
-      SETfirst_(vertices)= apex;
-      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
-      if (neighbor->toporient)
-        toporient= horizonskip & 0x1;
-      else
-        toporient= (horizonskip & 0x1) ^ 0x1;
-      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar && (qh->PREmerge || qh->MERGEexact)) {
-#ifndef qh_NOmerge
-        newfacet->f.samecycle= newfacet;
-        newfacet->mergehorizon= True;
-#endif
-      }
-      if (!qh->ONLYgood)
-        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
-      trace4((qh, qh->ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
-            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
-              neighbor->toporient, visible->id, visibleskip, flip));
-    }
-  }
-  return newfacet;
-} /* makenew_simplicial */
-
-/*---------------------------------
-
-  qh_matchneighbor(qh, newfacet, newskip, hashsize, hashcount )
-    either match subridge of newfacet with neighbor or add to hash_table
-
-  returns:
-    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
-
-  notes:
-    ridge is newfacet->vertices w/o newskip vertex
-    do not allocate memory (need to free hash_table cleanly)
-    uses linear hash chains
-
-  see also:
-    qh_matchduplicates
-
-  design:
-    for each possible matching facet in qh.hash_table
-      if vertices match
-        set ismatch, if facets have opposite orientation
-        if ismatch and matching facet doesn't have a match
-          match the facets by updating their neighbor sets
-        else
-          indicate a duplicate ridge
-          set facet hyperplane for later testing
-          add facet to hashtable
-          unless the other facet was already a duplicate ridge
-            mark both facets with a duplicate ridge
-            add other facet (if defined) to hash table
-*/
-void qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize, int *hashcount) {
-  boolT newfound= False;   /* True, if new facet is already in hash chain */
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *matchfacet;
-  int skip, matchskip;
-
-  hash= qh_gethash(qh, hashsize, newfacet->vertices, qh->hull_dim, 1,
-                     SETelem_(newfacet->vertices, newskip));
-  trace4((qh, qh->ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
-          newfacet->id, newskip, hash, *hashcount));
-  zinc_(Zhashlookup);
-  for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (facet == newfacet) {
-      newfound= True;
-      continue;
-    }
-    zinc_(Zhashtests);
-    if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-      if (SETelem_(newfacet->vertices, newskip) ==
-          SETelem_(facet->vertices, skip)) {
-        qh_precision(qh, "two facets with the same vertices");
-        qh_fprintf(qh, qh->ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
-          facet->id, newfacet->id);
-        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
-      }
-      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
-      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
-      if (ismatch && !matchfacet) {
-        SETelem_(facet->neighbors, skip)= newfacet;
-        SETelem_(newfacet->neighbors, newskip)= facet;
-        (*hashcount)--;
-        trace4((qh, qh->ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
-           facet->id, skip, newfacet->id, newskip));
-        return;
-      }
-      if (!qh->PREmerge && !qh->MERGEexact) {
-        qh_precision(qh, "a ridge with more than two neighbors");
-        qh_fprintf(qh, qh->ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
-                 facet->id, newfacet->id, getid_(matchfacet));
-        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
-      }
-      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
-      newfacet->dupridge= True;
-      if (!newfacet->normal)
-        qh_setfacetplane(qh, newfacet);
-      qh_addhash(newfacet, qh->hash_table, hashsize, hash);
-      (*hashcount)++;
-      if (!facet->normal)
-        qh_setfacetplane(qh, facet);
-      if (matchfacet != qh_DUPLICATEridge) {
-        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
-        facet->dupridge= True;
-        if (!facet->normal)
-          qh_setfacetplane(qh, facet);
-        if (matchfacet) {
-          matchskip= qh_setindex(matchfacet->neighbors, facet);
-          if (matchskip<0) {
-              qh_fprintf(qh, qh->ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
-                  matchfacet->id, facet->id);
-              qh_errexit2(qh, qh_ERRqhull, matchfacet, facet);
-          }
-          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
-          matchfacet->dupridge= True;
-          if (!matchfacet->normal)
-            qh_setfacetplane(qh, matchfacet);
-          qh_addhash(matchfacet, qh->hash_table, hashsize, hash);
-          *hashcount += 2;
-        }
-      }
-      trace4((qh, qh->ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
-           newfacet->id, newskip, facet->id, skip,
-           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
-           ismatch, hash));
-      return; /* end of duplicate ridge */
-    }
-  }
-  if (!newfound)
-    SETelem_(qh->hash_table, scan)= newfacet;  /* same as qh_addhash */
-  (*hashcount)++;
-  trace4((qh, qh->ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
-           newfacet->id, newskip, hash));
-} /* matchneighbor */
-
-
-/*---------------------------------
-
-  qh_matchnewfacets()
-    match newfacets in qh.newfacet_list to their newfacet neighbors
-
-  returns:
-    qh.newfacet_list with full neighbor sets
-      get vertices with nth neighbor by deleting nth vertex
-    if qh.PREmerge/MERGEexact or qh.FORCEoutput
-      sets facet->flippped if flipped normal (also prevents point partitioning)
-    if duplicate ridges and qh.PREmerge/MERGEexact
-      sets facet->dupridge
-      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
-
-  notes:
-    newfacets already have neighbor[0] (horizon facet)
-    assumes qh.hash_table is NULL
-    vertex->neighbors has not been updated yet
-    do not allocate memory after qh.hash_table (need to free it cleanly)
-
-  design:
-    delete neighbor sets for all new facets
-    initialize a hash table
-    for all new facets
-      match facet with neighbors
-    if unmatched facets (due to duplicate ridges)
-      for each new facet with a duplicate ridge
-        match it with a facet
-    check for flipped facets
-*/
-void qh_matchnewfacets(qhT *qh /* qh.newfacet_list */) {
-  int numnew=0, hashcount=0, newskip;
-  facetT *newfacet, *neighbor;
-  int dim= qh->hull_dim, hashsize, neighbor_i, neighbor_n;
-  setT *neighbors;
-#ifndef qh_NOtrace
-  int facet_i, facet_n, numfree= 0;
-  facetT *facet;
-#endif
-
-  trace1((qh, qh->ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
-  FORALLnew_facets {
-    numnew++;
-    {  /* inline qh_setzero(qh, newfacet->neighbors, 1, qh->hull_dim); */
-      neighbors= newfacet->neighbors;
-      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
-      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
-    }
-  }
-
-  qh_newhashtable(qh, numnew*(qh->hull_dim-1)); /* twice what is normally needed,
-                                     but every ridge could be DUPLICATEridge */
-  hashsize= qh_setsize(qh, qh->hash_table);
-  FORALLnew_facets {
-    for (newskip=1; newskiphull_dim; newskip++) /* furthest/horizon already matched */
-      /* hashsize>0 because hull_dim>1 and numnew>0 */
-      qh_matchneighbor(qh, newfacet, newskip, hashsize, &hashcount);
-#if 0   /* use the following to trap hashcount errors */
-    {
-      int count= 0, k;
-      facetT *facet, *neighbor;
-
-      count= 0;
-      FORALLfacet_(qh->newfacet_list) {  /* newfacet already in use */
-        for (k=1; k < qh->hull_dim; k++) {
-          neighbor= SETelemt_(facet->neighbors, k, facetT);
-          if (!neighbor || neighbor == qh_DUPLICATEridge)
-            count++;
-        }
-        if (facet == newfacet)
-          break;
-      }
-      if (count != hashcount) {
-        qh_fprintf(qh, qh->ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
-                 newfacet->id, hashcount, count);
-        qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
-      }
-    }
-#endif  /* end of trap code */
-  }
-  if (hashcount) {
-    FORALLnew_facets {
-      if (newfacet->dupridge) {
-        FOREACHneighbor_i_(qh, newfacet) {
-          if (neighbor == qh_DUPLICATEridge) {
-            qh_matchduplicates(qh, newfacet, neighbor_i, hashsize, &hashcount);
-                    /* this may report MERGEfacet */
-          }
-        }
-      }
-    }
-  }
-  if (hashcount) {
-    qh_fprintf(qh, qh->ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
-        hashcount);
-    qh_printhashtable(qh, qh->ferr);
-    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
-  }
-#ifndef qh_NOtrace
-  if (qh->IStracing >= 2) {
-    FOREACHfacet_i_(qh, qh->hash_table) {
-      if (!facet)
-        numfree++;
-    }
-    qh_fprintf(qh, qh->ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
-             numnew, numfree, qh_setsize(qh, qh->hash_table));
-  }
-#endif /* !qh_NOtrace */
-  qh_setfree(qh, &qh->hash_table);
-  if (qh->PREmerge || qh->MERGEexact) {
-    if (qh->IStracing >= 4)
-      qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
-    FORALLnew_facets {
-      if (newfacet->normal)
-        qh_checkflipped(qh, newfacet, NULL, qh_ALL);
-    }
-  }else if (qh->FORCEoutput)
-    qh_checkflipped_all(qh, qh->newfacet_list);  /* prints warnings for flipped */
-} /* matchnewfacets */
-
-
-/*---------------------------------
-
-  qh_matchvertices(qh, firstindex, verticesA, skipA, verticesB, skipB, same )
-    tests whether vertices match with a single skip
-    starts match at firstindex since all new facets have a common vertex
-
-  returns:
-    true if matched vertices
-    skip index for each set
-    sets same iff vertices have the same orientation
-
-  notes:
-    assumes skipA is in A and both sets are the same size
-
-  design:
-    set up pointers
-    scan both sets checking for a match
-    test orientation
-*/
-boolT qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
-       setT *verticesB, int *skipB, boolT *same) {
-  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
-
-  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
-  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
-  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
-  do if (elemAp != skipAp) {
-    while (*elemAp != *elemBp++) {
-      if (skipBp)
-        return False;
-      skipBp= elemBp;  /* one extra like FOREACH */
-    }
-  }while (*(++elemAp));
-  if (!skipBp)
-    skipBp= ++elemBp;
-  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
-  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
-  trace4((qh, qh->ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
-          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
-  return(True);
-} /* matchvertices */
-
-/*---------------------------------
-
-  qh_newfacet(qh)
-    return a new facet
-
-  returns:
-    all fields initialized or cleared   (NULL)
-    preallocates neighbors set
-*/
-facetT *qh_newfacet(qhT *qh) {
-  facetT *facet;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, (int)sizeof(facetT), freelistp, facet, facetT);
-  memset((char *)facet, (size_t)0, sizeof(facetT));
-  if (qh->facet_id == qh->tracefacet_id)
-    qh->tracefacet= facet;
-  facet->id= qh->facet_id++;
-  facet->neighbors= qh_setnew(qh, qh->hull_dim);
-#if !qh_COMPUTEfurthest
-  facet->furthestdist= 0.0;
-#endif
-#if qh_MAXoutside
-  if (qh->FORCEoutput && qh->APPROXhull)
-    facet->maxoutside= qh->MINoutside;
-  else
-    facet->maxoutside= qh->DISTround;
-#endif
-  facet->simplicial= True;
-  facet->good= True;
-  facet->newfacet= True;
-  trace4((qh, qh->ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
-  return(facet);
-} /* newfacet */
-
-
-/*---------------------------------
-
-  qh_newridge()
-    return a new ridge
-*/
-ridgeT *qh_newridge(qhT *qh) {
-  ridgeT *ridge;
-  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
-
-  qh_memalloc_(qh, (int)sizeof(ridgeT), freelistp, ridge, ridgeT);
-  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
-  zinc_(Ztotridges);
-  if (qh->ridge_id == UINT_MAX) {
-    qh_fprintf(qh, qh->ferr, 7074, "\
-qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
-  }
-  ridge->id= qh->ridge_id++;
-  trace4((qh, qh->ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
-  return(ridge);
-} /* newridge */
-
-
-/*---------------------------------
-
-  qh_pointid(qh, point )
-    return id for a point,
-    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
-
-  alternative code if point is in qh.first_point...
-    unsigned long id;
-    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
-
-  notes:
-    Valid points are non-negative
-    WARN64 -- id truncated to 32-bits, at most 2G points
-    NOerrors returned (QhullPoint::id)
-    if point not in point array
-      the code does a comparison of unrelated pointers.
-*/
-int qh_pointid(qhT *qh, pointT *point) {
-  ptr_intT offset, id;
-
-  if (!point || !qh)
-    return qh_IDnone;
-  else if (point == qh->interior_point)
-    return qh_IDinterior;
-  else if (point >= qh->first_point
-  && point < qh->first_point + qh->num_points * qh->hull_dim) {
-    offset= (ptr_intT)(point - qh->first_point);
-    id= offset / qh->hull_dim;
-  }else if ((id= qh_setindex(qh->other_points, point)) != -1)
-    id += qh->num_points;
-  else
-    return qh_IDunknown;
-  return (int)id;
-} /* pointid */
-
-/*---------------------------------
-
-  qh_removefacet(qh, facet )
-    unlinks facet from qh.facet_list,
-
-  returns:
-    updates qh.facet_list .newfacet_list .facet_next visible_list
-    decrements qh.num_facets
-
-  see:
-    qh_appendfacet
-*/
-void qh_removefacet(qhT *qh, facetT *facet) {
-  facetT *next= facet->next, *previous= facet->previous;
-
-  if (facet == qh->newfacet_list)
-    qh->newfacet_list= next;
-  if (facet == qh->facet_next)
-    qh->facet_next= next;
-  if (facet == qh->visible_list)
-    qh->visible_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st facet in qh->facet_list */
-    qh->facet_list= next;
-    qh->facet_list->previous= NULL;
-  }
-  qh->num_facets--;
-  trace4((qh, qh->ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
-} /* removefacet */
-
-
-/*---------------------------------
-
-  qh_removevertex(qh, vertex )
-    unlinks vertex from qh.vertex_list,
-
-  returns:
-    updates qh.vertex_list .newvertex_list
-    decrements qh.num_vertices
-*/
-void qh_removevertex(qhT *qh, vertexT *vertex) {
-  vertexT *next= vertex->next, *previous= vertex->previous;
-
-  if (vertex == qh->newvertex_list)
-    qh->newvertex_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st vertex in qh->vertex_list */
-    qh->vertex_list= vertex->next;
-    qh->vertex_list->previous= NULL;
-  }
-  qh->num_vertices--;
-  trace4((qh, qh->ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
-} /* removevertex */
-
-
-/*---------------------------------
-
-  qh_updatevertices()
-    update vertex neighbors and delete interior vertices
-
-  returns:
-    if qh.VERTEXneighbors, updates neighbors for each vertex
-      if qh.newvertex_list,
-         removes visible neighbors  from vertex neighbors
-      if qh.newfacet_list
-         adds new facets to vertex neighbors
-    if qh.visible_list
-       interior vertices added to qh.del_vertices for later partitioning
-
-  design:
-    if qh.VERTEXneighbors
-      deletes references to visible facets from vertex neighbors
-      appends new facets to the neighbor list for each vertex
-      checks all vertices of visible facets
-        removes visible facets from neighbor lists
-        marks unused vertices for deletion
-*/
-void qh_updatevertices(qhT *qh /*qh.newvertex_list, newfacet_list, visible_list*/) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
-  vertexT *vertex, **vertexp;
-
-  trace3((qh, qh->ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
-  if (qh->VERTEXneighbors) {
-    FORALLvertex_(qh->newvertex_list) {
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visible)
-          SETref_(neighbor)= NULL;
-      }
-      qh_setcompact(qh, vertex->neighbors);
-    }
-    FORALLnew_facets {
-      FOREACHvertex_(newfacet->vertices)
-        qh_setappend(qh, &vertex->neighbors, newfacet);
-    }
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          FOREACHneighbor_(vertex) { /* this can happen under merging */
-            if (!neighbor->visible)
-              break;
-          }
-          if (neighbor)
-            qh_setdel(vertex->neighbors, visible);
-          else {
-            vertex->deleted= True;
-            qh_setappend(qh, &qh->del_vertices, vertex);
-            trace2((qh, qh->ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
-          }
-        }
-      }
-    }
-  }else {  /* !VERTEXneighbors */
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          vertex->deleted= True;
-          qh_setappend(qh, &qh->del_vertices, vertex);
-          trace2((qh, qh->ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
-                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
-        }
-      }
-    }
-  }
-} /* updatevertices */
-
-
-
diff --git a/src/qhull/src/libqhull_r/poly_r.h b/src/qhull/src/libqhull_r/poly_r.h
deleted file mode 100644
index c71511bd6..000000000
--- a/src/qhull/src/libqhull_r/poly_r.h
+++ /dev/null
@@ -1,303 +0,0 @@
-/*
      ---------------------------------
-
-   poly_r.h
-   header file for poly_r.c and poly2_r.c
-
-   see qh-poly_r.htm, libqhull_r.h and poly_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/poly_r.h#5 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-#include "libqhull_r.h"
-
-/*===============   constants ========================== */
-
-/*----------------------------------
-
-  ALGORITHMfault
-    use as argument to checkconvex() to report errors during buildhull
-*/
-#define qh_ALGORITHMfault 0
-
-/*----------------------------------
-
-  DATAfault
-    use as argument to checkconvex() to report errors during initialhull
-*/
-#define qh_DATAfault 1
-
-/*----------------------------------
-
-  DUPLICATEridge
-    special value for facet->neighbor to indicate a duplicate ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge (facetT *)1L
-
-/*----------------------------------
-
-  MERGEridge       flag in facet
-    special value for facet->neighbor to indicate a merged ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge (facetT *)2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FORALLfacet_( facetlist ) { ... }
-    assign 'facet' to each facet in facetlist
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )
-
-/*----------------------------------
-
-  FORALLnew_facets { ... }
-    assign 'newfacet' to each facet in qh.newfacet_list
-
-  notes:
-    uses 'facetT *newfacet;'
-    at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for ( newfacet=qh->newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*----------------------------------
-
-  FORALLvertex_( vertexlist ) { ... }
-    assign 'vertex' to each vertex in vertexlist
-
-  notes:
-    uses 'vertexT *vertex;'
-    at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*----------------------------------
-
-  FORALLvisible_facets { ... }
-    assign 'visible' to each visible facet in qh.visible_list
-
-  notes:
-    uses 'vacetT *visible;'
-    at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh->visible_list; visible && visible->visible; visible= visible->next)
-
-/*----------------------------------
-
-  FORALLsame_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*----------------------------------
-
-  FORALLsame_cycle_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
-     for (same= newfacet->f.samecycle; \
-         same; same= (same == newfacet ?  NULL : same->f.samecycle))
-
-/*----------------------------------
-
-  FOREACHneighborA_( facet ) { ... }
-    assign 'neighborA' to each neighbor in facet->neighbors
-
-  FOREACHneighborA_( vertex ) { ... }
-    assign 'neighborA' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighborA, **neighborAp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*----------------------------------
-
-  FOREACHvisible_( facets ) { ... }
-    assign 'visible' to each facet in facets
-
-  notes:
-    uses 'facetT *facet, *facetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*----------------------------------
-
-  FOREACHnewfacet_( facets ) { ... }
-    assign 'newfacet' to each facet in facets
-
-  notes:
-    uses 'facetT *newfacet, *newfacetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*----------------------------------
-
-  FOREACHvertexA_( vertices ) { ... }
-    assign 'vertexA' to each vertex in vertices
-
-  notes:
-    uses 'vertexT *vertexA, *vertexAp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*----------------------------------
-
-  FOREACHvertexreverse12_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices
-    reverse order of first two vertices
-
-  notes:
-    uses 'vertexT *vertex, *vertexp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly_r.c in alphabetical order ================*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void    qh_appendfacet(qhT *qh, facetT *facet);
-void    qh_appendvertex(qhT *qh, vertexT *vertex);
-void    qh_attachnewfacets(qhT *qh /* qh.visible_list, qh.newfacet_list */);
-boolT   qh_checkflipped(qhT *qh, facetT *facet, realT *dist, boolT allerror);
-void    qh_delfacet(qhT *qh, facetT *facet);
-void    qh_deletevisible(qhT *qh /* qh.visible_list, qh.horizon_list */);
-setT   *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
-int     qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem);
-facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient, facetT *facet);
-void    qh_makenewplanes(qhT *qh /* qh.newfacet_list */);
-facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
-facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
-void    qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize,
-                          int *hashcount);
-void    qh_matchnewfacets(qhT *qh);
-boolT   qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
-                          setT *verticesB, int *skipB, boolT *same);
-facetT *qh_newfacet(qhT *qh);
-ridgeT *qh_newridge(qhT *qh);
-int     qh_pointid(qhT *qh, pointT *point);
-void    qh_removefacet(qhT *qh, facetT *facet);
-void    qh_removevertex(qhT *qh, vertexT *vertex);
-void    qh_updatevertices(qhT *qh);
-
-
-/*========== -prototypes poly2_r.c in alphabetical order ===========*/
-
-void    qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash);
-void    qh_check_bestdist(qhT *qh);
-void    qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2);
-void    qh_check_maxout(qhT *qh);
-void    qh_check_output(qhT *qh);
-void    qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
-void    qh_check_points(qhT *qh);
-void    qh_checkconvex(qhT *qh, facetT *facetlist, int fault);
-void    qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp);
-void    qh_checkflipped_all(qhT *qh, facetT *facetlist);
-void    qh_checkpolygon(qhT *qh, facetT *facetlist);
-void    qh_checkvertex(qhT *qh, vertexT *vertex);
-void    qh_clearcenters(qhT *qh, qh_CENTER type);
-void    qh_createsimplex(qhT *qh, setT *vertices);
-void    qh_delridge(qhT *qh, ridgeT *ridge);
-void    qh_delvertex(qhT *qh, vertexT *vertex);
-setT   *qh_facet3vertex(qhT *qh, facetT *facet);
-facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
-facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
-                          int *numpart);
-int     qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon);
-void    qh_findgood_all(qhT *qh, facetT *facetlist);
-void    qh_furthestnext(qhT *qh /* qh.facet_list */);
-void    qh_furthestout(qhT *qh, facetT *facet);
-void    qh_infiniteloop(qhT *qh, facetT *facet);
-void    qh_initbuild(qhT *qh);
-void    qh_initialhull(qhT *qh, setT *vertices);
-setT   *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints);
-vertexT *qh_isvertex(pointT *point, setT *vertices);
-vertexT *qh_makenewfacets(qhT *qh, pointT *point /*horizon_list, visible_list*/);
-void    qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount);
-void    qh_nearcoplanar(qhT *qh /* qh.facet_list */);
-vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
-int     qh_newhashtable(qhT *qh, int newsize);
-vertexT *qh_newvertex(qhT *qh, pointT *point);
-ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
-void    qh_outcoplanar(qhT *qh /* qh.facet_list */);
-pointT *qh_point(qhT *qh, int id);
-void    qh_point_add(qhT *qh, setT *set, pointT *point, void *elem);
-setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
-setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
-void    qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist);
-void    qh_printhashtable(qhT *qh, FILE *fp);
-void    qh_printlists(qhT *qh);
-void    qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list qh.newfacet_list qh.visible_list*/);
-void    qh_setvoronoi_all(qhT *qh);
-void    qh_triangulate(qhT *qh /*qh.facet_list*/);
-void    qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex);
-void    qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
-void    qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB);
-void    qh_triangulate_null(qhT *qh, facetT *facetA);
-void    qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB);
-setT   *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB);
-void    qh_vertexneighbors(qhT *qh /*qh.facet_list*/);
-boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFpoly */
diff --git a/src/qhull/src/libqhull_r/qh-geom_r.htm b/src/qhull/src/libqhull_r/qh-geom_r.htm
deleted file mode 100644
index eeefc0c75..000000000
--- a/src/qhull/src/libqhull_r/qh-geom_r.htm
+++ /dev/null
@@ -1,295 +0,0 @@
-
-
-
-
-geom_r.c, geom2_r.c -- geometric and floating point routines
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
-
    
-
-
-
    geom_r.c, geom2_r.c, random_r.c -- geometric and floating point routines
    
-
    
-
    Geometrically, a vertex is a point with d coordinates
-and a facet is a halfspace. A halfspace is defined by an
-oriented hyperplane through the facet's vertices. A hyperplane
-is defined by d normalized coefficients and an offset. A
-point is above a facet if its distance to the facet is
-positive.
    
-
-
    Qhull uses floating point coordinates for input points,
-vertices, halfspace equations, centrums, and an interior point.
    
-
-
    Qhull may be configured for single precision or double
-precision floating point arithmetic (see realT
-). 
    
-
-
    Each floating point operation may incur round-off error (see
-Merge). The maximum error for distance
-computations is determined at initialization. The roundoff error
-in halfspace computation is accounted for by computing the
-distance from vertices to the halfspace. 
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly •
-Qhull • Set •
-Stat • User 
    
-
-
    Index to geom_r.c,
-geom2_r.c, geom_r.h,
-random_r.c, random_r.h
-
    
-
-
-
-
    »geometric data types
-and constants
    
-
-
      
-
    • coordT coordinates and
-coefficients are stored as realT
      • 
-
    • pointT a point is an array
-of DIM3 coordinates 
      • 
-
    
-
-
    »mathematical macros
    
-
-
      
-
    • fabs_ returns the absolute
-value of a 
      • 
-
    • fmax_ returns the maximum
-value of a and b 
      • 
-
    • fmin_ returns the minimum
-value of a and b 
      • 
-
    • maximize_ maximize a value
-
      • 
-
    • minimize_ minimize a value
-
      • 
-
    • det2_ compute a 2-d
-determinate 
      • 
-
    • det3_ compute a 3-d
-determinate 
      • 
-
    • dX, dY, dZ compute the difference
-between two coordinates 
      • 
-
    
-
-
    »mathematical functions
    
-
-
-
-
    »computational geometry functions
    
-
-
-
-
    »point array functions
    
-
-
-
    »geometric facet functions
    
-
-
-
    »geometric roundoff functions
    
-
      
-
    • qh_detjoggle determine
-default joggle for points and distance roundoff error
      • 
-
    • qh_detroundoff
-determine maximum roundoff error and other precision constants
      • 
-
    • qh_distround compute
-maximum roundoff error due to a distance computation to a
-normalized hyperplane
      • 
-
    • qh_divzero divide by a
-number that is nearly zero 
      • 
-
    • qh_maxouter return maximum outer
-plane
      • 
-
    • qh_outerinner return actual
-outer and inner planes
-
    
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
-
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-globa_r.htm b/src/qhull/src/libqhull_r/qh-globa_r.htm
deleted file mode 100644
index 45437a059..000000000
--- a/src/qhull/src/libqhull_r/qh-globa_r.htm
+++ /dev/null
@@ -1,163 +0,0 @@
-
-
-
-
-global_r.c -- global variables and their functions
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
-
    
-
-
-
    global_r.c -- global variables and their functions
    
-
    
-
    Qhull uses a data structure, qhT, to store
-globally defined constants, lists, sets, and variables. It is passed as the
-first argument to most functions.
-
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly •
-Qhull • Set •
-Stat • User 
    
-
-
    Index to global_r.c and
-libqhull_r.h
    
-
-
-
-
    »Qhull's global
-variables
    
-
-
-
-
    »Global variable and
-initialization routines
    
-
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-io_r.htm b/src/qhull/src/libqhull_r/qh-io_r.htm
deleted file mode 100644
index 8a8a96300..000000000
--- a/src/qhull/src/libqhull_r/qh-io_r.htm
+++ /dev/null
@@ -1,305 +0,0 @@
-
-
-
-
-io_r.c -- input and output operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    io_r.c -- input and output operations
    
-
    
-
-
    Qhull provides a wide range of input
-and output options. To organize the code, most output formats use
-the same driver: 
    
-
-
    -    qh_printbegin( fp, format, facetlist, facets, printall );
-
-    FORALLfacet_( facetlist )
-      qh_printafacet( fp, format, facet, printall );
-
-    FOREACHfacet_( facets )
-      qh_printafacet( fp, format, facet, printall );
-
-    qh_printend( fp, format );
-
    
-
-
    Note the 'printall' flag. It selects whether or not
-qh_skipfacet() is tested. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom •
-Global • Io •
-Mem • Merge •
-Poly • Qhull •
-Set • Stat •
-User 
    
-
-
    Index to io_r.c and io_r.h
    
-
-
-
-
    »io_r.h constants and types
    
-
-
      
-
    • qh_MAXfirst maximum length
-of first two lines of stdin 
      • 
-
    • qh_WHITESPACE possible
-values of white space 
      • 
-
    • printvridgeT function to
-print results of qh_printvdiagram or qh_eachvoronoi
      • 
-
    
-
-
    »User level functions
    
-
-
-
-
    »Print functions for all
-output formats
    
-
-
-
-
    »Text output functions
    
-
-
-
    »Text utility functions
    
-
-
-
    »Geomview output functions
    
-
-
    »Geomview utility functions
    
-
-
    
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-mem_r.htm b/src/qhull/src/libqhull_r/qh-mem_r.htm
deleted file mode 100644
index db59119cb..000000000
--- a/src/qhull/src/libqhull_r/qh-mem_r.htm
+++ /dev/null
@@ -1,145 +0,0 @@
-
-
-
-
-mem_r.c -- memory operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    mem_r.c -- memory operations
    
-
    
-
    Qhull uses quick-fit memory allocation. It maintains a
-set of free lists for a variety of small allocations. A
-small request returns a block from the best fitting free
-list. If the free list is empty, Qhull allocates a block
-from a reserved buffer. 
    
-
    Use 'T5' to trace memory allocations.
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to mem_r.c and
-mem_r.h
    
-
-
    »mem_r.h data types and constants
    
-
      
-
    • ptr_intT for casting
-a void* to an integer-type 
      • 
-
    • qhmemT global memory
-structure for mem_r.c 
      • 
-
    • qh_NOmem disable memory allocation
      • 
-
    
-
    »mem_r.h macros
    
-
-
    »User level
-functions
    
-
-
-
    »Initialization and
-termination functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-merge_r.htm b/src/qhull/src/libqhull_r/qh-merge_r.htm
deleted file mode 100644
index 63e5135be..000000000
--- a/src/qhull/src/libqhull_r/qh-merge_r.htm
+++ /dev/null
@@ -1,366 +0,0 @@
-
-
-
-
-merge_r.c -- facet merge operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    merge_r.c -- facet merge operations
    
-
    
-
    Qhull handles precision problems by merged facets or joggled input.
-Except for redundant vertices, it corrects a problem by
-merging two facets. When done, all facets are clearly
-convex. See Imprecision in Qhull
-for further information. 
    
-
    Users may joggle the input ('QJn')
-instead of merging facets. 
    
-
    Qhull detects and corrects the following problems: 
    
-
      
-
    • More than two facets meeting at a ridge. When
-Qhull creates facets, it creates an even number
-of facets for each ridge. A convex hull always
-has two facets for each ridge. More than two
-facets may be created if non-adjacent facets
-share a vertex. This is called a duplicate
-ridge. In 2-d, a duplicate ridge would
-create a loop of facets. 
      • 
-
    
-
      
-
    • A facet contained in another facet. Facet
-merging may leave all vertices of one facet as a
-subset of the vertices of another facet. This is
-called a redundant facet. 
      • 
-
    
-
      
-
    • A facet with fewer than three neighbors. Facet
-merging may leave a facet with one or two
-neighbors. This is called a degenerate facet.
-
      • 
-
    
-
      
-
    • A facet with flipped orientation. A
-facet's hyperplane may define a halfspace that
-does not include the interior point.This is
-called a flipped facet. 
      • 
-
    
-
      
-
    • A coplanar horizon facet. A
-newly processed point may be coplanar with an
-horizon facet. Qhull creates a new facet without
-a hyperplane. It links new facets for the same
-horizon facet together. This is called a samecycle.
-The new facet or samecycle is merged into the
-horizon facet. 
      • 
-
    
-
      
-
    • Concave facets. A facet's centrum may be
-above a neighboring facet. If so, the facets meet
-at a concave angle. 
      • 
-
    
-
      
-
    • Coplanar facets. A facet's centrum may be
-coplanar with a neighboring facet (i.e., it is
-neither clearly below nor clearly above the
-facet's hyperplane). Qhull removes coplanar
-facets in independent sets sorted by angle.
      • 
-
    
-
      
-
    • Redundant vertex. A vertex may have fewer
-than three neighboring facets. If so, it is
-redundant and may be renamed to an adjacent
-vertex without changing the topological
-structure.This is called a redundant vertex.
-
      • 
-
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to merge_r.c and
-merge_r.h
    
-
-
-
    »merge_r.h data
-types, macros, and global sets
    
-
      
-
    • mergeT structure to
-identify a merge of two facets
      • 
-
    • FOREACHmerge_
-assign 'merge' to each merge in merges 
      • 
-
    • qh global sets
-qh.facet_mergeset contains non-convex merges
-while qh.degen_mergeset contains degenerate and
-redundant facets
      • 
-
    
-
    »merge_r.h
-constants
    
-
-
    »top-level merge
-functions
    
-
-
-
    »functions for
-identifying merges
    
-
-
-
    »functions for
-determining the best merge
    
-
-
-
    »functions for
-merging facets
    
-
-
-
    »functions for
-merging a cycle of facets
    
-
    If a point is coplanar with an horizon facet, the
-corresponding new facets are linked together (a samecycle)
-for merging.
    
-
-
    »functions
-for renaming a vertex
    
-
-
-
    »functions
-for identifying vertices for renaming
    
-
-
-
    »functions for check and
-trace
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-poly_r.htm b/src/qhull/src/libqhull_r/qh-poly_r.htm
deleted file mode 100644
index c5b6f2f83..000000000
--- a/src/qhull/src/libqhull_r/qh-poly_r.htm
+++ /dev/null
@@ -1,485 +0,0 @@
-
-
-
-
-poly_r.c, poly2_r.c -- polyhedron operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    poly_r.c, poly2_r.c -- polyhedron operations
    
-
    
-
-
    Qhull uses dimension-free terminology. Qhull builds a
-polyhedron in dimension d. A polyhedron is a
-simplicial complex of faces with geometric information for the
-top and bottom-level faces. A (d-1)-face is a facet,
-a (d-2)-face is a ridge, and a 0-face
-is a vertex. For example in 3-d, a facet is a polygon
-and a ridge is an edge. A facet is built from a ridge (the base)
-and a vertex (the apex). See
-Qhull's data structures.
    
-
-
    Qhull's primary data structure is a polyhedron. A
-polyhedron is a list of facets. Each facet has a set of
-neighboring facets and a set of vertices. Each facet has a
-hyperplane. For example, a tetrahedron has four facets.
-If its vertices are a, b, c, d, and its facets
-are 1, 2, 3, 4, the tetrahedron is 
    
-
    
-
      
-
    • facet 1 
        
-    
      • vertices: b c d 
        • 
-    
      • neighbors: 2 3 4 
        • 
-
      
-
      • 
-
    • facet 2 
        
-    
      • vertices: a c d 
        • 
-    
      • neighbors: 1 3 4 
        • 
-
      
-
      • 
-
    • facet 3 
        
-    
      • vertices: a b d 
        • 
-    
      • neighbors: 1 2 4 
        • 
-
      
-
      • 
-
    • facet 4 
        
-    
      • vertices: a b c 
        • 
-    
      • neighbors: 1 2 3 
        • 
-
      
-
      • 
-
    
-
    
-
    A facet may be simplicial or non-simplicial. In 3-d, a
-simplicial facet has three vertices and three
-neighbors. A nonsimplicial facet has more than
-three vertices and more than three neighbors. A
-nonsimplicial facet has a set of ridges and a centrum. 
    
-
    
-A simplicial facet has an orientation. An orientation
-is either top or bottom.
-The flag, facet->toporient,
-defines the orientation of the facet's vertices.  For example in 3-d,
-'top' is left-handed orientation (i.e., the vertex order follows the direction
-of the left-hand fingers when the thumb is pointing away from the center).
-Except for axis-parallel facets in 5-d and higher, topological orientation
-determines the geometric orientation of the facet's hyperplane.
-
-
    A nonsimplicial facet is due to merging two or more
-facets. The facet's ridge set determine a simplicial
-decomposition of the facet. Each ridge is a 1-face (i.e.,
-it has two vertices and two neighboring facets). The
-orientation of a ridge is determined by the order of the
-neighboring facets. The flag, facet->toporient,is
-ignored. 
    
-
    A nonsimplicial facet has a centrum for testing
-convexity. A centrum is a point on the facet's
-hyperplane that is near the center of the facet. Except
-for large facets, it is the arithmetic average of the
-facet's vertices. 
    
-
    A nonsimplicial facet is an approximation that is
-defined by offsets from the facet's hyperplane. When
-Qhull finishes, the outer plane is above all
-points while the inner plane is below the facet's
-vertices. This guarantees that any exact convex hull
-passes between the inner and outer planes. The outer
-plane is defined by facet->maxoutside while
-the inner plane is computed from the facet's vertices.
    
-
-
    Qhull 3.1 includes triangulation of non-simplicial facets
-('Qt').
-These facets,
-called tricoplanar, share the same normal. centrum, and Voronoi center.
-One facet (keepcentrum) owns these data structures.
-While tricoplanar facets are more accurate than the simplicial facets from
-joggled input, they
-may have zero area or flipped orientation.
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to poly_r.c,
-poly2_r.c, poly_r.h,
-and libqhull_r.h
    
-
-
    »Data
-types and global lists for polyhedrons
    
-
-
    »poly_r.h constants
    
-
      
-
    • ALGORITHMfault
-flag to not report errors in qh_checkconvex() 
      • 
-
    • DATAfault flag to
-report errors in qh_checkconvex() 
      • 
-
    • DUPLICATEridge
-special value for facet->neighbor to indicate
-a duplicate ridge 
      • 
-
    • MERGEridge
-special value for facet->neighbor to indicate
-a merged ridge 
      • 
-
    
-
    »Global FORALL
-macros
    
-
-
    »FORALL macros
    
-
-
    »FOREACH macros
    
-
-
    »Indexed
-FOREACH macros
    
-
      
-
    • FOREACHfacet_i_
-assign 'facet' and 'facet_i' to each facet in
-facet set 
      • 
-
    • FOREACHneighbor_i_
-assign 'neighbor' and 'neighbor_i' to each facet
-in facet->neighbors or vertex->neighbors
      • 
-
    • FOREACHpoint_i_
-assign 'point' and 'point_i' to each point in
-points set 
      • 
-
    • FOREACHridge_i_
-assign 'ridge' and 'ridge_i' to each ridge in
-ridges set 
      • 
-
    • FOREACHvertex_i_
-assign 'vertex' and 'vertex_i' to each vertex in
-vertices set 
      • 
-
    • FOREACHvertexreverse12_
-assign 'vertex' to each vertex in vertex set;
-reverse the order of first two vertices 
      • 
-
    
-
    »Other macros for polyhedrons
    
-
      
-
    • getid_ return ID for
-a facet, ridge, or vertex 
      • 
-
    • otherfacet_
-return neighboring facet for a ridge in a facet 
      • 
-
    
-
    »Facetlist
-functions
    
-
-
    »Facet
-functions
    
-
-
    »Vertex,
-ridge, and point functions
    
-
-
    »Hashtable functions
    
-
-
    »Allocation and
-deallocation functions
    
-
-
    »Check
-functions
    
-
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-qhull_r.htm b/src/qhull/src/libqhull_r/qh-qhull_r.htm
deleted file mode 100644
index 25d5e4972..000000000
--- a/src/qhull/src/libqhull_r/qh-qhull_r.htm
+++ /dev/null
@@ -1,279 +0,0 @@
-
-
-
-
-libqhull_r.c -- top-level functions and basic data types
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    libqhull_r.c -- top-level functions and basic data types
    
-
    
-
    Qhull implements the Quickhull algorithm for computing
-the convex hull. The Quickhull algorithm combines two
-well-known algorithms: the 2-d quickhull algorithm and
-the n-d beneath-beyond algorithm. See
-Description of Qhull. 
    
-
    This section provides an index to the top-level
-functions and base data types.  The top-level header file, libqhull_r.h,
-contains prototypes for these functions.
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to libqhull_r.c,
-libqhull_r.h, and
-unix_r.c
    
-
-
-
    »libqhull_r.h and unix_r.c
-data types and constants
    
-
      
-
    • flagT Boolean flag as
-a bit 
      • 
-
    • boolT boolean value,
-either True or False 
      • 
-
    • CENTERtype to
-distinguish facet->center 
      • 
-
    • qh_PRINT output
-formats for printing (qh.PRINTout) 
      • 
-
    • qh_ALL argument flag
-for selecting everything 
      • 
-
    • qh_ERR Qhull exit
-codes for indicating errors 
      • 
-
    • qh_FILEstderr Fake stderr
-to distinguish error output from normal output [C++ only]
      • 
-
    • qh_prompt version and long prompt for Qhull
      • 
-
    • qh_prompt2 synopsis for Qhull
      • 
-
    • qh_prompt3 concise prompt for Qhull
      • 
-
    • qh_version version stamp
      • 
-
    
-
-
    »libqhull_r.h other
-macros
    
-
      
-
    • traceN print trace
-message if qh.IStracing >= N. 
      • 
-
    • QHULL_UNUSED declare an
- unused variable to avoid warnings. 
      • 
-
    
-
-
    »Quickhull
-routines in call order
    
-
-
-
    »Top-level routines for initializing and terminating Qhull (in other modules)
    
-
-
-
    »Top-level routines for reading and modifying the input (in other modules)
    
-
-
-
    »Top-level routines for calling Qhull (in other modules)
    
-
-
-
    »Top-level routines for returning results (in other modules)
    
-
-
-
    »Top-level routines for testing and debugging (in other modules)
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-set_r.htm b/src/qhull/src/libqhull_r/qh-set_r.htm
deleted file mode 100644
index cf8ab63af..000000000
--- a/src/qhull/src/libqhull_r/qh-set_r.htm
+++ /dev/null
@@ -1,308 +0,0 @@
-
-
-
-
-qset_r.c -- set data type and operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    qset_r.c -- set data type and operations
    
-
    
-
    Qhull's data structures are constructed from sets. The
-functions and macros in qset_r.c construct, iterate, and
-modify these sets. They are the most frequently called
-functions in Qhull. For this reason, efficiency is the
-primary concern. 
    
-
    In Qhull, a set is represented by an unordered
-array of pointers with a maximum size and a NULL
-terminator (setT).
-Most sets correspond to mathematical sets
-(i.e., the pointers are unique). Some sets are sorted to
-enforce uniqueness. Some sets are ordered. For example,
-the order of vertices in a ridge determine the ridge's
-orientation. If you reverse the order of adjacent
-vertices, the orientation reverses. Some sets are not
-mathematical sets. They may be indexed as an array and
-they may include NULL pointers. 
    
-
    The most common operation on a set is to iterate its
-members. This is done with a 'FOREACH...' macro. Each set
-has a custom macro. For example, 'FOREACHvertex_'
-iterates over a set of vertices. Each vertex is assigned
-to the variable 'vertex' from the pointer 'vertexp'. 
    
-
    Most sets are constructed by appending elements to the
-set. The last element of a set is either NULL or the
-index of the terminating NULL for a partially full set.
-If a set is full, appending an element copies the set to
-a larger array. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global •
-Io • Mem •
-Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to qset_r.c and
-qset_r.h
    
-
-
    »Data types and
-constants
    
-
      
-
    • SETelemsize size
-of a set element in bytes 
      • 
-
    • setT a set with a
-maximum size and a current size
      • 
-
    • qh global sets
-global sets for temporary sets, etc. 
      • 
-
    
-
    »FOREACH macros
    
-
-
    »Access and
-size macros
    
-
-
    »Internal macros
    
-
      
-
    • SETsizeaddr_
-return pointer to end element of a set (indicates
-current size) 
      • 
-
    
-
-
    »address macros
    
-
      
-
    • SETaddr_ return
-address of a set's elements 
      • 
-
    • SETelemaddr_
-return address of the n'th element of a set 
      • 
-
    • SETref_ l_r.h.s. for
-modifying the current element in a FOREACH
-iteration 
      • 
-
    
-
-
    »Allocation and
-deallocation functions
    
-
-
-
    »Access and
-predicate functions 
    
-
-
-
    »Add functions
    
-
-
-
    »Check and print functions
    
-
-
-
    »Copy, compact, and zero functions
    
-
-
-
    »Delete functions
    
-
-
-
    »Temporary set functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-stat_r.htm b/src/qhull/src/libqhull_r/qh-stat_r.htm
deleted file mode 100644
index ea9d7fc56..000000000
--- a/src/qhull/src/libqhull_r/qh-stat_r.htm
+++ /dev/null
@@ -1,161 +0,0 @@
-
-
-
-
-stat_r.c -- statistical operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
-
    stat_r.c -- statistical operations
    
-
    
-
    Qhull records many statistics. These functions and
-macros make it inexpensive to add a statistic.
-
    As with Qhull's global variables, the statistics data structure is
-accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
-is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
-Statistics
-may be turned off in user_r.h. If so, all but the 'zz'
-statistics are ignored.
    
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to stat_r.c and
-stat_r.h
    
-
-
-
    »stat_r.h types
    
-
      
-
    • intrealT union of
-integer and real
      • 
-
    • qhstat global data
-structure for statistics 
      • 
-
    
-
    »stat_r.h
-constants
    
-
      
-
    • qh_KEEPstatistics 0 turns off most statistics
      • 
-
    • Z..., W... integer (Z) and real (W) statistics
-
      • 
-
    • ZZstat Z.../W... statistics that
-remain defined if qh_KEEPstatistics=0
-
      • 
-
    • ztype zdoc, zinc, etc.
-for definining statistics 
      • 
-
    
-
    »stat_r.h macros
    
-
      
-
    • MAYdebugx called
-frequently for error trapping 
      • 
-
    • zadd_/wadd_ add value
-to an integer or real statistic 
      • 
-
    • zdef_ define a
-statistic 
      • 
-
    • zinc_ increment an
-integer statistic 
      • 
-
    • zmax_/wmax_ update
-integer or real maximum statistic 
      • 
-
    • zmin_/wmin_ update
-integer or real minimum statistic 
      • 
-
    • zval_/wval_ set or
-return value of a statistic 
      • 
-
    
-
-
    »stat_r.c
-functions
    
-
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qh-user_r.htm b/src/qhull/src/libqhull_r/qh-user_r.htm
deleted file mode 100644
index 909fec656..000000000
--- a/src/qhull/src/libqhull_r/qh-user_r.htm
+++ /dev/null
@@ -1,271 +0,0 @@
-
-
-
-
-user_r.c -- user-definable operations
-
-
-
-
-
    Up: Home page for Qhull
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents
    
-To: Qhull functions, macros, and data structures
    
-To: Geom • Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    
-
    user_r.c -- user-definable operations
    
-
    
-
    This section contains functions and constants that the
-user may want to change. 
    
-
-
    
-
    Copyright © 1995-2015 C.B. Barber
    
-
    
-
    » Geom
-• Global
-• Io • Mem
-• Merge • Poly
-• Qhull • Set
-• Stat • User
-
    
-
    Index to user_r.c, usermem_r.c, userprintf_r.c, userprintf_rbox_r.c and
-user_r.h
    
-
-
-
    »Qhull library constants
    
-
-
-
-
    »user_r.h data
-types and configuration macros
    
-
-
-
    »definition constants
    
-
      
-
    • qh_DEFAULTbox
-define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) 
      • 
-
    • qh_INFINITE on
-output, indicates Voronoi center at infinity 
      • 
-
    • qh_ORIENTclock
-define convention for orienting facets
      • 
-
    • qh_ZEROdelaunay
-define facets that are ignored in Delaunay triangulations
      • 
-
    
-
-
    »joggle constants
    
-
-
-
    »performance
-related constants
    
-
-
-
    »memory constants
    
-
-
-
    »conditional compilation
    
-
      
-
    • compiler defined symbols,
-e.g., _STDC_ and _cplusplus
-
-
    • qh_COMPUTEfurthest
-    compute furthest distance to an outside point instead of storing it with the facet
-
    • qh_KEEPstatistics
-    enable statistic gathering and reporting with option 'Ts'
-
    • qh_MAXoutside
-record outer plane for each facet
-
    • qh_NOmerge
-disable facet merging
-
    • qh_NOtrace
-disable tracing with option 'T4'
-
    • qh_QHpointer
-access global data with pointer or static structure
-
    • qh_QUICKhelp
-use abbreviated help messages, e.g., for degenerate inputs
-
    
-
-
    »merge
-constants
    
-
-
-
    »user_r.c
-functions
    
-
-
-
    »usermem_r.c
-functions
    
-
      
-
    • qh_exit exit program, same as exit().  May be redefined as throw "QH10003.." by libqhullcpp/usermem_r-cpp.cpp
      • 
-
    • qh_fprintf_stderr print to stderr when qh->ferr is not defined.
      • 
-
    • qh_free free memory, same as free().
      • 
-
    • qh_malloc allocate memory, same as malloc()
      • 
-
    
-
-
    »userprintf_r.c
- and userprintf_rbox,c functions
    
-
      
-
    • qh_fprintf print
-information from Qhull, sames as fprintf(). 
      • 
-
    • qh_fprintf_rbox print
-information from Rbox, sames as fprintf(). 
      • 
-
    
-
-
     
    
-
    
-
    Up:
-Home page for
-Qhull 
    
-Up: Qhull manual: Table of Contents 
    
-Up: Programs
-• Options
-• Output
-• Formats
-• Geomview
-• Print
-• Qhull
-• Precision
-• Trace
-• Functions
    
-Up: Qhull code: Table of Contents 
    
-To: Qhull functions, macros, and data structures
    
-To: Geom •
-Global • Io
-• Mem • Merge
-• Poly • Qhull
-• Set • Stat
-• User
    
-
    
-
     
    
-
    
-
    The
-Geometry Center Home Page 
    
-
    Comments to: qhull@qhull.org
-
    
-Created: May 2, 1997 ---  Last modified: see top  
    
-
-
diff --git a/src/qhull/src/libqhull_r/qhull_r-exports.def b/src/qhull/src/libqhull_r/qhull_r-exports.def
deleted file mode 100644
index 325d57c3b..000000000
--- a/src/qhull/src/libqhull_r/qhull_r-exports.def
+++ /dev/null
@@ -1,404 +0,0 @@
-; qhull_r-exports.def -- msvc module-definition file
-;
-;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
-;   [jan'14] 391 symbols 
-;   Same as ../libqhullp/qhull-exports.def without DATA items (reentrant)
-;
-; $Id: //main/2015/qhull/src/libqhull_r/qhull_r-exports.def#3 $$Change: 2047 $
-; $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
-; 
-; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
-VERSION 7.0
-EXPORTS
-qh_addhash
-qh_addpoint
-qh_all_merges
-qh_allstatA
-qh_allstatB
-qh_allstatC
-qh_allstatD
-qh_allstatE
-qh_allstatE2
-qh_allstatF
-qh_allstatG
-qh_allstatH
-qh_allstatI
-qh_allstatistics
-qh_appendfacet
-qh_appendmergeset
-qh_appendprint
-qh_appendvertex
-qh_argv_to_command
-qh_argv_to_command_size
-qh_attachnewfacets
-qh_backnormal
-qh_basevertices
-qh_build_withrestart
-qh_buildhull
-qh_buildtracing
-qh_check_bestdist
-qh_check_dupridge
-qh_check_maxout
-qh_check_output
-qh_check_point
-qh_check_points
-qh_checkconnect
-qh_checkconvex
-qh_checkfacet
-qh_checkflags
-qh_checkflipped
-qh_checkflipped_all
-qh_checkpolygon
-qh_checkvertex
-qh_checkzero
-qh_clear_outputflags
-qh_clearcenters
-qh_clock
-qh_collectstatistics
-qh_compare_facetarea
-qh_compare_facetmerge
-qh_compare_facetvisit
-qh_compareangle
-qh_comparemerge
-qh_comparevisit
-qh_copyfilename
-qh_copynonconvex
-qh_copypoints
-qh_countfacets
-qh_createsimplex
-qh_crossproduct
-qh_degen_redundant_facet
-qh_degen_redundant_neighbors
-qh_deletevisible
-qh_delfacet
-qh_delridge
-qh_delvertex
-qh_determinant
-qh_detjoggle
-qh_detroundoff
-qh_detsimplex
-qh_detvnorm
-qh_detvridge
-qh_detvridge3
-qh_dfacet
-qh_distnorm
-qh_distplane
-qh_distround
-qh_divzero
-qh_dvertex
-qh_eachvoronoi
-qh_eachvoronoi_all
-qh_errexit
-qh_errexit2
-qh_errexit_rbox
-qh_errprint
-qh_exit
-qh_facet2point
-qh_facet3vertex
-qh_facetarea
-qh_facetarea_simplex
-qh_facetcenter
-qh_facetintersect
-qh_facetvertices
-qh_find_newvertex
-qh_findbest
-qh_findbest_test
-qh_findbestfacet
-qh_findbesthorizon
-qh_findbestlower
-qh_findbestneighbor
-qh_findbestnew
-qh_findfacet_all
-qh_findgood
-qh_findgood_all
-qh_findgooddist
-qh_findhorizon
-qh_flippedmerges
-qh_forcedmerges
-qh_fprintf
-qh_fprintf_rbox
-qh_fprintf_stderr
-qh_free
-qh_freebuffers
-qh_freebuild
-qh_freeqhull
-qh_furthestnext
-qh_furthestout
-qh_gausselim
-qh_geomplanes
-qh_getangle
-qh_getarea
-qh_getcenter
-qh_getcentrum
-qh_getdistance
-qh_gethash
-qh_getmergeset
-qh_getmergeset_initial
-qh_gram_schmidt
-qh_hashridge
-qh_hashridge_find
-qh_infiniteloop
-qh_init_A
-qh_init_B
-qh_init_qhull_command
-qh_initbuild
-qh_initflags
-qh_initialhull
-qh_initialvertices
-qh_initqhull_buffers
-qh_initqhull_globals
-qh_initqhull_mem
-qh_initqhull_outputflags
-qh_initqhull_start
-qh_initqhull_start2
-qh_initstatistics
-qh_initthresholds
-qh_inthresholds
-qh_isvertex
-qh_joggleinput
-qh_lib_check
-qh_makenew_nonsimplicial
-qh_makenew_simplicial
-qh_makenewfacet
-qh_makenewfacets
-qh_makenewplanes
-qh_makeridges
-qh_malloc
-qh_mark_dupridges
-qh_markkeep
-qh_markvoronoi
-qh_matchduplicates
-qh_matchneighbor
-qh_matchnewfacets
-qh_matchvertices
-qh_maxabsval
-qh_maxmin
-qh_maxouter
-qh_maxsimplex
-qh_maydropneighbor
-qh_memalloc
-qh_memfree
-qh_memfreeshort
-qh_meminit
-qh_meminitbuffers
-qh_memsetup
-qh_memsize
-qh_memstatistics
-qh_memtotal
-qh_merge_degenredundant
-qh_merge_nonconvex
-qh_mergecycle
-qh_mergecycle_all
-qh_mergecycle_facets
-qh_mergecycle_neighbors
-qh_mergecycle_ridges
-qh_mergecycle_vneighbors
-qh_mergefacet
-qh_mergefacet2d
-qh_mergeneighbors
-qh_mergeridges
-qh_mergesimplex
-qh_mergevertex_del
-qh_mergevertex_neighbors
-qh_mergevertices
-qh_minabsval
-qh_mindiff
-qh_nearcoplanar
-qh_nearvertex
-qh_neighbor_intersections
-qh_new_qhull
-qh_newfacet
-qh_newhashtable
-qh_newridge
-qh_newstats
-qh_newvertex
-qh_newvertices
-qh_nextfurthest
-qh_nextridge3d
-qh_normalize
-qh_normalize2
-qh_nostatistic
-qh_option
-qh_order_vertexneighbors
-qh_orientoutside
-qh_out1
-qh_out2n
-qh_out3n
-qh_outcoplanar
-qh_outerinner
-qh_partitionall
-qh_partitioncoplanar
-qh_partitionpoint
-qh_partitionvisible
-qh_point
-qh_point_add
-qh_pointdist
-qh_pointfacet
-qh_pointid
-qh_pointvertex
-qh_postmerge
-qh_precision
-qh_premerge
-qh_prepare_output
-qh_prependfacet
-qh_printafacet
-qh_printallstatistics
-qh_printbegin
-qh_printcenter
-qh_printcentrum
-qh_printend
-qh_printend4geom
-qh_printextremes
-qh_printextremes_2d
-qh_printextremes_d
-qh_printfacet
-qh_printfacet2geom
-qh_printfacet2geom_points
-qh_printfacet2math
-qh_printfacet3geom_nonsimplicial
-qh_printfacet3geom_points
-qh_printfacet3geom_simplicial
-qh_printfacet3math
-qh_printfacet3vertex
-qh_printfacet4geom_nonsimplicial
-qh_printfacet4geom_simplicial
-qh_printfacetNvertex_nonsimplicial
-qh_printfacetNvertex_simplicial
-qh_printfacetheader
-qh_printfacetlist
-qh_printfacetridges
-qh_printfacets
-qh_printhashtable
-qh_printhelp_degenerate
-qh_printhelp_narrowhull
-qh_printhelp_singular
-qh_printhyperplaneintersection
-qh_printline3geom
-qh_printlists
-qh_printmatrix
-qh_printneighborhood
-qh_printpoint
-qh_printpoint3
-qh_printpointid
-qh_printpoints
-qh_printpoints_out
-qh_printpointvect
-qh_printpointvect2
-qh_printridge
-qh_printspheres
-qh_printstatistics
-qh_printstatlevel
-qh_printstats
-qh_printsummary
-qh_printvdiagram
-qh_printvdiagram2
-qh_printvertex
-qh_printvertexlist
-qh_printvertices
-qh_printvneighbors
-qh_printvnorm
-qh_printvoronoi
-qh_printvridge
-qh_produce_output
-qh_produce_output2
-qh_projectdim3
-qh_projectinput
-qh_projectpoint
-qh_projectpoints
-qh_qhull
-qh_rand
-qh_randomfactor
-qh_randommatrix
-qh_rboxpoints
-qh_readfeasible
-qh_readpoints
-qh_reducevertices
-qh_redundant_vertex
-qh_remove_extravertices
-qh_removefacet
-qh_removevertex
-qh_rename_sharedvertex
-qh_renameridgevertex
-qh_renamevertex
-qh_resetlists
-qh_rotateinput
-qh_rotatepoints
-qh_roundi
-qh_scaleinput
-qh_scalelast
-qh_scalepoints
-qh_setaddnth
-qh_setaddsorted
-qh_setappend
-qh_setappend2ndlast
-qh_setappend_set
-qh_setcheck
-qh_setcompact
-qh_setcopy
-qh_setdel
-qh_setdelaunay
-qh_setdellast
-qh_setdelnth
-qh_setdelnthsorted
-qh_setdelsorted
-qh_setduplicate
-qh_setequal
-qh_setequal_except
-qh_setequal_skip
-qh_setfacetplane
-qh_setfeasible
-qh_setfree
-qh_setfree2
-qh_setfreelong
-qh_sethalfspace
-qh_sethalfspace_all
-qh_sethyperplane_det
-qh_sethyperplane_gauss
-qh_setin
-qh_setindex
-qh_setlarger
-qh_setlast
-qh_setnew
-qh_setnew_delnthsorted
-qh_setprint
-qh_setreplace
-qh_setsize
-qh_settemp
-qh_settempfree
-qh_settempfree_all
-qh_settemppop
-qh_settemppush
-qh_settruncate
-qh_setunique
-qh_setvoronoi_all
-qh_setzero
-qh_sharpnewfacets
-qh_skipfacet
-qh_skipfilename
-qh_srand
-qh_stddev
-qh_strtod
-qh_strtol
-qh_test_appendmerge
-qh_test_vneighbors
-qh_tracemerge
-qh_tracemerging
-qh_triangulate
-qh_triangulate_facet
-qh_triangulate_link
-qh_triangulate_mirror
-qh_triangulate_null
-qh_updatetested
-qh_updatevertices
-qh_user_memsizes
-qh_version
-qh_version2
-qh_vertexintersect
-qh_vertexintersect_new
-qh_vertexneighbors
-qh_vertexridges
-qh_vertexridges_facet
-qh_vertexsubset
-qh_voronoi_center
-qh_willdelete
-qh_zero
diff --git a/src/qhull/src/libqhull_r/qhull_ra.h b/src/qhull/src/libqhull_r/qhull_ra.h
deleted file mode 100644
index 5c5bd8779..000000000
--- a/src/qhull/src/libqhull_r/qhull_ra.h
+++ /dev/null
@@ -1,158 +0,0 @@
-/*
      ---------------------------------
-
-   qhull_ra.h
-   all header files for compiling qhull with reentrant code
-   included before C++ headers for user_r.h:QHULL_CRTDBG
-
-   see qh-qhull.htm
-
-   see libqhull_r.h for user-level definitions
-
-   see user_r.h for user-definable constants
-
-   defines internal functions for libqhull_r.c global_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/qhull_ra.h#6 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-
-   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
-           full parens around (x?y:z)
-           use '#include "libqhull_r/qhull_ra.h"' to avoid name clashes
-*/
-
-#ifndef qhDEFqhulla
-#define qhDEFqhulla 1
-
-#include "libqhull_r.h"  /* Includes user_r.h and data types */
-
-#include "stat_r.h"
-#include "random_r.h"
-#include "mem_r.h"
-#include "qset_r.h"
-#include "geom_r.h"
-#include "merge_r.h"
-#include "poly_r.h"
-#include "io_r.h"
-
-#include 
-#include 
-#include 
-#include     /* some compilers will not need float.h */
-#include 
-#include 
-#include 
-#include 
-#include 
-/*** uncomment here and qset_r.c
-     if string.h does not define memcpy()
-#include 
-*/
-
-#if qh_CLOCKtype == 2  /* defined in user_r.h from libqhull_r.h */
-#include 
-#include 
-#include 
-#endif
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4100)  /* unreferenced formal parameter */
-#pragma warning( disable : 4127)  /* conditional expression is constant */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/* ======= -macros- =========== */
-
-/*----------------------------------
-
-  traceN((qh, qh->ferr, 0Nnnn, "format\n", vars));
-    calls qh_fprintf if qh.IStracing >= N
-
-    Add debugging traps to the end of qh_fprintf
-
-  notes:
-    removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh->IStracing) qh_fprintf args;}
-#define trace1(args) {if (qh->IStracing >= 1) qh_fprintf args;}
-#define trace2(args) {if (qh->IStracing >= 2) qh_fprintf args;}
-#define trace3(args) {if (qh->IStracing >= 3) qh_fprintf args;}
-#define trace4(args) {if (qh->IStracing >= 4) qh_fprintf args;}
-#define trace5(args) {if (qh->IStracing >= 5) qh_fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/*----------------------------------
-
-  Define an unused variable to avoid compiler warnings
-
-  Derived from Qt's corelib/global/qglobal.h
-
-*/
-
-#if defined(__cplusplus) && defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
-template 
-inline void qhullUnused(T &x) { (void)x; }
-#  define QHULL_UNUSED(x) qhullUnused(x);
-#else
-#  define QHULL_UNUSED(x) (void)x;
-#endif
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/***** -libqhull_r.c prototypes (alphabetical after qhull) ********************/
-
-void    qh_qhull(qhT *qh);
-boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
-void    qh_buildhull(qhT *qh);
-void    qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet);
-void    qh_build_withrestart(qhT *qh);
-void    qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet);
-void    qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
-pointT *qh_nextfurthest(qhT *qh, facetT **visible);
-void    qh_partitionall(qhT *qh, setT *vertices, pointT *points,int npoints);
-void    qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist);
-void    qh_partitionpoint(qhT *qh, pointT *point, facetT *facet);
-void    qh_partitionvisible(qhT *qh, boolT allpoints, int *numpoints);
-void    qh_precision(qhT *qh, const char *reason);
-void    qh_printsummary(qhT *qh, FILE *fp);
-
-/***** -global_r.c internal prototypes (alphabetical) ***********************/
-
-void    qh_appendprint(qhT *qh, qh_PRINT format);
-void    qh_freebuild(qhT *qh, boolT allmem);
-void    qh_freebuffers(qhT *qh);
-void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-
-/***** -stat_r.c internal prototypes (alphabetical) ***********************/
-
-void    qh_allstatA(qhT *qh);
-void    qh_allstatB(qhT *qh);
-void    qh_allstatC(qhT *qh);
-void    qh_allstatD(qhT *qh);
-void    qh_allstatE(qhT *qh);
-void    qh_allstatE2(qhT *qh);
-void    qh_allstatF(qhT *qh);
-void    qh_allstatG(qhT *qh);
-void    qh_allstatH(qhT *qh);
-void    qh_freebuffers(qhT *qh);
-void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFqhulla */
diff --git a/src/qhull/src/libqhull_r/qset_r.c b/src/qhull/src/libqhull_r/qset_r.c
deleted file mode 100644
index 15cd3c0e2..000000000
--- a/src/qhull/src/libqhull_r/qset_r.c
+++ /dev/null
@@ -1,1340 +0,0 @@
-/*
      ---------------------------------
-
-   qset_r.c
-   implements set manipulations needed for quickhull
-
-   see qh-set_r.htm and qset_r.h
-
-   Be careful of strict aliasing (two pointers of different types
-   that reference the same location).  The last slot of a set is
-   either the actual size of the set plus 1, or the NULL terminator
-   of the set (i.e., setelemT).
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/qset_r.c#3 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "libqhull_r.h" /* for qhT and QHULL_CRTDBG */
-#include "qset_r.h"
-#include "mem_r.h"
-#include 
-#include 
-/*** uncomment here and qhull_ra.h
-     if string.h does not define memcpy()
-#include 
-*/
-
-#ifndef qhDEFlibqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void    qh_errexit(qhT *qh, int exitcode, facetT *, ridgeT *);
-void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#  pragma warning( disable : 4127)  /* conditional expression is constant */
-#  pragma warning( disable : 4706)  /* assignment within conditional function */
-#  endif
-#endif
-
-/*=============== internal macros ===========================*/
-
-/*============ functions in alphabetical order ===================*/
-
-/*----------------------------------
-
-  qh_setaddnth(qh, setp, nth, newelem)
-    adds newelem as n'th element of sorted or unsorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nth=0 is first element
-    errors if nth is out of bounds
-
-  design:
-    expand *setp if empty or full
-    move tail of *setp up one
-    insert newelem
-*/
-void qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem) {
-  int oldsize, i;
-  setelemT *sizep;          /* avoid strict aliasing */
-  setelemT *oldp, *newp;
-
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(qh, setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  oldsize= sizep->i - 1;
-  if (nth < 0 || nth > oldsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", *setp);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  sizep->i++;
-  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
-  newp= oldp+1;
-  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
-    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
-  newp->p= newelem;
-} /* setaddnth */
-
-
-/*----------------------------------
-
-  setaddsorted( setp, newelem )
-    adds an newelem into sorted *setp
-
-  notes:
-    *setp and newelem must be defined
-    *setp may be a temp set
-    nop if newelem already in set
-
-  design:
-    find newelem's position in *setp
-    insert newelem
-*/
-void qh_setaddsorted(qhT *qh, setT **setp, void *newelem) {
-  int newindex=0;
-  void *elem, **elemp;
-
-  FOREACHelem_(*setp) {          /* could use binary search instead */
-    if (elem < newelem)
-      newindex++;
-    else if (elem == newelem)
-      return;
-    else
-      break;
-  }
-  qh_setaddnth(qh, setp, newindex, newelem);
-} /* setaddsorted */
-
-
-/*---------------------------------
-
-  qh_setappend(qh, setp, newelem)
-    append newelem to *setp
-
-  notes:
-    *setp may be a temp set
-    *setp and newelem may be NULL
-
-  design:
-    expand *setp if empty or full
-    append newelem to *setp
-
-*/
-void qh_setappend(qhT *qh, setT **setp, void *newelem) {
-  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-  setelemT *endp;
-  int count;
-
-  if (!newelem)
-    return;
-  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-    qh_setlarger(qh, setp);
-    sizep= SETsizeaddr_(*setp);
-  }
-  count= (sizep->i)++ - 1;
-  endp= (setelemT *)SETelemaddr_(*setp, count, void);
-  (endp++)->p= newelem;
-  endp->p= NULL;
-} /* setappend */
-
-/*---------------------------------
-
-  qh_setappend_set(qh, setp, setA)
-    appends setA to *setp
-
-  notes:
-    *setp can not be a temp set
-    *setp and setA may be NULL
-
-  design:
-    setup for copy
-    expand *setp if it is too small
-    append all elements of setA to *setp
-*/
-void qh_setappend_set(qhT *qh, setT **setp, setT *setA) {
-  int sizeA, size;
-  setT *oldset;
-  setelemT *sizep;
-
-  if (!setA)
-    return;
-  SETreturnsize_(setA, sizeA);
-  if (!*setp)
-    *setp= qh_setnew(qh, sizeA);
-  sizep= SETsizeaddr_(*setp);
-  if (!(size= sizep->i))
-    size= (*setp)->maxsize;
-  else
-    size--;
-  if (size + sizeA > (*setp)->maxsize) {
-    oldset= *setp;
-    *setp= qh_setcopy(qh, oldset, sizeA);
-    qh_setfree(qh, &oldset);
-    sizep= SETsizeaddr_(*setp);
-  }
-  if (sizeA > 0) {
-    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
-    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
-  }
-} /* setappend_set */
-
-
-/*---------------------------------
-
-  qh_setappend2ndlast(qh, setp, newelem )
-    makes newelem the next to the last element in *setp
-
-  notes:
-    *setp must have at least one element
-    newelem must be defined
-    *setp may be a temp set
-
-  design:
-    expand *setp if empty or full
-    move last element of *setp up one
-    insert newelem
-*/
-void qh_setappend2ndlast(qhT *qh, setT **setp, void *newelem) {
-    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
-    setelemT *endp, *lastp;
-    int count;
-
-    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
-        qh_setlarger(qh, setp);
-        sizep= SETsizeaddr_(*setp);
-    }
-    count= (sizep->i)++ - 1;
-    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
-    lastp= endp-1;
-    *(endp++)= *lastp;
-    endp->p= NULL;    /* may overwrite *sizep */
-    lastp->p= newelem;
-} /* setappend2ndlast */
-
-/*---------------------------------
-
-  qh_setcheck(qh, set, typename, id )
-    check set for validity
-    report errors with typename and id
-
-  design:
-    checks that maxsize, actual size, and NULL terminator agree
-*/
-void qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id) {
-  int maxsize, size;
-  int waserr= 0;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  maxsize= set->maxsize;
-  if (size > maxsize || !maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
-             size, tname, id, maxsize);
-    waserr= 1;
-  }else if (set->e[size].p) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
-             tname, id, size-1, maxsize);
-    waserr= 1;
-  }
-  if (waserr) {
-    qh_setprint(qh, qh->qhmem.ferr, "ERRONEOUS", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setcheck */
-
-
-/*---------------------------------
-
-  qh_setcompact(qh, set )
-    remove internal NULLs from an unsorted set
-
-  returns:
-    updated set
-
-  notes:
-    set may be NULL
-    it would be faster to swap tail of set into holes, like qh_setdel
-
-  design:
-    setup pointers into set
-    skip NULLs while copying elements to start of set
-    update the actual size
-*/
-void qh_setcompact(qhT *qh, setT *set) {
-  int size;
-  void **destp, **elemp, **endp, **firstp;
-
-  if (!set)
-    return;
-  SETreturnsize_(set, size);
-  destp= elemp= firstp= SETaddr_(set, void);
-  endp= destp + size;
-  while (1) {
-    if (!(*destp++ = *elemp++)) {
-      destp--;
-      if (elemp > endp)
-        break;
-    }
-  }
-  qh_settruncate(qh, set, (int)(destp-firstp));   /* WARN64 */
-} /* setcompact */
-
-
-/*---------------------------------
-
-  qh_setcopy(qh, set, extra )
-    make a copy of a sorted or unsorted set with extra slots
-
-  returns:
-    new set
-
-  design:
-    create a newset with extra slots
-    copy the elements to the newset
-
-*/
-setT *qh_setcopy(qhT *qh, setT *set, int extra) {
-  setT *newset;
-  int size;
-
-  if (extra < 0)
-    extra= 0;
-  SETreturnsize_(set, size);
-  newset= qh_setnew(qh, size+extra);
-  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
-  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
-  return(newset);
-} /* setcopy */
-
-
-/*---------------------------------
-
-  qh_setdel(set, oldelem )
-    delete oldelem from an unsorted set
-
-  returns:
-    returns oldelem if found
-    returns NULL otherwise
-
-  notes:
-    set may be NULL
-    oldelem must not be NULL;
-    only deletes one copy of oldelem in set
-
-  design:
-    locate oldelem
-    update actual size if it was full
-    move the last element to the oldelem's location
-*/
-void *qh_setdel(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *elemp;
-  setelemT *lastp;
-
-  if (!set)
-    return NULL;
-  elemp= (setelemT *)SETaddr_(set, void);
-  while (elemp->p != oldelem && elemp->p)
-    elemp++;
-  if (elemp->p) {
-    sizep= SETsizeaddr_(set);
-    if (!(sizep->i)--)         /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-    elemp->p= lastp->p;      /* may overwrite itself */
-    lastp->p= NULL;
-    return oldelem;
-  }
-  return NULL;
-} /* setdel */
-
-
-/*---------------------------------
-
-  qh_setdellast(set)
-    return last element of set or NULL
-
-  notes:
-    deletes element from set
-    set may be NULL
-
-  design:
-    return NULL if empty
-    if full set
-      delete last element and set actual size
-    else
-      delete last element and update actual size
-*/
-void *qh_setdellast(setT *set) {
-  int setsize;  /* actually, actual_size + 1 */
-  int maxsize;
-  setelemT *sizep;
-  void *returnvalue;
-
-  if (!set || !(set->e[0].p))
-    return NULL;
-  sizep= SETsizeaddr_(set);
-  if ((setsize= sizep->i)) {
-    returnvalue= set->e[setsize - 2].p;
-    set->e[setsize - 2].p= NULL;
-    sizep->i--;
-  }else {
-    maxsize= set->maxsize;
-    returnvalue= set->e[maxsize - 1].p;
-    set->e[maxsize - 1].p= NULL;
-    sizep->i= maxsize;
-  }
-  return returnvalue;
-} /* setdellast */
-
-
-/*---------------------------------
-
-  qh_setdelnth(qh, set, nth )
-    deletes nth element from unsorted set
-    0 is first element
-
-  returns:
-    returns the element (needs type conversion)
-
-  notes:
-    errors if nth invalid
-
-  design:
-    setup points and check nth
-    delete nth element and overwrite with last element
-*/
-void *qh_setdelnth(qhT *qh, setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *elemp, *lastp;
-
-  sizep= SETsizeaddr_(set);
-  if ((sizep->i--)==0)         /*  if was a full set */
-    sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
-  if (nth < 0 || nth >= sizep->i) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
-  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
-  elem= elemp->p;
-  elemp->p= lastp->p;      /* may overwrite itself */
-  lastp->p= NULL;
-  return elem;
-} /* setdelnth */
-
-/*---------------------------------
-
-  qh_setdelnthsorted(qh, set, nth )
-    deletes nth element from sorted set
-
-  returns:
-    returns the element (use type conversion)
-
-  notes:
-    errors if nth invalid
-
-  see also:
-    setnew_delnthsorted
-
-  design:
-    setup points and check nth
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelnthsorted(qhT *qh, setT *set, int nth) {
-  void *elem;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  sizep= SETsizeaddr_(set);
-  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  newp= (setelemT *)SETelemaddr_(set, nth, void);
-  elem= newp->p;
-  oldp= newp+1;
-  while (((newp++)->p= (oldp++)->p))
-    ; /* copy remaining elements and NULL */
-  if ((sizep->i--)==0)         /*  if was a full set */
-    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-  return elem;
-} /* setdelnthsorted */
-
-
-/*---------------------------------
-
-  qh_setdelsorted(set, oldelem )
-    deletes oldelem from sorted set
-
-  returns:
-    returns oldelem if it was deleted
-
-  notes:
-    set may be NULL
-
-  design:
-    locate oldelem in set
-    copy remaining elements down one
-    update actual size
-*/
-void *qh_setdelsorted(setT *set, void *oldelem) {
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (!set)
-    return NULL;
-  newp= (setelemT *)SETaddr_(set, void);
-  while(newp->p != oldelem && newp->p)
-    newp++;
-  if (newp->p) {
-    oldp= newp+1;
-    while (((newp++)->p= (oldp++)->p))
-      ; /* copy remaining elements */
-    sizep= SETsizeaddr_(set);
-    if ((sizep->i--)==0)    /*  if was a full set */
-      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
-    return oldelem;
-  }
-  return NULL;
-} /* setdelsorted */
-
-
-/*---------------------------------
-
-  qh_setduplicate(qh, set, elemsize )
-    duplicate a set of elemsize elements
-
-  notes:
-    use setcopy if retaining old elements
-
-  design:
-    create a new set
-    for each elem of the old set
-      create a newelem
-      append newelem to newset
-*/
-setT *qh_setduplicate(qhT *qh, setT *set, int elemsize) {
-  void          *elem, **elemp, *newElem;
-  setT          *newSet;
-  int           size;
-
-  if (!(size= qh_setsize(qh, set)))
-    return NULL;
-  newSet= qh_setnew(qh, size);
-  FOREACHelem_(set) {
-    newElem= qh_memalloc(qh, elemsize);
-    memcpy(newElem, elem, (size_t)elemsize);
-    qh_setappend(qh, &newSet, newElem);
-  }
-  return newSet;
-} /* setduplicate */
-
-
-/*---------------------------------
-
-  qh_setendpointer( set )
-    Returns pointer to NULL terminator of a set's elements
-    set can not be NULL
-
-*/
-void **qh_setendpointer(setT *set) {
-
-  setelemT *sizep= SETsizeaddr_(set);
-  int n= sizep->i;
-  return (n ? &set->e[n-1].p : &sizep->p);
-} /* qh_setendpointer */
-
-/*---------------------------------
-
-  qh_setequal( setA, setB )
-    returns 1 if two sorted sets are equal, otherwise returns 0
-
-  notes:
-    either set may be NULL
-
-  design:
-    check size of each set
-    setup pointers
-    compare elements of each set
-*/
-int qh_setequal(setT *setA, setT *setB) {
-  void **elemAp, **elemBp;
-  int sizeA= 0, sizeB= 0;
-
-  if (setA) {
-    SETreturnsize_(setA, sizeA);
-  }
-  if (setB) {
-    SETreturnsize_(setB, sizeB);
-  }
-  if (sizeA != sizeB)
-    return 0;
-  if (!sizeA)
-    return 1;
-  elemAp= SETaddr_(setA, void);
-  elemBp= SETaddr_(setB, void);
-  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
-    return 1;
-  return 0;
-} /* setequal */
-
-
-/*---------------------------------
-
-  qh_setequal_except( setA, skipelemA, setB, skipelemB )
-    returns 1 if sorted setA and setB are equal except for skipelemA & B
-
-  returns:
-    false if either skipelemA or skipelemB are missing
-
-  notes:
-    neither set may be NULL
-
-    if skipelemB is NULL,
-      can skip any one element of setB
-
-  design:
-    setup pointers
-    search for skipelemA, skipelemB, and mismatches
-    check results
-*/
-int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
-  void **elemA, **elemB;
-  int skip=0;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  while (1) {
-    if (*elemA == skipelemA) {
-      skip++;
-      elemA++;
-    }
-    if (skipelemB) {
-      if (*elemB == skipelemB) {
-        skip++;
-        elemB++;
-      }
-    }else if (*elemA != *elemB) {
-      skip++;
-      if (!(skipelemB= *elemB++))
-        return 0;
-    }
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (skip != 2 || *elemB)
-    return 0;
-  return 1;
-} /* setequal_except */
-
-
-/*---------------------------------
-
-  qh_setequal_skip( setA, skipA, setB, skipB )
-    returns 1 if sorted setA and setB are equal except for elements skipA & B
-
-  returns:
-    false if different size
-
-  notes:
-    neither set may be NULL
-
-  design:
-    setup pointers
-    search for mismatches while skipping skipA and skipB
-*/
-int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
-  void **elemA, **elemB, **skipAp, **skipBp;
-
-  elemA= SETaddr_(setA, void);
-  elemB= SETaddr_(setB, void);
-  skipAp= SETelemaddr_(setA, skipA, void);
-  skipBp= SETelemaddr_(setB, skipB, void);
-  while (1) {
-    if (elemA == skipAp)
-      elemA++;
-    if (elemB == skipBp)
-      elemB++;
-    if (!*elemA)
-      break;
-    if (*elemA++ != *elemB++)
-      return 0;
-  }
-  if (*elemB)
-    return 0;
-  return 1;
-} /* setequal_skip */
-
-
-/*---------------------------------
-
-  qh_setfree(qh, setp )
-    frees the space occupied by a sorted or unsorted set
-
-  returns:
-    sets setp to NULL
-
-  notes:
-    set may be NULL
-
-  design:
-    free array
-    free set
-*/
-void qh_setfree(qhT *qh, setT **setp) {
-  int size;
-  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size <= qh->qhmem.LASTsize) {
-      qh_memfree_(qh, *setp, size, freelistp);
-    }else
-      qh_memfree(qh, *setp, size);
-    *setp= NULL;
-  }
-} /* setfree */
-
-
-/*---------------------------------
-
-  qh_setfree2(qh, setp, elemsize )
-    frees the space occupied by a set and its elements
-
-  notes:
-    set may be NULL
-
-  design:
-    free each element
-    free set
-*/
-void qh_setfree2(qhT *qh, setT **setp, int elemsize) {
-  void          *elem, **elemp;
-
-  FOREACHelem_(*setp)
-    qh_memfree(qh, elem, elemsize);
-  qh_setfree(qh, setp);
-} /* setfree2 */
-
-
-
-/*---------------------------------
-
-  qh_setfreelong(qh, setp )
-    frees a set only if it's in long memory
-
-  returns:
-    sets setp to NULL if it is freed
-
-  notes:
-    set may be NULL
-
-  design:
-    if set is large
-      free it
-*/
-void qh_setfreelong(qhT *qh, setT **setp) {
-  int size;
-
-  if (*setp) {
-    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
-    if (size > qh->qhmem.LASTsize) {
-      qh_memfree(qh, *setp, size);
-      *setp= NULL;
-    }
-  }
-} /* setfreelong */
-
-
-/*---------------------------------
-
-  qh_setin(set, setelem )
-    returns 1 if setelem is in a set, 0 otherwise
-
-  notes:
-    set may be NULL or unsorted
-
-  design:
-    scans set for setelem
-*/
-int qh_setin(setT *set, void *setelem) {
-  void *elem, **elemp;
-
-  FOREACHelem_(set) {
-    if (elem == setelem)
-      return 1;
-  }
-  return 0;
-} /* setin */
-
-
-/*---------------------------------
-
-  qh_setindex(set, atelem )
-    returns the index of atelem in set.
-    returns -1, if not in set or maxsize wrong
-
-  notes:
-    set may be NULL and may contain nulls.
-    NOerrors returned (qh_pointid, QhullPoint::id)
-
-  design:
-    checks maxsize
-    scans set for atelem
-*/
-int qh_setindex(setT *set, void *atelem) {
-  void **elem;
-  int size, i;
-
-  if (!set)
-    return -1;
-  SETreturnsize_(set, size);
-  if (size > set->maxsize)
-    return -1;
-  elem= SETaddr_(set, void);
-  for (i=0; i < size; i++) {
-    if (*elem++ == atelem)
-      return i;
-  }
-  return -1;
-} /* setindex */
-
-
-/*---------------------------------
-
-  qh_setlarger(qh, oldsetp )
-    returns a larger set that contains all elements of *oldsetp
-
-  notes:
-    the set is at least twice as large
-    if temp set, updates qh->qhmem.tempstack
-
-  design:
-    creates a new set
-    copies the old set to the new set
-    updates pointers in tempstack
-    deletes the old set
-*/
-void qh_setlarger(qhT *qh, setT **oldsetp) {
-  int size= 1;
-  setT *newset, *set, **setp, *oldset;
-  setelemT *sizep;
-  setelemT *newp, *oldp;
-
-  if (*oldsetp) {
-    oldset= *oldsetp;
-    SETreturnsize_(oldset, size);
-    qh->qhmem.cntlarger++;
-    qh->qhmem.totlarger += size+1;
-    newset= qh_setnew(qh, 2 * size);
-    oldp= (setelemT *)SETaddr_(oldset, void);
-    newp= (setelemT *)SETaddr_(newset, void);
-    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
-    sizep= SETsizeaddr_(newset);
-    sizep->i= size+1;
-    FOREACHset_((setT *)qh->qhmem.tempstack) {
-      if (set == oldset)
-        *(setp-1)= newset;
-    }
-    qh_setfree(qh, oldsetp);
-  }else
-    newset= qh_setnew(qh, 3);
-  *oldsetp= newset;
-} /* setlarger */
-
-
-/*---------------------------------
-
-  qh_setlast( set )
-    return last element of set or NULL (use type conversion)
-
-  notes:
-    set may be NULL
-
-  design:
-    return last element
-*/
-void *qh_setlast(setT *set) {
-  int size;
-
-  if (set) {
-    size= SETsizeaddr_(set)->i;
-    if (!size)
-      return SETelem_(set, set->maxsize - 1);
-    else if (size > 1)
-      return SETelem_(set, size - 2);
-  }
-  return NULL;
-} /* setlast */
-
-
-/*---------------------------------
-
-  qh_setnew(qh, setsize )
-    creates and allocates space for a set
-
-  notes:
-    setsize means the number of elements (!including the NULL terminator)
-    use qh_settemp/qh_setfreetemp if set is temporary
-
-  design:
-    allocate memory for set
-    roundup memory if small set
-    initialize as empty set
-*/
-setT *qh_setnew(qhT *qh, int setsize) {
-  setT *set;
-  int sizereceived; /* used if !qh_NOmem */
-  int size;
-  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
-
-  if (!setsize)
-    setsize++;
-  size= sizeof(setT) + setsize * SETelemsize;
-  if (size>0 && size <= qh->qhmem.LASTsize) {
-    qh_memalloc_(qh, size, freelistp, set, setT);
-#ifndef qh_NOmem
-    sizereceived= qh->qhmem.sizetable[ qh->qhmem.indextable[size]];
-    if (sizereceived > size)
-      setsize += (sizereceived - size)/SETelemsize;
-#endif
-  }else
-    set= (setT*)qh_memalloc(qh, size);
-  set->maxsize= setsize;
-  set->e[setsize].i= 1;
-  set->e[0].p= NULL;
-  return(set);
-} /* setnew */
-
-
-/*---------------------------------
-
-  qh_setnew_delnthsorted(qh, set, size, nth, prepend )
-    creates a sorted set not containing nth element
-    if prepend, the first prepend elements are undefined
-
-  notes:
-    set must be defined
-    checks nth
-    see also: setdelnthsorted
-
-  design:
-    create new set
-    setup pointers and allocate room for prepend'ed entries
-    append head of old set to new set
-    append tail of old set to new set
-*/
-setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend) {
-  setT *newset;
-  void **oldp, **newp;
-  int tailsize= size - nth -1, newsize;
-
-  if (tailsize < 0) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  newsize= size-1 + prepend;
-  newset= qh_setnew(qh, newsize);
-  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
-  oldp= SETaddr_(set, void);
-  newp= SETaddr_(newset, void) + prepend;
-  switch (nth) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
-    newp += nth;
-    oldp += nth;
-    break;
-  }
-  oldp++;
-  switch (tailsize) {
-  case 0:
-    break;
-  case 1:
-    *(newp++)= *oldp++;
-    break;
-  case 2:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 3:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  case 4:
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    *(newp++)= *oldp++;
-    break;
-  default:
-    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
-    newp += tailsize;
-  }
-  *newp= NULL;
-  return(newset);
-} /* setnew_delnthsorted */
-
-
-/*---------------------------------
-
-  qh_setprint(qh, fp, string, set )
-    print set elements to fp with identifying string
-
-  notes:
-    never errors
-*/
-void qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set) {
-  int size, k;
-
-  if (!set)
-    qh_fprintf(qh, fp, 9346, "%s set is null\n", string);
-  else {
-    SETreturnsize_(set, size);
-    qh_fprintf(qh, fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
-             string, set, set->maxsize, size);
-    if (size > set->maxsize)
-      size= set->maxsize+1;
-    for (k=0; k < size; k++)
-      qh_fprintf(qh, fp, 9348, " %p", set->e[k].p);
-    qh_fprintf(qh, fp, 9349, "\n");
-  }
-} /* setprint */
-
-/*---------------------------------
-
-  qh_setreplace(qh, set, oldelem, newelem )
-    replaces oldelem in set with newelem
-
-  notes:
-    errors if oldelem not in the set
-    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
-
-  design:
-    find oldelem
-    replace with newelem
-*/
-void qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem) {
-  void **elemp;
-
-  elemp= SETaddr_(set, void);
-  while (*elemp != oldelem && *elemp)
-    elemp++;
-  if (*elemp)
-    *elemp= newelem;
-  else {
-    qh_fprintf(qh, qh->qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
-       oldelem);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-} /* setreplace */
-
-
-/*---------------------------------
-
-  qh_setsize(qh, set )
-    returns the size of a set
-
-  notes:
-    errors if set's maxsize is incorrect
-    same as SETreturnsize_(set)
-    same code for qh_setsize [qset_r.c] and QhullSetBase::count
-
-  design:
-    determine actual size of set from maxsize
-*/
-int qh_setsize(qhT *qh, setT *set) {
-  int size;
-  setelemT *sizep;
-
-  if (!set)
-    return(0);
-  sizep= SETsizeaddr_(set);
-  if ((size= sizep->i)) {
-    size--;
-    if (size > set->maxsize) {
-      qh_fprintf(qh, qh->qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
-               size, set->maxsize);
-      qh_setprint(qh, qh->qhmem.ferr, "set: ", set);
-      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-    }
-  }else
-    size= set->maxsize;
-  return size;
-} /* setsize */
-
-/*---------------------------------
-
-  qh_settemp(qh, setsize )
-    return a stacked, temporary set of upto setsize elements
-
-  notes:
-    use settempfree or settempfree_all to release from qh->qhmem.tempstack
-    see also qh_setnew
-
-  design:
-    allocate set
-    append to qh->qhmem.tempstack
-
-*/
-setT *qh_settemp(qhT *qh, int setsize) {
-  setT *newset;
-
-  newset= qh_setnew(qh, setsize);
-  qh_setappend(qh, &qh->qhmem.tempstack, newset);
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
-       newset, newset->maxsize, qh_setsize(qh, qh->qhmem.tempstack));
-  return newset;
-} /* settemp */
-
-/*---------------------------------
-
-  qh_settempfree(qh, set )
-    free temporary set at top of qh->qhmem.tempstack
-
-  notes:
-    nop if set is NULL
-    errors if set not from previous   qh_settemp
-
-  to locate errors:
-    use 'T2' to find source and then find mis-matching qh_settemp
-
-  design:
-    check top of qh->qhmem.tempstack
-    free it
-*/
-void qh_settempfree(qhT *qh, setT **set) {
-  setT *stackedset;
-
-  if (!*set)
-    return;
-  stackedset= qh_settemppop(qh);
-  if (stackedset != *set) {
-    qh_settemppush(qh, stackedset);
-    qh_fprintf(qh, qh->qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
-             *set, qh_setsize(qh, *set), qh_setsize(qh, qh->qhmem.tempstack)+1,
-             stackedset, qh_setsize(qh, stackedset));
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(qh, set);
-} /* settempfree */
-
-/*---------------------------------
-
-  qh_settempfree_all(qh)
-    free all temporary sets in qh->qhmem.tempstack
-
-  design:
-    for each set in tempstack
-      free set
-    free qh->qhmem.tempstack
-*/
-void qh_settempfree_all(qhT *qh) {
-  setT *set, **setp;
-
-  FOREACHset_(qh->qhmem.tempstack)
-    qh_setfree(qh, &set);
-  qh_setfree(qh, &qh->qhmem.tempstack);
-} /* settempfree_all */
-
-/*---------------------------------
-
-  qh_settemppop(qh)
-    pop and return temporary set from qh->qhmem.tempstack
-
-  notes:
-    the returned set is permanent
-
-  design:
-    pop and check top of qh->qhmem.tempstack
-*/
-setT *qh_settemppop(qhT *qh) {
-  setT *stackedset;
-
-  stackedset= (setT*)qh_setdellast(qh->qhmem.tempstack);
-  if (!stackedset) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
-       qh_setsize(qh, qh->qhmem.tempstack)+1, stackedset, qh_setsize(qh, stackedset));
-  return stackedset;
-} /* settemppop */
-
-/*---------------------------------
-
-  qh_settemppush(qh, set )
-    push temporary set unto qh->qhmem.tempstack (makes it temporary)
-
-  notes:
-    duplicates settemp() for tracing
-
-  design:
-    append set to tempstack
-*/
-void qh_settemppush(qhT *qh, setT *set) {
-  if (!set) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  qh_setappend(qh, &qh->qhmem.tempstack, set);
-  if (qh->qhmem.IStracing >= 5)
-    qh_fprintf(qh, qh->qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
-      qh_setsize(qh, qh->qhmem.tempstack), set, qh_setsize(qh, set));
-} /* settemppush */
-
-
-/*---------------------------------
-
-  qh_settruncate(qh, set, size )
-    truncate set to size elements
-
-  notes:
-    set must be defined
-
-  see:
-    SETtruncate_
-
-  design:
-    check size
-    update actual size of set
-*/
-void qh_settruncate(qhT *qh, setT *set, int size) {
-
-  if (size < 0 || size > set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
-  set->e[size].p= NULL;
-} /* settruncate */
-
-/*---------------------------------
-
-  qh_setunique(qh, set, elem )
-    add elem to unsorted set unless it is already in set
-
-  notes:
-    returns 1 if it is appended
-
-  design:
-    if elem not in set
-      append elem to set
-*/
-int qh_setunique(qhT *qh, setT **set, void *elem) {
-
-  if (!qh_setin(*set, elem)) {
-    qh_setappend(qh, set, elem);
-    return 1;
-  }
-  return 0;
-} /* setunique */
-
-/*---------------------------------
-
-  qh_setzero(qh, set, index, size )
-    zero elements from index on
-    set actual size of set to size
-
-  notes:
-    set must be defined
-    the set becomes an indexed set (can not use FOREACH...)
-
-  see also:
-    qh_settruncate
-
-  design:
-    check index and size
-    update actual size
-    zero elements starting at e[index]
-*/
-void qh_setzero(qhT *qh, setT *set, int idx, int size) {
-  int count;
-
-  if (idx < 0 || idx >= size || size > set->maxsize) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
-    qh_setprint(qh, qh->qhmem.ferr, "", set);
-    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
-  }
-  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
-  count= size - idx + 1;   /* +1 for NULL terminator */
-  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
-} /* setzero */
-
-
diff --git a/src/qhull/src/libqhull_r/qset_r.h b/src/qhull/src/libqhull_r/qset_r.h
deleted file mode 100644
index 7ba199d6f..000000000
--- a/src/qhull/src/libqhull_r/qset_r.h
+++ /dev/null
@@ -1,502 +0,0 @@
-/*
      ---------------------------------
-
-   qset_r.h
-     header file for qset_r.c that implements set
-
-   see qh-set_r.htm and qset_r.c
-
-   only uses mem_r.c, malloc/free
-
-   for error handling, writes message and calls
-      qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL);
-
-   set operations satisfy the following properties:
-    - sets have a max size, the actual size (if different) is stored at the end
-    - every set is NULL terminated
-    - sets may be sorted or unsorted, the caller must distinguish this
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/qset_r.h#4 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFset
-#define qhDEFset 1
-
-#include 
-
-/*================= -structures- ===============*/
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
-#endif
-
-#ifndef DEFqhT
-#define DEFqhT 1
-typedef struct qhT qhT;          /* defined in libqhull_r.h */
-#endif
-
-/* [jan'15] Decided not to use countT.  Most sets are small.  The code uses signed tests */
-
-/*------------------------------------------
-
-setT
-  a set or list of pointers with maximum size and actual size.
-
-variations:
-  unsorted, unique   -- a list of unique pointers with NULL terminator
-                           user guarantees uniqueness
-  sorted             -- a sorted list of unique pointers with NULL terminator
-                           qset_r.c guarantees uniqueness
-  unsorted           -- a list of pointers terminated with NULL
-  indexed            -- an array of pointers with NULL elements
-
-structure for set of n elements:
-
-        --------------
-        |  maxsize
-        --------------
-        |  e[0] - a pointer, may be NULL for indexed sets
-        --------------
-        |  e[1]
-
-        --------------
-        |  ...
-        --------------
-        |  e[n-1]
-        --------------
-        |  e[n] = NULL
-        --------------
-        |  ...
-        --------------
-        |  e[maxsize] - n+1 or NULL (determines actual size of set)
-        --------------
-
-*/
-
-/*-- setelemT -- internal type to allow both pointers and indices
-*/
-typedef union setelemT setelemT;
-union setelemT {
-  void    *p;
-  int   i;         /* integer used for e[maxSize] */
-};
-
-struct setT {
-  int maxsize;          /* maximum number of elements (except NULL) */
-  setelemT e[1];        /* array of pointers, tail is NULL */
-                        /* last slot (unless NULL) is actual size+1
-                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
-                        /* this may generate a warning since e[] contains
-                           maxsize elements */
-};
-
-/*=========== -constants- =========================*/
-
-/*-------------------------------------
-
-  SETelemsize
-    size of a set element in bytes
-*/
-#define SETelemsize ((int)sizeof(setelemT))
-
-
-/*=========== -macros- =========================*/
-
-/*-------------------------------------
-
-   FOREACHsetelement_(type, set, variable)
-     define FOREACH iterator
-
-   declare:
-     assumes *variable and **variablep are declared
-     no space in "variable)" [DEC Alpha cc compiler]
-
-   each iteration:
-     variable is set element
-     variablep is one beyond variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example:
-     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
-
-   notes:
-     use FOREACHsetelement_i_() if need index or include NULLs
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##p= (type **)&((set)->e[0].p); \
-          (variable= *variable##p++);)
-
-/*------------------------------------------
-
-   FOREACHsetelement_i_(qh, type, set, variable)
-     define indexed FOREACH iterator
-
-   declare:
-     type *variable, variable_n, variable_i;
-
-   each iteration:
-     variable is set element, may be NULL
-     variable_i is index, variable_n is qh_setsize()
-
-   to repeat an element:
-     variable_i--; variable_n-- repeats for deleted element
-
-   at exit:
-     variable==NULL and variable_i==variable_n
-
-   example:
-     #define FOREACHfacet_i_( qh, facets ) FOREACHsetelement_i_( qh, facetT, facets, facet )
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_i_(qh, type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##_i= 0, variable= (type *)((set)->e[0].p), \
-                   variable##_n= qh_setsize(qh, set);\
-          variable##_i < variable##_n;\
-          variable= (type *)((set)->e[++variable##_i].p) )
-
-/*----------------------------------------
-
-   FOREACHsetelementreverse_(qh, type, set, variable)-
-     define FOREACH iterator in reverse order
-
-   declare:
-     assumes *variable and **variablep are declared
-     also declare 'int variabletemp'
-
-   each iteration:
-     variable is set element
-
-   to repeat an element:
-     variabletemp++; / *repeat* /
-
-   at exit:
-     variable is NULL
-
-   example:
-     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
-
-   notes:
-     use FOREACHsetelementreverse12_() to reverse first two elements
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse_(qh, type, set, variable) \
-        if (((variable= NULL), set)) for (\
-           variable##temp= qh_setsize(qh, set)-1, variable= qh_setlast(qh, set);\
-           variable; variable= \
-           ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
-
-/*-------------------------------------
-
-   FOREACHsetelementreverse12_(type, set, variable)-
-     define FOREACH iterator with e[1] and e[0] reversed
-
-   declare:
-     assumes *variable and **variablep are declared
-
-   each iteration:
-     variable is set element
-     variablep is one after variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example
-     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse12_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##p= (type **)&((set)->e[1].p); \
-          (variable= *variable##p); \
-          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
-              (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
-
-/*-------------------------------------
-
-   FOREACHelem_( set )-
-     iterate elements in a set
-
-   declare:
-     void *elem, *elemp;
-
-   each iteration:
-     elem is set element
-     elemp is one beyond
-
-   to repeat an element:
-     elemp--; / *repeat* /
-
-   at exit:
-     elem == NULL at end of loop
-
-   example:
-     FOREACHelem_(set) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
-
-/*-------------------------------------
-
-   FOREACHset_( set )-
-     iterate a set of sets
-
-   declare:
-     setT *set, **setp;
-
-   each iteration:
-     set is set element
-     setp is one beyond
-
-   to repeat an element:
-     setp--; / *repeat* /
-
-   at exit:
-     set == NULL at end of loop
-
-   example
-     FOREACHset_(sets) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
-
-/*-------------------------------------------
-
-   SETindex_( set, elem )
-     return index of elem in set
-
-   notes:
-     for use with FOREACH iteration
-     WARN64 -- Maximum set size is 2G
-
-   example:
-     i= SETindex_(ridges, ridge)
-*/
-#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))
-
-/*-----------------------------------------
-
-   SETref_( elem )
-     l.h.s. for modifying the current element in a FOREACH iteration
-
-   example:
-     SETref_(ridge)= anotherridge;
-*/
-#define SETref_(elem) (elem##p[-1])
-
-/*-----------------------------------------
-
-   SETelem_(set, n)
-     return the n'th element of set
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-      use SETelemt_() for type cast
-*/
-#define SETelem_(set, n)           ((set)->e[n].p)
-
-/*-----------------------------------------
-
-   SETelemt_(set, n, type)
-     return the n'th element of set as a type
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-*/
-#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
-
-/*-----------------------------------------
-
-   SETelemaddr_(set, n, type)
-     return address of the n'th element of a set
-
-   notes:
-      assumes that n is valid [0..size] and set is defined
-*/
-#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
-
-/*-----------------------------------------
-
-   SETfirst_(set)
-     return first element of set
-
-*/
-#define SETfirst_(set)             ((set)->e[0].p)
-
-/*-----------------------------------------
-
-   SETfirstt_(set, type)
-     return first element of set as a type
-
-*/
-#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
-
-/*-----------------------------------------
-
-   SETsecond_(set)
-     return second element of set
-
-*/
-#define SETsecond_(set)            ((set)->e[1].p)
-
-/*-----------------------------------------
-
-   SETsecondt_(set, type)
-     return second element of set as a type
-*/
-#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
-
-/*-----------------------------------------
-
-   SETaddr_(set, type)
-       return address of set's elements
-*/
-#define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))
-
-/*-----------------------------------------
-
-   SETreturnsize_(set, size)
-     return size of a set
-
-   notes:
-      set must be defined
-      use qh_setsize(qhT *qh, set) unless speed is critical
-*/
-#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
-
-/*-----------------------------------------
-
-   SETempty_(set)
-     return true(1) if set is empty
-
-   notes:
-      set may be NULL
-*/
-#define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))
-
-/*---------------------------------
-
-  SETsizeaddr_(set)
-    return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
-    Its type is setelemT* for strict aliasing
-    All SETelemaddr_ must be cast to setelemT
-
-
-  notes:
-    *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
-*/
-#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))
-
-/*-----------------------------------------
-
-   SETtruncate_(set, size)
-     truncate set to size
-
-   see:
-     qh_settruncate()
-
-*/
-#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
-      set->e[size].p= NULL;}
-
-/*======= prototypes in alphabetical order ============*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void  qh_setaddsorted(qhT *qh, setT **setp, void *elem);
-void  qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem);
-void  qh_setappend(qhT *qh, setT **setp, void *elem);
-void  qh_setappend_set(qhT *qh, setT **setp, setT *setA);
-void  qh_setappend2ndlast(qhT *qh, setT **setp, void *elem);
-void  qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id);
-void  qh_setcompact(qhT *qh, setT *set);
-setT *qh_setcopy(qhT *qh, setT *set, int extra);
-void *qh_setdel(setT *set, void *elem);
-void *qh_setdellast(setT *set);
-void *qh_setdelnth(qhT *qh, setT *set, int nth);
-void *qh_setdelnthsorted(qhT *qh, setT *set, int nth);
-void *qh_setdelsorted(setT *set, void *newelem);
-setT *qh_setduplicate(qhT *qh, setT *set, int elemsize);
-void **qh_setendpointer(setT *set);
-int   qh_setequal(setT *setA, setT *setB);
-int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
-int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
-void  qh_setfree(qhT *qh, setT **set);
-void  qh_setfree2(qhT *qh, setT **setp, int elemsize);
-void  qh_setfreelong(qhT *qh, setT **set);
-int   qh_setin(setT *set, void *setelem);
-int qh_setindex(setT *set, void *setelem);
-void  qh_setlarger(qhT *qh, setT **setp);
-void *qh_setlast(setT *set);
-setT *qh_setnew(qhT *qh, int size);
-setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend);
-void  qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set);
-void  qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem);
-int qh_setsize(qhT *qh, setT *set);
-setT *qh_settemp(qhT *qh, int setsize);
-void  qh_settempfree(qhT *qh, setT **set);
-void  qh_settempfree_all(qhT *qh);
-setT *qh_settemppop(qhT *qh);
-void  qh_settemppush(qhT *qh, setT *set);
-void  qh_settruncate(qhT *qh, setT *set, int size);
-int   qh_setunique(qhT *qh, setT **set, void *elem);
-void  qh_setzero(qhT *qh, setT *set, int idx, int size);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFset */
diff --git a/src/qhull/src/libqhull_r/random_r.c b/src/qhull/src/libqhull_r/random_r.c
deleted file mode 100644
index 1fefb51c3..000000000
--- a/src/qhull/src/libqhull_r/random_r.c
+++ /dev/null
@@ -1,247 +0,0 @@
-/*
      ---------------------------------
-
-   random_r.c and utilities
-     Park & Miller's minimimal standard random number generator
-     argc/argv conversion
-
-     Used by rbox.  Do not use 'qh' 
-*/
-
-#include "libqhull_r.h"
-#include "random_r.h"
-
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/*---------------------------------
-
- qh_argv_to_command(argc, argv, command, max_size )
-
-    build command from argc/argv
-    max_size is at least
-
- returns:
-    a space-delimited string of options (just as typed)
-    returns false if max_size is too short
-
- notes:
-    silently removes
-    makes option string easy to input and output
-    matches qh_argv_to_command_size()
-
-    argc may be 0
-*/
-int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
-  int i, remaining;
-  char *s;
-  *command= '\0';  /* max_size > 0 */
-
-  if (argc) {
-    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
-    || (s= strrchr( argv[0], '/')))
-        s++;
-    else
-        s= argv[0];
-    if ((int)strlen(s) < max_size)   /* WARN64 */
-        strcpy(command, s);
-    else
-        goto error_argv;
-    if ((s= strstr(command, ".EXE"))
-    ||  (s= strstr(command, ".exe")))
-        *s= '\0';
-  }
-  for (i=1; i < argc; i++) {
-    s= argv[i];
-    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
-    if (!*s || strchr(s, ' ')) {
-      char *t= command + strlen(command);
-      remaining -= 2;
-      if (remaining < 0) {
-        goto error_argv;
-      }
-      *t++= ' ';
-      *t++= '"';
-      while (*s) {
-        if (*s == '"') {
-          if (--remaining < 0)
-            goto error_argv;
-          *t++= '\\';
-        }
-        *t++= *s++;
-      }
-      *t++= '"';
-      *t= '\0';
-    }else if (remaining < 0) {
-      goto error_argv;
-    }else
-      strcat(command, " ");
-      strcat(command, s);
-  }
-  return 1;
-
-error_argv:
-  return 0;
-} /* argv_to_command */
-
-/*---------------------------------
-
-qh_argv_to_command_size(argc, argv )
-
-    return size to allocate for qh_argv_to_command()
-
-notes:
-    argc may be 0
-    actual size is usually shorter
-*/
-int qh_argv_to_command_size(int argc, char *argv[]) {
-    unsigned int count= 1; /* null-terminator if argc==0 */
-    int i;
-    char *s;
-
-    for (i=0; i0 && strchr(argv[i], ' ')) {
-        count += 2;  /* quote delimiters */
-        for (s=argv[i]; *s; s++) {
-          if (*s == '"') {
-            count++;
-          }
-        }
-      }
-    }
-    return count;
-} /* argv_to_command_size */
-
-/*---------------------------------
-
-  qh_rand()
-  qh_srand(qh, seed )
-    generate pseudo-random number between 1 and 2^31 -2
-
-  notes:
-    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
-
-    From Park & Miller's minimal standard random number generator
-      Communications of the ACM, 31:1192-1201, 1988.
-    Does not use 0 or 2^31 -1
-      this is silently enforced by qh_srand()
-    Can make 'Rn' much faster by moving qh_rand to qh_distplane
-*/
-
-/* Global variables and constants */
-
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773  /* m div a */
-#define qh_rand_r 2836    /* m mod a */
-
-int qh_rand(qhT *qh) {
-    int lo, hi, test;
-    int seed = qh->last_random;
-
-    hi = seed / qh_rand_q;  /* seed div q */
-    lo = seed % qh_rand_q;  /* seed mod q */
-    test = qh_rand_a * lo - qh_rand_r * hi;
-    if (test > 0)
-        seed= test;
-    else
-        seed= test + qh_rand_m;
-    qh->last_random= seed;
-    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
-    /* seed = qh_RANDOMmax;  for testing */
-    return seed;
-} /* rand */
-
-void qh_srand(qhT *qh, int seed) {
-    if (seed < 1)
-        qh->last_random= 1;
-    else if (seed >= qh_rand_m)
-        qh->last_random= qh_rand_m - 1;
-    else
-        qh->last_random= seed;
-} /* qh_srand */
-
-/*---------------------------------
-
-qh_randomfactor(qh, scale, offset )
-  return a random factor r * scale + offset
-
-notes:
-  qh.RANDOMa/b are defined in global_r.c
-  qh_RANDOMint requires 'qh'
-*/
-realT qh_randomfactor(qhT *qh, realT scale, realT offset) {
-    realT randr;
-
-    randr= qh_RANDOMint;
-    return randr * scale + offset;
-} /* randomfactor */
-
-/*---------------------------------
-
-qh_randommatrix(qh, buffer, dim, rows )
-  generate a random dim X dim matrix in range [-1,1]
-  assumes buffer is [dim+1, dim]
-
-  returns:
-    sets buffer to random numbers
-    sets rows to rows of buffer
-    sets row[dim] as scratch row
-
-  notes:
-    qh_RANDOMint requires 'qh'
-*/
-void qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **rows) {
-    int i, k;
-    realT **rowi, *coord, realr;
-
-    coord= buffer;
-    rowi= rows;
-    for (i=0; i < dim; i++) {
-        *(rowi++)= coord;
-        for (k=0; k < dim; k++) {
-            realr= qh_RANDOMint;
-            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
-        }
-    }
-    *rowi= coord;
-} /* randommatrix */
-
-/*---------------------------------
-
-  qh_strtol( s, endp) qh_strtod( s, endp)
-    internal versions of strtol() and strtod()
-    does not skip trailing spaces
-  notes:
-    some implementations of strtol()/strtod() skip trailing spaces
-*/
-double qh_strtod(const char *s, char **endp) {
-  double result;
-
-  result= strtod(s, endp);
-  if (s < (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtod */
-
-int qh_strtol(const char *s, char **endp) {
-  int result;
-
-  result= (int) strtol(s, endp, 10);     /* WARN64 */
-  if (s< (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtol */
diff --git a/src/qhull/src/libqhull_r/random_r.h b/src/qhull/src/libqhull_r/random_r.h
deleted file mode 100644
index dc884b33c..000000000
--- a/src/qhull/src/libqhull_r/random_r.h
+++ /dev/null
@@ -1,41 +0,0 @@
-/*
      ---------------------------------
-
-  random.h
-    header file for random and utility routines
-
-   see qh-geom_r.htm and random_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/random_r.h#4 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-*/
-
-#ifndef qhDEFrandom
-#define qhDEFrandom 1
-
-#include "libqhull_r.h"
-
-/*============= prototypes in alphabetical order ======= */
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
-int     qh_argv_to_command_size(int argc, char *argv[]);
-int     qh_rand(qhT *qh);
-void    qh_srand(qhT *qh, int seed);
-realT   qh_randomfactor(qhT *qh, realT scale, realT offset);
-void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
-int     qh_strtol(const char *s, char **endp);
-double  qh_strtod(const char *s, char **endp);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif /* qhDEFrandom */
-
-
-
diff --git a/src/qhull/src/libqhull_r/rboxlib_r.c b/src/qhull/src/libqhull_r/rboxlib_r.c
deleted file mode 100644
index 6c0c7e35e..000000000
--- a/src/qhull/src/libqhull_r/rboxlib_r.c
+++ /dev/null
@@ -1,842 +0,0 @@
-/*
      ---------------------------------
-
-   rboxlib_r.c
-     Generate input points
-
-   notes:
-     For documentation, see prompt[] of rbox_r.c
-     50 points generated for 'rbox D4'
-
-   WARNING:
-     incorrect range if qh_RANDOMmax is defined wrong (user_r.h)
-*/
-
-#include "libqhull_r.h"  /* First for user_r.h */
-#include "random_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ */
-#pragma warning( disable : 4706)  /* assignment within conditional expression. */
-#pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
-#endif
-
-#define MAXdim 200
-#define PI 3.1415926535897932384
-
-/* ------------------------------ prototypes ----------------*/
-int qh_roundi(qhT *qh, double a);
-void qh_out1(qhT *qh, double a);
-void qh_out2n(qhT *qh, double a, double b);
-void qh_out3n(qhT *qh, double a, double b, double c);
-void qh_outcoord(qhT *qh, int iscdd, double *coord, int dim);
-void qh_outcoincident(qhT *qh, int coincidentpoints, double radius, int iscdd, double *coord, int dim);
-
-void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-int     qh_rand(qhT *qh);
-void    qh_srand(qhT *qh, int seed);
-
-/*---------------------------------
-
-  qh_rboxpoints(qh, rbox_command )
-    Generate points to qh->fout according to rbox options
-    Report errors on qh->ferr
-
-  returns:
-    0 (qh_ERRnone) on success
-    1 (qh_ERRinput) on input error
-    4 (qh_ERRmem) on memory error
-    5 (qh_ERRqhull) on internal error
-
-  notes:
-    To avoid using stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user_r.c)
-
-  design:
-    Straight line code (consider defining a struct and functions):
-
-    Parse arguments into variables
-    Determine the number of points
-    Generate the points
-*/
-int qh_rboxpoints(qhT *qh, char* rbox_command) {
-  int i,j,k;
-  int gendim;
-  int coincidentcount=0, coincidenttotal=0, coincidentpoints=0;
-  int cubesize, diamondsize, seed=0, count, apex;
-  int dim=3 , numpoints= 0, totpoints, addpoints=0;
-  int issphere=0, isaxis=0,  iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
-  int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0;
-  int israndom=0, istime=0;
-  int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
-  double width=0.0, gap=0.0, radius=0.0, coincidentradius=0.0;
-  double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
-  double *coordp, *simplex= NULL, *simplexp;
-  int nthroot, mult[MAXdim];
-  double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
-  double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
-  double box= qh_DEFAULTbox; /* scale all numbers before output */
-  double randmax= qh_RANDOMmax;
-  char command[200], seedbuf[200];
-  char *s= command, *t, *first_point= NULL;
-  time_t timedata;
-  int exitcode;
-
-  exitcode= setjmp(qh->rbox_errexit);
-  if (exitcode) {
-    /* same code for error exit and normal return, qh->NOerrexit is set */
-    if (simplex)
-        qh_free(simplex);
-    return exitcode;
-  }
-
-  *command= '\0';
-  strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
-
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    if (isdigit(*s)) {
-      numpoints= qh_strtol(s, &s);
-      continue;
-    }
-    /* ============= read flags =============== */
-    switch (*s++) {
-    case 'c':
-      addcube= 1;
-      t= s;
-      while (isspace(*t))
-        t++;
-      if (*t == 'G')
-        cube= qh_strtod(++t, &s);
-      break;
-    case 'd':
-      adddiamond= 1;
-      t= s;
-      while (isspace(*t))
-        t++;
-      if (*t == 'G')
-        diamond= qh_strtod(++t, &s);
-      break;
-    case 'h':
-      iscdd= 1;
-      break;
-    case 'l':
-      isspiral= 1;
-      break;
-    case 'n':
-      NOcommand= 1;
-      break;
-    case 'r':
-      isregular= 1;
-      break;
-    case 's':
-      issphere= 1;
-      break;
-    case 't':
-      istime= 1;
-      if (isdigit(*s)) {
-        seed= qh_strtol(s, &s);
-        israndom= 0;
-      }else
-        israndom= 1;
-      break;
-    case 'x':
-      issimplex= 1;
-      break;
-    case 'y':
-      issimplex2= 1;
-      break;
-    case 'z':
-      qh->rbox_isinteger= 1;
-      break;
-    case 'B':
-      box= qh_strtod(s, &s);
-      isbox= 1;
-      break;
-    case 'C':
-      if (*s)
-        coincidentpoints=  qh_strtol(s, &s);
-      if (*s == ',') {
-        ++s;
-        coincidentradius=  qh_strtod(s, &s);
-      }
-      if (*s == ',') {
-        ++s;
-        coincidenttotal=  qh_strtol(s, &s);
-      }
-      if (*s && !isspace(*s)) {
-        qh_fprintf_rbox(qh, qh->ferr, 7080, "rbox error: arguments for 'Cn,r,m' are not 'int', 'float', and 'int'.  Remaining string is '%s'\n", s);
-        qh_errexit_rbox(qh, qh_ERRinput);
-      }
-      if (coincidentpoints==0){
-        qh_fprintf_rbox(qh, qh->ferr, 6268, "rbox error: missing arguments for 'Cn,r,m' where n is the number of coincident points, r is the radius (default 0.0), and m is the number of points\n");
-        qh_errexit_rbox(qh, qh_ERRinput);
-      }
-      if (coincidentpoints<0 || coincidenttotal<0 || coincidentradius<0.0){
-        qh_fprintf_rbox(qh, qh->ferr, 6269, "rbox error: negative arguments for 'Cn,m,r' where n (%d) is the number of coincident points, m (%d) is the number of points, and r (%.2g) is the radius (default 0.0)\n", coincidentpoints, coincidenttotal, coincidentradius);
-        qh_errexit_rbox(qh, qh_ERRinput);
-      }
-      break;
-    case 'D':
-      dim= qh_strtol(s, &s);
-      if (dim < 1
-      || dim > MAXdim) {
-        qh_fprintf_rbox(qh, qh->ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
-        qh_errexit_rbox(qh, qh_ERRinput);
-      }
-      break;
-    case 'G':
-      if (isdigit(*s))
-        gap= qh_strtod(s, &s);
-      else
-        gap= 0.5;
-      isgap= 1;
-      break;
-    case 'L':
-      if (isdigit(*s))
-        radius= qh_strtod(s, &s);
-      else
-        radius= 10;
-      islens= 1;
-      break;
-    case 'M':
-      ismesh= 1;
-      if (*s)
-        meshn= qh_strtod(s, &s);
-      if (*s == ',') {
-        ++s;
-        meshm= qh_strtod(s, &s);
-      }else
-        meshm= 0.0;
-      if (*s == ',') {
-        ++s;
-        meshr= qh_strtod(s, &s);
-      }else
-        meshr= sqrt(meshn*meshn + meshm*meshm);
-      if (*s && !isspace(*s)) {
-        qh_fprintf_rbox(qh, qh->ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
-        meshn= 3.0, meshm=4.0, meshr=5.0;
-      }
-      break;
-    case 'O':
-      qh->rbox_out_offset= qh_strtod(s, &s);
-      break;
-    case 'P':
-      if (!first_point)
-        first_point= s-1;
-      addpoints++;
-      while (*s && !isspace(*s))   /* read points later */
-        s++;
-      break;
-    case 'W':
-      width= qh_strtod(s, &s);
-      iswidth= 1;
-      break;
-    case 'Z':
-      if (isdigit(*s))
-        radius= qh_strtod(s, &s);
-      else
-        radius= 1.0;
-      isaxis= 1;
-      break;
-    default:
-      qh_fprintf_rbox(qh, qh->ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    if (*s && !isspace(*s)) {
-      qh_fprintf_rbox(qh, qh->ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-  }
-
-  /* ============= defaults, constants, and sizes =============== */
-  if (qh->rbox_isinteger && !isbox)
-    box= qh_DEFAULTzbox;
-  if (addcube) {
-    cubesize= (int)floor(ldexp(1.0,dim)+0.5);
-    if (cube == 0.0)
-      cube= box;
-  }else
-    cubesize= 0;
-  if (adddiamond) {
-    diamondsize= 2*dim;
-    if (diamond == 0.0)
-      diamond= box;
-  }else
-    diamondsize= 0;
-  if (islens) {
-    if (isaxis) {
-        qh_fprintf_rbox(qh, qh->ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
-        qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    if (radius <= 1.0) {
-        qh_fprintf_rbox(qh, qh->ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
-               radius);
-        qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    lensangle= asin(1.0/radius);
-    lensbase= radius * cos(lensangle);
-  }
-
-  if (!numpoints) {
-    if (issimplex2)
-        ; /* ok */
-    else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
-        qh_fprintf_rbox(qh, qh->ferr, 6192, "rbox error: missing count\n");
-        qh_errexit_rbox(qh, qh_ERRinput);
-    }else if (adddiamond + addcube + addpoints)
-        ; /* ok */
-    else {
-        numpoints= 50;  /* ./rbox D4 is the test case */
-        issphere= 1;
-    }
-  }
-  if ((issimplex + islens + isspiral + ismesh > 1)
-  || (issimplex + issphere + isspiral + ismesh > 1)) {
-    qh_fprintf_rbox(qh, qh->ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
-    qh_errexit_rbox(qh, qh_ERRinput);
-  }
-  if (coincidentpoints>0 && (numpoints == 0 || coincidenttotal > numpoints)) {
-    qh_fprintf_rbox(qh, qh->ferr, 6270, "rbox error: 'Cn,r,m' requested n coincident points for each of m points.  Either there is no points or m (%d) is greater than the number of points (%d).\n", coincidenttotal, numpoints);
-    qh_errexit_rbox(qh, qh_ERRinput);
-  }
-  if (coincidenttotal == 0)
-    coincidenttotal= numpoints;
-
-  /* ============= print header with total points =============== */
-  if (issimplex || ismesh)
-    totpoints= numpoints;
-  else if (issimplex2)
-    totpoints= numpoints+dim+1;
-  else if (isregular) {
-    totpoints= numpoints;
-    if (dim == 2) {
-        if (islens)
-          totpoints += numpoints - 2;
-    }else if (dim == 3) {
-        if (islens)
-          totpoints += 2 * numpoints;
-      else if (isgap)
-        totpoints += 1 + numpoints;
-      else
-        totpoints += 2;
-    }
-  }else
-    totpoints= numpoints + isaxis;
-  totpoints += cubesize + diamondsize + addpoints;
-  totpoints += coincidentpoints*coincidenttotal;
-
-  /* ============= seed randoms =============== */
-  if (istime == 0) {
-    for (s=command; *s; s++) {
-      if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
-        i= 'x';
-      else
-        i= *s;
-      seed= 11*seed + i;
-    }
-  }else if (israndom) {
-    seed= (int)time(&timedata);
-    sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
-    strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
-    t= strstr(command, " t ");
-    if (t)
-      strcpy(t+1, t+3); /* remove " t " */
-  } /* else, seed explicitly set to n */
-  qh_RANDOMseed_(qh, seed);
-
-  /* ============= print header =============== */
-
-  if (iscdd)
-      qh_fprintf_rbox(qh, qh->fout, 9391, "%s\nbegin\n        %d %d %s\n",
-      NOcommand ? "" : command,
-      totpoints, dim+1,
-      qh->rbox_isinteger ? "integer" : "real");
-  else if (NOcommand)
-      qh_fprintf_rbox(qh, qh->fout, 9392, "%d\n%d\n", dim, totpoints);
-  else
-      /* qh_fprintf_rbox special cases 9393 to append 'command' to the RboxPoints.comment() */
-      qh_fprintf_rbox(qh, qh->fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
-
-  /* ============= explicit points =============== */
-  if ((s= first_point)) {
-    while (s && *s) { /* 'P' */
-      count= 0;
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      while (*++s) {
-        qh_out1(qh, qh_strtod(s, &s));
-        count++;
-        if (isspace(*s) || !*s)
-          break;
-        if (*s != ',') {
-          qh_fprintf_rbox(qh, qh->ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
-          qh_errexit_rbox(qh, qh_ERRinput);
-        }
-      }
-      if (count < dim) {
-        for (k=dim-count; k--; )
-          qh_out1(qh, 0.0);
-      }else if (count > dim) {
-        qh_fprintf_rbox(qh, qh->ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
-                  count, dim, s);
-        qh_errexit_rbox(qh, qh_ERRinput);
-      }
-      qh_fprintf_rbox(qh, qh->fout, 9394, "\n");
-      while ((s= strchr(s, 'P'))) {
-        if (isspace(s[-1]))
-          break;
-      }
-    }
-  }
-
-  /* ============= simplex distribution =============== */
-  if (issimplex+issimplex2) {
-    if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
-      qh_fprintf_rbox(qh, qh->ferr, 6196, "rbox error: insufficient memory for simplex\n");
-      qh_errexit_rbox(qh, qh_ERRmem); /* qh_ERRmem */
-    }
-    simplexp= simplex;
-    if (isregular) {
-      for (i=0; ifout, 9395, "\n");
-      }
-    }
-    for (j=0; jferr, 6197, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    if (!isaxis || radius == 0.0) {
-      isaxis= 1;
-      radius= 1.0;
-    }
-    if (dim == 3) {
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      qh_out3n(qh, 0.0, 0.0, -box);
-      if (!isgap) {
-        if (iscdd)
-          qh_out1(qh, 1.0);
-        qh_out3n(qh, 0.0, 0.0, box);
-      }
-    }
-    angle= 0.0;
-    anglediff= 2.0 * PI/numpoints;
-    for (i=0; i < numpoints; i++) {
-      angle += anglediff;
-      x= radius * cos(angle);
-      y= radius * sin(angle);
-      if (dim == 2) {
-        if (iscdd)
-          qh_out1(qh, 1.0);
-        qh_out2n(qh, x*box, y*box);
-      }else {
-        norm= sqrt(1.0 + x*x + y*y);
-        if (iscdd)
-          qh_out1(qh, 1.0);
-        qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
-        if (isgap) {
-          x *= 1-gap;
-          y *= 1-gap;
-          norm= sqrt(1.0 + x*x + y*y);
-          if (iscdd)
-            qh_out1(qh, 1.0);
-          qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
-        }
-      }
-    }
-  }
-  /* ============= regular points for 'r Ln D2' =============== */
-  else if (isregular && islens && dim == 2) {
-    double cos_0;
-
-    angle= lensangle;
-    anglediff= 2 * lensangle/(numpoints - 1);
-    cos_0= cos(lensangle);
-    for (i=0; i < numpoints; i++, angle -= anglediff) {
-      x= radius * sin(angle);
-      y= radius * (cos(angle) - cos_0);
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      qh_out2n(qh, x*box, y*box);
-      if (i != 0 && i != numpoints - 1) {
-        if (iscdd)
-          qh_out1(qh, 1.0);
-        qh_out2n(qh, x*box, -y*box);
-      }
-    }
-  }
-  /* ============= regular points for 'r Ln D3' =============== */
-  else if (isregular && islens && dim != 2) {
-    if (dim != 3) {
-      qh_free(simplex);
-      qh_fprintf_rbox(qh, qh->ferr, 6198, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    angle= 0.0;
-    anglediff= 2* PI/numpoints;
-    if (!isgap) {
-      isgap= 1;
-      gap= 0.5;
-    }
-    offset= sqrt(radius * radius - (1-gap)*(1-gap)) - lensbase;
-    for (i=0; i < numpoints; i++, angle += anglediff) {
-      x= cos(angle);
-      y= sin(angle);
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      qh_out3n(qh, box*x, box*y, 0.0);
-      x *= 1-gap;
-      y *= 1-gap;
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      qh_out3n(qh, box*x, box*y, box * offset);
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      qh_out3n(qh, box*x, box*y, -box * offset);
-    }
-  }
-  /* ============= apex of 'Zn' distribution + gendim =============== */
-  else {
-    if (isaxis) {
-      gendim= dim-1;
-      if (iscdd)
-        qh_out1(qh, 1.0);
-      for (j=0; j < gendim; j++)
-        qh_out1(qh, 0.0);
-      qh_out1(qh, -box);
-      qh_fprintf_rbox(qh, qh->fout, 9398, "\n");
-    }else if (islens)
-      gendim= dim-1;
-    else
-      gendim= dim;
-    /* ============= generate random point in unit cube =============== */
-    for (i=0; i < numpoints; i++) {
-      norm= 0.0;
-      for (j=0; j < gendim; j++) {
-        randr= qh_RANDOMint;
-        coord[j]= 2.0 * randr/randmax - 1.0;
-        norm += coord[j] * coord[j];
-      }
-      norm= sqrt(norm);
-      /* ============= dim-1 point of 'Zn' distribution ========== */
-      if (isaxis) {
-        if (!isgap) {
-          isgap= 1;
-          gap= 1.0;
-        }
-        randr= qh_RANDOMint;
-        rangap= 1.0 - gap * randr/randmax;
-        factor= radius * rangap / norm;
-        for (j=0; jferr, 6199, "rbox error: spiral distribution is available only in 3d\n\n");
-          qh_errexit_rbox(qh, qh_ERRinput);
-        }
-        coord[0]= cos(2*PI*i/(numpoints - 1));
-        coord[1]= sin(2*PI*i/(numpoints - 1));
-        coord[2]= 2.0*(double)i/(double)(numpoints-1) - 1.0;
-      /* ============= point of 's' distribution =============== */
-      }else if (issphere) {
-        factor= 1.0/norm;
-        if (iswidth) {
-          randr= qh_RANDOMint;
-          factor *= 1.0 - width * randr/randmax;
-        }
-        for (j=0; j randmax/2)
-          coord[dim-1]= -coord[dim-1];
-      /* ============= project 'Wn' point toward boundary =============== */
-      }else if (iswidth && !issphere) {
-        j= qh_RANDOMint % gendim;
-        if (coord[j] < 0)
-          coord[j]= -1.0 - coord[j] * width;
-        else
-          coord[j]= 1.0 - coord[j] * width;
-      }
-      /* ============= scale point to box =============== */
-      for (k=0; k=0; k--) {
-        if (j & ( 1 << k))
-          qh_out1(qh, cube);
-        else
-          qh_out1(qh, -cube);
-      }
-      qh_fprintf_rbox(qh, qh->fout, 9400, "\n");
-    }
-  }
-
-  /* ============= write diamond vertices =============== */
-  if (adddiamond) {
-    for (j=0; j=0; k--) {
-        if (j/2 != k)
-          qh_out1(qh, 0.0);
-        else if (j & 0x1)
-          qh_out1(qh, diamond);
-        else
-          qh_out1(qh, -diamond);
-      }
-      qh_fprintf_rbox(qh, qh->fout, 9401, "\n");
-    }
-  }
-
-  if (iscdd)
-    qh_fprintf_rbox(qh, qh->fout, 9402, "end\nhull\n");
-
-  /* same code for error exit and normal return */
-  qh_free(simplex);
-  return qh_ERRnone;
-} /* rboxpoints */
-
-/*------------------------------------------------
-outxxx - output functions for qh_rboxpoints
-*/
-int qh_roundi(qhT *qh, double a) {
-  if (a < 0.0) {
-    if (a - 0.5 < INT_MIN) {
-      qh_fprintf_rbox(qh, qh->ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    return (int)(a - 0.5);
-  }else {
-    if (a + 0.5 > INT_MAX) {
-      qh_fprintf_rbox(qh, qh->ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
-      qh_errexit_rbox(qh, qh_ERRinput);
-    }
-    return (int)(a + 0.5);
-  }
-} /* qh_roundi */
-
-void qh_out1(qhT *qh, double a) {
-
-  if (qh->rbox_isinteger)
-    qh_fprintf_rbox(qh, qh->fout, 9403, "%d ", qh_roundi(qh, a+qh->rbox_out_offset));
-  else
-    qh_fprintf_rbox(qh, qh->fout, 9404, qh_REAL_1, a+qh->rbox_out_offset);
-} /* qh_out1 */
-
-void qh_out2n(qhT *qh, double a, double b) {
-
-  if (qh->rbox_isinteger)
-    qh_fprintf_rbox(qh, qh->fout, 9405, "%d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset));
-  else
-    qh_fprintf_rbox(qh, qh->fout, 9406, qh_REAL_2n, a+qh->rbox_out_offset, b+qh->rbox_out_offset);
-} /* qh_out2n */
-
-void qh_out3n(qhT *qh, double a, double b, double c) {
-
-  if (qh->rbox_isinteger)
-    qh_fprintf_rbox(qh, qh->fout, 9407, "%d %d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset), qh_roundi(qh, c+qh->rbox_out_offset));
-  else
-    qh_fprintf_rbox(qh, qh->fout, 9408, qh_REAL_3n, a+qh->rbox_out_offset, b+qh->rbox_out_offset, c+qh->rbox_out_offset);
-} /* qh_out3n */
-
-void qh_outcoord(qhT *qh, int iscdd, double *coord, int dim) {
-    double *p= coord;
-    int k;
-
-    if (iscdd)
-      qh_out1(qh, 1.0);
-    for (k=0; k < dim; k++)
-      qh_out1(qh, *(p++));
-    qh_fprintf_rbox(qh, qh->fout, 9396, "\n");
-} /* qh_outcoord */
-
-void qh_outcoincident(qhT *qh, int coincidentpoints, double radius, int iscdd, double *coord, int dim) {
-  double *p;
-  double randr, delta;
-  int i,k;
-  double randmax= qh_RANDOMmax;
-
-  for (i= 0; ifout, 9410, "\n");
-  }
-} /* qh_outcoincident */
-
-/*------------------------------------------------
-   Only called from qh_rboxpoints or qh_fprintf_rbox
-   qh_fprintf_rbox is only called from qh_rboxpoints
-*/
-void qh_errexit_rbox(qhT *qh, int exitcode)
-{
-    longjmp(qh->rbox_errexit, exitcode);
-} /* qh_errexit_rbox */
-
diff --git a/src/qhull/src/libqhull_r/stat_r.c b/src/qhull/src/libqhull_r/stat_r.c
deleted file mode 100644
index 0f3ff0d3d..000000000
--- a/src/qhull/src/libqhull_r/stat_r.c
+++ /dev/null
@@ -1,682 +0,0 @@
-/*
      ---------------------------------
-
-   stat_r.c
-   contains all statistics that are collected for qhull
-
-   see qh-stat_r.htm and stat_r.h
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/stat_r.c#5 $$Change: 2062 $
-   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "qhull_ra.h"
-
-/*========== functions in alphabetic order ================*/
-
-/*---------------------------------
-
-  qh_allstatA()
-    define statistics in groups of 20
-
-  notes:
-    (otherwise, 'gcc -O2' uses too much memory)
-    uses qhstat.next
-*/
-void qh_allstatA(qhT *qh) {
-
-   /* zdef_(type,name,doc,average) */
-  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
-  zdef_(zinc, Znewvertex, NULL, -1);
-  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
-  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
-  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
-  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
-
-  qh->qhstat.precision= qh->qhstat.next;  /* call qh_precision for each of these */
-  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
-  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
-  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
-  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
-  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
-  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
-  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
-  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
-  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
-  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
-  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
-}
-void qh_allstatB(qhT *qh) {
-  zzdef_(zdoc, Zdoc1, "summary information", -1);
-  zdef_(zinc, Zvertices, "number of vertices in output", -1);
-  zdef_(zinc, Znumfacets, "number of facets in output", -1);
-  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
-  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
-  zdef_(zinc, Znumridges, "number of ridges in output", -1);
-  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
-  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
-  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
-  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
-  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
-  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
-  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
-  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
-  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
-  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
-  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
-  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
-  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
-  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
-  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
-  zdef_(zinc, Zangle, NULL, -1);
-  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
-  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
-  zdef_(wadd, Wareatot, "total area of facets", -1);
-  zdef_(wmax, Wareamax, "  maximum facet area", -1);
-  zdef_(wmin, Wareamin, "  minimum facet area", -1);
-}
-void qh_allstatC(qhT *qh) {
-  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
-  zzdef_(zinc, Zprocessed, "points processed", -1);
-  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
-  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
-  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
-  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
-  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
-  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
-  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
-  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
-  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
-  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
-  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
-  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
-  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
-  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
-  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
-  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
-  zdef_(zinc, Zpbalance, "  number of trials", -1);
-  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
-  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
-  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
-  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
-  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
-  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
-  zdef_(zinc, Zgoodfacet, "good facets found", -1);
-  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
-  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
-  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
-  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
-}
-void qh_allstatD(qhT *qh) {
-  zdef_(zinc, Zvisit, "resets of visit_id", -1);
-  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
-  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
-  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
-
-  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
-  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
-  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
-  zdef_(zinc, Zfindbest, "calls to findbest", -1);
-  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
-  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
-  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
-  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
-  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
-  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
-  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
-  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
-  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
-  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
-  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
-  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
-  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
-  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
-}
-void qh_allstatE(qhT *qh) {
-  zdef_(zinc, Zpartinside, "inside points", -1);
-  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
-  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
-  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
-  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
-  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
-  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
-  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
-  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
-  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
-  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
-  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
-  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
-  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
-  zdef_(zinc, Zdistio, "distance tests for output", -1);
-  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
-  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
-  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
-  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
-  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
-}
-void qh_allstatE2(qhT *qh) {
-  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
-  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
-  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
-  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
-  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
-  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
-  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
-
-  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
-  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
-  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
-  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
-  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
-  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
-  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
-  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
-  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
-}
-void qh_allstatF(qhT *qh) {
-  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
-  zdef_(zinc, Zpremergetot, "merge iterations", -1);
-  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
-  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
-  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
-  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
-  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
-  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
-  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
-  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
-  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
-  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
-  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
-  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
-  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
-  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
-  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
-  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
-  zdef_(zinc, Zmergenew, "new facets merged", -1);
-  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
-  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
-  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
-  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
-  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
-  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
-  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
-}
-void qh_allstatG(qhT *qh) {
-  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
-  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
-  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
-  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
-  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
-  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
-  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
-  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
-  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
-  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
-  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
-  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
-  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
-  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
-  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
-  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
-  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
-}
-void qh_allstatH(qhT *qh) {
-  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
-  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
-  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
-  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
-  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
-  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
-  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
-  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
-  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
-  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
-  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
-  zdef_(zinc, Zremvertexdel, "  deleted", -1);
-  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
-  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
-  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
-  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
-  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
-  zdef_(zinc, Zvertexridge, NULL, -1);
-  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
-  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
-
-  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
-  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
-  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
-  zdef_(zadd, Zmempoints, "for input points, outside and coplanar sets, and qhT",-1);
-  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
-} /* allstat */
-
-void qh_allstatI(qhT *qh) {
-  qh->qhstat.vridges= qh->qhstat.next;
-  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
-  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
-  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
-  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
-  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
-  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
-  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
-  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
-  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
-  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
-  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
-  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
-  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
-
-  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
-  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
-  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
-  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
-  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
-  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
-  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
-} /* allstat */
-
-/*---------------------------------
-
-  qh_allstatistics()
-    reset printed flag for all statistics
-*/
-void qh_allstatistics(qhT *qh) {
-  int i;
-
-  for(i=ZEND; i--; )
-    qh->qhstat.printed[i]= False;
-} /* allstatistics */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_collectstatistics()
-    collect statistics for qh.facet_list
-
-*/
-void qh_collectstatistics(qhT *qh) {
-  facetT *facet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  realT dotproduct, dist;
-  int sizneighbors, sizridges, sizvertices, i;
-
-  qh->old_randomdist= qh->RANDOMdist;
-  qh->RANDOMdist= False;
-  zval_(Zmempoints)= qh->num_points * qh->normal_size + sizeof(qhT);
-  zval_(Zmemfacets)= 0;
-  zval_(Zmemridges)= 0;
-  zval_(Zmemvertices)= 0;
-  zval_(Zangle)= 0;
-  wval_(Wangle)= 0.0;
-  zval_(Znumridges)= 0;
-  zval_(Znumfacets)= 0;
-  zval_(Znumneighbors)= 0;
-  zval_(Znumvertices)= 0;
-  zval_(Znumvneighbors)= 0;
-  zval_(Znummergetot)= 0;
-  zval_(Znummergemax)= 0;
-  zval_(Zvertices)= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
-  if (qh->MERGING || qh->APPROXhull || qh->JOGGLEmax < REALmax/2)
-    wmax_(Wmaxoutside, qh->max_outside);
-  if (qh->MERGING)
-    wmin_(Wminvertex, qh->min_vertex);
-  FORALLfacets
-    facet->seen= False;
-  if (qh->DELAUNAY) {
-    FORALLfacets {
-      if (facet->upperdelaunay != qh->UPPERdelaunay)
-        facet->seen= True; /* remove from angle statistics */
-    }
-  }
-  FORALLfacets {
-    if (facet->visible && qh->NEWfacets)
-      continue;
-    sizvertices= qh_setsize(qh, facet->vertices);
-    sizneighbors= qh_setsize(qh, facet->neighbors);
-    sizridges= qh_setsize(qh, facet->ridges);
-    zinc_(Znumfacets);
-    zadd_(Znumvertices, sizvertices);
-    zmax_(Zmaxvertices, sizvertices);
-    zadd_(Znumneighbors, sizneighbors);
-    zmax_(Zmaxneighbors, sizneighbors);
-    zadd_(Znummergetot, facet->nummerge);
-    i= facet->nummerge; /* avoid warnings */
-    zmax_(Znummergemax, i);
-    if (!facet->simplicial) {
-      if (sizvertices == qh->hull_dim) {
-        zinc_(Znowsimplicial);
-      }else {
-        zinc_(Znonsimplicial);
-      }
-    }
-    if (sizridges) {
-      zadd_(Znumridges, sizridges);
-      zmax_(Zmaxridges, sizridges);
-    }
-    zadd_(Zmemfacets, sizeof(facetT) + qh->normal_size + 2*sizeof(setT)
-       + SETelemsize * (sizneighbors + sizvertices));
-    if (facet->ridges) {
-      zadd_(Zmemridges,
-         sizeof(setT) + SETelemsize * sizridges + sizridges *
-         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh->hull_dim-1))/2);
-    }
-    if (facet->outsideset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->outsideset));
-    if (facet->coplanarset)
-      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->coplanarset));
-    if (facet->seen) /* Delaunay upper envelope */
-      continue;
-    facet->seen= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
-          || neighbor->seen || !facet->normal || !neighbor->normal)
-        continue;
-      dotproduct= qh_getangle(qh, facet->normal, neighbor->normal);
-      zinc_(Zangle);
-      wadd_(Wangle, dotproduct);
-      wmax_(Wanglemax, dotproduct)
-      wmin_(Wanglemin, dotproduct)
-    }
-    if (facet->normal) {
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdiststat);
-        qh_distplane(qh, vertex->point, facet, &dist);
-        wmax_(Wvertexmax, dist);
-        wmin_(Wvertexmin, dist);
-      }
-    }
-  }
-  FORALLvertices {
-    if (vertex->deleted)
-      continue;
-    zadd_(Zmemvertices, sizeof(vertexT));
-    if (vertex->neighbors) {
-      sizneighbors= qh_setsize(qh, vertex->neighbors);
-      zadd_(Znumvneighbors, sizneighbors);
-      zmax_(Zmaxvneighbors, sizneighbors);
-      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
-    }
-  }
-  qh->RANDOMdist= qh->old_randomdist;
-} /* collectstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_initstatistics(qh)
-    initialize statistics
-
-  notes:
-  NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
-  On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
-  Also invoked by QhullQh().
-*/
-void qh_initstatistics(qhT *qh) {
-  int i;
-  realT realx;
-  int intx;
-
-  qh->qhstat.next= 0;
-  qh_allstatA(qh);
-  qh_allstatB(qh);
-  qh_allstatC(qh);
-  qh_allstatD(qh);
-  qh_allstatE(qh);
-  qh_allstatE2(qh);
-  qh_allstatF(qh);
-  qh_allstatG(qh);
-  qh_allstatH(qh);
-  qh_allstatI(qh);
-  if (qh->qhstat.next > (int)sizeof(qh->qhstat.id)) {
-    qh_fprintf(qh, qh->qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
-      qhstat.next %d should be <= sizeof(qh->qhstat.id) %d\n", qh->qhstat.next, (int)sizeof(qh->qhstat.id));
-#if 0 /* for locating error, Znumridges should be duplicated */
-    for(i=0; i < ZEND; i++) {
-      int j;
-      for(j=i+1; j < ZEND; j++) {
-        if (qh->qhstat.id[i] == qh->qhstat.id[j]) {
-          qh_fprintf(qh, qh->qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
-              qh->qhstat.id[i], i, j);
-        }
-      }
-    }
-#endif
-    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
-  }
-  qh->qhstat.init[zinc].i= 0;
-  qh->qhstat.init[zadd].i= 0;
-  qh->qhstat.init[zmin].i= INT_MAX;
-  qh->qhstat.init[zmax].i= INT_MIN;
-  qh->qhstat.init[wadd].r= 0;
-  qh->qhstat.init[wmin].r= REALmax;
-  qh->qhstat.init[wmax].r= -REALmax;
-  for(i=0; i < ZEND; i++) {
-    if (qh->qhstat.type[i] > ZTYPEreal) {
-      realx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r;
-      qh->qhstat.stats[i].r= realx;
-    }else if (qh->qhstat.type[i] != zdoc) {
-      intx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i;
-      qh->qhstat.stats[i].i= intx;
-    }
-  }
-} /* initstatistics */
-
-/*---------------------------------
-
-  qh_newstats(qh, )
-    returns True if statistics for zdoc
-
-  returns:
-    next zdoc
-*/
-boolT qh_newstats(qhT *qh, int idx, int *nextindex) {
-  boolT isnew= False;
-  int start, i;
-
-  if (qh->qhstat.type[qh->qhstat.id[idx]] == zdoc)
-    start= idx+1;
-  else
-    start= idx;
-  for(i= start; i < qh->qhstat.next && qh->qhstat.type[qh->qhstat.id[i]] != zdoc; i++) {
-    if (!qh_nostatistic(qh, qh->qhstat.id[i]) && !qh->qhstat.printed[qh->qhstat.id[i]])
-        isnew= True;
-  }
-  *nextindex= i;
-  return isnew;
-} /* newstats */
-
-/*---------------------------------
-
-  qh_nostatistic(qh, index )
-    true if no statistic to print
-*/
-boolT qh_nostatistic(qhT *qh, int i) {
-
-  if ((qh->qhstat.type[i] > ZTYPEreal
-       &&qh->qhstat.stats[i].r == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r)
-      || (qh->qhstat.type[i] < ZTYPEreal
-          &&qh->qhstat.stats[i].i == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i))
-    return True;
-  return False;
-} /* nostatistic */
-
-#if qh_KEEPstatistics
-/*---------------------------------
-
-  qh_printallstatistics(qh, fp, string )
-    print all statistics with header 'string'
-*/
-void qh_printallstatistics(qhT *qh, FILE *fp, const char *string) {
-
-  qh_allstatistics(qh);
-  qh_collectstatistics(qh);
-  qh_printstatistics(qh, fp, string);
-  qh_memstatistics(qh, fp);
-}
-
-
-/*---------------------------------
-
-  qh_printstatistics(qh, fp, string )
-    print statistics to a file with header 'string'
-    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
-
-  see:
-    qh_printallstatistics()
-*/
-void qh_printstatistics(qhT *qh, FILE *fp, const char *string) {
-  int i, k;
-  realT ave;
-
-  if (qh->num_points != qh->num_vertices) {
-    wval_(Wpbalance)= 0;
-    wval_(Wpbalance2)= 0;
-  }else
-    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  qh_fprintf(qh, fp, 9350, "\n\
-%s\n\
- qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh->rbox_command,
-     qh->qhull_command, qh_version, qh->qhull_options);
-  qh_fprintf(qh, fp, 9351, "\nprecision constants:\n\
- %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
- %6.2g max. roundoff error for distance computation('En')\n\
- %6.2g max. roundoff error for angle computations\n\
- %6.2g min. distance for outside points ('Wn')\n\
- %6.2g min. distance for visible facets ('Vn')\n\
- %6.2g max. distance for coplanar facets ('Un')\n\
- %6.2g max. facet width for recomputing centrum and area\n\
-",
-  qh->MAXabs_coord, qh->DISTround, qh->ANGLEround, qh->MINoutside,
-        qh->MINvisible, qh->MAXcoplanar, qh->WIDEfacet);
-  if (qh->KEEPnearinside)
-    qh_fprintf(qh, fp, 9352, "\
- %6.2g max. distance for near-inside points\n", qh->NEARinside);
-  if (qh->premerge_cos < REALmax/2) qh_fprintf(qh, fp, 9353, "\
- %6.2g max. cosine for pre-merge angle\n", qh->premerge_cos);
-  if (qh->PREmerge) qh_fprintf(qh, fp, 9354, "\
- %6.2g radius of pre-merge centrum\n", qh->premerge_centrum);
-  if (qh->postmerge_cos < REALmax/2) qh_fprintf(qh, fp, 9355, "\
- %6.2g max. cosine for post-merge angle\n", qh->postmerge_cos);
-  if (qh->POSTmerge) qh_fprintf(qh, fp, 9356, "\
- %6.2g radius of post-merge centrum\n", qh->postmerge_centrum);
-  qh_fprintf(qh, fp, 9357, "\
- %6.2g max. distance for merging two simplicial facets\n\
- %6.2g max. roundoff error for arithmetic operations\n\
- %6.2g min. denominator for divisions\n\
-  zero diagonal for Gauss: ", qh->ONEmerge, REALepsilon, qh->MINdenom);
-  for(k=0; k < qh->hull_dim; k++)
-    qh_fprintf(qh, fp, 9358, "%6.2e ", qh->NEARzero[k]);
-  qh_fprintf(qh, fp, 9359, "\n\n");
-  for(i=0 ; i < qh->qhstat.next; )
-    qh_printstats(qh, fp, i, &i);
-} /* printstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*---------------------------------
-
-  qh_printstatlevel(qh, fp, id )
-    print level information for a statistic
-
-  notes:
-    nop if id >= ZEND, printed, or same as initial value
-*/
-void qh_printstatlevel(qhT *qh, FILE *fp, int id) {
-#define NULLfield "       "
-
-  if (id >= ZEND || qh->qhstat.printed[id])
-    return;
-  if (qh->qhstat.type[id] == zdoc) {
-    qh_fprintf(qh, fp, 9360, "%s\n", qh->qhstat.doc[id]);
-    return;
-  }
-  if (qh_nostatistic(qh, id) || !qh->qhstat.doc[id])
-    return;
-  qh->qhstat.printed[id]= True;
-  if (qh->qhstat.count[id] != -1
-      && qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i == 0)
-    qh_fprintf(qh, fp, 9361, " *0 cnt*");
-  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] == -1)
-    qh_fprintf(qh, fp, 9362, "%7.2g", qh->qhstat.stats[id].r);
-  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] != -1)
-    qh_fprintf(qh, fp, 9363, "%7.2g", qh->qhstat.stats[id].r/ qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
-  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] == -1)
-    qh_fprintf(qh, fp, 9364, "%7d", qh->qhstat.stats[id].i);
-  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] != -1)
-    qh_fprintf(qh, fp, 9365, "%7.3g", (realT) qh->qhstat.stats[id].i / qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
-  qh_fprintf(qh, fp, 9366, " %s\n", qh->qhstat.doc[id]);
-} /* printstatlevel */
-
-
-/*---------------------------------
-
-  qh_printstats(qh, fp, index, nextindex )
-    print statistics for a zdoc group
-
-  returns:
-    next zdoc if non-null
-*/
-void qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex) {
-  int j, nexti;
-
-  if (qh_newstats(qh, idx, &nexti)) {
-    qh_fprintf(qh, fp, 9367, "\n");
-    for (j=idx; jqhstat.id[j]);
-  }
-  if (nextindex)
-    *nextindex= nexti;
-} /* printstats */
-
-#if qh_KEEPstatistics
-
-/*---------------------------------
-
-  qh_stddev(num, tot, tot2, ave )
-    compute the standard deviation and average from statistics
-
-    tot2 is the sum of the squares
-  notes:
-    computes r.m.s.:
-      (x-ave)^2
-      == x^2 - 2x tot/num +   (tot/num)^2
-      == tot2 - 2 tot tot/num + tot tot/num
-      == tot2 - tot ave
-*/
-realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
-  realT stddev;
-
-  *ave= tot/num;
-  stddev= sqrt(tot2/num - *ave * *ave);
-  return stddev;
-} /* stddev */
-
-#endif /* qh_KEEPstatistics */
-
-#if !qh_KEEPstatistics
-void    qh_collectstatistics(qhT *qh) {}
-void    qh_printallstatistics(qhT *qh, FILE *fp, char *string) {};
-void    qh_printstatistics(qhT *qh, FILE *fp, char *string) {}
-#endif
-
diff --git a/src/qhull/src/libqhull_r/stat_r.h b/src/qhull/src/libqhull_r/stat_r.h
deleted file mode 100644
index 75e7d1057..000000000
--- a/src/qhull/src/libqhull_r/stat_r.h
+++ /dev/null
@@ -1,533 +0,0 @@
-/*
      ---------------------------------
-
-   stat_r.h
-     contains all statistics that are collected for qhull
-
-   see qh-stat_r.htm and stat_r.c
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/libqhull_r/stat_r.h#5 $$Change: 2079 $
-   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-
-   recompile qhull if you change this file
-
-   Integer statistics are Z* while real statistics are W*.
-
-   define MAYdebugx to call a routine at every statistic event
-
-*/
-
-#ifndef qhDEFstat
-#define qhDEFstat 1
-
-/* Depends on realT.  Do not include libqhull_r to avoid circular dependency */
-
-#ifndef DEFqhT
-#define DEFqhT 1
-typedef struct qhT qhT;         /* Defined by libqhull_r.h */
-#endif
-
-#ifndef DEFqhstatT
-#define DEFqhstatT 1
-typedef struct qhstatT qhstatT; /* Defined here */
-#endif
-
-/*---------------------------------
-
-  qh_KEEPstatistics
-    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
-*/
-#ifndef qh_KEEPstatistics
-#define qh_KEEPstatistics 1
-#endif
-
-/*---------------------------------
-
-  Zxxx for integers, Wxxx for reals
-
-  notes:
-    be sure that all statistics are defined in stat_r.c
-      otherwise initialization may core dump
-    can pick up all statistics by:
-      grep '[zw].*_[(][ZW]' *.c >z.x
-    remove trailers with query">-
-    remove leaders with  query-replace-regexp [ ^I]+  (
-*/
-#if qh_KEEPstatistics
-enum qh_statistics {     /* alphabetical after Z/W */
-    Zacoplanar,
-    Wacoplanarmax,
-    Wacoplanartot,
-    Zangle,
-    Wangle,
-    Wanglemax,
-    Wanglemin,
-    Zangletests,
-    Wareatot,
-    Wareamax,
-    Wareamin,
-    Zavoidold,
-    Wavoidoldmax,
-    Wavoidoldtot,
-    Zback0,
-    Zbestcentrum,
-    Zbestdist,
-    Zbestlower,
-    Zbestlowerall,
-    Zbestloweralln,
-    Zbestlowerv,
-    Zcentrumtests,
-    Zcheckpart,
-    Zcomputefurthest,
-    Zconcave,
-    Wconcavemax,
-    Wconcavetot,
-    Zconcaveridges,
-    Zconcaveridge,
-    Zcoplanar,
-    Wcoplanarmax,
-    Wcoplanartot,
-    Zcoplanarangle,
-    Zcoplanarcentrum,
-    Zcoplanarhorizon,
-    Zcoplanarinside,
-    Zcoplanarpart,
-    Zcoplanarridges,
-    Wcpu,
-    Zcyclefacetmax,
-    Zcyclefacettot,
-    Zcyclehorizon,
-    Zcyclevertex,
-    Zdegen,
-    Wdegenmax,
-    Wdegentot,
-    Zdegenvertex,
-    Zdelfacetdup,
-    Zdelridge,
-    Zdelvertextot,
-    Zdelvertexmax,
-    Zdetsimplex,
-    Zdistcheck,
-    Zdistconvex,
-    Zdistgood,
-    Zdistio,
-    Zdistplane,
-    Zdiststat,
-    Zdistvertex,
-    Zdistzero,
-    Zdoc1,
-    Zdoc2,
-    Zdoc3,
-    Zdoc4,
-    Zdoc5,
-    Zdoc6,
-    Zdoc7,
-    Zdoc8,
-    Zdoc9,
-    Zdoc10,
-    Zdoc11,
-    Zdoc12,
-    Zdropdegen,
-    Zdropneighbor,
-    Zdupflip,
-    Zduplicate,
-    Wduplicatemax,
-    Wduplicatetot,
-    Zdupridge,
-    Zdupsame,
-    Zflipped,
-    Wflippedmax,
-    Wflippedtot,
-    Zflippedfacets,
-    Zfindbest,
-    Zfindbestmax,
-    Zfindbesttot,
-    Zfindcoplanar,
-    Zfindfail,
-    Zfindhorizon,
-    Zfindhorizonmax,
-    Zfindhorizontot,
-    Zfindjump,
-    Zfindnew,
-    Zfindnewmax,
-    Zfindnewtot,
-    Zfindnewjump,
-    Zfindnewsharp,
-    Zgauss0,
-    Zgoodfacet,
-    Zhashlookup,
-    Zhashridge,
-    Zhashridgetest,
-    Zhashtests,
-    Zinsidevisible,
-    Zintersect,
-    Zintersectfail,
-    Zintersectmax,
-    Zintersectnum,
-    Zintersecttot,
-    Zmaxneighbors,
-    Wmaxout,
-    Wmaxoutside,
-    Zmaxridges,
-    Zmaxvertex,
-    Zmaxvertices,
-    Zmaxvneighbors,
-    Zmemfacets,
-    Zmempoints,
-    Zmemridges,
-    Zmemvertices,
-    Zmergeflipdup,
-    Zmergehorizon,
-    Zmergeinittot,
-    Zmergeinitmax,
-    Zmergeinittot2,
-    Zmergeintohorizon,
-    Zmergenew,
-    Zmergesettot,
-    Zmergesetmax,
-    Zmergesettot2,
-    Zmergesimplex,
-    Zmergevertex,
-    Wmindenom,
-    Wminvertex,
-    Zminnorm,
-    Zmultiridge,
-    Znearlysingular,
-    Zneighbor,
-    Wnewbalance,
-    Wnewbalance2,
-    Znewfacettot,
-    Znewfacetmax,
-    Znewvertex,
-    Wnewvertex,
-    Wnewvertexmax,
-    Znoarea,
-    Znonsimplicial,
-    Znowsimplicial,
-    Znotgood,
-    Znotgoodnew,
-    Znotmax,
-    Znumfacets,
-    Znummergemax,
-    Znummergetot,
-    Znumneighbors,
-    Znumridges,
-    Znumvertices,
-    Znumvisibility,
-    Znumvneighbors,
-    Zonehorizon,
-    Zpartangle,
-    Zpartcoplanar,
-    Zpartflip,
-    Zparthorizon,
-    Zpartinside,
-    Zpartition,
-    Zpartitionall,
-    Zpartnear,
-    Zpbalance,
-    Wpbalance,
-    Wpbalance2,
-    Zpostfacets,
-    Zpremergetot,
-    Zprocessed,
-    Zremvertex,
-    Zremvertexdel,
-    Zrenameall,
-    Zrenamepinch,
-    Zrenameshare,
-    Zretry,
-    Wretrymax,
-    Zridge,
-    Wridge,
-    Wridgemax,
-    Zridge0,
-    Wridge0,
-    Wridge0max,
-    Zridgemid,
-    Wridgemid,
-    Wridgemidmax,
-    Zridgeok,
-    Wridgeok,
-    Wridgeokmax,
-    Zsearchpoints,
-    Zsetplane,
-    Ztestvneighbor,
-    Ztotcheck,
-    Ztothorizon,
-    Ztotmerge,
-    Ztotpartcoplanar,
-    Ztotpartition,
-    Ztotridges,
-    Ztotvertices,
-    Ztotvisible,
-    Ztricoplanar,
-    Ztricoplanarmax,
-    Ztricoplanartot,
-    Ztridegen,
-    Ztrimirror,
-    Ztrinull,
-    Wvertexmax,
-    Wvertexmin,
-    Zvertexridge,
-    Zvertexridgetot,
-    Zvertexridgemax,
-    Zvertices,
-    Zvisfacettot,
-    Zvisfacetmax,
-    Zvisit,
-    Zvisit2max,
-    Zvisvertextot,
-    Zvisvertexmax,
-    Zvvisit,
-    Zvvisit2max,
-    Zwidefacet,
-    Zwidevertices,
-    ZEND};
-
-/*---------------------------------
-
-  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
-
-  notes:
-    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
-*/
-#else
-enum qh_statistics {     /* for zzdef etc. macros */
-  Zback0,
-  Zbestdist,
-  Zcentrumtests,
-  Zcheckpart,
-  Zconcaveridges,
-  Zcoplanarhorizon,
-  Zcoplanarpart,
-  Zcoplanarridges,
-  Zcyclefacettot,
-  Zcyclehorizon,
-  Zdelvertextot,
-  Zdistcheck,
-  Zdistconvex,
-  Zdistzero,
-  Zdoc1,
-  Zdoc2,
-  Zdoc3,
-  Zdoc11,
-  Zflippedfacets,
-  Zgauss0,
-  Zminnorm,
-  Zmultiridge,
-  Znearlysingular,
-  Wnewvertexmax,
-  Znumvisibility,
-  Zpartcoplanar,
-  Zpartition,
-  Zpartitionall,
-  Zprocessed,
-  Zretry,
-  Zridge,
-  Wridge,
-  Wridgemax,
-  Zridge0,
-  Wridge0,
-  Wridge0max,
-  Zridgemid,
-  Wridgemid,
-  Wridgemidmax,
-  Zridgeok,
-  Wridgeok,
-  Wridgeokmax,
-  Zsetplane,
-  Ztotcheck,
-  Ztotmerge,
-    ZEND};
-#endif
-
-/*---------------------------------
-
-  ztype
-    the type of a statistic sets its initial value.
-
-  notes:
-    The type should be the same as the macro for collecting the statistic
-*/
-enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};
-
-/*========== macros and constants =============*/
-
-/*----------------------------------
-
-  MAYdebugx
-    define as maydebug() to be called frequently for error trapping
-*/
-#define MAYdebugx
-
-/*----------------------------------
-
-  zzdef_, zdef_( type, name, doc, -1)
-    define a statistic (assumes 'qhstat.next= 0;')
-
-  zdef_( type, name, doc, count)
-    define an averaged statistic
-    printed as name/count
-*/
-#define zzdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
-   qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
-#if qh_KEEPstatistics
-#define zdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
-   qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
-#else
-#define zdef_(type,name,doc,count)
-#endif
-
-/*----------------------------------
-
-  zzinc_( name ), zinc_( name)
-    increment an integer statistic
-*/
-#define zzinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
-#if qh_KEEPstatistics
-#define zinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
-#else
-#define zinc_(id) {}
-#endif
-
-/*----------------------------------
-
-  zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
-    add value to an integer or real statistic
-*/
-#define zzadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
-#define wwadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
-#if qh_KEEPstatistics
-#define zadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
-#define wadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
-#else
-#define zadd_(id, val) {}
-#define wadd_(id, val) {}
-#endif
-
-/*----------------------------------
-
-  zzval_( name ), zval_( name ), wwval_( name )
-    set or return value of a statistic
-*/
-#define zzval_(id) ((qh->qhstat.stats[id]).i)
-#define wwval_(id) ((qh->qhstat.stats[id]).r)
-#if qh_KEEPstatistics
-#define zval_(id) ((qh->qhstat.stats[id]).i)
-#define wval_(id) ((qh->qhstat.stats[id]).r)
-#else
-#define zval_(id) qh->qhstat.tempi
-#define wval_(id) qh->qhstat.tempr
-#endif
-
-/*----------------------------------
-
-  zmax_( id, val ), wmax_( id, value )
-    maximize id with val
-*/
-#define wwmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
-#if qh_KEEPstatistics
-#define zmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].i,(val));}
-#define wmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
-#else
-#define zmax_(id, val) {}
-#define wmax_(id, val) {}
-#endif
-
-/*----------------------------------
-
-  zmin_( id, val ), wmin_( id, value )
-    minimize id with val
-*/
-#if qh_KEEPstatistics
-#define zmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].i,(val));}
-#define wmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].r,(val));}
-#else
-#define zmin_(id, val) {}
-#define wmin_(id, val) {}
-#endif
-
-/*================== stat_r.h types ==============*/
-
-
-/*----------------------------------
-
-  intrealT
-    union of integer and real, used for statistics
-*/
-typedef union intrealT intrealT;    /* union of int and realT */
-union intrealT {
-    int i;
-    realT r;
-};
-
-/*----------------------------------
-
-  qhstat
-    Data structure for statistics, similar to qh and qhrbox
-
-    Allocated as part of qhT (libqhull_r.h)
-*/
-
-struct qhstatT {
-  intrealT   stats[ZEND];     /* integer and real statistics */
-  unsigned   char id[ZEND+10]; /* id's in print order */
-  const char *doc[ZEND];       /* array of documentation strings */
-  short int  count[ZEND];     /* -1 if none, else index of count to use */
-  char       type[ZEND];      /* type, see ztypes above */
-  char       printed[ZEND];   /* true, if statistic has been printed */
-  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
-
-  int        next;            /* next index for zdef_ */
-  int        precision;       /* index for precision problems */
-  int        vridges;         /* index for Voronoi ridges */
-  int        tempi;
-  realT      tempr;
-};
-
-/*========== function prototypes ===========*/
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-void    qh_allstatA(qhT *qh);
-void    qh_allstatB(qhT *qh);
-void    qh_allstatC(qhT *qh);
-void    qh_allstatD(qhT *qh);
-void    qh_allstatE(qhT *qh);
-void    qh_allstatE2(qhT *qh);
-void    qh_allstatF(qhT *qh);
-void    qh_allstatG(qhT *qh);
-void    qh_allstatH(qhT *qh);
-void    qh_allstatI(qhT *qh);
-void    qh_allstatistics(qhT *qh);
-void    qh_collectstatistics(qhT *qh);
-void    qh_initstatistics(qhT *qh);
-boolT   qh_newstats(qhT *qh, int idx, int *nextindex);
-boolT   qh_nostatistic(qhT *qh, int i);
-void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
-void    qh_printstatistics(qhT *qh, FILE *fp, const char *string);
-void    qh_printstatlevel(qhT *qh, FILE *fp, int id);
-void    qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex);
-realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-#endif   /* qhDEFstat */
diff --git a/src/qhull/src/libqhull_r/user_r.c b/src/qhull/src/libqhull_r/user_r.c
deleted file mode 100644
index bf7ed1d8d..000000000
--- a/src/qhull/src/libqhull_r/user_r.c
+++ /dev/null
@@ -1,527 +0,0 @@
-/*
      ---------------------------------
-
-   user.c
-   user redefinable functions
-
-   see user2_r.c for qh_fprintf, qh_malloc, qh_free
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   see libqhull_r.h for data structures, macros, and user-callable functions.
-
-   see user_eg.c, user_eg2.c, and unix.c for examples.
-
-   see user.h for user-definable constants
-
-      use qh_NOmem in mem_r.h to turn off memory management
-      use qh_NOmerge in user.h to turn off facet merging
-      set qh_KEEPstatistics in user.h to 0 to turn off statistics
-
-   This is unsupported software.  You're welcome to make changes,
-   but you're on your own if something goes wrong.  Use 'Tc' to
-   check frequently.  Usually qhull will report an error if
-   a data structure becomes inconsistent.  If so, it also reports
-   the last point added to the hull, e.g., 102.  You can then trace
-   the execution of qhull with "T4P102".
-
-   Please report any errors that you fix to qhull@qhull.org
-
-   Qhull-template is a template for calling qhull from within your application
-
-   if you recompile and load this module, then user.o will not be loaded
-   from qhull.a
-
-   you can add additional quick allocation sizes in qh_user_memsizes
-
-   if the other functions here are redefined to not use qh_print...,
-   then io.o will not be loaded from qhull.a.  See user_eg_r.c for an
-   example.  We recommend keeping io.o for the extra debugging
-   information it supplies.
-*/
-
-#include "qhull_ra.h"
-
-#include 
-
-/*---------------------------------
-
-  Qhull-template
-    Template for calling qhull from inside your program
-
-  returns:
-    exit code(see qh_ERR... in libqhull_r.h)
-    all memory freed
-
-  notes:
-    This can be called any number of times.
-
-*/
-#if 0
-{
-  int dim;                  /* dimension of points */
-  int numpoints;            /* number of points */
-  coordT *points;           /* array of coordinates for each point */
-  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
-  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
-  FILE *outfile= stdout;    /* output from qh_produce_output(qh)
-                               use NULL to skip qh_produce_output(qh) */
-  FILE *errfile= stderr;    /* error messages from qhull code */
-  int exitcode;             /* 0 if no error from qhull */
-  facetT *facet;            /* set by FORALLfacets */
-  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
-
-  qhT qh_qh;                /* Qhull's data structure.  First argument of most calls */
-  qhT *qh= &qh_qh;          /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  qh_zero(qh, errfile);
-
-  /* initialize dim, numpoints, points[], ismalloc here */
-  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh->facet_list' contains the convex hull */
-    FORALLfacets {
-       /* ... your code ... */
-    }
-  }
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
-}
-#endif
-
-/*---------------------------------
-
-  qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
-    Run qhull and return results in qh.
-    Returns exitcode (0 if no errors).
-    Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
-
-  notes:
-    do not modify points until finished with results.
-      The qhull data structure contains pointers into the points array.
-    do not call qhull functions before qh_new_qhull().
-      The qhull data structure is not initialized until qh_new_qhull().
-    do not call qh_init_A (global_r.c)
-
-    Default errfile is stderr, outfile may be null
-    qhull_cmd must start with "qhull "
-    projects points to a new point array for Delaunay triangulations ('d' and 'v')
-    transforms points into a new point array for halfspace intersection ('H')
-
-  see:
-    Qhull-template at the beginning of this file.
-    An example of using qh_new_qhull is user_eg_r.c
-*/
-int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
-                char *qhull_cmd, FILE *outfile, FILE *errfile) {
-  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
-     These parameters are not referenced after a longjmp() and hence not clobbered.
-     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
-  int exitcode, hulldim;
-  boolT new_ismalloc;
-  coordT *new_points;
-
-  if(!errfile){
-    errfile= stderr;
-  }
-  if (!qh->qhmem.ferr) {
-    qh_meminit(qh, errfile);
-  } else {
-    qh_memcheck(qh);
-  }
-  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
-    qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
-    return qh_ERRinput;
-  }
-  qh_initqhull_start(qh, NULL, outfile, errfile);
-  trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
-  exitcode = setjmp(qh->errexit);
-  if (!exitcode)
-  {
-    qh->NOerrexit = False;
-    qh_initflags(qh, qhull_cmd);
-    if (qh->DELAUNAY)
-      qh->PROJECTdelaunay= True;
-    if (qh->HALFspace) {
-      /* points is an array of halfspaces,
-         the last coordinate of each halfspace is its offset */
-      hulldim= dim-1;
-      qh_setfeasible(qh, hulldim);
-      new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
-      new_ismalloc= True;
-      if (ismalloc)
-        qh_free(points);
-    }else {
-      hulldim= dim;
-      new_points= points;
-      new_ismalloc= ismalloc;
-    }
-    qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    if (outfile) {
-      qh_produce_output(qh);
-    }else {
-      qh_prepare_output(qh);
-    }
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-  }
-  qh->NOerrexit = True;
-  return exitcode;
-} /* new_qhull */
-
-/*---------------------------------
-
-  qh_errexit(qh, exitcode, facet, ridge )
-    report and exit from an error
-    report facet and ridge if non-NULL
-    reports useful information such as last point processed
-    set qh.FORCEoutput to print neighborhood of facet
-
-  see:
-    qh_errexit2() in libqhull_r.c for printing 2 facets
-
-  design:
-    check for error within error processing
-    compute qh.hulltime
-    print facet and ridge (if any)
-    report commandString, options, qh.furthest_id
-    print summary and statistics (including precision statistics)
-    if qh_ERRsingular
-      print help text for singular data set
-    exit program via long jump (if defined) or exit()
-*/
-void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
-
-  if (qh->ERREXITcalled) {
-    qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh->ERREXITcalled= True;
-  if (!qh->QHULLfinished)
-    qh->hulltime= qh_CPUclock - qh->hulltime;
-  qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
-  qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
-  qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
-  if (qh->furthest_id >= 0) {
-    qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
-    if (zzval_(Ztotmerge))
-      qh_fprintf(qh, qh->ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
-    if (qh->QHULLfinished)
-      qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
-    else if (qh->POSTmerging)
-      qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
-    qh_fprintf(qh, qh->ferr, 8133, "\n");
-  }
-  if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
-    qh_produce_output(qh);
-  else if (exitcode != qh_ERRinput) {
-    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
-      qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
-      qh_printsummary(qh, qh->ferr);
-      if (qh->PRINTstatistics) {
-        qh_collectstatistics(qh);
-        qh_printstatistics(qh, qh->ferr, "at error exit");
-        qh_memstatistics(qh, qh->ferr);
-      }
-    }
-    if (qh->PRINTprecision)
-      qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
-  }
-  if (!exitcode)
-    exitcode= qh_ERRqhull;
-  else if (exitcode == qh_ERRsingular)
-    qh_printhelp_singular(qh, qh->ferr);
-  else if (exitcode == qh_ERRprec && !qh->PREmerge)
-    qh_printhelp_degenerate(qh, qh->ferr);
-  if (qh->NOerrexit) {
-    qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
-    qh_exit(qh_ERRqhull);
-  }
-  qh->ERREXITcalled= False;
-  qh->NOerrexit= True;
-  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
-  longjmp(qh->errexit, exitcode);
-} /* errexit */
-
-
-/*---------------------------------
-
-  qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
-    prints out the information of facets and ridges to fp
-    also prints neighbors and geomview output
-
-  notes:
-    except for string, any parameter may be NULL
-*/
-void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-  int i;
-
-  if (atfacet) {
-    qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
-    qh_printfacet(qh, qh->ferr, atfacet);
-  }
-  if (otherfacet) {
-    qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
-    qh_printfacet(qh, qh->ferr, otherfacet);
-  }
-  if (atridge) {
-    qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
-    qh_printridge(qh, qh->ferr, atridge);
-    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
-      qh_printfacet(qh, qh->ferr, atridge->top);
-    if (atridge->bottom
-        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
-      qh_printfacet(qh, qh->ferr, atridge->bottom);
-    if (!atfacet)
-      atfacet= atridge->top;
-    if (!otherfacet)
-      otherfacet= otherfacet_(atridge, atfacet);
-  }
-  if (atvertex) {
-    qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
-    qh_printvertex(qh, qh->ferr, atvertex);
-  }
-  if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
-    qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
-    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
-      qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
-                            !qh_ALL);
-  }
-} /* errprint */
-
-
-/*---------------------------------
-
-  qh_printfacetlist(qh, fp, facetlist, facets, printall )
-    print all fields for a facet list and/or set of facets to fp
-    if !printall,
-      only prints good facets
-
-  notes:
-    also prints all vertices
-*/
-void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
-  facetT *facet, **facetp;
-
-  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
-  FORALLfacet_(facetlist)
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
-  FOREACHfacet_(facets)
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
-  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
-} /* printfacetlist */
-
-
-/*---------------------------------
-
-  qh_printhelp_degenerate(qh, fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
-
-  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
-    qh_fprintf(qh, fp, 9368, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
-  else if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9369, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    qh_fprintf(qh, fp, 9370, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
-      qh_fprintf(qh, fp, 9371, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh->DELAUNAY && !qh->ATinfinity)
-      qh_fprintf(qh, fp, 9372, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    qh_fprintf(qh, fp, 9373, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh->DISTround);
-    qh_fprintf(qh, fp, 9374, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/*---------------------------------
-
-  qh_printhelp_narrowhull(qh, minangle )
-    Warn about a narrow hull
-
-  notes:
-    Alternatively, reduce qh_WARNnarrow in user.h
-
-*/
-void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
-
-    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
-produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
-last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
-See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-} /* printhelp_narrowhull */
-
-/*---------------------------------
-
-  qh_printhelp_singular(qh, fp )
-    prints descriptive message for singular input
-*/
-void qh_printhelp_singular(qhT *qh, FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  qh_fprintf(qh, fp, 9376, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh->hull_dim);
-  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    qh_fprintf(qh, fp, 9377, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh->DISTround);
-  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
-  qh_fprintf(qh, fp, 9378, "\n");
-  FORALLfacets {
-    qh_fprintf(qh, fp, 9379, "facet");
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh, qh->interior_point, facet, &dist);
-    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh->HALFspace)
-      qh_fprintf(qh, fp, 9382, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    qh_fprintf(qh, fp, 9383,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh->hull_dim >= qh_INITIALmax)
-      qh_fprintf(qh, fp, 9384, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh->hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9387, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh->DISTround);
-#if REALfloat
-    qh_fprintf(qh, fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
-#endif
-    qh_fprintf(qh, fp, 9389, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-  }
-} /* printhelp_singular */
-
-/*---------------------------------
-
-  qh_user_memsizes(qh)
-    allocate up to 10 additional, quick allocation sizes
-
-  notes:
-    increase maximum number of allocations in qh_initqhull_mem()
-*/
-void qh_user_memsizes(qhT *qh) {
-
-  QHULL_UNUSED(qh)
-  /* qh_memsize(qh, size); */
-} /* user_memsizes */
-
-
diff --git a/src/qhull/src/libqhull_r/user_r.h b/src/qhull/src/libqhull_r/user_r.h
deleted file mode 100644
index fc105b9ca..000000000
--- a/src/qhull/src/libqhull_r/user_r.h
+++ /dev/null
@@ -1,882 +0,0 @@
-/*
      ---------------------------------
-
-   user.h
-   user redefinable constants
-
-   for each source file, user_r.h is included first
-
-   see qh-user_r.htm.  see COPYING for copyright information.
-
-   See user_r.c for sample code.
-
-   before reading any code, review libqhull_r.h for data structure definitions
-
-Sections:
-   ============= qhull library constants ======================
-   ============= data types and configuration macros ==========
-   ============= performance related constants ================
-   ============= memory constants =============================
-   ============= joggle constants =============================
-   ============= conditional compilation ======================
-   ============= -merge constants- ============================
-
-Code flags --
-  NOerrors -- the code does not call qh_errexit()
-  WARN64 -- the code may be incompatible with 64-bit pointers
-
-*/
-
-#include 
-
-#ifndef qhDEFuser
-#define qhDEFuser 1
-
-/* Derived from Qt's corelib/global/qglobal.h */
-#if !defined(SAG_COM) && !defined(__CYGWIN__) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
-#   define QHULL_OS_WIN
-#elif defined(__MWERKS__) && defined(__INTEL__) /* Metrowerks discontinued before the release of Intel Macs */
-#   define QHULL_OS_WIN
-#endif
-
-/*============================================================*/
-/*============= qhull library constants ======================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  FILENAMElen -- max length for TI and TO filenames
-
-*/
-
-#define qh_FILENAMElen 500
-
-/*----------------------------------
-
-  msgcode -- Unique message codes for qh_fprintf
-
-  If add new messages, assign these values and increment in user.h and user_r.h
-  See QhullError.h for 10000 errors.
-
-  def counters =  [27, 1048, 2059, 3026, 4068, 5003,
-     6273, 7081, 8147, 9411, 10000, 11029]
-
-  See: qh_ERR* [libqhull_r.h]
-*/
-
-#define MSG_TRACE0 0
-#define MSG_TRACE1 1000
-#define MSG_TRACE2 2000
-#define MSG_TRACE3 3000
-#define MSG_TRACE4 4000
-#define MSG_TRACE5 5000
-#define MSG_ERROR  6000   /* errors written to qh.ferr */
-#define MSG_WARNING 7000
-#define MSG_STDERR  8000  /* log messages Written to qh.ferr */
-#define MSG_OUTPUT  9000
-#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp (QHULLlastError is in QhullError.h) */
-#define MSG_FIXUP  11000  /* FIXUP QH11... */
-#define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
-
-
-/*----------------------------------
-
-  qh_OPTIONline -- max length of an option line 'FO'
-*/
-#define qh_OPTIONline 80
-
-/*============================================================*/
-/*============= data types and configuration macros ==========*/
-/*============================================================*/
-
-/*----------------------------------
-
-  realT
-    set the size of floating point numbers
-
-  qh_REALdigits
-    maximimum number of significant digits
-
-  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
-    format strings for printf
-
-  qh_REALmax, qh_REALmin
-    maximum and minimum (near zero) values
-
-  qh_REALepsilon
-    machine roundoff.  Maximum roundoff error for addition and multiplication.
-
-  notes:
-   Select whether to store floating point numbers in single precision (float)
-   or double precision (double).
-
-   Use 'float' to save about 8% in time and 25% in space.  This is particularly
-   helpful if high-d where convex hulls are space limited.  Using 'float' also
-   reduces the printed size of Qhull's output since numbers have 8 digits of
-   precision.
-
-   Use 'double' when greater arithmetic precision is needed.  This is needed
-   for Delaunay triangulations and Voronoi diagrams when you are not merging
-   facets.
-
-   If 'double' gives insufficient precision, your data probably includes
-   degeneracies.  If so you should use facet merging (done by default)
-   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
-   You may also use option 'Po' to force output despite precision errors.
-
-   You may use 'long double', but many format statements need to be changed
-   and you may need a 'long double' square root routine.  S. Grundmann
-   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
-   much slower with little gain in precision.
-
-   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
-      returns False.  Use (a > REALmax/2) instead of (a == REALmax).
-
-   REALfloat =   1      all numbers are 'float' type
-             =   0      all numbers are 'double' type
-*/
-#define REALfloat 0
-
-#if (REALfloat == 1)
-#define realT float
-#define REALmax FLT_MAX
-#define REALmin FLT_MIN
-#define REALepsilon FLT_EPSILON
-#define qh_REALdigits 8   /* maximum number of significant digits */
-#define qh_REAL_1 "%6.8g "
-#define qh_REAL_2n "%6.8g %6.8g\n"
-#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
-
-#elif (REALfloat == 0)
-#define realT double
-#define REALmax DBL_MAX
-#define REALmin DBL_MIN
-#define REALepsilon DBL_EPSILON
-#define qh_REALdigits 16    /* maximum number of significant digits */
-#define qh_REAL_1 "%6.16g "
-#define qh_REAL_2n "%6.16g %6.16g\n"
-#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
-
-#else
-#error unknown float option
-#endif
-
-/*----------------------------------
-
-  countT
-    The type for counts and identifiers (e.g., the number of points, vertex identifiers)
-    Currently used by C++ code-only.  Decided against using it for setT because most sets are small.
-
-    Defined as 'int' for C-code compatibility and QH11026
-
-    FIXUP QH11026 countT may be defined as a unsigned value, but several code issues need to be solved first.  See countT in Changes.txt
-*/
-
-#ifndef DEFcountT
-#define DEFcountT 1
-typedef int countT;
-#endif
-#define COUNTmax 0x7fffffff
-
-
-/*----------------------------------
-
-  qh_CPUclock
-    define the clock() function for reporting the total time spent by Qhull
-    returns CPU ticks as a 'long int'
-    qh_CPUclock is only used for reporting the total time spent by Qhull
-
-  qh_SECticks
-    the number of clock ticks per second
-
-  notes:
-    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
-    to define a custom clock, set qh_CLOCKtype to 0
-
-    if your system does not use clock() to return CPU ticks, replace
-    qh_CPUclock with the corresponding function.  It is converted
-    to 'unsigned long' to prevent wrap-around during long runs.  By default,
-     defines clock_t as 'long'
-
-   Set qh_CLOCKtype to
-
-     1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
-                Note:  may fail if more than 1 hour elapsed time
-
-     2          use qh_clock() with POSIX times() (see global_r.c)
-*/
-#define qh_CLOCKtype 1  /* change to the desired number */
-
-#if (qh_CLOCKtype == 1)
-
-#if defined(CLOCKS_PER_SECOND)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SECOND
-
-#elif defined(CLOCKS_PER_SEC)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SEC
-
-#elif defined(CLK_TCK)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLK_TCK
-
-#else
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks 1E6
-#endif
-
-#elif (qh_CLOCKtype == 2)
-#define qh_CPUclock    qh_clock()  /* return CPU clock */
-#define qh_SECticks 100
-
-#else /* qh_CLOCKtype == ? */
-#error unknown clock option
-#endif
-
-/*----------------------------------
-
-  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
-    define random number generator
-
-    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
-    qh_RANDOMseed sets the random number seed for qh_RANDOMint
-
-  Set qh_RANDOMtype (default 5) to:
-    1       for random() with 31 bits (UCB)
-    2       for rand() with RAND_MAX or 15 bits (system 5)
-    3       for rand() with 31 bits (Sun)
-    4       for lrand48() with 31 bits (Solaris)
-    5       for qh_rand(qh) with 31 bits (included with Qhull, requires 'qh')
-
-  notes:
-    Random numbers are used by rbox to generate point sets.  Random
-    numbers are used by Qhull to rotate the input ('QRn' option),
-    simulate a randomized algorithm ('Qr' option), and to simulate
-    roundoff errors ('Rn' option).
-
-    Random number generators differ between systems.  Most systems provide
-    rand() but the period varies.  The period of rand() is not critical
-    since qhull does not normally use random numbers.
-
-    The default generator is Park & Miller's minimal standard random
-    number generator [CACM 31:1195 '88].  It is included with Qhull.
-
-    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
-    output will likely be invisible.
-*/
-#define qh_RANDOMtype 5   /* *** change to the desired number *** */
-
-#if (qh_RANDOMtype == 1)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
-#define qh_RANDOMint random()
-#define qh_RANDOMseed_(qh, seed) srandom(seed);
-
-#elif (qh_RANDOMtype == 2)
-#ifdef RAND_MAX
-#define qh_RANDOMmax ((realT)RAND_MAX)
-#else
-#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
-#endif
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 3)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 4)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
-#define qh_RANDOMint lrand48()
-#define qh_RANDOMseed_(qh, seed) srand48(seed);
-
-#elif (qh_RANDOMtype == 5)  /* 'qh' is an implicit parameter */
-#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
-#define qh_RANDOMint qh_rand(qh)
-#define qh_RANDOMseed_(qh, seed) qh_srand(qh, seed);
-/* unlike rand(), never returns 0 */
-
-#else
-#error: unknown random option
-#endif
-
-/*----------------------------------
-
-  qh_ORIENTclock
-    0 for inward pointing normals by Geomview convention
-*/
-#define qh_ORIENTclock 0
-
-
-/*============================================================*/
-/*============= joggle constants =============================*/
-/*============================================================*/
-
-/*----------------------------------
-
-qh_JOGGLEdefault
-default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
-
-notes:
-rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
-rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
-rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
-rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
-rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
-rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
-rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
-rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
-rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
-the later have about 20 points per facet, each of which may interfere
-
-pick a value large enough to avoid retries on most inputs
-*/
-#define qh_JOGGLEdefault 30000.0
-
-/*----------------------------------
-
-qh_JOGGLEincrease
-factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
-*/
-#define qh_JOGGLEincrease 10.0
-
-/*----------------------------------
-
-qh_JOGGLEretry
-if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
-
-notes:
-try twice at the original value in case of bad luck the first time
-*/
-#define qh_JOGGLEretry 2
-
-/*----------------------------------
-
-qh_JOGGLEagain
-every following qh_JOGGLEagain, increase qh.JOGGLEmax
-
-notes:
-1 is OK since it's already failed qh_JOGGLEretry times
-*/
-#define qh_JOGGLEagain 1
-
-/*----------------------------------
-
-qh_JOGGLEmaxincrease
-maximum qh.JOGGLEmax due to qh_JOGGLEincrease
-relative to qh.MAXwidth
-
-notes:
-qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
-*/
-#define qh_JOGGLEmaxincrease 1e-2
-
-/*----------------------------------
-
-qh_JOGGLEmaxretry
-stop after qh_JOGGLEmaxretry attempts
-*/
-#define qh_JOGGLEmaxretry 100
-
-/*============================================================*/
-/*============= performance related constants ================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  qh_HASHfactor
-    total hash slots / used hash slots.  Must be at least 1.1.
-
-  notes:
-    =2 for at worst 50% occupancy for qh.hash_table and normally 25% occupancy
-*/
-#define qh_HASHfactor 2
-
-/*----------------------------------
-
-  qh_VERIFYdirect
-    with 'Tv' verify all points against all facets if op count is smaller
-
-  notes:
-    if greater, calls qh_check_bestdist() instead
-*/
-#define qh_VERIFYdirect 1000000
-
-/*----------------------------------
-
-  qh_INITIALsearch
-     if qh_INITIALmax, search points up to this dimension
-*/
-#define qh_INITIALsearch 6
-
-/*----------------------------------
-
-  qh_INITIALmax
-    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
-
-  notes:
-    from points with non-zero determinants
-    use option 'Qs' to override (much slower)
-*/
-#define qh_INITIALmax 8
-
-/*============================================================*/
-/*============= memory constants =============================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  qh_MEMalign
-    memory alignment for qh_meminitbuffers() in global_r.c
-
-  notes:
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem_r.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.
-
-    If using gcc, best alignment is [fmax_() is defined in geom_r.h]
-              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
-*/
-#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
-
-/*----------------------------------
-
-  qh_MEMbufsize
-    size of additional memory buffers
-
-  notes:
-    used for qh_meminitbuffers() in global_r.c
-*/
-#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
-
-/*----------------------------------
-
-  qh_MEMinitbuf
-    size of initial memory buffer
-
-  notes:
-    use for qh_meminitbuffers() in global_r.c
-*/
-#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
-
-/*----------------------------------
-
-  qh_INFINITE
-    on output, indicates Voronoi center at infinity
-*/
-#define qh_INFINITE  -10.101
-
-/*----------------------------------
-
-  qh_DEFAULTbox
-    default box size (Geomview expects 0.5)
-
-  qh_DEFAULTbox
-    default box size for integer coorindate (rbox only)
-*/
-#define qh_DEFAULTbox 0.5
-#define qh_DEFAULTzbox 1e6
-
-/*============================================================*/
-/*============= conditional compilation ======================*/
-/*============================================================*/
-
-/*----------------------------------
-
-  __cplusplus
-    defined by C++ compilers
-
-  __MSC_VER
-    defined by Microsoft Visual C++
-
-  __MWERKS__ && __INTEL__
-    defined by Metrowerks when compiling for Windows (not Intel-based Macintosh)
-
-  __MWERKS__ && __POWERPC__
-    defined by Metrowerks when compiling for PowerPC-based Macintosh
-
-  __STDC__
-    defined for strict ANSI C
-*/
-
-/*----------------------------------
-
-  qh_COMPUTEfurthest
-    compute furthest distance to an outside point instead of storing it with the facet
-    =1 to compute furthest
-
-  notes:
-    computing furthest saves memory but costs time
-      about 40% more distance tests for partitioning
-      removes facet->furthestdist
-*/
-#define qh_COMPUTEfurthest 0
-
-/*----------------------------------
-
-  qh_KEEPstatistics
-    =0 removes most of statistic gathering and reporting
-
-  notes:
-    if 0, code size is reduced by about 4%.
-*/
-#define qh_KEEPstatistics 1
-
-/*----------------------------------
-
-  qh_MAXoutside
-    record outer plane for each facet
-    =1 to record facet->maxoutside
-
-  notes:
-    this takes a realT per facet and slightly slows down qhull
-    it produces better outer planes for geomview output
-*/
-#define qh_MAXoutside 1
-
-/*----------------------------------
-
-  qh_NOmerge
-    disables facet merging if defined
-
-  notes:
-    This saves about 10% space.
-
-    Unless 'Q0'
-      qh_NOmerge sets 'QJ' to avoid precision errors
-
-    #define qh_NOmerge
-
-  see:
-    qh_NOmem in mem_r.c
-
-    see user_r.c/user_eg.c for removing io_r.o
-*/
-
-/*----------------------------------
-
-  qh_NOtrace
-    no tracing if defined
-
-  notes:
-    This saves about 5% space.
-
-    #define qh_NOtrace
-*/
-
-#if 0  /* sample code */
-    exitcode= qh_new_qhull(qhT *qh, dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-    qh_freeqhull(qhT *qh, !qh_ALL); /* frees long memory used by second call */
-    qh_memfreeshort(qhT *qh, &curlong, &totlong);  /* frees short memory and memory allocator */
-#endif
-
-/*----------------------------------
-
-  qh_QUICKhelp
-    =1 to use abbreviated help messages, e.g., for degenerate inputs
-*/
-#define qh_QUICKhelp    0
-
-/*============================================================*/
-/*============= -merge constants- ============================*/
-/*============================================================*/
-/*
-   These constants effect facet merging.  You probably will not need
-   to modify them.  They effect the performance of facet merging.
-*/
-
-/*----------------------------------
-
-  qh_DIMmergeVertex
-    max dimension for vertex merging (it is not effective in high-d)
-*/
-#define qh_DIMmergeVertex 6
-
-/*----------------------------------
-
-  qh_DIMreduceBuild
-     max dimension for vertex reduction during build (slow in high-d)
-*/
-#define qh_DIMreduceBuild 5
-
-/*----------------------------------
-
-  qh_BESTcentrum
-     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
-     else, qh_findbestneighbor() tests all vertices (much better merges)
-
-  qh_BESTcentrum2
-     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
-*/
-#define qh_BESTcentrum 20
-#define qh_BESTcentrum2 2
-
-/*----------------------------------
-
-  qh_BESTnonconvex
-    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
-
-  notes:
-    It is needed because qh_findbestneighbor is slow for large facets
-*/
-#define qh_BESTnonconvex 15
-
-/*----------------------------------
-
-  qh_MAXnewmerges
-    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
-
-  notes:
-    It is needed because postmerge can merge many facets at once
-*/
-#define qh_MAXnewmerges 2
-
-/*----------------------------------
-
-  qh_MAXnewcentrum
-    if <= dim+n vertices (n approximates the number of merges),
-      reset the centrum in qh_updatetested() and qh_mergecycle_facets()
-
-  notes:
-    needed to reduce cost and because centrums may move too much if
-    many vertices in high-d
-*/
-#define qh_MAXnewcentrum 5
-
-/*----------------------------------
-
-  qh_COPLANARratio
-    for 3-d+ merging, qh.MINvisible is n*premerge_centrum
-
-  notes:
-    for non-merging, it's DISTround
-*/
-#define qh_COPLANARratio 3
-
-/*----------------------------------
-
-  qh_DISToutside
-    When is a point clearly outside of a facet?
-    Stops search in qh_findbestnew or qh_partitionall
-    qh_findbest uses qh.MINoutside since since it is only called if no merges.
-
-  notes:
-    'Qf' always searches for best facet
-    if !qh.MERGING, same as qh.MINoutside.
-    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
-      [Note: Zdelvertextot occurs normally with interior points]
-            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
-    When there is a sharp edge, need to move points to a
-    clearly good facet; otherwise may be lost in another partitioning.
-    if too big then O(n^2) behavior for partitioning in cone
-    if very small then important points not processed
-    Needed in qh_partitionall for
-      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
-    Needed in qh_findbestnew for many instances of
-      RBOX 1000 s Z1 G1e-13 t | QHULL Tv
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
-     fmax_((qh->MERGING ? 2 : 1)*qh->MINoutside, qh->max_outside))
-
-/*----------------------------------
-
-  qh_RATIOnearinside
-    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
-    qh_check_maxout().
-
-  notes:
-    This is overkill since do not know the correct value.
-    It effects whether 'Qc' reports all coplanar points
-    Not used for 'd' since non-extreme points are coplanar
-*/
-#define qh_RATIOnearinside 5
-
-/*----------------------------------
-
-  qh_SEARCHdist
-    When is a facet coplanar with the best facet?
-    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
-      (qh->max_outside + 2 * qh->DISTround + fmax_( qh->MINvisible, qh->MAXcoplanar)));
-
-/*----------------------------------
-
-  qh_USEfindbestnew
-     Always use qh_findbestnew for qh_partitionpoint, otherwise use
-     qh_findbestnew if merged new facet or sharpnewfacets.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
-
-/*----------------------------------
-
-  qh_WIDEcoplanar
-    n*MAXcoplanar or n*MINvisible for a WIDEfacet
-
-    if vertex is further than qh.WIDEfacet from the hyperplane
-    then its ridges are not counted in computing the area, and
-    the facet's centrum is frozen.
-
-  notes:
-   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
-      qh_WIDEcoplanar * qh.MINvisible);
-*/
-#define qh_WIDEcoplanar 6
-
-/*----------------------------------
-
-  qh_WIDEduplicate
-    Merge ratio for errexit from qh_forcedmerges due to duplicate ridge
-    Override with option Q12 no-wide-duplicate
-
-    Notes:
-      Merging a duplicate ridge can lead to very wide facets.
-      A future release of qhull will avoid duplicate ridges by removing duplicate sub-ridges from the horizon
-*/
-#define qh_WIDEduplicate 100
-
-/*----------------------------------
-
-  qh_MAXnarrow
-    max. cosine in initial hull that sets qh.NARROWhull
-
-  notes:
-    If qh.NARROWhull, the initial partition does not make
-    coplanar points.  If narrow, a coplanar point can be
-    coplanar to two facets of opposite orientations and
-    distant from the exact convex hull.
-
-    Conservative estimate.  Don't actually see problems until it is -1.0
-*/
-#define qh_MAXnarrow -0.99999999
-
-/*----------------------------------
-
-  qh_WARNnarrow
-    max. cosine in initial hull to warn about qh.NARROWhull
-
-  notes:
-    this is a conservative estimate.
-    Don't actually see problems until it is -1.0.  See qh-impre.htm
-*/
-#define qh_WARNnarrow -0.999999999999999
-
-/*----------------------------------
-
-  qh_ZEROdelaunay
-    a zero Delaunay facet occurs for input sites coplanar with their convex hull
-    the last normal coefficient of a zero Delaunay facet is within
-        qh_ZEROdelaunay * qh.ANGLEround of 0
-
-  notes:
-    qh_ZEROdelaunay does not allow for joggled input ('QJ').
-
-    You can avoid zero Delaunay facets by surrounding the input with a box.
-
-    Use option 'PDk:-n' to explicitly define zero Delaunay facets
-      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
-      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
-*/
-#define qh_ZEROdelaunay 2
-
-/*============================================================*/
-/*============= Microsoft DevStudio ==========================*/
-/*============================================================*/
-
-/*
-   Finding Memory Leaks Using the CRT Library
-   https://msdn.microsoft.com/en-us/library/x98tx3cf(v=vs.100).aspx
-
-   Reports enabled in qh_lib_check for Debug window and stderr
-
-   From 2005=>msvcr80d, 2010=>msvcr100d, 2012=>msvcr110d
-
-   Watch: {,,msvcr80d.dll}_crtBreakAlloc  Value from {n} in the leak report
-   _CrtSetBreakAlloc(689); // qh_lib_check() [global_r.c]
-
-   Examples
-     http://free-cad.sourceforge.net/SrcDocu/d2/d7f/MemDebug_8cpp_source.html
-     https://github.com/illlust/Game/blob/master/library/MemoryLeak.cpp
-*/
-#if 0   /* off (0) by default for QHULL_CRTDBG */
-#define QHULL_CRTDBG
-#endif
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)
-#define _CRTDBG_MAP_ALLOC
-#include 
-#include 
-#endif
-
-#endif /* qh_DEFuser */
-
-
-
diff --git a/src/qhull/src/libqhull_r/usermem_r.c b/src/qhull/src/libqhull_r/usermem_r.c
deleted file mode 100644
index 3297b0318..000000000
--- a/src/qhull/src/libqhull_r/usermem_r.c
+++ /dev/null
@@ -1,94 +0,0 @@
-/*
      ---------------------------------
-
-   usermem_r.c
-   qh_exit(), qh_free(), and qh_malloc()
-
-   See README.txt.
-
-   If you redefine one of these functions you must redefine all of them.
-   If you recompile and load this file, then usermem.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull_r.h for data structures, macros, and user-callable functions.
-   See user_r.c for qhull-related, redefinable functions
-   see user_r.h for user-definable constants
-   See userprintf_r.c for qh_fprintf and userprintf_rbox_r.c for qh_fprintf_rbox
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull_r.h"
-
-#include 
-#include 
-
-/*---------------------------------
-
-  qh_exit( exitcode )
-    exit program
-
-  notes:
-    qh_exit() is called when qh_errexit() and longjmp() are not available.
-
-    This is the only use of exit() in Qhull
-    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
-*/
-void qh_exit(int exitcode) {
-    exit(exitcode);
-} /* exit */
-
-/*---------------------------------
-
-  qh_fprintf_stderr( msgcode, format, list of args )
-    fprintf to stderr with msgcode (non-zero)
-
-  notes:
-    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
-    
-    It is typically followed by qh_errexit().
-
-    Redefine this function to avoid using stderr
-
-    Use qh_fprintf [userprintf_r.c] for normal printing
-*/
-void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    va_start(args, fmt);
-    if(msgcode)
-      fprintf(stderr, "QH%.4d ", msgcode);
-    vfprintf(stderr, fmt, args);
-    va_end(args);
-} /* fprintf_stderr */
-
-/*---------------------------------
-
-  qh_free(qhT *qh, mem )
-    free memory
-
-  notes:
-    same as free()
-    No calls to qh_errexit() 
-*/
-void qh_free(void *mem) {
-    free(mem);
-} /* free */
-
-/*---------------------------------
-
-    qh_malloc( mem )
-      allocate memory
-
-    notes:
-      same as malloc()
-*/
-void *qh_malloc(size_t size) {
-    return malloc(size);
-} /* malloc */
-
-
diff --git a/src/qhull/src/libqhull_r/userprintf_r.c b/src/qhull/src/libqhull_r/userprintf_r.c
deleted file mode 100644
index 6004491a1..000000000
--- a/src/qhull/src/libqhull_r/userprintf_r.c
+++ /dev/null
@@ -1,65 +0,0 @@
-/*
      ---------------------------------
-
-   userprintf_r.c
-   qh_fprintf()
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   If you recompile and load this file, then userprintf_r.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull_r.h for data structures, macros, and user-callable functions.
-   See user_r.c for qhull-related, redefinable functions
-   see user_r.h for user-definable constants
-   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
-   see Qhull.cpp and RboxPoints.cpp for examples.
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull_r.h"
-
-#include 
-#include 
-#include 
-
-/*---------------------------------
-
-   qh_fprintf(qh, fp, msgcode, format, list of args )
-     print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib_r.c
-
-   notes:
-     same as fprintf()
-     fgets() is not trapped like fprintf()
-     exit qh_fprintf via qh_errexit()
-     may be called for errors in qh_initstatistics and qh_meminit
-*/
-
-void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    if (!fp) {
-        if(!qh){
-            qh_fprintf_stderr(6241, "userprintf_r.c: fp and qh not defined for qh_fprintf '%s'", fmt);
-            qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
-        }
-        /* could use qh->qhmem.ferr, but probably better to be cautious */
-        qh_fprintf_stderr(6232, "Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf called.\n");
-        qh_errexit(qh, 6232, NULL, NULL);
-    }
-    va_start(args, fmt);
-    if (qh && qh->ANNOTATEoutput) {
-      fprintf(fp, "[QH%.4d]", msgcode);
-    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
-      fprintf(fp, "QH%.4d ", msgcode);
-    }
-    vfprintf(fp, fmt, args);
-    va_end(args);
-
-    /* Place debugging traps here. Use with option 'Tn' */
-
-} /* qh_fprintf */
-
diff --git a/src/qhull/src/libqhull_r/userprintf_rbox_r.c b/src/qhull/src/libqhull_r/userprintf_rbox_r.c
deleted file mode 100644
index 1e721a22a..000000000
--- a/src/qhull/src/libqhull_r/userprintf_rbox_r.c
+++ /dev/null
@@ -1,53 +0,0 @@
-/*
      ---------------------------------
-
-   userprintf_rbox_r.c
-   qh_fprintf_rbox()
-
-   see README.txt  see COPYING.txt for copyright information.
-
-   If you recompile and load this file, then userprintf_rbox_r.o will not be loaded
-   from qhull.a or qhull.lib
-
-   See libqhull_r.h for data structures, macros, and user-callable functions.
-   See user_r.c for qhull-related, redefinable functions
-   see user_r.h for user-definable constants
-   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
-   see Qhull.cpp and RboxPoints.cpp for examples.
-
-   Please report any errors that you fix to qhull@qhull.org
-*/
-
-#include "libqhull_r.h"
-
-#include 
-#include 
-#include 
-
-/*---------------------------------
-
-   qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
-     print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib_r.c
-
-   notes:
-     same as fprintf()
-     fgets() is not trapped like fprintf()
-     exit qh_fprintf_rbox via qh_errexit_rbox()
-*/
-
-void qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    if (!fp) {
-        qh_fprintf_stderr(6231, "Qhull internal error (userprintf_rbox_r.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
-        qh_errexit_rbox(qh, 6231);
-    }
-    if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
-      fprintf(fp, "QH%.4d ", msgcode);
-    va_start(args, fmt);
-    vfprintf(fp, fmt, args);
-    va_end(args);
-} /* qh_fprintf_rbox */
-
diff --git a/src/qhull/src/libqhullcpp/Coordinates.cpp b/src/qhull/src/libqhullcpp/Coordinates.cpp
deleted file mode 100644
index 806b438ab..000000000
--- a/src/qhull/src/libqhullcpp/Coordinates.cpp
+++ /dev/null
@@ -1,198 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/Coordinates.cpp#4 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/Coordinates.h"
-
-#include "libqhullcpp/functionObjects.h"
-#include "libqhullcpp/QhullError.h"
-
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//! Coordinates -- vector of coordT (normally double)
-
-#//!\name Constructor
-
-#//!\name Element access
-
-// Inefficient without result-value-optimization or implicitly shared object
-Coordinates Coordinates::
-mid(countT idx, countT length) const
-{
-    countT newLength= length;
-    if(length<0 || idx+length > count()){
-        newLength= count()-idx;
-    }
-    Coordinates result;
-    if(newLength>0){
-        std::copy(begin()+idx, begin()+(idx+newLength), std::back_inserter(result));
-    }
-    return result;
-}//mid
-
-coordT Coordinates::
-value(countT idx, const coordT &defaultValue) const
-{
-    return ((idx < 0 || idx >= count()) ? defaultValue : (*this)[idx]);
-}//value
-
-#//!\name GetSet
-
-Coordinates Coordinates::
-operator+(const Coordinates &other) const
-{
-    Coordinates result(*this);
-    std::copy(other.begin(), other.end(), std::back_inserter(result));
-    return result;
-}//operator+
-
-Coordinates & Coordinates::
-operator+=(const Coordinates &other)
-{
-    if(&other==this){
-        Coordinates clone(other);
-        std::copy(clone.begin(), clone.end(), std::back_inserter(*this));
-    }else{
-        std::copy(other.begin(), other.end(), std::back_inserter(*this));
-    }
-    return *this;
-}//operator+=
-
-#//!\name Read-write
-
-void Coordinates::
-append(int pointDimension, coordT *c)
-{
-    if(c){
-        coordT *p= c;
-        for(int i= 0; i(i-begin())); // WARN64 coordinate index
-            }
-            ++i;
-        }
-    }
-    return -1;
-}//indexOf
-
-countT Coordinates::
-lastIndexOf(const coordT &t, countT from) const
-{
-    if(from<0){
-        from += count();
-    }else if(from>=count()){
-        from= count()-1;
-    }
-    if(from>=0){
-        const_iterator i= begin()+from+1;
-        while(i-- != constBegin()){
-            if(*i==t){
-                return (static_cast(i-begin())); // WARN64 coordinate index
-            }
-        }
-    }
-    return -1;
-}//lastIndexOf
-
-void Coordinates::
-removeAll(const coordT &t)
-{
-    MutableCoordinatesIterator i(*this);
-    while(i.findNext(t)){
-        i.remove();
-    }
-}//removeAll
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::istream;
-using std::ostream;
-using std::string;
-using std::ws;
-using orgQhull::Coordinates;
-
-ostream &
-operator<<(ostream &os, const Coordinates &cs)
-{
-    Coordinates::const_iterator c= cs.begin();
-    for(countT i=cs.count(); i--; ){
-        os << *c++ << " ";
-    }
-    return os;
-}//operator<<
-
diff --git a/src/qhull/src/libqhullcpp/Coordinates.h b/src/qhull/src/libqhullcpp/Coordinates.h
deleted file mode 100644
index df8bd1138..000000000
--- a/src/qhull/src/libqhullcpp/Coordinates.h
+++ /dev/null
@@ -1,303 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/Coordinates.h#6 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHCOORDINATES_H
-#define QHCOORDINATES_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullIterator.h"
-
-#include  // ptrdiff_t, size_t
-#include 
-// Requires STL vector class.  Can use with another vector class such as QList.
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! An std::vector of point coordinates independent of dimension
-    //! Used by PointCoordinates for RboxPoints and by Qhull for feasiblePoint
-    //! A QhullPoint refers to previously allocated coordinates
-    class Coordinates;
-    class MutableCoordinatesIterator;
-
-class Coordinates {
-
-private:
-#//!\name Fields
-    std::vector coordinate_array;
-
-public:
-#//!\name Subtypes
-
-    class const_iterator;
-    class iterator;
-    typedef iterator Iterator;
-    typedef const_iterator ConstIterator;
-
-    typedef coordT              value_type;
-    typedef const value_type   *const_pointer;
-    typedef const value_type &  const_reference;
-    typedef value_type *        pointer;
-    typedef value_type &        reference;
-    typedef ptrdiff_t           difference_type;
-    typedef countT              size_type;
-
-#//!\name Construct
-                        Coordinates() {};
-    explicit            Coordinates(const std::vector &other) : coordinate_array(other) {}
-                        Coordinates(const Coordinates &other) : coordinate_array(other.coordinate_array) {}
-    Coordinates &       operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
-    Coordinates &       operator=(const std::vector &other) { coordinate_array= other; return *this; }
-                        ~Coordinates() {}
-
-#//!\name Conversion
-
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const { return coordinate_array; }
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList       toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-    countT              count() const { return static_cast(size()); }
-    coordT *            data() { return isEmpty() ? 0 : &at(0); }
-    const coordT *      data() const { return const_cast(isEmpty() ? 0 : &at(0)); }
-    bool                isEmpty() const { return coordinate_array.empty(); }
-    bool                operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
-    bool                operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
-    size_t              size() const { return coordinate_array.size(); }
-
-#//!\name Element access
-    coordT &            at(countT idx) { return coordinate_array.at(idx); }
-    const coordT &      at(countT idx) const { return coordinate_array.at(idx); }
-    coordT &            back() { return coordinate_array.back(); }
-    const coordT &      back() const { return coordinate_array.back(); }
-    coordT &            first() { return front(); }
-    const coordT &      first() const { return front(); }
-    coordT &            front() { return coordinate_array.front(); }
-    const coordT &      front() const { return coordinate_array.front(); }
-    coordT &            last() { return back(); }
-    const coordT &      last() const { return back(); }
-    Coordinates         mid(countT idx, countT length= -1) const; //!<\todo countT -1 indicates
-    coordT &            operator[](countT idx) { return coordinate_array.operator[](idx); }
-    const coordT &      operator[](countT idx) const { return coordinate_array.operator[](idx); }
-    coordT              value(countT idx, const coordT &defaultValue) const;
-
-#//!\name Iterator
-    iterator            begin() { return iterator(coordinate_array.begin()); }
-    const_iterator      begin() const { return const_iterator(coordinate_array.begin()); }
-    const_iterator      constBegin() const { return begin(); }
-    const_iterator      constEnd() const { return end(); }
-    iterator            end() { return iterator(coordinate_array.end()); }
-    const_iterator      end() const { return const_iterator(coordinate_array.end()); }
-
-#//!\name GetSet
-    Coordinates         operator+(const Coordinates &other) const;
-
-#//!\name Modify
-    void                append(int pointDimension, coordT *c);
-    void                append(const coordT &c) { push_back(c); }
-    void                clear() { coordinate_array.clear(); }
-    iterator            erase(iterator idx) { return iterator(coordinate_array.erase(idx.base())); }
-    iterator            erase(iterator beginIterator, iterator endIterator) { return iterator(coordinate_array.erase(beginIterator.base(), endIterator.base())); }
-    void                insert(countT before, const coordT &c) { insert(begin()+before, c); }
-    iterator            insert(iterator before, const coordT &c) { return iterator(coordinate_array.insert(before.base(), c)); }
-    void                move(countT from, countT to) { insert(to, takeAt(from)); }
-    Coordinates &       operator+=(const Coordinates &other);
-    Coordinates &       operator+=(const coordT &c) { append(c); return *this; }
-    Coordinates &       operator<<(const Coordinates &other) { return *this += other; }
-    Coordinates &       operator<<(const coordT &c) { return *this += c; }
-    void                pop_back() { coordinate_array.pop_back(); }
-    void                pop_front() { removeFirst(); }
-    void                prepend(const coordT &c) { insert(begin(), c); }
-    void                push_back(const coordT &c) { coordinate_array.push_back(c); }
-    void                push_front(const coordT &c) { insert(begin(), c); }
-                        //removeAll below
-    void                removeAt(countT idx) { erase(begin()+idx); }
-    void                removeFirst() { erase(begin()); }
-    void                removeLast() { erase(--end()); }
-    void                replace(countT idx, const coordT &c) { (*this)[idx]= c; }
-    void                reserve(countT i) { coordinate_array.reserve(i); }
-    void                swap(countT idx, countT other);
-    coordT              takeAt(countT idx);
-    coordT              takeFirst() { return takeAt(0); }
-    coordT              takeLast();
-
-#//!\name Search
-    bool                contains(const coordT &t) const;
-    countT              count(const coordT &t) const;
-    countT              indexOf(const coordT &t, countT from = 0) const;
-    countT              lastIndexOf(const coordT &t, countT from = -1) const;
-    void                removeAll(const coordT &t);
-
-#//!\name Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
-    // before const_iterator for conversion with comparison operators
-    // Reviewed corelib/tools/qlist.h and corelib/tools/qvector.h w/o QT_STRICT_ITERATORS
-    class iterator {
-
-    private:
-        std::vector::iterator i;
-        friend class const_iterator;
-
-    public:
-        typedef std::random_access_iterator_tag  iterator_category;
-        typedef coordT      value_type;
-        typedef value_type *pointer;
-        typedef value_type &reference;
-        typedef ptrdiff_t   difference_type;
-
-                        iterator() {}
-                        iterator(const iterator &other) { i= other.i; }
-        explicit        iterator(const std::vector::iterator &vi) { i= vi; }
-        iterator &      operator=(const iterator &other) { i= other.i; return *this; }
-        std::vector::iterator &base() { return i; }
-        coordT &        operator*() const { return *i; }
-        // No operator->() when the base type is double
-        coordT &        operator[](countT idx) const { return i[idx]; }
-
-        bool            operator==(const iterator &other) const { return i==other.i; }
-        bool            operator!=(const iterator &other) const { return i!=other.i; }
-        bool            operator<(const iterator &other) const { return i(const iterator &other) const { return i>other.i; }
-        bool            operator>=(const iterator &other) const { return i>=other.i; }
-              // reinterpret_cast to break circular dependency
-        bool            operator==(const Coordinates::const_iterator &other) const { return *this==reinterpret_cast(other); }
-        bool            operator!=(const Coordinates::const_iterator &other) const { return *this!=reinterpret_cast(other); }
-        bool            operator<(const Coordinates::const_iterator &other) const { return *this(other); }
-        bool            operator<=(const Coordinates::const_iterator &other) const { return *this<=reinterpret_cast(other); }
-        bool            operator>(const Coordinates::const_iterator &other) const { return *this>reinterpret_cast(other); }
-        bool            operator>=(const Coordinates::const_iterator &other) const { return *this>=reinterpret_cast(other); }
-
-        iterator &      operator++() { ++i; return *this; }
-        iterator        operator++(int) { return iterator(i++); }
-        iterator &      operator--() { --i; return *this; }
-        iterator        operator--(int) { return iterator(i--); }
-        iterator &      operator+=(countT idx) { i += idx; return *this; }
-        iterator &      operator-=(countT idx) { i -= idx; return *this; }
-        iterator        operator+(countT idx) const { return iterator(i+idx); }
-        iterator        operator-(countT idx) const { return iterator(i-idx); }
-        difference_type operator-(iterator other) const { return i-other.i; }
-    };//Coordinates::iterator
-
-#//!\name Coordinates::const_iterator
-    class const_iterator {
-
-    private:
-        std::vector::const_iterator i;
-
-    public:
-        typedef std::random_access_iterator_tag  iterator_category;
-        typedef coordT            value_type;
-        typedef const value_type *pointer;
-        typedef const value_type &reference;
-        typedef ptrdiff_t         difference_type;
-
-                        const_iterator() {}
-                        const_iterator(const const_iterator &other) { i= other.i; }
-                        const_iterator(const iterator &o) : i(o.i) {}
-        explicit        const_iterator(const std::vector::const_iterator &vi) { i= vi; }
-        const_iterator &operator=(const const_iterator &other) { i= other.i; return *this; }
-        const coordT &  operator*() const { return *i; }
-        // No operator->() when the base type is double
-        const coordT &  operator[](countT idx) const { return i[idx]; }
-
-        bool            operator==(const const_iterator &other) const { return i==other.i; }
-        bool            operator!=(const const_iterator &other) const { return i!=other.i; }
-        bool            operator<(const const_iterator &other) const { return i(const const_iterator &other) const { return i>other.i; }
-        bool            operator>=(const const_iterator &other) const { return i>=other.i; }
-
-        const_iterator & operator++() { ++i; return *this; } 
-        const_iterator  operator++(int) { return const_iterator(i++); }
-        const_iterator & operator--() { --i; return *this; }
-        const_iterator  operator--(int) { return const_iterator(i--); }
-        const_iterator & operator+=(countT idx) { i += idx; return *this; }
-        const_iterator & operator-=(countT idx) { i -= idx; return *this; }
-        const_iterator  operator+(countT idx) const { return const_iterator(i+idx); }
-        const_iterator  operator-(countT idx) const { return const_iterator(i-idx); }
-        difference_type operator-(const_iterator other) const { return i-other.i; }
-    };//Coordinates::const_iterator
-
-};//Coordinates
-
-//class CoordinatesIterator
-//QHULL_DECLARE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
-
-class CoordinatesIterator
-{
-    typedef Coordinates::const_iterator const_iterator;
-
-private:
-    const Coordinates * c;
-    const_iterator      i;
-
-public:
-                        CoordinatesIterator(const Coordinates &container): c(&container), i(c->constBegin()) {}
-    CoordinatesIterator &operator=(const Coordinates &container) { c= &container; i= c->constBegin(); return *this; }
-                        ~CoordinatesIterator() {}
-
-    bool                findNext(const coordT &t) { while (i != c->constEnd()) if(*i++ == t){ return true;} return false; }
-    bool                findPrevious(const coordT &t) { while (i != c->constBegin())if (*(--i) == t){ return true;} return false;  }
-    bool                hasNext() const { return i != c->constEnd(); }
-    bool                hasPrevious() const { return i != c->constBegin(); }
-    const coordT &      next() { return *i++; }
-    const coordT &      previous() { return *--i; }
-    const coordT &      peekNext() const { return *i; }
-    const coordT &      peekPrevious() const { const_iterator p= i; return *--p; }
-    void                toFront() { i= c->constBegin(); }
-    void                toBack() { i= c->constEnd(); }
-};//CoordinatesIterator
-
-//class MutableCoordinatesIterator
-//QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
-class MutableCoordinatesIterator
-{
-    typedef Coordinates::iterator iterator;
-    typedef Coordinates::const_iterator const_iterator;
-
-private:
-    Coordinates *       c;
-    iterator            i;
-    iterator            n;
-    bool                item_exists() const { return const_iterator(n) != c->constEnd(); }
-
-public:
-                        MutableCoordinatesIterator(Coordinates &container) : c(&container) { i= c->begin(); n= c->end(); }
-    MutableCoordinatesIterator &operator=(Coordinates &container) { c= &container; i= c->begin(); n= c->end(); return *this; }
-                        ~MutableCoordinatesIterator() {}
-
-    bool                findNext(const coordT &t) { while(c->constEnd()!=const_iterator(n= i)){ if(*i++==t){ return true;}} return false; }
-    bool                findPrevious(const coordT &t) { while(c->constBegin()!=const_iterator(i)){ if(*(n= --i)== t){ return true;}} n= c->end(); return false;  }
-    bool                hasNext() const { return (c->constEnd()!=const_iterator(i)); }
-    bool                hasPrevious() const { return (c->constBegin()!=const_iterator(i)); }
-    void                insert(const coordT &t) { n= i= c->insert(i, t); ++i; }
-    coordT &            next() { n= i++; return *n; }
-    coordT &            peekNext() const { return *i; }
-    coordT &            peekPrevious() const { iterator p= i; return *--p; }
-    coordT &            previous() { n= --i; return *n; }
-    void                remove() { if(c->constEnd()!=const_iterator(n)){ i= c->erase(n); n= c->end();} }
-    void                setValue(const coordT &t) const { if(c->constEnd()!=const_iterator(n)){ *n= t;} }
-    void                toFront() { i= c->begin(); n= c->end(); }
-    void                toBack() { i= c->end(); n= i; }
-    coordT &            value() { QHULL_ASSERT(item_exists()); return *n; }
-    const coordT &      value() const { QHULL_ASSERT(item_exists()); return *n; }
-};//MutableCoordinatesIterator
-
-
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);
-
-#endif // QHCOORDINATES_H
diff --git a/src/qhull/src/libqhullcpp/PointCoordinates.cpp b/src/qhull/src/libqhullcpp/PointCoordinates.cpp
deleted file mode 100644
index a5b71e901..000000000
--- a/src/qhull/src/libqhullcpp/PointCoordinates.cpp
+++ /dev/null
@@ -1,348 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/PointCoordinates.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/PointCoordinates.h"
-
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullPoint.h"
-
-#include 
-#include 
-
-using std::istream;
-using std::string;
-using std::ws;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//! PointCoordinates -- vector of PointCoordinates
-
-#//!\name Constructors
-
-PointCoordinates::
-PointCoordinates()
-: QhullPoints()
-, point_coordinates()
-, describe_points()
-{
-}
-
-PointCoordinates::
-PointCoordinates(const std::string &aComment)
-: QhullPoints()
-, point_coordinates()
-, describe_points(aComment)
-{
-}
-
-PointCoordinates::
-PointCoordinates(int pointDimension, const std::string &aComment)
-: QhullPoints()
-, point_coordinates()
-, describe_points(aComment)
-{
-    setDimension(pointDimension);
-}
-
-//! Qhull and QhullQh constructors are the same
-PointCoordinates::
-PointCoordinates(const Qhull &q)
-: QhullPoints(q)
-, point_coordinates()
-, describe_points()
-{
-}
-
-PointCoordinates::
-PointCoordinates(const Qhull &q, const std::string &aComment)
-: QhullPoints(q)
-, point_coordinates()
-, describe_points(aComment)
-{
-}
-
-PointCoordinates::
-PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment)
-: QhullPoints(q)
-, point_coordinates()
-, describe_points(aComment)
-{
-    setDimension(pointDimension);
-}
-
-PointCoordinates::
-PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
-: QhullPoints(q)
-, point_coordinates()
-, describe_points(aComment)
-{
-    setDimension(pointDimension);
-    append(coordinatesCount, c);
-}
-
-PointCoordinates::
-PointCoordinates(QhullQh *qqh)
-: QhullPoints(qqh)
-, point_coordinates()
-, describe_points()
-{
-}
-
-PointCoordinates::
-PointCoordinates(QhullQh *qqh, const std::string &aComment)
-: QhullPoints(qqh)
-, point_coordinates()
-, describe_points(aComment)
-{
-}
-
-PointCoordinates::
-PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment)
-: QhullPoints(qqh)
-, point_coordinates()
-, describe_points(aComment)
-{
-    setDimension(pointDimension);
-}
-
-PointCoordinates::
-PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
-: QhullPoints(qqh)
-, point_coordinates()
-, describe_points(aComment)
-{
-    setDimension(pointDimension);
-    append(coordinatesCount, c);
-}
-
-PointCoordinates::
-PointCoordinates(const PointCoordinates &other)
-: QhullPoints(other)
-, point_coordinates(other.point_coordinates)
-, describe_points(other.describe_points)
-{
-    makeValid();  // Update point_first and point_end
-}
-
-PointCoordinates & PointCoordinates::
-operator=(const PointCoordinates &other)
-{
-    QhullPoints::operator=(other);
-    point_coordinates= other.point_coordinates;
-    describe_points= other.describe_points;
-    makeValid(); // Update point_first and point_end
-    return *this;
-}//operator=
-
-PointCoordinates::
-~PointCoordinates()
-{ }
-
-#//!\name GetSet
-
-void PointCoordinates::
-checkValid() const
-{
-    if(getCoordinates().data()!=data()
-    || getCoordinates().count()!=coordinateCount()){
-        throw QhullError(10060, "Qhull error: first point (%x) is not PointCoordinates.data() or count (%d) is not PointCoordinates.count (%d)", coordinateCount(), getCoordinates().count(), 0.0, data());
-    }
-}//checkValid
-
-void PointCoordinates::
-setDimension(int i)
-{
-    if(i<0){
-        throw QhullError(10062, "Qhull error: can not set PointCoordinates dimension to %d", i);
-    }
-    int currentDimension=QhullPoints::dimension();
-    if(currentDimension!=0 && i!=currentDimension){
-        throw QhullError(10063, "Qhull error: can not change PointCoordinates dimension (from %d to %d)", currentDimension, i);
-    }
-    QhullPoints::setDimension(i);
-}//setDimension
-
-#//!\name Foreach
-
-Coordinates::ConstIterator PointCoordinates::
-beginCoordinates(countT pointIndex) const
-{
-    return point_coordinates.begin()+indexOffset(pointIndex);
-}
-
-Coordinates::Iterator PointCoordinates::
-beginCoordinates(countT pointIndex)
-{
-    return point_coordinates.begin()+indexOffset(pointIndex);
-}
-
-#//!\name Methods
-
-void PointCoordinates::
-append(countT coordinatesCount, const coordT *c)
-{
-    if(coordinatesCount<=0){
-        return;
-    }
-    if(includesCoordinates(c)){
-        throw QhullError(10065, "Qhull error: can not append a subset of PointCoordinates to itself.  The coordinates for point %d may move.", indexOf(c, QhullError::NOthrow));
-    }
-    reserveCoordinates(coordinatesCount);
-    std::copy(c, c+coordinatesCount, std::back_inserter(point_coordinates));
-    makeValid();
-}//append coordT
-
-void PointCoordinates::
-append(const PointCoordinates &other)
-{
-    setDimension(other.dimension());
-    append(other.coordinateCount(), other.data());
-}//append PointCoordinates
-
-void PointCoordinates::
-append(const QhullPoint &p)
-{
-    setDimension(p.dimension());
-    append(p.dimension(), p.coordinates());
-}//append QhullPoint
-
-void PointCoordinates::
-appendComment(const std::string &s){
-    if(char c= s[0] && describe_points.empty()){
-        if(c=='-' || isdigit(c)){
-            throw QhullError(10028, "Qhull argument error: comments can not start with a number or minus, %s", 0, 0, 0.0, s.c_str());
-        }
-    }
-    describe_points += s;
-}//appendComment
-
-//! Read PointCoordinates from istream.  First two numbers are dimension and count.  A non-digit starts a rboxCommand.
-//! Overwrites describe_points.  See qh_readpoints [io.c]
-void PointCoordinates::
-appendPoints(istream &in)
-{
-    int inDimension;
-    countT inCount;
-    in >> ws >> inDimension >> ws;
-    if(!in.good()){
-        in.clear();
-        string remainder;
-        getline(in, remainder);
-        throw QhullError(10005, "Qhull error: input did not start with dimension or count -- %s", 0, 0, 0, remainder.c_str());
-    }
-    char c= (char)in.peek();
-    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
-        getline(in, describe_points);
-        in >> ws;
-    }
-    in >> inCount >> ws;
-    if(!in.good()){
-        in.clear();
-        string remainder;
-        getline(in, remainder);
-        throw QhullError(10009, "Qhull error: input did not start with dimension and count -- %d %s", inDimension, 0, 0, remainder.c_str());
-    }
-    c= (char)in.peek();
-    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
-        getline(in, describe_points);
-        in >> ws;
-    }
-    if(inCount> p >> ws;
-        if(in.fail()){
-            in.clear();
-            string remainder;
-            getline(in, remainder);
-            throw QhullError(10008, "Qhull error: failed to read coordinate %d  of point %d\n   %s", coordinatesCount % inDimension, coordinatesCount/inDimension, 0, remainder.c_str());
-        }else{
-            point_coordinates.push_back(p);
-            coordinatesCount++;
-        }
-    }
-    if(coordinatesCount != inCount*inDimension){
-        if(coordinatesCount%inDimension==0){
-            throw QhullError(10006, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates", int(inCount), inDimension, 0.0, int(coordinatesCount/inDimension));
-        }else{
-            throw QhullError(10012, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates plus %f extra coordinates", inCount, inDimension, float(coordinatesCount%inDimension), coordinatesCount/inDimension);
-        }
-    }
-    makeValid();
-}//appendPoints istream
-
-PointCoordinates PointCoordinates::
-operator+(const PointCoordinates &other) const
-{
-    PointCoordinates pc= *this;
-    pc << other;
-    return pc;
-}//operator+
-
-void PointCoordinates::
-reserveCoordinates(countT newCoordinates)
-{
-    // vector::reserve is not const
-    point_coordinates.reserve((countT)point_coordinates.size()+newCoordinates); // WARN64
-    makeValid();
-}//reserveCoordinates
-
-#//!\name Helpers
-
-countT PointCoordinates::
-indexOffset(countT i) const {
-    countT n= i*dimension();
-    countT coordinatesCount= point_coordinates.count();
-    if(i<0 || n>coordinatesCount){
-        throw QhullError(10061, "Qhull error: point_coordinates is too short (%d) for point %d", coordinatesCount, i);
-    }
-    return n;
-}
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-
-using orgQhull::Coordinates;
-using orgQhull::PointCoordinates;
-
-ostream&
-operator<<(ostream &os, const PointCoordinates &p)
-{
-    p.checkValid();
-    countT count= p.count();
-    int dimension= p.dimension();
-    string comment= p.comment();
-    if(comment.empty()){
-        os << dimension << endl;
-    }else{
-        os << dimension << " " << comment << endl;
-    }
-    os << count << endl;
-    Coordinates::ConstIterator c= p.beginCoordinates();
-    for(countT i=0; i
-#include 
-
-#ifndef QHULL_NO_STL
-#include 
-#endif
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! QhullPoints with Coordinates and description
-    //! Inherited by RboxPoints
-    class PointCoordinates;
-
-class PointCoordinates : public QhullPoints {
-
-private:
-#//!\name Fields
-    Coordinates         point_coordinates;      //! std::vector of point coordinates
-                                                //! may have extraCoordinates()
-    std::string         describe_points;          //! Comment describing PointCoordinates
-
-public:
-#//!\name Construct
-    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
-    //! If Qhull/QhullQh is not initialized, then dimension()==0                        PointCoordinates();
-                        PointCoordinates();
-    explicit            PointCoordinates(const std::string &aComment);
-                        PointCoordinates(int pointDimension, const std::string &aComment);
-                        //! Qhull/QhullQh used for dimension() and QhullPoint equality
-    explicit            PointCoordinates(const Qhull &q);
-                        PointCoordinates(const Qhull &q, const std::string &aComment);
-                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment);
-                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
-                        //! Use append() and appendPoints() for Coordinates and vector
-    explicit            PointCoordinates(QhullQh *qqh);
-                        PointCoordinates(QhullQh *qqh, const std::string &aComment);
-                        PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment);
-                        PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
-                        //! Use append() and appendPoints() for Coordinates and vector
-                        PointCoordinates(const PointCoordinates &other);
-    PointCoordinates &  operator=(const PointCoordinates &other);
-                        ~PointCoordinates();
-
-#//!\name Convert
-    //! QhullPoints coordinates, constData, data, count, size
-#ifndef QHULL_NO_STL
-    void                append(const std::vector &otherCoordinates) { if(!otherCoordinates.empty()){ append((int)otherCoordinates.size(), &otherCoordinates[0]); } }
-    std::vector toStdVector() const { return point_coordinates.toStdVector(); }
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    void                append(const QList &pointCoordinates) { if(!pointCoordinates.isEmpty()){ append(pointCoordinates.count(), &pointCoordinates[0]); } }
-    QList       toQList() const { return point_coordinates.toQList(); }
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-    //! See QhullPoints for coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
-    void                checkValid() const;
-    std::string         comment() const { return describe_points; }
-    void                makeValid() { defineAs(point_coordinates.count(), point_coordinates.data()); }
-    const Coordinates & getCoordinates() const { return point_coordinates; }
-    void                setComment(const std::string &s) { describe_points= s; }
-    void                setDimension(int i);
-
-private:
-    //! disable QhullPoints.defineAs()
-    void                defineAs(countT coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
-public:
-
-#//!\name ElementAccess
-    //! See QhullPoints for at, back, first, front, last, mid, [], value
-
-#//!\name Foreach
-    //! See QhullPoints for begin, constBegin, end
-    Coordinates::ConstIterator  beginCoordinates() const { return point_coordinates.begin(); }
-    Coordinates::Iterator       beginCoordinates() { return point_coordinates.begin(); }
-    Coordinates::ConstIterator  beginCoordinates(countT pointIndex) const;
-    Coordinates::Iterator       beginCoordinates(countT pointIndex);
-    Coordinates::ConstIterator  endCoordinates() const { return point_coordinates.end(); }
-    Coordinates::Iterator       endCoordinates() { return point_coordinates.end(); }
-
-#//!\name Search
-    //! See QhullPoints for contains, count, indexOf, lastIndexOf
-
-#//!\name GetSet
-    PointCoordinates    operator+(const PointCoordinates &other) const;
-
-#//!\name Modify
-    //FIXUP QH11001: Add clear() and other modify operators from Coordinates.h.  Include QhullPoint::operator=()
-    void                append(countT coordinatesCount, const coordT *c);  //! Dimension previously defined
-    void                append(const coordT &c) { append(1, &c); } //! Dimension previously defined
-    void                append(const QhullPoint &p);
-    //! See convert for std::vector and QList
-    void                append(const Coordinates &c) { append(c.count(), c.data()); }
-    void                append(const PointCoordinates &other);
-    void                appendComment(const std::string &s);
-    void                appendPoints(std::istream &in);
-    PointCoordinates &  operator+=(const PointCoordinates &other) { append(other); return *this; }
-    PointCoordinates &  operator+=(const coordT &c) { append(c); return *this; }
-    PointCoordinates &  operator+=(const QhullPoint &p) { append(p); return *this; }
-    PointCoordinates &  operator<<(const PointCoordinates &other) { return *this += other; }
-    PointCoordinates &  operator<<(const coordT &c) { return *this += c; }
-    PointCoordinates &  operator<<(const QhullPoint &p) { return *this += p; }
-    // reserve() is non-const
-    void                reserveCoordinates(countT newCoordinates);
-
-#//!\name Helpers
-private:
-    int                 indexOffset(int i) const;
-
-};//PointCoordinates
-
-// No references to QhullPoint.  Prevents use of QHULL_DECLARE_SEQUENTIAL_ITERATOR(PointCoordinates, QhullPoint)
-class PointCoordinatesIterator
-{
-    typedef PointCoordinates::const_iterator const_iterator;
-
-private:
-    const PointCoordinates *c;
-    const_iterator      i;
-
-public:
-                        PointCoordinatesIterator(const PointCoordinates &container) : c(&container), i(c->constBegin()) {}
-                        PointCoordinatesIterator &operator=(const PointCoordinates &container) { c = &container; i = c->constBegin(); return *this; }
-
-    void                toFront() { i = c->constBegin(); }
-    void                toBack() { i = c->constEnd(); }
-    bool                hasNext() const { return i != c->constEnd(); }
-    const QhullPoint    next() { return *i++; }
-    const QhullPoint    peekNext() const { return *i; }
-    bool                hasPrevious() const { return i != c->constBegin(); }
-    const QhullPoint    previous() { return *--i; }
-    const QhullPoint    peekPrevious() const { const_iterator p = i; return *--p; }
-    bool                findNext(const QhullPoint &t) { while(i != c->constEnd()){ if (*i++ == t) return true;} return false; }
-    bool                findPrevious(const QhullPoint &t) { while(i != c->constBegin()){ if (*(--i) == t) return true;} return false;  }
-};//CoordinatesIterator
-
-// FIXUP QH11002:  Add MutablePointCoordinatesIterator after adding modify operators
-\
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &          operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
-
-#endif // QHPOINTCOORDINATES_H
diff --git a/src/qhull/src/libqhullcpp/Qhull.cpp b/src/qhull/src/libqhullcpp/Qhull.cpp
deleted file mode 100644
index 7124a15cd..000000000
--- a/src/qhull/src/libqhullcpp/Qhull.cpp
+++ /dev/null
@@ -1,352 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/Qhull.cpp#4 $$Change: 2078 $
-** $DateTime: 2016/02/07 16:53:56 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! Qhull -- invoke qhull from C++
-#//! Compile libqhull_r and Qhull together due to use of setjmp/longjmp()
-
-#include "libqhullcpp/Qhull.h"
-
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullQh.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullFacetList.h"
-
-#include 
-
-using std::cerr;
-using std::string;
-using std::vector;
-using std::ostream;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Global variables
-
-const char s_unsupported_options[]=" Fd TI ";
-const char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";
-
-#//!\name Constructor, destructor, etc.
-Qhull::
-Qhull()
-: qh_qh(0)
-, origin_point()
-, run_called(false)
-, feasible_point()
-{
-    allocateQhullQh();
-}//Qhull
-
-//! Invokes Qhull on rboxPoints
-//! Same as runQhull()
-//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
-//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
-Qhull::
-Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
-: qh_qh(0)
-, origin_point()
-, run_called(false)
-, feasible_point()
-{
-    allocateQhullQh();
-    runQhull(rboxPoints, qhullCommand2);
-}//Qhull rbox
-
-//! Invokes Qhull on a set of input points
-//! Same as runQhull()
-//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
-Qhull::
-Qhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
-: qh_qh(0)
-, origin_point()
-, run_called(false)
-, feasible_point()
-{
-    allocateQhullQh();
-    runQhull(inputComment2, pointDimension, pointCount, pointCoordinates, qhullCommand2);
-}//Qhull points
-
-void Qhull::
-allocateQhullQh()
-{
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-    qh_qh= new QhullQh;
-    void *p= qh_qh;
-    void *p2= static_cast(qh_qh);
-    char *s= static_cast(p);
-    char *s2= static_cast(p2);
-    if(s!=s2){
-        throw QhullError(10074, "Qhull error: QhullQh at a different address than base type QhT (%d bytes).  Please report compiler to qhull.org", int(s2-s));
-    }
-}//allocateQhullQh
-
-Qhull::
-~Qhull() throw()
-{
-    // Except for cerr, does not throw errors
-    if(qh_qh->hasQhullMessage()){
-        cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
-        cerr<< qh_qh->qhullMessage();
-        qh_qh->clearQhullMessage();
-    }
-    delete qh_qh;
-    qh_qh= 0;
-}//~Qhull
-
-#//!\name GetSet
-
-void Qhull::
-checkIfQhullInitialized()
-{
-    if(!initialized()){ // qh_initqhull_buffers() not called
-        throw QhullError(10023, "Qhull error: checkIfQhullInitialized failed.  Call runQhull() first.");
-    }
-}//checkIfQhullInitialized
-
-//! Return feasiblePoint for halfspace intersection
-//! If called before runQhull(), then it returns the value from setFeasiblePoint.  qh.feasible_string overrides this value if it is defined.
-Coordinates Qhull::
-feasiblePoint() const
-{
-    Coordinates result;
-    if(qh_qh->feasible_point){
-        result.append(qh_qh->hull_dim, qh_qh->feasible_point);
-    }else{
-        result= feasible_point;
-    }
-    return result;
-}//feasiblePoint
-
-//! Return origin point for qh.input_dim
-QhullPoint Qhull::
-inputOrigin()
-{
-    QhullPoint result= origin();
-    result.setDimension(qh_qh->input_dim);
-    return result;
-}//inputOrigin
-
-#//!\name GetValue
-
-double Qhull::
-area(){
-    checkIfQhullInitialized();
-    if(!qh_qh->hasAreaVolume){
-        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-            qh_getarea(qh_qh, qh_qh->facet_list);
-        }
-        qh_qh->NOerrexit= true;
-        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-    }
-    return qh_qh->totarea;
-}//area
-
-double Qhull::
-volume(){
-    checkIfQhullInitialized();
-    if(!qh_qh->hasAreaVolume){
-        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-            qh_getarea(qh_qh, qh_qh->facet_list);
-        }
-        qh_qh->NOerrexit= true;
-        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-    }
-    return qh_qh->totvol;
-}//volume
-
-#//!\name Foreach
-
-//! Define QhullVertex::neighborFacets().
-//! Automatically called if merging facets or computing the Voronoi diagram.
-//! Noop if called multiple times.
-void Qhull::
-defineVertexNeighborFacets(){
-    checkIfQhullInitialized();
-    if(!qh_qh->hasAreaVolume){
-        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-            qh_vertexneighbors(qh_qh);
-        }
-        qh_qh->NOerrexit= true;
-        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-    }
-}//defineVertexNeighborFacets
-
-QhullFacetList Qhull::
-facetList() const{
-    return QhullFacetList(beginFacet(), endFacet());
-}//facetList
-
-QhullPoints Qhull::
-points() const
-{
-    return QhullPoints(qh_qh, qh_qh->hull_dim, qh_qh->num_points*qh_qh->hull_dim, qh_qh->first_point);
-}//points
-
-QhullPointSet Qhull::
-otherPoints() const
-{
-    return QhullPointSet(qh_qh, qh_qh->other_points);
-}//otherPoints
-
-//! Return vertices of the convex hull.
-QhullVertexList Qhull::
-vertexList() const{
-    return QhullVertexList(beginVertex(), endVertex());
-}//vertexList
-
-#//!\name Methods
-
-void Qhull::
-outputQhull()
-{
-    checkIfQhullInitialized();
-    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-        qh_produce_output2(qh_qh);
-    }
-    qh_qh->NOerrexit= true;
-    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-}//outputQhull
-
-void Qhull::
-outputQhull(const char *outputflags)
-{
-    checkIfQhullInitialized();
-    string cmd(" "); // qh_checkflags skips first word
-    cmd += outputflags;
-    char *command= const_cast(cmd.c_str());
-    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-        qh_clear_outputflags(qh_qh);
-        char *s = qh_qh->qhull_command + strlen(qh_qh->qhull_command) + 1; //space
-        strncat(qh_qh->qhull_command, command, sizeof(qh_qh->qhull_command)-strlen(qh_qh->qhull_command)-1);
-        qh_checkflags(qh_qh, command, const_cast(s_not_output_options));
-        qh_initflags(qh_qh, s);
-        qh_initqhull_outputflags(qh_qh);
-        if(qh_qh->KEEPminArea < REALmax/2
-           || (0 != qh_qh->KEEParea + qh_qh->KEEPmerge + qh_qh->GOODvertex
-                    + qh_qh->GOODthreshold + qh_qh->GOODpoint + qh_qh->SPLITthresholds)){
-            facetT *facet;
-            qh_qh->ONLYgood= False;
-            FORALLfacet_(qh_qh->facet_list) {
-                facet->good= True;
-            }
-            qh_prepare_output(qh_qh);
-        }
-        qh_produce_output2(qh_qh);
-        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
-            qh_check_points(qh_qh);
-        }
-    }
-    qh_qh->NOerrexit= true;
-    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-}//outputQhull
-
-//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
-void Qhull::
-runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
-{
-    runQhull(rboxPoints.comment().c_str(), rboxPoints.dimension(), rboxPoints.count(), &*rboxPoints.coordinates(), qhullCommand2);
-}//runQhull, RboxPoints
-
-//! pointCoordinates is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
-//! Derived from qh_new_qhull [user.c]
-//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
-//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
-void Qhull::
-runQhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand)
-{
-  /* gcc may issue a "might be clobbered" warning for pointDimension and pointCoordinates [-Wclobbered].
-     These parameters are not referenced after a longjmp() and hence not clobbered.
-     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
-    if(run_called){
-        throw QhullError(10027, "Qhull error: runQhull called twice.  Only one call allowed.");
-    }
-    run_called= true;
-    string s("qhull ");
-    s += qhullCommand;
-    char *command= const_cast(s.c_str());
-    /************* Expansion of QH_TRY_ for debugging
-    int QH_TRY_status;
-    if(qh_qh->NOerrexit){
-        qh_qh->NOerrexit= False;
-        QH_TRY_status= setjmp(qh_qh->errexit);
-    }else{
-        QH_TRY_status= QH_TRY_ERROR;
-    }
-    if(!QH_TRY_status){
-    *************/
-    QH_TRY_(qh_qh){ // no object creation -- destructors are skipped on longjmp()
-        qh_checkflags(qh_qh, command, const_cast(s_unsupported_options));
-        qh_initflags(qh_qh, command);
-        *qh_qh->rbox_command= '\0';
-        strncat( qh_qh->rbox_command, inputComment, sizeof(qh_qh->rbox_command)-1);
-        if(qh_qh->DELAUNAY){
-            qh_qh->PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
-        }
-        pointT *newPoints= const_cast(pointCoordinates);
-        int newDimension= pointDimension;
-        int newIsMalloc= False;
-        if(qh_qh->HALFspace){
-            --newDimension;
-            initializeFeasiblePoint(newDimension);
-            newPoints= qh_sethalfspace_all(qh_qh, pointDimension, pointCount, newPoints, qh_qh->feasible_point);
-            newIsMalloc= True;
-        }
-        qh_init_B(qh_qh, newPoints, pointCount, newDimension, newIsMalloc);
-        qh_qhull(qh_qh);
-        qh_check_output(qh_qh);
-        qh_prepare_output(qh_qh);
-        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
-            qh_check_points(qh_qh);
-        }
-    }
-    qh_qh->NOerrexit= true;
-    for(int k= qh_qh->hull_dim; k--; ){  // Do not move into QH_TRY block.  It may throw an error
-        origin_point << 0.0;
-    }
-    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-}//runQhull
-
-#//!\name Helpers -- be careful of allocating C++ objects due to setjmp/longjmp() error handling by qh_... routines
-
-//! initialize qh.feasible_point for half-space intersection
-//! Sets from qh.feasible_string if available, otherwise from Qhull::feasible_point
-//! called only once from runQhull(), otherwise it leaks memory (the same as qh_setFeasible)
-void Qhull::
-initializeFeasiblePoint(int hulldim)
-{
-    if(qh_qh->feasible_string){
-        qh_setfeasible(qh_qh, hulldim);
-    }else{
-        if(feasible_point.isEmpty()){
-            qh_fprintf(qh_qh, qh_qh->ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or Qhull::setFeasiblePoint before runQhull()\n");
-            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
-        }
-        if(feasible_point.size()!=(size_t)hulldim){
-            qh_fprintf(qh_qh, qh_qh->ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasible_point.size());
-            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
-        }
-        if (!(qh_qh->feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
-            qh_fprintf(qh_qh, qh_qh->ferr, 6202, "qhull error: insufficient memory for feasible point\n");
-            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
-        }
-        coordT *t= qh_qh->feasible_point;
-        // No qh_... routines after here -- longjmp() ignores destructor
-        for(Coordinates::ConstIterator p=feasible_point.begin(); p.  It could be rewritten for another vector class such as QList
-   #define QHULL_USES_QT
-      Supply conversions to QT
-      qhulltest requires QT.  It is defined in RoadTest.h
-
-  #define QHULL_ASSERT
-      Defined by QhullError.h
-      It invokes assert()
-*/
-
-#//!\name Used here
-    class QhullFacetList;
-    class QhullPoints;
-    class QhullQh;
-    class RboxPoints;
-
-#//!\name Defined here
-    class Qhull;
-
-//! Interface to Qhull from C++
-class Qhull {
-
-private:
-#//!\name Members and friends
-    QhullQh *           qh_qh;          //! qhT for this instance
-    Coordinates         origin_point;   //! origin for qh_qh->hull_dim.  Set by runQhull()
-    bool                run_called;     //! True at start of runQhull.  Errors if call again.
-    Coordinates         feasible_point;  //! feasible point for half-space intersection (alternative to qh.feasible_string for qh.feasible_point)
-
-public:
-#//!\name Constructors
-                        Qhull();      //!< call runQhull() next
-                        Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
-                        Qhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
-                        ~Qhull() throw();
-private:                //! Disable copy constructor and assignment.  Qhull owns QhullQh.
-                        Qhull(const Qhull &);
-    Qhull &             operator=(const Qhull &);
-
-private:
-    void                allocateQhullQh();
-
-public:
-
-#//!\name GetSet
-    void                checkIfQhullInitialized();
-    int                 dimension() const { return qh_qh->input_dim; } //!< Dimension of input and result
-    void                disableOutputStream() { qh_qh->disableOutputStream(); }
-    void                enableOutputStream() { qh_qh->enableOutputStream(); }
-    countT              facetCount() const { return qh_qh->num_facets; }
-    Coordinates         feasiblePoint() const; 
-    int                 hullDimension() const { return qh_qh->hull_dim; } //!< Dimension of the computed hull
-    bool                hasOutputStream() const { return qh_qh->hasOutputStream(); }
-    bool                initialized() const { return (qh_qh->hull_dim>0); }
-    const char *        inputComment() const { return qh_qh->rbox_command; }
-    QhullPoint          inputOrigin();
-                        //! non-const due to QhullPoint
-    QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(qh_qh, origin_point.data()); }
-    QhullQh *           qh() const { return qh_qh; };
-    const char *        qhullCommand() const { return qh_qh->qhull_command; }
-    const char *        rboxCommand() const { return qh_qh->rbox_command; }
-    int                 rotateRandom() const { return qh_qh->ROTATErandom; } //!< Return QRn for repeating QR0 runs
-    void                setFeasiblePoint(const Coordinates &c) { feasible_point= c; } //!< Sets qh.feasible_point via initializeFeasiblePoint
-    countT              vertexCount() const { return qh_qh->num_vertices; }
-
-#//!\name Delegated to QhullQh
-    double              angleEpsilon() const { return qh_qh->angleEpsilon(); } //!< Epsilon for hyperplane angle equality
-    void                appendQhullMessage(const std::string &s) { qh_qh->appendQhullMessage(s); }
-    void                clearQhullMessage() { qh_qh->clearQhullMessage(); }
-    double              distanceEpsilon() const { return qh_qh->distanceEpsilon(); } //!< Epsilon for distance to hyperplane
-    double              factorEpsilon() const { return qh_qh->factorEpsilon(); }  //!< Factor for angleEpsilon and distanceEpsilon
-    std::string         qhullMessage() const { return qh_qh->qhullMessage(); }
-    bool                hasQhullMessage() const { return qh_qh->hasQhullMessage(); }
-    int                 qhullStatus() const { return qh_qh->qhullStatus(); }
-    void                setErrorStream(std::ostream *os) { qh_qh->setErrorStream(os); }
-    void                setFactorEpsilon(double a) { qh_qh->setFactorEpsilon(a); }
-    void                setOutputStream(std::ostream *os) { qh_qh->setOutputStream(os); }
-
-#//!\name ForEach
-    QhullFacet          beginFacet() const { return QhullFacet(qh_qh, qh_qh->facet_list); }
-    QhullVertex         beginVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_list); }
-    void                defineVertexNeighborFacets(); //!< Automatically called if merging facets or Voronoi diagram
-    QhullFacet          endFacet() const { return QhullFacet(qh_qh, qh_qh->facet_tail); }
-    QhullVertex         endVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_tail); }
-    QhullFacetList      facetList() const;
-    QhullFacet          firstFacet() const { return beginFacet(); }
-    QhullVertex         firstVertex() const { return beginVertex(); }
-    QhullPoints         points() const;
-    QhullPointSet       otherPoints() const;
-                        //! Same as points().coordinates()
-    coordT *            pointCoordinateBegin() const { return qh_qh->first_point; }
-    coordT *            pointCoordinateEnd() const { return qh_qh->first_point + qh_qh->num_points*qh_qh->hull_dim; }
-    QhullVertexList     vertexList() const;
-
-#//!\name Methods
-    double              area();
-    void                outputQhull();
-    void                outputQhull(const char * outputflags);
-    void                runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
-    void                runQhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
-    double              volume();
-
-#//!\name Helpers
-private:
-    void                initializeFeasiblePoint(int hulldim);
-};//Qhull
-
-}//namespace orgQhull
-
-#endif // QHULLCPP_H
diff --git a/src/qhull/src/libqhullcpp/QhullError.h b/src/qhull/src/libqhullcpp/QhullError.h
deleted file mode 100644
index 08d50aa0f..000000000
--- a/src/qhull/src/libqhullcpp/QhullError.h
+++ /dev/null
@@ -1,62 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullError.h#2 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLERROR_H
-#define QHULLERROR_H
-
-#include "libqhullcpp/RoadError.h"
-// No dependencies on libqhull
-
-#ifndef QHULL_ASSERT
-#define QHULL_ASSERT assert
-#include 
-#endif
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! QhullError -- std::exception class for Qhull
-    class QhullError;
-
-class QhullError : public RoadError {
-
-public:
-#//!\name Constants
-    enum {
-        QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
-        QHULLlastError= 10078,
-        NOthrow= 1 //! For flag to indexOf()
-    };
-
-#//!\name Constructors
-    // default constructors
-    QhullError() : RoadError() {};
-    QhullError(const QhullError &other) : RoadError(other) {}
-    QhullError(int code, const std::string &message) : RoadError(code, message) {};
-    QhullError(int code, const char *fmt) : RoadError(code, fmt) {};
-    QhullError(int code, const char *fmt, int d) : RoadError(code, fmt, d) {};
-    QhullError(int code, const char *fmt, int d, int d2) : RoadError(code, fmt, d, d2) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f) : RoadError(code, fmt, d, d2, f) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f, const char *s) : RoadError(code, fmt, d, d2, f, s) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f, const void *x) : RoadError(code, fmt, d, d2, f, x) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f, int i) : RoadError(code, fmt, d, d2, f, i) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f, long long i) : RoadError(code, fmt, d, d2, f, i) {};
-    QhullError(int code, const char *fmt, int d, int d2, float f, double e) : RoadError(code, fmt, d, d2, f, e) {};
-    QhullError &operator=(const QhullError &other) { this->RoadError::operator=(other); return *this; }
-    ~QhullError() throw() {}
-
-};//class QhullError
-
-
-}//namespace orgQhull
-
-#//!\name Global
-
-inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }
-
-#endif // QHULLERROR_H
diff --git a/src/qhull/src/libqhullcpp/QhullFacet.cpp b/src/qhull/src/libqhullcpp/QhullFacet.cpp
deleted file mode 100644
index 40d3828a4..000000000
--- a/src/qhull/src/libqhullcpp/QhullFacet.cpp
+++ /dev/null
@@ -1,519 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacet.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullFacet -- Qhull's facet structure, facetT, as a C++ class
-
-#include "libqhullcpp/QhullFacet.h"
-
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullSet.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullPointSet.h"
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/QhullVertex.h"
-
-#include 
-
-using std::endl;
-using std::ostream;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Class objects
-facetT QhullFacet::
-s_empty_facet= {0,0,0,0,{0},
-        0,0,0,0,0,
-        0,0,0,0,0,
-        0,0,0,0,0,
-        0,0,0,0,0,
-        0,0,0,0,0,
-        0,0,0,0,0,
-        0,0,0,0};
-
-#//!\name Constructors
-
-QhullFacet::
-QhullFacet(const Qhull &q) 
-: qh_facet(&s_empty_facet)
-, qh_qh(q.qh())
-{
-}
-
-QhullFacet::
-QhullFacet(const Qhull &q, facetT *f) 
-: qh_facet(f ? f : &s_empty_facet)
-, qh_qh(q.qh())
-{
-}
-
-#//!\name GetSet
-
-//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io_r.c]
-//! if printFormat=qh_PRINTtriangles and qh.DELAUNAY, returns centrum of a Delaunay facet
-//! Sets center if needed
-//! Code duplicated for PrintCenter and getCenter
-//! Returns QhullPoint() if none or qh_INFINITE
-QhullPoint QhullFacet::
-getCenter(qh_PRINT printFormat)
-{
-    if(!qh_qh){
-        // returns QhullPoint()
-    }else if(qh_qh->CENTERtype==qh_ASvoronoi){
-        if(!qh_facet->normal || !qh_facet->upperdelaunay || !qh_qh->ATinfinity){
-            if(!qh_facet->center){
-                QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-                    qh_facet->center= qh_facetcenter(qh_qh, qh_facet->vertices);
-                }
-                qh_qh->NOerrexit= true;
-                qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-            }
-            return QhullPoint(qh_qh, qh_qh->hull_dim-1, qh_facet->center);
-        }
-    }else if(qh_qh->CENTERtype==qh_AScentrum){
-        volatile int numCoords= qh_qh->hull_dim;
-        if(printFormat==qh_PRINTtriangles && qh_qh->DELAUNAY){
-            numCoords--;
-        }
-        if(!qh_facet->center){
-            QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-                qh_facet->center= qh_getcentrum(qh_qh, getFacetT());
-            }
-            qh_qh->NOerrexit= true;
-            qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-        }
-        return QhullPoint(qh_qh, numCoords, qh_facet->center);
-    }
-    return QhullPoint();
- }//getCenter
-
-//! Return innerplane clearly below the vertices
-//! from io_r.c[qh_PRINTinner]
-QhullHyperplane QhullFacet::
-innerplane() const{
-    QhullHyperplane h;
-    if(qh_qh){
-        realT inner;
-        // Does not error, TRY_QHULL_ not needed
-        qh_outerinner(qh_qh, const_cast(getFacetT()), NULL, &inner);
-        h= hyperplane();
-        h.setOffset(h.offset()-inner); //inner is negative
-    }
-    return h;
-}//innerplane
-
-//! Return outerplane clearly above all points
-//! from io_r.c[qh_PRINTouter]
-QhullHyperplane QhullFacet::
-outerplane() const{
-    QhullHyperplane h;
-    if(qh_qh){
-        realT outer;
-        // Does not error, TRY_QHULL_ not needed
-        qh_outerinner(qh_qh, const_cast(getFacetT()), &outer, NULL);
-        h= hyperplane();
-        h.setOffset(h.offset()-outer); //outer is positive
-    }
-    return h;
-}//outerplane
-
-//! Set by qh_triangulate for option 'Qt'.
-//! Errors if tricoplanar and facetArea() or qh_getarea() called first.
-QhullFacet QhullFacet::
-tricoplanarOwner() const
-{
-    if(qh_facet->tricoplanar){
-        if(qh_facet->isarea){
-            throw QhullError(10018, "Qhull error: facetArea() or qh_getarea() previously called.  triCoplanarOwner() is not available.");
-        }
-        return QhullFacet(qh_qh, qh_facet->f.triowner);
-    }
-    return QhullFacet(qh_qh); 
-}//tricoplanarOwner
-
-QhullPoint QhullFacet::
-voronoiVertex()
-{
-    if(qh_qh && qh_qh->CENTERtype!=qh_ASvoronoi){
-          throw QhullError(10052, "Error: QhullFacet.voronoiVertex() requires option 'v' (qh_ASvoronoi)");
-    }
-    return getCenter();
-}//voronoiVertex
-
-#//!\name Value
-
-//! Disables tricoplanarOwner()
-double QhullFacet::
-facetArea()
-{
-    if(qh_qh && !qh_facet->isarea){
-        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-            qh_facet->f.area= qh_facetarea(qh_qh, qh_facet);
-            qh_facet->isarea= True;
-        }
-        qh_qh->NOerrexit= true;
-        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-    }
-    return qh_facet->f.area;
-}//facetArea
-
-#//!\name Foreach
-
-QhullPointSet QhullFacet::
-coplanarPoints() const
-{
-    return QhullPointSet(qh_qh, qh_facet->coplanarset);
-}//coplanarPoints
-
-QhullFacetSet QhullFacet::
-neighborFacets() const
-{
-    return QhullFacetSet(qh_qh, qh_facet->neighbors);
-}//neighborFacets
-
-QhullPointSet QhullFacet::
-outsidePoints() const
-{
-    return QhullPointSet(qh_qh, qh_facet->outsideset);
-}//outsidePoints
-
-QhullRidgeSet QhullFacet::
-ridges() const
-{
-    return QhullRidgeSet(qh_qh, qh_facet->ridges);
-}//ridges
-
-QhullVertexSet QhullFacet::
-vertices() const
-{
-    return QhullVertexSet(qh_qh, qh_facet->vertices);
-}//vertices
-
-}//namespace orgQhull
-
-#//!\name operator<<
-
-using std::ostream;
-
-using orgQhull::QhullFacet;
-using orgQhull::QhullFacetSet;
-using orgQhull::QhullPoint;
-using orgQhull::QhullPointSet;
-using orgQhull::QhullRidge;
-using orgQhull::QhullRidgeSet;
-using orgQhull::QhullSetBase;
-using orgQhull::QhullVertexSet;
-
-ostream &
-operator<<(ostream &os, const QhullFacet::PrintFacet &pr)
-{
-    os << pr.message;
-    QhullFacet f= *pr.facet;
-    if(f.getFacetT()==0){ // Special values from set iterator
-        os << " NULLfacet" << endl;
-        return os;
-    }
-    if(f.getFacetT()==qh_MERGEridge){
-        os << " MERGEridge" << endl;
-        return os;
-    }
-    if(f.getFacetT()==qh_DUPLICATEridge){
-        os << " DUPLICATEridge" << endl;
-        return os;
-    }
-    os << f.printHeader();
-    if(!f.ridges().isEmpty()){
-        os << f.printRidges();
-    }
-    return os;
-}//operator<< PrintFacet
-
-//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [_r.]
-//! Code duplicated for PrintCenter and getCenter
-//! Sets center if needed
-ostream &
-operator<<(ostream &os, const QhullFacet::PrintCenter &pr)
-{
-    facetT *f= pr.facet->getFacetT();
-    if(pr.facet->qh()->CENTERtype!=qh_ASvoronoi && pr.facet->qh()->CENTERtype!=qh_AScentrum){
-        return os;
-    }
-    if (pr.message){
-        os << pr.message;
-    }
-    int numCoords;
-    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi){
-        numCoords= pr.facet->qh()->hull_dim-1;
-        if(!f->normal || !f->upperdelaunay || !pr.facet->qh()->ATinfinity){
-            if(!f->center){
-                f->center= qh_facetcenter(pr.facet->qh(), f->vertices);
-            }
-            for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
-            }
-        }else{
-            for(int k=0; kqh()->hull_dim;
-        if(pr.print_format==qh_PRINTtriangles && pr.facet->qh()->DELAUNAY){
-            numCoords--;
-        }
-        if(!f->center){
-            f->center= qh_getcentrum(pr.facet->qh(), f);
-        }
-        for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
-        }
-    }
-    if(pr.print_format==qh_PRINTgeom && numCoords==2){
-        os << " 0";
-    }
-    os << endl;
-    return os;
-}//operator<< PrintCenter
-
-//! Print flags for facet to stream.  Space prefix.  From qh_printfacetheader [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullFacet::PrintFlags &p)
-{
-    const facetT *f= p.facet->getFacetT();
-    if(p.message){
-        os << p.message;
-    }
-
-    os << (p.facet->isTopOrient() ? " top" : " bottom");
-    if(p.facet->isSimplicial()){
-        os << " simplicial";
-    }
-    if(p.facet->isTriCoplanar()){
-        os << " tricoplanar";
-    }
-    if(p.facet->isUpperDelaunay()){
-        os << " upperDelaunay";
-    }
-    if(f->visible){
-        os << " visible";
-    }
-    if(f->newfacet){
-        os << " new";
-    }
-    if(f->tested){
-        os << " tested";
-    }
-    if(!f->good){
-        os << " notG";
-    }
-    if(f->seen){
-        os << " seen";
-    }
-    if(f->coplanar){
-        os << " coplanar";
-    }
-    if(f->mergehorizon){
-        os << " mergehorizon";
-    }
-    if(f->keepcentrum){
-        os << " keepcentrum";
-    }
-    if(f->dupridge){
-        os << " dupridge";
-    }
-    if(f->mergeridge && !f->mergeridge2){
-        os << " mergeridge1";
-    }
-    if(f->mergeridge2){
-        os << " mergeridge2";
-    }
-    if(f->newmerge){
-        os << " newmerge";
-    }
-    if(f->flipped){
-        os << " flipped";
-    }
-    if(f->notfurthest){
-        os << " notfurthest";
-    }
-    if(f->degenerate){
-        os << " degenerate";
-    }
-    if(f->redundant){
-        os << " redundant";
-    }
-    os << endl;
-    return os;
-}//operator<< PrintFlags
-
-//! Print header for facet to stream. Space prefix.  From qh_printfacetheader [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullFacet::PrintHeader &pr)
-{
-    QhullFacet facet= *pr.facet;
-    facetT *f= facet.getFacetT();
-    os << "- f" << facet.id() << endl;
-    os << facet.printFlags("    - flags:");
-    if(f->isarea){
-        os << "    - area: " << f->f.area << endl; //FIXUP QH11010 2.2g
-    }else if(pr.facet->qh()->NEWfacets && f->visible && f->f.replace){
-        os << "    - replacement: f" << f->f.replace->id << endl;
-    }else if(f->newfacet){
-        if(f->f.samecycle && f->f.samecycle != f){
-            os << "    - shares same visible/horizon as f" << f->f.samecycle->id << endl;
-        }
-    }else if(f->tricoplanar /* !isarea */){
-        if(f->f.triowner){
-            os << "    - owner of normal & centrum is facet f" << f->f.triowner->id << endl;
-        }
-    }else if(f->f.newcycle){
-        os << "    - was horizon to f" << f->f.newcycle->id << endl;
-    }
-    if(f->nummerge){
-        os << "    - merges: " << f->nummerge << endl;
-    }
-    os << facet.hyperplane().print("    - normal: ", "\n    - offset: "); // FIXUP QH11010 %10.7g
-    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi || f->center){
-        os << facet.printCenter(qh_PRINTfacets, "    - center: ");
-    }
-#if qh_MAXoutside
-    if(f->maxoutside > pr.facet->qh()->DISTround){
-        os << "    - maxoutside: " << f->maxoutside << endl; //FIXUP QH11010 %10.7g
-    }
-#endif
-    QhullPointSet ps= facet.outsidePoints();
-    if(!ps.isEmpty()){
-        QhullPoint furthest= ps.last();
-        if (ps.size() < 6) {
-            os << "    - outside set(furthest p" << furthest.id() << "):" << endl;
-            for(QhullPointSet::iterator i=ps.begin(); i!=ps.end(); ++i){
-                QhullPoint p= *i;
-                os << p.print("     ");
-            }
-        }else if(ps.size()<21){
-            os << ps.print("    - outside set:");
-        }else{
-            os << "    - outside set:  " << ps.size() << " points.";
-            os << furthest.print("  Furthest");
-        }
-#if !qh_COMPUTEfurthest
-        os << "    - furthest distance= " << f->furthestdist << endl; //FIXUP QH11010 %2.2g
-#endif
-    }
-    QhullPointSet cs= facet.coplanarPoints();
-    if(!cs.isEmpty()){
-        QhullPoint furthest= cs.last();
-        if (cs.size() < 6) {
-            os << "    - coplanar set(furthest p" << furthest.id() << "):" << endl;
-            for(QhullPointSet::iterator i=cs.begin(); i!=cs.end(); ++i){
-                QhullPoint p= *i;
-                os << p.print("     ");
-            }
-        }else if(cs.size()<21){
-            os << cs.print("    - coplanar set:");
-        }else{
-            os << "    - coplanar set:  " << cs.size() << " points.";
-            os << furthest.print("  Furthest");
-        }
-        // FIXUP QH11027 Can/should zinc_(Zdistio) be called from C++ interface
-        double d= facet.distance(furthest);
-        os << "      furthest distance= " << d << endl; //FIXUP QH11010 %2.2g
-    }
-    QhullVertexSet vs= facet.vertices();
-    if(!vs.isEmpty()){
-        os << vs.print("    - vertices:");
-    }
-    QhullFacetSet fs= facet.neighborFacets();
-    fs.selectAll();
-    if(!fs.isEmpty()){
-        os << fs.printIdentifiers("    - neighboring facets:");
-    }
-    return os;
-}//operator<< PrintHeader
-
-
-//! Print ridges of facet to stream.  Same as qh_printfacetridges [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullFacet::PrintRidges &pr)
-{
-    const QhullFacet facet= *pr.facet;
-    facetT *f= facet.getFacetT();
-    QhullRidgeSet rs= facet.ridges();
-    if(!rs.isEmpty()){
-        if(f->visible && pr.facet->qh()->NEWfacets){
-            os << "    - ridges(ids may be garbage):";
-            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
-                QhullRidge r= *i;
-                os << " r" << r.id();
-            }
-            os << endl;
-        }else{
-            os << "    - ridges:" << endl;
-        }
-
-        // Keep track of printed ridges
-        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
-            QhullRidge r= *i;
-            r.getRidgeT()->seen= false;
-        }
-        int ridgeCount= 0;
-        if(facet.dimension()==3){
-            for(QhullRidge r= rs.first(); !r.getRidgeT()->seen; r= r.nextRidge3d(facet)){
-                r.getRidgeT()->seen= true;
-                os << r.print("");
-                ++ridgeCount;
-                if(!r.hasNextRidge3d(facet)){
-                    break;
-                }
-            }
-        }else {
-            QhullFacetSet ns(facet.neighborFacets());
-            for(QhullFacetSet::iterator i=ns.begin(); i!=ns.end(); ++i){
-                QhullFacet neighbor= *i;
-                QhullRidgeSet nrs(neighbor.ridges());
-                for(QhullRidgeSet::iterator j=nrs.begin(); j!=nrs.end(); ++j){
-                    QhullRidge r= *j;
-                    if(r.otherFacet(neighbor)==facet){
-                        r.getRidgeT()->seen= true;
-                        os << r.print("");
-                        ridgeCount++;
-                    }
-                }
-            }
-        }
-        if(ridgeCount!=rs.count()){
-            os << "     - all ridges:";
-            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
-                QhullRidge r= *i;
-                os << " r" << r.id();
-            }
-            os << endl;
-        }
-        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
-            QhullRidge r= *i;
-            if(!r.getRidgeT()->seen){
-                os << r.print("");
-            }
-        }
-    }
-    return os;
-}//operator<< PrintRidges
-
-// "No conversion" error if defined inline
-ostream &
-operator<<(ostream &os, QhullFacet &f)
-{
-    os << f.print("");
-    return os;
-}//<< QhullFacet
diff --git a/src/qhull/src/libqhullcpp/QhullFacet.h b/src/qhull/src/libqhullcpp/QhullFacet.h
deleted file mode 100644
index ae4f008fd..000000000
--- a/src/qhull/src/libqhullcpp/QhullFacet.h
+++ /dev/null
@@ -1,151 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacet.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLFACET_H
-#define QHULLFACET_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullHyperplane.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullSet.h"
-#include "libqhullcpp/QhullPointSet.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Coordinates;
-    class Qhull;
-    class QhullFacetSet;
-    class QhullRidge;
-    class QhullVertex;
-    class QhullVertexSet;
-
-#//!\name Defined here
-    class QhullFacet;
-    typedef QhullSet  QhullRidgeSet;
-
-//! A QhullFacet is the C++ equivalent to Qhull's facetT*
-class QhullFacet {
-
-#//!\name Defined here
-public:
-    typedef facetT *   base_type;  // for QhullVertexSet
-
-private:
-#//!\name Fields -- no additions (QhullFacetSet of facetT*)
-    facetT *            qh_facet;  //!< Corresponding facetT, may be 0 for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
-    QhullQh *           qh_qh;     //!< QhullQh/qhT for facetT, may be 0
-
-#//!\name Class objects
-    static facetT       s_empty_facet; // needed for shallow copy
-
-public:
-#//!\name Constructors
-                        QhullFacet() : qh_facet(&s_empty_facet), qh_qh(0) {}
-    explicit            QhullFacet(const Qhull &q);
-                        QhullFacet(const Qhull &q, facetT *f);
-    explicit            QhullFacet(QhullQh *qqh) : qh_facet(&s_empty_facet), qh_qh(qqh) {}
-                        QhullFacet(QhullQh *qqh, facetT *f) : qh_facet(f ? f : &s_empty_facet), qh_qh(qqh) {}
-                        // Creates an alias.  Does not copy QhullFacet.  Needed for return by value and parameter passing
-                        QhullFacet(const QhullFacet &other) : qh_facet(other.qh_facet ? other.qh_facet : &s_empty_facet), qh_qh(other.qh_qh) {}
-                        // Creates an alias.  Does not copy QhullFacet.  Needed for vector
-    QhullFacet &        operator=(const QhullFacet &other) { qh_facet= other.qh_facet ? other.qh_facet : &s_empty_facet; qh_qh= other.qh_qh; return *this; }
-                        ~QhullFacet() {}
-
-
-#//!\name GetSet
-    int                 dimension() const { return (qh_qh ? qh_qh->hull_dim : 0); }
-    QhullPoint          getCenter() { return getCenter(qh_PRINTpoints); }
-    QhullPoint          getCenter(qh_PRINT printFormat);
-    facetT *            getBaseT() const { return getFacetT(); } //!< For QhullSet
-                        // Do not define facetT().  It conflicts with return type facetT*
-    facetT *            getFacetT() const { return qh_facet; }
-    QhullHyperplane     hyperplane() const { return QhullHyperplane(qh_qh, dimension(), qh_facet->normal, qh_facet->offset); }
-    countT              id() const { return (qh_facet ? qh_facet->id : (int)qh_IDunknown); }
-    QhullHyperplane     innerplane() const;
-    bool                isValid() const { return qh_qh && qh_facet && qh_facet != &s_empty_facet; }
-    bool                isGood() const { return qh_facet && qh_facet->good; }
-    bool                isSimplicial() const { return qh_facet && qh_facet->simplicial; }
-    bool                isTopOrient() const { return qh_facet && qh_facet->toporient; }
-    bool                isTriCoplanar() const { return qh_facet && qh_facet->tricoplanar; }
-    bool                isUpperDelaunay() const { return qh_facet && qh_facet->upperdelaunay; }
-    QhullFacet          next() const { return QhullFacet(qh_qh, qh_facet->next); }
-    bool                operator==(const QhullFacet &other) const { return qh_facet==other.qh_facet; }
-    bool                operator!=(const QhullFacet &other) const { return !operator==(other); }
-    QhullHyperplane     outerplane() const;
-    QhullFacet          previous() const { return QhullFacet(qh_qh, qh_facet->previous); }
-    QhullQh *           qh() const { return qh_qh; }
-    QhullFacet          tricoplanarOwner() const;
-    QhullPoint          voronoiVertex();
-
-#//!\name value
-    //! Undefined if c.size() != dimension()
-    double              distance(const Coordinates &c) const { return distance(c.data()); }
-    double              distance(const pointT *p) const { return distance(QhullPoint(qh_qh, const_cast(p))); }
-    double              distance(const QhullPoint &p) const { return hyperplane().distance(p); }
-    double              facetArea();
-
-#//!\name foreach
-    // Can not inline.  Otherwise circular reference
-    QhullPointSet       coplanarPoints() const;
-    QhullFacetSet       neighborFacets() const;
-    QhullPointSet       outsidePoints() const;
-    QhullRidgeSet       ridges() const;
-    QhullVertexSet      vertices() const;
-
-#//!\name IO
-    struct PrintCenter{
-        QhullFacet *    facet;  // non-const due to facet.center()
-        const char *    message;
-        qh_PRINT        print_format;
-                        PrintCenter(QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), print_format(printFormat){}
-    };//PrintCenter
-    PrintCenter         printCenter(qh_PRINT printFormat, const char *message) { return PrintCenter(*this, printFormat, message); }
-
-    struct PrintFacet{
-        QhullFacet *    facet;  // non-const due to f->center()
-        const char *    message;
-        explicit        PrintFacet(QhullFacet &f, const char * s) : facet(&f), message(s) {}
-    };//PrintFacet
-    PrintFacet          print(const char *message) { return PrintFacet(*this, message); }
-
-    struct PrintFlags{
-        const QhullFacet *facet;
-        const char *    message;
-                        PrintFlags(const QhullFacet &f, const char *s) : facet(&f), message(s) {}
-    };//PrintFlags
-    PrintFlags          printFlags(const char *message) const { return PrintFlags(*this, message); }
-
-    struct PrintHeader{
-        QhullFacet *    facet;  // non-const due to f->center()
-                        PrintHeader(QhullFacet &f) : facet(&f) {}
-    };//PrintHeader
-    PrintHeader         printHeader() { return PrintHeader(*this); }
-
-    struct PrintRidges{
-        const QhullFacet *facet;
-                        PrintRidges(QhullFacet &f) : facet(&f) {}
-    };//PrintRidges
-    PrintRidges         printRidges() { return PrintRidges(*this); }
-
-};//class QhullFacet
-
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFacet &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintCenter &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFlags &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintHeader &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintRidges &pr);
-std::ostream &operator<<(std::ostream &os, orgQhull::QhullFacet &f); // non-const due to qh_getcenter()
-
-#endif // QHULLFACET_H
diff --git a/src/qhull/src/libqhullcpp/QhullFacetList.cpp b/src/qhull/src/libqhullcpp/QhullFacetList.cpp
deleted file mode 100644
index 9e6ddfe9e..000000000
--- a/src/qhull/src/libqhullcpp/QhullFacetList.cpp
+++ /dev/null
@@ -1,174 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetList.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullFacetList -- Qhull's linked facets, as a C++ class
-
-#include "libqhullcpp/QhullFacetList.h"
-
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullVertex.h"
-
-using std::string;
-using std::vector;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Constructors
-
-QhullFacetList::
-QhullFacetList(const Qhull &q, facetT *b, facetT *e ) 
-: QhullLinkedList(QhullFacet(q, b), QhullFacet(q, e))
-, select_all(false)
-{
-}
-
-#//!\name Conversions
-
-// See qt_qhull.cpp for QList conversions
-
-#ifndef QHULL_NO_STL
-std::vector QhullFacetList::
-toStdVector() const
-{
-    QhullLinkedListIterator i(*this);
-    std::vector vs;
-    while(i.hasNext()){
-        QhullFacet f= i.next();
-        if(isSelectAll() || f.isGood()){
-            vs.push_back(f);
-        }
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#ifndef QHULL_NO_STL
-//! Same as PrintVertices
-std::vector QhullFacetList::
-vertices_toStdVector() const
-{
-    std::vector vs;
-    QhullVertexSet qvs(qh(), first().getFacetT(), 0, isSelectAll());
-
-    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
-        vs.push_back(*i);
-    }
-    return vs;
-}//vertices_toStdVector
-#endif //QHULL_NO_STL
-
-#//!\name GetSet
-
-bool QhullFacetList::
-contains(const QhullFacet &facet) const
-{
-    if(isSelectAll()){
-        return QhullLinkedList::contains(facet);
-    }
-    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
-        QhullFacet f= *i;
-        if(f==facet && f.isGood()){
-            return true;
-        }
-    }
-    return false;
-}//contains
-
-int QhullFacetList::
-count() const
-{
-    if(isSelectAll()){
-        return QhullLinkedList::count();
-    }
-    int counter= 0;
-    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
-        if((*i).isGood()){
-            counter++;
-        }
-    }
-    return counter;
-}//count
-
-int QhullFacetList::
-count(const QhullFacet &facet) const
-{
-    if(isSelectAll()){
-        return QhullLinkedList::count(facet);
-    }
-    int counter= 0;
-    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
-        QhullFacet f= *i;
-        if(f==facet && f.isGood()){
-            counter++;
-        }
-    }
-    return counter;
-}//count
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using orgQhull::QhullFacet;
-using orgQhull::QhullFacetList;
-using orgQhull::QhullVertex;
-using orgQhull::QhullVertexSet;
-
-ostream &
-operator<<(ostream &os, const QhullFacetList::PrintFacetList &pr)
-{
-    os << pr.print_message;
-    QhullFacetList fs= *pr.facet_list;
-    os << "Vertices for " << fs.count() << " facets" << endl;
-    os << fs.printVertices();
-    os << fs.printFacets();
-    return os;
-}//operator<<
-
-//! Print facet list to stream.  From qh_printafacet [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullFacetList::PrintFacets &pr)
-{
-    for(QhullFacetList::const_iterator i= pr.facet_list->begin(); i != pr.facet_list->end(); ++i){
-        QhullFacet f= *i;
-        if(pr.facet_list->isSelectAll() || f.isGood()){
-            os << f.print("");
-        }
-    }
-    return os;
-}//printFacets
-
-//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io_r.c]
-//! Same as vertices_toStdVector
-ostream &
-operator<<(ostream &os, const QhullFacetList::PrintVertices &pr)
-{
-    QhullVertexSet vs(pr.facet_list->qh(), pr.facet_list->first().getFacetT(), NULL, pr.facet_list->isSelectAll());
-    for(QhullVertexSet::iterator i=vs.begin(); i!=vs.end(); ++i){
-        QhullVertex v= *i;
-        os << v.print("");
-    }
-    return os;
-}//printVertices
-
-std::ostream &
-operator<<(ostream &os, const QhullFacetList &fs)
-{
-    os << fs.printFacets();
-    return os;
-}//QhullFacetList
-
diff --git a/src/qhull/src/libqhullcpp/QhullFacetList.h b/src/qhull/src/libqhullcpp/QhullFacetList.h
deleted file mode 100644
index e61e56840..000000000
--- a/src/qhull/src/libqhullcpp/QhullFacetList.h
+++ /dev/null
@@ -1,106 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetList.h#2 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLFACETLIST_H
-#define QHULLFACETLIST_H
-
-#include "libqhullcpp/QhullLinkedList.h"
-#include "libqhullcpp/QhullFacet.h"
-
-#include 
-
-#ifndef QHULL_NO_STL
-#include 
-#endif
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-    class QhullFacet;
-    class QhullQh;
-
-#//!\name Defined here
-    //! QhullFacetList -- List of QhullFacet/facetT, as a C++ class.  
-    //!\see QhullFacetSet.h
-    class QhullFacetList;
-    //! QhullFacetListIterator -- if(f.isGood()){ ... }
-    typedef QhullLinkedListIterator QhullFacetListIterator;
-
-class QhullFacetList : public QhullLinkedList {
-
-#//!\name  Fields
-private:
-    bool                select_all;   //! True if include bad facets.  Default is false.
-
-#//!\name Constructors
-public:
-                        QhullFacetList(const Qhull &q, facetT *b, facetT *e);
-                        QhullFacetList(QhullQh *qqh, facetT *b, facetT *e);
-                        QhullFacetList(QhullFacet b, QhullFacet e) : QhullLinkedList(b, e), select_all(false) {}
-                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullFacetList(const QhullFacetList &other) : QhullLinkedList(*other.begin(), *other.end()), select_all(other.select_all) {}
-    QhullFacetList &    operator=(const QhullFacetList &other) { QhullLinkedList::operator =(other); select_all= other.select_all; return *this; }
-                        ~QhullFacetList() {}
-
-private:                //!Disable default constructor.  See QhullLinkedList
-                    QhullFacetList();
-public:
-
-#//!\name Conversion
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-    std::vector vertices_toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList   toQList() const;
-    QList  vertices_toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
-    countT              count() const;
-    bool                contains(const QhullFacet &f) const;
-    countT              count(const QhullFacet &f) const;
-    bool                isSelectAll() const { return select_all; }
-    QhullQh *           qh() const { return first().qh(); }
-    void                selectAll() { select_all= true; }
-    void                selectGood() { select_all= false; }
-                        //!< operator==() does not depend on isGood()
-
-#//!\name IO
-    struct PrintFacetList{
-        const QhullFacetList *facet_list;
-        const char *    print_message;   //!< non-null message
-                        PrintFacetList(const QhullFacetList &fl, const char *message) : facet_list(&fl), print_message(message) {}
-    };//PrintFacetList
-    PrintFacetList      print(const char *message) const  { return PrintFacetList(*this, message); }
-
-    struct PrintFacets{
-        const QhullFacetList *facet_list;
-                        PrintFacets(const QhullFacetList &fl) : facet_list(&fl) {}
-    };//PrintFacets
-    PrintFacets         printFacets() const { return PrintFacets(*this); }
-
-    struct PrintVertices{
-        const QhullFacetList *facet_list;
-                        PrintVertices(const QhullFacetList &fl) : facet_list(&fl) {}
-    };//PrintVertices
-    PrintVertices       printVertices() const { return PrintVertices(*this); }
-};//class QhullFacetList
-
-}//namespace orgQhull
-
-#//!\name == Global namespace =========================================
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacetList &p);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacets &p);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintVertices &p);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList &fs);
-
-#endif // QHULLFACETLIST_H
diff --git a/src/qhull/src/libqhullcpp/QhullFacetSet.cpp b/src/qhull/src/libqhullcpp/QhullFacetSet.cpp
deleted file mode 100644
index d30c21e26..000000000
--- a/src/qhull/src/libqhullcpp/QhullFacetSet.cpp
+++ /dev/null
@@ -1,147 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetSet.cpp#2 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullFacetSet -- Qhull's linked facets, as a C++ class
-
-#include "libqhullcpp/QhullFacetSet.h"
-
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullVertex.h"
-
-#ifndef QHULL_NO_STL
-using std::vector;
-#endif
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Conversions
-
-// See qt-qhull.cpp for QList conversions
-
-#ifndef QHULL_NO_STL
-std::vector QhullFacetSet::
-toStdVector() const
-{
-    QhullSetIterator i(*this);
-    std::vector vs;
-    while(i.hasNext()){
-        QhullFacet f= i.next();
-        if(isSelectAll() || f.isGood()){
-            vs.push_back(f);
-        }
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#//!\name GetSet
-
-bool QhullFacetSet::
-contains(const QhullFacet &facet) const
-{
-    if(isSelectAll()){
-        return QhullSet::contains(facet);
-    }
-    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
-        QhullFacet f= *i;
-        if(f==facet && f.isGood()){
-            return true;
-        }
-    }
-    return false;
-}//contains
-
-int QhullFacetSet::
-count() const
-{
-    if(isSelectAll()){
-        return QhullSet::count();
-    }
-    int counter= 0;
-    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
-        QhullFacet f= *i;
-        if(f.isGood()){
-            counter++;
-        }
-    }
-    return counter;
-}//count
-
-int QhullFacetSet::
-count(const QhullFacet &facet) const
-{
-    if(isSelectAll()){
-        return QhullSet::count(facet);
-    }
-    int counter= 0;
-    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
-        QhullFacet f= *i;
-        if(f==facet && f.isGood()){
-            counter++;
-        }
-    }
-    return counter;
-}//count
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using orgQhull::QhullFacet;
-using orgQhull::QhullFacetSet;
-
-ostream &
-operator<<(ostream &os, const QhullFacetSet &fs)
-{
-    os << fs.print("");
-    return os;
-}//<begin(); i!=p.facet_set->end(); ++i){
-        const QhullFacet f= *i;
-        if(f.getFacetT()==qh_MERGEridge){
-            os << " MERGE";
-        }else if(f.getFacetT()==qh_DUPLICATEridge){
-            os << " DUP";
-        }else if(p.facet_set->isSelectAll() || f.isGood()){
-            os << " f" << f.id();
-        }
-    }
-    os << endl;
-    return os;
-}//<
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-
-#//!\name Defined here
-    //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
-    class QhullFacetSet;
-    typedef QhullSetIterator QhullFacetSetIterator;
-
-class QhullFacetSet : public QhullSet {
-
-#//!\name Defined here
-public:
-    typedef facetT *   base_type;  // for QhullVertexSet
-
-private:
-#//!\name Fields
-    bool                select_all;   //! True if include bad facets.  Default is false.
-
-public:
-#//!\name Constructor
-                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-                        QhullFacetSet(const Qhull &q, setT *s) : QhullSet(q, s), select_all(false) {}
-                        QhullFacetSet(QhullQh *qqh, setT *s) : QhullSet(qqh, s), select_all(false) {}
-                        //!Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
-                        QhullFacetSet(const QhullFacetSet &other) : QhullSet(other), select_all(other.select_all) {}
-                        //!Assignment copies pointers but not contents.
-    QhullFacetSet &     operator=(const QhullFacetSet &other) { QhullSet::operator=(other); select_all= other.select_all; return *this; }
-
-private:
-                        //!Disable default constructor.  See QhullSetBase
-                        QhullFacetSet();
-public:
-
-#//!\name Conversion
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList   toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
-    countT              count() const;
-    bool                contains(const QhullFacet &f) const;
-    countT              count(const QhullFacet &f) const;
-    bool                isSelectAll() const { return select_all; }
-                        //! operator==() does not depend on isGood()
-    void                selectAll() { select_all= true; }
-    void                selectGood() { select_all= false; }
-
-#//!\name IO
-    // Not same as QhullFacetList#IO.  A QhullFacetSet is a component of a QhullFacetList.
-
-    struct PrintFacetSet{
-        const QhullFacetSet *facet_set;
-        const char *    print_message;  //!< non-null message
-                        PrintFacetSet(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
-    };//PrintFacetSet
-    const PrintFacetSet print(const char *message) const { return PrintFacetSet(message, this); }
-
-    struct PrintIdentifiers{
-        const QhullFacetSet *facet_set;
-        const char *    print_message;  //!< non-null message
-                        PrintIdentifiers(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
-    };//PrintIdentifiers
-    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
-
-};//class QhullFacetSet
-
-}//namespace orgQhull
-
-#//!\name == Global namespace =========================================
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet &fs);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintFacetSet &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintIdentifiers &p);
-
-#endif // QHULLFACETSET_H
diff --git a/src/qhull/src/libqhullcpp/QhullHyperplane.cpp b/src/qhull/src/libqhullcpp/QhullHyperplane.cpp
deleted file mode 100644
index ed5cc4bae..000000000
--- a/src/qhull/src/libqhullcpp/QhullHyperplane.cpp
+++ /dev/null
@@ -1,187 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullHyperplane.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/QhullHyperplane.h"
-
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullPoint.h"
-
-#include 
-
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Constructors
-
-QhullHyperplane::
-QhullHyperplane(const Qhull &q) 
-: hyperplane_coordinates(0)
-, qh_qh(q.qh())
-, hyperplane_offset(0.0)
-, hyperplane_dimension(0)
-{
-}
-
-QhullHyperplane::
-QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) 
-: hyperplane_coordinates(c)
-, qh_qh(q.qh())
-, hyperplane_offset(hyperplaneOffset)
-, hyperplane_dimension(hyperplaneDimension)
-{
-}
-
-#//!\name Conversions
-
-// See qt-qhull.cpp for QList conversions
-
-#ifndef QHULL_NO_STL
-std::vector QhullHyperplane::
-toStdVector() const
-{
-    QhullHyperplaneIterator i(*this);
-    std::vector fs;
-    while(i.hasNext()){
-        fs.push_back(i.next());
-    }
-    fs.push_back(hyperplane_offset);
-    return fs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#//!\name GetSet
-
-//! Return true if equal
-//! If qh_qh defined, tests qh.distanceEpsilon and qh.angleEpsilon
-//! otherwise, tests equal coordinates and offset
-bool QhullHyperplane::
-operator==(const QhullHyperplane &other) const
-{
-    if(hyperplane_dimension!=other.hyperplane_dimension || !hyperplane_coordinates || !other.hyperplane_coordinates){
-        return false;
-    }
-    double d= fabs(hyperplane_offset-other.hyperplane_offset);
-    if(d > (qh_qh ? qh_qh->distanceEpsilon() : 0.0)){
-        return false;
-    }
-    double angle= hyperplaneAngle(other);
-
-    double a= fabs(angle-1.0);
-    if(a > (qh_qh ? qh_qh->angleEpsilon() : 0.0)){
-        return false;
-    }
-    return true;
-}//operator==
-
-#//!\name Methods
-
-//! Return distance from point to hyperplane.
-//!   If greater than zero, the point is above the facet (i.e., outside).
-// qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
-//    Does not support RANDOMdist or logging
-double QhullHyperplane::
-distance(const QhullPoint &p) const
-{
-    const coordT *point= p.coordinates();
-    int dim= p.dimension();
-    QHULL_ASSERT(dim==dimension());
-    const coordT *normal= coordinates();
-    double dist;
-
-    switch (dim){
-  case 2:
-      dist= offset() + point[0] * normal[0] + point[1] * normal[1];
-      break;
-  case 3:
-      dist= offset() + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
-      break;
-  case 4:
-      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
-      break;
-  case 5:
-      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
-      break;
-  case 6:
-      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
-      break;
-  case 7:
-      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
-      break;
-  case 8:
-      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
-      break;
-  default:
-      dist= offset();
-      for (int k=dim; k--; )
-          dist += *point++ * *normal++;
-      break;
-    }
-    return dist;
-}//distance
-
-double QhullHyperplane::
-hyperplaneAngle(const QhullHyperplane &other) const
-{
-    volatile realT result= 0.0;
-    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
-        result= qh_getangle(qh_qh, hyperplane_coordinates, other.hyperplane_coordinates);
-    }
-    qh_qh->NOerrexit= true;
-    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
-    return result;
-}//hyperplaneAngle
-
-double QhullHyperplane::
-norm() const {
-    double d= 0.0;
-    const coordT *c= coordinates();
-    for (int k=dimension(); k--; ){
-        d += *c * *c;
-        ++c;
-    }
-    return sqrt(d);
-}//norm
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::ostream;
-using orgQhull::QhullHyperplane;
-
-#//!\name GetSet<<
-
-ostream &
-operator<<(ostream &os, const QhullHyperplane &p)
-{
-    os << p.print("");
-    return os;
-}
-
-ostream &
-operator<<(ostream &os, const QhullHyperplane::PrintHyperplane &pr)
-{
-    os << pr.print_message;
-    QhullHyperplane p= *pr.hyperplane;
-    const realT *c= p.coordinates();
-    for(int k=p.dimension(); k--; ){
-        realT r= *c++;
-        if(pr.print_message){
-            os << " " << r; // FIXUP QH11010 %8.4g
-        }else{
-            os << " " << r; // FIXUP QH11010 qh_REAL_1
-        }
-    }
-    os << pr.hyperplane_offset_message << " " << p.offset();
-    os << std::endl;
-    return os;
-}//PrintHyperplane
-
diff --git a/src/qhull/src/libqhullcpp/QhullHyperplane.h b/src/qhull/src/libqhullcpp/QhullHyperplane.h
deleted file mode 100644
index 2868ce5c9..000000000
--- a/src/qhull/src/libqhullcpp/QhullHyperplane.h
+++ /dev/null
@@ -1,123 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullHyperplane.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHHYPERPLANE_H
-#define QHHYPERPLANE_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullIterator.h"
-#include "libqhullcpp/QhullQh.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-    class QhullPoint;
-
-#//!\name Defined here
-    //! QhullHyperplane as an offset, dimension, and pointer to coordinates
-    class QhullHyperplane;
-    //! Java-style iterator for QhullHyperplane coordinates
-    class QhullHyperplaneIterator;
-
-class QhullHyperplane { // Similar to QhullPoint
-public:
-#//!\name Subtypes
-    typedef const coordT *                  iterator;
-    typedef const coordT *                  const_iterator;
-    typedef QhullHyperplane::iterator       Iterator;
-    typedef QhullHyperplane::const_iterator ConstIterator;
-
-private:
-#//!\name Fields
-    coordT *            hyperplane_coordinates;  //!< Normal to hyperplane.   facetT.normal is normalized to 1.0
-    QhullQh *           qh_qh;                  //!< qhT for distanceEpsilon() in operator==
-    coordT              hyperplane_offset;      //!< Distance from hyperplane to origin
-    int                 hyperplane_dimension;   //!< Dimension of hyperplane
-
-#//!\name Construct
-public:
-                        QhullHyperplane() : hyperplane_coordinates(0), qh_qh(0), hyperplane_offset(0.0), hyperplane_dimension(0) {}
-    explicit            QhullHyperplane(const Qhull &q);
-                        QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset);
-    explicit            QhullHyperplane(QhullQh *qqh) : hyperplane_coordinates(0), qh_qh(qqh), hyperplane_offset(0.0), hyperplane_dimension(0) {}
-                        QhullHyperplane(QhullQh *qqh, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), qh_qh(qqh), hyperplane_offset(hyperplaneOffset), hyperplane_dimension(hyperplaneDimension) {}
-                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for return by value and parameter passing.
-                        QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), qh_qh(other.qh_qh), hyperplane_offset(other.hyperplane_offset), hyperplane_dimension(other.hyperplane_dimension) {}
-                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for vector
-    QhullHyperplane &   operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; qh_qh= other.qh_qh; hyperplane_offset= other.hyperplane_offset; hyperplane_dimension= other.hyperplane_dimension; return *this; }
-                        ~QhullHyperplane() {}
-
-#//!\name Conversions --
-//! Includes offset at end
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList       toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-public:
-    const coordT *      coordinates() const { return hyperplane_coordinates; }
-    coordT *            coordinates() { return hyperplane_coordinates; }
-    void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
-    //! Creates an alias to other using the same qh_qh
-    void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
-    int                 dimension() const { return hyperplane_dimension; }
-    bool                isValid() const { return hyperplane_coordinates!=0 && hyperplane_dimension>0; }
-    coordT              offset() const { return hyperplane_offset; }
-    bool                operator==(const QhullHyperplane &other) const;
-    bool                operator!=(const QhullHyperplane &other) const { return !operator==(other); }
-    const coordT &      operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx
-#include 
-#include 
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! Only QHULL_DECLARE_SEQUENTIAL_ITERATOR is used in libqhullcpp.  The others need further development
-    //! QHULL_DECLARE_SEQUENTIAL_ITERATOR(C) -- Declare a Java-style iterator
-    //! QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C) -- Declare a mutable Java-style iterator
-    //! QHULL_DECLARE_SET_ITERATOR(C) -- Declare a set iterator
-    //! QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) -- Declare a mutable set iterator
-    //! Derived from Qt/core/tools/qiterator.h and qset_r.h/FOREACHsetelement_()
-
-// Stores C* as done in Mutable...  Assumes the container is not deleted.
-// C::const_iterator is an STL-style iterator that returns T&
-#define QHULL_DECLARE_SEQUENTIAL_ITERATOR(C, T) \
-    \
-    class C##Iterator \
-    { \
-        typedef C::const_iterator const_iterator; \
-        const C *c; \
-        const_iterator i; \
-        public: \
-        inline C##Iterator(const C &container) \
-        : c(&container), i(c->constBegin()) {} \
-        inline C##Iterator &operator=(const C &container) \
-        { c = &container; i = c->constBegin(); return *this; } \
-        inline void toFront() { i = c->constBegin(); } \
-        inline void toBack() { i = c->constEnd(); } \
-        inline bool hasNext() const { return i != c->constEnd(); } \
-        inline const T &next() { return *i++; } \
-        inline const T &peekNext() const { return *i; } \
-        inline bool hasPrevious() const { return i != c->constBegin(); } \
-        inline const T &previous() { return *--i; } \
-        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
-        inline bool findNext(const T &t) \
-        { while (i != c->constEnd()) if (*i++ == t) return true; return false; } \
-        inline bool findPrevious(const T &t) \
-        { while (i != c->constBegin()) if (*(--i) == t) return true; \
-        return false;  } \
-    };//C##Iterator
-
-// Remove setShareable() from Q_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR
-// Uses QHULL_ASSERT (assert.h)
-// Duplicated in MutablePointIterator without insert or remove
-// Not used in libqhullcpp.  See Coordinates.h
-#define QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C, T) \
-    class Mutable##C##Iterator \
-    { \
-        typedef C::iterator iterator; \
-        typedef C::const_iterator const_iterator; \
-        C *c; \
-        iterator i, n; \
-        inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
-        public: \
-        inline Mutable##C##Iterator(C &container) \
-        : c(&container) \
-        { i = c->begin(); n = c->end(); } \
-        inline ~Mutable##C##Iterator() \
-        {} \
-        inline Mutable##C##Iterator &operator=(C &container) \
-        { c = &container; \
-        i = c->begin(); n = c->end(); return *this; } \
-        inline void toFront() { i = c->begin(); n = c->end(); } \
-        inline void toBack() { i = c->end(); n = i; } \
-        inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
-        inline T &next() { n = i++; return *n; } \
-        inline T &peekNext() const { return *i; } \
-        inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
-        inline T &previous() { n = --i; return *n; } \
-        inline T &peekPrevious() const { iterator p = i; return *--p; } \
-        inline void remove() \
-        { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
-        inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
-        inline T &value() { QHULL_ASSERT(item_exists()); return *n; } \
-        inline const T &value() const { QHULL_ASSERT(item_exists()); return *n; } \
-        inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
-        inline bool findNext(const T &t) \
-        { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
-        inline bool findPrevious(const T &t) \
-        { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
-        n = c->end(); return false;  } \
-    };//Mutable##C##Iterator
-
-// Not used in libqhullcpp.
-#define QHULL_DECLARE_SET_ITERATOR(C) \
-\
-    template  \
-    class Qhull##C##Iterator \
-    { \
-        typedef typename Qhull##C::const_iterator const_iterator; \
-        Qhull##C c; \
-        const_iterator i; \
-    public: \
-        inline Qhull##C##Iterator(const Qhull##C &container) \
-        : c(container), i(c.constBegin()) {} \
-        inline Qhull##C##Iterator &operator=(const Qhull##C &container) \
-        { c = container; i = c.constBegin(); return *this; } \
-        inline void toFront() { i = c.constBegin(); } \
-        inline void toBack() { i = c.constEnd(); } \
-        inline bool hasNext() const { return i != c.constEnd(); } \
-        inline const T &next() { return *i++; } \
-        inline const T &peekNext() const { return *i; } \
-        inline bool hasPrevious() const { return i != c.constBegin(); } \
-        inline const T &previous() { return *--i; } \
-        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
-        inline bool findNext(const T &t) \
-        { while (i != c.constEnd()) if (*i++ == t) return true; return false; } \
-        inline bool findPrevious(const T &t) \
-        { while (i != c.constBegin()) if (*(--i) == t) return true; \
-        return false;  } \
-    };//Qhull##C##Iterator
-
-// Not used in libqhullcpp.
-#define QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) \
-\
-template  \
-class QhullMutable##C##Iterator \
-{ \
-    typedef typename Qhull##C::iterator iterator; \
-    typedef typename Qhull##C::const_iterator const_iterator; \
-    Qhull##C *c; \
-    iterator i, n; \
-    inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
-public: \
-    inline Mutable##C##Iterator(Qhull##C &container) \
-        : c(&container) \
-    { c->setSharable(false); i = c->begin(); n = c->end(); } \
-    inline ~Mutable##C##Iterator() \
-    { c->setSharable(true); } \
-    inline Mutable##C##Iterator &operator=(Qhull##C &container) \
-    { c->setSharable(true); c = &container; c->setSharable(false); \
-      i = c->begin(); n = c->end(); return *this; } \
-    inline void toFront() { i = c->begin(); n = c->end(); } \
-    inline void toBack() { i = c->end(); n = i; } \
-    inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
-    inline T &next() { n = i++; return *n; } \
-    inline T &peekNext() const { return *i; } \
-    inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
-    inline T &previous() { n = --i; return *n; } \
-    inline T &peekPrevious() const { iterator p = i; return *--p; } \
-    inline void remove() \
-    { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
-    inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
-    inline T &value() { Q_ASSERT(item_exists()); return *n; } \
-    inline const T &value() const { Q_ASSERT(item_exists()); return *n; } \
-    inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
-    inline bool findNext(const T &t) \
-    { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
-    inline bool findPrevious(const T &t) \
-    { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
-      n = c->end(); return false;  } \
-};//QhullMutable##C##Iterator
-
-}//namespace orgQhull
-
-#endif // QHULLITERATOR_H
-
diff --git a/src/qhull/src/libqhullcpp/QhullLinkedList.h b/src/qhull/src/libqhullcpp/QhullLinkedList.h
deleted file mode 100644
index d4caf52c1..000000000
--- a/src/qhull/src/libqhullcpp/QhullLinkedList.h
+++ /dev/null
@@ -1,388 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullLinkedList.h#7 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLLINKEDLIST_H
-#define QHULLLINKEDLIST_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullError.h"
-
-#include   // ptrdiff_t, size_t
-
-#ifdef QHULL_USES_QT
-#include 
-#endif
-
-#ifndef QHULL_NO_STL
-#include 
-#include 
-#include 
-#endif
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! QhullLinkedList -- A linked list modeled on QLinkedList.
-    //!   T is an opaque type with T(B *b), b=t.getBaseT(), t=t.next(), and t=t.prev().  The end node is a sentinel.
-    //!   QhullQh/qhT owns the contents.
-    //!   QhullLinkedList does not define erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList()
-    //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull_r.h/FORALLfacets_()
-    //! QhullLinkedList::const_iterator -- STL-style iterator
-    //! QhullLinkedList::iterator -- STL-style iterator
-    //! QhullLinkedListIterator -- Java-style iterator
-    //!   Derived from Qt/core/tools/qiterator.h
-    //!   Works with Qt's foreach keyword [Qt/src/corelib/global/qglobal.h]
-
-template 
-class QhullLinkedList
-{
-#//!\name Defined here
-public:
-    class const_iterator;
-    class iterator;
-    typedef const_iterator  ConstIterator;
-    typedef iterator    Iterator;
-    typedef ptrdiff_t   difference_type;
-    typedef countT      size_type;
-    typedef T           value_type;
-    typedef const value_type *const_pointer;
-    typedef const value_type &const_reference;
-    typedef value_type *pointer;
-    typedef value_type &reference;
-
-#//!\name Fields
-private:
-    T                   begin_node;
-    T                   end_node;     //! Sentinel node at end of list
-
-#//!\name Constructors
-public:
-                        QhullLinkedList(T b, T e) : begin_node(b), end_node(e) {}
-                        //! Copy constructor copies begin_node and end_node, but not the list elements.  Needed for return by value and parameter passing.
-                        QhullLinkedList(const QhullLinkedList &other) : begin_node(other.begin_node), end_node(other.end_node) {}
-                        //! Copy assignment copies begin_node and end_node, but not the list elements.
-                        QhullLinkedList & operator=(const QhullLinkedList &other) { begin_node= other.begin_node; end_node= other.end_node; return *this; }
-                        ~QhullLinkedList() {}
-
-private:
-                        //!disabled since a sentinel must be allocated as the private type
-                        QhullLinkedList() {}
-
-public:
-
-#//!\name Conversions
-#ifndef QHULL_NO_STL
-    std::vector      toStdVector() const;
-#endif
-#ifdef QHULL_USES_QT
-    QList            toQList() const;
-#endif
-
-#//!\name GetSet
-    countT              count() const;
-                        //count(t) under #//!\name Search
-    bool                isEmpty() const { return (begin_node==end_node); }
-    bool                operator==(const QhullLinkedList &o) const;
-    bool                operator!=(const QhullLinkedList &o) const { return !operator==(o); }
-    size_t              size() const { return count(); }
-
-#//!\name Element access
-    //! For back() and last(), return T instead of T& (T is computed)
-    const T             back() const { return last(); }
-    T                   back() { return last(); }
-    const T &           first() const { QHULL_ASSERT(!isEmpty()); return begin_node; }
-    T &                 first() { QHULL_ASSERT(!isEmpty()); return begin_node; }
-    const T &           front() const { return first(); }
-    T &                 front() { return first(); }
-    const T             last() const { QHULL_ASSERT(!isEmpty()); return *--end(); }
-    T                   last() { QHULL_ASSERT(!isEmpty()); return *--end(); }
-
-#//!\name Modify -- Allocation of opaque types not implemented.
-
-#//!\name Search
-    bool                contains(const T &t) const;
-    countT              count(const T &t) const;
-
-#//!\name Iterator
-    iterator            begin() { return begin_node; }
-    const_iterator      begin() const { return begin_node; }
-    const_iterator      constBegin() const { return begin_node; }
-    const_iterator      constEnd() const { return end_node; }
-    iterator            end() { return end_node; }
-    const_iterator      end() const { return end_node; }
-
-    class iterator {
-
-    private:
-        T               i;
-        friend class const_iterator;
-
-    public:
-        typedef std::bidirectional_iterator_tag  iterator_category;
-        typedef T           value_type;
-        typedef value_type *pointer;
-        typedef value_type &reference;
-        typedef ptrdiff_t   difference_type;
-
-                        iterator() : i() {}
-                        iterator(const T &t) : i(t) {}  //!< Automatic conversion to iterator
-                        iterator(const iterator &o) : i(o.i) {}
-        iterator &      operator=(const iterator &o) { i= o.i; return *this; }
-
-        const T &       operator*() const { return i; }
-        T &             operator*() { return i; }
-        // Do not define operator[]
-        const T *       operator->() const { return &i; }
-        T *             operator->() { return &i; }
-        bool            operator==(const iterator &o) const { return i == o.i; }
-        bool            operator!=(const iterator &o) const { return !operator==(o); }
-        bool            operator==(const const_iterator &o) const { return i==reinterpret_cast(o).i; }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-        iterator &      operator++() { i= i.next(); return *this; }
-        iterator        operator++(int) { iterator o= i; i= i.next(); return o; }
-        iterator &      operator--() { i= i.previous(); return *this; }
-        iterator        operator--(int) { iterator o= i; i= i.previous(); return o; }
-        iterator        operator+(int j) const;
-        iterator        operator-(int j) const { return operator+(-j); }
-        iterator &      operator+=(int j) { return (*this= *this + j); }
-        iterator &      operator-=(int j) { return (*this= *this - j); }
-    };//QhullLinkedList::iterator
-
-    class const_iterator {
-
-    private:
-        T               i;
-
-    public:
-        typedef std::bidirectional_iterator_tag  iterator_category;
-        typedef T                 value_type;
-        typedef const value_type *pointer;
-        typedef const value_type &reference;
-        typedef ptrdiff_t         difference_type;
-
-                        const_iterator() : i() {}
-                        const_iterator(const T &t) : i(t) {}  //!< Automatic conversion to const_iterator
-                        const_iterator(const iterator &o) : i(o.i) {}
-                        const_iterator(const const_iterator &o) : i(o.i) {}
-        const_iterator &operator=(const const_iterator &o) { i= o.i; return *this; }
-
-        const T &       operator*() const { return i; }
-        const T *       operator->() const { return i; }
-        bool            operator==(const const_iterator &o) const { return i == o.i; }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-                        // No comparisons or iterator diff
-        const_iterator &operator++() { i= i.next(); return *this; }
-        const_iterator  operator++(int) { const_iterator o= i; i= i.next(); return o; }
-        const_iterator &operator--() { i= i.previous(); return *this; }
-        const_iterator  operator--(int) { const_iterator o= i; i= i.previous(); return o; }
-        const_iterator  operator+(int j) const;
-        const_iterator  operator-(int j) const { return operator+(-j); }
-        const_iterator &operator+=(int j) { return (*this= *this + j); }
-        const_iterator &operator-=(int j) { return (*this= *this - j); }
-    };//QhullLinkedList::const_iterator
-
-};//QhullLinkedList
-
-template 
-class QhullLinkedListIterator // FIXUP QH11016 define QhullMutableLinkedListIterator
-{
-    typedef typename QhullLinkedList::const_iterator const_iterator;
-    const QhullLinkedList *c;
-    const_iterator      i;
-
-public:
-                        QhullLinkedListIterator(const QhullLinkedList &container) : c(&container), i(c->constBegin()) {}
-    QhullLinkedListIterator & operator=(const QhullLinkedList &container) { c= &container; i= c->constBegin(); return *this; }
-    bool                findNext(const T &t);
-    bool                findPrevious(const T &t);
-    bool                hasNext() const { return i != c->constEnd(); }
-    bool                hasPrevious() const { return i != c->constBegin(); }
-    T                   next() { return *i++; }
-    T                   peekNext() const { return *i; }
-    T                   peekPrevious() const { const_iterator p= i; return *--p; }
-    T                   previous() { return *--i; }
-    void                toFront() { i= c->constBegin(); }
-    void                toBack() { i= c->constEnd(); }
-};//QhullLinkedListIterator
-
-#//!\name == Definitions =========================================
-
-#//!\name Conversion
-
-#ifndef QHULL_NO_STL
-template 
-std::vector QhullLinkedList::
-toStdVector() const
-{
-    std::vector tmp;
-    std::copy(constBegin(), constEnd(), std::back_inserter(tmp));
-    return tmp;
-}//toStdVector
-#endif
-
-#ifdef QHULL_USES_QT
-template 
-QList  QhullLinkedList::
-toQList() const
-{
-    QhullLinkedListIterator i(*this);
-    QList ls;
-    while(i.hasNext()){
-        ls.append(i.next());
-    }
-    return ls;
-}//toQList
-#endif
-
-#//!\name GetSet
-
-template 
-countT QhullLinkedList::
-count() const
-{
-    const_iterator i= begin_node;
-    countT c= 0;
-    while(i != end_node){
-        c++;
-        i++;
-    }
-    return c;
-}//count
-
-#//!\name Search
-
-template 
-bool QhullLinkedList::
-contains(const T &t) const
-{
-    const_iterator i= begin_node;
-    while(i != end_node){
-        if(i==t){
-            return true;
-        }
-        i++;
-    }
-    return false;
-}//contains
-
-template 
-countT QhullLinkedList::
-count(const T &t) const
-{
-    const_iterator i= begin_node;
-    countT c= 0;
-    while(i != end_node){
-        if(i==t){
-            c++;
-        }
-        i++;
-    }
-    return c;
-}//count
-
-template 
-bool QhullLinkedList::
-operator==(const QhullLinkedList &l) const
-{
-    if(begin_node==l.begin_node){
-        return (end_node==l.end_node);
-    }
-    T i= begin_node;
-    T il= l.begin_node;
-    while(i != end_node){
-        if(i != il){
-            return false;
-        }
-        i= static_cast(i.next());
-        il= static_cast(il.next());
-    }
-    if(il != l.end_node){
-        return false;
-    }
-    return true;
-}//operator==
-
-#//!\name Iterator
-
-template 
-typename QhullLinkedList::iterator  QhullLinkedList::iterator::
-operator+(int j) const
-{
-    T n= i;
-    if(j>0){
-        while(j--){
-            n= n.next();
-        }
-    }else{
-        while(j++){
-            n= n.previous();
-        }
-    }
-    return iterator(n);
-}//operator+
-
-template 
-typename QhullLinkedList::const_iterator  QhullLinkedList::const_iterator::
-operator+(int j) const
-{
-    T n= i;
-    if(j>0){
-        while(j--){
-            n= n.next();
-        }
-    }else{
-        while(j++){
-            n= n.previous();
-        }
-    }
-    return const_iterator(n);
-}//operator+
-
-#//!\name QhullLinkedListIterator
-
-template 
-bool QhullLinkedListIterator::
-findNext(const T &t)
-{
-    while(i != c->constEnd()){
-        if (*i++ == t){
-            return true;
-        }
-    }
-    return false;
-}//findNext
-
-template 
-bool QhullLinkedListIterator::
-findPrevious(const T &t)
-{
-    while(i!=c->constBegin()){
-        if(*(--i)==t){
-            return true;
-        }
-    }
-    return false;
-}//findNext
-
-}//namespace orgQhull
-
-#//!\name Global
-
-template 
-std::ostream &
-operator<<(std::ostream &os, const orgQhull::QhullLinkedList &qs)
-{
-    typename orgQhull::QhullLinkedList::const_iterator i;
-    for(i= qs.begin(); i != qs.end(); ++i){
-        os << *i;
-    }
-    return os;
-}//operator<<
-
-#endif // QHULLLINKEDLIST_H
-
diff --git a/src/qhull/src/libqhullcpp/QhullPoint.cpp b/src/qhull/src/libqhullcpp/QhullPoint.cpp
deleted file mode 100644
index f5e912460..000000000
--- a/src/qhull/src/libqhullcpp/QhullPoint.cpp
+++ /dev/null
@@ -1,203 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoint.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/QhullPoint.h"
-
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/Qhull.h"
-
-#include 
-#include 
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Constructors
-
-
-QhullPoint::
-QhullPoint(const Qhull &q) 
-: point_coordinates(0)
-, qh_qh(q.qh())
-, point_dimension(q.hullDimension())
-{
-}//QhullPoint
-
-QhullPoint::
-QhullPoint(const Qhull &q, coordT *c) 
-: point_coordinates(c)
-, qh_qh(q.qh())
-, point_dimension(q.hullDimension())
-{
-    QHULL_ASSERT(q.hullDimension()>0);
-}//QhullPoint dim, coordT
-
-QhullPoint::
-QhullPoint(const Qhull &q, int pointDimension, coordT *c) 
-: point_coordinates(c)
-, qh_qh(q.qh())
-, point_dimension(pointDimension)
-{
-}//QhullPoint dim, coordT
-
-//! QhullPoint of Coordinates with point_dimension==c.count()
-QhullPoint::
-QhullPoint(const Qhull &q, Coordinates &c) 
-: point_coordinates(c.data())
-, qh_qh(q.qh())
-, point_dimension(c.count())
-{
-}//QhullPoint Coordinates
-
-#//!\name Conversions
-
-// See qt-qhull.cpp for QList conversion
-
-#ifndef QHULL_NO_STL
-std::vector QhullPoint::
-toStdVector() const
-{
-    QhullPointIterator i(*this);
-    std::vector vs;
-    while(i.hasNext()){
-        vs.push_back(i.next());
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#//!\name GetSet
-
-//! QhullPoint is equal if it has the same address and dimension
-//! If !qh_qh, returns true if dimension and coordinates are equal
-//! If qh_qh, returns true if the distance between points is less than qh_qh->distanceEpsilon()
-//!\todo Compares distance with distance-to-hyperplane (distanceEpsilon).   Is that correct?
-bool QhullPoint::
-operator==(const QhullPoint &other) const
-{
-    if(point_dimension!=other.point_dimension){
-        return false;
-    }
-    const coordT *c= point_coordinates;
-    const coordT *c2= other.point_coordinates;
-    if(c==c2){
-        return true;
-    }
-    if(!c || !c2){
-        return false;
-    }
-    if(!qh_qh || qh_qh->hull_dim==0){
-        for(int k= point_dimension; k--; ){
-            if(*c++ != *c2++){
-                return false;
-            }
-        }
-        return true;
-    }
-    double dist2= 0.0;
-    for(int k= point_dimension; k--; ){
-        double diff= *c++ - *c2++;
-        dist2 += diff*diff;
-    }
-    dist2= sqrt(dist2);
-    return (dist2 < qh_qh->distanceEpsilon());
-}//operator==
-
-#//!\name Methods
-
-//! Return distance between two points.
-double QhullPoint::
-distance(const QhullPoint &p) const
-{
-    const coordT *c= point_coordinates;
-    const coordT *c2= p.point_coordinates;
-    int dim= point_dimension;
-    if(dim!=p.point_dimension){
-        throw QhullError(10075, "QhullPoint error: Expecting dimension %d for distance().  Got %d", dim, p.point_dimension);
-    }
-    if(!c || !c2){
-        throw QhullError(10076, "QhullPoint error: Cannot compute distance() for undefined point");
-    }
-    double dist;
-
-    switch(dim){
-  case 2:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]);
-      break;
-  case 3:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]);
-      break;
-  case 4:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]);
-      break;
-  case 5:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]);
-      break;
-  case 6:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]);
-      break;
-  case 7:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]);
-      break;
-  case 8:
-      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]) + (c[7]-c2[7])*(c[7]-c2[7]);
-      break;
-  default:
-      dist= 0.0;
-      for(int k=dim; k--; ){
-          dist += (*c - *c2) * (*c - *c2);
-          ++c;
-          ++c2;
-      }
-      break;
-    }
-    return sqrt(dist);
-}//distance
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::ostream;
-using orgQhull::QhullPoint;
-
-//! Same as qh_printpointid [io.c]
-ostream &
-operator<<(ostream &os, const QhullPoint::PrintPoint &pr)
-{
-    QhullPoint p= *pr.point; 
-    countT i= p.id();
-    if(pr.point_message){
-        if(*pr.point_message){
-            os << pr.point_message << " ";
-        }
-        if(pr.with_identifier && (i!=qh_IDunknown) && (i!=qh_IDnone)){
-            os << "p" << i << ": ";
-        }
-    }
-    const realT *c= p.coordinates();
-    for(int k=p.dimension(); k--; ){
-        realT r= *c++;
-        if(pr.point_message){
-            os << " " << r; // FIXUP QH11010 %8.4g
-        }else{
-            os << " " << r; // FIXUP QH11010 qh_REAL_1
-        }
-    }
-    os << std::endl;
-    return os;
-}//printPoint
-
-ostream & 
-operator<<(ostream &os, const QhullPoint &p)
-{
-    os << p.print(""); 
-    return os;
-}//operator<<
diff --git a/src/qhull/src/libqhullcpp/QhullPoint.h b/src/qhull/src/libqhullcpp/QhullPoint.h
deleted file mode 100644
index 17f94ab36..000000000
--- a/src/qhull/src/libqhullcpp/QhullPoint.h
+++ /dev/null
@@ -1,136 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoint.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHPOINT_H
-#define QHPOINT_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullIterator.h"
-#include "libqhullcpp/QhullQh.h"
-#include "libqhullcpp/Coordinates.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    class QhullPoint;  //!<  QhullPoint as a pointer and dimension to shared memory
-    class QhullPointIterator; //!< Java-style iterator for QhullPoint coordinates
-
-#//!\name Used here
-    class Qhull;
-
-//! A QhullPoint is a dimension and an array of coordinates.
-//! With Qhull/QhullQh, a QhullPoint has an identifier.  Point equality is relative to qh.distanceEpsilon
-class QhullPoint {
-
-#//!\name Iterators
-public:
-    typedef coordT *                    base_type;  // for QhullPointSet
-    typedef const coordT *              iterator;
-    typedef const coordT *              const_iterator;
-    typedef QhullPoint::iterator        Iterator;
-    typedef QhullPoint::const_iterator  ConstIterator;
-
-#//!\name Fields
-protected: // For QhullPoints::iterator, QhullPoints::const_iterator
-    coordT *            point_coordinates;  //!< Pointer to first coordinate,   0 if undefined
-    QhullQh *           qh_qh;              //!< qhT for this instance of Qhull.  0 if undefined.
-                                            //!< operator==() returns true if points within sqrt(qh_qh->distanceEpsilon())
-                                            //!< If !qh_qh, id() is -3, and operator==() requires equal coordinates
-    int                 point_dimension;    //!< Default dimension is qh_qh->hull_dim
-public:
-
-#//!\name Constructors
-    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
-    //! If Qhull/QhullQh is not initialized, then QhullPoint.dimension() is zero unless explicitly set
-    //! Cannot define QhullPoints(int pointDimension) since it is ambiguous with QhullPoints(QhullQh *qqh)
-                        QhullPoint() : point_coordinates(0), qh_qh(0), point_dimension(0) {}
-                        QhullPoint(int pointDimension, coordT *c) : point_coordinates(c), qh_qh(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>0); }
-    explicit            QhullPoint(const Qhull &q);
-                        QhullPoint(const Qhull &q, coordT *c);
-                        QhullPoint(const Qhull &q, Coordinates &c);
-                        QhullPoint(const Qhull &q, int pointDimension, coordT *c);
-    explicit            QhullPoint(QhullQh *qqh) : point_coordinates(0), qh_qh(qqh), point_dimension(qqh->hull_dim) {}
-                        QhullPoint(QhullQh *qqh, coordT *c) : point_coordinates(c), qh_qh(qqh), point_dimension(qqh->hull_dim) { QHULL_ASSERT(qqh->hull_dim>0); }
-                        QhullPoint(QhullQh *qqh, Coordinates &c) : point_coordinates(c.data()), qh_qh(qqh), point_dimension(c.count()) {}
-                        QhullPoint(QhullQh *qqh, int pointDimension, coordT *c) : point_coordinates(c), qh_qh(qqh), point_dimension(pointDimension) {}
-                        //! Creates an alias.  Does not make a deep copy of the point.  Needed for return by value and parameter passing.
-                        QhullPoint(const QhullPoint &other) : point_coordinates(other.point_coordinates), qh_qh(other.qh_qh), point_dimension(other.point_dimension) {}
-                        //! Creates an alias.  Does not make a deep copy of the point.  Needed for vector
-    QhullPoint &        operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; qh_qh= other.qh_qh; point_dimension= other.point_dimension; return *this; }
-                        ~QhullPoint() {}
-
-
-#//!\name Conversions
-
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList       toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-public:
-    const coordT *      coordinates() const { return point_coordinates; }  //!< 0 if undefined
-    coordT *            coordinates() { return point_coordinates; }        //!< 0 if undefined
-    void                defineAs(coordT *c) { QHULL_ASSERT(point_dimension>0); point_coordinates= c; }
-    void                defineAs(int pointDimension, coordT *c) { QHULL_ASSERT(pointDimension>=0); point_coordinates= c; point_dimension= pointDimension; }
-    void                defineAs(QhullPoint &other) { point_coordinates= other.point_coordinates; qh_qh= other.qh_qh; point_dimension= other.point_dimension; }
-    int                 dimension() const { return point_dimension; }
-    coordT *            getBaseT() const { return point_coordinates; } // for QhullPointSet
-    countT              id() const { return qh_pointid(qh_qh, point_coordinates); } // NOerrors
-    bool                isValid() const { return (point_coordinates!=0 && point_dimension>0); };
-    bool                operator==(const QhullPoint &other) const;
-    bool                operator!=(const QhullPoint &other) const { return ! operator==(other); }
-    const coordT &      operator[](int idx) const { QHULL_ASSERT(point_coordinates!=0 && idx>=0 && idx=0 && idx
-#include 
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-// Implemented via QhullSet.h
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using orgQhull::QhullPoint;
-using orgQhull::QhullPointSet;
-using orgQhull::QhullPointSetIterator;
-
-ostream &
-operator<<(ostream &os, const QhullPointSet::PrintIdentifiers &pr)
-{
-    os << pr.print_message;
-    const QhullPointSet s= *pr.point_set;
-    QhullPointSetIterator i(s);
-    while(i.hasNext()){
-        if(i.hasPrevious()){
-            os << " ";
-        }
-        const QhullPoint point= i.next();
-        countT id= point.id();
-        os << "p" << id;
-
-    }
-    os << endl;
-    return os;
-}//PrintIdentifiers
-
-ostream &
-operator<<(ostream &os, const QhullPointSet::PrintPointSet &pr)
-{
-    os << pr.print_message;
-    const QhullPointSet s= *pr.point_set;
-    for(QhullPointSet::const_iterator i=s.begin(); i != s.end(); ++i){
-        const QhullPoint point= *i;
-        os << point;
-    }
-    return os;
-}//printPointSet
-
-
diff --git a/src/qhull/src/libqhullcpp/QhullPointSet.h b/src/qhull/src/libqhullcpp/QhullPointSet.h
deleted file mode 100644
index 8562e170e..000000000
--- a/src/qhull/src/libqhullcpp/QhullPointSet.h
+++ /dev/null
@@ -1,77 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullPointSet.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLPOINTSET_H
-#define QHULLPOINTSET_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullSet.h"
-#include "libqhullcpp/QhullPoint.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-    class QhullPoint;
-
-#//!\name Defined here
-    //! QhullPointSet -- a set of coordinate pointers with input dimension
-    // with const_iterator and iterator
-    class QhullPointSet;
-
-class QhullPointSet : public QhullSet {
-
-private:
-#//!\name Fields
-    // no fields
-public:
-
-#//!\name Construct
-                        QhullPointSet(const Qhull &q, setT *s) : QhullSet(q, s) {}
-                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-                        QhullPointSet(QhullQh *qqh, setT *s) : QhullSet(qqh, s) {}
-                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullPointSet(const QhullPointSet &other) : QhullSet(other) {}
-                        //!Assignment copies pointers but not contents.
-    QhullPointSet &     operator=(const QhullPointSet &other) { QhullSet::operator=(other); return *this; }
-                        ~QhullPointSet() {}
-
-                        //!Default constructor disabled.
-private:
-                        QhullPointSet();
-public:
-
-#//!\name IO
-    struct PrintIdentifiers{
-        const QhullPointSet *point_set;
-        const char *    print_message; //!< non-null message
-        PrintIdentifiers(const char *message, const QhullPointSet *s) : point_set(s), print_message(message) {}
-    };//PrintIdentifiers
-    PrintIdentifiers printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
-
-    struct PrintPointSet{
-        const QhullPointSet *point_set;
-        const char *    print_message;  //!< non-null message
-        PrintPointSet(const char *message, const QhullPointSet &s) : point_set(&s), print_message(message) {}
-    };//PrintPointSet
-    PrintPointSet       print(const char *message) const { return PrintPointSet(message, *this); }
-
-};//QhullPointSet
-
-typedef QhullSetIterator  QhullPointSetIterator;
-
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintIdentifiers &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintPointSet &pr);
-
-#endif // QHULLPOINTSET_H
diff --git a/src/qhull/src/libqhullcpp/QhullPoints.cpp b/src/qhull/src/libqhullcpp/QhullPoints.cpp
deleted file mode 100644
index 2320b5007..000000000
--- a/src/qhull/src/libqhullcpp/QhullPoints.cpp
+++ /dev/null
@@ -1,320 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoints.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/QhullPoints.h"
-
-#include "libqhullcpp/Qhull.h"
-
-#include 
-
-#ifndef QHULL_NO_STL
-#include 
-#endif
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Constructors
-
-QhullPoints::
-QhullPoints(const Qhull &q)
-: point_first(0)
-, point_end(0)
-, qh_qh(q.qh())
-, point_dimension(q.hullDimension())
-{
-}//QhullPoints Qhull
-
-QhullPoints::
-QhullPoints(const Qhull &q, countT coordinateCount2, coordT *c)
-: point_first(c)
-, point_end(c+coordinateCount2)
-, qh_qh(q.qh())
-, point_dimension(q.hullDimension())
-{
-    QHULL_ASSERT(q.hullDimension());
-    QHULL_ASSERT(coordinateCount2>=0);
-}//QhullPoints Qhull dim
-
-QhullPoints::
-QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c)
-: point_first(c)
-, point_end(c+coordinateCount2)
-, qh_qh(q.qh())
-, point_dimension(pointDimension)
-{
-    QHULL_ASSERT(pointDimension>=0);
-    QHULL_ASSERT(coordinateCount2>=0);
-}//QhullPoints Qhull dim coordT
-
-QhullPoints::
-QhullPoints(QhullQh *qqh, int pointDimension, countT coordinateCount2, coordT *c)
-: point_first(c)
-, point_end(c+coordinateCount2)
-, qh_qh(qqh)
-, point_dimension(pointDimension)
-{
-    QHULL_ASSERT(pointDimension>=0);
-    QHULL_ASSERT(coordinateCount2>=0);
-}//QhullPoints QhullQh dim coordT
-
-#//!\name Conversions
-// See qt-qhull.cpp for QList conversion
-
-#ifndef QHULL_NO_STL
-std::vector QhullPoints::
-toStdVector() const
-{
-    QhullPointsIterator i(*this);
-    std::vector vs;
-    while(i.hasNext()){
-        vs.push_back(i.next());
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#//!\name GetSet
-
-countT QhullPoints::
-extraCoordinatesCount() const
-{
-    if(point_dimension>0){
-        return (countT)((point_end-point_first)%(size_t)point_dimension);
-    }
-    return 0;
-}//extraCoordinatesCount
-
-//! QhullPoints is equal if the same address, or if the coordinates are identical
-//! Use QhullPoint.operator==() for DISTround equality
-bool QhullPoints::
-operator==(const QhullPoints &other) const
-{
-    if((point_end-point_first) != (other.point_end-other.point_first)){
-        return false;
-    }
-    if(point_dimension!=other.point_dimension){
-        return false;
-    }
-    if(point_first==other.point_first){
-        return true;
-    }
-    if(!qh_qh || qh_qh->hull_dim==0){
-        const coordT *c= point_first;
-        const coordT *c2= other.point_first;
-        while(chull_dim : 0);
-    point_first= 0;
-    point_end= 0;
-}//resetQhullQh
-
-QhullPoint QhullPoints::
-value(countT idx) const
-{
-    QhullPoint p(qh_qh);
-    if(idx>=0 && idx=0 && idx=n){
-        n= 0;
-    }else if(length<0 || idx+length>=n){
-        n -= idx;
-    }else{
-        n -= idx+length;
-    }
-    return QhullPoints(qh_qh, point_dimension, n*point_dimension, point_first+idx*point_dimension);
-}//mid
-
-#//!\name QhullPointsIterator
-
-bool QhullPointsIterator::
-findNext(const QhullPoint &p)
-{
-    while(i!=ps->constEnd()){
-        if(*i++ == p){
-            return true;
-        }
-    }
-    return false;
-}//findNext
-
-bool QhullPointsIterator::
-findPrevious(const QhullPoint &p)
-{
-    while(i!=ps->constBegin()){
-        if(*--i == p){
-            return true;
-        }
-    }
-    return false;
-}//findPrevious
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::ostream;
-using orgQhull::QhullPoint;
-using orgQhull::QhullPoints;
-using orgQhull::QhullPointsIterator;
-
-ostream &
-operator<<(ostream &os, const QhullPoints &p)
-{
-    QhullPointsIterator i(p);
-    while(i.hasNext()){
-        os << i.next();
-    }
-    return os;
-}//operator<  // ptrdiff_t, size_t
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    class QhullPoints;          //!< One or more points Coordinate pointers with dimension and iterators
-    class QhullPointsIterator;  //!< Java-style iterator
-
-//! QhullPoints are an array of QhullPoint as pointers into an array of coordinates.
-//! For Qhull/QhullQh, QhullPoints must use hull_dim.  Can change QhullPoint to input_dim if needed for Delaunay input site
-class QhullPoints {
-
-private:
-#//!\name Fields
-    coordT *            point_first; //!< First coordinate of an array of points of point_dimension
-    coordT *            point_end;   //!< End of point coordinates (end>=first).  Trailing coordinates ignored
-    QhullQh *           qh_qh;       //!< Maybe initialized NULL to allow ownership by RboxPoints
-                                     //!< qh_qh used for QhullPoint() and qh_qh->hull_dim in constructor
-    int                 point_dimension;  //!< Dimension, >=0
-
-public:
-#//!\name Subtypes
-    class const_iterator;
-    class iterator;
-    typedef QhullPoints::const_iterator ConstIterator;
-    typedef QhullPoints::iterator       Iterator;
-
-#//!\name Construct
-    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
-    //! If Qhull/QhullQh is not initialized, then QhullPoints.dimension() is zero unless explicitly set
-    //! Cannot define QhullPoints(int pointDimension) since it is ambiguous with QhullPoints(QhullQh *qqh)
-                        QhullPoints() : point_first(0), point_end(0), qh_qh(0), point_dimension(0) { }
-                        QhullPoints(int pointDimension, countT coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), qh_qh(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
-    explicit            QhullPoints(const Qhull &q);
-                        QhullPoints(const Qhull &q, countT coordinateCount2, coordT *c);
-                        QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c);
-    explicit            QhullPoints(QhullQh *qqh) : point_first(0), point_end(0), qh_qh(qqh), point_dimension(qqh ? qqh->hull_dim : 0) { }
-                        QhullPoints(QhullQh *qqh, countT coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), qh_qh(qqh), point_dimension(qqh ? qqh->hull_dim : 0) { QHULL_ASSERT(qqh && qqh->hull_dim>0); }
-                        QhullPoints(QhullQh *qqh, int pointDimension, countT coordinateCount2, coordT *c);
-                        //! Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
-                        QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), qh_qh(other.qh_qh), point_dimension(other.point_dimension) {}
-    QhullPoints &       operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; return *this; }
-                        ~QhullPoints() {}
-
-public:
-
-#//!\name Conversion
-
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList   toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name GetSet
-    // Constructs QhullPoint.  Cannot return reference.
-    const QhullPoint    at(countT idx) const { /* point_first==0 caught by point_end assert */ coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p=0 && coordinatesCount>=0 && c!=0); point_first= c; point_end= c+coordinatesCount; point_dimension= pointDimension; }
-    void                defineAs(countT coordinatesCount, coordT *c) { QHULL_ASSERT((point_dimension>0 && coordinatesCount>=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
-    void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; }
-    int                 dimension() const { return point_dimension; }
-    ConstIterator       end() const { return ConstIterator(qh_qh, point_dimension, point_end); }
-    Iterator            end() { return Iterator(qh_qh, point_dimension, point_end); }
-    coordT *            extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
-    countT              extraCoordinatesCount() const;  // WARN64
-    // Constructs QhullPoint.  Cannot return reference.
-    const QhullPoint    first() const { return QhullPoint(qh_qh, point_dimension, point_first); }
-    QhullPoint          first() { return QhullPoint(qh_qh, point_dimension, point_first); }
-    // Constructs QhullPoint.  Cannot return reference.
-    const QhullPoint    front() const { return first(); }
-    QhullPoint          front() { return first(); }
-    bool                includesCoordinates(const coordT *c) const { return c>=point_first && c(other)); return *this; }
-
-        // Need 'const QhullPoint' to maintain const
-        const QhullPoint & operator*() const { return *this; }
-        QhullPoint &    operator*() { return *this; }
-        const QhullPoint * operator->() const { return this; }
-        QhullPoint *    operator->() { return this; }
-        // value instead of reference since advancePoint() modifies self
-        QhullPoint      operator[](countT idx) const { QhullPoint result= *this; result.advancePoint(idx); return result; }
-        bool            operator==(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return (point_coordinates==o.point_coordinates && point_dimension==o.point_dimension); }
-        bool            operator!=(const iterator &o) const { return !operator==(o); }
-        bool            operator<(const iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates < o.point_coordinates; }
-        bool            operator<=(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates <= o.point_coordinates; }
-        bool            operator>(const iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates > o.point_coordinates; }
-        bool            operator>=(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates >= o.point_coordinates; }
-        // reinterpret_cast to break circular dependency
-        bool            operator==(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return (point_coordinates==reinterpret_cast(o).point_coordinates && point_dimension==reinterpret_cast(o).point_dimension); }
-        bool            operator!=(const QhullPoints::const_iterator &o) const { return !operator==(reinterpret_cast(o)); }
-        bool            operator<(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates < reinterpret_cast(o).point_coordinates; }
-        bool            operator<=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates <= reinterpret_cast(o).point_coordinates; }
-        bool            operator>(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates > reinterpret_cast(o).point_coordinates; }
-        bool            operator>=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates >= reinterpret_cast(o).point_coordinates; }
-        iterator &      operator++() { advancePoint(1); return *this; }
-        iterator        operator++(int) { iterator n= *this; operator++(); return iterator(n); }
-        iterator &      operator--() { advancePoint(-1); return *this; }
-        iterator        operator--(int) { iterator n= *this; operator--(); return iterator(n); }
-        iterator &      operator+=(countT idx) { advancePoint(idx); return *this; }
-        iterator &      operator-=(countT idx) { advancePoint(-idx); return *this; }
-        iterator        operator+(countT idx) const { iterator n= *this; n.advancePoint(idx); return n; }
-        iterator        operator-(countT idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
-        difference_type operator-(iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
-    };//QhullPoints::iterator
-
-#//!\name QhullPoints::const_iterator
-    //!\todo FIXUP QH11018 const_iterator same as iterator.  SHould have a common definition
-    class const_iterator : public QhullPoint {
-
-    public:
-        typedef std::random_access_iterator_tag  iterator_category;
-        typedef QhullPoint          value_type;
-        typedef const value_type *  pointer;
-        typedef const value_type &  reference;
-        typedef ptrdiff_t           difference_type;
-
-                        const_iterator(const QhullPoints::iterator &o) : QhullPoint(*o) {}
-        explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.qh(), ps.dimension(), ps.coordinates()) {}
-                        const_iterator(const int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
-                        const_iterator(const Qhull &q, coordT *c): QhullPoint(q, c) {}
-                        const_iterator(const Qhull &q, int pointDimension, coordT *c): QhullPoint(q, pointDimension, c) {}
-                        const_iterator(QhullQh *qqh, coordT *c): QhullPoint(qqh, c) {}
-                        const_iterator(QhullQh *qqh, int pointDimension, coordT *c): QhullPoint(qqh, pointDimension, c) {}
-                        const_iterator(const const_iterator &o) : QhullPoint(*o) {}
-        const_iterator &operator=(const const_iterator &o) { defineAs(const_cast(o)); return *this; }
-
-        // value/non-const since advancePoint(1), etc. modifies self
-        const QhullPoint & operator*() const { return *this; }
-        const QhullPoint * operator->() const { return this; }
-        // value instead of reference since advancePoint() modifies self
-        const QhullPoint operator[](countT idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
-        bool            operator==(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return (point_coordinates==o.point_coordinates && point_dimension==o.point_dimension); }
-        bool            operator!=(const const_iterator &o) const { return ! operator==(o); }
-        bool            operator<(const const_iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates < o.point_coordinates; }
-        bool            operator<=(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates <= o.point_coordinates; }
-        bool            operator>(const const_iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates > o.point_coordinates; }
-        bool            operator>=(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates >= o.point_coordinates; }
-        const_iterator &operator++() { advancePoint(1); return *this; }
-        const_iterator  operator++(int) { const_iterator n= *this; operator++(); return const_iterator(n); }
-        const_iterator &operator--() { advancePoint(-1); return *this; }
-        const_iterator  operator--(int) { const_iterator n= *this; operator--(); return const_iterator(n); }
-        const_iterator &operator+=(countT idx) { advancePoint(idx); return *this; }
-        const_iterator &operator-=(countT idx) { advancePoint(-idx); return *this; }
-        const_iterator  operator+(countT idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
-        const_iterator  operator-(countT idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
-        difference_type operator-(const_iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
-    };//QhullPoints::const_iterator
-
-#//!\name IO
-    struct PrintPoints{
-        const QhullPoints  *points;
-        const char *    point_message;
-        bool            with_identifier;
-        PrintPoints(const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), with_identifier(withIdentifier) {}
-    };//PrintPoints
-    PrintPoints          print(const char *message) const { return PrintPoints(message, false, *this); }
-    PrintPoints          printWithIdentifier(const char *message) const { return PrintPoints(message, true, *this); }
-};//QhullPoints
-
-// Instead of QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
-class QhullPointsIterator
-{
-    typedef QhullPoints::const_iterator const_iterator;
-
-#//!\name Fields
-private:
-    const QhullPoints  *ps;
-    const_iterator      i;
-
-public:
-                        QhullPointsIterator(const QhullPoints &other) : ps(&other), i(ps->constBegin()) {}
-    QhullPointsIterator &operator=(const QhullPoints &other) { ps = &other; i = ps->constBegin(); return *this; }
-
-    bool                findNext(const QhullPoint &t);
-    bool                findPrevious(const QhullPoint &t);
-    bool                hasNext() const { return i != ps->constEnd(); }
-    bool                hasPrevious() const { return i != ps->constBegin(); }
-    QhullPoint          next() { return *i++; }
-    QhullPoint          peekNext() const { return *i; }
-    QhullPoint          peekPrevious() const { const_iterator p = i; return *--p; }
-    QhullPoint          previous() { return *--i; }
-    void                toBack() { i = ps->constEnd(); }
-    void                toFront() { i = ps->constBegin(); }
-};//QhullPointsIterator
-
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
-std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
-
-#endif // QHULLPOINTS_H
diff --git a/src/qhull/src/libqhullcpp/QhullQh.cpp b/src/qhull/src/libqhullcpp/QhullQh.cpp
deleted file mode 100644
index 363533700..000000000
--- a/src/qhull/src/libqhullcpp/QhullQh.cpp
+++ /dev/null
@@ -1,237 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullQh.cpp#5 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullQh -- Qhull's global data structure, qhT, as a C++ class
-
-
-#include "libqhullcpp/QhullQh.h"
-
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullStat.h"
-
-#include 
-#include 
-
-#include 
-
-using std::cerr;
-using std::string;
-using std::vector;
-using std::ostream;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Global variables
-const double QhullQh::
-default_factor_epsilon= 1.0;
-
-#//!\name Constructor, destructor, etc.
-
-//! Derived from qh_new_qhull[user.c]
-QhullQh::
-QhullQh()
-: qhull_status(qh_ERRnone)
-, qhull_message()
-, error_stream(0)
-, output_stream(0)
-, factor_epsilon(QhullQh::default_factor_epsilon)
-, use_output_stream(false)
-{
-    // NOerrors: TRY_QHULL_ not needed since these routines do not call qh_errexit()
-    qh_meminit(this, NULL);
-    qh_initstatistics(this);
-    qh_initqhull_start2(this, NULL, NULL, qh_FILEstderr);  // Initialize qhT
-    this->ISqhullQh= True;
-}//QhullQh
-
-QhullQh::
-~QhullQh()
-{
-    checkAndFreeQhullMemory();
-}//~QhullQh
-
-#//!\name Methods
-
-//! Check memory for internal consistency
-//! Free global memory used by qh_initbuild and qh_buildhull
-//! Zero the qhT data structure, except for memory (qhmemT) and statistics (qhstatT)
-//! Check and free short memory (e.g., facetT)
-//! Zero the qhmemT data structure
-void QhullQh::
-checkAndFreeQhullMemory()
-{
-#ifdef qh_NOmem
-    qh_freeqhull(this, qh_ALL);
-#else
-    qh_memcheck(this);
-    qh_freeqhull(this, !qh_ALL);
-    countT curlong;
-    countT totlong;
-    qh_memfreeshort(this, &curlong, &totlong);
-    if (curlong || totlong)
-        throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
-#endif
-}//checkAndFreeQhullMemory
-
-#//!\name Messaging
-
-void QhullQh::
-appendQhullMessage(const string &s)
-{
-    if(output_stream && use_output_stream && this->USEstdout){ 
-        *output_stream << s;
-    }else if(error_stream){
-        *error_stream << s;
-    }else{
-        qhull_message += s;
-    }
-}//appendQhullMessage
-
-//! clearQhullMessage does not throw errors (~Qhull)
-void QhullQh::
-clearQhullMessage()
-{
-    qhull_status= qh_ERRnone;
-    qhull_message.clear();
-    RoadError::clearGlobalLog();
-}//clearQhullMessage
-
-//! hasQhullMessage does not throw errors (~Qhull)
-bool QhullQh::
-hasQhullMessage() const
-{
-    return (!qhull_message.empty() || qhull_status!=qh_ERRnone);
-    //FIXUP QH11006 -- inconsistent usage with Rbox.  hasRboxMessage just tests rbox_status.  No appendRboxMessage()
-}
-
-void QhullQh::
-maybeThrowQhullMessage(int exitCode)
-{
-    if(!NOerrexit){
-        if(qhull_message.size()>0){
-            qhull_message.append("\n");
-        }
-        if(exitCode || qhull_status==qh_ERRnone){
-            qhull_status= 10073;
-        }else{
-            qhull_message.append("QH10073: ");
-        }
-        qhull_message.append("Cannot call maybeThrowQhullMessage() from QH_TRY_().  Or missing 'qh->NOerrexit=true;' after QH_TRY_(){...}.");
-    }
-    if(qhull_status==qh_ERRnone){
-        qhull_status= exitCode;
-    }
-    if(qhull_status!=qh_ERRnone){
-        QhullError e(qhull_status, qhull_message);
-        clearQhullMessage();
-        throw e; // FIXUP QH11007: copy constructor is expensive if logging
-    }
-}//maybeThrowQhullMessage
-
-void QhullQh::
-maybeThrowQhullMessage(int exitCode, int noThrow)  throw()
-{
-    QHULL_UNUSED(noThrow);
-
-    if(qhull_status==qh_ERRnone){
-        qhull_status= exitCode;
-    }
-    if(qhull_status!=qh_ERRnone){
-        QhullError e(qhull_status, qhull_message);
-        e.logErrorLastResort();
-    }
-}//maybeThrowQhullMessage
-
-//! qhullMessage does not throw errors (~Qhull)
-std::string QhullQh::
-qhullMessage() const
-{
-    if(qhull_message.empty() && qhull_status!=qh_ERRnone){
-        return "qhull: no message for error.  Check cerr or error stream\n";
-    }else{
-        return qhull_message;
-    }
-}//qhullMessage
-
-int QhullQh::
-qhullStatus() const
-{
-    return qhull_status;
-}//qhullStatus
-
-void QhullQh::
-setErrorStream(ostream *os)
-{
-    error_stream= os;
-}//setErrorStream
-
-//! Updates use_output_stream
-void QhullQh::
-setOutputStream(ostream *os)
-{
-    output_stream= os;
-    use_output_stream= (os!=0);
-}//setOutputStream
-
-}//namespace orgQhull
-
-/*---------------------------------
-
-  qh_fprintf(qhT *qh, fp, msgcode, format, list of args )
-    replaces qh_fprintf() in userprintf_r.c
-
-notes:
-    only called from libqhull
-    same as fprintf() and RboxPoints.qh_fprintf_rbox()
-    fgets() is not trapped like fprintf()
-    Do not throw errors from here.  Use qh_errexit;
-*/
-extern "C"
-void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    using namespace orgQhull;
-
-    if(!qh->ISqhullQh){
-        qh_fprintf_stderr(10025, "Qhull error: qh_fprintf called from a Qhull instance without QhullQh defined\n");
-        qh_exit(10025);
-    }
-    QhullQh *qhullQh= static_cast(qh);
-    va_start(args, fmt);
-    if(msgcode=MSG_ERROR && msgcodeqhull_statusqhull_status>=MSG_WARNING){
-                qhullQh->qhull_status= msgcode;
-            }
-        }
-        char newMessage[MSG_MAXLEN];
-        // RoadError will add the message tag
-        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-        qhullQh->appendQhullMessage(newMessage);
-        va_end(args);
-        return;
-    }
-    if(qhullQh->output_stream && qhullQh->use_output_stream){
-        char newMessage[MSG_MAXLEN];
-        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-        *qhullQh->output_stream << newMessage;
-        va_end(args);
-        return;
-    }
-    // FIXUP QH11008: how do users trap messages and handle input?  A callback?
-    char newMessage[MSG_MAXLEN];
-    vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-    qhullQh->appendQhullMessage(newMessage);
-    va_end(args);
-} /* qh_fprintf */
diff --git a/src/qhull/src/libqhullcpp/QhullQh.h b/src/qhull/src/libqhullcpp/QhullQh.h
deleted file mode 100644
index c3b277ff0..000000000
--- a/src/qhull/src/libqhullcpp/QhullQh.h
+++ /dev/null
@@ -1,110 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullQh.h#2 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLQH_H
-#define QHULLQH_H
-
-#include "libqhull_r/qhull_ra.h"
-
-#include 
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
-/* setjmp should not be implemented with 'catch' */
-#endif
-
-//! Use QH_TRY_ or QH_TRY_NOTHROW_ to call a libqhull_r routine that may invoke qh_errexit()
-//! QH_TRY_(qh){...} qh->NOerrexit=true;
-//! No object creation -- longjmp() skips object destructors
-//! To test for error when done -- qh->maybeThrowQhullMessage(QH_TRY_status);
-//! Use the same compiler for QH_TRY_, libqhullcpp, and libqhull_r.  setjmp() is not portable between compilers.
-
-#define QH_TRY_ERROR 10071
-
-#define QH_TRY_(qh) \
-    int QH_TRY_status; \
-    if(qh->NOerrexit){ \
-        qh->NOerrexit= False; \
-        QH_TRY_status= setjmp(qh->errexit); \
-    }else{ \
-        throw QhullError(QH_TRY_ERROR, "Cannot invoke QH_TRY_() from inside a QH_TRY_.  Or missing 'qh->NOerrexit=true' after previously called QH_TRY_(qh){...}"); \
-    } \
-    if(!QH_TRY_status)
-
-#define QH_TRY_NO_THROW_(qh) \
-    int QH_TRY_status; \
-    if(qh->NOerrexit){ \
-        qh->NOerrexit= False; \
-        QH_TRY_status= setjmp(qh->errexit); \
-    }else{ \
-        QH_TRY_status= QH_TRY_ERROR; \
-    } \
-    if(!QH_TRY_status)
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! QhullQh -- Qhull's global data structure, qhT, as a C++ class
-    class QhullQh;
-
-//! POD type equivalent to qhT.  No virtual members
-class QhullQh : public qhT {
-
-#//!\name Constants
-
-#//!\name Fields
-private:
-    int                 qhull_status;   //!< qh_ERRnone if valid
-    std::string         qhull_message;  //!< Returned messages from libqhull_r
-    std::ostream *      error_stream;   //!< overrides errorMessage, use appendQhullMessage()
-    std::ostream *      output_stream;  //!< send output to stream
-    double              factor_epsilon; //!< Factor to increase ANGLEround and DISTround for hyperplane equality
-    bool                use_output_stream; //!< True if using output_stream
-
-    friend void         ::qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-
-    static const double default_factor_epsilon;  //!< Default factor_epsilon is 1.0, never updated
-
-#//!\name Constructors
-public:
-                        QhullQh();
-                        ~QhullQh();
-private:
-                        //!disable copy constructor and assignment
-                        QhullQh(const QhullQh &);
-    QhullQh &           operator=(const QhullQh &);
-public:
-
-#//!\name GetSet
-    double              factorEpsilon() const { return factor_epsilon; }
-    void                setFactorEpsilon(double a) { factor_epsilon= a; }
-    void                disableOutputStream() { use_output_stream= false; }
-    void                enableOutputStream() { use_output_stream= true; }
-
-#//!\name Messaging
-    void                appendQhullMessage(const std::string &s);
-    void                clearQhullMessage();
-    std::string         qhullMessage() const;
-    bool                hasOutputStream() const { return use_output_stream; }
-    bool                hasQhullMessage() const;
-    void                maybeThrowQhullMessage(int exitCode);
-    void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
-    int                 qhullStatus() const;
-    void                setErrorStream(std::ostream *os);
-    void                setOutputStream(std::ostream *os);
-
-#//!\name Methods
-    double              angleEpsilon() const { return this->ANGLEround*factor_epsilon; } //!< Epsilon for hyperplane angle equality
-    void                checkAndFreeQhullMemory();
-    double              distanceEpsilon() const { return this->DISTround*factor_epsilon; } //!< Epsilon for distance to hyperplane
-
-};//class QhullQh
-
-}//namespace orgQhull
-
-#endif // QHULLQH_H
diff --git a/src/qhull/src/libqhullcpp/QhullRidge.cpp b/src/qhull/src/libqhullcpp/QhullRidge.cpp
deleted file mode 100644
index 7a0181280..000000000
--- a/src/qhull/src/libqhullcpp/QhullRidge.cpp
+++ /dev/null
@@ -1,124 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullRidge.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullRidge -- Qhull's ridge structure, ridgeT, as a C++ class
-
-#include "libqhullcpp/QhullRidge.h"
-
-#include "libqhullcpp/QhullSets.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/Qhull.h"
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Class objects
-ridgeT QhullRidge::
-s_empty_ridge= {0,0,0,0,0,
-                0,0};
-
-#//!\name Constructors
-
-QhullRidge::QhullRidge(const Qhull &q)
-: qh_ridge(&s_empty_ridge)
-, qh_qh(q.qh())
-{
-}//Default
-
-QhullRidge::QhullRidge(const Qhull &q, ridgeT *r)
-: qh_ridge(r ? r : &s_empty_ridge)
-, qh_qh(q.qh())
-{
-}//ridgeT
-
-#//!\name foreach
-
-//! Return True if nextRidge3d
-//! Simplicial facets may have incomplete ridgeSets
-//! Does not use qh_errexit()
-bool QhullRidge::
-hasNextRidge3d(const QhullFacet &f) const
-{
-    if(!qh_qh){
-        return false;
-    }
-    vertexT *v= 0;
-    // Does not call qh_errexit(), TRY_QHULL_ not needed
-    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
-    return (ridge!=0);
-}//hasNextRidge3d
-
-//! Return next ridge and optional vertex for a 3d facet and ridge
-//! Does not use qh_errexit()
-QhullRidge QhullRidge::
-nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const
-{
-    vertexT *v= 0;
-    ridgeT *ridge= 0;
-    if(qh_qh){
-        // Does not call qh_errexit(), TRY_QHULL_ not needed
-        ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
-        if(!ridge){
-            throw QhullError(10030, "Qhull error nextRidge3d:  missing next ridge for facet %d ridge %d.  Does facet contain ridge?", f.id(), id());
-        }
-    }
-    if(nextVertex!=0){
-        *nextVertex= QhullVertex(qh_qh, v);
-    }
-    return QhullRidge(qh_qh, ridge);
-}//nextRidge3d
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using orgQhull::QhullRidge;
-using orgQhull::QhullVertex;
-
-ostream &
-operator<<(ostream &os, const QhullRidge &r)
-{
-    os << r.print("");
-    return os;
-}//<< QhullRidge
-
-//! Duplicate of qh_printridge [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullRidge::PrintRidge &pr)
-{
-    if(*pr.print_message){
-        os << pr.print_message << " ";
-    }else{
-        os << "     - ";
-    }
-    QhullRidge r= *pr.ridge;
-    os << "r" << r.id();
-    if(r.getRidgeT()->tested){
-        os << " tested";
-    }
-    if(r.getRidgeT()->nonconvex){
-        os << " nonconvex";
-    }
-    os << endl;
-    os << r.vertices().print("           vertices:");
-    if(r.getRidgeT()->top && r.getRidgeT()->bottom){
-        os << "           between f" << r.topFacet().id() << " and f" << r.bottomFacet().id() << endl;
-    }else if(r.getRidgeT()->top){
-        os << "           top f" << r.topFacet().id() << endl;
-    }else if(r.getRidgeT()->bottom){
-        os << "           bottom f" << r.bottomFacet().id() << endl;
-    }
-
-    return os;
-}//<< PrintRidge
diff --git a/src/qhull/src/libqhullcpp/QhullRidge.h b/src/qhull/src/libqhullcpp/QhullRidge.h
deleted file mode 100644
index 924340fb0..000000000
--- a/src/qhull/src/libqhullcpp/QhullRidge.h
+++ /dev/null
@@ -1,112 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullRidge.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLRIDGE_H
-#define QHULLRIDGE_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullSet.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/QhullVertexSet.h"
-#include "libqhullcpp/QhullFacet.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-    class QhullVertex;
-    class QhullVertexSet;
-    class QhullFacet;
-
-#//!\name Defined here
-    //! QhullRidge -- Qhull's ridge structure, ridgeT [libqhull.h], as a C++ class
-    class QhullRidge;
-    typedef QhullSet  QhullRidgeSet;
-    typedef QhullSetIterator  QhullRidgeSetIterator;
-    // see QhullSets.h for QhullRidgeSet and QhullRidgeSetIterator -- avoids circular references
-
-/************************
-a ridge is hull_dim-1 simplex between two neighboring facets.  If the
-facets are non-simplicial, there may be more than one ridge between
-two facets.  E.G. a 4-d hypercube has two triangles between each pair
-of neighboring facets.
-
-topological information:
-    vertices            a set of vertices
-    top,bottom          neighboring facets with orientation
-
-geometric information:
-    tested              True if ridge is clearly convex
-    nonconvex           True if ridge is non-convex
-*/
-
-class QhullRidge {
-
-#//!\name Defined here
-public:
-    typedef ridgeT *   base_type;  // for QhullRidgeSet
-
-#//!\name Fields
-private:
-    ridgeT *            qh_ridge;  //!< Corresponding ridgeT, never 0
-    QhullQh *           qh_qh;     //!< QhullQh/qhT for ridgeT, may be 0
-
-#//!\name Class objects
-    static ridgeT       s_empty_ridge;
-
-public:
-#//!\name Constants
-
-#//!\name Constructors
-                        QhullRidge() : qh_ridge(&s_empty_ridge), qh_qh(0) {}
-    explicit            QhullRidge(const Qhull &q);
-                        QhullRidge(const Qhull &q, ridgeT *r);
-    explicit            QhullRidge(QhullQh *qqh) : qh_ridge(&s_empty_ridge), qh_qh(qqh) {}
-                        QhullRidge(QhullQh *qqh, ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge), qh_qh(qqh) {}
-                        // Creates an alias.  Does not copy QhullRidge.  Needed for return by value and parameter passing
-                        QhullRidge(const QhullRidge &other) : qh_ridge(other.qh_ridge), qh_qh(other.qh_qh) {}
-                        // Creates an alias.  Does not copy QhullRidge.  Needed for vector
-    QhullRidge &        operator=(const QhullRidge &other) { qh_ridge= other.qh_ridge; qh_qh= other.qh_qh; return *this; }
-                        ~QhullRidge() {}
-
-#//!\name GetSet
-    QhullFacet          bottomFacet() const { return QhullFacet(qh_qh, qh_ridge->bottom); }
-    int                 dimension() const { return ((qh_qh && qh_qh->hull_dim) ? qh_qh->hull_dim-1 : 0); }
-    ridgeT *            getBaseT() const { return getRidgeT(); } //!< For QhullSet
-    ridgeT *            getRidgeT() const { return qh_ridge; }
-    countT              id() const { return qh_ridge->id; }
-    bool                isValid() const { return (qh_qh && qh_ridge != &s_empty_ridge); }
-    bool                operator==(const QhullRidge &other) const { return qh_ridge==other.qh_ridge; }
-    bool                operator!=(const QhullRidge &other) const { return !operator==(other); }
-    QhullFacet          otherFacet(const QhullFacet &f) const { return QhullFacet(qh_qh, (qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top)); }
-    QhullFacet          topFacet() const { return QhullFacet(qh_qh, qh_ridge->top); }
-
-#//!\name foreach
-    bool                hasNextRidge3d(const QhullFacet &f) const;
-    QhullRidge          nextRidge3d(const QhullFacet &f) const { return nextRidge3d(f, 0); }
-    QhullRidge          nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const;
-    QhullVertexSet      vertices() const { return QhullVertexSet(qh_qh, qh_ridge->vertices); }
-
-#//!\name IO
-
-    struct PrintRidge{
-        const QhullRidge *ridge;
-        const char *    print_message;    //!< non-null message
-                        PrintRidge(const char *message, const QhullRidge &r) : ridge(&r), print_message(message) {}
-    };//PrintRidge
-    PrintRidge          print(const char* message) const { return PrintRidge(message, *this); }
-};//class QhullRidge
-
-}//namespace orgQhull
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge &r);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge::PrintRidge &pr);
-
-#endif // QHULLRIDGE_H
diff --git a/src/qhull/src/libqhullcpp/QhullSet.cpp b/src/qhull/src/libqhullcpp/QhullSet.cpp
deleted file mode 100644
index dfdc3c51f..000000000
--- a/src/qhull/src/libqhullcpp/QhullSet.cpp
+++ /dev/null
@@ -1,62 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullSet.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullSet -- Qhull's set structure, setT, as a C++ class
-
-#include "libqhullcpp/QhullSet.h"
-
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullError.h"
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Class objects
-
-setT QhullSetBase::
-s_empty_set;
-
-#//!\name Constructors
-
-QhullSetBase::
-QhullSetBase(const Qhull &q, setT *s) 
-: qh_set(s ? s : &s_empty_set)
-, qh_qh(q.qh())
-{
-}
-
-#//!\name Class methods
-
-// Same code for qh_setsize [qset_r.c] and QhullSetBase::count [static]
-countT QhullSetBase::
-count(const setT *set)
-{
-    countT size;
-    const setelemT *sizep;
-
-    if (!set){
-        return(0);
-    }
-    sizep= SETsizeaddr_(set);
-    if ((size= sizep->i)) {
-        size--;
-        if (size > set->maxsize) {
-            // FIXUP QH11022 How to add additional output to a error? -- qh_setprint(qhmem.ferr, "set: ", set);
-            throw QhullError(10032, "QhullSet internal error: current set size %d is greater than maximum size %d\n",
-                size, set->maxsize);
-        }
-    }else{
-        size= set->maxsize;
-    }
-    return size;
-}//count
-
-}//namespace orgQhull
-
diff --git a/src/qhull/src/libqhullcpp/QhullSet.h b/src/qhull/src/libqhullcpp/QhullSet.h
deleted file mode 100644
index afb6b51d9..000000000
--- a/src/qhull/src/libqhullcpp/QhullSet.h
+++ /dev/null
@@ -1,462 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullSet.h#6 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QhullSet_H
-#define QhullSet_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullQh.h"
-
-#include   // ptrdiff_t, size_t
-
-#ifndef QHULL_NO_STL
-#include 
-#endif
-
-#ifdef QHULL_USES_QT
- #include 
-#endif
-
-namespace orgQhull {
-
-#//!\name Used here
-    class Qhull;
-
-#//!\name Defined here
-    class QhullSetBase;  //! Base class for QhullSet
-    //! QhullSet defined below
-    //! QhullSetIterator defined below
-    //! \see QhullPointSet, QhullLinkedList
-
-//! QhullSetBase is a wrapper for Qhull's setT of void* pointers
-//! \see libqhull_r/qset.h
-class QhullSetBase {
-
-private:
-#//!\name Fields --
-    setT *              qh_set;
-    QhullQh *           qh_qh;             //! Provides access to setT memory allocator
-
-#//!\name Class objects
-    static setT         s_empty_set;  //! Used if setT* is NULL
-
-public:
-#//!\name Constructors
-                        QhullSetBase(const Qhull &q, setT *s);
-                        QhullSetBase(QhullQh *qqh, setT *s) : qh_set(s ? s : &s_empty_set), qh_qh(qqh) {}
-                        //! Copy constructor copies the pointer but not the set.  Needed for return by value and parameter passing.
-                        QhullSetBase(const QhullSetBase &other) : qh_set(other.qh_set), qh_qh(other.qh_qh) {}
-    QhullSetBase &      operator=(const QhullSetBase &other) { qh_set= other.qh_set; qh_qh= other.qh_qh; return *this; }
-                        ~QhullSetBase() {}
-
-private:
-                        //!disabled since memory allocation for QhullSet not defined
-                        QhullSetBase() {}
-public:
-
-#//!\name GetSet
-    countT              count() const { return QhullSetBase::count(qh_set); }
-    void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; } //!< Not type-safe since setT may contain any type
-    void                forceEmpty() { qh_set= &s_empty_set; }
-    setT *              getSetT() const { return qh_set; }
-    bool                isEmpty() const { return SETempty_(qh_set); }
-    QhullQh *           qh() const { return qh_qh; }
-    setT **             referenceSetT() { return &qh_set; }
-    size_t              size() const { return QhullSetBase::count(qh_set); }
-
-#//!\name Element
-protected:
-    void **             beginPointer() const { return &qh_set->e[0].p; }
-    void **             elementPointer(countT idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
-                        //! Always points to 0
-    void **             endPointer() const { return qh_setendpointer(qh_set); }
-
-#//!\name Class methods
-public:
-    static countT       count(const setT *set);
-    //s may be null
-    static bool         isEmpty(const setT *s) { return SETempty_(s); }
-};//QhullSetBase
-
-
-//! QhullSet -- A read-only wrapper to Qhull's collection class, setT.
-//!  QhullSet is similar to STL's  and Qt's QVector
-//!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
-//!  T is a Qhull type that defines 'base_type' and getBaseT() (e.g., QhullFacet with base_type 'facetT *'
-//!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
-//!  QhullSetIterator is faster than STL-style iterator/const_iterator
-//!  Qhull's FOREACHelement_() [qset_r.h] maybe more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
-//!  Derived from QhullLinkedList.h and Qt/core/tools/qlist.h w/o QT_STRICT_ITERATORS
-template 
-class QhullSet : public QhullSetBase {
-
-private:
-#//!\name Fields -- see QhullSetBase
-
-#//!\name Class objects
-    static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
-
-public:
-#//!\name Defined here
-    class iterator;
-    class const_iterator;
-    typedef typename QhullSet::iterator Iterator;
-    typedef typename QhullSet::const_iterator ConstIterator;
-
-#//!\name Constructors
-                        QhullSet(const Qhull &q, setT *s) : QhullSetBase(q, s) { }
-                        QhullSet(QhullQh *qqh, setT *s) : QhullSetBase(qqh, s) { }
-                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-                        //Copy constructor copies pointer but not contents.  Needed for return by value.
-                        QhullSet(const QhullSet &other) : QhullSetBase(other) {}
-    QhullSet &       operator=(const QhullSet &other) { QhullSetBase::operator=(other); return *this; }
-                        ~QhullSet() {}
-
-private:
-                        //!Disable default constructor.  See QhullSetBase
-                        QhullSet();
-public:
-
-#//!\name Conversion
-
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif
-#ifdef QHULL_USES_QT
-    QList toQList() const;
-#endif
-
-#//!\name GetSet -- see QhullSetBase for count(), empty(), isEmpty(), size()
-    using QhullSetBase::count;
-    using QhullSetBase::isEmpty;
-    // operator== defined for QhullSets of the same type
-    bool                operator==(const QhullSet &other) const { return qh_setequal(getSetT(), other.getSetT()); }
-    bool                operator!=(const QhullSet &other) const { return !operator==(other); }
-
-#//!\name Element access
-    // Constructs T.  Cannot return reference.
-    const T             at(countT idx) const { return operator[](idx); }
-    // Constructs T.  Cannot return reference.
-    const T             back() const { return last(); }
-    T                   back() { return last(); }
-    //! end element is NULL
-    const typename T::base_type * constData() const { return reinterpret_cast(beginPointer()); }
-    typename T::base_type *     data() { return reinterpret_cast(beginPointer()); }
-    const typename T::base_type *data() const { return reinterpret_cast(beginPointer()); }
-    typename T::base_type *     endData() { return reinterpret_cast(endPointer()); }
-    const typename T::base_type * endData() const { return reinterpret_cast(endPointer()); }
-    // Constructs T.  Cannot return reference.
-    const T             first() const { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
-    T                   first() { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
-    // Constructs T.  Cannot return reference.
-    const T             front() const { return first(); }
-    T                   front() { return first(); }
-    // Constructs T.  Cannot return reference.
-    const T             last() const { QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
-    T                   last() { QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
-    // mid() not available.  No setT constructor
-    // Constructs T.  Cannot return reference.
-    const T             operator[](countT idx) const { const typename T::base_type *p= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
-    T                   operator[](countT idx) { typename T::base_type *p= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
-    const T             second() const { return operator[](1); }
-    T                   second() { return operator[](1); }
-    T                   value(countT idx) const;
-    T                   value(countT idx, const T &defaultValue) const;
-
-#//!\name Read-write -- Not available, no setT constructor
-
-#//!\name iterator
-    iterator            begin() { return iterator(qh(), reinterpret_cast(beginPointer())); }
-    const_iterator      begin() const { return const_iterator(qh(), data()); }
-    const_iterator      constBegin() const { return const_iterator(qh(), data()); }
-    const_iterator      constEnd() const { return const_iterator(qh(), endData()); }
-    iterator            end() { return iterator(qh(), endData()); }
-    const_iterator      end() const { return const_iterator(qh(), endData()); }
-
-#//!\name Search
-    bool                contains(const T &t) const;
-    countT              count(const T &t) const;
-    countT              indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
-    countT              lastIndexOf(const T &t) const;
-
-    // before const_iterator for conversion with comparison operators
-    class iterator {
-        friend class const_iterator;
-    private:
-        typename T::base_type *  i;  // e.g., facetT**, first for debugger
-        QhullQh *       qh_qh;
-
-    public:
-        typedef ptrdiff_t       difference_type;
-        typedef std::bidirectional_iterator_tag  iterator_category;
-        typedef T               value_type;
-
-                        iterator(QhullQh *qqh, typename T::base_type *p) : i(p), qh_qh(qqh) {}
-                        iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
-        iterator &      operator=(const iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
-
-        // Constructs T.  Cannot return reference.  
-        T               operator*() const { return T(qh_qh, *i); }
-        //operator->() n/a, value-type
-        // Constructs T.  Cannot return reference.  
-        T               operator[](countT idx) const { return T(qh_qh, *(i+idx)); } //!< No error checking
-        bool            operator==(const iterator &o) const { return i == o.i; }
-        bool            operator!=(const iterator &o) const { return !operator==(o); }
-        bool            operator==(const const_iterator &o) const { return (i==reinterpret_cast(o).i); }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-
-        //! Assumes same point set
-        countT          operator-(const iterator &o) const { return (countT)(i-o.i); } //WARN64
-        bool            operator>(const iterator &o) const { return i>o.i; }
-        bool            operator<=(const iterator &o) const { return !operator>(o); }
-        bool            operator<(const iterator &o) const { return i=(const iterator &o) const { return !operator<(o); }
-        bool            operator>(const const_iterator &o) const { return (i > reinterpret_cast(o).i); }
-        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
-        bool            operator<(const const_iterator &o) const { return (i < reinterpret_cast(o).i); }
-        bool            operator>=(const const_iterator &o) const { return !operator<(o); }
-
-        //! No error checking
-        iterator &      operator++() { ++i; return *this; }
-        iterator        operator++(int) { iterator o= *this; ++i; return o; }
-        iterator &      operator--() { --i; return *this; }
-        iterator        operator--(int) { iterator o= *this; --i; return o; }
-        iterator        operator+(countT j) const { return iterator(qh_qh, i+j); }
-        iterator        operator-(countT j) const { return operator+(-j); }
-        iterator &      operator+=(countT j) { i += j; return *this; }
-        iterator &      operator-=(countT j) { i -= j; return *this; }
-    };//QhullPointSet::iterator
-
-    class const_iterator {
-    private:
-        const typename T::base_type *  i;  // e.g., const facetT**, first for debugger
-        QhullQh *       qh_qh;
-
-    public:
-        typedef ptrdiff_t       difference_type;
-        typedef std::random_access_iterator_tag  iterator_category;
-        typedef T               value_type;
-
-                        const_iterator(QhullQh *qqh, const typename T::base_type * p) : i(p), qh_qh(qqh) {}
-                        const_iterator(const const_iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
-                        const_iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
-        const_iterator &operator=(const const_iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
-
-        // Constructs T.  Cannot return reference.  Retaining 'const T' return type for consistency with QList/QVector
-        const T         operator*() const { return T(qh_qh, *i); }
-        const T         operator[](countT idx) const { return T(qh_qh, *(i+idx)); }  //!< No error checking
-        //operator->() n/a, value-type
-        bool            operator==(const const_iterator &o) const { return i == o.i; }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-
-        //! Assumes same point set
-        countT          operator-(const const_iterator &o) { return (countT)(i-o.i); } //WARN64
-        bool            operator>(const const_iterator &o) const { return i>o.i; }
-        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
-        bool            operator<(const const_iterator &o) const { return i=(const const_iterator &o) const { return !operator<(o); }
-
-        //!< No error checking
-        const_iterator &operator++() { ++i; return *this; }
-        const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
-        const_iterator &operator--() { --i; return *this; }
-        const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
-        const_iterator  operator+(int j) const { return const_iterator(qh_qh, i+j); }
-        const_iterator  operator-(int j) const { return operator+(-j); }
-        const_iterator &operator+=(int j) { i += j; return *this; }
-        const_iterator &operator-=(int j) { i -= j; return *this; }
-    };//QhullPointSet::const_iterator
-
-};//class QhullSet
-
-
-//! Faster then interator/const_iterator due to T::base_type
-template 
-class QhullSetIterator {
-
-#//!\name Subtypes
-    typedef typename QhullSet::const_iterator const_iterator;
-
-private:
-#//!\name Fields
-    const typename T::base_type *  i;  // e.g., facetT**, first for debugger
-    const typename T::base_type *  begin_i;  // must be initialized after i
-    const typename T::base_type *  end_i;
-    QhullQh *                qh_qh;
-
-public:
-#//!\name Constructors
-                        QhullSetIterator(const QhullSet &s) : i(s.data()), begin_i(i), end_i(s.endData()), qh_qh(s.qh()) {}
-                        QhullSetIterator(const QhullSetIterator &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i), qh_qh(o.qh_qh) {}
-    QhullSetIterator &operator=(const QhullSetIterator &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; qh_qh= o.qh_qh; return *this; }
-
-#//!\name ReadOnly
-    countT              countRemaining() { return (countT)(end_i-i); } // WARN64
-
-#//!\name Search
-    bool                findNext(const T &t);
-    bool                findPrevious(const T &t);
-
-#//!\name Foreach
-    bool                hasNext() const { return i != end_i; }
-    bool                hasPrevious() const { return i != begin_i; }
-    T                   next() { return T(qh_qh, *i++); }
-    T                   peekNext() const { return T(qh_qh, *i); }
-    T                   peekPrevious() const { const typename T::base_type *p = i; return T(qh_qh, *--p); }
-    T                   previous() { return T(qh_qh, *--i); }
-    void                toBack() { i = end_i; }
-    void                toFront() { i = begin_i; }
-};//class QhullSetIterator
-
-#//!\name == Definitions =========================================
-
-#//!\name Conversions
-
-// See qt-qhull.cpp for QList conversion
-
-#ifndef QHULL_NO_STL
-template 
-std::vector QhullSet::
-toStdVector() const
-{
-	typename QhullSet::const_iterator i = begin();
-	typename QhullSet::const_iterator e = end();
-    std::vector vs;
-    while(i!=e){
-        vs.push_back(*i++);
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-#ifdef QHULL_USES_QT
-template 
-QList QhullSet::
-toQList() const
-{
-    QhullSet::const_iterator i= begin();
-    QhullSet::const_iterator e= end();
-    QList vs;
-    while(i!=e){
-        vs.append(*i++);
-    }
-    return vs;
-}//toQList
-#endif
-
-#//!\name Element
-
-template 
-T QhullSet::
-value(countT idx) const
-{
-    // Avoid call to qh_setsize() and assert in elementPointer()
-    const typename T::base_type *p= reinterpret_cast(&SETelem_(getSetT(), idx));
-    return (idx>=0 && p
-T QhullSet::
-value(countT idx, const T &defaultValue) const
-{
-    // Avoid call to qh_setsize() and assert in elementPointer()
-    const typename T::base_type *p= reinterpret_cast(&SETelem_(getSetT(), idx));
-    return (idx>=0 && p
-bool QhullSet::
-contains(const T &t) const
-{
-    setT *s= getSetT();
-    void *p= t.getBaseT();  // contains() is not inline for better error reporting
-    int result= qh_setin(s, p);
-    return result!=0;
-}//contains
-
-template 
-countT QhullSet::
-count(const T &t) const
-{
-    countT n= 0;
-    const typename T::base_type *i= data();
-    const typename T::base_type *e= endData();
-    typename T::base_type p= t.getBaseT();
-    while(i
-countT QhullSet::
-lastIndexOf(const T &t) const
-{
-    const typename T::base_type *b= data();
-    const typename T::base_type *i= endData();
-    typename T::base_type p= t.getBaseT();
-    while(--i>=b){
-        if(*i==p){
-            break;
-        }
-    }
-    return (countT)(i-b); // WARN64
-}//lastIndexOf
-
-#//!\name QhullSetIterator
-
-template 
-bool QhullSetIterator::
-findNext(const T &t)
-{
-    typename T::base_type p= t.getBaseT();
-    while(i!=end_i){
-        if(*(++i)==p){
-            return true;
-        }
-    }
-    return false;
-}//findNext
-
-template 
-bool QhullSetIterator::
-findPrevious(const T &t)
-{
-    typename T::base_type p= t.getBaseT();
-    while(i!=begin_i){
-        if(*(--i)==p){
-            return true;
-        }
-    }
-    return false;
-}//findPrevious
-
-}//namespace orgQhull
-
-
-#//!\name == Global namespace =========================================
-
-template 
-std::ostream &
-operator<<(std::ostream &os, const orgQhull::QhullSet &qs)
-{
-    const typename T::base_type *i= qs.data();
-    const typename T::base_type *e= qs.endData();
-    while(i!=e){
-        os << T(qs.qh(), *i++);
-    }
-    return os;
-}//operator<<
-
-#endif // QhullSet_H
diff --git a/src/qhull/src/libqhullcpp/QhullSets.h b/src/qhull/src/libqhullcpp/QhullSets.h
deleted file mode 100644
index d0f200cbc..000000000
--- a/src/qhull/src/libqhullcpp/QhullSets.h
+++ /dev/null
@@ -1,27 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullSets.h#2 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLSETS_H
-#define QHULLSETS_H
-
-#include "libqhullcpp/QhullSet.h"
-
-namespace orgQhull {
-
-    //See: QhullFacetSet.h
-    //See: QhullPointSet.h
-    //See: QhullVertexSet.h
-
-    // Avoid circular references between QhullFacet, QhullRidge, and QhullVertex
-    class QhullRidge;
-    typedef QhullSet  QhullRidgeSet;
-    typedef QhullSetIterator  QhullRidgeSetIterator;
-
-}//namespace orgQhull
-
-#endif // QHULLSETS_H
diff --git a/src/qhull/src/libqhullcpp/QhullStat.cpp b/src/qhull/src/libqhullcpp/QhullStat.cpp
deleted file mode 100644
index c4fe6c491..000000000
--- a/src/qhull/src/libqhullcpp/QhullStat.cpp
+++ /dev/null
@@ -1,42 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullStat.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullStat -- Qhull's global data structure, statT, as a C++ class
-
-#include "libqhullcpp/QhullStat.h"
-
-#include "libqhullcpp/QhullError.h"
-
-#include 
-#include 
-
-using std::cerr;
-using std::string;
-using std::vector;
-using std::ostream;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Constructor, destructor, etc.
-
-//! If qh_QHpointer==0, invoke with placement new on qh_stat;
-QhullStat::
-QhullStat()
-{
-}//QhullStat
-
-QhullStat::
-~QhullStat()
-{
-}//~QhullStat
-
-}//namespace orgQhull
-
diff --git a/src/qhull/src/libqhullcpp/QhullStat.h b/src/qhull/src/libqhullcpp/QhullStat.h
deleted file mode 100644
index 54bde8fc7..000000000
--- a/src/qhull/src/libqhullcpp/QhullStat.h
+++ /dev/null
@@ -1,49 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullStat.h#2 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLSTAT_H
-#define QHULLSTAT_H
-
-#include "libqhull_r/qhull_ra.h"
-
-#include 
-#include 
-
-namespace orgQhull {
-
-#//!\name defined here
-    //! QhullStat -- Qhull's statistics, qhstatT, as a C++ class
-    //! Statistics defined with zzdef_() control Qhull's behavior, summarize its result, and report precision problems.
-    class QhullStat;
-
-class QhullStat : public qhstatT {
-
-private:
-#//!\name Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members
-
-public:
-#//!\name Constants
-
-#//!\name class methods
-
-#//!\name constructor, assignment, destructor, invariant
-                        QhullStat();
-                        ~QhullStat();
-
-private:
-    //!disable copy constructor and assignment
-                        QhullStat(const QhullStat &);
-    QhullStat &         operator=(const QhullStat &);
-public:
-
-#//!\name Access
-};//class QhullStat
-
-}//namespace orgQhull
-
-#endif // QHULLSTAT_H
diff --git a/src/qhull/src/libqhullcpp/QhullVertex.cpp b/src/qhull/src/libqhullcpp/QhullVertex.cpp
deleted file mode 100644
index fd7aef089..000000000
--- a/src/qhull/src/libqhullcpp/QhullVertex.cpp
+++ /dev/null
@@ -1,112 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertex.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullVertex -- Qhull's vertex structure, vertexT, as a C++ class
-
-#include "libqhullcpp/QhullVertex.h"
-
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/QhullFacet.h"
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//!\name Class objects
-vertexT QhullVertex::
-s_empty_vertex= {0,0,0,0,0,
-                 0,0,0,0,0,
-                 0};
-
-#//!\name Constructors
-
-QhullVertex::QhullVertex(const Qhull &q)
-: qh_vertex(&s_empty_vertex)
-, qh_qh(q.qh())
-{
-}//Default
-
-QhullVertex::QhullVertex(const Qhull &q, vertexT *v)
-: qh_vertex(v ? v : &s_empty_vertex)
-, qh_qh(q.qh())
-{
-}//vertexT
-
-#//!\name foreach
-
-//! Return neighboring facets for a vertex
-//! If neither merging nor Voronoi diagram, requires Qhull::defineVertexNeighborFacets() beforehand.
-QhullFacetSet QhullVertex::
-neighborFacets() const
-{
-    if(!neighborFacetsDefined()){
-        throw QhullError(10034, "Qhull error: neighboring facets of vertex %d not defined.  Please call Qhull::defineVertexNeighborFacets() beforehand.", id());
-    }
-    return QhullFacetSet(qh_qh, qh_vertex->neighbors);
-}//neighborFacets
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using std::string;
-using std::vector;
-using orgQhull::QhullPoint;
-using orgQhull::QhullFacet;
-using orgQhull::QhullFacetSet;
-using orgQhull::QhullFacetSetIterator;
-using orgQhull::QhullVertex;
-
-//! Duplicate of qh_printvertex [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullVertex::PrintVertex &pr)
-{
-    QhullVertex v= *pr.vertex;
-    QhullPoint p= v.point();
-    if(*pr.print_message){
-        os << pr.print_message << " ";
-    }else{
-        os << "- ";
-    }
-    os << "p" << p.id() << " (v" << v.id() << "): ";
-    const realT *c= p.coordinates();
-    for(int k= p.dimension(); k--; ){
-        os << " " << *c++; // FIXUP QH11010 %5.2g
-    }
-    if(v.getVertexT()->deleted){
-        os << " deleted";
-    }
-    if(v.getVertexT()->delridge){
-        os << " ridgedeleted";
-    }
-    os << endl;
-    if(v.neighborFacetsDefined()){
-        QhullFacetSetIterator i= v.neighborFacets();
-        if(i.hasNext()){
-            os << " neighborFacets:";
-            countT count= 0;
-            while(i.hasNext()){
-                if(++count % 100 == 0){
-                    os << endl << "     ";
-                }
-                QhullFacet f= i.next();
-                os << " f" << f.id();
-            }
-            os << endl;
-        }
-    }
-    return os;
-}//<< PrintVertex
-
diff --git a/src/qhull/src/libqhullcpp/QhullVertex.h b/src/qhull/src/libqhullcpp/QhullVertex.h
deleted file mode 100644
index 0137766db..000000000
--- a/src/qhull/src/libqhullcpp/QhullVertex.h
+++ /dev/null
@@ -1,104 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertex.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHULLVERTEX_H
-#define QHULLVERTEX_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullLinkedList.h"
-#include "libqhullcpp/QhullSet.h"
-
-#include 
-
-namespace orgQhull {
-
-#//!\name Used here
-    class QhullFacetSet;
-
-#//!\name Defined here
-    //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull_r.h], as a C++ class
-    class QhullVertex;
-    typedef QhullLinkedList QhullVertexList;
-    typedef QhullLinkedListIterator QhullVertexListIterator;
-
-
-/*********************
-  topological information:
-    next,previous       doubly-linked list of all vertices
-    neighborFacets           set of adjacent facets (only if qh.VERTEXneighbors)
-
-  geometric information:
-    point               array of DIM coordinates
-*/
-
-class QhullVertex {
-
-#//!\name Defined here
-public:
-    typedef vertexT *   base_type;  // for QhullVertexSet
-
-private:
-#//!\name Fields
-    vertexT *           qh_vertex;  //!< Corresponding vertexT, never 0
-    QhullQh *           qh_qh;      //!< QhullQh/qhT for vertexT, may be 0
-
-#//!\name Class objects
-    static vertexT      s_empty_vertex;  // needed for shallow copy
-
-public:
-#//!\name Constants
-
-#//!\name Constructors
-                        QhullVertex() : qh_vertex(&s_empty_vertex), qh_qh(0) {}
-    explicit            QhullVertex(const Qhull &q);
-                        QhullVertex(const Qhull &q, vertexT *v);
-    explicit            QhullVertex(QhullQh *qqh) : qh_vertex(&s_empty_vertex), qh_qh(qqh) {}
-                        QhullVertex(QhullQh *qqh, vertexT *v) : qh_vertex(v ? v : &s_empty_vertex), qh_qh(qqh) {}
-                        // Creates an alias.  Does not copy QhullVertex.  Needed for return by value and parameter passing
-                        QhullVertex(const QhullVertex &other) : qh_vertex(other.qh_vertex), qh_qh(other.qh_qh) {}
-                        // Creates an alias.  Does not copy QhullVertex.  Needed for vector
-    QhullVertex &       operator=(const QhullVertex &other) { qh_vertex= other.qh_vertex; qh_qh= other.qh_qh; return *this; }
-                        ~QhullVertex() {}
-
-#//!\name GetSet
-    int                 dimension() const { return (qh_qh ? qh_qh->hull_dim : 0); }
-    vertexT *           getBaseT() const { return getVertexT(); } //!< For QhullSet
-    vertexT *           getVertexT() const { return qh_vertex; }
-    countT              id() const { return qh_vertex->id; }
-    bool                isValid() const { return (qh_qh && qh_vertex != &s_empty_vertex); }
-                        //! True if defineVertexNeighborFacets() already called.  Auotomatically set for facet merging, Voronoi diagrams
-    bool                neighborFacetsDefined() const { return qh_vertex->neighbors != 0; }
-    QhullVertex         next() const { return QhullVertex(qh_qh, qh_vertex->next); }
-    bool                operator==(const QhullVertex &other) const { return qh_vertex==other.qh_vertex; }
-    bool                operator!=(const QhullVertex &other) const { return !operator==(other); }
-    QhullPoint          point() const { return QhullPoint(qh_qh, qh_vertex->point); }
-    QhullVertex         previous() const { return QhullVertex(qh_qh, qh_vertex->previous); }
-    QhullQh *           qh() const { return qh_qh; }
-
-#//!\name foreach
-    //See also QhullVertexList
-    QhullFacetSet       neighborFacets() const;
-
-#//!\name IO
-    struct PrintVertex{
-        const QhullVertex *vertex;
-        const char *    print_message;    //!< non-null message
-                        PrintVertex(const char *message, const QhullVertex &v) : vertex(&v), print_message(message) {}
-    };//PrintVertex
-    PrintVertex         print(const char *message) const { return PrintVertex(message, *this); }
-};//class QhullVertex
-
-}//namespace orgQhull
-
-#//!\name GLobal
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex::PrintVertex &pr);
-inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(""); return os; }
-
-#endif // QHULLVERTEX_H
diff --git a/src/qhull/src/libqhullcpp/QhullVertexSet.cpp b/src/qhull/src/libqhullcpp/QhullVertexSet.cpp
deleted file mode 100644
index 00ba62d19..000000000
--- a/src/qhull/src/libqhullcpp/QhullVertexSet.cpp
+++ /dev/null
@@ -1,161 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertexSet.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! QhullVertexSet -- Qhull's linked Vertexs, as a C++ class
-
-#include "libqhullcpp/QhullVertexSet.h"
-
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::string;
-using std::vector;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
-                                    /* setjmp should not be implemented with 'catch' */
-#endif
-
-namespace orgQhull {
-
-QhullVertexSet::
-QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets)
-: QhullSet(q.qh(), 0)
-, qhsettemp_defined(false)
-{
-    QH_TRY_(q.qh()){ // no object creation -- destructors skipped on longjmp()
-        setT *vertices= qh_facetvertices(q.qh(), facetlist, facetset, allfacets);
-        defineAs(vertices);
-        qhsettemp_defined= true;
-    }
-    q.qh()->NOerrexit= true;
-    q.qh()->maybeThrowQhullMessage(QH_TRY_status);
-}//QhullVertexSet facetlist facetset
-
-//! Return tempory QhullVertexSet of vertices for a list and/or a set of facets
-//! Sets qhsettemp_defined (disallows copy constructor and assignment to prevent double-free)
-QhullVertexSet::
-QhullVertexSet(QhullQh *qqh, facetT *facetlist, setT *facetset, bool allfacets)
-: QhullSet(qqh, 0)
-, qhsettemp_defined(false)
-{
-    QH_TRY_(qh()){ // no object creation -- destructors skipped on longjmp()
-        setT *vertices= qh_facetvertices(qh(), facetlist, facetset, allfacets);
-        defineAs(vertices);
-        qhsettemp_defined= true;
-    }
-    qh()->NOerrexit= true;
-    qh()->maybeThrowQhullMessage(QH_TRY_status);
-}//QhullVertexSet facetlist facetset
-
-//! Copy constructor for argument passing and returning a result
-//! Only copies a pointer to the set.
-//! Throws an error if qhsettemp_defined, otherwise have a double-free
-//!\todo Convert QhullVertexSet to a shared pointer with reference counting
-QhullVertexSet::
-QhullVertexSet(const QhullVertexSet &other)
-: QhullSet(other)
-, qhsettemp_defined(false)
-{
-    if(other.qhsettemp_defined){
-        throw QhullError(10077, "QhullVertexSet: Cannot use copy constructor since qhsettemp_defined (e.g., QhullVertexSet for a set and/or list of QhFacet).  Contains %d vertices", other.count());
-    }
-}//copy constructor
-
-//! Copy assignment only copies a pointer to the set.
-//! Throws an error if qhsettemp_defined, otherwise have a double-free
-QhullVertexSet & QhullVertexSet::
-operator=(const QhullVertexSet &other)
-{
-    QhullSet::operator=(other);
-    qhsettemp_defined= false;
-    if(other.qhsettemp_defined){
-        throw QhullError(10078, "QhullVertexSet: Cannot use copy constructor since qhsettemp_defined (e.g., QhullVertexSet for a set and/or list of QhFacet).  Contains %d vertices", other.count());
-    }
-    return *this;
-}//assignment
-
-void QhullVertexSet::
-freeQhSetTemp()
-{
-    if(qhsettemp_defined){
-        qhsettemp_defined= false;
-        QH_TRY_(qh()){ // no object creation -- destructors skipped on longjmp()
-            qh_settempfree(qh(), referenceSetT()); // errors if not top of tempstack or if qhmem corrupted
-        }
-        qh()->NOerrexit= true;
-        qh()->maybeThrowQhullMessage(QH_TRY_status, QhullError::NOthrow);
-    }
-}//freeQhSetTemp
-
-QhullVertexSet::
-~QhullVertexSet()
-{
-    freeQhSetTemp();
-}//~QhullVertexSet
-
-//FIXUP -- Move conditional, QhullVertexSet code to QhullVertexSet.cpp
-#ifndef QHULL_NO_STL
-std::vector QhullVertexSet::
-toStdVector() const
-{
-    QhullSetIterator i(*this);
-    std::vector vs;
-    while(i.hasNext()){
-        QhullVertex v= i.next();
-        vs.push_back(v);
-    }
-    return vs;
-}//toStdVector
-#endif //QHULL_NO_STL
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-using std::endl;
-using std::ostream;
-using orgQhull::QhullPoint;
-using orgQhull::QhullVertex;
-using orgQhull::QhullVertexSet;
-using orgQhull::QhullVertexSetIterator;
-
-//! Print Vertex identifiers to stream.  Space prefix.  From qh_printVertexheader [io_r.c]
-ostream &
-operator<<(ostream &os, const QhullVertexSet::PrintIdentifiers &pr)
-{
-    os << pr.print_message;
-    for(QhullVertexSet::const_iterator i= pr.vertex_set->begin(); i!=pr.vertex_set->end(); ++i){
-        const QhullVertex v= *i;
-        os << " v" << v.id();
-    }
-    os << endl;
-    return os;
-}//<
-
-namespace orgQhull {
-
-#//!\name Used here
-
-#//!\name Defined here
-    //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
-    //! See Qhull
-    class QhullVertexSet;
-    typedef QhullSetIterator QhullVertexSetIterator;
-
-class QhullVertexSet : public QhullSet {
-
-private:
-#//!\name Fields
-    bool                qhsettemp_defined;  //! Set was allocated with qh_settemp()
-
-public:
-#//!\name Constructor
-                        QhullVertexSet(const Qhull &q, setT *s) : QhullSet(q, s), qhsettemp_defined(false) {}
-                        QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets);
-                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-                        QhullVertexSet(QhullQh *qqh, setT *s) : QhullSet(qqh, s), qhsettemp_defined(false) {}
-                        QhullVertexSet(QhullQh *qqh, facetT *facetlist, setT *facetset, bool allfacets);
-                        //Copy constructor and assignment copies pointer but not contents.  Throws error if qhsettemp_defined.  Needed for return by value.
-                        QhullVertexSet(const QhullVertexSet &other);
-    QhullVertexSet &    operator=(const QhullVertexSet &other);
-                        ~QhullVertexSet();
-
-private:                //!Default constructor disabled.  Will implement allocation later
-                        QhullVertexSet();
-public:
-
-#//!\name Destructor
-    void                freeQhSetTemp();
-
-#//!\name Conversion
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif //QHULL_NO_STL
-#ifdef QHULL_USES_QT
-    QList   toQList() const;
-#endif //QHULL_USES_QT
-
-#//!\name IO
-    struct PrintVertexSet{
-        const QhullVertexSet *vertex_set;
-        const char *    print_message;     //!< non-null message
-                        
-                        PrintVertexSet(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
-    };//PrintVertexSet
-    const PrintVertexSet print(const char *message) const { return PrintVertexSet(message, this); }
-
-    struct PrintIdentifiers{
-        const QhullVertexSet *vertex_set;
-        const char *    print_message;    //!< non-null message
-                        PrintIdentifiers(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
-    };//PrintIdentifiers
-    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
-
-};//class QhullVertexSet
-
-}//namespace orgQhull
-
-#//!\name Global
-
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintVertexSet &pr);
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintIdentifiers &p);
-inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(""); return os; }
-
-#endif // QHULLVERTEXSET_H
diff --git a/src/qhull/src/libqhullcpp/RboxPoints.cpp b/src/qhull/src/libqhullcpp/RboxPoints.cpp
deleted file mode 100644
index d7acd9fce..000000000
--- a/src/qhull/src/libqhullcpp/RboxPoints.cpp
+++ /dev/null
@@ -1,224 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RboxPoints.cpp#3 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include "libqhullcpp/RboxPoints.h"
-
-#include "libqhullcpp/QhullError.h"
-
-#include 
-
-using std::cerr;
-using std::endl;
-using std::istream;
-using std::ostream;
-using std::ostringstream;
-using std::string;
-using std::vector;
-using std::ws;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
-#endif
-
-namespace orgQhull {
-
-#//! RboxPoints -- generate random PointCoordinates for qhull (rbox)
-
-
-#//!\name Constructors
-RboxPoints::
-RboxPoints()
-: PointCoordinates("rbox")
-, rbox_new_count(0)
-, rbox_status(qh_ERRnone)
-, rbox_message()
-{
-    allocateQhullQh();
-}
-
-//! Allocate and generate points according to rboxCommand
-//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
-//! Same as appendPoints()
-RboxPoints::
-RboxPoints(const char *rboxCommand)
-: PointCoordinates("rbox")
-, rbox_new_count(0)
-, rbox_status(qh_ERRnone)
-, rbox_message()
-{
-    allocateQhullQh();
-    // rbox arguments added to comment() via qh_rboxpoints > qh_fprintf_rbox
-    appendPoints(rboxCommand);
-}
-
-RboxPoints::
-~RboxPoints()
-{
-    delete qh();
-    resetQhullQh(0);
-}
-
-// RboxPoints and qh_rboxpoints has several fields in qhT (rbox_errexit..cpp_object)
-// It shares last_random with qh_rand and qh_srand
-// The other fields are unused
-void RboxPoints::
-allocateQhullQh()
-{
-    QHULL_LIB_CHECK /* Check for compatible library */
-    resetQhullQh(new QhullQh);
-}//allocateQhullQh
-
-#//!\name Messaging
-
-void RboxPoints::
-clearRboxMessage()
-{
-    rbox_status= qh_ERRnone;
-    rbox_message.clear();
-}//clearRboxMessage
-
-std::string RboxPoints::
-rboxMessage() const
-{
-    if(rbox_status!=qh_ERRnone){
-        return rbox_message;
-    }
-    if(isEmpty()){
-        return "rbox warning: no points generated\n";
-    }
-    return "rbox: OK\n";
-}//rboxMessage
-
-int RboxPoints::
-rboxStatus() const
-{
-    return rbox_status;
-}
-
-bool RboxPoints::
-hasRboxMessage() const
-{
-    return (rbox_status!=qh_ERRnone);
-}
-
-#//!\name Methods
-
-//! Appends points as defined by rboxCommand
-//! Appends rboxCommand to comment
-//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
-void RboxPoints::
-appendPoints(const char *rboxCommand)
-{
-    string s("rbox ");
-    s += rboxCommand;
-    char *command= const_cast(s.c_str());
-    if(qh()->cpp_object){
-        throw QhullError(10001, "Qhull error: conflicting user of cpp_object for RboxPoints::appendPoints() or corrupted qh_qh");
-    }
-    if(extraCoordinatesCount()!=0){
-        throw QhullError(10067, "Qhull error: Extra coordinates (%d) prior to calling RboxPoints::appendPoints.  Was %s", extraCoordinatesCount(), 0, 0.0, comment().c_str());
-    }
-    countT previousCount= count();
-    qh()->cpp_object= this;           // for qh_fprintf_rbox()
-    int status= qh_rboxpoints(qh(), command);
-    qh()->cpp_object= 0;
-    if(rbox_status==qh_ERRnone){
-        rbox_status= status;
-    }
-    if(rbox_status!=qh_ERRnone){
-        throw QhullError(rbox_status, rbox_message);
-    }
-    if(extraCoordinatesCount()!=0){
-        throw QhullError(10002, "Qhull error: extra coordinates (%d) for PointCoordinates (%x)", extraCoordinatesCount(), 0, 0.0, coordinates());
-    }
-    if(previousCount+newCount()!=count()){
-        throw QhullError(10068, "Qhull error: rbox specified %d points but got %d points for command '%s'", newCount(), count()-previousCount, 0.0, comment().c_str());
-    }
-}//appendPoints
-
-}//namespace orgQhull
-
-#//!\name Global functions
-
-/*---------------------------------
-
-  qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
-    fp is ignored (replaces qh_fprintf_rbox() in userprintf_rbox.c)
-    cpp_object == RboxPoints
-
-notes:
-    only called from qh_rboxpoints()
-    same as fprintf() and Qhull.qh_fprintf()
-    fgets() is not trapped like fprintf()
-    Do not throw errors from here.  Use qh_errexit_rbox;
-    A similar technique can be used for qh_fprintf to capture all of its output
-*/
-extern "C"
-void qh_fprintf_rbox(qhT *qh, FILE*, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    using namespace orgQhull;
-
-    if(!qh->cpp_object){
-        qh_errexit_rbox(qh, 10072);
-    }
-    RboxPoints *out= reinterpret_cast(qh->cpp_object);
-    va_start(args, fmt);
-    if(msgcoderbox_message += newMessage;
-        if(out->rbox_statusrbox_status>=MSG_STDERR){
-            out->rbox_status= msgcode;
-        }
-        va_end(args);
-        return;
-    }
-    switch(msgcode){
-    case 9391:
-    case 9392:
-        out->rbox_message += "RboxPoints error: options 'h', 'n' not supported.\n";
-        qh_errexit_rbox(qh, 10010);
-        /* never returns */
-    case 9393:  // FIXUP QH11026 countT vs. int
-        {
-            int dimension= va_arg(args, int);
-            string command(va_arg(args, char*));
-            countT count= va_arg(args, countT);
-            out->setDimension(dimension);
-            out->appendComment(" \"");
-            out->appendComment(command.substr(command.find(' ')+1));
-            out->appendComment("\"");
-            out->setNewCount(count);
-            out->reservePoints();
-        }
-        break;
-    case 9407:
-        *out << va_arg(args, int);
-        // fall through
-    case 9405:
-        *out << va_arg(args, int);
-        // fall through
-    case 9403:
-        *out << va_arg(args, int);
-        break;
-    case 9408:
-        *out << va_arg(args, double);
-        // fall through
-    case 9406:
-        *out << va_arg(args, double);
-        // fall through
-    case 9404:
-        *out << va_arg(args, double);
-        break;
-    }
-    va_end(args);
-} /* qh_fprintf_rbox */
-
diff --git a/src/qhull/src/libqhullcpp/RboxPoints.h b/src/qhull/src/libqhullcpp/RboxPoints.h
deleted file mode 100644
index e8ec72b14..000000000
--- a/src/qhull/src/libqhullcpp/RboxPoints.h
+++ /dev/null
@@ -1,69 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RboxPoints.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef RBOXPOINTS_H
-#define RBOXPOINTS_H
-
-#include "libqhull_r/qhull_ra.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/PointCoordinates.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! RboxPoints -- generate random PointCoordinates for Qhull
-    class RboxPoints;
-
-class RboxPoints : public PointCoordinates {
-
-private:
-#//!\name Fields and friends
-                        //! PointCoordinates.qh() is owned by RboxPoints
-    countT              rbox_new_count;     //! Number of points for PointCoordinates
-    int                 rbox_status;    //! error status from rboxpoints.  qh_ERRnone if none.
-    std::string         rbox_message;   //! stderr from rboxpoints
-
-    // '::' is required for friend references
-    friend void ::qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
-
-public:
-#//!\name Construct
-                        RboxPoints();
-    explicit            RboxPoints(const char *rboxCommand);
-                        ~RboxPoints();
-private:                // Disable copy constructor and assignment.  RboxPoints owns QhullQh.
-                        RboxPoints(const RboxPoints &);
-                        RboxPoints &operator=(const RboxPoints &);
-private:
-    void                allocateQhullQh();
-
-public:
-#//!\name GetSet
-    void                clearRboxMessage();
-    countT              newCount() const { return rbox_new_count; }
-    std::string         rboxMessage() const;
-    int                 rboxStatus() const;
-    bool                hasRboxMessage() const;
-    void                setNewCount(countT pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }
-
-#//!\name Modify
-    void                appendPoints(const char* rboxCommand);
-    using               PointCoordinates::appendPoints;
-    void                reservePoints() { reserveCoordinates((count()+newCount())*dimension()); }
-};//class RboxPoints
-
-}//namespace orgQhull
-
-#endif // RBOXPOINTS_H
diff --git a/src/qhull/src/libqhullcpp/RoadError.cpp b/src/qhull/src/libqhullcpp/RoadError.cpp
deleted file mode 100644
index 1d41ec1bc..000000000
--- a/src/qhull/src/libqhullcpp/RoadError.cpp
+++ /dev/null
@@ -1,158 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RoadError.cpp#2 $$Change: 2066 $
-** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! RoadError -- All exceptions thrown by Qhull are RoadErrors
-#//! Do not throw RoadError's from destructors.  Use e.logError() instead.
-
-#include "libqhullcpp/RoadError.h"
-
-#include 
-#include 
-#include 
-
-using std::cerr;
-using std::cout;
-using std::string;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Class fields
-
-//! Identifies error messages from Qhull and Road for web searches.
-//! See QhullError.h#QHULLlastError and user.h#MSG_ERROR
-const char * RoadError::
-ROADtag= "QH";
-
-std::ostringstream RoadError::
-global_log;
-
-#//!\name Constructor
-
-RoadError::
-RoadError()
-: error_code(0)
-, log_event()
-, error_message()
-{ }
-
-RoadError::
-RoadError(const RoadError &other)
-: error_code(other.error_code)
-, log_event(other.log_event)
-, error_message(other.error_message)
-{
-}//copy construct
-
-RoadError::
-RoadError(int code, const std::string &message)
-: error_code(code)
-, log_event(message.c_str())
-, error_message(log_event.toString(ROADtag, error_code))
-{
-    log_event.cstr_1= error_message.c_str(); // overwrites initial value
-}
-
-RoadError::
-RoadError(int code, const char *fmt)
-: error_code(code)
-, log_event(fmt)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d)
-: error_code(code)
-, log_event(fmt, d)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2)
-: error_code(code)
-, log_event(fmt, d, d2)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f)
-: error_code(code)
-, log_event(fmt, d, d2, f)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f, const char *s)
-: error_code(code)
-, log_event(fmt, d, d2, f, s)
-, error_message(log_event.toString(ROADtag, code)) // char * may go out of scope
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f, const void *x)
-: error_code(code)
-, log_event(fmt, d, d2, f, x)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f, int i)
-: error_code(code)
-, log_event(fmt, d, d2, f, i)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f, long long i)
-: error_code(code)
-, log_event(fmt, d, d2, f, i)
-, error_message()
-{ }
-
-RoadError::
-RoadError(int code, const char *fmt, int d, int d2, float f, double e)
-: error_code(code)
-, log_event(fmt, d, d2, f, e)
-, error_message()
-{ }
-
-RoadError & RoadError::
-operator=(const RoadError &other)
-{
-    error_code= other.error_code;
-    error_message= other.error_message;
-    log_event= other.log_event;
-    return *this;
-}//operator=
-
-#//!\name Virtual
-const char * RoadError::
-what() const throw()
-{
-    if(error_message.empty()){
-        error_message= log_event.toString(ROADtag, error_code);
-    }
-    return error_message.c_str();
-}//what
-
-#//!\name Updates
-
-//! Log error instead of throwing it.
-//! Not reentrant, so avoid using it if possible
-//!\todo Redesign with a thread-local stream or a reentrant ostringstream
-void RoadError::
-logErrorLastResort() const
-{
-    global_log << what() << endl;
-}//logError
-
-
-}//namespace orgQhull
-
diff --git a/src/qhull/src/libqhullcpp/RoadError.h b/src/qhull/src/libqhullcpp/RoadError.h
deleted file mode 100644
index 1c9f6cdd5..000000000
--- a/src/qhull/src/libqhullcpp/RoadError.h
+++ /dev/null
@@ -1,88 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RoadError.h#4 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef ROADERROR_H
-#define ROADERROR_H
-
-#include "libqhull_r/user_r.h"  /* for QHULL_CRTDBG */
-#include "libqhullcpp/RoadLogEvent.h"
-
-#include 
-#include 
-#include 
-#include 
-
-using std::endl;
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! RoadError -- Report and log errors
-    //!  See discussion in Saylan, G., "Practical C++ error handling in hybrid environments," Dr. Dobb's Journal, p. 50-55, March 2007.
-    //!   He uses an auto_ptr to track a stringstream.  It constructs a string on the fly.  RoadError uses the copy constructor to transform RoadLogEvent into a string
-    class RoadError;
-
-class RoadError : public std::exception {
-
-private:
-#//!\name Fields
-    int                 error_code;  //! Non-zero code (not logged), maybe returned as program status
-    RoadLogEvent        log_event;   //! Format string w/ arguments
-    mutable std::string error_message;  //! Formated error message.  Must be after log_event.
-
-#//!\name Class fields
-    static const char  *  ROADtag;
-    static std::ostringstream  global_log; //!< May be replaced with any ostream object
-                                    //!< Not reentrant -- only used by RoadError::logErrorLastResort()
-
-public:
-#//!\name Constants
-
-#//!\name Constructors
-    RoadError();
-    RoadError(const RoadError &other);  //! Called on throw, generates error_message
-    RoadError(int code, const std::string &message);
-    RoadError(int code, const char *fmt);
-    RoadError(int code, const char *fmt, int d);
-    RoadError(int code, const char *fmt, int d, int d2);
-    RoadError(int code, const char *fmt, int d, int d2, float f);
-    RoadError(int code, const char *fmt, int d, int d2, float f, const char *s);
-    RoadError(int code, const char *fmt, int d, int d2, float f, const void *x);
-    RoadError(int code, const char *fmt, int d, int d2, float f, int i);
-    RoadError(int code, const char *fmt, int d, int d2, float f, long long i);
-    RoadError(int code, const char *fmt, int d, int d2, float f, double e);
-
-    RoadError &         operator=(const RoadError &other);
-                        ~RoadError() throw() {};
-
-#//!\name Class methods
-
-    static void         clearGlobalLog() { global_log.seekp(0); }
-    static bool         emptyGlobalLog() { return global_log.tellp()<=0; }
-    static const char  *stringGlobalLog() { return global_log.str().c_str(); }
-
-#//!\name Virtual
-    virtual const char *what() const throw();
-
-#//!\name GetSet
-    bool                isValid() const { return log_event.isValid(); }
-    int                 errorCode() const { return error_code; };
-   // FIXUP QH11021 should RoadError provide errorMessage().  Currently what()
-    RoadLogEvent        roadLogEvent() const { return log_event; };
-
-#//!\name Update
-    void                logErrorLastResort() const;
-};//class RoadError
-
-}//namespace orgQhull
-
-#//!\name Global
-
-inline std::ostream &   operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
-
-#endif // ROADERROR_H
diff --git a/src/qhull/src/libqhullcpp/RoadLogEvent.cpp b/src/qhull/src/libqhullcpp/RoadLogEvent.cpp
deleted file mode 100644
index 9a9cf5960..000000000
--- a/src/qhull/src/libqhullcpp/RoadLogEvent.cpp
+++ /dev/null
@@ -1,122 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RoadLogEvent.cpp#3 $$Change: 2066 $
-** $Date: 2016/01/18 $$Author: bbarber $
-**
-****************************************************************************/
-
-#//! RoadLogEvent -- All exceptions thrown by Qhull are RoadErrors
-
-#include "libqhullcpp/RoadLogEvent.h"
-
-#include 
-#include 
-#include 
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::string;
-
-#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
-#endif
-
-namespace orgQhull {
-
-#//!\name Conversion
-string RoadLogEvent::
-toString(const char *tag, int code) const
-{
-    ostringstream os;
-    if(tag && code){
-        os << tag << code;
-        if(format_string){
-            os << " ";
-        }
-    }
-    if(!format_string){
-        return os.str();
-    }
-    const char *s= format_string;
-    int dCount= 0;  // Count of %d
-    int fCount= 0;  // Count of %f
-    char extraCode= '\0';
-    while(*s){
-        if(*s!='%'){
-            os << *s++;
-        }else{
-            char c= *++s;
-            s++;
-            switch(c){
-            case 'd':
-                if(++dCount>2){
-                    os << " ERROR_three_%d_in_format ";
-                }else if(dCount==2){
-                    os << int_2;
-                }else{
-                    os << int_1;
-                }
-                break;
-            case 'e':
-                if(firstExtraCode(os, c, &extraCode)){
-                    os << double_1;
-                }
-                break;
-            case 'f':
-                if(++fCount>1){
-                    os << " ERROR_two_%f_in_format ";
-                }else{
-                    os << float_1;
-                }
-                break;
-            case 'i':
-                if(firstExtraCode(os, c, &extraCode)){
-                    os << int64_1;
-                }
-                break;
-            case 's':
-                if(firstExtraCode(os, c, &extraCode)){
-                    os << cstr_1;
-                }
-                break;
-            case 'u':
-                if(firstExtraCode(os, c, &extraCode)){
-                    os << "0x" << std::hex << int64_1 << std::dec;
-                }
-                break;
-            case 'x':
-                if(firstExtraCode(os, c, &extraCode)){
-                    os << void_1;
-                }
-                break;
-            case '%':
-                os << c;
-                break;
-            default:
-                os << " ERROR_%" << c << "_not_defined_in_format";
-                break;
-            }
-        }
-    }
-    if(s[-1]!='\n'){
-        os << endl;
-    }
-    return os.str();
-}//toString
-
-#//!\name Class helpers (static)
-
-//! True if this char is the first extra code
-bool RoadLogEvent::
-firstExtraCode(std::ostream &os, char c, char *extraCode){
-    if(*extraCode){
-        os << " ERROR_%" << *extraCode << "_and_%" << c << "_in_format ";
-        return false;
-    }
-    *extraCode= c;
-    return true;
-}//firstExtraCode
-
-}//namespace orgQhull
-
diff --git a/src/qhull/src/libqhullcpp/RoadLogEvent.h b/src/qhull/src/libqhullcpp/RoadLogEvent.h
deleted file mode 100644
index 7c4cfba0d..000000000
--- a/src/qhull/src/libqhullcpp/RoadLogEvent.h
+++ /dev/null
@@ -1,77 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/RoadLogEvent.h#1 $$Change: 1981 $
-** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef ROADLOGEVENT_H
-#define ROADLOGEVENT_H
-
-#include 
-#include 
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-    //! RoadLogEvent -- Record an event for the RoadLog
-    struct RoadLogEvent;
-
-struct RoadLogEvent {
-
-public:
-#//!\name Fields
-    const char *    format_string; //! Format string (a literal with format codes, for logging)
-    int             int_1;       //! Integer argument (%d, for logging)
-    int             int_2;       //! Integer argument (%d, for logging)
-    float           float_1;     //! Float argument (%f, for logging)
-    union {                      //! One additional argument (for logging)
-        const char *cstr_1;      //!   Cstr argument (%s) -- type checked at construct-time
-        const void *void_1;      //!   Void* argument (%x) -- Use upper-case codes for object types
-        long long   int64_1;     //!   signed int64 (%i).  Ambiguous if unsigned is also defined.
-        double      double_1;    //!   Double argument (%e)
-    };
-
-#//!\name Constants
-
-#//!\name Constructors
-    RoadLogEvent() : format_string(0), int_1(0), int_2(0), float_1(0), int64_1(0) {};
-    explicit RoadLogEvent(const char *fmt) : format_string(fmt), int_1(0), int_2(0), float_1(0), int64_1(0) {};
-    RoadLogEvent(const char *fmt, int d) : format_string(fmt), int_1(d), int_2(0), float_1(0), int64_1(0) {};
-    RoadLogEvent(const char *fmt, int d, int d2) : format_string(fmt), int_1(d), int_2(d2), float_1(0), int64_1(0) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(0) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f, const char *s) : format_string(fmt), int_1(d), int_2(d2), float_1(f), cstr_1(s) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f, const void *x) : format_string(fmt), int_1(d), int_2(d2), float_1(f), void_1(x) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f, int i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f, long long i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
-    RoadLogEvent(const char *fmt, int d, int d2, float f, double g) : format_string(fmt), int_1(d), int_2(d2), float_1(f), double_1(g) {};
-    ~RoadLogEvent() {};
-    //! Default copy constructor and assignment
-
-#//!\name GetSet
-    bool                isValid() const { return format_string!=0; }
-    int                 int1() const { return int_1; };
-    int                 int2() const { return int_2; };
-    float               float1() const { return float_1; };
-    const char *        format() const { return format_string; };
-    const char *        cstr1() const { return cstr_1; };
-    const void *        void1() const { return void_1; };
-    long long           int64() const { return int64_1; };
-    double              double1() const { return double_1; };
-
-#//!\name Conversion
-
-    std::string        toString(const char* tag, int code) const;
-
-private:
-#//!\name Class helpers
-    static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);
-
-
-};//class RoadLogEvent
-
-}//namespace orgQhull
-
-#endif // ROADLOGEVENT_H
diff --git a/src/qhull/src/libqhullcpp/functionObjects.h b/src/qhull/src/libqhullcpp/functionObjects.h
deleted file mode 100644
index 3645c0713..000000000
--- a/src/qhull/src/libqhullcpp/functionObjects.h
+++ /dev/null
@@ -1,67 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/functionObjects.h#1 $$Change: 1981 $
-** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef QHFUNCTIONOBJECTS_H
-#define QHFUNCTIONOBJECTS_H
-
-#include 
-#include 
-
-namespace orgQhull {
-
-#//!\name Defined here
-
-    //! Sum of absolute values of the elements in a container
-    class AbsoluteSumOf;
-    //! Sum of the elements in a container
-    class SumOf;
-    //! Sum of squares of the elements in a container
-    class SumSquaresOf;
-
-#//!\name Class
-
-//! Absolute sum of the elements in a container
-class AbsoluteSumOf
-{
-private:
-    double sum;
-public:
-    inline AbsoluteSumOf() : sum(0.0) {}
-    inline void operator()(double v) { sum += fabs(v); }
-    inline operator double() { return sum; }
-};//AbsoluteSumOf
-
-//! Sum of the elements in a container
-class SumOf
-{
-private:
-    double sum;
-public:
-    inline SumOf() : sum(0.0) {}
-    inline void operator()(double v) { sum += v; }
-    inline operator double() { return sum; }
-};//SumOf
-
-
-//! Sum of squares of the elements in a container
-class SumSquaresOf
-{
-private:
-    double sum;
-public:
-    inline SumSquaresOf() : sum(0.0) {}
-    inline void operator()(double v) { sum += v*v; }
-    inline operator double() { return sum; }
-};//SumSquaresOf
-
-
-}//orgQhull
-
-
-#endif //QHFUNCTIONOBJECTS_H
-
diff --git a/src/qhull/src/libqhullcpp/libqhullcpp.pro b/src/qhull/src/libqhullcpp/libqhullcpp.pro
deleted file mode 100644
index 89b967bef..000000000
--- a/src/qhull/src/libqhullcpp/libqhullcpp.pro
+++ /dev/null
@@ -1,71 +0,0 @@
-# -------------------------------------------------
-# libqhullcpp.pro -- Qt project for Qhull cpp shared library
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-DESTDIR = ../../lib
-TEMPLATE = lib
-# Do not create libqhullcpp as a shared library.  Qhull C++ classes may change layout and size. 
-CONFIG += staticlib warn_on
-CONFIG -= qt rtti
-build_pass:CONFIG(debug, debug|release):{
-   TARGET = qhullcpp_d
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release):{
-   TARGET = qhullcpp
-   OBJECTS_DIR = Release
-}
-MOC_DIR = moc
-
-INCLUDEPATH += ../../src
-INCLUDEPATH += $$PWD # for MOC_DIR
-
-CONFIG += qhull_warn_shadow qhull_warn_conversion
-
-SOURCES += ../libqhullcpp/Coordinates.cpp
-SOURCES += ../libqhullcpp/PointCoordinates.cpp
-SOURCES += ../libqhullcpp/Qhull.cpp
-SOURCES += ../libqhullcpp/QhullFacet.cpp
-SOURCES += ../libqhullcpp/QhullFacetList.cpp
-SOURCES += ../libqhullcpp/QhullFacetSet.cpp
-SOURCES += ../libqhullcpp/QhullHyperplane.cpp
-SOURCES += ../libqhullcpp/QhullPoint.cpp
-SOURCES += ../libqhullcpp/QhullPoints.cpp
-SOURCES += ../libqhullcpp/QhullPointSet.cpp
-SOURCES += ../libqhullcpp/QhullQh.cpp
-SOURCES += ../libqhullcpp/QhullRidge.cpp
-SOURCES += ../libqhullcpp/QhullSet.cpp
-SOURCES += ../libqhullcpp/QhullStat.cpp
-SOURCES += ../libqhullcpp/QhullVertex.cpp
-SOURCES += ../libqhullcpp/QhullVertexSet.cpp
-SOURCES += ../libqhullcpp/RboxPoints.cpp
-SOURCES += ../libqhullcpp/RoadError.cpp
-SOURCES += ../libqhullcpp/RoadLogEvent.cpp
-
-HEADERS += ../libqhullcpp/Coordinates.h
-HEADERS += ../libqhullcpp/functionObjects.h
-HEADERS += ../libqhullcpp/PointCoordinates.h
-HEADERS += ../libqhullcpp/Qhull.h
-HEADERS += ../libqhullcpp/QhullError.h
-HEADERS += ../libqhullcpp/QhullFacet.h
-HEADERS += ../libqhullcpp/QhullFacetList.h
-HEADERS += ../libqhullcpp/QhullFacetSet.h
-HEADERS += ../libqhullcpp/QhullHyperplane.h
-HEADERS += ../libqhullcpp/QhullIterator.h
-HEADERS += ../libqhullcpp/QhullLinkedList.h
-HEADERS += ../libqhullcpp/QhullPoint.h
-HEADERS += ../libqhullcpp/QhullPoints.h
-HEADERS += ../libqhullcpp/QhullPointSet.h
-HEADERS += ../libqhullcpp/QhullQh.h
-HEADERS += ../libqhullcpp/QhullRidge.h
-HEADERS += ../libqhullcpp/QhullSet.h
-HEADERS += ../libqhullcpp/QhullSets.h
-HEADERS += ../libqhullcpp/QhullStat.h
-HEADERS += ../libqhullcpp/QhullVertex.h
-HEADERS += ../libqhullcpp/QhullVertexSet.h
-HEADERS += ../libqhullcpp/RboxPoints.h
-HEADERS += ../libqhullcpp/RoadError.h
-HEADERS += ../libqhullcpp/RoadLogEvent.h
diff --git a/src/qhull/src/libqhullcpp/qt-qhull.cpp b/src/qhull/src/libqhullcpp/qt-qhull.cpp
deleted file mode 100644
index 895f591a8..000000000
--- a/src/qhull/src/libqhullcpp/qt-qhull.cpp
+++ /dev/null
@@ -1,130 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/libqhullcpp/qt-qhull.cpp#1 $$Change: 1981 $
-** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
-**
-****************************************************************************/
-
-#include 
-#include "qhulltest/RoadTest.h"
-
-#ifndef QHULL_USES_QT
-#define QHULL_USES_QT 1
-#endif
-
-#include "Coordinates.h"
-#include "QhullFacetList.h"
-#include "QhullFacetSet.h"
-#include "QhullHyperplane.h"
-#include "QhullPoint.h"
-#include "QhullPoints.h"
-#include "QhullPointSet.h"
-#include "QhullVertex.h"
-#include "QhullVertexSet.h"
-
-namespace orgQhull {
-
-#//!\name Conversions
-
-QList Coordinates::
-toQList() const
-{
-    CoordinatesIterator i(*this);
-    QList cs;
-    while(i.hasNext()){
-        cs.append(i.next());
-    }
-    return cs;
-}//toQList
-
-QList QhullFacetList::
-toQList() const
-{
-    QhullLinkedListIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        QhullFacet f= i.next();
-        if(isSelectAll() || f.isGood()){
-            vs.append(f);
-        }
-    }
-    return vs;
-}//toQList
-
-//! Same as PrintVertices
-QList QhullFacetList::
-vertices_toQList() const
-{
-    QList vs;
-    QhullVertexSet qvs(qh(), first().getFacetT(), NULL, isSelectAll());
-    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
-        vs.push_back(*i);
-    }
-    return vs;
-}//vertices_toQList
-
-QList QhullFacetSet::
-toQList() const
-{
-    QhullSetIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        QhullFacet f= i.next();
-        if(isSelectAll() || f.isGood()){
-            vs.append(f);
-        }
-    }
-    return vs;
-}//toQList
-
-#ifdef QHULL_USES_QT
-QList QhullHyperplane::
-toQList() const
-{
-    QhullHyperplaneIterator i(*this);
-    QList fs;
-    while(i.hasNext()){
-        fs.append(i.next());
-    }
-    fs.append(hyperplane_offset);
-    return fs;
-}//toQList
-#endif //QHULL_USES_QT
-
-QList QhullPoint::
-toQList() const
-{
-    QhullPointIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        vs.append(i.next());
-    }
-    return vs;
-}//toQList
-
-QList QhullPoints::
-toQList() const
-{
-    QhullPointsIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        vs.append(i.next());
-    }
-    return vs;
-}//toQList
-
-/******
-QList QhullPointSet::
-toQList() const
-{
-    QhullPointSetIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        vs.append(i.next());
-    }
-    return vs;
-}//toQList
-*/
-}//orgQhull
-
diff --git a/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp b/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp
deleted file mode 100644
index bb9534d09..000000000
--- a/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp
+++ /dev/null
@@ -1,93 +0,0 @@
-/*
      ---------------------------------
-
-   usermem_r-cpp.cpp
-
-   Redefine qh_exit() as 'throw std::runtime_error("QH10003 ...")'
-
-   This file is not included in the Qhull builds.
-
-   qhull_r calls qh_exit() when qh_errexit() is not available.  For example,
-   it calls qh_exit() if you linked the wrong qhull library.
-
-   The C++ interface avoids most of the calls to qh_exit().
-
-   If needed, include usermem_r-cpp.o before libqhullstatic_r.a.  You may need to
-   override duplicate symbol errors (e.g. /FORCE:MULTIPLE for DevStudio).  It
-   may produce a warning about throwing an error from C code.
-*/
-
-extern "C" {
-    void    qh_exit(int exitcode);
-}
-
-#include 
-#include 
-
-/*---------------------------------
-
-  qh_exit( exitcode )
-    exit program
-
-  notes:
-    same as exit()
-*/
-void qh_exit(int exitcode) {
-    exitcode= exitcode;
-    throw std::runtime_error("QH10003 Qhull error.  See stderr or errfile.");
-} /* exit */
-
-/*---------------------------------
-
-  qh_fprintf_stderr( msgcode, format, list of args )
-    fprintf to stderr with msgcode (non-zero)
-
-  notes:
-    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
-
-    It is typically followed by qh_errexit().
-
-    Redefine this function to avoid using stderr
-
-    Use qh_fprintf [userprintf_r.c] for normal printing
-*/
-void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    va_start(args, fmt);
-    if(msgcode)
-      fprintf(stderr, "QH%.4d ", msgcode);
-    vfprintf(stderr, fmt, args);
-    va_end(args);
-} /* fprintf_stderr */
-
-/*---------------------------------
-
-  qh_free(qhT *qh, mem )
-    free memory
-
-  notes:
-    same as free()
-    No calls to qh_errexit()
-*/
-void qh_free(void *mem) {
-    free(mem);
-} /* free */
-
-/*---------------------------------
-
-    qh_malloc( mem )
-      allocate memory
-
-    notes:
-      same as malloc()
-*/
-void *qh_malloc(size_t size) {
-    return malloc(size);
-} /* malloc */
-
-
diff --git a/src/qhull/src/libqhullstatic/libqhullstatic.pro b/src/qhull/src/libqhullstatic/libqhullstatic.pro
deleted file mode 100644
index 1a516db73..000000000
--- a/src/qhull/src/libqhullstatic/libqhullstatic.pro
+++ /dev/null
@@ -1,19 +0,0 @@
-# -------------------------------------------------
-# libqhullstatic.pro -- Qt project for Qhull static library
-#   Built with qh_QHpointer=0.  See libqhullp.pro
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-include(../qhull-libqhull-src.pri)
-
-DESTDIR = ../../lib
-TEMPLATE = lib
-CONFIG += staticlib warn_on
-CONFIG -= qt
-build_pass:CONFIG(debug, debug|release):{
-    TARGET = qhullstatic_d
-    OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release):{
-    TARGET = qhullstatic
-    OBJECTS_DIR = Release
-}
diff --git a/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro b/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro
deleted file mode 100644
index 2f5bf4d07..000000000
--- a/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro
+++ /dev/null
@@ -1,21 +0,0 @@
-# -------------------------------------------------
-# libqhullstatic_r.pro -- Qt project for Qhull static library
-#
-# It uses reeentrant Qhull
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-DESTDIR = ../../lib
-TEMPLATE = lib
-CONFIG += staticlib warn_on
-CONFIG -= qt
-build_pass:CONFIG(debug, debug|release):{
-    TARGET = qhullstatic_rd
-    OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release):{
-    TARGET = qhullstatic_r
-    OBJECTS_DIR = Release
-}
-
-include(../qhull-libqhull-src_r.pri)
diff --git a/src/qhull/src/qconvex/qconvex.c b/src/qhull/src/qconvex/qconvex.c
deleted file mode 100644
index 41bd666da..000000000
--- a/src/qhull/src/qconvex/qconvex.c
+++ /dev/null
@@ -1,326 +0,0 @@
-/*
      ---------------------------------
-
-   qconvex.c
-      compute convex hulls using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull/libqhull.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qconvex
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qconvex.htm */
-char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qconvex- compute the convex hull\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar points with nearest facet\n\
-    Qi   - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
-    Qbk:n   - scale coord k so that low bound is n\n\
-      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
-    QbB  - scale input to unit cube centered at the origin\n\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    QGn  - good facet if visible from point n, -n for not visible\n\
-    QVn  - good facet if it includes point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar point\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each facet\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    n    - normals with offsets\n\
-    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
-    p    - point coordinates \n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each facet\n\
-    FA   - compute total area and volume for option 's'\n\
-    Fc   - count plus coplanar points for each facet\n\
-           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
-    FC   - centrum for each facet\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - inner plane for each facet\n\
-    FI   - ID for each facet\n\
-    Fm   - merge count for each facet (511 max)\n\
-    Fn   - count plus neighboring facets for each facet\n\
-    FN   - count plus neighboring facets for each point\n\
-    Fo   - outer plane (or max_outside) for each facet\n\
-    FO   - options and precision constants\n\
-    FP   - nearest vertex for each coplanar point\n\
-    FQ   - command used for qconvex\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                      for output: #vertices, #facets,\n\
-                                  #coplanar points, #non-simplicial facets\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0) \n\
-                    #real (2) tot area, tot volume\n\
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
-    Fv   - count plus vertices for each facet\n\
-    FV   - average of vertices (a feasible point for 'H')\n\
-    Fx   - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d, and 4-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qconvex- compute the convex hull.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qconvex.htm):\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each facet\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
-    Fx   - extreme points (convex hull vertices)\n\
-    FA   - report total area and volume\n\
-    FS   - compute total area and volume\n\
-    o    - OFF format (dim, n, points, facets)\n\
-    G    - Geomview output (2-d, 3-d, and 4-d)\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    QVn  - print facets that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
-    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
-    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
-    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
-    rbox c D7 | qconvex FA TF1000\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    normals        OFF_format     points\n\
- summary        facet_dump\n\
-\n\
- Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
- FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
- Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
- FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
- Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
- PMerge_keep    Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
- QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
- QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh NOerrexit = False;
-    qh_checkflags(qh qhull_command, hidden_options);
-    qh_initflags(qh qhull_command);
-    points= qh_readpoints(&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh_ALL);
-#else
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qconvex/qconvex.pro b/src/qhull/src/qconvex/qconvex.pro
deleted file mode 100644
index 1bf631bff..000000000
--- a/src/qhull/src/qconvex/qconvex.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# qconvex.pro -- Qt project file for qconvex.exe
-# -------------------------------------------------
-
-include(../qhull-app-c.pri)
-
-TARGET = qconvex
-
-SOURCES += qconvex.c
diff --git a/src/qhull/src/qconvex/qconvex_r.c b/src/qhull/src/qconvex/qconvex_r.c
deleted file mode 100644
index abf68ce37..000000000
--- a/src/qhull/src/qconvex/qconvex_r.c
+++ /dev/null
@@ -1,328 +0,0 @@
-/*
      ---------------------------------
-
-   qconvex.c
-      compute convex hulls using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qconvex
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qconvex.htm */
-char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qconvex- compute the convex hull\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar points with nearest facet\n\
-    Qi   - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
-    Qbk:n   - scale coord k so that low bound is n\n\
-      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
-    QbB  - scale input to unit cube centered at the origin\n\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    QGn  - good facet if visible from point n, -n for not visible\n\
-    QVn  - good facet if it includes point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar point\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each facet\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    n    - normals with offsets\n\
-    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
-    p    - point coordinates \n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each facet\n\
-    FA   - compute total area and volume for option 's'\n\
-    Fc   - count plus coplanar points for each facet\n\
-           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
-    FC   - centrum for each facet\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - inner plane for each facet\n\
-    FI   - ID for each facet\n\
-    Fm   - merge count for each facet (511 max)\n\
-    Fn   - count plus neighboring facets for each facet\n\
-    FN   - count plus neighboring facets for each point\n\
-    Fo   - outer plane (or max_outside) for each facet\n\
-    FO   - options and precision constants\n\
-    FP   - nearest vertex for each coplanar point\n\
-    FQ   - command used for qconvex\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                      for output: #vertices, #facets,\n\
-                                  #coplanar points, #non-simplicial facets\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0) \n\
-                    #real (2) tot area, tot volume\n\
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
-    Fv   - count plus vertices for each facet\n\
-    FV   - average of vertices (a feasible point for 'H')\n\
-    Fx   - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d, and 4-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qconvex- compute the convex hull.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qconvex.htm):\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each facet\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
-    Fx   - extreme points (convex hull vertices)\n\
-    FA   - report total area and volume\n\
-    FS   - compute total area and volume\n\
-    o    - OFF format (dim, n, points, facets)\n\
-    G    - Geomview output (2-d, 3-d, and 4-d)\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    QVn  - print facets that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
-    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
-    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
-    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
-    rbox c D7 | qconvex FA TF1000\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    normals        OFF_format     points\n\
- summary        facet_dump\n\
-\n\
- Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
- FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
- Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
- FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
- Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
- PMerge_keep    Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
- QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
- QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
-  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh->NOerrexit = False;
-    qh_checkflags(qh, qh->qhull_command, hidden_options);
-    qh_initflags(qh, qh->qhull_command);
-    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option(qh, "Qxact_merge", NULL, NULL);
-      qh->MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(qh, points, numpoints, dim, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);
-    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    exitcode= qh_ERRnone;
-  }
-  qh->NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh, qh_ALL);
-#else
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qdelaunay/qdelaun.c b/src/qhull/src/qdelaunay/qdelaun.c
deleted file mode 100644
index 9011d9fcc..000000000
--- a/src/qhull/src/qdelaunay/qdelaun.c
+++ /dev/null
@@ -1,315 +0,0 @@
-/*
      ---------------------------------
-
-   qdelaun.c
-     compute Delaunay triangulations and furthest-point Delaunay
-     triangulations using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull/libqhull.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qdelau_f.htm and qdelaun.htm */
-char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qdelaunay- compute the Delaunay triangulation\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qu   - compute furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    Qz   - add point-at-infinity to Delaunay triangulation\n\
-    QGn  - print Delaunay region if visible from point n, -n if not\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each Delaunay region\n\
-    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
-    o    - OFF format (dim, points, and facets as a paraboloid)\n\
-    p    - point coordinates (lifted to a paraboloid)\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each Delaunay region\n\
-    FA   - compute total area for option 's'\n\
-    Fc   - count plus coincident points for each Delaunay region\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each Delaunay region\n\
-    Fm   - merge count for each Delaunay region (511 max)\n\
-    FM   - Maple output (2-d only, lifted to a paraboloid)\n\
-    Fn   - count plus neighboring region for each Delaunay region\n\
-    FN   - count plus neighboring region for each point\n\
-    FO   - options and precision constants\n\
-    FP   - nearest point and distance for each coincident point\n\
-    FQ   - command used for qdelaunay\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                    for output: #vertices, #Delaunay regions,\n\
-                                #coincident points, #non-simplicial regions\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0)\n\
-                    #real (2), tot area, 0\n\
-    Fv   - count plus vertices for each Delaunay region\n\
-    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d and 3-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc     - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-    Gt   - transparent outer ridges to view 3-d Delaunay\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest Delaunay regions by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
-    PFn  - keep Delaunay regions whose area is at least n\n\
-    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
-    PMn  - keep n Delaunay regions with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qdelaunay- compute the Delaunay triangulation.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qdelaun.htm):\n\
-    Qu   - furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each Delaunay region\n\
-    Fx   - extreme points (vertices of the convex hull)\n\
-    o    - OFF format (shows the points lifted to a paraboloid)\n\
-    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
-    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
-    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
-    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
-    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    OFF_format     points_lifted  summary\n\
- facet_dump\n\
-\n\
- Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
- FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
- FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
- Fvertices      Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
- QVertex_good   Qzinfinite\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh NOerrexit = False;
-    qh_option("delaunay  Qbbound-last", NULL, NULL);
-    qh DELAUNAY= True;     /* 'd'   */
-    qh SCALElast= True;    /* 'Qbb' */
-    qh KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
-    qh_checkflags(qh qhull_command, hidden_options);
-    qh_initflags(qh qhull_command);
-    points= qh_readpoints(&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh_ALL);
-#else
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qdelaunay/qdelaun_r.c b/src/qhull/src/qdelaunay/qdelaun_r.c
deleted file mode 100644
index 0854b8bb9..000000000
--- a/src/qhull/src/qdelaunay/qdelaun_r.c
+++ /dev/null
@@ -1,317 +0,0 @@
-/*
      ---------------------------------
-
-   qdelaun.c
-     compute Delaunay triangulations and furthest-point Delaunay
-     triangulations using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qdelau_f.htm and qdelaun.htm */
-char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qdelaunay- compute the Delaunay triangulation\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qu   - compute furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    Qz   - add point-at-infinity to Delaunay triangulation\n\
-    QGn  - print Delaunay region if visible from point n, -n if not\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each Delaunay region\n\
-    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
-    o    - OFF format (dim, points, and facets as a paraboloid)\n\
-    p    - point coordinates (lifted to a paraboloid)\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each Delaunay region\n\
-    FA   - compute total area for option 's'\n\
-    Fc   - count plus coincident points for each Delaunay region\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each Delaunay region\n\
-    Fm   - merge count for each Delaunay region (511 max)\n\
-    FM   - Maple output (2-d only, lifted to a paraboloid)\n\
-    Fn   - count plus neighboring region for each Delaunay region\n\
-    FN   - count plus neighboring region for each point\n\
-    FO   - options and precision constants\n\
-    FP   - nearest point and distance for each coincident point\n\
-    FQ   - command used for qdelaunay\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                    for output: #vertices, #Delaunay regions,\n\
-                                #coincident points, #non-simplicial regions\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0)\n\
-                    #real (2), tot area, 0\n\
-    Fv   - count plus vertices for each Delaunay region\n\
-    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d and 3-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc     - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-    Gt   - transparent outer ridges to view 3-d Delaunay\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest Delaunay regions by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
-    PFn  - keep Delaunay regions whose area is at least n\n\
-    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
-    PMn  - keep n Delaunay regions with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qdelaunay- compute the Delaunay triangulation.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qdelaun.htm):\n\
-    Qu   - furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each Delaunay region\n\
-    Fx   - extreme points (vertices of the convex hull)\n\
-    o    - OFF format (shows the points lifted to a paraboloid)\n\
-    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
-    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
-    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
-    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
-    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    OFF_format     points_lifted  summary\n\
- facet_dump\n\
-\n\
- Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
- FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
- FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
- Fvertices      Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
- QVertex_good   Qzinfinite\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
-  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh->NOerrexit = False;
-    qh_option(qh, "delaunay  Qbbound-last", NULL, NULL);
-    qh->DELAUNAY= True;     /* 'd'   */
-    qh->SCALElast= True;    /* 'Qbb' */
-    qh->KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
-    qh_checkflags(qh, qh->qhull_command, hidden_options);
-    qh_initflags(qh, qh->qhull_command);
-    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option(qh, "Qxact_merge", NULL, NULL);
-      qh->MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(qh, points, numpoints, dim, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);
-    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    exitcode= qh_ERRnone;
-  }
-  qh->NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh, qh_ALL);
-#else
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qdelaunay/qdelaunay.pro b/src/qhull/src/qdelaunay/qdelaunay.pro
deleted file mode 100644
index 138ac0589..000000000
--- a/src/qhull/src/qdelaunay/qdelaunay.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# qdelaunay.pro -- Qt project file for qvoronoi.exe
-# -------------------------------------------------
-
-include(../qhull-app-c.pri)
-
-TARGET = qdelaunay
-
-SOURCES += qdelaun.c
diff --git a/src/qhull/src/qhalf/qhalf.c b/src/qhull/src/qhalf/qhalf.c
deleted file mode 100644
index 4a5889ed7..000000000
--- a/src/qhull/src/qhalf/qhalf.c
+++ /dev/null
@@ -1,316 +0,0 @@
-/*
      ---------------------------------
-
-   qhalf.c
-     compute the intersection of halfspaces about a point
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull/libqhull.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qhalf.htm */
-char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qhalf- compute the intersection of halfspaces about a point\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    optional interior point: dimension, 1, coordinates\n\
-    first lines: dimension+1 and number of halfspaces\n\
-    other lines: halfspace coefficients followed by offset\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar halfspaces\n\
-    Qi   - keep other redundant halfspaces\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    Qs   - search all halfspaces for the initial simplex\n\
-    QGn  - print intersection if visible to halfspace n, -n for not\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when halfspace n added to intersection\n\
-    TMn  - turn on tracing at merge n\n\
-    TWn  - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
-    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar halfspace\n\
-    Wn   - min facet width for outside halfspace (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (dual convex hull)\n\
-    i    - non-redundant halfspaces incident to each intersection\n\
-    m    - Mathematica output (dual convex hull)\n\
-    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
-    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fc   - count plus redundant halfspaces for each intersection\n\
-         -   Qc (default) for coplanar and Qi for other redundant\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each intersection\n\
-    Fm   - merge count for each intersection (511 max)\n\
-    FM   - Maple output (dual convex hull)\n\
-    Fn   - count plus neighboring intersections for each intersection\n\
-    FN   - count plus intersections for each non-redundant halfspace\n\
-    FO   - options and precision constants\n\
-    Fp   - dim, count, and intersection coordinates\n\
-    FP   - nearest halfspace and distance for each redundant halfspace\n\
-    FQ   - command used for qhalf\n\
-    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
-                      for output: #non-redundant, #intersections, #coplanar\n\
-                                  halfspaces, #non-simplicial intersections\n\
-                    #real (2), max outer plane, min vertex\n\
-    Fv   - count plus non-redundant halfspaces for each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
-    Ga   - all points (i.e., transformed halfspaces) as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
-    Gi   - inner planes (i.e., halfspace intersections) only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets (i.e., intersections) by area\n\
-    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n- drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhalf- halfspace intersection about a point.  Qhull %s\n\
-    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qhalf.htm):\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    Fp   - intersection coordinates\n\
-    Fv   - non-redundant halfspaces incident to each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-    o    - OFF file format (dual convex hull)\n\
-    G    - Geomview output (dual convex hull)\n\
-    m    - Mathematica output (dual convex hull)\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
-    rbox c | qconvex FQ FV n | qhalf s i\n\
-    rbox c | qconvex FQ FV n | qhalf s o\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper_case options take an argument.\n\
-\n\
- incidences     Geomview       mathematica    OFF_format     point_dual\n\
- summary        facet_dump\n\
-\n\
- Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
- Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
- FQhalf         Fsummary       Fv_halfspace   FMaple         Fx_non_redundant\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
- Qsearch_1st    Qtriangulate   QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh NOerrexit = False;
-    qh_option("Halfspace", NULL, NULL);
-    qh HALFspace= True;    /* 'H'   */
-    qh_checkflags(qh qhull_command, hidden_options);
-    qh_initflags(qh qhull_command);
-    if (qh SCALEinput) {
-      fprintf(qh ferr, "\
-qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
-             Use 'Qbk:0Bk:0 to drop dimension k.\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    points= qh_readpoints(&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh_ALL);
-#else
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qhalf/qhalf.pro b/src/qhull/src/qhalf/qhalf.pro
deleted file mode 100644
index ebad38789..000000000
--- a/src/qhull/src/qhalf/qhalf.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# qhalf.pro -- Qt project file for qconvex.exe
-# -------------------------------------------------
-
-include(../qhull-app-c.pri)
-
-TARGET = qhalf
-
-SOURCES += qhalf.c
diff --git a/src/qhull/src/qhalf/qhalf_r.c b/src/qhull/src/qhalf/qhalf_r.c
deleted file mode 100644
index c49d777f9..000000000
--- a/src/qhull/src/qhalf/qhalf_r.c
+++ /dev/null
@@ -1,318 +0,0 @@
-/*
      ---------------------------------
-
-   qhalf.c
-     compute the intersection of halfspaces about a point
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qhalf.htm */
-char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qhalf- compute the intersection of halfspaces about a point\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    optional interior point: dimension, 1, coordinates\n\
-    first lines: dimension+1 and number of halfspaces\n\
-    other lines: halfspace coefficients followed by offset\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar halfspaces\n\
-    Qi   - keep other redundant halfspaces\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    Qs   - search all halfspaces for the initial simplex\n\
-    QGn  - print intersection if visible to halfspace n, -n for not\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when halfspace n added to intersection\n\
-    TMn  - turn on tracing at merge n\n\
-    TWn  - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
-    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar halfspace\n\
-    Wn   - min facet width for outside halfspace (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (dual convex hull)\n\
-    i    - non-redundant halfspaces incident to each intersection\n\
-    m    - Mathematica output (dual convex hull)\n\
-    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
-    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fc   - count plus redundant halfspaces for each intersection\n\
-         -   Qc (default) for coplanar and Qi for other redundant\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each intersection\n\
-    Fm   - merge count for each intersection (511 max)\n\
-    FM   - Maple output (dual convex hull)\n\
-    Fn   - count plus neighboring intersections for each intersection\n\
-    FN   - count plus intersections for each non-redundant halfspace\n\
-    FO   - options and precision constants\n\
-    Fp   - dim, count, and intersection coordinates\n\
-    FP   - nearest halfspace and distance for each redundant halfspace\n\
-    FQ   - command used for qhalf\n\
-    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
-                      for output: #non-redundant, #intersections, #coplanar\n\
-                                  halfspaces, #non-simplicial intersections\n\
-                    #real (2), max outer plane, min vertex\n\
-    Fv   - count plus non-redundant halfspaces for each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
-    Ga   - all points (i.e., transformed halfspaces) as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
-    Gi   - inner planes (i.e., halfspace intersections) only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets (i.e., intersections) by area\n\
-    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n- drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhalf- halfspace intersection about a point.  Qhull %s\n\
-    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qhalf.htm):\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    Fp   - intersection coordinates\n\
-    Fv   - non-redundant halfspaces incident to each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-    o    - OFF file format (dual convex hull)\n\
-    G    - Geomview output (dual convex hull)\n\
-    m    - Mathematica output (dual convex hull)\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
-    rbox c | qconvex FQ FV n | qhalf s i\n\
-    rbox c | qconvex FQ FV n | qhalf s o\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper_case options take an argument.\n\
-\n\
- incidences     Geomview       mathematica    OFF_format     point_dual\n\
- summary        facet_dump\n\
-\n\
- Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
- Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
- FQhalf         Fsummary       Fv_halfspace   FMaple         Fx_non_redundant\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
- Qsearch_1st    Qtriangulate   QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
-  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh->NOerrexit = False;
-    qh_option(qh, "Halfspace", NULL, NULL);
-    qh->HALFspace= True;    /* 'H'   */
-    qh_checkflags(qh, qh->qhull_command, hidden_options);
-    qh_initflags(qh, qh->qhull_command);
-    if (qh->SCALEinput) {
-      fprintf(qh->ferr, "\
-qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
-             Use 'Qbk:0Bk:0 to drop dimension k.\n");
-      qh_errexit(qh, qh_ERRinput, NULL, NULL);
-    }
-    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option(qh, "Qxact_merge", NULL, NULL);
-      qh->MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(qh, points, numpoints, dim, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);
-    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    exitcode= qh_ERRnone;
-  }
-  qh->NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh, qh_ALL);
-#else
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qhull-all.pro b/src/qhull/src/qhull-all.pro
deleted file mode 100644
index 1d3a0ac6f..000000000
--- a/src/qhull/src/qhull-all.pro
+++ /dev/null
@@ -1,94 +0,0 @@
-# -------------------------------------------------
-# qhull-all.pro -- Qt project to build executables and static libraries
-#
-# To build with Qt on mingw
-#   Download Qt SDK, install Perl
-#   /c/qt/2010.05/qt> ./configure -static -platform win32-g++ -fast -no-qt3support
-#
-# To build DevStudio sln and proj files (Qhull ships with cmake derived files)
-# qmake is in Qt's bin directory
-# mkdir -p build && cd build && qmake -tp vc -r ../src/qhull-all.pro
-# Additional Library Directories -- C:\qt\Qt5.2.0\5.2.0\msvc2012_64\lib
-# libqhullcpp and libqhullstatic refered to $(QTDIR) but apparently didn't retrieve (should be %QTDIR%?)
-# libqhull_r also needs ..\..\lib
-# Need to change build/x64/Debug/*.lib to lib/ (or copy libs by hand, each time)
-# Additional Build Dependencies
-# See README.txt -- Need to add Build Dependencies, disable rtti, rename targets to qhull.dll, qhull6_p.dll and qhull6_pd.dll
-# -------------------------------------------------
-
-TEMPLATE = subdirs
-CONFIG += ordered
-
-SUBDIRS += libqhull_r      #shared library with reentrant code
-SUBDIRS += libqhullstatic  #static library
-SUBDIRS += libqhullstatic_r #static library with reentrant code
-SUBDIRS += libqhullcpp     #static library for C++ interface with libqhullstatic_r
-
-SUBDIRS += qhull           #qhull program linked to libqhullstatic_r
-SUBDIRS += rbox         
-SUBDIRS += qconvex         #qhull programs linked to libqhullstatic
-SUBDIRS += qdelaunay
-SUBDIRS += qhalf
-SUBDIRS += qvoronoi
-
-SUBDIRS += user_eg         #user programs linked to libqhull_r
-SUBDIRS += user_eg2  
-SUBDIRS += user_eg3        #user program with libqhullcpp and libqhullstatic_r
-
-SUBDIRS += qhulltest       #C++ test program with Qt, libqhullcpp, and libqhullstatic_r
-SUBDIRS += testqset        #test program for qset.c with mem.c
-SUBDIRS += testqset_r      #test program for qset_r.c with mem_r.c
-                           #See eg/q_test for qhull tests
-
-OTHER_FILES += Changes.txt
-OTHER_FILES += CMakeLists.txt
-OTHER_FILES += Make-config.sh
-OTHER_FILES += ../Announce.txt
-OTHER_FILES += ../CMakeLists.txt
-OTHER_FILES += ../COPYING.txt
-OTHER_FILES += ../File_id.diz
-OTHER_FILES += ../index.htm
-OTHER_FILES += ../Makefile
-OTHER_FILES += ../README.txt
-OTHER_FILES += ../REGISTER.txt
-OTHER_FILES += ../eg/q_eg
-OTHER_FILES += ../eg/q_egtest
-OTHER_FILES += ../eg/q_test
-OTHER_FILES += ../html/index.htm
-OTHER_FILES += ../html/qconvex.htm
-OTHER_FILES += ../html/qdelau_f.htm
-OTHER_FILES += ../html/qdelaun.htm
-OTHER_FILES += ../html/qhalf.htm
-OTHER_FILES += ../html/qh-code.htm
-OTHER_FILES += ../html/qh-eg.htm
-OTHER_FILES += ../html/qh-faq.htm
-OTHER_FILES += ../html/qh-get.htm
-OTHER_FILES += ../html/qh-impre.htm
-OTHER_FILES += ../html/qh-optc.htm
-OTHER_FILES += ../html/qh-optf.htm
-OTHER_FILES += ../html/qh-optg.htm
-OTHER_FILES += ../html/qh-opto.htm
-OTHER_FILES += ../html/qh-optp.htm
-OTHER_FILES += ../html/qh-optq.htm
-OTHER_FILES += ../html/qh-optt.htm
-OTHER_FILES += ../html/qh-quick.htm
-OTHER_FILES += ../html/qhull.htm
-OTHER_FILES += ../html/qhull.man
-OTHER_FILES += ../html/qhull.txt
-OTHER_FILES += ../html/qhull-cpp.xml
-OTHER_FILES += ../html/qvoron_f.htm
-OTHER_FILES += ../html/qvoronoi.htm
-OTHER_FILES += ../html/rbox.htm
-OTHER_FILES += ../html/rbox.man
-OTHER_FILES += ../html/rbox.txt
-OTHER_FILES += ../src/libqhull/Makefile
-OTHER_FILES += ../src/libqhull_r/Makefile
-OTHER_FILES += ../src/libqhull_r/qhull_r-exports.def
-OTHER_FILES += ../src/qconvex/qconvex_r.c
-OTHER_FILES += ../src/qdelaunay/qdelaun_r.c
-OTHER_FILES += ../src/qhalf/qhalf_r.c
-OTHER_FILES += ../src/qhull/rbox_r.c
-OTHER_FILES += ../src/qvoronoi/qvoronoi_r.c
-OTHER_FILES += ../src/qhull/unix.c
-OTHER_FILES += ../src/user_eg/user_eg.c
-OTHER_FILES += ../src/user_eg2/user_eg2.c
diff --git a/src/qhull/src/qhull-app-c.pri b/src/qhull/src/qhull-app-c.pri
deleted file mode 100644
index 05e5a00f2..000000000
--- a/src/qhull/src/qhull-app-c.pri
+++ /dev/null
@@ -1,24 +0,0 @@
-# -------------------------------------------------
-# qhull-app-c.pri -- Qt include project for C qhull applications linked to libqhull
-# -------------------------------------------------
-
-include(qhull-warn.pri)
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-
-LIBS += -L../../lib
-build_pass:CONFIG(debug, debug|release){
-   LIBS += -lqhullstatic_d
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   LIBS += -lqhullstatic
-   OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-INCLUDEPATH += ..
-CONFIG += qhull_warn_conversion
-
diff --git a/src/qhull/src/qhull-app-c_r.pri b/src/qhull/src/qhull-app-c_r.pri
deleted file mode 100644
index 9c2ef5600..000000000
--- a/src/qhull/src/qhull-app-c_r.pri
+++ /dev/null
@@ -1,26 +0,0 @@
-# -------------------------------------------------
-# qhull-app-c_r.pri -- Qt include project for C qhull applications linked to qhullstatic_r
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(qhull-warn.pri)
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-
-LIBS += -L../../lib
-build_pass:CONFIG(debug, debug|release){
-   LIBS += -lqhullstatic_rd
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   LIBS += -lqhullstatic_r
-   OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-INCLUDEPATH += ..
-CONFIG += qhull_warn_conversion
-
diff --git a/src/qhull/src/qhull-app-cpp.pri b/src/qhull/src/qhull-app-cpp.pri
deleted file mode 100644
index a6f17d8ec..000000000
--- a/src/qhull/src/qhull-app-cpp.pri
+++ /dev/null
@@ -1,23 +0,0 @@
-# -------------------------------------------------
-# qhull-app-cpp.pri -- Qt include project for qhull as C++ classes
-# -------------------------------------------------
-
-include(qhull-warn.pri)
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= rtti
-LIBS += -L../../lib
-build_pass:CONFIG(debug, debug|release){
-   LIBS += -lqhullcpp_d
-   LIBS += -lqhullstatic_rd  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp-d.lib
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   LIBS += -lqhullcpp
-   LIBS += -lqhullstatic_r  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp.lib
-   OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-INCLUDEPATH += ../../src # "libqhull_r/qhull_a.h"
diff --git a/src/qhull/src/qhull-app-shared.pri b/src/qhull/src/qhull-app-shared.pri
deleted file mode 100644
index 1f4026a6a..000000000
--- a/src/qhull/src/qhull-app-shared.pri
+++ /dev/null
@@ -1,27 +0,0 @@
-# -------------------------------------------------
-# qhull-app-shared.pri -- Deprecated Qt include project for C qhull applications linked with libqhull (shared library)
-# -------------------------------------------------
-
-include(qhull-warn.pri)
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-
-LIBS += -L../../lib
-build_pass:CONFIG(debug, debug|release){
-   LIBS += -lqhull_d
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   LIBS += -lqhull
-   OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-win32-msvc* : DEFINES += qh_dllimport # libqhull/user.h
-
-INCLUDEPATH += ../libqhull
-CONFIG += qhull_warn_conversion
-
-
diff --git a/src/qhull/src/qhull-app-shared_r.pri b/src/qhull/src/qhull-app-shared_r.pri
deleted file mode 100644
index e55c1a65f..000000000
--- a/src/qhull/src/qhull-app-shared_r.pri
+++ /dev/null
@@ -1,29 +0,0 @@
-# -------------------------------------------------
-# qhull-app-shared_r.pri -- Qt include project for C qhull applications linked with libqhull_r (shared library)
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(qhull-warn.pri)
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-
-LIBS += -L../../lib
-build_pass:CONFIG(debug, debug|release){
-   LIBS += -lqhull_rd
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   LIBS += -lqhull_r
-   OBJECTS_DIR = Release
-}
-win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
-
-win32-msvc* : DEFINES += qh_dllimport # libqhull_r/user.h
-
-INCLUDEPATH += ..
-CONFIG += qhull_warn_conversion
-
-
diff --git a/src/qhull/src/qhull-libqhull-src.pri b/src/qhull/src/qhull-libqhull-src.pri
deleted file mode 100644
index e7aff3f78..000000000
--- a/src/qhull/src/qhull-libqhull-src.pri
+++ /dev/null
@@ -1,39 +0,0 @@
-# -------------------------------------------------
-# qhull-libqhull-src.pri -- Qt include project for libqhull sources and headers
-#   libqhull.pro, libqhullp.pro, and libqhulldll.pro are the same for SOURCES and HEADERS
-# -------------------------------------------------
-
-# Order object files by frequency of execution.  Small files at end.
-# Current directory is caller
-
-# libqhull/libqhull.pro and ../qhull-libqhull-src.pri have the same SOURCES and HEADERS
-SOURCES += ../libqhull/global.c
-SOURCES += ../libqhull/stat.c
-SOURCES += ../libqhull/geom2.c
-SOURCES += ../libqhull/poly2.c
-SOURCES += ../libqhull/merge.c
-SOURCES += ../libqhull/libqhull.c
-SOURCES += ../libqhull/geom.c
-SOURCES += ../libqhull/poly.c
-SOURCES += ../libqhull/qset.c
-SOURCES += ../libqhull/mem.c
-SOURCES += ../libqhull/random.c
-SOURCES += ../libqhull/usermem.c
-SOURCES += ../libqhull/userprintf.c
-SOURCES += ../libqhull/io.c
-SOURCES += ../libqhull/user.c
-SOURCES += ../libqhull/rboxlib.c
-SOURCES += ../libqhull/userprintf_rbox.c
-
-# [2014] qmake locates the headers in the shadow build directory not the src directory
-HEADERS += ../libqhull/geom.h
-HEADERS += ../libqhull/io.h
-HEADERS += ../libqhull/libqhull.h
-HEADERS += ../libqhull/mem.h
-HEADERS += ../libqhull/merge.h
-HEADERS += ../libqhull/poly.h
-HEADERS += ../libqhull/random.h
-HEADERS += ../libqhull/qhull_a.h
-HEADERS += ../libqhull/qset.h
-HEADERS += ../libqhull/stat.h
-HEADERS += ../libqhull/user.h
diff --git a/src/qhull/src/qhull-libqhull-src_r.pri b/src/qhull/src/qhull-libqhull-src_r.pri
deleted file mode 100644
index 3b53291b1..000000000
--- a/src/qhull/src/qhull-libqhull-src_r.pri
+++ /dev/null
@@ -1,39 +0,0 @@
-# -------------------------------------------------
-# qhull-libqhull-src_r.pri -- Qt include project for libqhull_r sources and headers
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-# Order object files by frequency of execution.  Small files at end.
-# Current directory is caller
-
-# libqhull_r/libqhull_r.pro and ../qhull-libqhull-src_r.pri have the same SOURCES and HEADERS
-SOURCES += ../libqhull_r/global_r.c
-SOURCES += ../libqhull_r/stat_r.c
-SOURCES += ../libqhull_r/geom2_r.c
-SOURCES += ../libqhull_r/poly2_r.c
-SOURCES += ../libqhull_r/merge_r.c
-SOURCES += ../libqhull_r/libqhull_r.c
-SOURCES += ../libqhull_r/geom_r.c
-SOURCES += ../libqhull_r/poly_r.c
-SOURCES += ../libqhull_r/qset_r.c
-SOURCES += ../libqhull_r/mem_r.c
-SOURCES += ../libqhull_r/random_r.c
-SOURCES += ../libqhull_r/usermem_r.c
-SOURCES += ../libqhull_r/userprintf_r.c
-SOURCES += ../libqhull_r/io_r.c
-SOURCES += ../libqhull_r/user_r.c
-SOURCES += ../libqhull_r/rboxlib_r.c
-SOURCES += ../libqhull_r/userprintf_rbox_r.c
-
-HEADERS += ../libqhull_r/geom_r.h
-HEADERS += ../libqhull_r/io_r.h
-HEADERS += ../libqhull_r/libqhull_r.h
-HEADERS += ../libqhull_r/mem_r.h
-HEADERS += ../libqhull_r/merge_r.h
-HEADERS += ../libqhull_r/poly_r.h
-HEADERS += ../libqhull_r/random_r.h
-HEADERS += ../libqhull_r/qhull_ra.h
-HEADERS += ../libqhull_r/qset_r.h
-HEADERS += ../libqhull_r/stat_r.h
-HEADERS += ../libqhull_r/user_r.h
diff --git a/src/qhull/src/qhull-warn.pri b/src/qhull/src/qhull-warn.pri
deleted file mode 100644
index 7d0e7fa2f..000000000
--- a/src/qhull/src/qhull-warn.pri
+++ /dev/null
@@ -1,57 +0,0 @@
-# -------------------------------------------------
-# qhull-warn.pri -- Qt project warnings for warn_on
-#   CONFIG += qhull_warn_all        # Qhull compiles with all warnings except for qhull_warn_shadow and qhull_warn_conversion
-#   CONFIG += qhull_warn_conversion # Warn in Qt and Qhull about conversion errors
-#   CONFIG += qhull_warn_error      # Turn warnings into errors
-#   CONFIG += qhull_warn_shadow     # Warn in Qt about shadowing of functions and fields
-# -------------------------------------------------
-
-# [apr'11] VERSION works erratically for msvc builds
-# VERSION = 7.2.0
-qhull_SOVERSION = 7
-
-# Uncomment to report warnings as errors
-#CONFIG += qhull_warn_error
-
-*g++{
-    qhull_warn_error{
-        QMAKE_CFLAGS_WARN_ON += -Werror
-        QMAKE_CXXFLAGS_WARN_ON += -Werror
-    }
-
-    QMAKE_CFLAGS_WARN_ON += -Wcast-qual -Wextra -Wshadow -Wwrite-strings
-
-    QMAKE_CXXFLAGS_WARN_ON += -Wcast-qual -Wextra -Wwrite-strings
-    QMAKE_CXXFLAGS_WARN_ON += -Wno-sign-conversion
-
-    qhull_warn_shadow{
-        QMAKE_CXXFLAGS_WARN_ON += -Wshadow     # Shadowing occurs in Qt, e.g., nested foreach
-    }
-
-    qhull_warn_conversion{
-        QMAKE_CFLAGS_WARN_ON += -Wno-sign-conversion   # libqhullstatic has many size_t vs. int warnings
-        QMAKE_CFLAGS_WARN_ON += -Wconversion           # libqhullstatic has no workaround for bit-field conversions
-        QMAKE_CXXFLAGS_WARN_ON += -Wconversion         # Qt has conversion errors for qbitarray and qpalette
-    }
-
-    qhull_warn_all{
-        QMAKE_CFLAGS_WARN_ON += -Waddress -Warray-bounds -Wchar-subscripts -Wclobbered -Wcomment -Wempty-body
-        QMAKE_CFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wimplicit-function-declaration -Wimplicit-int
-        QMAKE_CFLAGS_WARN_ON += -Wmain -Wmissing-braces -Wmissing-field-initializers -Wmissing-parameter-type
-        QMAKE_CFLAGS_WARN_ON += -Wnonnull -Wold-style-declaration -Woverride-init -Wparentheses
-        QMAKE_CFLAGS_WARN_ON += -Wpointer-sign -Wreturn-type -Wsequence-point -Wsign-compare
-        QMAKE_CFLAGS_WARN_ON += -Wsign-compare -Wstrict-aliasing -Wstrict-overflow=1 -Wswitch
-        QMAKE_CFLAGS_WARN_ON += -Wtrigraphs -Wtype-limits -Wuninitialized -Wuninitialized
-        QMAKE_CFLAGS_WARN_ON += -Wunknown-pragmas -Wunused-function -Wunused-label -Wunused-parameter
-        QMAKE_CFLAGS_WARN_ON += -Wunused-value -Wunused-variable -Wvolatile-register-var
-
-        QMAKE_CXXFLAGS_WARN_ON += -Waddress -Warray-bounds -Wc++0x-compat -Wchar-subscripts
-        QMAKE_CXXFLAGS_WARN_ON += -Wclobbered -Wcomment -Wempty-body -Wenum-compare
-        QMAKE_CXXFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wmain -Wmissing-braces
-        QMAKE_CXXFLAGS_WARN_ON += -Wmissing-field-initializers -Wparentheses -Wreorder -Wreturn-type
-        QMAKE_CXXFLAGS_WARN_ON += -Wsequence-point -Wsign-compare -Wsign-compare -Wstrict-aliasing
-        QMAKE_CXXFLAGS_WARN_ON += -Wstrict-overflow=1 -Wswitch -Wtrigraphs -Wtype-limits
-        QMAKE_CXXFLAGS_WARN_ON += -Wuninitialized -Wunknown-pragmas -Wunused-function -Wunused-label
-        QMAKE_CXXFLAGS_WARN_ON += -Wunused-parameter -Wunused-value -Wunused-variable -Wvolatile-register-var
-    }
-}
diff --git a/src/qhull/src/qhull/qhull.pro b/src/qhull/src/qhull/qhull.pro
deleted file mode 100644
index 839372856..000000000
--- a/src/qhull/src/qhull/qhull.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# qhull.pro -- Qt project file for qhull.exe with libqhullstatic_r
-# -------------------------------------------------
-
-include(../qhull-app-c_r.pri)
-
-TARGET = qhull
-
-SOURCES += unix_r.c
diff --git a/src/qhull/src/qhull/unix.c b/src/qhull/src/qhull/unix.c
deleted file mode 100644
index 892a819c3..000000000
--- a/src/qhull/src/qhull/unix.c
+++ /dev/null
@@ -1,372 +0,0 @@
-/*
      ---------------------------------
-
-   unix.c
-     command line interface to qhull
-         includes SIOUX interface for Macintoshes
-
-   see qh-qhull.htm
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/qhull/unix.c#4 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-*/
-
-#include "libqhull/libqhull.h"
-#include "libqhull/qset.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  see:
-    concise prompt below
-*/
-char qh_prompta[]= "\n\
-qhull- compute convex hulls and related structures.\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-    halfspaces:  use dim plus one and put offset after coefficients.\n\
-                 May be preceded by a single interior point ('H').\n\
-\n\
-options:\n\
-    d    - Delaunay triangulation by lifting points to a paraboloid\n\
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
-    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
-    v Qu - furthest-site Voronoi diagram\n\
-    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar points with nearest facet\n\
-    Qi   - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
-    Qbk:n   - scale coord k so that low bound is n\n\
-      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
-    QbB  - scale input to unit cube centered at the origin\n\
-    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qf   - partition point to furthest outside facet\n\
-    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
-    Qm   - only process points that would increase max_outside\n\
-    Qr   - process random outside points instead of furthest ones\n\
-    Qs   - search all points for the initial simplex\n\
-    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
-              returns furthest-site Delaunay triangulation\n\
-    Qv   - test vertex neighbors for convexity\n\
-    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
-    Qz   - add point-at-infinity to Delaunay triangulation\n\
-    QGn  - good facet if visible from point n, -n for not visible\n\
-    QVn  - good facet if it includes point n, -n if not\n\
-    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
-    Q1     - sort merges by type instead of angle\n\
-    Q2   - merge all non-convex at once instead of independent sets\n\
-    Q3   - do not merge redundant vertices\n\
-    Q4   - avoid old->new merges\n\
-    Q5   - do not correct outer planes at end of qhull\n\
-    Q6   - do not pre-merge concave or coplanar facets\n\
-    Q7   - depth-first processing instead of breadth-first\n\
-    Q8   - do not process near-inside points\n\
-    Q9   - process furthest of furthest points\n\
-    Q10  - no special processing for narrow distributions\n\
-    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
-    Q12  - no error on wide merge due to duplicate ridge\n\
-\n\
-";
-char qh_promptc[]= "\
-Topts- Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Ta   - annotate output with message codes\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TRn  - rerun qhull n times.  Use with 'QJn'\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    En   - max roundoff error for distance computation\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
-    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
-    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each facet\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    o    - OFF format (dim, points and facets; Voronoi regions)\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each facet\n\
-    FA   - compute total area and volume for option 's'\n\
-    Fc   - count plus coplanar points for each facet\n\
-           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
-    FC   - centrum or Voronoi center for each facet\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - inner plane for each facet\n\
-           for 'v', separating hyperplanes for bounded Voronoi regions\n\
-    FI   - ID of each facet\n\
-    Fm   - merge count for each facet (511 max)\n\
-    FM   - Maple output (2-d and 3-d)\n\
-    Fn   - count plus neighboring facets for each facet\n\
-    FN   - count plus neighboring facets for each point\n\
-    Fo   - outer plane (or max_outside) for each facet\n\
-           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
-    FO   - options and precision constants\n\
-    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
-    FP   - nearest vertex and distance for each coplanar point\n\
-    FQ   - command used for qhull\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0)\n\
-                    #real (2) tot area, tot volume\n\
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
-    Fv   - count plus vertices for each facet\n\
-           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
-    FV   - average of vertices (a feasible point for 'H')\n\
-    Fx   - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-    Gt   - for 3-d 'd', transparent outer ridges\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhull- compute convex hulls and related structures.  Qhull %s\n\
-    input (stdin): dimension, n, point coordinates\n\
-    comments start with a non-numeric character\n\
-    halfspace: use dim+1 and put offsets after coefficients\n\
-\n\
-options (qh-quick.htm):\n\
-    d    - Delaunay triangulation by lifting points to a paraboloid\n\
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
-    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
-    v Qu - furthest-site Voronoi diagram\n\
-    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    .    - concise list of all options\n\
-    -    - one-line description of each option\n\
-    -V   - version\n\
-\n\
-Output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each facet\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
-           if 'v', Voronoi vertices\n\
-    Fp   - halfspace intersections\n\
-    Fx   - extreme points (convex hull vertices)\n\
-    FA   - compute total area and volume\n\
-    o    - OFF format (if 'v', outputs Voronoi regions)\n\
-    G    - Geomview output (2-d, 3-d and 4-d)\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    QVn  - print facets that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA\n\
-    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
-    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
-    rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp\n\
-    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
-    rbox y 1000 W0 | qhull                    rbox c | qhull n\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
- incidences     mathematica    normals        OFF_format     points\n\
- summary\n\
-\n\
- Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
- FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
- Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
- FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
- Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
- Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
- QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
- QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
-\n\
- Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
- Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
- Q10_no_narrow  Q11_trinormals Q12_no_wide_dup\n\
-\n\
- T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
- Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
- TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
- Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh_initflags(qh qhull_command);
-    points= qh_readpoints(&numpoints, &dim, &ismalloc);
-    qh_init_B(points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull( qh_ALL);
-#else
-  qh_freeqhull( !qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qhull/unix_r.c b/src/qhull/src/qhull/unix_r.c
deleted file mode 100644
index 3f999f7fa..000000000
--- a/src/qhull/src/qhull/unix_r.c
+++ /dev/null
@@ -1,374 +0,0 @@
-/*
      ---------------------------------
-
-   unix.c
-     command line interface to qhull
-         includes SIOUX interface for Macintoshes
-
-   see qh-qhull.htm
-
-   Copyright (c) 1993-2015 The Geometry Center.
-   $Id: //main/2015/qhull/src/qhull/unix_r.c#6 $$Change: 2066 $
-   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
-*/
-
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  see:
-    concise prompt below
-*/
-char qh_prompta[]= "\n\
-qhull- compute convex hulls and related structures.\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-    halfspaces:  use dim plus one and put offset after coefficients.\n\
-                 May be preceded by a single interior point ('H').\n\
-\n\
-options:\n\
-    d    - Delaunay triangulation by lifting points to a paraboloid\n\
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
-    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
-    v Qu - furthest-site Voronoi diagram\n\
-    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar points with nearest facet\n\
-    Qi   - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
-    Qbk:n   - scale coord k so that low bound is n\n\
-      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
-    QbB  - scale input to unit cube centered at the origin\n\
-    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qf   - partition point to furthest outside facet\n\
-    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
-    Qm   - only process points that would increase max_outside\n\
-    Qr   - process random outside points instead of furthest ones\n\
-    Qs   - search all points for the initial simplex\n\
-    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
-              returns furthest-site Delaunay triangulation\n\
-    Qv   - test vertex neighbors for convexity\n\
-    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
-    Qz   - add point-at-infinity to Delaunay triangulation\n\
-    QGn  - good facet if visible from point n, -n for not visible\n\
-    QVn  - good facet if it includes point n, -n if not\n\
-    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
-    Q1     - sort merges by type instead of angle\n\
-    Q2   - merge all non-convex at once instead of independent sets\n\
-    Q3   - do not merge redundant vertices\n\
-    Q4   - avoid old->new merges\n\
-    Q5   - do not correct outer planes at end of qhull\n\
-    Q6   - do not pre-merge concave or coplanar facets\n\
-    Q7   - depth-first processing instead of breadth-first\n\
-    Q8   - do not process near-inside points\n\
-    Q9   - process furthest of furthest points\n\
-    Q10  - no special processing for narrow distributions\n\
-    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
-    Q12  - no error on wide merge due to duplicate ridge\n\
-\n\
-";
-char qh_promptc[]= "\
-Topts- Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Ta   - annotate output with message codes\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TRn  - rerun qhull n times.  Use with 'QJn'\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    En   - max roundoff error for distance computation\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
-    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
-    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each facet\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    o    - OFF format (dim, points and facets; Voronoi regions)\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each facet\n\
-    FA   - compute total area and volume for option 's'\n\
-    Fc   - count plus coplanar points for each facet\n\
-           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
-    FC   - centrum or Voronoi center for each facet\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - inner plane for each facet\n\
-           for 'v', separating hyperplanes for bounded Voronoi regions\n\
-    FI   - ID of each facet\n\
-    Fm   - merge count for each facet (511 max)\n\
-    FM   - Maple output (2-d and 3-d)\n\
-    Fn   - count plus neighboring facets for each facet\n\
-    FN   - count plus neighboring facets for each point\n\
-    Fo   - outer plane (or max_outside) for each facet\n\
-           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
-    FO   - options and precision constants\n\
-    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
-    FP   - nearest vertex and distance for each coplanar point\n\
-    FQ   - command used for qhull\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0)\n\
-                    #real (2) tot area, tot volume\n\
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
-    Fv   - count plus vertices for each facet\n\
-           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
-    FV   - average of vertices (a feasible point for 'H')\n\
-    Fx   - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-    Gt   - for 3-d 'd', transparent outer ridges\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhull- compute convex hulls and related structures.  Qhull %s\n\
-    input (stdin): dimension, n, point coordinates\n\
-    comments start with a non-numeric character\n\
-    halfspace: use dim+1 and put offsets after coefficients\n\
-\n\
-options (qh-quick.htm):\n\
-    d    - Delaunay triangulation by lifting points to a paraboloid\n\
-    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
-    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
-    v Qu - furthest-site Voronoi diagram\n\
-    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    .    - concise list of all options\n\
-    -    - one-line description of each option\n\
-    -V   - version\n\
-\n\
-Output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each facet\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
-           if 'v', Voronoi vertices\n\
-    Fp   - halfspace intersections\n\
-    Fx   - extreme points (convex hull vertices)\n\
-    FA   - compute total area and volume\n\
-    o    - OFF format (if 'v', outputs Voronoi regions)\n\
-    G    - Geomview output (2-d, 3-d and 4-d)\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    QVn  - print facets that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA\n\
-    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
-    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
-    rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp\n\
-    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
-    rbox y 1000 W0 | qhull                    rbox c | qhull n\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
- incidences     mathematica    normals        OFF_format     points\n\
- summary\n\
-\n\
- Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
- FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
- Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
- FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
- Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
- Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
- QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
- QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
-\n\
- Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
- Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
- Q10_no_narrow  Q11_trinormals Q12_no_wide_dup\n\
-\n\
- T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
- Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
- TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
- Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
-  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh->NOerrexit = False;
-    qh_initflags(qh, qh->qhull_command);
-    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
-    qh_init_B(qh, points, numpoints, dim, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);
-    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    exitcode= qh_ERRnone;
-  }
-  qh->NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh, qh_ALL);
-#else
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qhulltest/Coordinates_test.cpp b/src/qhull/src/qhulltest/Coordinates_test.cpp
deleted file mode 100644
index 3e8658a5b..000000000
--- a/src/qhull/src/qhulltest/Coordinates_test.cpp
+++ /dev/null
@@ -1,539 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/Coordinates_test.cpp#2 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/Coordinates.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class Coordinates_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void t_construct();
-    void t_convert();
-    void t_element();
-    void t_readonly();
-    void t_operator();
-    void t_const_iterator();
-    void t_iterator();
-    void t_coord_iterator();
-    void t_mutable_coord_iterator();
-    void t_readwrite();
-    void t_search();
-    void t_io();
-};//Coordinates_test
-
-void
-add_Coordinates_test()
-{
-    new Coordinates_test();  // RoadTest::s_testcases
-}
-
-void Coordinates_test::
-t_construct()
-{
-    Coordinates c;
-    QCOMPARE(c.size(), 0U);
-    QVERIFY(c.isEmpty());
-    c << 1.0;
-    QCOMPARE(c.count(), 1);
-    Coordinates c2(c);
-    c2 << 2.0;
-    QCOMPARE(c2.count(), 2);
-    Coordinates c3;
-    c3 = c2;
-    QCOMPARE(c3.count(), 2);
-    QCOMPARE(c3[0]+c3[1], 3.0);
-    QVERIFY(c2==c3);
-    std::vector vc;
-    vc.push_back(3.0);
-    vc.push_back(4.0);
-    Coordinates c4(vc);
-    QCOMPARE(c4[0]+c4[1], 7.0);
-    Coordinates c5(c3);
-    QVERIFY(c5==c3);
-    c5= vc;
-    QVERIFY(c5!=c3);
-    QVERIFY(c5==c4);
-}//t_construct
-
-void Coordinates_test::
-t_convert()
-{
-    Coordinates c;
-    c << 1.0 << 3.0;
-    QCOMPARE(c.data()[1], 3.0);
-    coordT *c2= c.data();
-    const coordT *c3= c.data();
-    QCOMPARE(c2, c3);
-    std::vector vc= c.toStdVector();
-    QCOMPARE((size_t)vc.size(), c.size());
-    for(int k= (int)vc.size(); k--; ){
-        QCOMPARE(vc[k], c[k]);
-    }
-    QList qc= c.toQList();
-    QCOMPARE(qc.count(), c.count());
-    for(int k= qc.count(); k--; ){
-        QCOMPARE(qc[k], c[k]);
-    }
-    Coordinates c4;
-    c4= std::vector(2, 0.0);
-    QCOMPARE(c4.back(), 0.0);
-    Coordinates c5(std::vector(2, 0.0));
-    QCOMPARE(c4.size(), c5.size());
-    QVERIFY(c4==c5);
-}//t_convert
-
-void Coordinates_test::
-t_element()
-{
-    Coordinates c;
-    c << 1.0 << -2.0;
-    c.at(1)= -3;
-    QCOMPARE(c.at(1), -3.0);
-    QCOMPARE(c.back(), -3.0);
-    QCOMPARE(c.front(), 1.0);
-    c[1]= -2.0;
-    QCOMPARE(c[1],-2.0);
-    QCOMPARE(c.first(), 1.0);
-    c.first()= 2.0;
-    QCOMPARE(c.first(), 2.0);
-    QCOMPARE(c.last(), -2.0);
-    c.last()= 0.0;
-    QCOMPARE(c.first()+c.last(), 2.0);
-    coordT *c4= &c.first();
-    const coordT *c5= &c.first();
-    QCOMPARE(c4, c5);
-    coordT *c6= &c.last();
-    const coordT *c7= &c.last();
-    QCOMPARE(c6, c7);
-    Coordinates c2= c.mid(1);
-    QCOMPARE(c2.count(), 1);
-    c << 3.0;
-    Coordinates c3= c.mid(1,1);
-    QCOMPARE(c2, c3);
-    QCOMPARE(c3.value(-1, -1.0), -1.0);
-    QCOMPARE(c3.value(3, 4.0), 4.0);
-    QCOMPARE(c.value(2, 4.0), 3.0);
-}//t_element
-
-void Coordinates_test::
-t_readonly()
-{
-    Coordinates c;
-    QCOMPARE(c.size(), 0u);
-    QCOMPARE(c.count(), 0);
-    QVERIFY(c.isEmpty());
-    c << 1.0 << -2.0;
-    QCOMPARE(c.size(), 2u);
-    QCOMPARE(c.count(), 2);
-    QVERIFY(!c.isEmpty());
-}//t_readonly
-
-void Coordinates_test::
-t_operator()
-{
-    Coordinates c;
-    Coordinates c2(c);
-    QVERIFY(c==c2);
-    QVERIFY(!(c!=c2));
-    c << 1.0;
-    QVERIFY(!(c==c2));
-    QVERIFY(c!=c2);
-    c2 << 1.0;
-    QVERIFY(c==c2);
-    QVERIFY(!(c!=c2));
-    c[0]= 0.0;
-    QVERIFY(c!=c2);
-    Coordinates c3= c+c2;
-    QCOMPARE(c3.count(), 2);
-    QCOMPARE(c3[0], 0.0);
-    QCOMPARE(c3[1], 1.0);
-    c3 += c3;
-    QCOMPARE(c3.count(), 4);
-    QCOMPARE(c3[2], 0.0);
-    QCOMPARE(c3[3], 1.0);
-    c3 += c2;
-    QCOMPARE(c3[4], 1.0);
-    c3 += 5.0;
-    QCOMPARE(c3.count(), 6);
-    QCOMPARE(c3[5], 5.0);
-    // << checked above
-}//t_operator
-
-void Coordinates_test::
-t_const_iterator()
-{
-    Coordinates c;
-    QCOMPARE(c.begin(), c.end());
-    // begin and end checked elsewhere
-    c << 1.0 << 3.0;
-    Coordinates::const_iterator i= c.begin();
-    QCOMPARE(*i, 1.0);
-    QCOMPARE(i[1], 3.0);
-    // i[1]= -3.0; // compiler error
-    // operator-> is not applicable to double
-    QCOMPARE(*i++, 1.0);
-    QCOMPARE(*i, 3.0);
-    QCOMPARE(*i--, 3.0);
-    QCOMPARE(*i, 1.0);
-    QCOMPARE(*(i+1), 3.0);
-    QCOMPARE(*++i, 3.0);
-    QCOMPARE(*(i-1), 1.0);
-    QCOMPARE(*--i, 1.0);
-    QVERIFY(i==c.begin());
-    QVERIFY(i==c.constBegin());
-    QVERIFY(i!=c.end());
-    QVERIFY(i!=c.constEnd());
-    QVERIFY(i=c.begin());
-    QVERIFY(i+1<=c.end());
-    QVERIFY(i+1>c.begin());
-    Coordinates::iterator i2= c.begin();
-    Coordinates::const_iterator i3(i2);
-    QCOMPARE(*i3, 1.0);
-    QCOMPARE(i3[1], 3.0);
-}//t_const_iterator
-
-void Coordinates_test::
-t_iterator()
-{
-    Coordinates c;
-    QCOMPARE(c.begin(), c.end());
-    // begin and end checked elsewhere
-    c << 1.0 << 3.0;
-    Coordinates::iterator i= c.begin();
-    QCOMPARE(*i, 1.0);
-    QCOMPARE(i[1], 3.0);
-    *i= -1.0;
-    QCOMPARE(*i, -1.0);
-    i[1]= -3.0;
-    QCOMPARE(i[1], -3.0);
-    *i= 1.0;
-    // operator-> is not applicable to double
-    QCOMPARE(*i++, 1.0);
-    QCOMPARE(*i, -3.0);
-    *i= 3.0;
-    QCOMPARE(*i--, 3.0);
-    QCOMPARE(*i, 1.0);
-    QCOMPARE(*(i+1), 3.0);
-    QCOMPARE(*++i, 3.0);
-    QCOMPARE(*(i-1), 1.0);
-    QCOMPARE(*--i, 1.0);
-    QVERIFY(i==c.begin());
-    QVERIFY(i==c.constBegin());
-    QVERIFY(i!=c.end());
-    QVERIFY(i!=c.constEnd());
-    QVERIFY(i=c.begin());
-    QVERIFY(i+1<=c.end());
-    QVERIFY(i+1>c.begin());
-}//t_iterator
-
-void Coordinates_test::
-t_coord_iterator()
-{
-    Coordinates c;
-    c << 1.0 << 3.0;
-    CoordinatesIterator i(c);
-    CoordinatesIterator i2= c;
-    QVERIFY(i.findNext(1.0));
-    QVERIFY(!i.findNext(2.0));
-    QVERIFY(!i.findNext(3.0));
-    QVERIFY(i.findPrevious(3.0));
-    QVERIFY(!i.findPrevious(2.0));
-    QVERIFY(!i.findPrevious(1.0));
-    QVERIFY(i2.findNext(3.0));
-    QVERIFY(i2.findPrevious(3.0));
-    QVERIFY(i2.findNext(3.0));
-    QVERIFY(i2.findPrevious(1.0));
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i.toBack();
-    i2.toFront();
-    QVERIFY(!i.hasNext());
-    QVERIFY(i.hasPrevious());
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    Coordinates c2;
-    i2= c2;
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    i2.toBack();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekPrevious(), 3.0);
-    QCOMPARE(i.previous(), 3.0);
-    QCOMPARE(i.previous(), 1.0);
-    QVERIFY(!i.hasPrevious());
-    QCOMPARE(i.peekNext(), 1.0);
-    // i.peekNext()= 1.0; // compiler error
-    QCOMPARE(i.next(), 1.0);
-    QCOMPARE(i.peekNext(), 3.0);
-    QCOMPARE(i.next(), 3.0);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), 1.0);
-}//t_coord_iterator
-
-void Coordinates_test::
-t_mutable_coord_iterator()
-{
-    // Same tests as CoordinatesIterator
-    Coordinates c;
-    c << 1.0 << 3.0;
-    MutableCoordinatesIterator i(c);
-    MutableCoordinatesIterator i2= c;
-    QVERIFY(i.findNext(1.0));
-    QVERIFY(!i.findNext(2.0));
-    QVERIFY(!i.findNext(3.0));
-    QVERIFY(i.findPrevious(3.0));
-    QVERIFY(!i.findPrevious(2.0));
-    QVERIFY(!i.findPrevious(1.0));
-    QVERIFY(i2.findNext(3.0));
-    QVERIFY(i2.findPrevious(3.0));
-    QVERIFY(i2.findNext(3.0));
-    QVERIFY(i2.findPrevious(1.0));
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i.toBack();
-    i2.toFront();
-    QVERIFY(!i.hasNext());
-    QVERIFY(i.hasPrevious());
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    Coordinates c2;
-    i2= c2;
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    i2.toBack();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekPrevious(), 3.0);
-    QCOMPARE(i.peekPrevious(), 3.0);
-    QCOMPARE(i.previous(), 3.0);
-    QCOMPARE(i.previous(), 1.0);
-    QVERIFY(!i.hasPrevious());
-    QCOMPARE(i.peekNext(), 1.0);
-    QCOMPARE(i.next(), 1.0);
-    QCOMPARE(i.peekNext(), 3.0);
-    QCOMPARE(i.next(), 3.0);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), 1.0);
-
-    // Mutable tests
-    i.toFront();
-    i.peekNext()= -1.0;
-    QCOMPARE(i.peekNext(), -1.0);
-    QCOMPARE((i.next()= 1.0), 1.0);
-    QCOMPARE(i.peekPrevious(), 1.0);
-    i.remove();
-    QCOMPARE(c.count(), 1);
-    i.remove();
-    QCOMPARE(c.count(), 1);
-    QCOMPARE(i.peekNext(), 3.0);
-    i.insert(1.0);
-    i.insert(2.0);
-    QCOMPARE(c.count(), 3);
-    QCOMPARE(i.peekNext(), 3.0);
-    QCOMPARE(i.peekPrevious(), 2.0);
-    i.peekPrevious()= -2.0;
-    QCOMPARE(i.peekPrevious(), -2.0);
-    QCOMPARE((i.previous()= 2.0), 2.0);
-    QCOMPARE(i.peekNext(), 2.0);
-    i.toBack();
-    i.remove();
-    QCOMPARE(c.count(), 3); // unchanged
-    i.toFront();
-    i.remove();
-    QCOMPARE(c.count(), 3); // unchanged
-    QCOMPARE(i.peekNext(), 1.0);
-    i.remove();
-    QCOMPARE(c.count(), 3); // unchanged
-    i.insert(0.0);
-    QCOMPARE(c.count(), 4);
-    QCOMPARE(i.value(), 0.0);
-    QCOMPARE(i.peekPrevious(), 0.0);
-    i.setValue(-10.0);
-    QCOMPARE(c.count(), 4); // unchanged
-    QCOMPARE(i.peekNext(), 1.0);
-    QCOMPARE(i.peekPrevious(), -10.0);
-    i.findNext(1.0);
-    i.setValue(-1.0);
-    QCOMPARE(i.peekPrevious(), -1.0);
-    i.setValue(1.0);
-    QCOMPARE(i.peekPrevious(), 1.0);
-    QCOMPARE(i.value(), 1.0);
-    i.findPrevious(1.0);
-    i.setValue(-1.0);
-    QCOMPARE(i.peekNext(), -1.0);
-    i.toBack();
-    QCOMPARE(i.previous(), 3.0);
-    i.setValue(-3.0);
-    QCOMPARE(i.peekNext(), -3.0);
-    double d= i.value();
-    QCOMPARE(d, -3.0);
-    QCOMPARE(i.previous(), 2.0);
-}//t_mutable_coord_iterator
-
-void Coordinates_test::
-t_readwrite()
-{
-    Coordinates c;
-    c.clear();
-    QCOMPARE(c.count(), 0);
-    c << 1.0 << 3.0;
-    c.clear();
-    QCOMPARE(c.count(), 0);
-    coordT c2[4]= { 0.0, 1.0, 2.0, 3.0};
-    c.append(4, c2);
-    QCOMPARE(c.count(), 4);
-    QCOMPARE(c[0], 0.0);
-    QCOMPARE(c[1], 1.0);
-    QCOMPARE(c[3], 3.0);
-    c.clear();
-    c << 1.0 << 3.0;
-    c.erase(c.begin(), c.end());
-    QCOMPARE(c.count(), 0);
-    c << 1.0 << 0.0;
-    Coordinates::iterator i= c.erase(c.begin());
-    QCOMPARE(*i, 0.0);
-    i= c.insert(c.end(), 1.0);
-    QCOMPARE(*i, 1.0);
-    QCOMPARE(c.count(), 2);
-    c.pop_back();
-    QCOMPARE(c.count(), 1);   // 0
-    QCOMPARE(c[0], 0.0);
-    c.push_back(2.0);
-    QCOMPARE(c.count(), 2);
-    c.append(3.0);
-    QCOMPARE(c.count(), 3);   // 0, 2, 3
-    QCOMPARE(c[2], 3.0);
-    c.insert(0, 4.0);
-    QCOMPARE(c[0], 4.0);
-    QCOMPARE(c[3], 3.0);
-    c.insert(c.count(), 5.0);
-    QCOMPARE(c.count(), 5);   // 4, 0, 2, 3, 5
-    QCOMPARE(c[4], 5.0);
-    c.move(4, 0);
-    QCOMPARE(c.count(), 5);   // 5, 4, 0, 2, 3
-    QCOMPARE(c[0], 5.0);
-    c.pop_front();
-    QCOMPARE(c.count(), 4);
-    QCOMPARE(c[0], 4.0);
-    c.prepend(6.0);
-    QCOMPARE(c.count(), 5);   // 6, 4, 0, 2, 3
-    QCOMPARE(c[0], 6.0);
-    c.push_front(7.0);
-    QCOMPARE(c.count(), 6);
-    QCOMPARE(c[0], 7.0);
-    c.removeAt(1);
-    QCOMPARE(c.count(), 5);   // 7, 4, 0, 2, 3
-    QCOMPARE(c[1], 4.0);
-    c.removeFirst();
-    QCOMPARE(c.count(), 4);   // 4, 0, 2, 3
-    QCOMPARE(c[0], 4.0);
-    c.removeLast();
-    QCOMPARE(c.count(), 3);
-    QCOMPARE(c.last(), 2.0);
-    c.replace(2, 8.0);
-    QCOMPARE(c.count(), 3);   // 4, 0, 8
-    QCOMPARE(c[2], 8.0);
-    c.swap(0, 2);
-    QCOMPARE(c[2], 4.0);
-    double d= c.takeAt(2);
-    QCOMPARE(c.count(), 2);   // 8, 0
-    QCOMPARE(d, 4.0);
-    double d2= c.takeFirst();
-    QCOMPARE(c.count(), 1);   // 0
-    QCOMPARE(d2, 8.0);
-    double d3= c.takeLast();
-    QVERIFY(c.isEmpty()); \
-    QCOMPARE(d3, 0.0);
-}//t_readwrite
-
-void Coordinates_test::
-t_search()
-{
-    Coordinates c;
-    c << 1.0 << 3.0 << 1.0;
-    QVERIFY(c.contains(1.0));
-    QVERIFY(c.contains(3.0));
-    QVERIFY(!c.contains(0.0));
-    QCOMPARE(c.count(1.0), 2);
-    QCOMPARE(c.count(3.0), 1);
-    QCOMPARE(c.count(0.0), 0);
-    QCOMPARE(c.indexOf(1.0), 0);
-    QCOMPARE(c.indexOf(3.0), 1);
-    QCOMPARE(c.indexOf(1.0, -1), 2);
-    QCOMPARE(c.indexOf(3.0, -1), -1);
-    QCOMPARE(c.indexOf(3.0, -2), 1);
-    QCOMPARE(c.indexOf(1.0, -3), 0);
-    QCOMPARE(c.indexOf(1.0, -4), 0);
-    QCOMPARE(c.indexOf(1.0, 1), 2);
-    QCOMPARE(c.indexOf(3.0, 2), -1);
-    QCOMPARE(c.indexOf(1.0, 2), 2);
-    QCOMPARE(c.indexOf(1.0, 3), -1);
-    QCOMPARE(c.indexOf(1.0, 4), -1);
-    QCOMPARE(c.lastIndexOf(1.0), 2);
-    QCOMPARE(c.lastIndexOf(3.0), 1);
-    QCOMPARE(c.lastIndexOf(1.0, -1), 2);
-    QCOMPARE(c.lastIndexOf(3.0, -1), 1);
-    QCOMPARE(c.lastIndexOf(3.0, -2), 1);
-    QCOMPARE(c.lastIndexOf(1.0, -3), 0);
-    QCOMPARE(c.lastIndexOf(1.0, -4), -1);
-    QCOMPARE(c.lastIndexOf(1.0, 1), 0);
-    QCOMPARE(c.lastIndexOf(3.0, 2), 1);
-    QCOMPARE(c.lastIndexOf(1.0, 2), 2);
-    QCOMPARE(c.lastIndexOf(1.0, 3), 2);
-    QCOMPARE(c.lastIndexOf(1.0, 4), 2);
-    c.removeAll(3.0);
-    QCOMPARE(c.count(), 2);
-    c.removeAll(4.0);
-    QCOMPARE(c.count(), 2);
-    c.removeAll(1.0);
-    QCOMPARE(c.count(), 0);
-    c.removeAll(4.0);
-    QCOMPARE(c.count(), 0);
-}//t_search
-
-void Coordinates_test::
-t_io()
-{
-    Coordinates c;
-    c << 1.0 << 2.0 << 3.0;
-    ostringstream os;
-    os << "Coordinates 1-2-3\n" << c;
-    cout << os.str();
-    QString s= QString::fromStdString(os.str());
-    QCOMPARE(s.count("2"), 2);
-}//t_io
-
-}//orgQhull
-
-#include "moc/Coordinates_test.moc"
diff --git a/src/qhull/src/qhulltest/PointCoordinates_test.cpp b/src/qhull/src/qhulltest/PointCoordinates_test.cpp
deleted file mode 100644
index 09285954d..000000000
--- a/src/qhull/src/qhulltest/PointCoordinates_test.cpp
+++ /dev/null
@@ -1,478 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/PointCoordinates_test.cpp#2 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/PointCoordinates.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-using std::stringstream;
-
-namespace orgQhull {
-
-class PointCoordinates_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void t_construct_q();
-    void t_construct_qh();
-    void t_convert();
-    void t_getset();
-    void t_element();
-    void t_foreach();
-    void t_search();
-    void t_modify();
-    void t_append_points();
-    void t_coord_iterator();
-    void t_io();
-};//PointCoordinates_test
-
-void
-add_PointCoordinates_test()
-{
-    new PointCoordinates_test();  // RoadTest::s_testcases
-}
-
-void PointCoordinates_test::
-t_construct_q()
-{
-    Qhull q;
-    PointCoordinates pc(q);
-    QCOMPARE(pc.size(), 0U);
-    QCOMPARE(pc.coordinateCount(), 0);
-    QCOMPARE(pc.dimension(), 0);
-    QCOMPARE(pc.coordinates(), (coordT *)0);
-    QVERIFY(pc.isEmpty());
-    pc.checkValid();
-    PointCoordinates pc7(q, 2, "test explicit dimension");
-    QCOMPARE(pc7.dimension(), 2);
-    QCOMPARE(pc7.count(), 0);
-    QVERIFY(pc7.isEmpty());
-    QCOMPARE(pc7.comment(), std::string("test explicit dimension"));
-    pc7.checkValid();
-    PointCoordinates pc2(q, "Test pc2");
-    QCOMPARE(pc2.count(), 0);
-    QVERIFY(pc2.isEmpty());
-    QCOMPARE(pc2.comment(), std::string("Test pc2"));
-    pc2.checkValid();
-    PointCoordinates pc3(q, 3, "Test 3-d pc3");
-    QCOMPARE(pc3.dimension(), 3);
-    QVERIFY(pc3.isEmpty());
-    pc3.checkValid();
-    coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
-    PointCoordinates pc4(q, 2, "Test 2-d pc4", 6, c);
-    QCOMPARE(pc4.dimension(), 2);
-    QCOMPARE(pc4.count(), 3);
-    QCOMPARE(pc4.size(), 3u);
-    QVERIFY(!pc4.isEmpty());
-    pc4.checkValid();
-    QhullPoint p= pc4[2];
-    QCOMPARE(p[1], 5.0);
-    // QhullPoint refers to PointCoordinates
-    p[1] += 1.0;
-    QCOMPARE(pc4[2][1], 6.0);
-    PointCoordinates pc5(q, 4, "Test 4-d pc5 with insufficient coordinates", 6, c);
-    QCOMPARE(pc5.dimension(), 4);
-    QCOMPARE(pc5.count(), 1);
-    QCOMPARE(pc5.extraCoordinatesCount(), 2);
-    QCOMPARE(pc5.extraCoordinates()[1], 5.0);
-    QVERIFY(!pc5.isEmpty());;
-    std::vector vc;
-    vc.push_back(3.0);
-    vc.push_back(4.0);
-    vc.push_back(5.0);
-    vc.push_back(6.0);
-    vc.push_back(7.0);
-    vc.push_back(9.0);
-    pc5.append(2, &vc[3]); // Copy of vc[]
-    pc5.checkValid();
-    QhullPoint p5(q, 4, &vc[1]);
-    QCOMPARE(pc5[1], p5);
-    PointCoordinates pc6(pc5); // Makes copy of point_coordinates
-    QCOMPARE(pc6[1], p5);
-    QVERIFY(pc6==pc5);
-    QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
-    pc5[1][0] += 1.0;
-    QCOMPARE(pc5[1], p6);
-    QVERIFY(pc5[1]!=p5);
-    QVERIFY(pc6!=pc5);
-    pc6= pc5;
-    QVERIFY(pc6==pc5);
-    PointCoordinates pc8(q);
-    pc6= pc8;
-    QVERIFY(pc6!=pc5);
-    QVERIFY(pc6.isEmpty());
-}//t_construct_q
-
-void PointCoordinates_test::
-t_construct_qh()
-{
-    QhullQh qh;
-    PointCoordinates pc(&qh);
-    QCOMPARE(pc.size(), 0U);
-    QCOMPARE(pc.coordinateCount(), 0);
-    QCOMPARE(pc.dimension(), 0);
-    QCOMPARE(pc.coordinates(), (coordT *)0);
-    QVERIFY(pc.isEmpty());
-    pc.checkValid();
-    PointCoordinates pc7(&qh, 2, "test explicit dimension");
-    QCOMPARE(pc7.dimension(), 2);
-    QCOMPARE(pc7.count(), 0);
-    QVERIFY(pc7.isEmpty());
-    QCOMPARE(pc7.comment(), std::string("test explicit dimension"));
-    pc7.checkValid();
-    PointCoordinates pc2(&qh, "Test pc2");
-    QCOMPARE(pc2.count(), 0);
-    QVERIFY(pc2.isEmpty());
-    QCOMPARE(pc2.comment(), std::string("Test pc2"));
-    pc2.checkValid();
-    PointCoordinates pc3(&qh, 3, "Test 3-d pc3");
-    QCOMPARE(pc3.dimension(), 3);
-    QVERIFY(pc3.isEmpty());
-    pc3.checkValid();
-    coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
-    PointCoordinates pc4(&qh, 2, "Test 2-d pc4", 6, c);
-    QCOMPARE(pc4.dimension(), 2);
-    QCOMPARE(pc4.count(), 3);
-    QCOMPARE(pc4.size(), 3u);
-    QVERIFY(!pc4.isEmpty());
-    pc4.checkValid();
-    QhullPoint p= pc4[2];
-    QCOMPARE(p[1], 5.0);
-    // QhullPoint refers to PointCoordinates
-    p[1] += 1.0;
-    QCOMPARE(pc4[2][1], 6.0);
-    PointCoordinates pc5(&qh, 4, "Test 4-d pc5 with insufficient coordinates", 6, c);
-    QCOMPARE(pc5.dimension(), 4);
-    QCOMPARE(pc5.count(), 1);
-    QCOMPARE(pc5.extraCoordinatesCount(), 2);
-    QCOMPARE(pc5.extraCoordinates()[1], 5.0);
-    QVERIFY(!pc5.isEmpty());;
-    std::vector vc;
-    vc.push_back(3.0);
-    vc.push_back(4.0);
-    vc.push_back(5.0);
-    vc.push_back(6.0);
-    vc.push_back(7.0);
-    vc.push_back(9.0);
-    pc5.append(2, &vc[3]); // Copy of vc[]
-    pc5.checkValid();
-    QhullPoint p5(&qh, 4, &vc[1]);
-    QCOMPARE(pc5[1], p5);
-    PointCoordinates pc6(pc5); // Makes copy of point_coordinates
-    QCOMPARE(pc6[1], p5);
-    QVERIFY(pc6==pc5);
-    QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
-    pc5[1][0] += 1.0;
-    QCOMPARE(pc5[1], p6);
-    QVERIFY(pc5[1]!=p5);
-    QVERIFY(pc6!=pc5);
-    pc6= pc5;
-    QVERIFY(pc6==pc5);
-    PointCoordinates pc8(&qh);
-    pc6= pc8;
-    QVERIFY(pc6!=pc5);
-    QVERIFY(pc6.isEmpty());
-}//t_construct_qh
-
-void PointCoordinates_test::
-t_convert()
-{
-    Qhull q;
-    //defineAs tested above
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates ps(q, 3, "two 3-d points", 6, c);
-    QCOMPARE(ps.dimension(), 3);
-    QCOMPARE(ps.size(), 2u);
-    const coordT *c2= ps.constData();
-    QVERIFY(c!=c2);
-    QCOMPARE(c[0], c2[0]);
-    const coordT *c3= ps.data();
-    QCOMPARE(c3, c2);
-    coordT *c4= ps.data();
-    QCOMPARE(c4, c2);
-    std::vector vs= ps.toStdVector();
-    QCOMPARE(vs.size(), 6u);
-    QCOMPARE(vs[5], 5.0);
-    QList qs= ps.toQList();
-    QCOMPARE(qs.size(), 6);
-    QCOMPARE(qs[5], 5.0);
-}//t_convert
-
-void PointCoordinates_test::
-t_getset()
-{
-    // See t_construct() for test of coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
-    // See t_construct() for test of checkValid, comment, setDimension
-    Qhull q;
-    PointCoordinates pc(q, "Coordinates c");
-    pc.setComment("New comment");
-    QCOMPARE(pc.comment(), std::string("New comment"));
-    pc.checkValid();
-    pc.makeValid();  // A no-op
-    pc.checkValid();
-    Coordinates cs= pc.getCoordinates();
-    QVERIFY(cs.isEmpty());
-    PointCoordinates pc2(pc);
-    pc.setDimension(3);
-    QVERIFY(pc2!=pc);
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    pc.append(6, c);
-    pc.checkValid();
-    pc.makeValid();  // A no-op
-    QhullPoint p= pc[0];
-    QCOMPARE(p[2], 2.0);
-    try{
-        pc.setDimension(2);
-        QFAIL("setDimension(2) did not fail for 3-d.");
-    }catch (const std::exception &e) {
-        const char *s= e.what();
-        cout << "INFO   : Caught " << s;
-    }
-}//t_getset
-
-void PointCoordinates_test::
-t_element()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates pc(q, 2, "2-d points", 6, c);
-    QhullPoint p= pc.at(0);
-    QCOMPARE(p, pc[0]);
-    QCOMPARE(p, pc.first());
-    QCOMPARE(p, pc.value(0));
-    p= pc.back();
-    QCOMPARE(p, pc[2]);
-    QCOMPARE(p, pc.last());
-    QCOMPARE(p, pc.value(2));
-    QhullPoints ps= pc.mid(1, 2);
-    QCOMPARE(ps[1], p);
-}//t_element
-
-void PointCoordinates_test::
-t_foreach()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates pc(q, 2, "2-d points", 6, c);
-    QhullPoints::Iterator i= pc.begin();
-    QhullPoint p= pc[0];
-    QCOMPARE(*i, p);
-    QCOMPARE((*i)[0], 0.0);
-    QhullPoint p3= pc[2];
-    i= pc.end();
-    QCOMPARE(i[-1], p3);
-    const PointCoordinates pc2(q, 2, "2-d points", 6, c);
-    QhullPoints::ConstIterator i2= pc.begin();
-    const QhullPoint p0= pc2[0];
-    QCOMPARE(*i2, p0);
-    QCOMPARE((*i2)[0], 0.0);
-    QhullPoints::ConstIterator i3= i2;
-    QCOMPARE(i3, i2);
-    QCOMPARE((*i3)[0], 0.0);
-    i3= pc.constEnd();
-    --i3;
-    QhullPoint p2= pc2[2];
-    QCOMPARE(*i3, p2);
-    i= pc.end();
-    QVERIFY(i-1==i3);
-    i2= pc2.end();
-    QVERIFY(i2-1!=i3);
-    QCOMPARE(*(i2-1), *i3);
-    foreach(QhullPoint p3, pc){ //Qt only
-        QVERIFY(p3[0]>=0.0);
-        QVERIFY(p3[0]<=5.0);
-    }
-    Coordinates::ConstIterator i4= pc.beginCoordinates();
-    QCOMPARE(*i4, 0.0);
-    Coordinates::Iterator i5= pc.beginCoordinates();
-    QCOMPARE(*i5, 0.0);
-    i4= pc.beginCoordinates(1);
-    QCOMPARE(*i4, 2.0);
-    i5= pc.beginCoordinates(1);
-    QCOMPARE(*i5, 2.0);
-    i4= pc.endCoordinates();
-    QCOMPARE(*--i4, 5.0);
-    i5= pc.endCoordinates();
-    QCOMPARE(*--i5, 5.0);
-}//t_foreach
-
-void PointCoordinates_test::
-t_search()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates pc(q, 2, "2-d points", 6, c);
-    QhullPoint p0= pc[0];
-    QhullPoint p2= pc[2];
-    QVERIFY(pc.contains(p0));
-    QVERIFY(pc.contains(p2));
-    QCOMPARE(pc.count(p0), 1);
-    QCOMPARE(pc.indexOf(p2), 2);
-    QCOMPARE(pc.lastIndexOf(p0), 0);
-}//t_search
-
-void PointCoordinates_test::
-t_modify()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates pc(q, 2, "2-d points", 6, c);
-    coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    PointCoordinates pc5(q, 2, "test explicit dimension");
-    pc5.append(6, c3); // 0-5
-    QVERIFY(pc5==pc);
-    PointCoordinates pc2(q, 2, "2-d");
-    coordT c2[]= {6.0, 7.0, 8.0, 9.0, 10.0, 11.0};
-    pc2.append(6, c2);
-    QCOMPARE(pc2.count(), 3);
-    pc2.append(14.0);
-    QCOMPARE(pc2.count(), 3);
-    QCOMPARE(pc2.extraCoordinatesCount(), 1);
-    pc2.append(15.0); // 6-11, 14,15
-    QCOMPARE(pc2.count(), 4);
-    QCOMPARE(pc2.extraCoordinatesCount(), 0);
-    QhullPoint p(pc[0]);
-    pc2.append(p); // 6-11, 14,15, 0,1
-    QCOMPARE(pc2.count(), 5);
-    QCOMPARE(pc2.extraCoordinatesCount(), 0);
-    QCOMPARE(pc2.lastIndexOf(p), 4);
-    pc.append(pc2); // Invalidates p
-    QCOMPARE(pc.count(), 8); // 0-11, 14,15, 0,1
-    QCOMPARE(pc.extraCoordinatesCount(), 0);
-    QCOMPARE(pc.lastIndexOf(pc[0]), 7);
-    pc.appendComment(" operators");
-    QCOMPARE(pc.comment(), std::string("2-d points operators"));
-    pc.checkValid();
-    // see t_append_points for appendPoints
-    PointCoordinates pc3= pc+pc2;
-    pc3.checkValid();
-    QCOMPARE(pc3.count(), 13);
-    QCOMPARE(pc3[6][0], 14.0);
-    QCOMPARE(pc3[8][0], 6.0);
-    pc3 += pc;
-    QCOMPARE(pc3.count(), 21);
-    QCOMPARE(pc3[14][0], 2.0);
-    pc3 += 12.0;
-    pc3 += 14.0;
-    QCOMPARE(pc3.count(), 22);
-    QCOMPARE(pc3.last()[0], 12.0);
-    // QhullPoint p3= pc3.first(); // += throws error because append may move the data
-    QhullPoint p3= pc2.first();
-    pc3 += p3;
-    QCOMPARE(pc3.count(), 23);
-    QCOMPARE(pc3.last()[0], 6.0);
-    pc3 << pc;
-    QCOMPARE(pc3.count(), 31);
-    QCOMPARE(pc3.last()[0], 0.0);
-    pc3 << 12.0 << 14.0;
-    QCOMPARE(pc3.count(), 32);
-    QCOMPARE(pc3.last()[0], 12.0);
-    PointCoordinates pc4(pc3);
-    pc4.reserveCoordinates(100);
-    QVERIFY(pc3==pc4);
-}//t_modify
-
-void PointCoordinates_test::
-t_append_points()
-{
-    Qhull q;
-    PointCoordinates pc(q, 2, "stringstream");
-    stringstream s("2 3 1 2 3 4 5 6");
-    pc.appendPoints(s);
-    QCOMPARE(pc.count(), 3);
-}//t_append_points
-
-void PointCoordinates_test::
-t_coord_iterator()
-{
-    Qhull q;
-    PointCoordinates c(q, 2, "2-d");
-    c << 0.0 << 1.0 << 2.0 << 3.0 << 4.0 << 5.0;
-    PointCoordinatesIterator i(c);
-    QhullPoint p0(c[0]);
-    QhullPoint p1(c[1]);
-    QhullPoint p2(c[2]);
-    coordT c2[] = {-1.0, -2.0};
-    QhullPoint p3(q, 2, c2);
-    PointCoordinatesIterator i2= c;
-    QVERIFY(i.findNext(p1));
-    QVERIFY(!i.findNext(p1));
-    QVERIFY(!i.findNext(p2));
-    QVERIFY(!i.findNext(p3));
-    QVERIFY(i.findPrevious(p2));
-    QVERIFY(!i.findPrevious(p2));
-    QVERIFY(!i.findPrevious(p0));
-    QVERIFY(!i.findPrevious(p3));
-    QVERIFY(i2.findNext(p2));
-    QVERIFY(i2.findPrevious(p0));
-    QVERIFY(i2.findNext(p1));
-    QVERIFY(i2.findPrevious(p0));
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i.toBack();
-    i2.toFront();
-    QVERIFY(!i.hasNext());
-    QVERIFY(i.hasPrevious());
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    PointCoordinates c3(q);
-    PointCoordinatesIterator i3= c3;
-    QVERIFY(!i3.hasNext());
-    QVERIFY(!i3.hasPrevious());
-    i3.toBack();
-    QVERIFY(!i3.hasNext());
-    QVERIFY(!i3.hasPrevious());
-    QCOMPARE(i.peekPrevious(), p2);
-    QCOMPARE(i.previous(), p2);
-    QCOMPARE(i.previous(), p1);
-    QCOMPARE(i.previous(), p0);
-    QVERIFY(!i.hasPrevious());
-    QCOMPARE(i.peekNext(), p0);
-    // i.peekNext()= 1.0; // compiler error
-    QCOMPARE(i.next(), p0);
-    QCOMPARE(i.peekNext(), p1);
-    QCOMPARE(i.next(), p1);
-    QCOMPARE(i.next(), p2);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), p0);
-}//t_coord_iterator
-
-void PointCoordinates_test::
-t_io()
-{
-    Qhull q;
-    PointCoordinates c(q);
-    ostringstream os;
-    os << "PointCoordinates 0-d\n" << c;
-    c.setDimension(2);
-    c << 1.0 << 2.0 << 3.0 << 1.0 << 2.0 << 3.0;
-    os << "PointCoordinates 1,2 3,1 2,3\n" << c;
-    cout << os.str();
-    QString s= QString::fromStdString(os.str());
-    QCOMPARE(s.count("0"), 3);
-    QCOMPARE(s.count("2"), 5);
-}//t_io
-
-}//orgQhull
-
-#include "moc/PointCoordinates_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullFacetList_test.cpp b/src/qhull/src/qhulltest/QhullFacetList_test.cpp
deleted file mode 100644
index 5a09d01da..000000000
--- a/src/qhull/src/qhulltest/QhullFacetList_test.cpp
+++ /dev/null
@@ -1,196 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullFacetList_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullFacetList.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/QhullVertexSet.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/RboxPoints.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullFacetList_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct_qh();
-    void t_construct_q();
-    void t_convert();
-    void t_readonly();
-    void t_foreach();
-    void t_io();
-};//QhullFacetList_test
-
-void
-add_QhullFacetList_test()
-{
-    new QhullFacetList_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullFacetList_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullFacetList_test::
-t_construct_qh()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacetList fs2= q.facetList();
-    QVERIFY(!fs2.isEmpty());
-    QCOMPARE(fs2.count(),6);
-    QhullFacetList fs3(q.endFacet(), q.endFacet());
-    QVERIFY(fs3.isEmpty());
-    QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
-    QCOMPARE(fs4.count(), 1);
-    QhullFacetList fs5(q.beginFacet(), q.endFacet());
-    QCOMPARE(fs2.count(), fs5.count());
-    QVERIFY(fs2==fs5);
-    QhullFacetList fs6= fs2; // copy constructor
-    QVERIFY(fs6==fs2);
-    std::vector fv= fs2.toStdVector();
-    QCOMPARE(fv.size(), 6u);
-}//t_construct_qh
-
-void QhullFacetList_test::
-t_construct_q()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacetList fs2= q.facetList();
-    QVERIFY(!fs2.isEmpty());
-    QCOMPARE(fs2.count(),6);
-    QhullFacetList fs3(q.endFacet(), q.endFacet());
-    QVERIFY(fs3.isEmpty());
-    QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
-    QCOMPARE(fs4.count(), 1);
-    QhullFacetList fs5(q.beginFacet(), q.endFacet());
-    QCOMPARE(fs2.count(), fs5.count());
-    QVERIFY(fs2==fs5);
-    QhullFacetList fs6= fs2; // copy constructor
-    QVERIFY(fs6==fs2);
-    std::vector fv= fs2.toStdVector();
-    QCOMPARE(fv.size(), 6u);
-}//t_construct_q
-
-void QhullFacetList_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0 QV2");  // rotated unit cube
-    QhullFacetList fs2= q.facetList();
-    QVERIFY(!fs2.isSelectAll());
-    QVERIFY(!fs2.isEmpty());
-    QCOMPARE(fs2.count(),3);
-    std::vector fv= fs2.toStdVector();
-    QCOMPARE(fv.size(), 3u);
-    QList fv2= fs2.toQList();
-    QCOMPARE(fv2.size(), 3);
-    std::vector fv5= fs2.vertices_toStdVector();
-    QCOMPARE(fv5.size(), 7u);
-    QList fv6= fs2.vertices_toQList();
-    QCOMPARE(fv6.size(), 7);
-    fs2.selectAll();
-    QVERIFY(fs2.isSelectAll());
-    std::vector fv3= fs2.toStdVector();
-    QCOMPARE(fv3.size(), 6u);
-    QList fv4= fs2.toQList();
-    QCOMPARE(fv4.size(), 6);
-    std::vector fv7= fs2.vertices_toStdVector();
-    QCOMPARE(fv7.size(), 8u);
-    QList fv8= fs2.vertices_toQList();
-    QCOMPARE(fv8.size(), 8);
-}//t_convert
-
-//! Spot check properties and read-only.  See QhullLinkedList_test
-void QhullFacetList_test::
-t_readonly()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
-    QhullFacetList fs= q.facetList();
-    QVERIFY(!fs.isSelectAll());
-    QCOMPARE(fs.count(), 3);
-    QCOMPARE(fs.first(), q.firstFacet());
-    fs.selectAll();
-    QVERIFY(fs.isSelectAll());
-    QCOMPARE(fs.count(), 6);
-    fs.selectGood();
-    QVERIFY(!fs.isSelectAll());
-    QCOMPARE(fs.count(), 3);
-    fs.selectAll();
-    QVERIFY(fs.isSelectAll());
-    QCOMPARE(fs.count(), 6);
-    QhullFacet f= fs.first();
-    QhullFacet f2= fs.last();
-    fs.selectAll();
-    QVERIFY(fs.contains(f));
-    QVERIFY(fs.contains(f2));
-    QVERIFY(f.isGood());
-    QVERIFY(!f2.isGood());
-    fs.selectGood();
-    QVERIFY(fs.contains(f));
-    QVERIFY(!fs.contains(f2));
-}//t_readonly
-
-void QhullFacetList_test::
-t_foreach()
-{
-    RboxPoints rcube("c");
-    // Spot check predicates and accessors.  See QhullLinkedList_test
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullFacetList fs= q.facetList();
-    QVERIFY(fs.contains(q.firstFacet()));
-    QhullFacet f= q.firstFacet().next();
-    QVERIFY(fs.contains(f));
-    QCOMPARE(fs.first(), *fs.begin());
-    QCOMPARE(*(fs.end()-1), fs.last());
-    QCOMPARE(fs.first(), q.firstFacet());
-    QCOMPARE(*fs.begin(), q.beginFacet());
-    QCOMPARE(*fs.end(), q.endFacet());
-}//t_foreach
-
-void QhullFacetList_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
-        QhullFacetList fs= q.facetList();
-        ostringstream os;
-        os << fs.print("Show all of FacetList\n");
-        os << "\nFacets only\n" << fs;
-        os << "\nVertices only\n" << fs.printVertices();
-        cout << os.str();
-        QString facets= QString::fromStdString(os.str());
-        QCOMPARE(facets.count("(v"), 2*7+12*3*2);
-        QCOMPARE(facets.count(QRegExp("f\\d")), 2*3*7 + 13*3*2);
-    }
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullFacetList_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullFacetSet_test.cpp b/src/qhull/src/qhulltest/QhullFacetSet_test.cpp
deleted file mode 100644
index a7fe123a2..000000000
--- a/src/qhull/src/qhulltest/QhullFacetSet_test.cpp
+++ /dev/null
@@ -1,153 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullFacetSet_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/RboxPoints.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullFacetSet_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_convert();
-    void t_readonly();
-    void t_foreach();
-    void t_io();
-};//QhullFacetSet_test
-
-void
-add_QhullFacetSet_test()
-{
-    new QhullFacetSet_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullFacetSet_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullFacetSet_test::
-t_construct()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacet f= q.firstFacet();
-    QhullFacetSet fs2= f.neighborFacets();
-    QVERIFY(!fs2.isEmpty());
-    QCOMPARE(fs2.count(),4);
-    QhullFacetSet fs4= fs2; // copy constructor
-    QVERIFY(fs4==fs2);
-    QhullFacetSet fs3(q, q.qh()->facet_mergeset);
-    QVERIFY(fs3.isEmpty());
-}//t_construct
-
-void QhullFacetSet_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    Qhull q2(rcube,"QR0 QV2");  // rotated unit cube
-    QhullFacet f2= q2.firstFacet();
-    QhullFacetSet fs2= f2.neighborFacets();
-    QVERIFY(!fs2.isSelectAll());
-    QCOMPARE(fs2.count(),2);
-    std::vector fv= fs2.toStdVector();
-    QCOMPARE(fv.size(), 2u);
-    QList fv2= fs2.toQList();
-    QCOMPARE(fv2.size(), 2);
-    fs2.selectAll();
-    QVERIFY(fs2.isSelectAll());
-    std::vector fv3= fs2.toStdVector();
-    QCOMPARE(fv3.size(), 4u);
-    QList fv4= fs2.toQList();
-    QCOMPARE(fv4.size(), 4);
-}//t_convert
-
-//! Spot check properties and read-only.  See QhullSet_test
-void QhullFacetSet_test::
-t_readonly()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
-    QhullFacetSet fs= q.firstFacet().neighborFacets();
-    QVERIFY(!fs.isSelectAll());
-    QCOMPARE(fs.count(), 2);
-    fs.selectAll();
-    QVERIFY(fs.isSelectAll());
-    QCOMPARE(fs.count(), 4);
-    fs.selectGood();
-    QVERIFY(!fs.isSelectAll());
-    QCOMPARE(fs.count(), 2);
-    QhullFacet f= fs.first();
-    QhullFacet f2= fs.last();
-    fs.selectAll();
-    QVERIFY(fs.contains(f));
-    QVERIFY(fs.contains(f2));
-    QVERIFY(f.isGood());
-    QVERIFY(!f2.isGood());
-    fs.selectGood();
-    QVERIFY(fs.contains(f));
-    QVERIFY(!fs.contains(f2));
-}//t_readonly
-
-void QhullFacetSet_test::
-t_foreach()
-{
-    RboxPoints rcube("c");
-    // Spot check predicates and accessors.  See QhullLinkedList_test
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacetSet fs= q.firstFacet().neighborFacets();
-    QVERIFY(!fs.contains(q.firstFacet()));
-    QVERIFY(fs.contains(fs.first()));
-    QhullFacet f= q.firstFacet().next();
-    if(!fs.contains(f)){  // check if 'f' is the facet opposite firstFacet()
-        f= f.next();
-    }
-    QVERIFY(fs.contains(f));
-    QCOMPARE(fs.first(), *fs.begin());
-    QCOMPARE(*(fs.end()-1), fs.last());
-}//t_foreach
-
-void QhullFacetSet_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
-        QhullFacetSet fs= q.firstFacet().neighborFacets();
-        ostringstream os;
-        os << fs.print("Neighbors of first facet with point 0");
-        os << fs.printIdentifiers("\nFacet identifiers: ");
-        cout << os.str();
-        QString facets= QString::fromStdString(os.str());
-        QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
-    }
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullFacetSet_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullFacet_test.cpp b/src/qhull/src/qhulltest/QhullFacet_test.cpp
deleted file mode 100644
index 271f63753..000000000
--- a/src/qhull/src/qhulltest/QhullFacet_test.cpp
+++ /dev/null
@@ -1,283 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullFacet_test.cpp#4 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/Coordinates.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullFacetList.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/QhullPointSet.h"
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullFacet_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct_qh();
-    void t_constructConvert();
-    void t_getSet();
-    void t_value();
-    void t_foreach();
-    void t_io();
-};//QhullFacet_test
-
-void
-add_QhullFacet_test()
-{
-    new QhullFacet_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullFacet_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullFacet_test::
-t_construct_qh()
-{
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    QhullQh qh;
-    QhullFacet f(&qh);
-    QVERIFY(!f.isValid());
-    QCOMPARE(f.dimension(),0);
-}//t_construct_qh
-
-void QhullFacet_test::
-t_constructConvert()
-{
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    Qhull q2;
-    QhullFacet f(q2);
-    QVERIFY(!f.isValid());
-    QCOMPARE(f.dimension(),0);
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullFacet f2(q.beginFacet());
-    QCOMPARE(f2.dimension(),3);
-    f= f2; // copy assignment
-    QVERIFY(f.isValid());
-    QCOMPARE(f.dimension(),3);
-    QhullFacet f5= f2;
-    QVERIFY(f5==f2);
-    QVERIFY(f5==f);
-    QhullFacet f3(q, f2.getFacetT());
-    QCOMPARE(f,f3);
-    QhullFacet f4(q, f2.getBaseT());
-    QCOMPARE(f,f4);
-}//t_constructConvert
-
-void QhullFacet_test::
-t_getSet()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        cout << " rbox c | qhull Qt QR0 QR" << q.rotateRandom() << "   distanceEpsilon " << q.distanceEpsilon() << endl;
-        QCOMPARE(q.facetCount(), 12);
-        QCOMPARE(q.vertexCount(), 8);
-        QhullFacetListIterator i(q.facetList());
-        while(i.hasNext()){
-            const QhullFacet f= i.next();
-            cout << f.id() << endl;
-            QCOMPARE(f.dimension(),3);
-            QVERIFY(f.id()>0 && f.id()<=39);
-            QVERIFY(f.isValid());
-            if(i.hasNext()){
-                QCOMPARE(f.next(), i.peekNext());
-                QVERIFY(f.next()!=f);
-            }
-            QVERIFY(i.hasPrevious());
-            QCOMPARE(f, i.peekPrevious());
-        }
-
-        // test tricoplanarOwner
-        QhullFacet facet = q.beginFacet();
-        QhullFacet tricoplanarOwner = facet.tricoplanarOwner();
-        int tricoplanarCount= 0;
-        i.toFront();
-        while(i.hasNext()){
-            const QhullFacet f= i.next();
-            if(f.tricoplanarOwner()==tricoplanarOwner){
-                tricoplanarCount++;
-            }
-        }
-        QCOMPARE(tricoplanarCount, 2);
-        int tricoplanarCount2= 0;
-        foreach (QhullFacet f, q.facetList()){  // Qt only
-            QhullHyperplane h= f.hyperplane();
-            cout << "Hyperplane: " << h;
-            QCOMPARE(h.count(), 3);
-            QCOMPARE(h.offset(), -0.5);
-            double n= h.norm();
-            QCOMPARE(n, 1.0);
-            QhullHyperplane hi= f.innerplane();
-            QCOMPARE(hi.count(), 3);
-            double innerOffset= hi.offset()+0.5;
-            cout << "InnerPlane: " << hi << "   innerOffset+0.5 " << innerOffset << endl;
-            QVERIFY(innerOffset >= 0.0-(2*q.distanceEpsilon())); // A guessed epsilon.  It needs to account for roundoff due to rotation of the vertices
-            QhullHyperplane ho= f.outerplane();
-            QCOMPARE(ho.count(), 3);
-            double outerOffset= ho.offset()+0.5;
-            cout << "OuterPlane: " << ho << "   outerOffset+0.5 " << outerOffset << endl;
-            QVERIFY(outerOffset <= 0.0+(2*q.distanceEpsilon())); // A guessed epsilon.  It needs to account for roundoff due to rotation of the vertices
-            QVERIFY(outerOffset-innerOffset < 1e-7);
-            for(int k= 0; k<3; k++){
-                QVERIFY(ho[k]==hi[k]);
-                QVERIFY(ho[k]==h[k]);
-            }
-            QhullPoint center= f.getCenter();
-            cout << "Center: " << center;
-            double d= f.distance(center);
-            QVERIFY(d < innerOffset-outerOffset);
-            QhullPoint center2= f.getCenter(qh_PRINTcentrums);
-            QCOMPARE(center, center2);
-            if(f.tricoplanarOwner()==tricoplanarOwner){
-                tricoplanarCount2++;
-            }
-            cout << endl;
-        }
-        QCOMPARE(tricoplanarCount2, 2);
-        Qhull q2(rcube,"d Qz Qt QR0");  // 3-d triangulation of Delaunay triangulation (the cube)
-        cout << " rbox c | qhull d Qz Qt QR0 QR" << q2.rotateRandom() << "   distanceEpsilon " << q2.distanceEpsilon() << endl;
-        QhullFacet f2= q2.firstFacet();
-        QhullPoint center3= f2.getCenter(qh_PRINTtriangles);
-        QCOMPARE(center3.dimension(), 3);
-        QhullPoint center4= f2.getCenter();
-        QCOMPARE(center4.dimension(), 4);
-        for(int k= 0; k<3; k++){
-            QVERIFY(center4[k]==center3[k]);
-        }
-        Qhull q3(rcube,"v Qz QR0");  // Voronoi diagram of a cube (one vertex)
-        cout << " rbox c | qhull v Qz QR0 QR" << q3.rotateRandom() << "   distanceEpsilon " << q3.distanceEpsilon() << endl;
-
-        q3.setFactorEpsilon(400); // Voronoi vertices are not necessarily within distance episilon
-        QhullPoint origin= q3.inputOrigin();
-        int voronoiCount= 0;
-        foreach(QhullFacet f, q3.facetList()){ //Qt only
-            if(f.isGood()){
-                ++voronoiCount;
-                QhullPoint p= f.voronoiVertex();
-                cout << p.print("Voronoi vertex: ")
-                    << " Is it within " << q3.factorEpsilon() << " * distanceEpsilon (" << q3.distanceEpsilon() << ") of the origin?" << endl;
-                QCOMPARE(p, origin);
-            }
-        }
-        QCOMPARE(voronoiCount, 1);
-    }
-}//t_getSet
-
-void QhullFacet_test::
-t_value()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        coordT c[]= {0.0, 0.0, 0.0};
-        foreach (QhullFacet f, q.facetList()){  // Qt only
-            double d= f.distance(q.origin());
-            QCOMPARE(d, -0.5);
-            double d0= f.distance(c);
-            QCOMPARE(d0, -0.5);
-            double facetArea= f.facetArea();
-            QCOMPARE(facetArea, 1.0);
-            #if qh_MAXoutside
-                double maxoutside= f.getFacetT()->maxoutside;
-                QVERIFY(maxoutside<1e-7);
-            #endif
-        }
-    }
-}//t_value
-
-void QhullFacet_test::
-t_foreach()
-{
-    RboxPoints rcube("c W0 300");  // cube plus 300 points on its surface
-    {
-        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
-        int coplanarCount= 0;
-        foreach(const QhullFacet f, q.facetList()){
-            QhullPointSet coplanars= f.coplanarPoints();
-            coplanarCount += coplanars.count();
-            QhullFacetSet neighbors= f.neighborFacets();
-            QCOMPARE(neighbors.count(), 4);
-            QhullPointSet outsides= f.outsidePoints();
-            QCOMPARE(outsides.count(), 0);
-            QhullRidgeSet ridges= f.ridges();
-            QCOMPARE(ridges.count(), 4);
-            QhullVertexSet vertices= f.vertices();
-            QCOMPARE(vertices.count(), 4);
-            int ridgeCount= 0;
-            QhullRidge r= ridges.first();
-            for(int r0= r.id(); ridgeCount==0 || r.id()!=r0; r= r.nextRidge3d(f)){
-                ++ridgeCount;
-                if(!r.hasNextRidge3d(f)){
-                    QFAIL("Unexpected simplicial facet.  They only have ridges to non-simplicial neighbors.");
-                }
-            }
-            QCOMPARE(ridgeCount, 4);
-        }
-        QCOMPARE(coplanarCount, 300);
-    }
-}//t_foreach
-
-void QhullFacet_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        QhullFacet f= q.beginFacet();
-        cout << f;
-        ostringstream os;
-        os << f.print("\nWith a message\n");
-        os << "\nPrint header for the same facet\n";
-        os << f.printHeader();
-        os << "\nPrint each component\n";
-        os << f.printFlags("    - flags:");
-        os << f.printCenter(qh_PRINTfacets, "    - center: ");
-        os << f.printRidges();
-        cout << os.str();
-        ostringstream os2;
-        os2 << f;
-        QString facetString2= QString::fromStdString(os2.str());
-        facetString2.replace(QRegExp("\\s\\s+"), " ");
-        ostringstream os3;
-        q.qh()->setOutputStream(&os3);
-        q.outputQhull("f");
-        QString facetsString= QString::fromStdString(os3.str());
-        QString facetString3= facetsString.mid(facetsString.indexOf("- f1\n"));
-        facetString3= facetString3.left(facetString3.indexOf("\n- f")+1);
-        facetString3.replace(QRegExp("\\s\\s+"), " ");
-        QCOMPARE(facetString2, facetString3);
-    }
-}//t_io
-
-// toQhullFacet is static_cast only
-
-}//orgQhull
-
-#include "moc/QhullFacet_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullHyperplane_test.cpp b/src/qhull/src/qhulltest/QhullHyperplane_test.cpp
deleted file mode 100644
index d016989a9..000000000
--- a/src/qhull/src/qhulltest/QhullHyperplane_test.cpp
+++ /dev/null
@@ -1,429 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullHyperplane_test.cpp#4 $$Change: 2064 $
-** $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullHyperplane.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullFacetList.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/Qhull.h"
-
-#include 
-#include 
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullHyperplane_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_construct_qh();
-    void t_convert();
-    void t_readonly();
-    void t_define();
-    void t_value();
-    void t_operator();
-    void t_iterator();
-    void t_const_iterator();
-    void t_qhullHyperplane_iterator();
-    void t_io();
-};//QhullHyperplane_test
-
-void
-add_QhullHyperplane_test()
-{
-    new QhullHyperplane_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullHyperplane_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullHyperplane_test::
-t_construct()
-{
-    QhullHyperplane h4;
-    QVERIFY(!h4.isValid());
-    QCOMPARE(h4.dimension(), 0);
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullHyperplane h(q);
-    QVERIFY(!h.isValid());
-    QCOMPARE(h.dimension(), 0);
-    QCOMPARE(h.coordinates(),static_cast(0));
-    QhullFacet f= q.firstFacet();
-    QhullHyperplane h2(f.hyperplane());
-    QVERIFY(h2.isValid());
-    QCOMPARE(h2.dimension(), 3);
-    h= h2;
-    QCOMPARE(h, h2);
-    QhullHyperplane h3(q, h2.dimension(), h2.coordinates(), h2.offset());
-    QCOMPARE(h2, h3);
-    QhullHyperplane h5= h2; // copy constructor
-    QVERIFY(h5==h2);
-}//t_construct
-
-void QhullHyperplane_test::
-t_construct_qh()
-{
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullFacet f= q.firstFacet();
-    QhullHyperplane h2(f.hyperplane());
-    QVERIFY(h2.isValid());
-    QCOMPARE(h2.dimension(), 3);
-    // h= h2;  // copy assignment disabled, ambiguous
-    QhullHyperplane h3(q.qh(), h2.dimension(), h2.coordinates(), h2.offset());
-    QCOMPARE(h2, h3);
-    QhullHyperplane h5= h2; // copy constructor
-    QVERIFY(h5==h2);
-}//t_construct_qh
-
-void QhullHyperplane_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullHyperplane h= q.firstFacet().hyperplane();
-    std::vector fs= h.toStdVector();
-    QCOMPARE(fs.size(), 4u);
-    double offset= fs.back();
-    fs.pop_back();
-    QCOMPARE(offset, -0.5);
-
-    double squareNorm= inner_product(fs.begin(), fs.end(), fs.begin(), 0.0);
-    QCOMPARE(squareNorm, 1.0);
-    QList qs= h.toQList();
-    QCOMPARE(qs.size(), 4);
-    double offset2= qs.takeLast();
-    QCOMPARE(offset2, -0.5);
-    double squareNorm2= std::inner_product(qs.begin(), qs.end(), qs.begin(), 0.0);
-    QCOMPARE(squareNorm2, 1.0);
-}//t_convert
-
-void QhullHyperplane_test::
-t_readonly()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QhullFacetList fs= q.facetList();
-        QhullFacetListIterator i(fs);
-        while(i.hasNext()){
-            QhullFacet f= i.next();
-            QhullHyperplane h= f.hyperplane();
-            int id= f.id();
-            cout << "h" << id << endl;
-            QVERIFY(h.isValid());
-            QCOMPARE(h.dimension(),3);
-            const coordT *c= h.coordinates();
-            coordT *c2= h.coordinates();
-            QCOMPARE(c, c2);
-            const coordT *c3= h.begin();
-            QCOMPARE(c, c3);
-            QCOMPARE(h.offset(), -0.5);
-            int j= h.end()-h.begin();
-            QCOMPARE(j, 3);
-            double squareNorm= std::inner_product(h.begin(), h.end(), h.begin(), 0.0);
-            QCOMPARE(squareNorm, 1.0);
-        }
-        QhullHyperplane h2= fs.first().hyperplane();
-        QhullHyperplane h3= fs.last().hyperplane();
-        QVERIFY(h2!=h3);
-        QVERIFY(h3.coordinates()!=h2.coordinates());
-    }
-}//t_readonly
-
-void QhullHyperplane_test::
-t_define()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QhullFacetList fs= q.facetList();
-        QhullHyperplane h= fs.first().hyperplane();
-        QhullHyperplane h2= h;
-        QVERIFY(h==h2);
-        QhullHyperplane h3= fs.last().hyperplane();
-        QVERIFY(h2!=h3);
-
-        QhullHyperplane h4= h3;
-        h4.defineAs(h2);
-        QVERIFY(h2==h4);
-        QhullHyperplane p5= h3;
-        p5.defineAs(h2.dimension(), h2.coordinates(), h2.offset());
-        QVERIFY(h2==p5);
-        QhullHyperplane h6= h3;
-        h6.setCoordinates(h2.coordinates());
-        QCOMPARE(h2.coordinates(), h6.coordinates());
-        h6.setOffset(h2.offset());
-        QCOMPARE(h2.offset(), h6.offset());
-        QVERIFY(h2==h6);
-        h6.setDimension(2);
-        QCOMPARE(h6.dimension(), 2);
-        QVERIFY(h2!=h6);
-    }
-}//t_define
-
-void QhullHyperplane_test::
-t_value()
-{
-    RboxPoints rcube("c G1");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullFacet f= q.firstFacet();
-    QhullFacet f2= f.neighborFacets().at(0);
-    const QhullHyperplane h= f.hyperplane();
-    const QhullHyperplane h2= f2.hyperplane();   // At right angles
-    double dist= h.distance(q.origin());
-    QCOMPARE(dist, -1.0);
-    double norm= h.norm();
-    QCOMPARE(norm, 1.0);
-    double angle= h.hyperplaneAngle(h2);
-    cout << "angle " << angle << endl;
-    QCOMPARE(angle+1.0, 1.0); // qFuzzyCompare does not work for 0.0
-    QVERIFY(h==h);
-    QVERIFY(h!=h2);
-}//t_value
-
-void QhullHyperplane_test::
-t_operator()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    const QhullHyperplane h= q.firstFacet().hyperplane();
-    //operator== and operator!= tested elsewhere
-    const coordT *c= h.coordinates();
-    for(int k=h.dimension(); k--; ){
-        QCOMPARE(c[k], h[k]);
-    }
-    //h[0]= 10.0; // compiler error, const
-    QhullHyperplane h2= q.firstFacet().hyperplane();
-    h2[0]= 10.0;  // Overwrites Hyperplane coordinate!
-    QCOMPARE(h2[0], 10.0);
-}//t_operator
-
-void QhullHyperplane_test::
-t_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullHyperplane h= q.firstFacet().hyperplane();
-        QCOMPARE(h.count(), 3);
-        QCOMPARE(h.size(), 3u);
-        QhullHyperplane::Iterator i= h.begin();
-        QhullHyperplane::iterator i2= h.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= h.begin();
-        QVERIFY(i==i2);
-        i2= h.end();
-        QVERIFY(i!=i2);
-        double d3= *i;
-        i2--;
-        double d2= *i2;
-        QCOMPARE(d3, h[0]);
-        QCOMPARE(d2, h[2]);
-        QhullHyperplane::Iterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3), h[1]);
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        QhullHyperplane::ConstIterator i4= h.begin();
-        QVERIFY(i==i4); // iterator COMP const_iterator
-        QVERIFY(i<=i4);
-        QVERIFY(i>=i4);
-        QVERIFY(i4==i); // const_iterator COMP iterator
-        QVERIFY(i4<=i);
-        QVERIFY(i4>=i);
-        QVERIFY(i>=i4);
-        QVERIFY(i4<=i);
-        QVERIFY(i2!=i4);
-        QVERIFY(i2>i4);
-        QVERIFY(i2>=i4);
-        QVERIFY(i4!=i2);
-        QVERIFY(i4i);
-        QVERIFY(i4>=i);
-
-        i= h.begin();
-        i2= h.begin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, h[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, h.begin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2 += 3, h.end());
-        QCOMPARE(i2 -= 3, h.begin());
-        QCOMPARE(i2+0, h.begin());
-        QCOMPARE(i2+3, h.end());
-        i2 += 3;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-3;
-        QCOMPARE(i, h.begin());
-        QCOMPARE(i2-i, 3);
-
-        //h.begin end tested above
-
-        // QhullHyperplane is const-only
-    }
-}//t_iterator
-
-void QhullHyperplane_test::
-t_const_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullHyperplane h= q.firstFacet().hyperplane();
-        QhullHyperplane::ConstIterator i= h.begin();
-        QhullHyperplane::const_iterator i2= h.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= h.begin();
-        QVERIFY(i==i2);
-        i2= h.end();
-        QVERIFY(i!=i2);
-        double d3= *i;
-        i2--;
-        double d2= *i2;
-        QCOMPARE(d3, h[0]);
-        QCOMPARE(d2, h[2]);
-        QhullHyperplane::ConstIterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3), h[1]);
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        // See t_iterator for const_iterator COMP iterator
-
-        i= h.begin();
-        i2= h.constBegin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, h[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, h.constBegin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2+=3, h.constEnd());
-        QCOMPARE(i2-=3, h.constBegin());
-        QCOMPARE(i2+0, h.constBegin());
-        QCOMPARE(i2+3, h.constEnd());
-        i2 += 3;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-3;
-        QCOMPARE(i, h.constBegin());
-        QCOMPARE(i2-i, 3);
-
-        // QhullHyperplane is const-only
-    }
-}//t_const_iterator
-
-void QhullHyperplane_test::
-t_qhullHyperplane_iterator()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullHyperplane h = q.firstFacet().hyperplane();
-    QhullHyperplaneIterator i2(h);
-    QCOMPARE(h.dimension(), 3);
-    QhullHyperplaneIterator i= h;
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i2.toBack();
-    i.toFront();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    // i at front, i2 at end/back, 3 coordinates
-    QCOMPARE(i.peekNext(), h[0]);
-    QCOMPARE(i2.peekPrevious(), h[2]);
-    QCOMPARE(i2.previous(), h[2]);
-    QCOMPARE(i2.previous(), h[1]);
-    QCOMPARE(i2.previous(), h[0]);
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekNext(), h[0]);
-    // i.peekNext()= 1.0; // compiler error, i is const
-    QCOMPARE(i.next(), h[0]);
-    QCOMPARE(i.peekNext(), h[1]);
-    QCOMPARE(i.next(), h[1]);
-    QCOMPARE(i.next(), h[2]);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), h[0]);
-}//t_qhullHyperplane_iterator
-
-void QhullHyperplane_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        QhullHyperplane h= q.firstFacet().hyperplane();
-        ostringstream os;
-        os << "Hyperplane:\n";
-        os << h;
-        os << h.print("message");
-        os << h.print(" and a message ", " offset ");
-        cout << os.str();
-        QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count("1"), 3);
-        // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
-    }
-}//t_io
-
-
-}//orgQhull
-
-#include "moc/QhullHyperplane_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullLinkedList_test.cpp b/src/qhull/src/qhulltest/QhullLinkedList_test.cpp
deleted file mode 100644
index e0cde4050..000000000
--- a/src/qhull/src/qhulltest/QhullLinkedList_test.cpp
+++ /dev/null
@@ -1,330 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullLinkedList_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h"
-
-#include "libqhullcpp/QhullLinkedList.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/RboxPoints.h"
-
-namespace orgQhull {
-
-class QhullLinkedList_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_convert();
-    void t_element();
-    void t_search();
-    void t_iterator();
-    void t_const_iterator();
-    void t_QhullLinkedList_iterator();
-    void t_io();
-};//QhullLinkedList_test
-
-void
-add_QhullLinkedList_test()
-{
-    new QhullLinkedList_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullLinkedList_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullLinkedList_test::
-t_construct()
-{
-    // QhullLinkedList vs; //private (compiler error).  No memory allocation
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QCOMPARE(q.facetCount(), 12);
-        QhullVertexList vs = QhullVertexList(q.beginVertex(), q.endVertex());
-        QCOMPARE(vs.count(), 8);
-        QCOMPARE(vs.size(), 8u);
-        QVERIFY(!vs.isEmpty());
-        QhullVertexList vs2 = q.vertexList();
-        QCOMPARE(vs2.count(), 8);
-        QCOMPARE(vs2.size(),8u);
-        QVERIFY(!vs2.isEmpty());
-        QVERIFY(vs==vs2);
-        // vs= vs2; // disabled.  Would not copy the vertices
-        QhullVertexList vs3= vs2; // copy constructor
-        QVERIFY(vs3==vs2);
-    }
-}//t_construct
-
-void QhullLinkedList_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QCOMPARE(q.facetCount(), 12);
-        QhullVertexList vs = q.vertexList();
-        QCOMPARE(vs.size(), 8u);
-        QVERIFY(!vs.isEmpty());
-        std::vector vs2= vs.toStdVector();
-        QCOMPARE(vs2.size(), vs.size());
-        QhullVertexList::Iterator i= vs.begin();
-        for(int k= 0; k<(int)vs2.size(); k++){
-            QCOMPARE(vs2[k], *i++);
-        }
-        QList vs3= vs.toQList();
-        QCOMPARE(vs3.count(), vs.count());
-        i= vs.begin();
-        for(int k= 0; k
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullPointSet.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullFacetList.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-
-namespace orgQhull {
-
-class QhullPointSet_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_convert();
-    void t_element();
-    void t_iterator();
-    void t_const_iterator();
-    void t_search();
-    void t_pointset_iterator();
-    void t_io();
-};//QhullPointSet_test
-
-void
-add_QhullPointSet_test()
-{
-    new QhullPointSet_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullPointSet_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullPointSet_test::
-t_construct()
-{
-    // Default constructor is disallowed (i.e., private)
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    int coplanarCount= 0;
-    foreach(QhullFacet f, q.facetList()){
-        QhullPointSet ps(q, f.getFacetT()->outsideset);
-        QVERIFY(ps.isEmpty());
-        QCOMPARE(ps.count(), 0);
-        QCOMPARE(ps.size(), 0u);
-        QhullPointSet ps2(q.qh(), f.getFacetT()->coplanarset);
-        QVERIFY(!ps2.isEmpty());
-        coplanarCount += ps2.count();
-        QCOMPARE(ps2.count(), (int)ps2.size());
-        QhullPointSet ps3(ps2);
-        QVERIFY(!ps3.isEmpty());
-        QCOMPARE(ps3.count(), ps2.count());
-        QVERIFY(ps3==ps2);
-        QVERIFY(ps3!=ps);
-        QhullPointSet ps4= ps3;
-        QVERIFY(ps4==ps2);
-    }
-    QCOMPARE(coplanarCount, 1000);
-}//t_construct
-
-void QhullPointSet_test::
-t_convert()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=1);   // Sometimes no coplanar points
-    std::vector vs= ps.toStdVector();
-    QCOMPARE(vs.size(), ps.size());
-    QhullPoint p= ps[0];
-    QhullPoint p2= vs[0];
-    QCOMPARE(p, p2);
-    QList qs= ps.toQList();
-    QCOMPARE(qs.size(), static_cast(ps.size()));
-    QhullPoint p3= qs[0];
-    QCOMPARE(p3, p);
-}//t_convert
-
-// readonly tested in t_construct
-//   empty, isEmpty, ==, !=, size
-
-void QhullPointSet_test::
-t_element()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    QhullPoint p= ps[0];
-    QCOMPARE(p, ps[0]);
-    QhullPoint p2= ps[ps.count()-1];
-    QCOMPARE(ps.at(1), ps[1]);
-    QCOMPARE(ps.second(), ps[1]);
-    QCOMPARE(ps.first(), p);
-    QCOMPARE(ps.front(), ps.first());
-    QCOMPARE(ps.last(), p2);
-    QCOMPARE(ps.back(), ps.last());
-    QhullPoint p8(q);
-    QCOMPARE(ps.value(2), ps[2]);
-    QCOMPARE(ps.value(-1), p8);
-    QCOMPARE(ps.value(ps.count()), p8);
-    QCOMPARE(ps.value(ps.count(), p), p);
-    QVERIFY(ps.value(1, p)!=p);
-    QhullPointSet ps8= f.coplanarPoints();
-    QhullPointSet::Iterator i= ps8.begin();
-    foreach(QhullPoint p9, ps){  // Qt only
-        QCOMPARE(p9.dimension(), 3);
-        QCOMPARE(p9, *i++);
-    }
-}//t_element
-
-void QhullPointSet_test::
-t_iterator()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    QhullPointSet::Iterator i= ps.begin();
-    QhullPointSet::iterator i2= ps.begin();
-    QVERIFY(i==i2);
-    QVERIFY(i>=i2);
-    QVERIFY(i<=i2);
-    i= ps.begin();
-    QVERIFY(i==i2);
-    i2= ps.end();
-    QVERIFY(i!=i2);
-    QhullPoint p= *i;
-    QCOMPARE(p.dimension(), q.dimension());
-    QCOMPARE(p, ps[0]);
-    i2--;
-    QhullPoint p2= *i2;
-    QCOMPARE(p2.dimension(), q.dimension());
-    QCOMPARE(p2, ps.last());
-    QhullPointSet::Iterator i5(i2);
-    QCOMPARE(*i2, *i5);
-    QhullPointSet::Iterator i3= i+1;
-    QVERIFY(i!=i3);
-    QCOMPARE(i[1], *i3);
-    (i3= i)++;
-    QCOMPARE((*i3)[0], ps[1][0]);
-    QCOMPARE((*i3).dimension(), 3);
-
-    QVERIFY(i==i);
-    QVERIFY(i!=i3);
-    QVERIFY(ii);
-    QVERIFY(i3>=i);
-
-    QhullPointSet::ConstIterator i4= ps.begin();
-    QVERIFY(i==i4); // iterator COMP const_iterator
-    QVERIFY(i<=i4);
-    QVERIFY(i>=i4);
-    QVERIFY(i4==i); // const_iterator COMP iterator
-    QVERIFY(i4<=i);
-    QVERIFY(i4>=i);
-    QVERIFY(i>=i4);
-    QVERIFY(i4<=i);
-    QVERIFY(i2!=i4);
-    QVERIFY(i2>i4);
-    QVERIFY(i2>=i4);
-    QVERIFY(i4!=i2);
-    QVERIFY(i4i);
-    QVERIFY(i4>=i);
-    i4= ps.constBegin();
-    QVERIFY(i==i4); // iterator COMP const_iterator
-    QCOMPARE(i4+ps.count(), ps.constEnd());
-
-    i= ps.begin();
-    i2= ps.begin();
-    QCOMPARE(i, i2++);
-    QCOMPARE(*i2, ps[1]);
-    QCOMPARE(++i, i2);
-    QCOMPARE(i, i2--);
-    QCOMPARE(i2, ps.begin());
-    QCOMPARE(--i, i2);
-    QCOMPARE(i2+=ps.count(), ps.end());
-    QCOMPARE(i2-=ps.count(), ps.begin());
-    QCOMPARE(i2+0, ps.begin());
-    QCOMPARE(i2+ps.count(), ps.end());
-    i2 += ps.count();
-    i= i2-0;
-    QCOMPARE(i, i2);
-    i= i2-ps.count();
-    QCOMPARE(i, ps.begin());
-    QCOMPARE(i2-i, ps.count());
-
-    //ps.begin end tested above
-
-    // QhullPointSet is const-only
-}//t_iterator
-
-void QhullPointSet_test::
-t_const_iterator()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    QhullPointSet::ConstIterator i= ps.begin();
-    QhullPointSet::const_iterator i2= ps.begin();
-    QVERIFY(i==i2);
-    QVERIFY(i>=i2);
-    QVERIFY(i<=i2);
-
-    // See t_iterator for const_iterator COMP iterator
-
-    i= ps.begin();
-    QVERIFY(i==i2);
-    i2= ps.end();
-    QVERIFY(i!=i2);
-    QhullPoint p= *i; // QhullPoint is the base class for QhullPointSet::iterator
-    QCOMPARE(p.dimension(), q.dimension());
-    QCOMPARE(p, ps[0]);
-    i2--;
-    QhullPoint p2= *i2;
-    QCOMPARE(p2.dimension(), q.dimension());
-    QCOMPARE(p2, ps.last());
-    QhullPointSet::ConstIterator i5(i2);
-    QCOMPARE(*i2, *i5);
-
-
-    QhullPointSet::ConstIterator i3= i+1;
-    QVERIFY(i!=i3);
-    QCOMPARE(i[1], *i3);
-
-    QVERIFY(i==i);
-    QVERIFY(i!=i3);
-    QVERIFY(ii);
-    QVERIFY(i3>=i);
-
-    // QhullPointSet is const-only
-}//t_const_iterator
-
-
-void QhullPointSet_test::
-t_search()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    QhullPoint p= ps.first();
-    QhullPoint p2= ps.last();
-    QVERIFY(ps.contains(p));
-    QVERIFY(ps.contains(p2));
-    QVERIFY(p!=p2);
-    QhullPoint p3= ps[2];
-    QVERIFY(ps.contains(p3));
-    QVERIFY(p!=p3);
-    QCOMPARE(ps.indexOf(p), 0);
-    QCOMPARE(ps.indexOf(p2), ps.count()-1);
-    QCOMPARE(ps.indexOf(p3), 2);
-    QhullPoint p4(q);
-    QCOMPARE(ps.indexOf(p4), -1);
-    QCOMPARE(ps.lastIndexOf(p), 0);
-    QCOMPARE(ps.lastIndexOf(p2), ps.count()-1);
-    QCOMPARE(ps.lastIndexOf(p3), 2);
-    QCOMPARE(ps.lastIndexOf(p4), -1);
-}//t_search
-
-void QhullPointSet_test::
-t_pointset_iterator()
-{
-    RboxPoints rcube("c W0 1000");
-    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps2= f.outsidePoints();
-    QVERIFY(ps2.count()==0); // No outside points after constructing the convex hull
-    QhullPointSetIterator i2= ps2;
-    QCOMPARE(i2.countRemaining(), 0);
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    i2.toBack();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    QhullPointSetIterator i(ps);
-    i2= ps;
-    QCOMPARE(i2.countRemaining(), ps.count());
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i2.toBack();
-    QCOMPARE(i2.countRemaining(), 0);
-    i.toFront();
-    QCOMPARE(i.countRemaining(), ps.count());
-    QCOMPARE(i2.countRemaining(), 0);
-    QVERIFY(!i2.hasNext());
-    QVERIFY(i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    QhullPoint p= ps[0];
-    QhullPoint p2(ps[0]);
-    QCOMPARE(p, p2);
-    QVERIFY(p==p2);
-    QhullPoint p3(ps.last());
- // p2[0]= 0.0;
-    QVERIFY(p==p2);
-    QCOMPARE(i2.peekPrevious(), p3);
-    QCOMPARE(i2.previous(), p3);
-    QCOMPARE(i2.previous(), ps[ps.count()-2]);
-    QVERIFY(i2.hasPrevious());
-    QCOMPARE(i.peekNext(), p);
-    // i.peekNext()= 1.0; // compiler error
-    QCOMPARE(i.next(), p);
-    QCOMPARE(i.countRemaining(), ps.count()-1);
-    QhullPoint p4= i.peekNext();
-    QVERIFY(p4!=p3);
-    QCOMPARE(i.next(), p4);
-    QVERIFY(i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), p);
-}//t_pointset_iterator
-
-void QhullPointSet_test::
-t_io()
-{
-    ostringstream os;
-    RboxPoints rcube("c W0 120");
-    Qhull q(rcube,"Qc");  // cube with 100 coplanar points
-    QhullFacet f= q.firstFacet();
-    QhullPointSet ps= f.coplanarPoints();
-    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
-    os << "QhullPointSet from coplanarPoints\n" << ps << endl;
-    os << ps.print("\nWith message\n");
-    os << ps.printIdentifiers("\nCoplanar points: ");
-    os << "\nAs a point set:\n";
-    os << ps;
-    cout << os.str();
-    QString s= QString::fromStdString(os.str());
-    QCOMPARE(s.count(" 0.5\n"), 3*ps.count());
-    QCOMPARE(s.count("p"), ps.count()+4);
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullPointSet_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullPoint_test.cpp b/src/qhull/src/qhulltest/QhullPoint_test.cpp
deleted file mode 100644
index 1528086a1..000000000
--- a/src/qhull/src/qhulltest/QhullPoint_test.cpp
+++ /dev/null
@@ -1,437 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullPoint_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/Coordinates.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullPoint.h"
-#include "libqhullcpp/Qhull.h"
-
-#include 
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullPoint_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_convert();
-    void t_readonly();
-    void t_define();
-    void t_operator();
-    void t_iterator();
-    void t_const_iterator();
-    void t_qhullpoint_iterator();
-    void t_method();
-    void t_io();
-};//QhullPoint_test
-
-void
-add_QhullPoint_test()
-{
-    new QhullPoint_test();  // RoadTest::s_testcases
-}
-
-//Executed after each test
-void QhullPoint_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullPoint_test::
-t_construct()
-{
-    QhullPoint p12;
-    QVERIFY(!p12.isValid());
-    QCOMPARE(p12.coordinates(), (coordT *)0);
-    QCOMPARE(p12.dimension(), 0);
-    QCOMPARE(p12.qh(), (QhullQh *)0);
-    QCOMPARE(p12.id(), -3);
-    QCOMPARE(p12.begin(), p12.end());
-    QCOMPARE(p12.constBegin(), p12.constEnd());
-
-    RboxPoints rcube("c");
-    Qhull q(rcube, "Qt QR0");  // triangulation of rotated unit cube
-    QhullPoint p(q);
-    QVERIFY(!p.isValid());
-    QCOMPARE(p.dimension(),3);
-    QCOMPARE(p.coordinates(),static_cast(0));
-    QhullPoint p7(q.qh());
-    QCOMPARE(p, p7);
-
-    // copy constructor and copy assignment
-    QhullVertex v2(q.beginVertex());
-    QhullPoint p2(v2.point());
-    QVERIFY(p2.isValid());
-    QCOMPARE(p2.dimension(),3);
-    QVERIFY(p2!=p12);
-    p= p2;
-    QCOMPARE(p, p2);
-
-    QhullPoint p3(q, p2.dimension(), p2.coordinates());
-    QCOMPARE(p3, p2);
-    QhullPoint p8(q, p2.coordinates()); // Qhull defines dimension
-    QCOMPARE(p8, p2);
-    QhullPoint p9(q.qh(), p2.dimension(), p2.coordinates());
-    QCOMPARE(p9, p2);
-    QhullPoint p10(q.qh(), p2.coordinates()); // Qhull defines dimension
-    QCOMPARE(p10, p2);
-
-    Coordinates c;
-    c << 0.0 << 0.0 << 0.0;
-    QhullPoint p6(q, c);
-    QCOMPARE(p6, q.origin());
-    QhullPoint p11(q.qh(), c);
-    QCOMPARE(p11, q.origin());
-
-    QhullPoint p5= p2; // copy constructor
-    QVERIFY(p5==p2);
-}//t_construct
-
-void QhullPoint_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullVertex v= q.firstVertex();
-    QhullPoint p= v.point();
-    std::vector vs= p.toStdVector();
-    QCOMPARE(vs.size(), 3u);
-    for(int k=3; k--; ){
-        QCOMPARE(vs[k], p[k]);
-    }
-    QList qs= p.toQList();
-    QCOMPARE(qs.size(), 3);
-    for(int k=3; k--; ){
-        QCOMPARE(qs[k], p[k]);
-    }
-}//t_convert
-
-void QhullPoint_test::
-t_readonly()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QhullVertexList vs= q.vertexList();
-        cout << "Point ids in 'rbox c'\n";
-        QhullVertexListIterator i(vs);
-        while(i.hasNext()){
-            QhullPoint p= i.next().point();
-            int id= p.id();
-            cout << "p" << id << endl;
-            QVERIFY(p.isValid());
-            QCOMPARE(p.dimension(),3);
-            QCOMPARE(id, p.id());
-            QVERIFY(p.id()>=0 && p.id()<9);
-            const coordT *c= p.coordinates();
-            coordT *c2= p.coordinates();
-            QCOMPARE(c, c2);
-            QCOMPARE(p.dimension(), 3);
-            QCOMPARE(q.qh(), p.qh());
-        }
-        QhullPoint p2= vs.first().point();
-        QhullPoint p3= vs.last().point();
-        QVERIFY(p2!=p3);
-        QVERIFY(p3.coordinates()!=p2.coordinates());
-    }
-}//t_readonly
-
-void QhullPoint_test::
-t_define()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QhullVertexList vs= q.vertexList();
-        QhullPoint p= vs.first().point();
-        QhullPoint p2= p;
-        QVERIFY(p==p2);
-        QhullPoint p3= vs.last().point();
-        QVERIFY(p2!=p3);
-        int idx= (p3.coordinates()-p2.coordinates())/p2.dimension();
-        QVERIFY(idx>-8 && idx<8);
-        p2.advancePoint(idx);
-        QVERIFY(p2==p3);
-        p2.advancePoint(-idx);
-        QVERIFY(p2==p);
-        p2.advancePoint(0);
-        QVERIFY(p2==p);
-
-        QhullPoint p4= p3;
-        QVERIFY(p4==p3);
-        p4.defineAs(p2);
-        QVERIFY(p2==p4);
-        QhullPoint p5= p3;
-        p5.defineAs(p2.dimension(), p2.coordinates());
-        QVERIFY(p2==p5);
-        QhullPoint p6= p3;
-        p6.setCoordinates(p2.coordinates());
-        QCOMPARE(p2.coordinates(), p6.coordinates());
-        QVERIFY(p2==p6);
-        p6.setDimension(2);
-        QCOMPARE(p6.dimension(), 2);
-        QVERIFY(p2!=p6);
-    }
-}//t_define
-
-void QhullPoint_test::
-t_operator()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    const QhullPoint p= q.firstVertex().point();
-    //operator== and operator!= tested elsewhere
-    const coordT *c= p.coordinates();
-    for(int k=p.dimension(); k--; ){
-        QCOMPARE(c[k], p[k]);
-    }
-    //p[0]= 10.0; // compiler error, const
-    QhullPoint p2= q.firstVertex().point();
-    p2[0]= 10.0;  // Overwrites point coordinate
-    QCOMPARE(p2[0], 10.0);
-}//t_operator
-
-void QhullPoint_test::
-t_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullPoint p2(q);
-        QCOMPARE(p2.begin(), p2.end());
-
-        QhullPoint p= q.firstVertex().point();
-        QhullPoint::Iterator i= p.begin();
-        QhullPoint::iterator i2= p.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= p.begin();
-        QVERIFY(i==i2);
-        i2= p.end();
-        QVERIFY(i!=i2);
-        double d3= *i;
-        i2--;
-        double d2= *i2;
-        QCOMPARE(d3, p[0]);
-        QCOMPARE(d2, p[2]);
-        QhullPoint::Iterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3), p[1]);
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        QhullPoint::ConstIterator i4= p.begin();
-        QVERIFY(i==i4); // iterator COMP const_iterator
-        QVERIFY(i<=i4);
-        QVERIFY(i>=i4);
-        QVERIFY(i4==i); // const_iterator COMP iterator
-        QVERIFY(i4<=i);
-        QVERIFY(i4>=i);
-        QVERIFY(i>=i4);
-        QVERIFY(i4<=i);
-        QVERIFY(i2!=i4);
-        QVERIFY(i2>i4);
-        QVERIFY(i2>=i4);
-        QVERIFY(i4!=i2);
-        QVERIFY(i4i);
-        QVERIFY(i4>=i);
-
-        i= p.begin();
-        i2= p.begin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, p[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, p.begin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2 += 3, p.end());
-        QCOMPARE(i2 -= 3, p.begin());
-        QCOMPARE(i2+0, p.begin());
-        QCOMPARE(i2+3, p.end());
-        i2 += 3;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-3;
-        QCOMPARE(i, p.begin());
-        QCOMPARE(i2-i, 3);
-
-        //p.begin end tested above
-
-        // QhullPoint is const-only
-    }
-}//t_iterator
-
-void QhullPoint_test::
-t_const_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullPoint p= q.firstVertex().point();
-        QhullPoint::ConstIterator i= p.begin();
-        QhullPoint::const_iterator i2= p.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= p.begin();
-        QVERIFY(i==i2);
-        i2= p.end();
-        QVERIFY(i!=i2);
-        double d3= *i;
-        i2--;
-        double d2= *i2;
-        QCOMPARE(d3, p[0]);
-        QCOMPARE(d2, p[2]);
-        QhullPoint::ConstIterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3), p[1]);
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        // See t_iterator for const_iterator COMP iterator
-
-        i= p.begin();
-        i2= p.constBegin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, p[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, p.constBegin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2+=3, p.constEnd());
-        QCOMPARE(i2-=3, p.constBegin());
-        QCOMPARE(i2+0, p.constBegin());
-        QCOMPARE(i2+3, p.constEnd());
-        i2 += 3;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-3;
-        QCOMPARE(i, p.constBegin());
-        QCOMPARE(i2-i, 3);
-
-        // QhullPoint is const-only
-    }
-}//t_const_iterator
-
-void QhullPoint_test::
-t_qhullpoint_iterator()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-
-    QhullPoint p2(q);
-    QhullPointIterator i= p2;
-    QCOMPARE(p2.dimension(), 3);
-    QVERIFY(!i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i.toBack();
-    QVERIFY(!i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    QhullPoint p = q.firstVertex().point();
-    QhullPointIterator i2(p);
-    QCOMPARE(p.dimension(), 3);
-    i= p;
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i2.toBack();
-    i.toFront();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    // i at front, i2 at end/back, 3 coordinates
-    QCOMPARE(i.peekNext(), p[0]);
-    QCOMPARE(i2.peekPrevious(), p[2]);
-    QCOMPARE(i2.previous(), p[2]);
-    QCOMPARE(i2.previous(), p[1]);
-    QCOMPARE(i2.previous(), p[0]);
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekNext(), p[0]);
-    // i.peekNext()= 1.0; // compiler error, i is const
-    QCOMPARE(i.next(), p[0]);
-    QCOMPARE(i.peekNext(), p[1]);
-    QCOMPARE(i.next(), p[1]);
-    QCOMPARE(i.next(), p[2]);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), p[0]);
-}//t_qhullpoint_iterator
-
-void QhullPoint_test::
-t_method()
-{
-    // advancePoint tested above
-    RboxPoints rcube("c");
-    Qhull q(rcube, "");
-    QhullPoint p = q.firstVertex().point();
-    double dist= p.distance(q.origin());
-    QCOMPARE(dist, sqrt(double(2.0+1.0))/2); // half diagonal of unit cube
-}//t_qhullpoint_iterator
-
-void QhullPoint_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        QhullPoint p= q.beginVertex().point();
-        ostringstream os;
-        os << "Point:\n";
-        os << p;
-        os << "Point w/ print:\n";
-        os << p.print(" message ");
-        os << p.printWithIdentifier(" Point with id and a message ");
-        cout << os.str();
-        QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count("p"), 2);
-    }
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullPoint_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullPoints_test.cpp b/src/qhull/src/qhulltest/QhullPoints_test.cpp
deleted file mode 100644
index c2d8347e2..000000000
--- a/src/qhull/src/qhulltest/QhullPoints_test.cpp
+++ /dev/null
@@ -1,561 +0,0 @@
-/****************************************************************************
-**
-** Copyright (p) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullPoints_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled header
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullPoints.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-
-namespace orgQhull {
-
-class QhullPoints_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct_q();
-    void t_construct_qh();
-    void t_convert();
-    void t_getset();
-    void t_element();
-    void t_iterator();
-    void t_const_iterator();
-    void t_search();
-    void t_points_iterator();
-    void t_io();
-};//QhullPoints_test
-
-void
-add_QhullPoints_test()
-{
-    new QhullPoints_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullPoints_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullPoints_test::
-t_construct_q()
-{
-    Qhull q;
-    QhullPoints ps(q);
-    QCOMPARE(ps.dimension(), 0);
-    QVERIFY(ps.isEmpty());
-    QCOMPARE(ps.count(), 0);
-    QCOMPARE(ps.size(), 0u);
-    QCOMPARE(ps.coordinateCount(), 0);
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps2(q);
-    ps2.defineAs(2, 6, c);
-    QCOMPARE(ps2.dimension(), 2);
-    QVERIFY(!ps2.isEmpty());
-    QCOMPARE(ps2.count(), 3);
-    QCOMPARE(ps2.size(), 3u);
-    QCOMPARE(ps2.coordinates(), c);
-    QhullPoints ps3(q, 2, 6, c);
-    QCOMPARE(ps3.dimension(), 2);
-    QVERIFY(!ps3.isEmpty());
-    QCOMPARE(ps3.coordinates(), ps2.coordinates());
-    QVERIFY(ps3==ps2);
-    QVERIFY(ps3!=ps);
-    QhullPoints ps4= ps3;
-    QVERIFY(ps4==ps3);
-    // ps4= ps3; //compiler error
-    QhullPoints ps5(ps4);
-    QVERIFY(ps5==ps4);
-    QVERIFY(!(ps5!=ps4));
-    coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps6(q, 2, 6, c2);
-    QVERIFY(ps6==ps2);
-
-    RboxPoints rbox("c D2");
-    Qhull q2(rbox, "");
-    QhullPoints ps8(q2);
-    QCOMPARE(ps8.dimension(), 2);
-    QCOMPARE(ps8.count(), 0);
-    QCOMPARE(ps8.size(), 0u);
-    QCOMPARE(ps8.coordinateCount(), 0);
-    coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps9(q2, 6, c3);
-    QCOMPARE(ps9.dimension(), 2);
-    QCOMPARE(ps9.coordinateCount(), 6);
-    QCOMPARE(ps9.count(), 3);
-    QCOMPARE(ps9.coordinates(), c3);
-    QCOMPARE(ps9, ps2);  // DISTround
-    c3[1]= 1.0+1e-17;
-    QCOMPARE(ps9, ps2);  // DISTround
-    c3[1]= 1.0+1e-15;
-    QVERIFY(ps9!=ps2);  // DISTround
-
-    ps9.defineAs(6, c2);
-    QCOMPARE(ps9.dimension(), 2);
-    QCOMPARE(ps9.coordinateCount(), 6);
-    QCOMPARE(ps9.count(), 3);
-    QCOMPARE(ps9.coordinates(), c2);
-}//t_construct_q
-
-void QhullPoints_test::
-t_construct_qh()
-{
-    Qhull q;
-    QhullQh *qh= q.qh();
-    QhullPoints ps(qh);
-    QCOMPARE(ps.dimension(), 0);
-    QVERIFY(ps.isEmpty());
-    QCOMPARE(ps.count(), 0);
-    QCOMPARE(ps.size(), 0u);
-    QCOMPARE(ps.coordinateCount(), 0);
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps2(qh);
-    ps2.defineAs(2, 6, c);
-    QCOMPARE(ps2.dimension(), 2);
-    QVERIFY(!ps2.isEmpty());
-    QCOMPARE(ps2.count(), 3);
-    QCOMPARE(ps2.size(), 3u);
-    QCOMPARE(ps2.coordinates(), c);
-    QhullPoints ps3(qh, 2, 6, c);
-    QCOMPARE(ps3.dimension(), 2);
-    QVERIFY(!ps3.isEmpty());
-    QCOMPARE(ps3.coordinates(), ps2.coordinates());
-    QVERIFY(ps3==ps2);
-    QVERIFY(ps3!=ps);
-    QhullPoints ps4= ps3;
-    QVERIFY(ps4==ps3);
-    // ps4= ps3; //compiler error
-    QhullPoints ps5(ps4);
-    QVERIFY(ps5==ps4);
-    QVERIFY(!(ps5!=ps4));
-    coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps6(qh, 2, 6, c2);
-    QVERIFY(ps6==ps2);
-
-    RboxPoints rbox("c D2");
-    Qhull q2(rbox, "");
-    QhullPoints ps8(q2.qh());
-    QCOMPARE(ps8.dimension(), 2);
-    QCOMPARE(ps8.count(), 0);
-    QCOMPARE(ps8.size(), 0u);
-    QCOMPARE(ps8.coordinateCount(), 0);
-    coordT c3[]= {10.0, 11.0, 12.0, 13.0, 14.0, 15.0};
-    QhullPoints ps9(q2.qh(), 6, c3);
-    QCOMPARE(ps9.dimension(), 2);
-    QCOMPARE(ps9.coordinateCount(), 6);
-    QCOMPARE(ps9.count(), 3);
-    QCOMPARE(ps9.coordinates(), c3);
-    ps9.defineAs(6, c2);
-    QCOMPARE(ps9.dimension(), 2);
-    QCOMPARE(ps9.coordinateCount(), 6);
-    QCOMPARE(ps9.count(), 3);
-    QCOMPARE(ps9.coordinates(), c2);
-}//t_construct_qh
-
-void QhullPoints_test::
-t_convert()
-{
-    Qhull q;
-    //defineAs tested above
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps(q, 3, 6, c);
-    QCOMPARE(ps.dimension(), 3);
-    QCOMPARE(ps.size(), 2u);
-    const coordT *c2= ps.constData();
-    QCOMPARE(c, c2);
-    const coordT *c3= ps.data();
-    QCOMPARE(c, c3);
-    coordT *c4= ps.data();
-    QCOMPARE(c, c4);
-    std::vector vs= ps.toStdVector();
-    QCOMPARE(vs.size(), 2u);
-    QhullPoint p= vs[1];
-    QCOMPARE(p[2], 5.0);
-    QList qs= ps.toQList();
-    QCOMPARE(qs.size(), 2);
-    QhullPoint p2= qs[1];
-    QCOMPARE(p2[2], 5.0);
-}//t_convert
-
-void QhullPoints_test::
-t_getset()
-{
-    Qhull q;
-    //See t_construct for coordinates, count, defineAs, dimension, isempty, ==, !=, size
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps(q, 3, 6, c);
-    QhullPoints ps2(q, 3, 6, c);
-    QCOMPARE(ps2.dimension(), 3);
-    QCOMPARE(ps2.coordinates(), c);
-    QCOMPARE(ps2.count(), 2);
-    QCOMPARE(ps2.coordinateCount(), 6);
-    coordT c2[]= {-1.0, -2.0, -3.0, -4.0, -5.0, -6.0};
-    ps2.defineAs(6, c2);
-    QCOMPARE(ps2.coordinates(), c2);
-    QCOMPARE(ps2.count(), 2);
-    QCOMPARE(ps2.size(), 2u);
-    QCOMPARE(ps2.dimension(), 3);
-    QVERIFY(!ps2.isEmpty());
-    QVERIFY(ps!=ps2);
-    // ps2= ps; // assignment not available, compiler error
-    ps2.defineAs(ps);
-    QVERIFY(ps==ps2);
-    ps2.setDimension(2);
-    QCOMPARE(ps2.dimension(), 2);
-    QCOMPARE(ps2.coordinates(), c);
-    QVERIFY(!ps2.isEmpty());
-    QCOMPARE(ps2.count(), 3);
-    QCOMPARE(ps2.size(), 3u);
-    QVERIFY(ps!=ps2);
-    QhullPoints ps3(ps2);
-    ps3.setDimension(3);
-    ps3.defineAs(5, c2);
-    QCOMPARE(ps3.count(), 1);
-    QCOMPARE(ps3.extraCoordinatesCount(), 2);
-    QCOMPARE(ps3.extraCoordinates()[0], -4.0);
-    QVERIFY(ps3.includesCoordinates(ps3.data()));
-    QVERIFY(ps3.includesCoordinates(ps3.data()+ps3.count()-1));
-    QVERIFY(!ps3.includesCoordinates(ps3.data()-1));
-    QVERIFY(!ps3.includesCoordinates(ps3.data()+ps3.coordinateCount()));
-}//t_getset
-
-
-void QhullPoints_test::
-t_element()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps(q, 2, 6, c);
-    QCOMPARE(ps.count(), 3);
-    QhullPoint p(q, 2, c);
-    QCOMPARE(ps[0], p);
-    QCOMPARE(ps.at(1), ps[1]);
-    QCOMPARE(ps.first(), p);
-    QCOMPARE(ps.front(), ps.first());
-    QCOMPARE(ps.last(), ps.at(2));
-    QCOMPARE(ps.back(), ps.last());
-    QhullPoints ps2= ps.mid(2);
-    QCOMPARE(ps2.count(), 1);
-    QhullPoints ps3= ps.mid(3);
-    QVERIFY(ps3.isEmpty());
-    QhullPoints ps4= ps.mid(10);
-    QVERIFY(ps4.isEmpty());
-    QhullPoints ps5= ps.mid(-1);
-    QVERIFY(ps5.isEmpty());
-    QhullPoints ps6= ps.mid(1, 1);
-    QCOMPARE(ps6.count(), 1);
-    QCOMPARE(ps6[0], ps[1]);
-    QhullPoints ps7= ps.mid(1, 10);
-    QCOMPARE(ps7.count(), 2);
-    QCOMPARE(ps7[1], ps[2]);
-    QhullPoint p8(q);
-    QCOMPARE(ps.value(2), ps[2]);
-    QCOMPARE(ps.value(-1), p8);
-    QCOMPARE(ps.value(3), p8);
-    QCOMPARE(ps.value(3, p), p);
-    QVERIFY(ps.value(1, p)!=p);
-    foreach(QhullPoint p9, ps){  // Qt only
-        QCOMPARE(p9.dimension(), 2);
-        QVERIFY(p9[0]==0.0 || p9[0]==2.0 || p9[0]==4.0);
-    }
-}//t_element
-
-void QhullPoints_test::
-t_iterator()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0};
-    QhullPoints ps(q, 1, 3, c);
-    QCOMPARE(ps.dimension(), 1);
-    QhullPoints::Iterator i(ps);
-    QhullPoints::iterator i2= ps.begin();
-    QVERIFY(i==i2);
-    QVERIFY(i>=i2);
-    QVERIFY(i<=i2);
-    i= ps.begin();
-    QVERIFY(i==i2);
-    i2= ps.end();
-    QVERIFY(i!=i2);
-    QhullPoint p(i); // QhullPoint is the base class for QhullPoints::iterator
-    QCOMPARE(p.dimension(), ps.dimension());
-    QCOMPARE(p.coordinates(), ps.coordinates());
-    i2--;
-    QhullPoint p2= *i2;
-    QCOMPARE(p[0], 0.0);
-    QCOMPARE(p2[0], 2.0);
-    QhullPoints::Iterator i5(i2);
-    QCOMPARE(*i2, *i5);
-    coordT c3[]= {0.0, -1.0, -2.0};
-    QhullPoints::Iterator i3(q, 1, c3);
-    QVERIFY(i!=i3);
-    QCOMPARE(*i, *i3);
-
-    (i3= i)++;
-    QCOMPARE((*i3)[0], 1.0);
-    QCOMPARE(i3->dimension(), 1);
-    QCOMPARE(i3[0][0], 1.0);
-    QCOMPARE(i3[0], ps[1]);
-
-    QVERIFY(i==i);
-    QVERIFY(i!=i2);
-    QVERIFY(ii);
-    QVERIFY(i2>=i);
-
-    QhullPoints::ConstIterator i4(q, 1, c);
-    QVERIFY(i==i4); // iterator COMP const_iterator
-    QVERIFY(i<=i4);
-    QVERIFY(i>=i4);
-    QVERIFY(i4==i); // const_iterator COMP iterator
-    QVERIFY(i4<=i);
-    QVERIFY(i4>=i);
-    QVERIFY(i>=i4);
-    QVERIFY(i4<=i);
-    QVERIFY(i2!=i4);
-    QVERIFY(i2>i4);
-    QVERIFY(i2>=i4);
-    QVERIFY(i4!=i2);
-    QVERIFY(i4i);
-    QVERIFY(i4>=i);
-
-    i= ps.begin();
-    i2= ps.begin();
-    QCOMPARE(i, i2++);
-    QCOMPARE(*i2, ps[1]);
-    QCOMPARE(++i, i2);
-    QCOMPARE(i, i2--);
-    QCOMPARE(i2, ps.begin());
-    QCOMPARE(--i, i2);
-    QCOMPARE(i2+=3, ps.end());
-    QCOMPARE(i2-=3, ps.begin());
-    QCOMPARE(i2+0, ps.begin());
-    QCOMPARE(i2+3, ps.end());
-    i2 += 3;
-    i= i2-0;
-    QCOMPARE(i, i2);
-    i= i2-3;
-    QCOMPARE(i, ps.begin());
-    QCOMPARE(i2-i, 3);
-
-    //ps.begin end tested above
-
-    // QhullPoints is const-only
-}//t_iterator
-
-void QhullPoints_test::
-t_const_iterator()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0};
-    const QhullPoints ps(q, 1, 3, c);
-    QhullPoints::ConstIterator i(ps);
-    QhullPoints::const_iterator i2= ps.begin();
-    QVERIFY(i==i2);
-    QVERIFY(i>=i2);
-    QVERIFY(i<=i2);
-    i= ps.begin();
-    QVERIFY(i==i2);
-    i2= ps.end();
-    QVERIFY(i!=i2);
-    QhullPoint p(i);
-    QCOMPARE(p.dimension(), ps.dimension());
-    QCOMPARE(p.coordinates(), ps.coordinates());
-    i2--;
-    QhullPoint p2= *i2;
-    QCOMPARE(p[0], 0.0);
-    QCOMPARE(p2[0], 2.0);
-    QhullPoints::ConstIterator i5(i2);
-    QCOMPARE(*i2, *i5);
-    coordT c3[]= {0.0, -1.0, -2.0};
-    QhullPoints::ConstIterator i3(q, 1, c3);
-    QVERIFY(i!=i3);
-    QCOMPARE(*i, *i3);
-
-    (i3= i)++;
-    QCOMPARE((*i3)[0], 1.0);
-    QCOMPARE(i3->dimension(), 1);
-    QCOMPARE(i3[0][0], 1.0);
-    QCOMPARE(i3[0][0], 1.0);
-    QCOMPARE(i3[0], ps[1]);
-
-    QVERIFY(i==i);
-    QVERIFY(i!=i2);
-    QVERIFY(ii);
-    QVERIFY(i2>=i);
-
-    // See t_iterator for const_iterator COMP iterator
-
-    i= ps.begin();
-    i2= ps.constBegin();
-    QCOMPARE(i, i2++);
-    QCOMPARE(*i2, ps[1]);
-    QCOMPARE(++i, i2);
-    QCOMPARE(i, i2--);
-    QCOMPARE(i2, ps.constBegin());
-    QCOMPARE(--i, i2);
-    QCOMPARE(i2+=3, ps.constEnd());
-    QCOMPARE(i2-=3, ps.constBegin());
-    QCOMPARE(i2+0, ps.constBegin());
-    QCOMPARE(i2+3, ps.constEnd());
-    i2 += 3;
-    i= i2-0;
-    QCOMPARE(i, i2);
-    i= i2-3;
-    QCOMPARE(i, ps.constBegin());
-    QCOMPARE(i2-i, 3);
-
-    // QhullPoints is const-only
-}//t_const_iterator
-
-
-void QhullPoints_test::
-t_search()
-{
-    Qhull q;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 0, 1};
-    QhullPoints ps(q, 2, 8, c); //2-d array of 4 points
-    QhullPoint p= ps.first();
-    QhullPoint p2= ps.last();
-    QVERIFY(ps.contains(p));
-    QVERIFY(ps.contains(p2));
-    QVERIFY(p==p2);
-    QhullPoint p5= ps[2];
-    QVERIFY(p!=p5);
-    QVERIFY(ps.contains(p5));
-    coordT c2[]= {0.0, 1.0, 2.0, 3.0};
-    QhullPoint p3(q, 2, c2); //2-d point
-    QVERIFY(ps.contains(p3));
-    QhullPoint p4(q, 3, c2); //3-d point
-    QVERIFY(!ps.contains(p4));
-    p4.defineAs(2, c); //2-d point
-    QVERIFY(ps.contains(p4));
-    p4.defineAs(2, c+1); //2-d point
-    QVERIFY(!ps.contains(p4));
-    QhullPoint p6(q, 2, c2+2); //2-d point
-    QCOMPARE(ps.count(p), 2);
-    QCOMPARE(ps.count(p2), 2);
-    QCOMPARE(ps.count(p3), 2);
-    QCOMPARE(ps.count(p4), 0);
-    QCOMPARE(ps.count(p6), 1);
-    QCOMPARE(ps.indexOf(&ps[0][0]), 0);
-    //QCOMPARE(ps.indexOf(ps.end()), -1); //ps.end() is a QhullPoint which may match
-    QCOMPARE(ps.indexOf(0), -1);
-    QCOMPARE(ps.indexOf(&ps[3][0]), 3);
-    QCOMPARE(ps.indexOf(&ps[3][1], QhullError::NOthrow), 3);
-    QCOMPARE(ps.indexOf(ps.data()+ps.coordinateCount(), QhullError::NOthrow), -1);
-    QCOMPARE(ps.indexOf(p), 0);
-    QCOMPARE(ps.indexOf(p2), 0);
-    QCOMPARE(ps.indexOf(p3), 0);
-    QCOMPARE(ps.indexOf(p4), -1);
-    QCOMPARE(ps.indexOf(p5), 2);
-    QCOMPARE(ps.indexOf(p6), 1);
-    QCOMPARE(ps.lastIndexOf(p), 3);
-    QCOMPARE(ps.lastIndexOf(p4), -1);
-    QCOMPARE(ps.lastIndexOf(p6), 1);
-    QhullPoints ps3(q);
-    QCOMPARE(ps3.indexOf(ps3.data()), -1);
-    QCOMPARE(ps3.indexOf(ps3.data()+1, QhullError::NOthrow), -1);
-    QCOMPARE(ps3.indexOf(p), -1);
-    QCOMPARE(ps3.lastIndexOf(p), -1);
-    QhullPoints ps4(q, 2, 0, c);
-    QCOMPARE(ps4.indexOf(p), -1);
-    QCOMPARE(ps4.lastIndexOf(p), -1);
-}//t_search
-
-void QhullPoints_test::
-t_points_iterator()
-{
-    Qhull q;
-    coordT c2[]= {0.0};
-    QhullPoints ps2(q, 0, 0, c2); // 0-dimensional
-    QhullPointsIterator i2= ps2;
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    i2.toBack();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps(q, 3, 6, c); // 3-dimensional
-    QhullPointsIterator i(ps);
-    i2= ps;
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i2.toBack();
-    i.toFront();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    QhullPoint p= ps[0];
-    QhullPoint p2(ps[0]);
-    QCOMPARE(p, p2);
-    QVERIFY(p==p2);
-    QhullPoint p3(ps[1]);
- // p2[0]= 0.0;
-    QVERIFY(p==p2);
-    QCOMPARE(i2.peekPrevious(), p3);
-    QCOMPARE(i2.previous(), p3);
-    QCOMPARE(i2.previous(), p);
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekNext(), p);
-    // i.peekNext()= 1.0; // compiler error
-    QCOMPARE(i.next(), p);
-    QCOMPARE(i.peekNext(), p3);
-    QCOMPARE(i.next(), p3);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), p);
-}//t_points_iterator
-
-void QhullPoints_test::
-t_io()
-{
-    Qhull q;
-    QhullPoints ps(q);
-    ostringstream os;
-    os << "Empty QhullPoints\n" << ps << endl;
-    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
-    QhullPoints ps2(q, 3, 6, c); // 3-dimensional explicit
-    os << "QhullPoints from c[]\n" << ps2 << endl;
-
-    RboxPoints rcube("c");
-    Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullPoints ps3= q2.points();
-    os << "QhullPoints\n" << ps3;
-    os << ps3.print("message\n");
-    os << ps3.printWithIdentifier("w/ identifiers\n");
-    cout << os.str();
-    QString s= QString::fromStdString(os.str());
-    QCOMPARE(s.count("p"), 8+1);
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullPoints_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullRidge_test.cpp b/src/qhull/src/qhulltest/QhullRidge_test.cpp
deleted file mode 100644
index 420a7f06d..000000000
--- a/src/qhull/src/qhulltest/QhullRidge_test.cpp
+++ /dev/null
@@ -1,159 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullRidge_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullRidge_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_getSet();
-    void t_foreach();
-    void t_io();
-};//QhullRidge_test
-
-void
-add_QhullRidge_test()
-{
-    new QhullRidge_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullRidge_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullRidge_test::
-t_construct()
-{
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
-    QhullRidge r(q);
-    QVERIFY(!r.isValid());
-    QCOMPARE(r.dimension(),2);
-    QhullFacet f(q.firstFacet());
-    QhullRidgeSet rs(f.ridges());
-    QVERIFY(!rs.isEmpty()); // Simplicial facets do not have ridges()
-    QhullRidge r2(rs.first());
-    QCOMPARE(r2.dimension(), 2); // One dimension lower than the facet
-    r= r2;
-    QVERIFY(r.isValid());
-    QCOMPARE(r.dimension(), 2);
-    QhullRidge r3(q, r2.getRidgeT());
-    QCOMPARE(r,r3);
-    QhullRidge r4(q, r2.getBaseT());
-    QCOMPARE(r,r4);
-    QhullRidge r5= r2; // copy constructor
-    QVERIFY(r5==r2);
-    QVERIFY(r5==r);
-}//t_construct
-
-void QhullRidge_test::
-t_getSet()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
-        QCOMPARE(q.facetCount(), 6);
-        QCOMPARE(q.vertexCount(), 8);
-        QhullFacet f(q.firstFacet());
-        QhullRidgeSet rs= f.ridges();
-        QhullRidgeSetIterator i(rs);
-        while(i.hasNext()){
-            const QhullRidge r= i.next();
-            cout << r.id() << endl;
-            QVERIFY(r.bottomFacet()!=r.topFacet());
-            QCOMPARE(r.dimension(), 2); // Ridge one-dimension less than facet
-            QVERIFY(r.id()>=0 && r.id()<9*27);
-            QVERIFY(r.isValid());
-            QVERIFY(r==r);
-            QVERIFY(r==i.peekPrevious());
-            QCOMPARE(r.otherFacet(r.bottomFacet()),r.topFacet());
-            QCOMPARE(r.otherFacet(r.topFacet()),r.bottomFacet());
-        }
-    }
-}//t_getSet
-
-void QhullRidge_test::
-t_foreach()
-{
-    RboxPoints rcube("c");  // cube
-    {
-        Qhull q(rcube, "QR0"); // rotated cube
-        QhullFacet f(q.firstFacet());
-        foreach (const QhullRidge &r, f.ridges()){  // Qt only
-            QhullVertexSet vs= r.vertices();
-            QCOMPARE(vs.count(), 2);
-            foreach (const QhullVertex &v, vs){  // Qt only
-                QVERIFY(f.vertices().contains(v));
-            }
-        }
-        QhullRidgeSet rs= f.ridges();
-        QhullRidge r= rs.first();
-        QhullRidge r2= r;
-        QList vs;
-        int count= 0;
-        while(!count || r2!=r){
-            ++count;
-            QhullVertex v(q);
-            QVERIFY2(r2.hasNextRidge3d(f),"A cube should only have non-simplicial facets.");
-            QhullRidge r3= r2.nextRidge3d(f, &v);
-            QVERIFY(!vs.contains(v));
-            vs << v;
-            r2= r2.nextRidge3d(f);
-            QCOMPARE(r3, r2);
-        }
-        QCOMPARE(vs.count(), rs.count());
-        QCOMPARE(count, rs.count());
-    }
-}//t_foreach
-
-void QhullRidge_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        QhullFacet f(q.firstFacet());
-        QhullRidgeSet rs= f.ridges();
-        QhullRidge r= rs.first();
-        ostringstream os;
-        os << "Ridges\n" << rs << "Ridge\n" << r;
-        os << r.print("\nRidge with message");
-        cout << os.str();
-        QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count(" r"), 6);
-    }
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullRidge_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullSet_test.cpp b/src/qhull/src/qhulltest/QhullSet_test.cpp
deleted file mode 100644
index 87fcf4acf..000000000
--- a/src/qhull/src/qhulltest/QhullSet_test.cpp
+++ /dev/null
@@ -1,434 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullSet_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullRidge.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/RboxPoints.h"
-
-#include 
-
-using std::cout;
-using std::endl;
-
-namespace orgQhull {
-
-class QhullSet_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_qhullsetbase();
-    void t_convert();
-    void t_element();
-    void t_search();
-    void t_iterator();
-    void t_const_iterator();
-    void t_qhullset_iterator();
-    void t_io();
-};//QhullSet_test
-
-void
-add_QhullSet_test()
-{
-    new QhullSet_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullSet_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-// Test QhullFacetSet and QhullSet.
-// Use QhullRidgeSet to test methods overloaded by QhullFacetSet
-
-void QhullSet_test::
-t_qhullsetbase()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
-        // Fake an empty set.  Default constructor not defined.  No memory allocation.
-        QhullFacet f4 = q.beginFacet();
-        QhullFacetSet fs = f4.neighborFacets();
-        fs.defineAs(q.qh()->other_points); // Force an empty set
-        QVERIFY(fs.isEmpty());
-        QCOMPARE(fs.count(), 0);
-        QCOMPARE(fs.size(), 0u);
-        QCOMPARE(fs.begin(), fs.end()); // beginPointer(), endPointer()
-        QVERIFY(QhullSetBase::isEmpty(fs.getSetT()));
-
-        QhullRidgeSet rs = f4.ridges();
-        QVERIFY(!rs.isEmpty());
-        QCOMPARE(rs.count(), 4);
-        QCOMPARE(rs.size(), 4u);
-        QVERIFY(rs.begin()!=rs.end());
-        QVERIFY(!QhullSetBase::isEmpty(rs.getSetT()));
-        QhullRidgeSet rs2= rs; // copy constructor
-        // rs= rs2; // disabled.  Would not copy ridges
-        QCOMPARE(rs2, rs);
-
-        QCOMPARE(q.facetCount(), 6);
-        QhullFacet f = q.beginFacet();
-        QhullFacetSet fs2 = f.neighborFacets();
-        QCOMPARE(fs2.count(), 4);
-        QCOMPARE(fs2.size(), 4u);
-        QVERIFY(!fs2.isEmpty());
-        QVERIFY(!QhullSetBase::isEmpty(fs2.getSetT()));
-        QVERIFY(fs!=fs2);
-        setT *s= fs2.getSetT();
-        fs.defineAs(s);
-        QVERIFY(fs==fs2);
-        QCOMPARE(fs[1], fs2[1]); // elementPointer
-        QhullFacetSet fs3(fs2);
-        QVERIFY(fs3==fs);
-        // fs= fs2; // disabled.  Would not copy facets
-        QhullFacetSet fs4= fs2; // copy constructor
-        QVERIFY(fs4==fs2);
-    }
-}//t_qhullsetbase
-
-// constructors tested by t_qhullsetbase
-
-void QhullSet_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullFacet f= q.firstFacet();
-        f= f.next();
-        QhullRidgeSet rs= f.ridges();
-        QCOMPARE(rs.count(),4);
-        std::vector rv= rs.toStdVector();
-        QCOMPARE(rv.size(), 4u);
-        QList rv2= rs.toQList();
-        QCOMPARE(rv2.size(), 4);
-        std::vector::iterator i= rv.begin();
-        foreach(QhullRidge r, rv2){  // Qt only
-            QhullRidge r2= *i++;
-            QCOMPARE(r, r2);
-        }
-
-        Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QCOMPARE(q2.facetCount(), 12);
-        QhullFacet f2 = q2.beginFacet();
-        QhullFacetSet fs = f2.neighborFacets();
-        QCOMPARE(fs.size(), 3U);
-        std::vector vs= fs.toStdVector();
-        QCOMPARE(vs.size(), fs.size());
-        for(int k= fs.count(); k--; ){
-            QCOMPARE(vs[k], fs[k]);
-        }
-        QList qv= fs.toQList();
-        QCOMPARE(qv.count(), fs.count());
-        for(int k= fs.count(); k--; ){
-            QCOMPARE(qv[k], fs[k]);
-        }
-    }
-}//t_convert
-
-//ReadOnly (count, isEmpty) tested by t_convert
-//  operator== tested by t_search
-
-void QhullSet_test::
-t_element()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacet f = q.beginFacet();
-    QhullFacetSet fs = f.neighborFacets();
-
-    QCOMPARE(fs.at(1), fs[1]);
-    QCOMPARE(fs.first(), fs[0]);
-    QCOMPARE(fs.front(), fs.first());
-    QCOMPARE(fs.last(), fs.at(3));
-    QCOMPARE(fs.back(), fs.last());
-    facetT **d = fs.data();
-    facetT * const *d2= fs.data();
-    facetT * const *d3= fs.constData();
-    QVERIFY(d==d2);
-    QVERIFY(d2==d3);
-    QCOMPARE(QhullFacet(q, *d), fs.first());
-    QhullFacetSet::iterator i(q.qh(), d+4);
-    QCOMPARE(i, fs.end());
-    QCOMPARE(d[4], static_cast(0));
-    QhullFacet f4(q, d[4]);
-    QVERIFY(!f4.isValid());
-    QCOMPARE(fs.second(), fs[1]);
-    const QhullFacet f2= fs.second();
-    QVERIFY(f2==fs[1]);
-    const QhullFacet f3= fs[1];
-    QCOMPARE(f2, f3);
-
-    QCOMPARE(fs.value(2), fs[2]);
-    QCOMPARE(fs.value(-1), QhullFacet());
-    QCOMPARE(fs.value(10), QhullFacet());
-    QCOMPARE(fs.value(2, f), fs[2]);
-    QCOMPARE(fs.value(4, f), f);
-    // mid() not available (read-only)
-}//t_element
-
-void QhullSet_test::
-t_search()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    QhullFacet f = q.beginFacet();
-    QhullFacetSet fs = f.neighborFacets();
-    QhullFacet f2= *fs.begin();
-    QhullFacet f3= fs.last();
-    QVERIFY(fs.contains(f2));
-    QVERIFY(fs.contains(f3));
-    QVERIFY(!fs.contains(f));
-
-    QhullFacetSet fs2= f2.neighborFacets();
-    QVERIFY(fs==fs);
-    QVERIFY(fs!=fs2);
-    QCOMPARE(fs.count(f2), 1);
-    QCOMPARE(fs.count(f3), 1);
-    QCOMPARE(fs.count(f), 0);
-    QCOMPARE(fs.indexOf(f2), 0);
-    QCOMPARE(fs.indexOf(f3), 3);
-    QCOMPARE(fs.indexOf(f), -1);
-    QCOMPARE(fs.lastIndexOf(f2), 0);
-    QCOMPARE(fs.lastIndexOf(f3), 3);
-    QCOMPARE(fs.lastIndexOf(f), -1);
-}//t_search
-
-void QhullSet_test::
-t_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullFacet f = q.beginFacet();
-        QhullFacetSet fs = f.neighborFacets();
-        QhullFacetSet::Iterator i= fs.begin();
-        QhullFacetSet::iterator i2= fs.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= fs.begin();
-        QVERIFY(i==i2);
-        i2= fs.end();
-        QVERIFY(i!=i2);
-        QhullFacet f3(*i);
-        i2--;
-        QhullFacet f2= *i2;
-        QCOMPARE(f3.id(), fs[0].id());
-        QCOMPARE(f2.id(), fs[3].id());
-        QhullFacetSet::Iterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3).id(), fs[1].id());
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        QhullFacetSet::ConstIterator i4= fs.begin();
-        QVERIFY(i==i4); // iterator COMP const_iterator
-        QVERIFY(i<=i4);
-        QVERIFY(i>=i4);
-        QVERIFY(i4==i); // const_iterator COMP iterator
-        QVERIFY(i4<=i);
-        QVERIFY(i4>=i);
-        QVERIFY(i>=i4);
-        QVERIFY(i4<=i);
-        QVERIFY(i2!=i4);
-        QVERIFY(i2>i4);
-        QVERIFY(i2>=i4);
-        QVERIFY(i4!=i2);
-        QVERIFY(i4i);
-        QVERIFY(i4>=i);
-
-        i= fs.begin();
-        i2= fs.begin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, fs[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, fs.begin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2 += 4, fs.end());
-        QCOMPARE(i2 -= 4, fs.begin());
-        QCOMPARE(i2+0, fs.begin());
-        QCOMPARE(i2+4, fs.end());
-        i2 += 4;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-4;
-        QCOMPARE(i, fs.begin());
-        QCOMPARE(i2-i, 4);
-
-        //fs.begin end tested above
-
-        // QhullFacetSet is const-only
-    }
-}//t_iterator
-
-void QhullSet_test::
-t_const_iterator()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0");  // rotated unit cube
-        QhullFacet f = q.beginFacet();
-        QhullFacetSet fs = f.neighborFacets();
-        QhullFacetSet::ConstIterator i= fs.begin();
-        QhullFacetSet::const_iterator i2= fs.begin();
-        QVERIFY(i==i2);
-        QVERIFY(i>=i2);
-        QVERIFY(i<=i2);
-        i= fs.begin();
-        QVERIFY(i==i2);
-        i2= fs.end();
-        QVERIFY(i!=i2);
-        QhullFacet f3(*i);
-        i2--;
-        QhullFacet f2= *i2;
-        QCOMPARE(f3.id(), fs[0].id());
-        QCOMPARE(f2.id(), fs[3].id());
-        QhullFacetSet::ConstIterator i3(i2);
-        QCOMPARE(*i2, *i3);
-
-        (i3= i)++;
-        QCOMPARE((*i3).id(), fs[1].id());
-        QVERIFY(i==i);
-        QVERIFY(i!=i2);
-        QVERIFY(ii);
-        QVERIFY(i2>=i);
-
-        // See t_iterator for const_iterator COMP iterator
-
-        i= fs.begin();
-        i2= fs.constBegin();
-        QCOMPARE(i, i2++);
-        QCOMPARE(*i2, fs[1]);
-        QCOMPARE(++i, i2);
-        QCOMPARE(i, i2--);
-        QCOMPARE(i2, fs.constBegin());
-        QCOMPARE(--i, i2);
-        QCOMPARE(i2+=4, fs.constEnd());
-        QCOMPARE(i2-=4, fs.constBegin());
-        QCOMPARE(i2+0, fs.constBegin());
-        QCOMPARE(i2+4, fs.constEnd());
-        i2 += 4;
-        i= i2-0;
-        QCOMPARE(i, i2);
-        i= i2-4;
-        QCOMPARE(i, fs.constBegin());
-        QCOMPARE(i2-i, 4);
-
-        // QhullFacetSet is const-only
-    }
-}//t_const_iterator
-
-void QhullSet_test::
-t_qhullset_iterator()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    // Fake an empty set.  Default constructor not defined.  No memory allocation.
-    QhullFacet f = q.beginFacet();
-    QhullFacetSet fs = f.neighborFacets();
-    fs.defineAs(q.qh()->other_points);
-    QhullFacetSetIterator i(fs);
-    QCOMPARE(fs.count(), 0);
-    QVERIFY(!i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i.toBack();
-    QVERIFY(!i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    QhullFacet f2 = q.beginFacet();
-    QhullFacetSet fs2 = f2.neighborFacets();
-    QhullFacetSetIterator i2(fs2);
-    QCOMPARE(fs2.count(), 4);
-    i= fs2;
-    QVERIFY(i2.hasNext());
-    QVERIFY(!i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-    i2.toBack();
-    i.toFront();
-    QVERIFY(!i2.hasNext());
-    QVERIFY(i2.hasPrevious());
-    QVERIFY(i.hasNext());
-    QVERIFY(!i.hasPrevious());
-
-    // i at front, i2 at end/back, 4 neighbors
-    QhullFacetSet fs3 = f2.neighborFacets(); // same as fs2
-    QhullFacet f3(fs2[0]);
-    QhullFacet f4= fs3[0];
-    QCOMPARE(f3, f4);
-    QVERIFY(f3==f4);
-    QhullFacet f5(fs3[1]);
-    QVERIFY(f4!=f5);
-    QhullFacet f6(fs3[2]);
-    QhullFacet f7(fs3[3]);
-    QCOMPARE(i2.peekPrevious(), f7);
-    QCOMPARE(i2.previous(), f7);
-    QCOMPARE(i2.previous(), f6);
-    QCOMPARE(i2.previous(), f5);
-    QCOMPARE(i2.previous(), f4);
-    QVERIFY(!i2.hasPrevious());
-    QCOMPARE(i.peekNext(), f4);
-    // i.peekNext()= 1.0; // compiler error
-    QCOMPARE(i.next(), f4);
-    QCOMPARE(i.peekNext(), f5);
-    QCOMPARE(i.next(), f5);
-    QCOMPARE(i.next(), f6);
-    QCOMPARE(i.next(), f7);
-    QVERIFY(!i.hasNext());
-    i.toFront();
-    QCOMPARE(i.next(), f4);
-}//t_qhullset_iterator
-
-void QhullSet_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    // Fake an empty set.  Default constructor not defined.  No memory allocation.
-    QhullFacet f= q.beginFacet();
-    QhullFacetSet fs= f.neighborFacets();
-    fs.defineAs(q.qh()->other_points);
-    cout << "INFO:     empty set" << fs << std::endl;
-    QhullFacet f2= q.beginFacet();
-    QhullFacetSet fs2= f2.neighborFacets();
-    cout << "INFO:   Neighboring facets\n";
-    cout << fs2 << std::endl;
-
-    QhullRidgeSet rs= f.ridges();
-    cout << "INFO:   Ridges for a facet\n";
-    cout << rs << std::endl;
-}//t_io
-
-}//namespace orgQhull
-
-#include "moc/QhullSet_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullVertexSet_test.cpp b/src/qhull/src/qhulltest/QhullVertexSet_test.cpp
deleted file mode 100644
index 41caacd29..000000000
--- a/src/qhull/src/qhulltest/QhullVertexSet_test.cpp
+++ /dev/null
@@ -1,152 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullVertexSet_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullVertexSet.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/RboxPoints.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullVertexSet_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_convert();
-    void t_readonly();
-    void t_foreach();
-    void t_io();
-};//QhullVertexSet_test
-
-void
-add_QhullVertexSet_test()
-{
-    new QhullVertexSet_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullVertexSet_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullVertexSet_test::
-t_construct()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
-    QhullFacet f= q.firstFacet();
-    QhullVertexSet vs= f.vertices();
-    QVERIFY(!vs.isEmpty());
-    QCOMPARE(vs.count(),4);
-    QhullVertexSet vs4= vs; // copy constructor
-    QVERIFY(vs4==vs);
-    QhullVertexSet vs3(q, q.qh()->del_vertices);
-    QVERIFY(vs3.isEmpty());
-}//t_construct
-
-void QhullVertexSet_test::
-t_convert()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0 QV2");  // rotated unit cube with "good" facets adjacent to point 0
-    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
-    QhullFacet f= q.firstFacet();
-    QhullVertexSet vs2= f.vertices();
-    QCOMPARE(vs2.count(),4);
-    std::vector fv= vs2.toStdVector();
-    QCOMPARE(fv.size(), 4u);
-    QList fv2= vs2.toQList();
-    QCOMPARE(fv2.size(), 4);
-    std::vector fv3= vs2.toStdVector();
-    QCOMPARE(fv3.size(), 4u);
-    QList fv4= vs2.toQList();
-    QCOMPARE(fv4.size(), 4);
-}//t_convert
-
-//! Spot check properties and read-only.  See QhullSet_test
-void QhullVertexSet_test::
-t_readonly()
-{
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
-    QhullVertexSet vs= q.firstFacet().vertices();
-    QCOMPARE(vs.count(), 4);
-    QCOMPARE(vs.count(), 4);
-    QhullVertex v= vs.first();
-    QhullVertex v2= vs.last();
-    QVERIFY(vs.contains(v));
-    QVERIFY(vs.contains(v2));
-}//t_readonly
-
-void QhullVertexSet_test::
-t_foreach()
-{
-    RboxPoints rcube("c");
-    // Spot check predicates and accessors.  See QhullLinkedList_test
-    Qhull q(rcube,"QR0");  // rotated unit cube
-    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
-    QhullVertexSet vs= q.firstFacet().vertices();
-    QVERIFY(vs.contains(vs.first()));
-    QVERIFY(vs.contains(vs.last()));
-    QCOMPARE(vs.first(), *vs.begin());
-    QCOMPARE(*(vs.end()-1), vs.last());
-}//t_foreach
-
-void QhullVertexSet_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
-        cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
-        QhullVertexSet vs= q.firstFacet().vertices();
-        ostringstream os;
-        os << vs.print("Vertices of first facet with point 0");
-        os << vs.printIdentifiers("\nVertex identifiers: ");
-        cout<< os.str();
-        QString vertices= QString::fromStdString(os.str());
-        QCOMPARE(vertices.count(QRegExp(" v[0-9]")), 4);
-    }
-}//t_io
-
-#ifdef QHULL_USES_QT
-QList QhullVertexSet::
-toQList() const
-{
-    QhullSetIterator i(*this);
-    QList vs;
-    while(i.hasNext()){
-        QhullVertex v= i.next();
-        vs.append(v);
-    }
-    return vs;
-}//toQList
-#endif //QHULL_USES_QT
-
-}//orgQhull
-
-#include "moc/QhullVertexSet_test.moc"
diff --git a/src/qhull/src/qhulltest/QhullVertex_test.cpp b/src/qhull/src/qhulltest/QhullVertex_test.cpp
deleted file mode 100644
index fb6ec9640..000000000
--- a/src/qhull/src/qhulltest/QhullVertex_test.cpp
+++ /dev/null
@@ -1,184 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/QhullVertex_test.cpp#3 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/Coordinates.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullFacetSet.h"
-#include "libqhullcpp/QhullVertexSet.h"
-#include "libqhullcpp/Qhull.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::ostream;
-using std::string;
-
-namespace orgQhull {
-
-class QhullVertex_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_constructConvert();
-    void t_getSet();
-    void t_foreach();
-    void t_io();
-};//QhullVertex_test
-
-void
-add_QhullVertex_test()
-{
-    new QhullVertex_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void QhullVertex_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void QhullVertex_test::
-t_constructConvert()
-{
-    QhullVertex v6;
-    QVERIFY(!v6.isValid());
-    QCOMPARE(v6.dimension(),0);
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-    QhullVertex v(q);
-    QVERIFY(!v.isValid());
-    QCOMPARE(v.dimension(),3);
-    QhullVertex v2(q.beginVertex());
-    QCOMPARE(v2.dimension(),3);
-    v= v2;  // copy assignment
-    QVERIFY(v.isValid());
-    QCOMPARE(v.dimension(),3);
-    QhullVertex v5= v2; // copy constructor
-    QVERIFY(v5==v2);
-    QVERIFY(v5==v);
-    QhullVertex v3(q, v2.getVertexT());
-    QCOMPARE(v,v3);
-    QhullVertex v4(q, v2.getBaseT());
-    QCOMPARE(v,v4);
-}//t_constructConvert
-
-void QhullVertex_test::
-t_getSet()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
-        QCOMPARE(q.facetCount(), 12);
-        QCOMPARE(q.vertexCount(), 8);
-
-        // Also spot-test QhullVertexList.  See QhullLinkedList_test.cpp
-        QhullVertexList vs= q.vertexList();
-        QhullVertexListIterator i(vs);
-        while(i.hasNext()){
-            const QhullVertex v= i.next();
-            cout << v.id() << endl;
-            QCOMPARE(v.dimension(),3);
-            QVERIFY(v.id()>=0 && v.id()<9);
-            QVERIFY(v.isValid());
-            if(i.hasNext()){
-                QCOMPARE(v.next(), i.peekNext());
-                QVERIFY(v.next()!=v);
-                QVERIFY(v.next().previous()==v);
-            }
-            QVERIFY(i.hasPrevious());
-            QCOMPARE(v, i.peekPrevious());
-        }
-
-        // test point()
-        foreach (QhullVertex v, q.vertexList()){  // Qt only
-            QhullPoint p= v.point();
-            int j= p.id();
-            cout << "Point " << j << ":\n" << p << endl;
-            QVERIFY(j>=0 && j<8);
-        }
-    }
-}//t_getSet
-
-void QhullVertex_test::
-t_foreach()
-{
-    RboxPoints rcube("c W0 300");  // 300 points on surface of cube
-    {
-        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
-        foreach (QhullVertex v, q.vertexList()){  // Qt only
-            QhullFacetSet fs= v.neighborFacets();
-            QCOMPARE(fs.count(), 3);
-            foreach (QhullFacet f, fs){  // Qt only
-                QVERIFY(f.vertices().contains(v));
-            }
-        }
-    }
-}//t_foreach
-
-void QhullVertex_test::
-t_io()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q(rcube, "");
-        QhullVertex v= q.beginVertex();
-        ostringstream os;
-        os << "Vertex and vertices:\n";
-        os << v;
-        QhullVertexSet vs= q.firstFacet().vertices();
-        os << vs;
-        os << "\nVertex and vertices with message:\n";
-        os << v.print("Vertex");
-        os << vs.print("\nVertices:");
-        cout << os.str();
-        QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count("(v"), 10);
-        QCOMPARE(s.count(": f"), 2);
-    }
-    RboxPoints r10("10 D3");  // Without QhullVertex::facetNeighbors
-    {
-        Qhull q(r10, "");
-        QhullVertex v= q.beginVertex();
-        ostringstream os;
-        os << "\nTry again with simplicial facets.  No neighboring facets listed for vertices.\n";
-        os << "Vertex and vertices:\n";
-        os << v;
-        q.defineVertexNeighborFacets();
-        os << "This time with neighborFacets() defined for all vertices:\n";
-        os << v;
-        cout << os.str();
-        QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count(": f"), 1);
-
-        Qhull q2(r10, "v"); // Voronoi diagram
-        QhullVertex v2= q2.beginVertex();
-        ostringstream os2;
-        os2 << "\nTry again with Voronoi diagram of simplicial facets.  Neighboring facets automatically defined for vertices.\n";
-        os2 << "Vertex and vertices:\n";
-        os2 << v2;
-        cout << os2.str();
-        QString s2= QString::fromStdString(os2.str());
-        QCOMPARE(s2.count(": f"), 1);
-    }
-}//t_io
-
-}//orgQhull
-
-#include "moc/QhullVertex_test.moc"
diff --git a/src/qhull/src/qhulltest/Qhull_test.cpp b/src/qhull/src/qhulltest/Qhull_test.cpp
deleted file mode 100644
index cc3918a05..000000000
--- a/src/qhull/src/qhulltest/Qhull_test.cpp
+++ /dev/null
@@ -1,360 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/Qhull_test.cpp#4 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "qhulltest/RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/Qhull.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullFacetList.h"
-
-using std::cout;
-using std::endl;
-using std::string;
-
-namespace orgQhull {
-
-//! Test C++ interface to Qhull
-//! See eg/q_test for tests of Qhull commands
-class Qhull_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void cleanup();
-    void t_construct();
-    void t_attribute();
-    void t_message();
-    void t_getSet();
-    void t_getQh();
-    void t_getValue();
-    void t_foreach();
-    void t_modify();
-};//Qhull_test
-
-void
-add_Qhull_test()
-{
-    new Qhull_test();  // RoadTest::s_testcases
-}
-
-//Executed after each testcase
-void Qhull_test::
-cleanup()
-{
-    RoadTest::cleanup();
-}
-
-void Qhull_test::
-t_construct()
-{
-    {
-        Qhull q;
-        QCOMPARE(q.dimension(),0);
-        QVERIFY(q.qh()!=0);
-        QCOMPARE(QString(q.qhullCommand()),QString(""));
-        QCOMPARE(QString(q.rboxCommand()),QString(""));
-        try{
-            QCOMPARE(q.area(),0.0);
-            QFAIL("area() did not fail.");
-        }catch (const std::exception &e) {
-            cout << "INFO   : Caught " << e.what();
-        }
-    }
-    {
-        RboxPoints rbox("10000");
-        Qhull q(rbox, "QR0"); // Random points in a randomly rotated cube.
-        QCOMPARE(q.dimension(),3);
-        QVERIFY(q.volume() < 1.0);
-        QVERIFY(q.volume() > 0.99);
-    }
-    {
-        double points[] = {
-            0, 0,
-            1, 0,
-            1, 1
-        };
-        Qhull q("triangle", 2, 3, points, "");
-        QCOMPARE(q.dimension(),2);
-        QCOMPARE(q.facetCount(),3);
-        QCOMPARE(q.vertexCount(),3);
-        QCOMPARE(q.dimension(),2);
-        QCOMPARE(q.area(), 2.0+sqrt(2.0)); // length of boundary
-        QCOMPARE(q.volume(), 0.5);        // the 2-d area
-    }
-}//t_construct
-
-void Qhull_test::
-t_attribute()
-{
-    RboxPoints rcube("c");
-    {
-        double normals[] = {
-            0,  -1, -0.5,
-           -1,   0, -0.5,
-            1,   0, -0.5,
-            0,   1, -0.5
-        };
-        Qhull q;
-        Coordinates feasible;
-        feasible << 0.0 << 0.0;
-        q.setFeasiblePoint(feasible);
-        Coordinates c(std::vector(2, 0.0));
-        QVERIFY(q.feasiblePoint()==c);
-        q.setOutputStream(&cout);
-        q.runQhull("normals of square", 3, 4, normals, "H"); // halfspace intersect
-        QVERIFY(q.feasiblePoint()==c); // from qh.feasible_point after runQhull()
-        QCOMPARE(q.facetList().count(), 4); // Vertices of square
-        cout << "Expecting summary of halfspace intersection\n";
-        q.outputQhull();
-        q.qh()->disableOutputStream();  // Same as q.disableOutputStream()
-        cout << "Expecting no output from qh_fprintf() in Qhull.cpp\n";
-        q.outputQhull();
-    }
-}//t_attribute
-
-//! No QhullMessage for errors outside of qhull
-void Qhull_test::
-t_message()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q;
-        QCOMPARE(q.qhullMessage(), string(""));
-        QCOMPARE(q.qhullStatus(), qh_ERRnone);
-        QVERIFY(!q.hasQhullMessage());
-        try{
-            q.runQhull(rcube, "Fd");
-            QFAIL("runQhull Fd did not fail.");
-        }catch (const std::exception &e) {
-            const char *s= e.what();
-            cout << "INFO   : Caught " << s;
-            QCOMPARE(QString::fromStdString(s).left(6), QString("QH6029"));
-            // FIXUP QH11025 -- review decision to clearQhullMessage at QhullError()            // Cleared when copied to QhullError
-            QVERIFY(!q.hasQhullMessage());
-            // QCOMPARE(q.qhullMessage(), QString::fromStdString(s).remove(0, 7));
-            // QCOMPARE(q.qhullStatus(), 6029);
-            q.clearQhullMessage();
-            QVERIFY(!q.hasQhullMessage());
-        }
-        q.appendQhullMessage("Append 1");
-        QVERIFY(q.hasQhullMessage());
-        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1"));
-        q.appendQhullMessage("\nAppend 2\n");
-        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1\nAppend 2\n"));
-        q.clearQhullMessage();
-        QVERIFY(!q.hasQhullMessage());
-        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString(""));
-    }
-    {
-        cout << "INFO   : Error stream without output stream\n";
-        Qhull q;
-        q.setErrorStream(&cout);
-        q.setOutputStream(0);
-        try{
-            q.runQhull(rcube, "Fd");
-            QFAIL("runQhull Fd did not fail.");
-        }catch (const QhullError &e) {
-            cout << "INFO   : Caught " << e;
-            QCOMPARE(e.errorCode(), 6029);
-        }
-        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
-        //QVERIFY(q.hasQhullMessage());
-        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(6), QString("QH6029"));
-        q.clearQhullMessage();
-        QVERIFY(!q.hasQhullMessage());
-    }
-    {
-        cout << "INFO   : Error output sent to output stream without error stream\n";
-        Qhull q;
-        q.setErrorStream(0);
-        q.setOutputStream(&cout);
-        try{
-            q.runQhull(rcube, "Tz H0");
-            QFAIL("runQhull TZ did not fail.");
-        }catch (const std::exception &e) {
-            const char *s= e.what();
-            cout << "INFO   : Caught " << s;
-            QCOMPARE(QString::fromLatin1(s).left(6), QString("QH6023"));
-        }
-        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
-        //QVERIFY(q.hasQhullMessage());
-        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(17), QString("qhull: no message"));
-        //QCOMPARE(q.qhullStatus(), 6023);
-        q.clearQhullMessage();
-        QVERIFY(!q.hasQhullMessage());
-    }
-    {
-        cout << "INFO   : No error stream or output stream\n";
-        Qhull q;
-        q.setErrorStream(0);
-        q.setOutputStream(0);
-        try{
-            q.runQhull(rcube, "Fd");
-            QFAIL("outputQhull did not fail.");
-        }catch (const std::exception &e) {
-            const char *s= e.what();
-            cout << "INFO   : Caught " << s;
-            QCOMPARE(QString::fromLatin1(s).left(6), QString("QH6029"));
-        }
-        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
-        //QVERIFY(q.hasQhullMessage());
-        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(9), QString("qhull err"));
-        //QCOMPARE(q.qhullStatus(), 6029);
-        q.clearQhullMessage();
-        QVERIFY(!q.hasQhullMessage());
-    }
-}//t_message
-
-void Qhull_test::
-t_getSet()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q;
-        QVERIFY(!q.initialized());
-        q.runQhull(rcube, "s");
-        QVERIFY(q.initialized());
-        QCOMPARE(q.dimension(), 3);
-        QhullPoint p= q.origin();
-        QCOMPARE(p.dimension(), 3);
-        QCOMPARE(p[0]+p[1]+p[2], 0.0);
-        q.setErrorStream(&cout);
-        q.outputQhull();
-    }
-    {
-        Qhull q;
-        q.runQhull(rcube, "");
-        q.setOutputStream(&cout);
-        q.outputQhull();
-    }
-}//t_getSet
-
-void Qhull_test::
-t_getQh()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q;
-        q.runQhull(rcube, "s");
-        QCOMPARE(QString(q.qhullCommand()), QString("qhull s"));
-        QCOMPARE(QString(q.rboxCommand()), QString("rbox \"c\""));
-        QCOMPARE(q.facetCount(), 6);
-        QCOMPARE(q.vertexCount(), 8);
-        // Sample fields from Qhull's qhT [libqhull.h]
-        QCOMPARE(q.qh()->ALLpoints, 0u);
-        QCOMPARE(q.qh()->GOODpoint, 0);
-        QCOMPARE(q.qh()->IStracing, 0);
-        QCOMPARE(q.qh()->MAXcoplanar+1.0, 1.0); // fuzzy compare
-        QCOMPARE(q.qh()->MERGING, 1u);
-        QCOMPARE(q.qh()->input_dim, 3);
-        QCOMPARE(QString(q.qh()->qhull_options).left(8), QString("  run-id"));
-        QCOMPARE(q.qh()->num_facets, 6);
-        QCOMPARE(q.qh()->hasTriangulation, 0u);
-        QCOMPARE(q.qh()->max_outside - q.qh()->min_vertex + 1.0, 1.0); // fuzzy compare
-        QCOMPARE(*q.qh()->gm_matrix+1.0, 1.0); // fuzzy compare
-    }
-}//t_getQh
-
-void Qhull_test::
-t_getValue()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q;
-        q.runQhull(rcube, "");
-        QCOMPARE(q.area(), 6.0);
-        QCOMPARE(q.volume(), 1.0);
-    }
-}//t_getValue
-
-void Qhull_test::
-t_foreach()
-{
-    RboxPoints rcube("c");
-    {
-        Qhull q;
-        QCOMPARE(q.beginFacet(),q.endFacet());
-        QCOMPARE(q.beginVertex(),q.endVertex());
-        q.runQhull(rcube, "");
-        QCOMPARE(q.facetList().count(), 6);
-
-        // defineVertexNeighborFacets() tested in QhullVertex_test::t_io()
-
-        QhullFacetList facets(q.beginFacet(), q.endFacet());
-        QCOMPARE(facets.count(), 6);
-        QCOMPARE(q.firstFacet(), q.beginFacet());
-        QhullVertexList vertices(q.beginVertex(), q.endVertex());
-        QCOMPARE(vertices.count(), 8);
-        QCOMPARE(q.firstVertex(), q.beginVertex());
-        QhullPoints ps= q.points();
-        QCOMPARE(ps.count(), 8);
-        QhullPointSet ps2= q.otherPoints();
-        QCOMPARE(ps2.count(), 0);
-        // ps2= q.otherPoints(); //disabled, would not copy the points
-        QCOMPARE(q.facetCount(), 6);
-        QCOMPARE(q.vertexCount(), 8);
-        coordT *c= q.pointCoordinateBegin(); // of q.points()
-        QVERIFY(*c==0.5 || *c==-0.5);
-        coordT *c3= q.pointCoordinateEnd();
-        QVERIFY(c3[-1]==0.5 || c3[-1]==-0.5);
-        QCOMPARE(c3-c, 8*3);
-        QCOMPARE(q.vertexList().count(), 8);
-    }
-}//t_foreach
-
-void Qhull_test::
-t_modify()
-{
-    //addPoint() tested in t_foreach
-    RboxPoints diamond("d");
-    Qhull q(diamond, "o");
-    q.setOutputStream(&cout);
-    cout << "Expecting vertexList and facetList of a 3-d diamond.\n";
-    q.outputQhull();
-    cout << "Expecting normals of a 3-d diamond.\n";
-    q.outputQhull("n");
-    // runQhull tested in t_attribute(), t_message(), etc.
-}//t_modify
-
-}//orgQhull
-
-// Redefine Qhull's usermem_r.c in order to report erroneous calls to qh_exit
-void qh_exit(int exitcode) {
-    cout << "FAIL!  : Qhull called qh_exit().  Qhull's error handling not available.\n.. See the corresponding Qhull:qhull_message or setErrorStream().\n";
-    exit(exitcode);
-}
-void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    va_start(args, fmt);
-    if(msgcode)
-        fprintf(stderr, "QH%.4d ", msgcode);
-    vfprintf(stderr, fmt, args);
-    va_end(args);
-} /* fprintf_stderr */
-void qh_free(void *mem) {
-    free(mem);
-}
-void *qh_malloc(size_t size) {
-    return malloc(size);
-}
-
-#if 0
-template<> char * QTest::
-toString(const std::string &s)
-{
-    QByteArray ba = s.c_str();
-    return qstrdup(ba.data());
-}
-#endif
-
-#include "moc/Qhull_test.moc"
diff --git a/src/qhull/src/qhulltest/RboxPoints_test.cpp b/src/qhull/src/qhulltest/RboxPoints_test.cpp
deleted file mode 100644
index 4f4ea984f..000000000
--- a/src/qhull/src/qhulltest/RboxPoints_test.cpp
+++ /dev/null
@@ -1,215 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2006-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/RboxPoints_test.cpp#2 $$Change: 2062 $
-** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullError.h"
-
-using std::cout;
-using std::endl;
-using std::ostringstream;
-using std::string;
-using std::stringstream;
-
-namespace orgQhull {
-
-//! Test C++ interface to Rbox
-//! See eg/q_test for tests of rbox commands
-class RboxPoints_test : public RoadTest
-{
-    Q_OBJECT
-
-#//!\name Test slots
-private slots:
-    void t_construct();
-    void t_error();
-    void t_test();
-    void t_getSet();
-    void t_foreach();
-    void t_change();
-    void t_ostream();
-};
-
-void
-add_RboxPoints_test()
-{
-    new RboxPoints_test();  // RoadTest::s_testcases
-}
-
-void RboxPoints_test::
-t_construct()
-{
-    RboxPoints rp;
-    QCOMPARE(rp.dimension(), 0);
-    QCOMPARE(rp.count(), 0);
-    QVERIFY(QString::fromStdString(rp.comment()) != QString(""));
-    QVERIFY(rp.isEmpty());
-    QVERIFY(!rp.hasRboxMessage());
-    QCOMPARE(rp.rboxStatus(), qh_ERRnone);
-    QCOMPARE(QString::fromStdString(rp.rboxMessage()), QString("rbox warning: no points generated\n"));
-
-    RboxPoints rp2("c"); // 3-d cube
-    QCOMPARE(rp2.dimension(), 3);
-    QCOMPARE(rp2.count(), 8);
-    QCOMPARE(QString::fromStdString(rp2.comment()), QString("rbox \"c\""));
-    QVERIFY(!rp2.isEmpty());
-    QVERIFY(!rp2.hasRboxMessage());
-    QCOMPARE(rp2.rboxStatus(), qh_ERRnone);
-    QCOMPARE(QString::fromStdString(rp2.rboxMessage()), QString("rbox: OK\n"));
-}//t_construct
-
-void RboxPoints_test::
-t_error()
-{
-    RboxPoints rp;
-    try{
-        rp.appendPoints("D0 c");
-        QFAIL("'D0 c' did not fail.");
-    }catch (const std::exception &e) {
-        const char *s= e.what();
-        cout << "INFO   : Caught " << s;
-        QCOMPARE(QString(s).left(6), QString("QH6189"));
-        QVERIFY(rp.hasRboxMessage());
-        QCOMPARE(QString::fromStdString(rp.rboxMessage()).left(8), QString("rbox err"));
-        QCOMPARE(rp.rboxStatus(), 6189);
-        rp.clearRboxMessage();
-        QVERIFY(!rp.hasRboxMessage());
-    }
-    try{
-        RboxPoints rp2;
-        rp2.setDimension(-1);
-        QFAIL("setDimension(-1) did not fail.");
-    }catch (const RoadError &e) {
-        const char *s= e.what();
-        cout << "INFO   : Caught " << s;
-        QCOMPARE(QString(s).left(7), QString("QH10062"));
-        QCOMPARE(e.errorCode(), 10062);
-        QCOMPARE(QString::fromStdString(e.what()), QString(s));
-        RoadLogEvent logEvent= e.roadLogEvent();
-        QCOMPARE(logEvent.int1(), -1);
-    }
-}//t_error
-
-void RboxPoints_test::
-t_test()
-{
-    // isEmpty -- t_construct
-}//t_test
-
-void RboxPoints_test::
-t_getSet()
-{
-    // comment -- t_construct
-    // count -- t_construct
-    // dimension -- t_construct
-
-    RboxPoints rp;
-    QCOMPARE(rp.dimension(), 0);
-    rp.setDimension(2);
-    QCOMPARE(rp.dimension(), 2);
-    try{
-        rp.setDimension(102);
-        QFAIL("setDimension(102) did not fail.");
-    }catch (const std::exception &e) {
-        cout << "INFO   : Caught " << e.what();
-    }
-    QCOMPARE(rp.newCount(), 0);
-    rp.appendPoints("D2 P1 P2");
-    QCOMPARE(rp.count(), 2);
-    QCOMPARE(rp.newCount(), 2); // From previous appendPoints();
-    PointCoordinates pc(rp.qh(), 2, "Test qh() and <<");
-    pc << 1.0 << 0.0 << 2.0 << 0.0;
-    QCOMPARE(pc.dimension(), 2);
-    QCOMPARE(pc.count(), 2);
-    QVERIFY(rp==pc);
-    rp.setNewCount(10);  // Normally only used by appendPoints for rbox processing
-    QCOMPARE(rp.newCount(), 10);
-    rp.reservePoints();
-    QVERIFY(rp==pc);
-}//t_getSet
-
-void RboxPoints_test::
-t_foreach()
-{
-    RboxPoints rp("c");
-    Coordinates::ConstIterator cci= rp.beginCoordinates();
-    orgQhull::Coordinates::Iterator ci= rp.beginCoordinates();
-    QCOMPARE(*cci, -0.5);
-    QCOMPARE(*ci, *cci);
-    int i=1;
-    while(++cci
-#include "RoadTest.h" // QT_VERSION
-
-#include 
-
-using std::cout;
-using std::endl;
-
-namespace orgQhull {
-
-#//!\name class variable
-
-QList RoadTest::
-s_testcases;
-
-int RoadTest::
-s_test_count= 0;
-
-int RoadTest::
-s_test_fail= 0;
-
-QStringList RoadTest::
-s_failed_tests;
-
-#//!\name Slot
-
-//! Executed after each test
-void RoadTest::
-cleanup()
-{
-    s_test_count++;
-    if(QTest::currentTestFailed()){
-        recordFailedTest();
-    }
-}//cleanup
-
-#//!\name Helper
-
-void RoadTest::
-recordFailedTest()
-{
-    s_test_fail++;
-    QString className= metaObject()->className();
-    s_failed_tests << className + "::" + QTest::currentTestFunction();
-}
-
-#//!\name class function
-
-void RoadTest::
-deleteTests()
-{
-    foreach(RoadTest *testcase, s_testcases){
-        delete testcase;
-    }
-    s_failed_tests.clear();
-}
-
-int RoadTest::
-runTests(QStringList arguments)
-{
-    int result= 0; // assume success
-
-    foreach(RoadTest *testcase, s_testcases){
-        try{
-            result += QTest::qExec(testcase, arguments);
-        }catch(const std::exception &e){
-            cout << "FAIL!  : Threw error ";
-            cout << e.what() << endl;
-    s_test_count++;
-            testcase->recordFailedTest();
-            // Qt 4.5.2 OK.  In Qt 4.3.3, qtestcase did not clear currentTestObject
-        }
-    }
-    if(s_test_fail){
-        cout << "Failed " << s_test_fail << " of " << s_test_count << " tests.\n";
-        cout << s_failed_tests.join("\n").toLocal8Bit().constData() << std::endl;
-    }else{
-        cout << "Passed " << s_test_count << " tests.\n";
-    }
-    return result;
-}//runTests
-
-}//orgQhull
-
-#include "moc/moc_RoadTest.cpp"
diff --git a/src/qhull/src/qhulltest/RoadTest.h b/src/qhull/src/qhulltest/RoadTest.h
deleted file mode 100644
index adfe0bf8c..000000000
--- a/src/qhull/src/qhulltest/RoadTest.h
+++ /dev/null
@@ -1,102 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/RoadTest.h#2 $$Change: 2062 $
-** $Date: 2016/01/17 $$Author: bbarber $
-**
-****************************************************************************/
-
-#ifndef ROADTEST_H
-#define ROADTEST_H
-
-//pre-compiled with RoadTest.h
-#include     // Qt C++ Framework
-#include 
-
-#define QHULL_USES_QT 1
-
-namespace orgQhull {
-
-#//!\name Defined here
-
-    //! RoadTest -- Generic test for Qt's QTest
-    class RoadTest;
-    //! TESTadd_(t) -- Add a RoadTest
-
-/** Test Name objects using Qt's QTestLib
-
-Template:
-
-class Name_test : public RoadTest
-{
-    Q_OBJECT
-#//!\name Test slot
-private slots:
-    void t_name();
-    //Executed before any test
-    void initTestCase();
-    void init();          // Each test
-    //Executed after each test
-    void cleanup(); //RoadTest::cleanup();
-    // Executed after last test
-    void cleanupTestCase();
-};
-
-void
-add_Name_test()
-{
-    new Name_test();  // RoadTest::s_testcases
-}
-
-Send additional output to cout
-*/
-
-class RoadTest : public QObject
-{
-    Q_OBJECT
-
-#//!\name Class globals
-protected:
-    static QList
-                        s_testcases; ///! List of testcases to execute.  Initialized via add_...()
-    static int          s_test_count; ///! Total number of tests executed
-    static int          s_test_fail; ///! Number of failed tests
-    static QStringList  s_failed_tests; ///! List of failed tests
-
-#//!\name Test slots
-public slots:
-    void cleanup();
-
-public:
-#//!\name Constructors, etc.
-                        RoadTest()  { s_testcases.append(this); }
-    virtual             ~RoadTest() {} // Derived from QObject
-
-#//!\name Helper
-    void                recordFailedTest();
-
-
-#//!\name Class functions
-    static void         deleteTests();
-    static int          runTests(QStringList arguments);
-
-};//RoadTest
-
-#define TESTadd_(t) extern void t(); t();
-
-
-}//orgQhull
-
-namespace QTest{
-
-template<>
-inline char *
-toString(const std::string &s)
-{
-    return qstrdup(s.c_str());
-}
-
-}//namespace QTest
-
-#endif //ROADTEST_H
-
diff --git a/src/qhull/src/qhulltest/qhulltest.cpp b/src/qhull/src/qhulltest/qhulltest.cpp
deleted file mode 100644
index 5bfe16e9c..000000000
--- a/src/qhull/src/qhulltest/qhulltest.cpp
+++ /dev/null
@@ -1,94 +0,0 @@
-/****************************************************************************
-**
-** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
-** $Id: //main/2015/qhull/src/qhulltest/qhulltest.cpp#5 $$Change: 2079 $
-** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
-**
-****************************************************************************/
-
-//pre-compiled headers
-#include "libqhull_r/user_r.h"
-
-#include 
-#include "RoadTest.h" // QT_VERSION
-
-#include "libqhullcpp/RoadError.h"
-#include "libqhull_r/qhull_ra.h"
-
-#include 
-#include 
-#include 
-
-using std::cout;
-using std::endl;
-
-namespace orgQhull {
-
-void addQhullTests(QStringList &args)
-{
-    TESTadd_(add_Qhull_test);
-
-    if(args.contains("--all")){
-        args.removeAll("--all");
-        // up-to-date
-        TESTadd_(add_Coordinates_test);
-        TESTadd_(add_PointCoordinates_test);
-        TESTadd_(add_QhullFacet_test);
-        TESTadd_(add_QhullFacetList_test);
-        TESTadd_(add_QhullFacetSet_test);
-        TESTadd_(add_QhullHyperplane_test);
-        TESTadd_(add_QhullLinkedList_test);
-        TESTadd_(add_QhullPoint_test);
-        TESTadd_(add_QhullPoints_test);
-        TESTadd_(add_QhullPointSet_test);
-        TESTadd_(add_QhullRidge_test);
-        TESTadd_(add_QhullSet_test);
-        TESTadd_(add_QhullVertex_test);
-        TESTadd_(add_QhullVertexSet_test);
-        TESTadd_(add_RboxPoints_test);
-        // qhullStat
-        TESTadd_(add_Qhull_test);
-    }//--all
-}//addQhullTests
-
-int main(int argc, char *argv[])
-{
-
-    QCoreApplication app(argc, argv);
-    QStringList args= app.arguments();
-    bool isAll= args.contains("--all");
-
-    QHULL_LIB_CHECK /* Check for compatible library */
-
-    addQhullTests(args);
-    int status=1010;
-    try{
-        status= RoadTest::runTests(args);
-    }catch(const std::exception &e){
-        cout << "FAIL!  : runTests() did not catch error\n";
-        cout << e.what() << endl;
-        if(!RoadError::emptyGlobalLog()){
-            cout << RoadError::stringGlobalLog() << endl;
-            RoadError::clearGlobalLog();
-        }
-    }
-    if(!RoadError::emptyGlobalLog()){
-        cout << RoadError::stringGlobalLog() << endl;
-        RoadError::clearGlobalLog();
-    }
-    if(isAll){
-        cout << "Finished test of libqhullcpp.  Test libqhull_r with eg/q_test after building libqhull_r/Makefile" << endl;
-    }else{
-        cout << "Finished test of one class.  Test all classes with 'qhulltest --all'" << endl;
-    }
-    RoadTest::deleteTests();
-    return status;
-}
-
-}//orgQhull
-
-int main(int argc, char *argv[])
-{
-    return orgQhull::main(argc, argv); // Needs RoadTest:: for TESTadd_() linkage
-}
-
diff --git a/src/qhull/src/qhulltest/qhulltest.pro b/src/qhull/src/qhulltest/qhulltest.pro
deleted file mode 100644
index 0da34d375..000000000
--- a/src/qhull/src/qhulltest/qhulltest.pro
+++ /dev/null
@@ -1,36 +0,0 @@
-# -------------------------------------------------
-# qhulltest.pro -- Qt project for qhulltest.exe (QTestLib)
-# cd $qh/build/qhulltest && qmake -tp vc -r ../../src/qhulltest/qhulltest.pro
-# -------------------------------------------------
-
-include(../qhull-app-cpp.pri)
-
-TARGET = qhulltest
-QT += testlib
-MOC_DIR = moc
-INCLUDEPATH += ..  # for MOC_DIR
-
-PRECOMPILED_HEADER = RoadTest.h
-
-HEADERS += RoadTest.h
-
-SOURCES += ../libqhullcpp/qt-qhull.cpp
-SOURCES += Coordinates_test.cpp
-SOURCES += PointCoordinates_test.cpp
-SOURCES += Qhull_test.cpp
-SOURCES += QhullFacet_test.cpp
-SOURCES += QhullFacetList_test.cpp
-SOURCES += QhullFacetSet_test.cpp
-SOURCES += QhullHyperplane_test.cpp
-SOURCES += QhullLinkedList_test.cpp
-SOURCES += QhullPoint_test.cpp
-SOURCES += QhullPoints_test.cpp
-SOURCES += QhullPointSet_test.cpp
-SOURCES += QhullRidge_test.cpp
-SOURCES += QhullSet_test.cpp
-SOURCES += qhulltest.cpp
-SOURCES += QhullVertex_test.cpp
-SOURCES += QhullVertexSet_test.cpp
-SOURCES += RboxPoints_test.cpp
-SOURCES += RoadTest.cpp
-
diff --git a/src/qhull/src/qvoronoi/qvoronoi.c b/src/qhull/src/qvoronoi/qvoronoi.c
deleted file mode 100644
index b93d23711..000000000
--- a/src/qhull/src/qvoronoi/qvoronoi.c
+++ /dev/null
@@ -1,303 +0,0 @@
-/*
      ---------------------------------
-
-   qvoronoi.c
-     compute Voronoi diagrams and furthest-point Voronoi
-     diagrams using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull/libqhull.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qvoron_f.htm and qvoronoi.htm
-   QJ and Qt are deprecated, but allowed for backwards compatibility
-*/
-char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qvoronoi- compute the Voronoi diagram\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qu   - compute furthest-site Voronoi diagram\n\
-\n\
-Qhull control options:\n\
-    Qz   - add point-at-infinity to Voronoi diagram\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    QGn  - Voronoi vertices if visible from point n, -n if not\n\
-    QVn  - Voronoi vertices for input point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - statistics\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Wn   - min facet width for non-coincident point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    s    - summary to stderr\n\
-    p    - Voronoi vertices\n\
-    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
-    i    - Delaunay regions (use 'Pp' to avoid warning)\n\
-    f    - facet dump\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fc   - count plus coincident points (by Voronoi vertex)\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - separating hyperplanes for bounded Voronoi regions\n\
-    FI   - ID for each Voronoi vertex\n\
-    Fm   - merge count for each Voronoi vertex (511 max)\n\
-    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
-    FN   - count and Voronoi vertices for each Voronoi region\n\
-    Fo   - separating hyperplanes for unbounded Voronoi regions\n\
-    FO   - options and precision constants\n\
-    FP   - nearest point and distance for each coincident point\n\
-    FQ   - command used for qvoronoi\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                    for output: #Voronoi regions, #Voronoi vertices,\n\
-                                #coincident points, #non-simplicial regions\n\
-                    #real (2), max outer plane and min vertex\n\
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
-    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d only)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest Voronoi vertices by 'area'\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
-    PFn  - keep Voronoi vertices whose 'area' is at least n\n\
-    PG   - print neighbors of good Voronoi vertices\n\
-    PMn  - keep n Voronoi vertices with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qvoronoi- compute the Voronoi diagram.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qvoronoi.htm):\n\
-    Qu   - compute furthest-site Voronoi diagram\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    p    - Voronoi vertices\n\
-    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
-    FN   - count and Voronoi vertices for each Voronoi region\n\
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
-    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
-    G    - Geomview output (2-d only)\n\
-    QVn  - Voronoi vertices for input point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi\n\
-rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv\n\
-rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo\n\
-rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- OFF_format     p_vertices     i_delaunay     summary        facet_dump\n\
-\n\
- Fcoincident    Fd_cdd_in      FD_cdd_out     FF-dump-xridge Fi_bounded\n\
- Fxtremes       Fmerges        Fneighbors     FNeigh_region  FOptions\n\
- Fo_unbounded   FPoint_near    FQvoronoi      Fsummary       Fvoronoi\n\
- FIDs\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- QG_vertex_good Qsearch_1st    Qupper_voronoi QV_point_good  Qzinfinite\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh NOerrexit= False;
-    qh_option("voronoi  _bbound-last  _coplanar-keep", NULL, NULL);
-    qh DELAUNAY= True;     /* 'v'   */
-    qh VORONOI= True;
-    qh SCALElast= True;    /* 'Qbb' */
-    qh_checkflags(qh qhull_command, hidden_options);
-    qh_initflags(qh qhull_command);
-    points= qh_readpoints(&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option("_merge-exact", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh_ALL);
-#else
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/qvoronoi/qvoronoi.pro b/src/qhull/src/qvoronoi/qvoronoi.pro
deleted file mode 100644
index 4646c8447..000000000
--- a/src/qhull/src/qvoronoi/qvoronoi.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# qvoronoi.pro -- Qt project file for qvoronoi.exe
-# -------------------------------------------------
-
-include(../qhull-app-c.pri)
-
-TARGET = qvoronoi
-
-SOURCES += qvoronoi.c
diff --git a/src/qhull/src/qvoronoi/qvoronoi_r.c b/src/qhull/src/qvoronoi/qvoronoi_r.c
deleted file mode 100644
index 6323c8b49..000000000
--- a/src/qhull/src/qvoronoi/qvoronoi_r.c
+++ /dev/null
@@ -1,305 +0,0 @@
-/*
      ---------------------------------
-
-   qvoronoi.c
-     compute Voronoi diagrams and furthest-point Voronoi
-     diagrams using qhull
-
-   see unix.c for full interface
-
-   Copyright (c) 1993-2015, The Geometry Center
-*/
-
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if __cplusplus
-extern "C" {
-  int isatty(int);
-}
-
-#elif _MSC_VER
-#include 
-#define isatty _isatty
-/* int _isatty(int); */
-
-#else
-int isatty(int);  /* returns 1 if stdin is a tty
-                   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of libqhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qvoron_f.htm and qvoronoi.htm
-   QJ and Qt are deprecated, but allowed for backwards compatibility
-*/
-char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qvoronoi- compute the Voronoi diagram\n\
-    http://www.qhull.org  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-    comments:    start with a non-numeric character\n\
-\n\
-options:\n\
-    Qu   - compute furthest-site Voronoi diagram\n\
-\n\
-Qhull control options:\n\
-    Qz   - add point-at-infinity to Voronoi diagram\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    QGn  - Voronoi vertices if visible from point n, -n if not\n\
-    QVn  - Voronoi vertices for input point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - statistics\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Wn   - min facet width for non-coincident point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    s    - summary to stderr\n\
-    p    - Voronoi vertices\n\
-    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
-    i    - Delaunay regions (use 'Pp' to avoid warning)\n\
-    f    - facet dump\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fc   - count plus coincident points (by Voronoi vertex)\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - separating hyperplanes for bounded Voronoi regions\n\
-    FI   - ID for each Voronoi vertex\n\
-    Fm   - merge count for each Voronoi vertex (511 max)\n\
-    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
-    FN   - count and Voronoi vertices for each Voronoi region\n\
-    Fo   - separating hyperplanes for unbounded Voronoi regions\n\
-    FO   - options and precision constants\n\
-    FP   - nearest point and distance for each coincident point\n\
-    FQ   - command used for qvoronoi\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                    for output: #Voronoi regions, #Voronoi vertices,\n\
-                                #coincident points, #non-simplicial regions\n\
-                    #real (2), max outer plane and min vertex\n\
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
-    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d only)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest Voronoi vertices by 'area'\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
-    PFn  - keep Voronoi vertices whose 'area' is at least n\n\
-    PG   - print neighbors of good Voronoi vertices\n\
-    PMn  - keep n Voronoi vertices with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-    -V   - version\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qvoronoi- compute the Voronoi diagram.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-    comments start with a non-numeric character\n\
-\n\
-options (qvoronoi.htm):\n\
-    Qu   - compute furthest-site Voronoi diagram\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-    -V   - version\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    p    - Voronoi vertices\n\
-    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
-    FN   - count and Voronoi vertices for each Voronoi region\n\
-    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
-    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
-    G    - Geomview output (2-d only)\n\
-    QVn  - Voronoi vertices for input point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi\n\
-rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv\n\
-rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo\n\
-rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- OFF_format     p_vertices     i_delaunay     summary        facet_dump\n\
-\n\
- Fcoincident    Fd_cdd_in      FD_cdd_out     FF-dump-xridge Fi_bounded\n\
- Fxtremes       Fmerges        Fneighbors     FNeigh_region  FOptions\n\
- Fo_unbounded   FPoint_near    FQvoronoi      Fsummary       Fvoronoi\n\
- FIDs\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- QG_vertex_good Qsearch_1st    Qupper_voronoi QV_point_good  Qzinfinite\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    reads points
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK /* Check for compatible library */
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_version,
-                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_version);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
-      fprintf(stdout, "%s\n", qh_version2);
-      exit(qh_ERRnone);
-  }
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
-  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh->NOerrexit = False;
-    qh_option(qh, "voronoi  _bbound-last  _coplanar-keep", NULL, NULL);
-    qh->DELAUNAY= True;     /* 'v'   */
-    qh->VORONOI= True;
-    qh->SCALElast= True;    /* 'Qbb' */
-    qh_checkflags(qh, qh->qhull_command, hidden_options);
-    qh_initflags(qh, qh->qhull_command);
-    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option(qh, "_merge-exact", NULL, NULL);
-      qh->MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B(qh, points, numpoints, dim, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);
-    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    exitcode= qh_ERRnone;
-  }
-  qh->NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull(qh, qh_ALL);
-#else
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/rbox/rbox.c b/src/qhull/src/rbox/rbox.c
deleted file mode 100644
index d7c51b1aa..000000000
--- a/src/qhull/src/rbox/rbox.c
+++ /dev/null
@@ -1,88 +0,0 @@
-/*
      ---------------------------------
-
-   rbox.c
-     rbox program for generating input points for qhull.
-
-   notes:
-     50 points generated for 'rbox D4'
-
-*/
-
-#include "libqhull/libqhull.h"
-#include "libqhull/random.h"
-
-#include 
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#endif
-
-char prompt[]= "\n\
--rbox- generate various point distributions.  Default is random in cube.\n\
-\n\
-args (any order, space separated):                    Version: 2016/01/18\n\
-  3000    number of random points in cube, lens, spiral, sphere or grid\n\
-  D3      dimension 3-d\n\
-  c       add a unit cube to the output ('c G2.0' sets size)\n\
-  d       add a unit diamond to the output ('d G2.0' sets size)\n\
-  l       generate a regular 3-d spiral\n\
-  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
-  s       generate cospherical points\n\
-  x       generate random points in simplex, may use 'r' or 'Wn'\n\
-  y       same as 'x', plus simplex\n\
-  Cn,r,m  add n nearly coincident points within radius r of m points\n\
-  Pn,m,r  add point [n,m,r] first, pads with 0, maybe repeated\n\
-\n\
-  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.\n\
-  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
-          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.\n\
-  W0.1    random distribution within 0.1 of the cube's or sphere's surface\n\
-  Z0.5 s  random points in a 0.5 disk projected to a sphere\n\
-  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
-\n\
-  Bn      bounding box coordinates, default %2.2g\n\
-  h       output as homogeneous coordinates for cdd\n\
-  n       remove command line from the first line of output\n\
-  On      offset coordinates by n\n\
-  t       use time as the random number seed(default is command line)\n\
-  tn      use n as the random number seed\n\
-  z       print integer coordinates, default 'Bn' is %2.2g\n\
-";
-
-/*--------------------------------------------
--rbox-  main procedure of rbox application
-*/
-int main(int argc, char **argv) {
-  char *command;
-  int command_size;
-  int return_status;
-
-  QHULL_LIB_CHECK_RBOX
-
-  if (argc == 1) {
-    printf(prompt, qh_DEFAULTbox, qh_DEFAULTzbox);
-    return 1;
-  }
-  if (argc == 2 && strcmp(argv[1], "D4")==0)
-    qh_fprintf_stderr(0, "\nStarting the rbox smoketest for qhull.  An immediate failure indicates\nthat non-reentrant rbox was linked to reentrant routines.  An immediate\nfailure of qhull may indicate that qhull was linked to the wrong\nqhull library.  Also try 'rbox D4 | qhull T1'\n");
-
-  command_size= qh_argv_to_command_size(argc, argv);
-  if ((command= (char *)qh_malloc((size_t)command_size))) {
-    if (!qh_argv_to_command(argc, argv, command, command_size)) {
-      qh_fprintf_stderr(6264, "rbox internal error: allocated insufficient memory (%d) for arguments\n", command_size);
-      return_status= qh_ERRinput;
-    }else{
-      return_status= qh_rboxpoints(stdout, stderr, command);
-    }
-    qh_free(command);
-  }else {
-    qh_fprintf_stderr(6265, "rbox error: insufficient memory for %d bytes\n", command_size);
-    return_status= qh_ERRmem;
-  }
-  return return_status;
-}/*main*/
-
diff --git a/src/qhull/src/rbox/rbox.pro b/src/qhull/src/rbox/rbox.pro
deleted file mode 100644
index 6c21bdb6d..000000000
--- a/src/qhull/src/rbox/rbox.pro
+++ /dev/null
@@ -1,9 +0,0 @@
-# -------------------------------------------------
-# rbox.pro -- Qt project for rbox.exe with libqhullstatic
-# -------------------------------------------------
-
-include(../qhull-app-c.pri)
-
-TARGET = rbox
-
-SOURCES += rbox.c
diff --git a/src/qhull/src/rbox/rbox_r.c b/src/qhull/src/rbox/rbox_r.c
deleted file mode 100644
index 6ec74d914..000000000
--- a/src/qhull/src/rbox/rbox_r.c
+++ /dev/null
@@ -1,78 +0,0 @@
-
-/*
      ---------------------------------
-
-   rbox.c
-     rbox program for generating input points for qhull.
-
-   notes:
-     50 points generated for 'rbox D4'
-
-*/
-
-#include "libqhull_r/libqhull_r.h"
-#include "libqhull/random_r.h"
-
-#include 
-#include 
-#include 
-#include 
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#endif
-
-char prompt[]= "\n\
--rbox- generate various point distributions.  Default is random in cube.\n\
-\n\
-args (any order, space separated):                    Version: 2016/01/18 r\n\
-  3000    number of random points in cube, lens, spiral, sphere or grid\n\
-  D3      dimension 3-d\n\
-  c       add a unit cube to the output ('c G2.0' sets size)\n\
-  d       add a unit diamond to the output ('d G2.0' sets size)\n\
-  l       generate a regular 3-d spiral\n\
-  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
-  s       generate cospherical points\n\
-  x       generate random points in simplex, may use 'r' or 'Wn'\n\
-  y       same as 'x', plus simplex\n\
-  Cn,r,m  add n nearly coincident points within radius r of m points\n\
-  Pn,m,r  add point [n,m,r] first, pads with 0, maybe repeated\n\
-\n\
-  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.\n\
-  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
-          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.\n\
-  W0.1    random distribution within 0.1 of the cube's or sphere's surface\n\
-  Z0.5 s  random points in a 0.5 disk projected to a sphere\n\
-  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
-\n\
-  Bn      bounding box coordinates, default %2.2g\n\
-  h       output as homogeneous coordinates for cdd\n\
-  n       remove command line from the first line of output\n\
-  On      offset coordinates by n\n\
-  t       use time as the random number seed(default is command line)\n\
-  tn      use n as the random number seed\n\
-  z       print integer coordinates, default 'Bn' is %2.2g\n\
-";
-
-/*--------------------------------------------
--rbox-  main procedure of rbox application
-*/
-int main(int argc, char **argv) {
-  int return_status;
-  qhT qh_qh;
-  qhT *qh= &qh_qh;
-
-  QHULL_LIB_CHECK_RBOX
-
-  if (argc == 1) {
-    printf(prompt, qh_DEFAULTbox, qh_DEFAULTzbox);
-    return 1;
-  }
-  if (argc == 2 && strcmp(argv[1], "D4")==0)
-    qh_fprintf_stderr(0, "\nStarting the rbox smoketest for qhull.  An immediate failure indicates\nthat reentrant rbox was linked to non-reentrant routines.  An immediate\nfailure of qhull may indicate that qhull was linked to the wrong\nqhull library.  Also try 'rbox D4 | qhull T1'\n");
-
-  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /*no qh_errexit, sets qh->qhull_command */
-  return_status= qh_rboxpoints(qh, qh->qhull_command); /* Traps its own errors, qh_errexit_rbox() */
-  return return_status;
-}/*main*/
-
diff --git a/src/qhull/src/testqset/testqset.c b/src/qhull/src/testqset/testqset.c
deleted file mode 100644
index 61057eef9..000000000
--- a/src/qhull/src/testqset/testqset.c
+++ /dev/null
@@ -1,891 +0,0 @@
-/*
      ---------------------------------
-
-   testset.c -- test qset.c and its use of mem.c
-
-   The test sets are pointers to int.  Normally a set is a pointer to a type (e.g., facetT, ridgeT, etc.).
-   For consistency in notation, an "int" is typedef'd to i2T
-
-Functions and macros from qset.h.  Counts occurrences in this test.  Does not correspond to thoroughness.
-    qh_setaddsorted -- 4 tests
-    qh_setaddnth -- 1 test
-    qh_setappend -- 7 tests
-    qh_setappend_set -- 1 test
-    qh_setappend2ndlast -- 1 test
-    qh_setcheck -- lots of tests
-    qh_setcompact -- 7 tests
-    qh_setcopy -- 3 tests
-    qh_setdel -- 1 tests
-    qh_setdellast -- 1 tests
-    qh_setdelnth -- 2 tests
-    qh_setdelnthsorted -- 2 tests
-    qh_setdelsorted -- 1 test
-    qh_setduplicate -- not testable here
-    qh_setequal -- 4 tests
-    qh_setequal_except -- 2 tests
-    qh_setequal_skip -- 2 tests
-    qh_setfree -- 11+ tests
-    qh_setfree2 -- not testable here
-    qh_setfreelong -- 2 tests
-    qh_setin -- 3 tests
-    qh_setindex -- 4 tests
-    qh_setlarger -- 1 test
-    qh_setlast -- 2 tests
-    qh_setnew -- 6 tests
-    qh_setnew_delnthsorted
-    qh_setprint -- tested elsewhere
-    qh_setreplace -- 1 test
-    qh_setsize -- 9+ tests
-    qh_settemp -- 2 tests
-    qh_settempfree -- 1 test
-    qh_settempfree_all -- 1 test
-    qh_settemppop -- 1 test
-    qh_settemppush -- 1 test
-    qh_settruncate -- 3 tests
-    qh_setunique -- 3 tests
-    qh_setzero -- 1 test
-    FOREACHint_ -- 2 test
-    FOREACHint4_
-    FOREACHint_i_ -- 1 test
-    FOREACHintreverse_
-    FOREACHintreverse12_
-    FOREACHsetelement_ -- 1 test
-    FOREACHsetelement_i_ -- 1 test
-    FOREACHsetelementreverse_ -- 1 test
-    FOREACHsetelementreverse12_ -- 1 test
-    SETelem_ -- 3 tests
-    SETelemaddr_ -- 2 tests
-    SETelemt_ -- not tested (generic)
-    SETempty_ -- 1 test
-    SETfirst_ -- 4 tests
-    SETfirstt_ -- 2 tests
-    SETindex_ -- 2 tests
-    SETref_ -- 2 tests
-    SETreturnsize_ -- 2 tests
-    SETsecond_ -- 1 test
-    SETsecondt_ -- 2 tests
-    SETtruncate_ -- 2 tests
-
-    Copyright (c) 2012-2015 C.B. Barber. All rights reserved.
-    $Id: //main/2015/qhull/src/testqset/testqset.c#4 $$Change: 2062 $
-    $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
-*/
-
-#include "libqhull/user.h"  /* QHULL_CRTDBG */
-#include "libqhull/qset.h"
-#include "libqhull/mem.h"
-
-#include 
-#include 
-#include 
-#include 
-
-typedef int i2T;
-#define MAXerrorCount 100 /* quit after n errors */
-
-#define FOREACHint_( ints ) FOREACHsetelement_( i2T, ints, i2)
-#define FOREACHint4_( ints ) FOREACHsetelement_( i2T, ints, i4)
-#define FOREACHint_i_( ints ) FOREACHsetelement_i_( i2T, ints, i2)
-#define FOREACHintreverse_( ints ) FOREACHsetelementreverse_( i2T, ints, i2)
-#define FOREACHintreverse12_( ints ) FOREACHsetelementreverse12_( i2T, ints, i2)
-
-enum {
-    MAXint= 0x7fffffff,
-};
-
-char prompt[]= "testqset N [M] [T5] -- Test qset.c and mem.c\n\
-  \n\
-  If this test fails then qhull will not work.\n\
-  \n\
-  Test qsets of 0..N integers with a check every M iterations (default ~log10)\n\
-  Additional checking and logging if M is 1\n\
-  \n\
-  T5 turns on memory logging (qset does not log)\n\
-  \n\
-  For example:\n\
-    testqset 10000\n\
-";
-
-int error_count= 0;  /* Global error_count.  checkSetContents() keeps its own error count.  It exits on too many errors */
-
-/* Macros normally defined in geom.h */
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/* Macros normally defined in user.h */
-
-#define realT double
-#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
-#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
-#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
-
-/* Macros normally defined in QhullSet.h */
-
-
-/* Functions normally defined in user.h for usermem.c */
-
-void    qh_exit(int exitcode);
-void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-
-/* Normally defined in user.c */
-
-void    qh_errexit(int exitcode, void *f, void *r)
-{
-    (void)f; /* unused */
-    (void)r; /* unused */
-    qh_exit(exitcode);
-}
-
-/* Normally defined in userprintf.c */
-
-void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... )
-{
-    static int needs_cr= 0;  /* True if qh_fprintf needs a CR */
-
-    size_t fmtlen= strlen(fmt);
-    va_list args;
-
-    if (!fp) {
-        /* Do not use qh_fprintf_stderr.  This is a standalone program */
-        fprintf(stderr, "QH6232 qh_fprintf: fp not defined for '%s'", fmt);
-        qh_errexit(6232, NULL, NULL);
-    }
-    if(fmtlen>0){
-        if(fmt[fmtlen-1]=='\n'){
-            if(needs_cr && fmtlen>1){
-                fprintf(fp, "\n");
-            }
-            needs_cr= 0;
-        }else{
-            needs_cr= 1;
-        }
-    }
-    if(msgcode>=6000 && msgcode<7000){
-        fprintf(fp, "Error TQ%d ", msgcode);
-    }
-    va_start(args, fmt);
-    vfprintf(fp, fmt, args);
-    va_end(args);
-}
-
-/* Defined below in order of use */
-int main(int argc, char **argv);
-void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel);
-void setupMemory(int tracelevel, int numInts, int **intarray);
-
-void testSetappendSettruncate(int numInts, int *intarray, int checkEvery);
-void testSetdelSetadd(int numInts, int *intarray, int checkEvery);
-void testSetappendSet(int numInts, int *intarray, int checkEvery);
-void testSetcompactCopy(int numInts, int *intarray, int checkEvery);
-void testSetequalInEtc(int numInts, int *intarray, int checkEvery);
-void testSettemp(int numInts, int *intarray, int checkEvery);
-void testSetlastEtc(int numInts, int *intarray, int checkEvery);
-void testSetdelsortedEtc(int numInts, int *intarray, int checkEvery);
-
-int log_i(setT *set, const char *s, int i, int numInts, int checkEvery);
-void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC);
-
-int main(int argc, char **argv) {
-    int *intarray= NULL;
-    int numInts;
-    int checkEvery= MAXint;
-    int curlong, totlong;
-    int traceLevel= 4; /* 4 normally, no tracing since qset does not log.  5 for memory tracing */
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user.h */
-    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
-    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
-#endif
-
-    readOptions(argc, argv, prompt, &numInts, &checkEvery, &traceLevel);
-    setupMemory(traceLevel, numInts, &intarray);
-
-    testSetappendSettruncate(numInts, intarray, checkEvery);
-    testSetdelSetadd(numInts, intarray, checkEvery);
-    testSetappendSet(numInts, intarray, checkEvery);
-    testSetcompactCopy(numInts, intarray, checkEvery);
-    testSetequalInEtc(numInts, intarray, checkEvery);
-    testSettemp(numInts, intarray, checkEvery);
-    testSetlastEtc(numInts, intarray, checkEvery);
-    testSetdelsortedEtc(numInts, intarray, checkEvery);
-    printf("\n\nNot testing qh_setduplicate and qh_setfree2.\n  These routines use heap-allocated set contents.  See qhull tests.\n");
-
-    qh_memstatistics(stdout);
-    qh_memfreeshort(&curlong, &totlong);
-    if (curlong || totlong){
-        qh_fprintf(stderr, 8043, "qh_memfreeshort: did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
-        error_count++;
-    }
-    if(error_count){
-        qh_fprintf(stderr, 8012, "testqset: %d errors\n\n", error_count);
-        exit(1);
-    }else{
-        printf("testqset: OK\n\n");
-    }
-    return 0;
-}/*main*/
-
-void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel)
-{
-    long numIntsArg;
-    long checkEveryArg;
-    char *endp;
-    int isTracing= 0;
-
-    if (argc < 2 || argc > 4) {
-        printf("%s", promptstr);
-        exit(0);
-    }
-    numIntsArg= strtol(argv[1], &endp, 10);
-    if(numIntsArg<1){
-        qh_fprintf(stderr, 6301, "First argument should be 1 or greater.  Got '%s'\n", argv[1]);
-        exit(1);
-    }
-    if(numIntsArg>MAXint){
-        qh_fprintf(stderr, 6302, "qset does not currently support 64-bit ints.  Maximum count is %d\n", MAXint);
-        exit(1);
-    }
-    *numInts= (int)numIntsArg;
-
-    if(argc==3 && argv[2][0]=='T' && argv[2][1]=='5' ){
-        isTracing= 1;
-        *traceLevel= 5;
-    }
-    if(argc==4 || (argc==3 && !isTracing)){
-        checkEveryArg= strtol(argv[2], &endp, 10);
-        if(checkEveryArg<1){
-            qh_fprintf(stderr, 6321, "checkEvery argument should be 1 or greater.  Got '%s'\n", argv[2]);
-            exit(1);
-        }
-        if(checkEveryArg>MAXint){
-            qh_fprintf(stderr, 6322, "qset does not currently support 64-bit ints.  Maximum checkEvery is %d\n", MAXint);
-            exit(1);
-        }
-        if(argc==4){
-            if(argv[3][0]=='T' && argv[3][1]=='5' ){
-                isTracing= 1;
-                *traceLevel= 5;
-            }else{
-                qh_fprintf(stderr, 6242, "Optional third argument must be 'T5'.  Got '%s'\n", argv[3]);
-                exit(1);
-            }
-        }
-        *checkEvery= (int)checkEveryArg;
-    }
-}/*readOptions*/
-
-void setupMemory(int tracelevel, int numInts, int **intarray)
-{
-    int i;
-    if(numInts<0 || numInts*(int)sizeof(int)<0){
-        qh_fprintf(stderr, 6303, "qset does not currently support 64-bit ints.  Integer overflow\n");
-        exit(1);
-    }
-    *intarray= qh_malloc(numInts * sizeof(int));
-    if(!*intarray){
-        qh_fprintf(stderr, 6304, "Failed to allocate %d bytes of memory\n", numInts * sizeof(int));
-        exit(1);
-    }
-    for(i= 0; i=2){
-        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
-        qh_settruncate(ints, numInts/2);
-        checkSetContents("qh_settruncate by half", ints, numInts/2, 0, -1, -1);
-    }
-    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
-    qh_settruncate(ints, 0);
-    checkSetContents("qh_settruncate", ints, 0, -1, -1, -1);
-
-    qh_fprintf(stderr, 8003, "\n\nTesting qh_setappend2ndlast 0,0..%d.  Test 0", numInts-1);
-    qh_setfree(&ints);
-    ints= qh_setnew(4);
-    qh_setappend(&ints, intarray+0);
-    for(i= 0; i=2){
-        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
-        SETtruncate_(ints, numInts/2);
-        checkSetContents("SETtruncate_ by half", ints, numInts/2, 0, -1, -1);
-    }
-    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
-    SETtruncate_(ints, 0);
-    checkSetContents("SETtruncate_", ints, 0, -1, -1, -1);
-
-    qh_setfree(&ints);
-}/*testSetappendSettruncate*/
-
-void testSetdelSetadd(int numInts, int *intarray, int checkEvery)
-{
-    setT *ints=qh_setnew(1);
-    int i,j,isCheck;
-
-    qh_fprintf(stderr, 8003, "\n\nTesting qh_setdelnthsorted and qh_setaddnth 1..%d. Test", numInts-1);
-    for(j=1; j3){
-                qh_setdelsorted(ints, intarray+i/2);
-                checkSetContents("qh_setdelsorted", ints, j-1, 0, i/2+1, -1);
-                qh_setaddsorted(&ints, intarray+i/2);
-                checkSetContents("qh_setaddsorted i/2", ints, j, 0, 0, -1);
-            }
-            qh_setdellast(ints);
-            checkSetContents("qh_setdellast", ints, (j ? j-1 : 0), 0, -1, -1);
-            if(j>0){
-                qh_setaddsorted(&ints, intarray+j-1);
-                checkSetContents("qh_setaddsorted j-1", ints, j, 0, -1, -1);
-            }
-            if(j>4){
-                qh_setdelnthsorted(ints, i/2);
-                if (checkEvery==1)
-                  checkSetContents("qh_setdelnthsorted", ints, j-1, 0, i/2+1, -1);
-                /* test qh_setdelnth and move-to-front */
-                qh_setdelsorted(ints, intarray+i/2+1);
-                checkSetContents("qh_setdelsorted 2", ints, j-2, 0, i/2+2, -1);
-                qh_setaddsorted(&ints, intarray+i/2+1);
-                if (checkEvery==1)
-                  checkSetContents("qh_setaddsorted i/2+1", ints, j-1, 0, i/2+1, -1);
-                qh_setaddsorted(&ints, intarray+i/2);
-                checkSetContents("qh_setaddsorted i/2 again", ints, j, 0, -1, -1);
-            }
-            qh_setfree(&ints2);
-            ints2= qh_setcopy(ints, 0);
-            qh_setcompact(ints);
-            qh_setcompact(ints2);
-            checkSetContents("qh_setcompact", ints, j, 0, 0, -1);
-            checkSetContents("qh_setcompact 2", ints2, j, 0, 0, -1);
-            qh_setcompact(ints);
-            checkSetContents("qh_setcompact 3", ints, j, 0, 0, -1);
-            qh_setfree(&ints2);
-        }
-    }
-    qh_setfreelong(&ints);
-    if(ints){
-        qh_setfree(&ints); /* Was quick memory */
-    }
-}/*testSetdelsortedEtc*/
-
-void testSetequalInEtc(int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    setT *ints3= NULL;
-    int i,j,n;
-
-    qh_fprintf(stderr, 8019, "\n\nTesting qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                if(qh_setequal(ints, ints2)){
-                    qh_fprintf(stderr, 6324, "testSetequalInEtc: non-empty set equal to empty set\n", j);
-                    error_count++;
-                }
-                qh_setfree(&ints3);
-                ints3= qh_setcopy(ints, 0);
-                checkSetContents("qh_setreplace", ints3, j, 0, -1, -1);
-                qh_setreplace(ints3, intarray+j/2, intarray+j/2+1);
-                if(j==1){
-                    checkSetContents("qh_setreplace 2", ints3, j, j/2+1, -1, -1);
-                }else if(j==2){
-                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, -1);
-                }else{
-                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, j/2+1);
-                }
-                if(qh_setequal(ints, ints3)){
-                    qh_fprintf(stderr, 6325, "testSetequalInEtc: modified set equal to original set at %d/2\n", j);
-                    error_count++;
-                }
-                if(!qh_setequal_except(ints, intarray+j/2, ints3, intarray+j/2+1)){
-                    qh_fprintf(stderr, 6326, "qh_setequal_except: modified set not equal to original set except modified\n", j);
-                    error_count++;
-                }
-                if(qh_setequal_except(ints, intarray+j/2, ints3, intarray)){
-                    qh_fprintf(stderr, 6327, "qh_setequal_except: modified set equal to original set with wrong excepts\n", j);
-                    error_count++;
-                }
-                if(!qh_setequal_skip(ints, j/2, ints3, j/2)){
-                    qh_fprintf(stderr, 6328, "qh_setequal_skip: modified set not equal to original set except modified\n", j);
-                    error_count++;
-                }
-                if(j>2 && qh_setequal_skip(ints, j/2, ints3, 0)){
-                    qh_fprintf(stderr, 6329, "qh_setequal_skip: modified set equal to original set with wrong excepts\n", j);
-                    error_count++;
-                }
-                if(intarray+j/2+1!=qh_setdel(ints3, intarray+j/2+1)){
-                    qh_fprintf(stderr, 6330, "qh_setdel: failed to find added element\n", j);
-                    error_count++;
-                }
-                checkSetContents("qh_setdel", ints3, j-1, 0, j-1, (j==1 ? -1 : j/2+1));  /* swaps last element with deleted element */
-                if(j>3){
-                    qh_setdelnth(ints3, j/2); /* Delete at the same location as the original replace, for only one out-of-order element */
-                    checkSetContents("qh_setdelnth", ints3, j-2, 0, j-2, (j==2 ? -1 : j/2+1));
-                }
-                if(qh_setin(ints3, intarray+j/2)){
-                    qh_fprintf(stderr, 6331, "qh_setin: found deleted element\n");
-                    error_count++;
-                }
-                if(j>4 && !qh_setin(ints3, intarray+1)){
-                    qh_fprintf(stderr, 6332, "qh_setin: did not find second element\n");
-                    error_count++;
-                }
-                if(j>4 && !qh_setin(ints3, intarray+j-2)){
-                    qh_fprintf(stderr, 6333, "qh_setin: did not find last element\n");
-                    error_count++;
-                }
-                if(-1!=qh_setindex(ints2, intarray)){
-                    qh_fprintf(stderr, 6334, "qh_setindex: found element in empty set\n");
-                    error_count++;
-                }
-                if(-1!=qh_setindex(ints3, intarray+j/2)){
-                    qh_fprintf(stderr, 6335, "qh_setindex: found deleted element in set\n");
-                    error_count++;
-                }
-                if(0!=qh_setindex(ints, intarray)){
-                    qh_fprintf(stderr, 6336, "qh_setindex: did not find first in set\n");
-                    error_count++;
-                }
-                if(j-1!=qh_setindex(ints, intarray+j-1)){
-                    qh_fprintf(stderr, 6337, "qh_setindex: did not find last in set\n");
-                    error_count++;
-                }
-            }
-            qh_setfree(&ints2);
-        }
-    }
-    qh_setfree(&ints3);
-    qh_setfreelong(&ints);
-    if(ints){
-        qh_setfree(&ints); /* Was quick memory */
-    }
-}/*testSetequalInEtc*/
-
-
-void testSetlastEtc(int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    int i,j,prepend;
-
-    qh_fprintf(stderr, 8020, "\n\nTesting qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                if(intarray+j-1!=qh_setlast(ints)){
-                    qh_fprintf(stderr, 6338, "qh_setlast: wrong last element\n");
-                    error_count++;
-                }
-                prepend= (j<100 ? j/4 : 0);
-                ints2= qh_setnew_delnthsorted(ints, qh_setsize(ints), j/2, prepend);
-                if(qh_setsize(ints2)!=j+prepend-1){
-                    qh_fprintf(stderr, 6345, "qh_setnew_delnthsorted: Expecting %d elements, got %d\n", j+prepend-1, qh_setsize(ints2));
-                    error_count++;
-                }
-                /* Define prepended elements.  Otherwise qh_setdelnthsorted may fail */
-                for(i= 0; i2){
-                    qh_setzero(ints2, j/2, j-1);  /* max size may be j-1 */
-                    if(qh_setsize(ints2)!=j-1){
-                        qh_fprintf(stderr, 6342, "qh_setzero: Expecting %d elements, got %d\n", j, qh_setsize(ints2));
-                        error_count++;
-                    }
-                    qh_setcompact(ints2);
-                    checkSetContents("qh_setzero", ints2, j/2, 0, -1, -1);
-                }
-            }
-            qh_setfree(&ints2);
-        }
-    }
-    qh_setfreelong(&ints);
-    if(ints){
-        qh_setfree(&ints); /* Was quick memory */
-    }
-}/*testSetlastEtc*/
-
-void testSettemp(int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    setT *ints3= NULL;
-    int i,j;
-
-    qh_fprintf(stderr, 8021, "\n\nTesting qh_settemp* 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                qh_settemppush(ints);
-                ints3= qh_settemppop();
-                if(ints!=ints3){
-                    qh_fprintf(stderr, 6343, "qh_settemppop: didn't pop the push\n");
-                    error_count++;
-                }
-            }
-            qh_settempfree(&ints2);
-        }
-    }
-    qh_setfreelong(&ints);
-    if(ints){
-        qh_setfree(&ints); /* Was quick memory */
-    }
-}/*testSettemp*/
-
-/* Check that a set contains count elements
-   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
-   Use -1 for missing ranges
-   Returns -1 if should check results
-*/
-int log_i(setT *set, const char *s, int i, int numInts, int checkEvery)
-{
-    int j= i;
-    int scale= 1;
-    int e= 0;
-    int *i2, **i2p;
-
-    if(*s || checkEvery==1){
-        if(i<10){
-            qh_fprintf(stderr, 8004, " %s%d", s, i);
-        }else{
-            if(i==11 && checkEvery==1){
-                qh_fprintf(stderr, 8005, "\nResults after 10: ");
-                FOREACHint_(set){
-                    qh_fprintf(stderr, 8006, " %d", *i2);
-                }
-                qh_fprintf(stderr, 8007, " Continue");
-            }
-            while((j= j/10)>=1){
-                scale *= 10;
-                e++;
-            }
-            if(i==numInts-1){
-                qh_fprintf(stderr, 8008, " %s%d", s, i);
-            }else if(i==scale){
-                if(i<=1000){
-                    qh_fprintf(stderr, 8010, " %s%d", s, i);
-                }else{
-                    qh_fprintf(stderr, 8009, " %s1e%d", s, e);
-                }
-            }
-        }
-    }
-    if(i<1000 || i%checkEvery==0 || i== scale || i==numInts-1){
-        return 1;
-    }
-    return 0;
-}/*log_i*/
-
-/* Check that a set contains count elements
-   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
-   Use -1 for missing ranges
-*/
-void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC)
-{
-
-    i2T *i2, **i2p;
-    int i2_i, i2_n;
-    int prev= -1; /* avoid warning */
-    int i;
-    int first= -3;
-    int second= -3;
-    int rangeCount=1;
-    int actualSize= 0;
-
-    qh_setcheck(set, name, 0);
-    if(set){
-        SETreturnsize_(set, actualSize);  /* normally used only when speed is critical */
-        if(*qh_setendpointer(set)!=NULL){
-            qh_fprintf(stderr, 6344, "%s: qh_setendpointer(), 0x%x, is not NULL terminator of set 0x%x", name, qh_setendpointer(set), set);
-            error_count++;
-        }
-    }
-    if(actualSize!=qh_setsize(set)){
-        qh_fprintf(stderr, 6305, "%s: SETreturnsize_() returned %d while qh_setsize() returns %d\n", name, actualSize, qh_setsize(set));
-        error_count++;
-    }else if(actualSize!=count){
-        qh_fprintf(stderr, 6306, "%s: Expecting %d elements for set.  Got %d elements\n", name, count, actualSize);
-        error_count++;
-    }
-    if(SETempty_(set)){
-        if(count!=0){
-            qh_fprintf(stderr, 6307, "%s: Got empty set instead of count %d, rangeA %d, rangeB %d, rangeC %d\n", name, count, rangeA, rangeB, rangeC);
-            error_count++;
-        }
-    }else{
-        /* Must be first, otherwise trips msvc 8 */
-        i2T **p= SETaddr_(set, i2T);
-        if(*p!=SETfirstt_(set, i2T)){
-            qh_fprintf(stderr, 6309, "%s: SETaddr_(set, i2t) [%p] is not the same as SETfirst_(set) [%p]\n", name, SETaddr_(set, i2T), SETfirst_(set));
-            error_count++;
-        }
-        first= *(int *)SETfirst_(set);
-        if(SETfirst_(set)!=SETfirstt_(set, i2T)){
-            qh_fprintf(stderr, 6308, "%s: SETfirst_(set) [%p] is not the same as SETfirstt_(set, i2T [%p]\n", name, SETfirst_(set), SETfirstt_(set, i2T));
-            error_count++;
-        }
-        if(qh_setsize(set)>1){
-            second= *(int *)SETsecond_(set);
-            if(SETsecond_(set)!=SETsecondt_(set, i2T)){
-                qh_fprintf(stderr, 6310, "%s: SETsecond_(set) [%p] is not the same as SETsecondt_(set, i2T) [%p]\n", name, SETsecond_(set), SETsecondt_(set, i2T));
-                error_count++;
-            }
-        }
-    }
-    /* Test first run of ints in set*/
-    i= 0;
-    FOREACHint_(set){
-        if(i2!=SETfirst_(set) && *i2!=prev+1){
-            break;
-        }
-        prev= *i2;
-        if(SETindex_(set, i2)!=i){
-            qh_fprintf(stderr, 6311, "%s: Expecting SETIndex_(set, pointer-to-%d) to be %d.  Got %d\n", name, *i2, i, SETindex_(set, i2));
-            error_count++;;
-        }
-        if(i2!=SETref_(i2)){
-            qh_fprintf(stderr, 6312, "%s: SETref_(i2) [%p] does not point to i2 (the %d'th element)\n", name, SETref_(i2), i);
-            error_count++;;
-        }
-        i++;
-    }
-    FOREACHint_i_(set){
-        /* Must be first conditional, otherwise it trips up msvc 8 */
-        i2T **p= SETelemaddr_(set, i2_i, i2T);
-        if(i2!=*p){
-            qh_fprintf(stderr, 6320, "%s: SETelemaddr_(set, %d, i2T) [%p] does not point to i2\n", name, i2_i, SETelemaddr_(set, i2_i, int));
-            error_count++;;
-        }
-        if(i2_i==0){
-            if(first!=*i2){
-                qh_fprintf(stderr, 6314, "%s: First element is %d instead of SETfirst %d\n", name, *i2, first);
-                error_count++;;
-            }
-            if(rangeA!=*i2){
-                qh_fprintf(stderr, 6315, "%s: starts with %d instead of rangeA %d\n", name, *i2, rangeA);
-                error_count++;;
-            }
-            prev= rangeA;
-        }else{
-            if(i2_i==1 && second!=*i2){
-                qh_fprintf(stderr, 6316, "%s: Second element is %d instead of SETsecond %d\n", name, *i2, second);
-                error_count++;;
-            }
-            if(prev+1==*i2){
-                prev++;
-            }else{
-                if(*i2==rangeB){
-                    prev= rangeB;
-                    rangeB= -1;
-                    rangeCount++;
-                }else if(rangeB==-1 && *i2==rangeC){
-                    prev= rangeC;
-                    rangeC= -1;
-                    rangeCount++;
-                }else{
-                    prev++;
-                    qh_fprintf(stderr, 6317, "%s: Expecting %d'th element to be %d.  Got %d\n", name, i2_i, prev, *i2);
-                    error_count++;
-                }
-            }
-        }
-        if(i2!=SETelem_(set, i2_i)){
-            qh_fprintf(stderr, 6318, "%s: SETelem_(set, %d) [%p] is not i2 [%p] (the %d'th element)\n", name, i2_i, SETelem_(set, i2_i), i2, i2_i);
-            error_count++;;
-        }
-        if(SETelemt_(set, i2_i, i2T)!=SETelem_(set, i2_i)){   /* Normally SETelemt_ is used for generic sets */
-            qh_fprintf(stderr, 6319, "%s: SETelemt_(set, %d, i2T) [%p] is not SETelem_(set, %d) [%p] (the %d'th element)\n", name, i2_i, SETelemt_(set, i2_i, int), i2_i, SETelem_(set, i2_i), i2_i);
-            error_count++;;
-        }
-    }
-    if(error_count>=MAXerrorCount){
-        qh_fprintf(stderr, 8011, "testqset: Stop testing after %d errors\n", error_count);
-        exit(1);
-    }
-}/*checkSetContents*/
-
diff --git a/src/qhull/src/testqset/testqset.pro b/src/qhull/src/testqset/testqset.pro
deleted file mode 100644
index 3f69048aa..000000000
--- a/src/qhull/src/testqset/testqset.pro
+++ /dev/null
@@ -1,30 +0,0 @@
-# -------------------------------------------------
-# testqset.pro -- Qt project file for testqset.exe
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-TARGET = testqset
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-CONFIG += qhull_warn_conversion
-
-build_pass:CONFIG(debug, debug|release){
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   OBJECTS_DIR = Release
-}
-
-INCLUDEPATH += ..
-
-SOURCES += testqset.c
-SOURCES += ../libqhull/qset.c
-SOURCES += ../libqhull/mem.c
-SOURCES += ../libqhull/usermem.c
-
-HEADERS += ../libqhull/mem.h
-HEADERS += ../libqhull/qset.h
-
diff --git a/src/qhull/src/testqset_r/testqset_r.c b/src/qhull/src/testqset_r/testqset_r.c
deleted file mode 100644
index 9a6d496e4..000000000
--- a/src/qhull/src/testqset_r/testqset_r.c
+++ /dev/null
@@ -1,890 +0,0 @@
-/*
      ---------------------------------
-
-   testset.c -- test qset.c and its use of mem.c
-
-   The test sets are pointers to int.  Normally a set is a pointer to a type (e.g., facetT, ridgeT, etc.).
-   For consistency in notation, an "int" is typedef'd to i2T
-
-Functions and macros from qset.h.  Counts occurrences in this test.  Does not correspond to thoroughness.
-    qh_setaddsorted -- 4 tests
-    qh_setaddnth -- 1 test
-    qh_setappend -- 7 tests
-    qh_setappend_set -- 1 test
-    qh_setappend2ndlast -- 1 test
-    qh_setcheck -- lots of tests
-    qh_setcompact -- 7 tests
-    qh_setcopy -- 3 tests
-    qh_setdel -- 1 tests
-    qh_setdellast -- 1 tests
-    qh_setdelnth -- 2 tests
-    qh_setdelnthsorted -- 2 tests
-    qh_setdelsorted -- 1 test
-    qh_setduplicate -- not testable here
-    qh_setequal -- 4 tests
-    qh_setequal_except -- 2 tests
-    qh_setequal_skip -- 2 tests
-    qh_setfree -- 11+ tests
-    qh_setfree2 -- not testable here
-    qh_setfreelong -- 2 tests
-    qh_setin -- 3 tests
-    qh_setindex -- 4 tests
-    qh_setlarger -- 1 test
-    qh_setlast -- 2 tests
-    qh_setnew -- 6 tests
-    qh_setnew_delnthsorted
-    qh_setprint -- tested elsewhere
-    qh_setreplace -- 1 test
-    qh_setsize -- 9+ tests
-    qh_settemp -- 2 tests
-    qh_settempfree -- 1 test
-    qh_settempfree_all -- 1 test
-    qh_settemppop -- 1 test
-    qh_settemppush -- 1 test
-    qh_settruncate -- 3 tests
-    qh_setunique -- 3 tests
-    qh_setzero -- 1 test
-    FOREACHint_ -- 2 test
-    FOREACHint4_
-    FOREACHint_i_ -- 1 test
-    FOREACHintreverse_
-    FOREACHintreverse12_
-    FOREACHsetelement_ -- 1 test
-    FOREACHsetelement_i_ -- 1 test
-    FOREACHsetelementreverse_ -- 1 test
-    FOREACHsetelementreverse12_ -- 1 test
-    SETelem_ -- 3 tests
-    SETelemaddr_ -- 2 tests
-    SETelemt_ -- not tested (generic)
-    SETempty_ -- 1 test
-    SETfirst_ -- 4 tests
-    SETfirstt_ -- 2 tests
-    SETindex_ -- 2 tests
-    SETref_ -- 2 tests
-    SETreturnsize_ -- 2 tests
-    SETsecond_ -- 1 test
-    SETsecondt_ -- 2 tests
-    SETtruncate_ -- 2 tests
-
-    Copyright (c) 2012-2015 C.B. Barber. All rights reserved.
-    $Id: //main/2015/qhull/src/testqset_r/testqset_r.c#5 $$Change: 2064 $
-    $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
-*/
-
-#include "libqhull_r/user_r.h"  /* QHULL_CRTDBG */
-#include "libqhull_r/qset_r.h"
-#include "libqhull_r/mem_r.h"
-#include "libqhull_r/libqhull_r.h"
-
-#include 
-#include 
-#include 
-#include 
-
-typedef int i2T;
-#define MAXerrorCount 100 /* quit after n errors */
-
-#define FOREACHint_( ints ) FOREACHsetelement_( i2T, ints, i2)
-#define FOREACHint4_( ints ) FOREACHsetelement_( i2T, ints, i4)
-#define FOREACHint_i_( qh, ints ) FOREACHsetelement_i_( qh, i2T, ints, i2)
-#define FOREACHintreverse_( qh, ints ) FOREACHsetelementreverse_( qh, i2T, ints, i2)
-#define FOREACHintreverse12_( ints ) FOREACHsetelementreverse12_( i2T, ints, i2)
-
-enum {
-    MAXint= 0x7fffffff,
-};
-
-char prompt[]= "testqset_r N [M] [T5] -- Test reentrant qset_r.c and mem_r.c\n\
-  \n\
-  If this test fails then reentrant Qhull will not work.\n\
-  \n\
-  Test qsets of 0..N integers with a check every M iterations (default ~log10)\n\
-  Additional checking and logging if M is 1\n\
-  \n\
-  T5 turns on memory logging (qset does not log)\n\
-  \n\
-  For example:\n\
-    testqset_r 10000\n\
-";
-
-int error_count= 0;  /* Global error_count.  checkSetContents(qh) keeps its own error count.  It exits on too many errors */
-
-/* Macros normally defined in geom.h */
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/* Macros normally defined in QhullSet.h */
-
-/* Functions normally defined in user_r.h for usermem_r.c */
-
-void    qh_exit(int exitcode);
-void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
-void    qh_free(void *mem);
-void   *qh_malloc(size_t size);
-
-/* Normally defined in user_r.c */
-
-void    qh_errexit(qhT *qh, int exitcode, facetT *f, ridgeT *r)
-{
-    (void)f; /* unused */
-    (void)r; /* unused */
-    (void)qh; /* unused */
-    qh_exit(exitcode);
-}
-
-/* Normally defined in userprintf.c */
-
-void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... )
-{
-    static int needs_cr= 0;  /* True if qh_fprintf needs a CR. testqset_r is not itself reentrant */
-
-    size_t fmtlen= strlen(fmt);
-    va_list args;
-
-    if (!fp) {
-        /* Do not use qh_fprintf_stderr.  This is a standalone program */
-        if(!qh)
-            fprintf(stderr, "QH6241 qh_fprintf: fp and qh not defined for '%s'", fmt);
-        else
-            fprintf(stderr, "QH6232 qh_fprintf: fp is 0.  Was wrong qh_fprintf called for '%s'", fmt);
-        qh_errexit(qh, 6232, NULL, NULL);
-    }
-    if(fmtlen>0){
-        if(fmt[fmtlen-1]=='\n'){
-            if(needs_cr && fmtlen>1){
-                fprintf(fp, "\n");
-            }
-            needs_cr= 0;
-        }else{
-            needs_cr= 1;
-        }
-    }
-    if(msgcode>=6000 && msgcode<7000){
-        fprintf(fp, "Error TQ%d ", msgcode);
-    }
-    va_start(args, fmt);
-    vfprintf(fp, fmt, args);
-    va_end(args);
-}
-
-/* Defined below in order of use */
-int main(int argc, char **argv);
-void readOptions(qhT *qh, int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel);
-void setupMemory(qhT *qh, int tracelevel, int numInts, int **intarray);
-
-void testSetappendSettruncate(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetdelSetadd(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetappendSet(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetcompactCopy(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetequalInEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSettemp(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetlastEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
-void testSetdelsortedEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
-
-int log_i(qhT *qh, setT *set, const char *s, int i, int numInts, int checkEvery);
-void checkSetContents(qhT *qh, const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC);
-
-int main(int argc, char **argv) {
-    int *intarray= NULL;
-    int numInts;
-    int checkEvery= MAXint;
-    int curlong, totlong;
-    int traceLevel= 4; /* 4 normally, no tracing since qset does not log.  Option 'T5' for memory tracing */
-    qhT qh_qh;
-    qhT *qh= &qh_qh;
-
-#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
-    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
-    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
-    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
-#endif
-
-    readOptions(qh, argc, argv, prompt, &numInts, &checkEvery, &traceLevel);
-    setupMemory(qh, traceLevel, numInts, &intarray);
-
-    testSetappendSettruncate(qh, numInts, intarray, checkEvery);
-    testSetdelSetadd(qh, numInts, intarray, checkEvery);
-    testSetappendSet(qh, numInts, intarray, checkEvery);
-    testSetcompactCopy(qh, numInts, intarray, checkEvery);
-    testSetequalInEtc(qh, numInts, intarray, checkEvery);
-    testSettemp(qh, numInts, intarray, checkEvery);
-    testSetlastEtc(qh, numInts, intarray, checkEvery);
-    testSetdelsortedEtc(qh, numInts, intarray, checkEvery);
-    printf("\n\nNot testing qh_setduplicate and qh_setfree2.\n  These routines use heap-allocated set contents.  See qhull tests.\n");
-
-    qh_memstatistics(qh, stdout);
-    qh_memfreeshort(qh, &curlong, &totlong);
-    if (curlong || totlong){
-        qh_fprintf(qh, stderr, 8043, "qh_memfreeshort: did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
-        error_count++;
-    }
-    if(error_count){
-        qh_fprintf(qh, stderr, 8012, "testqset: %d errors\n\n", error_count);
-        exit(1);
-    }else{
-        printf("testqset_r: OK\n\n");
-    }
-    return 0;
-}/*main*/
-
-void readOptions(qhT *qh, int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel)
-{
-    long numIntsArg;
-    long checkEveryArg;
-    char *endp;
-    int isTracing= 0;
-
-    if (argc < 2 || argc > 4) {
-        printf("%s", promptstr);
-        exit(0);
-    }
-    numIntsArg= strtol(argv[1], &endp, 10);
-    if(numIntsArg<1){
-        qh_fprintf(qh, stderr, 6301, "First argument should be 1 or greater.  Got '%s'\n", argv[1]);
-        exit(1);
-    }
-    if(numIntsArg>MAXint){
-        qh_fprintf(qh, stderr, 6302, "qset does not currently support 64-bit ints.  Maximum count is %d\n", MAXint);
-        exit(1);
-    }
-    *numInts= (int)numIntsArg;
-
-    if(argc==3 && argv[2][0]=='T' && argv[2][1]=='5' ){
-        isTracing= 1;
-        *traceLevel= 5;
-    }
-    if(argc==4 || (argc==3 && !isTracing)){
-        checkEveryArg= strtol(argv[2], &endp, 10);
-        if(checkEveryArg<1){
-            qh_fprintf(qh, stderr, 6321, "checkEvery argument should be 1 or greater.  Got '%s'\n", argv[2]);
-            exit(1);
-        }
-        if(checkEveryArg>MAXint){
-            qh_fprintf(qh, stderr, 6322, "qset does not currently support 64-bit ints.  Maximum checkEvery is %d\n", MAXint);
-            exit(1);
-        }
-        if(argc==4){
-            if(argv[3][0]=='T' && argv[3][1]=='5' ){
-                isTracing= 1;
-                *traceLevel= 5;
-            }else{
-                qh_fprintf(qh, stderr, 6242, "Optional third argument must be 'T5'.  Got '%s'\n", argv[3]);
-                exit(1);
-            }
-        }
-        *checkEvery= (int)checkEveryArg;
-    }
-}/*readOptions*/
-
-void setupMemory(qhT *qh, int tracelevel, int numInts, int **intarray)
-{
-    int i;
-    if(numInts<0 || numInts*(int)sizeof(int)<0){
-        qh_fprintf(qh, stderr, 6303, "qset does not currently support 64-bit ints.  Integer overflow\n");
-        exit(1);
-    }
-    *intarray= qh_malloc(numInts * sizeof(int));
-    if(!*intarray){
-        qh_fprintf(qh, stderr, 6304, "Failed to allocate %d bytes of memory\n", numInts * sizeof(int));
-        exit(1);
-    }
-    for(i= 0; i=2){
-        isCheck= log_i(qh, ints, "n", numInts/2, numInts, checkEvery);
-        qh_settruncate(qh, ints, numInts/2);
-        checkSetContents(qh, "qh_settruncate by half", ints, numInts/2, 0, -1, -1);
-    }
-    isCheck= log_i(qh, ints, "n", 0, numInts, checkEvery);
-    qh_settruncate(qh, ints, 0);
-    checkSetContents(qh, "qh_settruncate", ints, 0, -1, -1, -1);
-
-    qh_fprintf(qh, stderr, 8003, "\n\nTesting qh_setappend2ndlast 0,0..%d.  Test 0", numInts-1);
-    qh_setfree(qh, &ints);
-    ints= qh_setnew(qh, 4);
-    qh_setappend(qh, &ints, intarray+0);
-    for(i= 0; i=2){
-        isCheck= log_i(qh, ints, "n", numInts/2, numInts, checkEvery);
-        SETtruncate_(ints, numInts/2);
-        checkSetContents(qh, "SETtruncate_ by half", ints, numInts/2, 0, -1, -1);
-    }
-    isCheck= log_i(qh, ints, "n", 0, numInts, checkEvery);
-    SETtruncate_(ints, 0);
-    checkSetContents(qh, "SETtruncate_", ints, 0, -1, -1, -1);
-
-    qh_setfree(qh, &ints);
-}/*testSetappendSettruncate*/
-
-void testSetdelSetadd(qhT *qh, int numInts, int *intarray, int checkEvery)
-{
-    setT *ints=qh_setnew(qh, 1);
-    int i,j,isCheck;
-
-    qh_fprintf(qh, stderr, 8003, "\n\nTesting qh_setdelnthsorted and qh_setaddnth 1..%d. Test", numInts-1);
-    for(j=1; j3){
-                qh_setdelsorted(ints, intarray+i/2);
-                checkSetContents(qh, "qh_setdelsorted", ints, j-1, 0, i/2+1, -1);
-                qh_setaddsorted(qh, &ints, intarray+i/2);
-                checkSetContents(qh, "qh_setaddsorted i/2", ints, j, 0, 0, -1);
-            }
-            qh_setdellast(ints);
-            checkSetContents(qh, "qh_setdellast", ints, (j ? j-1 : 0), 0, -1, -1);
-            if(j>0){
-                qh_setaddsorted(qh, &ints, intarray+j-1);
-                checkSetContents(qh, "qh_setaddsorted j-1", ints, j, 0, -1, -1);
-            }
-            if(j>4){
-                qh_setdelnthsorted(qh, ints, i/2);
-                if (checkEvery==1)
-                  checkSetContents(qh, "qh_setdelnthsorted", ints, j-1, 0, i/2+1, -1);
-                /* test qh_setdelnth and move-to-front */
-                qh_setdelsorted(ints, intarray+i/2+1);
-                checkSetContents(qh, "qh_setdelsorted 2", ints, j-2, 0, i/2+2, -1);
-                qh_setaddsorted(qh, &ints, intarray+i/2+1);
-                if (checkEvery==1)
-                  checkSetContents(qh, "qh_setaddsorted i/2+1", ints, j-1, 0, i/2+1, -1);
-                qh_setaddsorted(qh, &ints, intarray+i/2);
-                checkSetContents(qh, "qh_setaddsorted i/2 again", ints, j, 0, -1, -1);
-            }
-            qh_setfree(qh, &ints2);
-            ints2= qh_setcopy(qh, ints, 0);
-            qh_setcompact(qh, ints);
-            qh_setcompact(qh, ints2);
-            checkSetContents(qh, "qh_setcompact", ints, j, 0, 0, -1);
-            checkSetContents(qh, "qh_setcompact 2", ints2, j, 0, 0, -1);
-            qh_setcompact(qh, ints);
-            checkSetContents(qh, "qh_setcompact 3", ints, j, 0, 0, -1);
-            qh_setfree(qh, &ints2);
-        }
-    }
-    qh_setfreelong(qh, &ints);
-    if(ints){
-        qh_setfree(qh, &ints); /* Was quick memory */
-    }
-}/*testSetdelsortedEtc*/
-
-void testSetequalInEtc(qhT *qh, int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    setT *ints3= NULL;
-    int i,j,n;
-
-    qh_fprintf(qh, stderr, 8019, "\n\nTesting qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                if(qh_setequal(ints, ints2)){
-                    qh_fprintf(qh, stderr, 6324, "testSetequalInEtc: non-empty set equal to empty set\n", j);
-                    error_count++;
-                }
-                qh_setfree(qh, &ints3);
-                ints3= qh_setcopy(qh, ints, 0);
-                checkSetContents(qh, "qh_setreplace", ints3, j, 0, -1, -1);
-                qh_setreplace(qh, ints3, intarray+j/2, intarray+j/2+1);
-                if(j==1){
-                    checkSetContents(qh, "qh_setreplace 2", ints3, j, j/2+1, -1, -1);
-                }else if(j==2){
-                    checkSetContents(qh, "qh_setreplace 3", ints3, j, 0, j/2+1, -1);
-                }else{
-                    checkSetContents(qh, "qh_setreplace 3", ints3, j, 0, j/2+1, j/2+1);
-                }
-                if(qh_setequal(ints, ints3)){
-                    qh_fprintf(qh, stderr, 6325, "testSetequalInEtc: modified set equal to original set at %d/2\n", j);
-                    error_count++;
-                }
-                if(!qh_setequal_except(ints, intarray+j/2, ints3, intarray+j/2+1)){
-                    qh_fprintf(qh, stderr, 6326, "qh_setequal_except: modified set not equal to original set except modified\n", j);
-                    error_count++;
-                }
-                if(qh_setequal_except(ints, intarray+j/2, ints3, intarray)){
-                    qh_fprintf(qh, stderr, 6327, "qh_setequal_except: modified set equal to original set with wrong excepts\n", j);
-                    error_count++;
-                }
-                if(!qh_setequal_skip(ints, j/2, ints3, j/2)){
-                    qh_fprintf(qh, stderr, 6328, "qh_setequal_skip: modified set not equal to original set except modified\n", j);
-                    error_count++;
-                }
-                if(j>2 && qh_setequal_skip(ints, j/2, ints3, 0)){
-                    qh_fprintf(qh, stderr, 6329, "qh_setequal_skip: modified set equal to original set with wrong excepts\n", j);
-                    error_count++;
-                }
-                if(intarray+j/2+1!=qh_setdel(ints3, intarray+j/2+1)){
-                    qh_fprintf(qh, stderr, 6330, "qh_setdel: failed to find added element\n", j);
-                    error_count++;
-                }
-                checkSetContents(qh, "qh_setdel", ints3, j-1, 0, j-1, (j==1 ? -1 : j/2+1));  /* swaps last element with deleted element */
-                if(j>3){
-                    qh_setdelnth(qh, ints3, j/2); /* Delete at the same location as the original replace, for only one out-of-order element */
-                    checkSetContents(qh, "qh_setdelnth", ints3, j-2, 0, j-2, (j==2 ? -1 : j/2+1));
-                }
-                if(qh_setin(ints3, intarray+j/2)){
-                    qh_fprintf(qh, stderr, 6331, "qh_setin: found deleted element\n");
-                    error_count++;
-                }
-                if(j>4 && !qh_setin(ints3, intarray+1)){
-                    qh_fprintf(qh, stderr, 6332, "qh_setin: did not find second element\n");
-                    error_count++;
-                }
-                if(j>4 && !qh_setin(ints3, intarray+j-2)){
-                    qh_fprintf(qh, stderr, 6333, "qh_setin: did not find last element\n");
-                    error_count++;
-                }
-                if(-1!=qh_setindex(ints2, intarray)){
-                    qh_fprintf(qh, stderr, 6334, "qh_setindex: found element in empty set\n");
-                    error_count++;
-                }
-                if(-1!=qh_setindex(ints3, intarray+j/2)){
-                    qh_fprintf(qh, stderr, 6335, "qh_setindex: found deleted element in set\n");
-                    error_count++;
-                }
-                if(0!=qh_setindex(ints, intarray)){
-                    qh_fprintf(qh, stderr, 6336, "qh_setindex: did not find first in set\n");
-                    error_count++;
-                }
-                if(j-1!=qh_setindex(ints, intarray+j-1)){
-                    qh_fprintf(qh, stderr, 6337, "qh_setindex: did not find last in set\n");
-                    error_count++;
-                }
-            }
-            qh_setfree(qh, &ints2);
-        }
-    }
-    qh_setfree(qh, &ints3);
-    qh_setfreelong(qh, &ints);
-    if(ints){
-        qh_setfree(qh, &ints); /* Was quick memory */
-    }
-}/*testSetequalInEtc*/
-
-
-void testSetlastEtc(qhT *qh, int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    int i,j,prepend;
-
-    qh_fprintf(qh, stderr, 8020, "\n\nTesting qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                if(intarray+j-1!=qh_setlast(ints)){
-                    qh_fprintf(qh, stderr, 6338, "qh_setlast: wrong last element\n");
-                    error_count++;
-                }
-                prepend= (j<100 ? j/4 : 0);
-                ints2= qh_setnew_delnthsorted(qh, ints, qh_setsize(qh, ints), j/2, prepend);
-                if(qh_setsize(qh, ints2)!=j+prepend-1){
-                    qh_fprintf(qh, stderr, 6345, "qh_setnew_delnthsorted: Expecting %d elements, got %d\n", j+prepend-1, qh_setsize(qh, ints2));
-                    error_count++;
-                }
-                /* Define prepended elements.  Otherwise qh_setdelnthsorted may fail */
-                for(i= 0; i2){
-                    qh_setzero(qh, ints2, j/2, j-1);  /* max size may be j-1 */
-                    if(qh_setsize(qh, ints2)!=j-1){
-                        qh_fprintf(qh, stderr, 6342, "qh_setzero: Expecting %d elements, got %d\n", j, qh_setsize(qh, ints2));
-                        error_count++;
-                    }
-                    qh_setcompact(qh, ints2);
-                    checkSetContents(qh, "qh_setzero", ints2, j/2, 0, -1, -1);
-                }
-            }
-            qh_setfree(qh, &ints2);
-        }
-    }
-    qh_setfreelong(qh, &ints);
-    if(ints){
-        qh_setfree(qh, &ints); /* Was quick memory */
-    }
-}/*testSetlastEtc*/
-
-void testSettemp(qhT *qh, int numInts, int *intarray, int checkEvery)
-{
-    setT *ints= NULL;
-    setT *ints2= NULL;
-    setT *ints3= NULL;
-    int i,j;
-
-    qh_fprintf(qh, stderr, 8021, "\n\nTesting qh_settemp* 0..%d. Test", numInts-1);
-    for(j=0; j0){
-                qh_settemppush(qh, ints);
-                ints3= qh_settemppop(qh);
-                if(ints!=ints3){
-                    qh_fprintf(qh, stderr, 6343, "qh_settemppop: didn't pop the push\n");
-                    error_count++;
-                }
-            }
-            qh_settempfree(qh, &ints2);
-        }
-    }
-    qh_setfreelong(qh, &ints);
-    if(ints){
-        qh_setfree(qh, &ints); /* Was quick memory */
-    }
-}/*testSettemp*/
-
-/* Check that a set contains count elements
-   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
-   Use -1 for missing ranges
-   Returns -1 if should check results
-*/
-int log_i(qhT *qh, setT *set, const char *s, int i, int numInts, int checkEvery)
-{
-    int j= i;
-    int scale= 1;
-    int e= 0;
-    int *i2, **i2p;
-
-    if(*s || checkEvery==1){
-        if(i<10){
-            qh_fprintf(qh, stderr, 8004, " %s%d", s, i);
-        }else{
-            if(i==11 && checkEvery==1){
-                qh_fprintf(qh, stderr, 8005, "\nResults after 10: ");
-                FOREACHint_(set){
-                    qh_fprintf(qh, stderr, 8006, " %d", *i2);
-                }
-                qh_fprintf(qh, stderr, 8007, " Continue");
-            }
-            while((j= j/10)>=1){
-                scale *= 10;
-                e++;
-            }
-            if(i==numInts-1){
-                qh_fprintf(qh, stderr, 8008, " %s%d", s, i);
-            }else if(i==scale){
-                if(i<=1000){
-                    qh_fprintf(qh, stderr, 8010, " %s%d", s, i);
-                }else{
-                    qh_fprintf(qh, stderr, 8009, " %s1e%d", s, e);
-                }
-            }
-        }
-    }
-    if(i<1000 || i%checkEvery==0 || i== scale || i==numInts-1){
-        return 1;
-    }
-    return 0;
-}/*log_i*/
-
-/* Check that a set contains count elements
-   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
-   Use -1 for missing ranges
-*/
-void checkSetContents(qhT *qh, const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC)
-{
-
-    i2T *i2, **i2p;
-    int i2_i, i2_n;
-    int prev= -1; /* avoid warning */
-    int i;
-    int first= -3;
-    int second= -3;
-    int rangeCount=1;
-    int actualSize= 0;
-
-    qh_setcheck(qh, set, name, 0);
-    if(set){
-        SETreturnsize_(set, actualSize);  /* normally used only when speed is critical */
-        if(*qh_setendpointer(set)!=NULL){
-            qh_fprintf(qh, stderr, 6344, "%s: qh_setendpointer(set), 0x%x, is not NULL terminator of set 0x%x", name, qh_setendpointer(set), set);
-            error_count++;
-        }
-    }
-    if(actualSize!=qh_setsize(qh, set)){
-        qh_fprintf(qh, stderr, 6305, "%s: SETreturnsize_(qh) returned %d while qh_setsize(qh) returns %d\n", name, actualSize, qh_setsize(qh, set));
-        error_count++;
-    }else if(actualSize!=count){
-        qh_fprintf(qh, stderr, 6306, "%s: Expecting %d elements for set.  Got %d elements\n", name, count, actualSize);
-        error_count++;
-    }
-    if(SETempty_(set)){
-        if(count!=0){
-            qh_fprintf(qh, stderr, 6307, "%s: Got empty set instead of count %d, rangeA %d, rangeB %d, rangeC %d\n", name, count, rangeA, rangeB, rangeC);
-            error_count++;
-        }
-    }else{
-        /* Must be first, otherwise trips msvc 8 */
-        i2T **p= SETaddr_(set, i2T);
-        if(*p!=SETfirstt_(set, i2T)){
-            qh_fprintf(qh, stderr, 6309, "%s: SETaddr_(set, i2t) [%p] is not the same as SETfirst_(set) [%p]\n", name, SETaddr_(set, i2T), SETfirst_(set));
-            error_count++;
-        }
-        first= *(int *)SETfirst_(set);
-        if(SETfirst_(set)!=SETfirstt_(set, i2T)){
-            qh_fprintf(qh, stderr, 6308, "%s: SETfirst_(set) [%p] is not the same as SETfirstt_(set, i2T [%p]\n", name, SETfirst_(set), SETfirstt_(set, i2T));
-            error_count++;
-        }
-        if(qh_setsize(qh, set)>1){
-            second= *(int *)SETsecond_(set);
-            if(SETsecond_(set)!=SETsecondt_(set, i2T)){
-                qh_fprintf(qh, stderr, 6310, "%s: SETsecond_(set) [%p] is not the same as SETsecondt_(set, i2T) [%p]\n", name, SETsecond_(set), SETsecondt_(set, i2T));
-                error_count++;
-            }
-        }
-    }
-    /* Test first run of ints in set*/
-    i= 0;
-    FOREACHint_(set){
-        if(i2!=SETfirst_(set) && *i2!=prev+1){
-            break;
-        }
-        prev= *i2;
-        if(SETindex_(set, i2)!=i){
-            qh_fprintf(qh, stderr, 6311, "%s: Expecting SETindex_(set, pointer-to-%d) to be %d.  Got %d\n", name, *i2, i, SETindex_(set, i2));
-            error_count++;;
-        }
-        if(i2!=SETref_(i2)){
-            qh_fprintf(qh, stderr, 6312, "%s: SETref_(i2) [%p] does not point to i2 (the %d'th element)\n", name, SETref_(i2), i);
-            error_count++;;
-        }
-        i++;
-    }
-    FOREACHint_i_(qh, set){
-        /* Must be first conditional, otherwise it trips up msvc 8 */
-        i2T **p= SETelemaddr_(set, i2_i, i2T);
-        if(i2!=*p){
-            qh_fprintf(qh, stderr, 6320, "%s: SETelemaddr_(set, %d, i2T) [%p] does not point to i2\n", name, i2_i, SETelemaddr_(set, i2_i, int));
-            error_count++;;
-        }
-        if(i2_i==0){
-            if(first!=*i2){
-                qh_fprintf(qh, stderr, 6314, "%s: First element is %d instead of SETfirst %d\n", name, *i2, first);
-                error_count++;;
-            }
-            if(rangeA!=*i2){
-                qh_fprintf(qh, stderr, 6315, "%s: starts with %d instead of rangeA %d\n", name, *i2, rangeA);
-                error_count++;;
-            }
-            prev= rangeA;
-        }else{
-            if(i2_i==1 && second!=*i2){
-                qh_fprintf(qh, stderr, 6316, "%s: Second element is %d instead of SETsecond %d\n", name, *i2, second);
-                error_count++;;
-            }
-            if(prev+1==*i2){
-                prev++;
-            }else{
-                if(*i2==rangeB){
-                    prev= rangeB;
-                    rangeB= -1;
-                    rangeCount++;
-                }else if(rangeB==-1 && *i2==rangeC){
-                    prev= rangeC;
-                    rangeC= -1;
-                    rangeCount++;
-                }else{
-                    prev++;
-                    qh_fprintf(qh, stderr, 6317, "%s: Expecting %d'th element to be %d.  Got %d\n", name, i2_i, prev, *i2);
-                    error_count++;
-                }
-            }
-        }
-        if(i2!=SETelem_(set, i2_i)){
-            qh_fprintf(qh, stderr, 6318, "%s: SETelem_(set, %d) [%p] is not i2 [%p] (the %d'th element)\n", name, i2_i, SETelem_(set, i2_i), i2, i2_i);
-            error_count++;;
-        }
-        if(SETelemt_(set, i2_i, i2T)!=SETelem_(set, i2_i)){   /* Normally SETelemt_ is used for generic sets */
-            qh_fprintf(qh, stderr, 6319, "%s: SETelemt_(set, %d, i2T) [%p] is not SETelem_(set, %d) [%p] (the %d'th element)\n", name, i2_i, SETelemt_(set, i2_i, int), i2_i, SETelem_(set, i2_i), i2_i);
-            error_count++;;
-        }
-    }
-    if(error_count>=MAXerrorCount){
-        qh_fprintf(qh, stderr, 8011, "testqset: Stop testing after %d errors\n", error_count);
-        exit(1);
-    }
-}/*checkSetContents*/
-
diff --git a/src/qhull/src/testqset_r/testqset_r.pro b/src/qhull/src/testqset_r/testqset_r.pro
deleted file mode 100644
index 951e0624e..000000000
--- a/src/qhull/src/testqset_r/testqset_r.pro
+++ /dev/null
@@ -1,30 +0,0 @@
-# -------------------------------------------------
-# testqset_r.pro -- Qt project file for testqset_r.exe
-# -------------------------------------------------
-
-include(../qhull-warn.pri)
-
-TARGET = testqset_r
-
-DESTDIR = ../../bin
-TEMPLATE = app
-CONFIG += console warn_on
-CONFIG -= qt
-CONFIG += qhull_warn_conversion
-
-build_pass:CONFIG(debug, debug|release){
-   OBJECTS_DIR = Debug
-}else:build_pass:CONFIG(release, debug|release){
-   OBJECTS_DIR = Release
-}
-
-INCLUDEPATH += ..
-
-SOURCES += testqset_r.c
-SOURCES += ../libqhull_r/qset_r.c
-SOURCES += ../libqhull_r/mem_r.c
-SOURCES += ../libqhull_r/usermem_r.c
-
-HEADERS += ../libqhull_r/mem_r.h
-HEADERS += ../libqhull_r/qset_r.h
-
diff --git a/src/qhull/src/user_eg/user_eg.c b/src/qhull/src/user_eg/user_eg.c
deleted file mode 100644
index 9c5fee51b..000000000
--- a/src/qhull/src/user_eg/user_eg.c
+++ /dev/null
@@ -1,330 +0,0 @@
-/*
      ---------------------------------
-
-  user_eg.c
-  sample code for calling qhull() from an application
-
-  call with:
-
-     user_eg "cube/diamond options" "delaunay options" "halfspace options"
-
-  for example:
-
-     user_eg                             # return summaries
-
-     user_eg "n" "o" "Fp"                # return normals, OFF, points
-
-     user_eg "n Qt" "o" "Fp"             # triangulated cube
-
-     user_eg "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
-                                         # 'v' returns Voronoi
-                                         # transform is rotated for halfspaces
-
-   main() makes three runs of qhull.
-
-     1) compute the convex hull of a cube
-
-     2a) compute the Delaunay triangulation of random points
-
-     2b) find the Delaunay triangle closest to a point.
-
-     3) compute the halfspace intersection of a diamond
-
- notes:
-
-   For another example, see main() in unix.c and user_eg2.c.
-   These examples, call qh_qhull() directly.  They allow
-   tighter control on the code loaded with Qhull.
-
-   For a C++ example, see user_eg3/user_eg3_r.cpp
-
-   Summaries are sent to stderr if other output formats are used
-
-   compiled by 'make bin/user_eg'
-
-   see libqhull.h for data structures, macros, and user-callable functions.
-*/
-
-#define qh_QHimport
-#include "libqhull/qhull_a.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary(void);
-void makecube(coordT *points, int numpoints, int dim);
-void makeDelaunay(coordT *points, int numpoints, int dim, int seed);
-void findDelaunay(int dim);
-void makehalf(coordT *points, int numpoints, int dim);
-
-/*-------------------------------------------------
--print_summary()
-*/
-void print_summary(void) {
-  facetT *facet;
-  int k;
-
-  printf("\n%d vertices and %d facets with normals:\n",
-                 qh num_vertices, qh num_facets);
-  FORALLfacets {
-    for (k=0; k < qh hull_dim; k++)
-      printf("%6.2g ", facet->normal[k]);
-    printf("\n");
-  }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
-  points is numpoints X dim
-*/
-void makecube(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; jlocate a facet with qh_findbestfacet()
-*/
-void findDelaunay(int dim) {
-  int k;
-  coordT point[ 100];
-  boolT isoutside;
-  realT bestdist;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  for (k= 0; k < dim; k++)
-    point[k]= 0.5;
-  qh_setdelaunay(dim+1, 1, point);
-  facet= qh_findbestfacet(point, qh_ALL, &bestdist, &isoutside);
-  if (facet->tricoplanar) {
-    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
-       facet->id);
-    qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  FOREACHvertex_(facet->vertices) {
-    for (k=0; k < dim; k++)
-      printf("%5.2f ", vertex->point[k]);
-    printf("\n");
-  }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-dimensional diamond
-  points is numpoints X dim+1
-
-  each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; j&1'\n\n");
-
-#if qh_QHpointer  /* see user.h */
-  if (qh_qh){
-      printf("QH6233: Qhull link error.  The global variable qh_qh was not initialized\n\
-to NULL by global.c.  Please compile user_eg.c with -Dqh_QHpointer_dllimport\n\
-as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
-      return -1;
-  }
-#endif
-
-  /*
-    Run 1: convex hull
-  */
-  printf( "\ncompute convex hull of cube after rotating input\n");
-  sprintf(flags, "qhull s Tcv %s", argc >= 2 ? argv[1] : "");
-  numpoints= SIZEcube;
-  makecube(points, numpoints, DIM);
-  for (i=numpoints; i--; )
-    rows[i]= points+dim*i;
-  qh_printmatrix(outfile, "input", rows, numpoints, dim);
-  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh facet_list' contains the convex hull */
-    print_summary();
-    FORALLfacets {
-       /* ... your code ... */
-    }
-  }
-  qh_freeqhull(!qh_ALL);                   /* free long memory  */
-  qh_memfreeshort(&curlong, &totlong);    /* free short memory and memory allocator */
-  if (curlong || totlong)
-    fprintf(errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
-  /*
-    Run 2: Delaunay triangulation
-  */
-
-  printf( "\ncompute %d-d Delaunay triangulation\n", dim);
-  sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-  numpoints= SIZEcube;
-  makeDelaunay(points, numpoints, dim, (int)time(NULL));
-  for (i=numpoints; i--; )
-    rows[i]= points+dim*i;
-  qh_printmatrix(outfile, "input", rows, numpoints, dim);
-  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh facet_list' contains the convex hull */
-    /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
-       call qh_setvoronoi_all() after qh_new_qhull(). */
-    print_summary();
-    FORALLfacets {
-       /* ... your code ... */
-    }
-    printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
-    exitcode= setjmp(qh errexit);
-    if (!exitcode) {
-      /* Trap Qhull errors in findDelaunay().  Without the setjmp(), Qhull
-         will exit() after reporting an error */
-      qh NOerrexit= False;
-      findDelaunay(DIM);
-    }
-    qh NOerrexit= True;
-  }
-#if qh_QHpointer  /* see user.h */
-  {
-    qhT *oldqhA, *oldqhB;
-    coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */
-
-    printf( "\nsave first triangulation and compute a new triangulation\n");
-    oldqhA= qh_save_qhull();
-    sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-    numpoints= SIZEcube;
-    makeDelaunay(pointsB, numpoints, dim, (int)time(NULL)+1);
-    for (i=numpoints; i--; )
-      rows[i]= pointsB+dim*i;
-    qh_printmatrix(outfile, "input", rows, numpoints, dim);
-    exitcode= qh_new_qhull(dim, numpoints, pointsB, ismalloc,
-                      flags, outfile, errfile);
-    if (!exitcode)
-      print_summary();
-    printf( "\nsave second triangulation and restore first one\n");
-    oldqhB= qh_save_qhull();
-    qh_restore_qhull(&oldqhA);
-    print_summary();
-    printf( "\nfree first triangulation and restore second one.\n");
-    qh_freeqhull(qh_ALL);               /* free short and long memory used by first call */
-                                         /* do not use qh_memfreeshort */
-    qh_restore_qhull(&oldqhB);
-    print_summary();
-  }
-#endif
-  qh_freeqhull(!qh_ALL);                 /* free long memory */
-  qh_memfreeshort(&curlong, &totlong);  /* free short memory and memory allocator */
-  if (curlong || totlong)
-    fprintf(errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
-  /*
-    Run 3: halfspace intersection about the origin
-  */
-  printf( "\ncompute halfspace intersection about the origin for a diamond\n");
-  sprintf(flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
-  numpoints= SIZEcube;
-  makehalf(points, numpoints, dim);
-  for (i=numpoints; i--; )
-    rows[i]= points+(dim+1)*i;
-  qh_printmatrix(outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
-  /* use qh_sethalfspace_all to transform the halfspaces yourself.
-     If so, set 'qh feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
-  */
-  exitcode= qh_new_qhull(dim+1, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode)
-    print_summary();
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)  /* could also check previous runs */
-    fprintf(stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/user_eg/user_eg.pro b/src/qhull/src/user_eg/user_eg.pro
deleted file mode 100644
index 9dda01009..000000000
--- a/src/qhull/src/user_eg/user_eg.pro
+++ /dev/null
@@ -1,11 +0,0 @@
-# -------------------------------------------------
-# user_eg.pro -- Qt project for Qhull demonstration using shared Qhull library
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(../qhull-app-shared_r.pri)
-
-TARGET = user_eg
-
-SOURCES += user_eg_r.c
diff --git a/src/qhull/src/user_eg/user_eg_r.c b/src/qhull/src/user_eg/user_eg_r.c
deleted file mode 100644
index 21b0ccf4e..000000000
--- a/src/qhull/src/user_eg/user_eg_r.c
+++ /dev/null
@@ -1,326 +0,0 @@
-/*
      ---------------------------------
-
-  user_eg_r.c
-  sample code for calling qhull() from an application.  Uses reentrant libqhull_r
-
-  call with:
-
-     user_eg "cube/diamond options" "delaunay options" "halfspace options"
-
-  for example:
-
-     user_eg                             # return summaries
-
-     user_eg "n" "o" "Fp"                # return normals, OFF, points
-
-     user_eg "n Qt" "o" "Fp"             # triangulated cube
-
-     user_eg "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
-                                         # 'v' returns Voronoi
-                                         # transform is rotated for halfspaces
-
-   main() makes three runs of qhull.
-
-     1) compute the convex hull of a cube
-
-     2a) compute the Delaunay triangulation of random points
-
-     2b) find the Delaunay triangle closest to a point.
-
-     3) compute the halfspace intersection of a diamond
-
- notes:
-
-   For another example, see main() in unix_r.c and user_eg2_r.c.
-   These examples, call qh_qhull() directly.  They allow
-   tighter control on the code loaded with Qhull.
-
-   For a C++ example, see user_eg3/user_eg3_r.cpp
-
-   Summaries are sent to stderr if other output formats are used
-
-   compiled by 'make bin/user_eg'
-
-   see libqhull.h for data structures, macros, and user-callable functions.
-*/
-
-#define qh_QHimport
-#include "libqhull_r/qhull_ra.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary(qhT *qh);
-void makecube(coordT *points, int numpoints, int dim);
-void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim, int seed);
-void findDelaunay(qhT *qh, int dim);
-void makehalf(coordT *points, int numpoints, int dim);
-
-/*-------------------------------------------------
--print_summary(qh)
-*/
-void print_summary(qhT *qh) {
-  facetT *facet;
-  int k;
-
-  printf("\n%d vertices and %d facets with normals:\n",
-                 qh->num_vertices, qh->num_facets);
-  FORALLfacets {
-    for (k=0; k < qh->hull_dim; k++)
-      printf("%6.2g ", facet->normal[k]);
-    printf("\n");
-  }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
-  points is numpoints X dim
-*/
-void makecube(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; jlocate a facet with qh_findbestfacet()
-*/
-void findDelaunay(qhT *qh, int dim) {
-  int k;
-  coordT point[ 100];
-  boolT isoutside;
-  realT bestdist;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  for (k= 0; k < dim; k++)
-    point[k]= 0.5;
-  qh_setdelaunay(qh, dim+1, 1, point);
-  facet= qh_findbestfacet(qh, point, qh_ALL, &bestdist, &isoutside);
-  if (facet->tricoplanar) {
-    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
-       facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  FOREACHvertex_(facet->vertices) {
-    for (k=0; k < dim; k++)
-      printf("%5.2f ", vertex->point[k]);
-    printf("\n");
-  }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-dimensional diamond
-  points is numpoints X dim+1
-
-  each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; j&1'\n\n");
-
-  /*
-    Run 1: convex hull
-  */
-  printf( "\ncompute convex hull of cube after rotating input\n");
-  sprintf(flags, "qhull s Tcv %s", argc >= 2 ? argv[1] : "");
-  numpoints= SIZEcube;
-  makecube(points, numpoints, DIM);
-  for (i=numpoints; i--; )
-    rows[i]= points+dim*i;
-  qh_printmatrix(qh, outfile, "input", rows, numpoints, dim);
-  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh->facet_list' contains the convex hull */
-    print_summary(qh);
-    FORALLfacets {
-       /* ... your code ... */
-    }
-  }
-  qh_freeqhull(qh, !qh_ALL);                   /* free long memory  */
-  qh_memfreeshort(qh, &curlong, &totlong);    /* free short memory and memory allocator */
-  if (curlong || totlong)
-    fprintf(errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
-  /*
-    Run 2: Delaunay triangulation, reusing the previous qh/qh_qh
-  */
-
-  printf( "\ncompute %d-d Delaunay triangulation\n", dim);
-  sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-  numpoints= SIZEcube;
-  makeDelaunay(qh, points, numpoints, dim, (int)time(NULL));
-  for (i=numpoints; i--; )
-    rows[i]= points+dim*i;
-  qh_printmatrix(qh, outfile, "input", rows, numpoints, dim);
-  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode) {                  /* if no error */
-    /* 'qh->facet_list' contains the convex hull */
-    /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
-       call qh_setvoronoi_all() after qh_new_qhull(). */
-    print_summary(qh);
-    FORALLfacets {
-       /* ... your code ... */
-    }
-    printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
-    exitcode= setjmp(qh->errexit);
-    if (!exitcode) {
-      /* Trap Qhull errors in findDelaunay().  Without the setjmp(), Qhull
-         will exit() after reporting an error */
-      qh->NOerrexit= False;
-      findDelaunay(qh, DIM);
-    }
-    qh->NOerrexit= True;
-  }
-  {
-    coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */
-
-    qhT qh_qhB;    /* Create a new instance of Qhull (qhB) */
-    qhT *qhB= &qh_qhB;
-    qh_zero(qhB, errfile);
-
-    printf( "\nCompute a new triangulation as a separate instance of Qhull\n");
-    sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-    numpoints= SIZEcube;
-    makeDelaunay(qhB, pointsB, numpoints, dim, (int)time(NULL)+1);
-    for (i=numpoints; i--; )
-      rows[i]= pointsB+dim*i;
-    qh_printmatrix(qhB, outfile, "input", rows, numpoints, dim);
-    exitcode= qh_new_qhull(qhB, dim, numpoints, pointsB, ismalloc,
-                      flags, outfile, errfile);
-    if (!exitcode)
-      print_summary(qhB);
-    printf( "\nFree memory allocated by the new instance of Qhull, and redisplay the old results.\n");
-    qh_freeqhull(qhB, !qh_ALL);                 /* free long memory */
-    qh_memfreeshort(qhB, &curlong, &totlong);  /* free short memory and memory allocator */
-    if (curlong || totlong)
-        fprintf(errfile, "qhull internal warning (user_eg, #4): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
-    printf( "\n\n");
-    print_summary(qh);  /* The other instance is unchanged */
-    /* Exiting the block frees qh_qhB */
-  }
-  qh_freeqhull(qh, !qh_ALL);                 /* free long memory */
-  qh_memfreeshort(qh, &curlong, &totlong);  /* free short memory and memory allocator */
-  if (curlong || totlong)
-    fprintf(errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
-  /*
-    Run 3: halfspace intersection about the origin
-  */
-  printf( "\ncompute halfspace intersection about the origin for a diamond\n");
-  sprintf(flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
-  numpoints= SIZEcube;
-  makehalf(points, numpoints, dim);
-  for (i=numpoints; i--; )
-    rows[i]= points+(dim+1)*i;
-  qh_printmatrix(qh, outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
-  /* use qh_sethalfspace_all to transform the halfspaces yourself.
-     If so, set 'qh->feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
-  */
-  exitcode= qh_new_qhull(qh, dim+1, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-  if (!exitcode)
-    print_summary(qh);
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)  /* could also check previous runs */
-    fprintf(stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-  return exitcode;
-} /* main */
-
diff --git a/src/qhull/src/user_eg2/user_eg2.c b/src/qhull/src/user_eg2/user_eg2.c
deleted file mode 100644
index a455f025d..000000000
--- a/src/qhull/src/user_eg2/user_eg2.c
+++ /dev/null
@@ -1,746 +0,0 @@
-/*
      ---------------------------------
-
-  user_eg2.c
-
-  sample code for calling qhull() from an application.
-
-  See user_eg.c for a simpler method using qh_new_qhull().
-  The method used here and in unix.c gives you additional
-  control over Qhull.
-
-  See user_eg3/user_eg3_r.cpp for a C++ example
-
-  call with:
-
-     user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"
-
-  for example:
-
-     user_eg2                             # return summaries
-
-     user_eg2 "n" "o" "Fp"                # return normals, OFF, points
-
-     user_eg2 "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
-                                         # 'v' returns Voronoi
-                                         # transform is rotated for halfspaces
-
-   main() makes three runs of qhull.
-
-     1) compute the convex hull of a cube, and incrementally add a diamond
-
-     2a) compute the Delaunay triangulation of random points, and add points.
-
-     2b) find the Delaunay triangle closest to a point.
-
-     3) compute the halfspace intersection of a diamond, and add a cube
-
- notes:
-
-   summaries are sent to stderr if other output formats are used
-
-   derived from unix.c and compiled by 'make bin/user_eg2'
-
-   see libqhull.h for data structures, macros, and user-callable functions.
-
-   If you want to control all output to stdio and input to stdin,
-   set the #if below to "1" and delete all lines that contain "io.c".
-   This prevents the loading of io.o.  Qhull will
-   still write to 'qh ferr' (stderr) for error reporting and tracing.
-
-   Defining #if 1, also prevents user.o from being loaded.
-*/
-
-#include "libqhull/qhull_a.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary(void);
-void makecube(coordT *points, int numpoints, int dim);
-void adddiamond(coordT *points, int numpoints, int numnew, int dim);
-void makeDelaunay(coordT *points, int numpoints, int dim);
-void addDelaunay(coordT *points, int numpoints, int numnew, int dim);
-void findDelaunay(int dim);
-void makehalf(coordT *points, int numpoints, int dim);
-void addhalf(coordT *points, int numpoints, int numnew, int dim, coordT *feasible);
-
-/*-------------------------------------------------
--print_summary()
-*/
-void print_summary(void) {
-  facetT *facet;
-  int k;
-
-  printf("\n%d vertices and %d facets with normals:\n",
-                 qh num_vertices, qh num_facets);
-  FORALLfacets {
-    for (k=0; k < qh hull_dim; k++)
-      printf("%6.2g ", facet->normal[k]);
-    printf("\n");
-  }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
-  points is numpoints X dim
-*/
-void makecube(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; jlocate a facet with qh_findbestfacet()
-*/
-void findDelaunay(int dim) {
-  int k;
-  coordT point[ 100];
-  boolT isoutside;
-  realT bestdist;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  for (k= 0; k < dim-1; k++)
-    point[k]= 0.5;
-  qh_setdelaunay(dim, 1, point);
-  facet= qh_findbestfacet(point, qh_ALL, &bestdist, &isoutside);
-  if (facet->tricoplanar) {
-    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
-       facet->id);
-    qh_errexit(qh_ERRqhull, facet, NULL);
-  }
-  FOREACHvertex_(facet->vertices) {
-    for (k=0; k < dim-1; k++)
-      printf("%5.2f ", vertex->point[k]);
-    printf("\n");
-  }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-d diamond
-  points is numpoints X dim+1
-
-  each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; j= 2 ? argv[1] : "");
-    qh_initflags(options);
-    printf( "\ncompute triangulated convex hull of cube after rotating input\n");
-    makecube(array[0], SIZEcube, DIM);
-    qh_init_B(array[0], SIZEcube, DIM, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_triangulate();  /* requires option 'Q11' if want to add points */
-    print_summary();
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    printf( "\nadd points in a diamond\n");
-    adddiamond(array[0], SIZEcube, SIZEdiamond, DIM);
-    qh_check_output();
-    print_summary();
-    qh_produce_output();  /* delete this line to help avoid io.c */
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-  }
-  qh NOerrexit= True;
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf(stderr, "qhull warning (user_eg, run 1): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-
-  /*
-    Run 2: Delaunay triangulation
-  */
-  qh_init_A(stdin, stdout, stderr, 0, NULL);
-  exitcode= setjmp(qh errexit);
-  if (!exitcode) {
-    coordT array[TOTpoints][DIM];
-
-    strcat(qh rbox_command, "user_eg Delaunay");
-    sprintf(options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-    qh_initflags(options);
-    printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
-    makeDelaunay(array[0], SIZEcube, DIM);
-    /* Instead of makeDelaunay with qh_setdelaunay, you may
-       produce a 2-d array of points, set DIM to 2, and set
-       qh PROJECTdelaunay to True.  qh_init_B will call
-       qh_projectinput to project the points to the paraboloid
-       and add a point "at-infinity".
-    */
-    qh_init_B(array[0], SIZEcube, DIM, ismalloc);
-    qh_qhull();
-    /* If you want Voronoi ('v') without qh_produce_output(), call
-       qh_setvoronoi_all() after qh_qhull() */
-    qh_check_output();
-    print_summary();
-    qh_produce_output();  /* delete this line to help avoid io.c */
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    printf( "\nadd points to triangulation\n");
-    addDelaunay(array[0], SIZEcube, SIZEdiamond, DIM);
-    qh_check_output();
-    qh_produce_output();  /* delete this line to help avoid io.c */
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
-    findDelaunay(DIM);
-  }
-  qh NOerrexit= True;
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf(stderr, "qhull warning (user_eg, run 2): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-
-  /*
-    Run 3: halfspace intersection
-  */
-  qh_init_A(stdin, stdout, stderr, 0, NULL);
-  exitcode= setjmp(qh errexit);
-  if (!exitcode) {
-    coordT array[TOTpoints][DIM+1];  /* +1 for halfspace offset */
-    pointT *points;
-
-    strcat(qh rbox_command, "user_eg halfspaces");
-    sprintf(options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
-    qh_initflags(options);
-    printf( "\ncompute halfspace intersection about the origin for a diamond\n");
-    makehalf(array[0], SIZEcube, DIM);
-    qh_setfeasible(DIM); /* from io.c, sets qh feasible_point from 'Hn,n' */
-    /* you may malloc and set qh feasible_point directly.  It is only used for
-       option 'Fp' */
-    points= qh_sethalfspace_all( DIM+1, SIZEcube, array[0], qh feasible_point);
-    qh_init_B(points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();  /* delete this line to help avoid io.c */
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    printf( "\nadd halfspaces for cube to intersection\n");
-    addhalf(array[0], SIZEcube, SIZEdiamond, DIM, qh feasible_point);
-    qh_check_output();
-    qh_produce_output();  /* delete this line to help avoid io.c */
-    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-  }
-  qh NOerrexit= True;
-  qh NOerrexit= True;
-  qh_freeqhull(!qh_ALL);
-  qh_memfreeshort(&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf(stderr, "qhull warning (user_eg, run 3): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-  return exitcode;
-} /* main */
-
-#if 1    /* use 1 to prevent loading of io.o and user.o */
-/*-------------------------------------------
--errexit- return exitcode to system after an error
-  assumes exitcode non-zero
-  prints useful information
-  see qh_errexit2() in libqhull.c for 2 facets
-*/
-void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
-  QHULL_UNUSED(facet);
-  QHULL_UNUSED(ridge);
-
-  if (qh ERREXITcalled) {
-    fprintf(qh ferr, "qhull error while processing previous error.  Exit program\n");
-    exit(1);
-  }
-  qh ERREXITcalled= True;
-  if (!qh QHULLfinished)
-    qh hulltime= (unsigned)clock() - qh hulltime;
-  fprintf(qh ferr, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
-  fprintf(qh ferr, "Options selected:\n%s\n", qh qhull_options);
-  if (qh furthest_id >= 0) {
-    fprintf(qh ferr, "\nLast point added to hull was p%d", qh furthest_id);
-    if (zzval_(Ztotmerge))
-      fprintf(qh ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
-    if (qh QHULLfinished)
-      fprintf(qh ferr, "\nQhull has finished constructing the hull.");
-    else if (qh POSTmerging)
-      fprintf(qh ferr, "\nQhull has started post-merging");
-    fprintf(qh ferr, "\n\n");
-  }
-  if (qh NOerrexit) {
-    fprintf(qh ferr, "qhull error while ending program.  Exit program\n");
-    exit(1);
-  }
-  if (!exitcode)
-    exitcode= qh_ERRqhull;
-  qh NOerrexit= True;
-  longjmp(qh errexit, exitcode);
-} /* errexit */
-
-
-/*-------------------------------------------
--errprint- prints out the information of the erroneous object
-    any parameter may be NULL, also prints neighbors and geomview output
-*/
-void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-
-  fprintf(qh ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
-           string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
-           getid_(atvertex));
-} /* errprint */
-
-
-void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
-  facetT *facet, **facetp;
-
-  /* remove these calls to help avoid io.c */
-  qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
-  FORALLfacet_(facetlist)                                              /*io.c*/
-    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
-  FOREACHfacet_(facets)                                                /*io.c*/
-    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
-  qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);  /*io.c*/
-
-  FORALLfacet_(facetlist)
-    fprintf( qh ferr, "facet f%d\n", facet->id);
-} /* printfacetlist */
-
-/* qh_printhelp_degenerate( fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(FILE *fp) {
-
-  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
-    qh_fprintf(fp, 9368, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
-  else if (!qh_QUICKhelp) {
-    qh_fprintf(fp, 9369, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    qh_fprintf(fp, 9370, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
-      qh_fprintf(fp, 9371, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh DELAUNAY && !qh ATinfinity)
-      qh_fprintf(fp, 9372, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    qh_fprintf(fp, 9373, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh DISTround);
-    qh_fprintf(fp, 9374, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/* qh_printhelp_narrowhull( minangle )
-     Warn about a narrow hull
-
-  notes:
-    Alternatively, reduce qh_WARNnarrow in user.h
-
-*/
-void qh_printhelp_narrowhull(FILE *fp, realT minangle) {
-
-    qh_fprintf(fp, 9375, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
-or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
-this warning.  See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-} /* printhelp_narrowhull */
-
-/* qh_printhelp_singular
-      prints descriptive message for singular input
-*/
-void qh_printhelp_singular(FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  qh_fprintf(fp, 9376, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh hull_dim);
-  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    qh_fprintf(fp, 9377, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh DISTround);
-  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, -1);
-  qh_fprintf(fp, 9378, "\n");
-  FORALLfacets {
-    qh_fprintf(fp, 9379, "facet");
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh interior_point, facet, &dist);
-    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh HALFspace)
-      qh_fprintf(fp, 9382, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    qh_fprintf(fp, 9383,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh hull_dim >= qh_INITIALmax)
-      qh_fprintf(fp, 9384, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    qh_fprintf(fp, 9387, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh DISTround);
-#if REALfloat
-    qh_fprintf(fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
-#endif
-    qh_fprintf(fp, 9389, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-    if (qh DELAUNAY && !qh ATinfinity)
-      qh_fprintf(fp, 9390, "\n\n\
-This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
-  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
-  - or use 'QJ' to joggle the input and avoid co-circular data\n");
-  }
-} /* printhelp_singular */
-
-
-/*-----------------------------------------
--user_memsizes- allocate up to 10 additional, quick allocation sizes
-*/
-void qh_user_memsizes(void) {
-
-  /* qh_memsize(size); */
-} /* user_memsizes */
-
-#endif
diff --git a/src/qhull/src/user_eg2/user_eg2.pro b/src/qhull/src/user_eg2/user_eg2.pro
deleted file mode 100644
index c841bfe13..000000000
--- a/src/qhull/src/user_eg2/user_eg2.pro
+++ /dev/null
@@ -1,11 +0,0 @@
-# -------------------------------------------------
-# user_eg2.pro -- Qt project for Qhull demonstration using the static Qhull library
-#
-# It uses reentrant Qhull
-# -------------------------------------------------
-
-include(../qhull-app-c_r.pri)
-
-TARGET = user_eg2
-
-SOURCES += user_eg2_r.c
diff --git a/src/qhull/src/user_eg2/user_eg2_r.c b/src/qhull/src/user_eg2/user_eg2_r.c
deleted file mode 100644
index 2f8b4e6c7..000000000
--- a/src/qhull/src/user_eg2/user_eg2_r.c
+++ /dev/null
@@ -1,742 +0,0 @@
-/*
      ---------------------------------
-
-  user_eg2_r.c
-
-  sample code for calling qhull() from an application.
-
-  See user_eg_r.c for a simpler method using qh_new_qhull().
-  The method used here and in unix_r.c gives you additional
-  control over Qhull.
-
-  See user_eg3/user_eg3_r.cpp for a C++ example
-
-  call with:
-
-     user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"
-
-  for example:
-
-     user_eg2                             # return summaries
-
-     user_eg2 "n" "o" "Fp"                # return normals, OFF, points
-
-     user_eg2 "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
-                                         # 'v' returns Voronoi
-                                         # transform is rotated for halfspaces
-
-   main() makes three runs of qhull.
-
-     1) compute the convex hull of a cube, and incrementally add a diamond
-
-     2a) compute the Delaunay triangulation of random points, and add points.
-
-     2b) find the Delaunay triangle closest to a point.
-
-     3) compute the halfspace intersection of a diamond, and add a cube
-
- notes:
-
-   summaries are sent to stderr if other output formats are used
-
-   derived from unix.c and compiled by 'make bin/user_eg2'
-
-   see libqhull.h for data structures, macros, and user-callable functions.
-
-   If you want to control all output to stdio and input to stdin,
-   set the #if below to "1" and delete all lines that contain "io.c".
-   This prevents the loading of io.o.  Qhull will
-   still write to 'qh->ferr' (stderr) for error reporting and tracing.
-
-   Defining #if 1, also prevents user.o from being loaded.
-*/
-
-#include "libqhull_r/qhull_ra.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary(qhT *qh);
-void makecube(coordT *points, int numpoints, int dim);
-void adddiamond(qhT *qh, coordT *points, int numpoints, int numnew, int dim);
-void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim);
-void addDelaunay(qhT *qh, coordT *points, int numpoints, int numnew, int dim);
-void findDelaunay(qhT *qh, int dim);
-void makehalf(coordT *points, int numpoints, int dim);
-void addhalf(qhT *qh, coordT *points, int numpoints, int numnew, int dim, coordT *feasible);
-
-/*-------------------------------------------------
--print_summary(qh)
-*/
-void print_summary(qhT *qh) {
-  facetT *facet;
-  int k;
-
-  printf("\n%d vertices and %d facets with normals:\n",
-                 qh->num_vertices, qh->num_facets);
-  FORALLfacets {
-    for (k=0; k < qh->hull_dim; k++)
-      printf("%6.2g ", facet->normal[k]);
-    printf("\n");
-  }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
-  points is numpoints X dim
-*/
-void makecube(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; jfirst_point)  /* in case of 'QRn' */
-      qh->num_points= numpoints+j+1;
-    /* qh.num_points sets the size of the points array.  You may
-       allocate the points elsewhere.  If so, qh_addpoint records
-       the point's address in qh->other_points
-    */
-    for (k=dim; k--; ) {
-      if (j/2 == k)
-        point[k]= (j & 1) ? 2.0 : -2.0;
-      else
-        point[k]= 0.0;
-    }
-    facet= qh_findbestfacet(qh, point, !qh_ALL, &bestdist, &isoutside);
-    if (isoutside) {
-      if (!qh_addpoint(qh, point, facet, False))
-        break;  /* user requested an early exit with 'TVn' or 'TCn' */
-    }
-    printf("%d vertices and %d facets\n",
-                 qh->num_vertices, qh->num_facets);
-    /* qh_produce_output(); */
-  }
-  if (qh->DOcheckmax)
-    qh_check_maxout(qh);
-  else if (qh->KEEPnearinside)
-    qh_nearcoplanar(qh);
-} /*.adddiamond.*/
-
-/*--------------------------------------------------
--makeDelaunay- set points for dim-1 Delaunay triangulation of random points
-  points is numpoints X dim.  Each point is projected to a paraboloid.
-*/
-void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim) {
-  int j,k, seed;
-  coordT *point, realr;
-
-  seed= (int)time(NULL); /* time_t to int */
-  printf("seed: %d\n", seed);
-  qh_RANDOMseed_(qh, seed);
-  for (j=0; jfirst_point)  /* in case of 'QRn' */
-      qh->num_points= numpoints+j+1;
-    /* qh.num_points sets the size of the points array.  You may
-       allocate the point elsewhere.  If so, qh_addpoint records
-       the point's address in qh->other_points
-    */
-    for (k= 0; k < dim-1; k++) {
-      realr= qh_RANDOMint;
-      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
-    }
-    qh_setdelaunay(qh, dim, 1, point);
-    facet= qh_findbestfacet(qh, point, !qh_ALL, &bestdist, &isoutside);
-    if (isoutside) {
-      if (!qh_addpoint(qh, point, facet, False))
-        break;  /* user requested an early exit with 'TVn' or 'TCn' */
-    }
-    qh_printpoint(qh, stdout, "added point", point);
-    printf("%d points, %d extra points, %d vertices, and %d facets in total\n",
-                  qh->num_points, qh_setsize(qh, qh->other_points),
-                  qh->num_vertices, qh->num_facets);
-
-    /* qh_produce_output(qh); */
-  }
-  if (qh->DOcheckmax)
-    qh_check_maxout(qh);
-  else if (qh->KEEPnearinside)
-    qh_nearcoplanar(qh);
-} /*.addDelaunay.*/
-
-/*--------------------------------------------------
--findDelaunay- find Delaunay triangle for [0.5,0.5,...]
-  assumes dim < 100
-notes:
-  calls qh_setdelaunay() to project the point to a parabaloid
-warning:
-  This is not implemented for tricoplanar facets ('Qt'),
-  See locate a facet with qh_findbestfacet()
-*/
-void findDelaunay(qhT *qh, int dim) {
-  int k;
-  coordT point[ 100];
-  boolT isoutside;
-  realT bestdist;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  for (k= 0; k < dim-1; k++)
-    point[k]= 0.5;
-  qh_setdelaunay(qh, dim, 1, point);
-  facet= qh_findbestfacet(qh, point, qh_ALL, &bestdist, &isoutside);
-  if (facet->tricoplanar) {
-    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
-       facet->id);
-    qh_errexit(qh, qh_ERRqhull, facet, NULL);
-  }
-  FOREACHvertex_(facet->vertices) {
-    for (k=0; k < dim-1; k++)
-      printf("%5.2f ", vertex->point[k]);
-    printf("\n");
-  }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-d diamond
-  points is numpoints X dim+1
-
-  each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf(coordT *points, int numpoints, int dim) {
-  int j,k;
-  coordT *point;
-
-  for (j=0; jnum_points, qh_setsize(qh, qh->other_points),
-                  qh->num_vertices, qh->num_facets);
-    /* qh_produce_output(qh); */
-  }
-  if (qh->DOcheckmax)
-    qh_check_maxout(qh);
-  else if (qh->KEEPnearinside)
-    qh_nearcoplanar(qh);
-} /*.addhalf.*/
-
-#define DIM 3     /* dimension of points, must be < 31 for SIZEcube */
-#define SIZEcube (1<&1'\n\n");
-
-  ismalloc= False;      /* True if qh_freeqhull should 'free(array)' */
-  /*
-    Run 1: convex hull
-  */
-  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
-  exitcode= setjmp(qh->errexit);
-  if (!exitcode) {
-    coordT array[TOTpoints][DIM];
-
-    qh->NOerrexit= False;
-    strcat(qh->rbox_command, "user_eg2 cube example");
-    sprintf(options, "qhull s Tcv Q11 %s ", argc >= 2 ? argv[1] : "");
-    qh_initflags(qh, options);
-    printf( "\ncompute triangulated convex hull of cube after rotating input\n");
-    makecube(array[0], SIZEcube, DIM);
-    qh_init_B(qh, array[0], SIZEcube, DIM, ismalloc);
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_triangulate(qh);  /* requires option 'Q11' if want to add points */
-    print_summary(qh);
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    printf( "\nadd points in a diamond\n");
-    adddiamond(qh, array[0], SIZEcube, SIZEdiamond, DIM);
-    qh_check_output(qh);
-    print_summary(qh);
-    qh_produce_output(qh);  /* delete this line to help avoid io.c */
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-  }
-  qh->NOerrexit= True;
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-      fprintf(stderr, "qhull warning (user_eg2, run 1): did not free %d bytes of long memory (%d pieces)\n",
-          totlong, curlong);
-  /*
-    Run 2: Delaunay triangulation
-  */
-  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
-  exitcode= setjmp(qh->errexit);
-  if (!exitcode) {
-    coordT array[TOTpoints][DIM];
-
-    qh->NOerrexit= False;
-    strcat(qh->rbox_command, "user_eg2 Delaunay example");
-    sprintf(options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
-    qh_initflags(qh, options);
-    printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
-    makeDelaunay(qh, array[0], SIZEcube, DIM);
-    /* Instead of makeDelaunay with qh_setdelaunay, you may
-       produce a 2-d array of points, set DIM to 2, and set
-       qh->PROJECTdelaunay to True.  qh_init_B will call
-       qh_projectinput to project the points to the paraboloid
-       and add a point "at-infinity".
-    */
-    qh_init_B(qh, array[0], SIZEcube, DIM, ismalloc);
-    qh_qhull(qh);
-    /* If you want Voronoi ('v') without qh_produce_output(), call
-       qh_setvoronoi_all() after qh_qhull() */
-    qh_check_output(qh);
-    print_summary(qh);
-    qh_produce_output(qh);  /* delete this line to help avoid io.c */
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    printf( "\nadd points to triangulation\n");
-    addDelaunay(qh, array[0], SIZEcube, SIZEdiamond, DIM);
-    qh_check_output(qh);
-    qh_produce_output(qh);  /* delete this line to help avoid io.c */
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
-    findDelaunay(qh, DIM);
-  }
-  qh->NOerrexit= True;
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong) 
-      fprintf(stderr, "qhull warning (user_eg2, run 2): did not free %d bytes of long memory (%d pieces)\n",
-         totlong, curlong);
-  /*
-    Run 3: halfspace intersection
-  */
-  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
-  exitcode= setjmp(qh->errexit);
-  if (!exitcode) {
-    coordT array[TOTpoints][DIM+1];  /* +1 for halfspace offset */
-    pointT *points;
-
-    qh->NOerrexit= False;
-    strcat(qh->rbox_command, "user_eg2 halfspace example");
-    sprintf(options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
-    qh_initflags(qh, options);
-    printf( "\ncompute halfspace intersection about the origin for a diamond\n");
-    makehalf(array[0], SIZEcube, DIM);
-    qh_setfeasible(qh, DIM); /* from io.c, sets qh->feasible_point from 'Hn,n' */
-    /* you may malloc and set qh->feasible_point directly.  It is only used for
-       option 'Fp' */
-    points= qh_sethalfspace_all(qh, DIM+1, SIZEcube, array[0], qh->feasible_point);
-    qh_init_B(qh, points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
-    qh_qhull(qh);
-    qh_check_output(qh);
-    qh_produce_output(qh);  /* delete this line to help avoid io.c */
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-    printf( "\nadd halfspaces for cube to intersection\n");
-    addhalf(qh, array[0], SIZEcube, SIZEdiamond, DIM, qh->feasible_point);
-    qh_check_output(qh);
-    qh_produce_output(qh);  /* delete this line to help avoid io.c */
-    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
-      qh_check_points(qh);
-  }
-  qh->NOerrexit= True;
-  qh->NOerrexit= True;
-  qh_freeqhull(qh, !qh_ALL);
-  qh_memfreeshort(qh, &curlong, &totlong);
-  if (curlong || totlong)
-      fprintf(stderr, "qhull warning (user_eg2, run 3): did not free %d bytes of long memory (%d pieces)\n",
-          totlong, curlong);
-  return exitcode;
-} /* main */
-
-#if 1    /* use 1 to prevent loading of io.o and user.o */
-/*-------------------------------------------
--errexit- return exitcode to system after an error
-  assumes exitcode non-zero
-  prints useful information
-  see qh_errexit2() in libqhull.c for 2 facets
-*/
-void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
-  QHULL_UNUSED(facet);
-  QHULL_UNUSED(ridge);
-
-  if (qh->ERREXITcalled) {
-    fprintf(qh->ferr, "qhull error while processing previous error.  Exit program\n");
-    exit(1);
-  }
-  qh->ERREXITcalled= True;
-  if (!qh->QHULLfinished)
-    qh->hulltime= (unsigned)clock() - qh->hulltime;
-  fprintf(qh->ferr, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
-  fprintf(qh->ferr, "Options selected:\n%s\n", qh->qhull_options);
-  if (qh->furthest_id >= 0) {
-    fprintf(qh->ferr, "\nLast point added to hull was p%d", qh->furthest_id);
-    if (zzval_(Ztotmerge))
-      fprintf(qh->ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
-    if (qh->QHULLfinished)
-      fprintf(qh->ferr, "\nQhull has finished constructing the hull.");
-    else if (qh->POSTmerging)
-      fprintf(qh->ferr, "\nQhull has started post-merging");
-    fprintf(qh->ferr, "\n\n");
-  }
-  if (qh->NOerrexit) {
-    fprintf(qh->ferr, "qhull error while ending program.  Exit program\n");
-    exit(1);
-  }
-  if (!exitcode)
-    exitcode= qh_ERRqhull;
-  qh->NOerrexit= True;
-  longjmp(qh->errexit, exitcode);
-} /* errexit */
-
-
-/*-------------------------------------------
--errprint- prints out the information of the erroneous object
-    any parameter may be NULL, also prints neighbors and geomview output
-*/
-void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-
-  fprintf(qh->ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
-           string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
-           getid_(atvertex));
-} /* errprint */
-
-
-void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
-  facetT *facet, **facetp;
-
-  /* remove these calls to help avoid io.c */
-  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
-  FORALLfacet_(facetlist)                                              /*io.c*/
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
-  FOREACHfacet_(facets)                                                /*io.c*/
-    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
-  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);  /*io.c*/
-
-  FORALLfacet_(facetlist)
-    fprintf( qh->ferr, "facet f%d\n", facet->id);
-} /* printfacetlist */
-
-/* qh_printhelp_degenerate( fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
-
-  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
-    qh_fprintf(qh, fp, 9368, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
-  else if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9369, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    qh_fprintf(qh, fp, 9370, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
-      qh_fprintf(qh, fp, 9371, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh->DELAUNAY && !qh->ATinfinity)
-      qh_fprintf(qh, fp, 9372, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    qh_fprintf(qh, fp, 9373, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh->DISTround);
-    qh_fprintf(qh, fp, 9374, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/* qh_printhelp_narrowhull( minangle )
-     Warn about a narrow hull
-
-  notes:
-    Alternatively, reduce qh_WARNnarrow in user.h
-
-*/
-void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
-
-    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
-or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
-this warning.  See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-} /* printhelp_narrowhull */
-
-/* qh_printhelp_singular
-      prints descriptive message for singular input
-*/
-void qh_printhelp_singular(qhT *qh, FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  qh_fprintf(qh, fp, 9376, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh->hull_dim);
-  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    qh_fprintf(qh, fp, 9377, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh->DISTround);
-  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, -1);
-  qh_fprintf(qh, fp, 9378, "\n");
-  FORALLfacets {
-    qh_fprintf(qh, fp, 9379, "facet");
-    FOREACHvertex_(facet->vertices)
-      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh, qh->interior_point, facet, &dist);
-    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh->HALFspace)
-      qh_fprintf(qh, fp, 9382, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    qh_fprintf(qh, fp, 9383,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh->hull_dim >= qh_INITIALmax)
-      qh_fprintf(qh, fp, 9384, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh->hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    qh_fprintf(qh, fp, 9387, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh->DISTround);
-#if REALfloat
-    qh_fprintf(qh, fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
-#endif
-    qh_fprintf(qh, fp, 9389, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-    if (qh->DELAUNAY && !qh->ATinfinity)
-      qh_fprintf(qh, fp, 9390, "\n\n\
-This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
-  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
-  - or use 'QJ' to joggle the input and avoid co-circular data\n");
-  }
-} /* printhelp_singular */
-
-
-/*-----------------------------------------
--user_memsizes- allocate up to 10 additional, quick allocation sizes
-*/
-void qh_user_memsizes(qhT *qh) {
-
-  QHULL_UNUSED(qh);
-  /* qh_memsize(qh, size); */
-} /* user_memsizes */
-
-#endif
diff --git a/src/qhull/src/user_eg3/user_eg3.pro b/src/qhull/src/user_eg3/user_eg3.pro
deleted file mode 100644
index 35372fbf9..000000000
--- a/src/qhull/src/user_eg3/user_eg3.pro
+++ /dev/null
@@ -1,12 +0,0 @@
-# -------------------------------------------------
-# user_eg3.pro -- Qt project for cpp demonstration user_eg3.exe
-#
-# The C++ interface requires reentrant Qhull.
-# -------------------------------------------------
-
-include(../qhull-app-cpp.pri)
-
-TARGET = user_eg3
-CONFIG -= qt
-
-SOURCES += user_eg3_r.cpp
diff --git a/src/qhull/src/user_eg3/user_eg3_r.cpp b/src/qhull/src/user_eg3/user_eg3_r.cpp
deleted file mode 100644
index 5257872ab..000000000
--- a/src/qhull/src/user_eg3/user_eg3_r.cpp
+++ /dev/null
@@ -1,162 +0,0 @@
-#//! user_eg3_r.cpp -- Invoke rbox and qhull from C++
-
-#include "libqhullcpp/RboxPoints.h"
-#include "libqhullcpp/QhullError.h"
-#include "libqhullcpp/QhullQh.h"
-#include "libqhullcpp/QhullFacet.h"
-#include "libqhullcpp/QhullFacetList.h"
-#include "libqhullcpp/QhullLinkedList.h"
-#include "libqhullcpp/QhullVertex.h"
-#include "libqhullcpp/Qhull.h"
-
-#include    /* for printf() of help message */
-#include 
-#include 
-
-using std::cerr;
-using std::cin;
-using std::cout;
-using std::endl;
-
-using orgQhull::Qhull;
-using orgQhull::QhullError;
-using orgQhull::QhullFacet;
-using orgQhull::QhullFacetList;
-using orgQhull::QhullQh;
-using orgQhull::RboxPoints;
-using orgQhull::QhullVertex;
-using orgQhull::QhullVertexSet;
-
-int main(int argc, char **argv);
-int user_eg3(int argc, char **argv);
-
-char prompt[]= "\n\
-user_eg3 -- demonstrate calling rbox and qhull from C++.\n\
-\n\
-user_eg3 is statically linked to reentrant qhull.  If user_eg3\n\
-fails immediately, it is probably linked to the non-reentrant qhull.\n\
-Try 'user_eg3 rbox qhull \"T1\"'\n\
-\n\
-  eg-100                       Run the example in qh-code.htm\n\
-  rbox \"200 D4\" ...            Generate points from rbox\n\
-  qhull \"d p\" ...              Run qhull and produce output\n\
-  qhull-cout \"o\" ...           Run qhull and produce output to cout\n\
-  qhull \"T1\" ...               Run qhull with level-1 trace to cerr\n\
-  facets                       Print facets when done\n\
-\n\
-For example\n\
-  user_eg3 rbox qhull\n\
-  user_eg3 rbox qhull d\n\
-  user_eg3 rbox \"10 D2\"  \"2 D2\" qhull  \"s p\" facets\n\
-\n\
-";
-
-
-/*--------------------------------------------
--user_eg3-  main procedure of user_eg3 application
-*/
-int main(int argc, char **argv) {
-
-    QHULL_LIB_CHECK
-
-    if(argc==1){
-        cout << prompt;
-        return 1;
-    }
-    try{
-        return user_eg3(argc, argv);
-    }catch(QhullError &e){
-        cerr << e.what() << std::endl;
-        return e.errorCode();
-    }
-}//main
-
-int user_eg3(int argc, char **argv)
-{
-    if(strcmp(argv[1], "eg-100")==0){
-        RboxPoints rbox("100");
-        Qhull q(rbox, "");
-        QhullFacetList facets= q.facetList();
-        cout << facets;
-        return 0;
-    }
-    bool printFacets= false;
-    RboxPoints rbox;
-    Qhull qhull;
-    int readingRbox= 0;
-    int readingQhull= 0;
-    for(int i=1; i