Added qhull library to xs/src and cmake
This commit is contained in:
Lukas Matena
Enrico Turri
parent
168d38df2b
commit
211790f8c3
@ -459,7 +459,7 @@ if(APPLE)
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# Ignore undefined symbols of the perl interpreter, they will be found in the caller image.
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target_link_libraries(XS "-undefined dynamic_lookup")
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endif()
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target_link_libraries(XS libslic3r libslic3r_gui admesh miniz clipper nowide polypartition poly2tri semver avrdude)
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target_link_libraries(XS libslic3r libslic3r_gui admesh miniz clipper nowide polypartition poly2tri semver avrdude qhull)
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if(SLIC3R_PROFILE)
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target_link_libraries(XS Shiny)
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endif()
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@ -540,6 +540,10 @@ endif()
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add_subdirectory(src/avrdude)
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add_subdirectory(src/qhull)
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include_directories(${LIBDIR}/qhull/src)
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message(STATUS ${LIBDIR}/qhull/src)
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## REQUIRED packages
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# Find and configure boost
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47
xs/src/qhull/Announce.txt
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47
xs/src/qhull/Announce.txt
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@ -0,0 +1,47 @@
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Qhull 2015.2 2016/01/18
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http://www.qhull.org
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git@github.com:qhull/qhull.git
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http://www.geomview.org
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Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams,
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furthest-site Voronoi diagrams, and halfspace intersections about a point.
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It runs in 2-d, 3-d, 4-d, or higher. It implements the Quickhull algorithm
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for computing convex hulls. Qhull handles round-off errors from floating
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point arithmetic. It can approximate a convex hull.
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The program includes options for hull volume, facet area, partial hulls,
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input transformations, randomization, tracing, multiple output formats, and
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execution statistics. The program can be called from within your application.
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You can view the results in 2-d, 3-d and 4-d with Geomview.
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To download Qhull:
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http://www.qhull.org/download
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git@github.com:qhull/qhull.git
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Download qhull-96.ps for:
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Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The
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Quickhull Algorithm for Convex Hulls," ACM Trans. on
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Mathematical Software, 22(4):469-483, Dec. 1996.
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http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405
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Abstract:
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The convex hull of a set of points is the smallest convex set that contains
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the points. This article presents a practical convex hull algorithm that
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combines the two-dimensional Quickhull Algorithm with the general dimension
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Beneath-Beyond Algorithm. It is similar to the randomized, incremental
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algorithms for convex hull and Delaunay triangulation. We provide empirical
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evidence that the algorithm runs faster when the input contains non-extreme
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points, and that it uses less memory.
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Computational geometry algorithms have traditionally assumed that input sets
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are well behaved. When an algorithm is implemented with floating point
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arithmetic, this assumption can lead to serious errors. We briefly describe
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a solution to this problem when computing the convex hull in two, three, or
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four dimensions. The output is a set of "thick" facets that contain all
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possible exact convex hulls of the input. A variation is effective in five
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or more dimensions.
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128
xs/src/qhull/CMakeLists.txt
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128
xs/src/qhull/CMakeLists.txt
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@ -0,0 +1,128 @@
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# This CMake file is written specifically to integrate qhull library with Slic3rPE
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# (see https://github.com/prusa3d/Slic3r for more information about the project)
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#
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# Only original libraries qhullstatic_r and qhullcpp are included.
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# They are built as a single statically linked library.
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#
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# Created by modification of the original qhull CMakeLists.
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# Lukas Matena (25.7.2018), lukasmatena@seznam.cz
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project(qhull)
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cmake_minimum_required(VERSION 2.6)
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# Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, qhull-warn.pri
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set(qhull_VERSION2 "2015.2 2016/01/18") # not used, See global.c, global_r.c, rbox.c, rbox_r.c
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set(qhull_VERSION "7.2.0") # Advance every release
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#include(CMakeModules/CheckLFS.cmake)
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#option(WITH_LFS "Enable Large File Support" ON)
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#check_lfs(WITH_LFS)
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message(STATUS "qhull Version: ${qhull_VERSION} (static linking)")
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set(libqhull_HEADERS
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# reentrant qhull HEADERS:
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src/libqhull_r/libqhull_r.h
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src/libqhull_r/geom_r.h
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src/libqhull_r/io_r.h
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src/libqhull_r/mem_r.h
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src/libqhull_r/merge_r.h
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src/libqhull_r/poly_r.h
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src/libqhull_r/qhull_ra.h
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src/libqhull_r/qset_r.h
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src/libqhull_r/random_r.h
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src/libqhull_r/stat_r.h
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src/libqhull_r/user_r.h
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# C++ interface to reentrant Qhull HEADERS:
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src/libqhullcpp/Coordinates.h
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src/libqhullcpp/functionObjects.h
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src/libqhullcpp/PointCoordinates.h
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src/libqhullcpp/Qhull.h
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src/libqhullcpp/QhullError.h
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src/libqhullcpp/QhullFacet.h
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src/libqhullcpp/QhullFacetList.h
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src/libqhullcpp/QhullFacetSet.h
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src/libqhullcpp/QhullHyperplane.h
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src/libqhullcpp/QhullIterator.h
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src/libqhullcpp/QhullLinkedList.h
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src/libqhullcpp/QhullPoint.h
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src/libqhullcpp/QhullPoints.h
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src/libqhullcpp/QhullPointSet.h
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src/libqhullcpp/QhullQh.h
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src/libqhullcpp/QhullRidge.h
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src/libqhullcpp/QhullSet.h
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src/libqhullcpp/QhullSets.h
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src/libqhullcpp/QhullStat.h
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src/libqhullcpp/QhullVertex.h
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src/libqhullcpp/QhullVertexSet.h
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src/libqhullcpp/RboxPoints.h
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src/libqhullcpp/RoadError.h
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src/libqhullcpp/RoadLogEvent.h
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src/qhulltest/RoadTest.h
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)
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set(libqhull_SOURCES
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# reentrant qhull SOURCES:
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src/libqhull_r/global_r.c
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src/libqhull_r/stat_r.c
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src/libqhull_r/geom2_r.c
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src/libqhull_r/poly2_r.c
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src/libqhull_r/merge_r.c
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src/libqhull_r/libqhull_r.c
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src/libqhull_r/geom_r.c
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src/libqhull_r/poly_r.c
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src/libqhull_r/qset_r.c
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src/libqhull_r/mem_r.c
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src/libqhull_r/random_r.c
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src/libqhull_r/usermem_r.c
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src/libqhull_r/userprintf_r.c
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src/libqhull_r/io_r.c
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src/libqhull_r/user_r.c
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src/libqhull_r/rboxlib_r.c
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src/libqhull_r/userprintf_rbox_r.c
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# C++ interface to reentrant Qhull SOURCES:
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src/libqhullcpp/Coordinates.cpp
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src/libqhullcpp/PointCoordinates.cpp
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src/libqhullcpp/Qhull.cpp
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src/libqhullcpp/QhullFacet.cpp
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src/libqhullcpp/QhullFacetList.cpp
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src/libqhullcpp/QhullFacetSet.cpp
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src/libqhullcpp/QhullHyperplane.cpp
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src/libqhullcpp/QhullPoint.cpp
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src/libqhullcpp/QhullPointSet.cpp
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src/libqhullcpp/QhullPoints.cpp
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src/libqhullcpp/QhullQh.cpp
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src/libqhullcpp/QhullRidge.cpp
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src/libqhullcpp/QhullSet.cpp
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src/libqhullcpp/QhullStat.cpp
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src/libqhullcpp/QhullVertex.cpp
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src/libqhullcpp/QhullVertexSet.cpp
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src/libqhullcpp/RboxPoints.cpp
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src/libqhullcpp/RoadError.cpp
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src/libqhullcpp/RoadLogEvent.cpp
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# headers for both (libqhullr and libqhullcpp:
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${libqhull_HEADERS}
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)
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##################################################
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# combined library (reentrant qhull and qhullcpp) for Slic3r:
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set(qhull_STATIC qhull)
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add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES})
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set_target_properties(${qhull_STATIC} PROPERTIES
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VERSION ${qhull_VERSION})
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if(UNIX)
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target_link_libraries(${qhull_STATIC} m)
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endif(UNIX)
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##################################################
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# LIBDIR is defined in the main xs CMake file:
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target_include_directories(${qhull_STATIC} PRIVATE ${LIBDIR}/qhull/src)
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38
xs/src/qhull/COPYING.txt
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38
xs/src/qhull/COPYING.txt
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Qhull, Copyright (c) 1993-2015
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C.B. Barber
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Arlington, MA
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and
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The National Science and Technology Research Center for
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Computation and Visualization of Geometric Structures
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(The Geometry Center)
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University of Minnesota
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email: qhull@qhull.org
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This software includes Qhull from C.B. Barber and The Geometry Center.
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Qhull is copyrighted as noted above. Qhull is free software and may
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be obtained via http from www.qhull.org. It may be freely copied, modified,
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and redistributed under the following conditions:
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1. All copyright notices must remain intact in all files.
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2. A copy of this text file must be distributed along with any copies
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of Qhull that you redistribute; this includes copies that you have
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modified, or copies of programs or other software products that
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include Qhull.
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3. If you modify Qhull, you must include a notice giving the
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name of the person performing the modification, the date of
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modification, and the reason for such modification.
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4. When distributing modified versions of Qhull, or other software
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products that include Qhull, you must provide notice that the original
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source code may be obtained as noted above.
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5. There is no warranty or other guarantee of fitness for Qhull, it is
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provided solely "as is". Bug reports or fixes may be sent to
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qhull_bug@qhull.org; the authors may or may not act on them as
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they desire.
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623
xs/src/qhull/README.txt
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623
xs/src/qhull/README.txt
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This distribution of qhull library is only meant for interfacing qhull with Slic3rPE
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(https://github.com/prusa3d/Slic3r).
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The qhull source file was acquired from https://github.com/qhull/qhull at revision
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f0bd8ceeb84b554d7cdde9bbfae7d3351270478c.
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No changes to the qhull library were made, except for
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- setting REALfloat=1 in user_r.h to enforce calculations in floats
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- modifying CMakeLists.txt (the original was renamed to origCMakeLists.txt)
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Many thanks to C. Bradford Barber and all contributors.
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Lukas Matena (lukasmatena@seznam.cz)
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25.7.2018
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See original contents of the README file below.
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======================================================================================
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======================================================================================
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======================================================================================
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Name
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qhull, rbox 2015.2 2016/01/18
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Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
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Documentation:
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html/index.htm
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<http://www.qhull.org/html>
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Available from:
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<http://www.qhull.org>
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<http://www.qhull.org/download>
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<http://github.com/qhull/qhull> (git@github.com:qhull/qhull.git)
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News and a paper:
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<http://www.qhull.org/news>
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405>
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Version 1 (simplicial only):
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<http://www.qhull.org/download/qhull-1.0.tar.gz>
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Purpose
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Qhull is a general dimension convex hull program that reads a set
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of points from stdin, and outputs the smallest convex set that contains
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the points to stdout. It also generates Delaunay triangulations, Voronoi
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diagrams, furthest-site Voronoi diagrams, and halfspace intersections
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about a point.
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Rbox is a useful tool in generating input for Qhull; it generates
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hypercubes, diamonds, cones, circles, simplices, spirals,
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lattices, and random points.
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Qhull produces graphical output for Geomview. This helps with
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understanding the output. <http://www.geomview.org>
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Environment requirements
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Qhull and rbox should run on all 32-bit and 64-bit computers. Use
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an ANSI C or C++ compiler to compile the program. The software is
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self-contained. It comes with examples and test scripts.
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Qhull's C++ interface uses the STL. The C++ test program uses QTestLib
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from the Qt Framework. Qhull's C++ interface may change without
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notice. Eventually, it will move into the qhull shared library.
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Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt
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before using or distributing Qhull.
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To cite Qhull, please use
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Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull
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algorithm for convex hulls," ACM Trans. on Mathematical Software,
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22(4):469-483, Dec 1996, http://www.qhull.org.
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To modify Qhull, particularly the C++ interface
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Qhull is on GitHub
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(http://github.com/qhull/qhull, git@github.com:qhull/qhull.git)
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For internal documentation, see html/qh-code.htm
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To install Qhull
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Qhull is precompiled for Windows 32-bit, otherwise it needs compilation.
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Qhull includes Makefiles for gcc and other targets, CMakeLists.txt for CMake,
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.sln/.vcproj/.vcxproj files for Microsoft Visual Studio, and .pro files
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for Qt Creator. It compiles under Windows with mingw.
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Install and build instructions follow.
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See the end of this document for a list of distributed files.
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-----------------
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Installing Qhull on Windows 10, 8, 7 (32- or 64-bit), Windows XP, and Windows NT
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The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe,
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qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files,
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and source files. Qhull.exe and user-eg3.exe are compiled with the reentrant
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library while the other executables use the non-reentrant library.
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To install Qhull:
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- Unzip the files into a directory (e.g., named 'qhull')
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- Click on QHULL-GO or open a command window into Qhull's bin directory.
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- Test with 'rbox D4 | qhull'
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To uninstall Qhull
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- Delete the qhull directory
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To learn about Qhull:
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- Execute 'qconvex' for a synopsis and examples.
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- Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points.
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- Execute 'rbox 10 | qconvex i TO file' to write results to 'file'.
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- Browse the documentation: qhull\html\index.htm
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- If an error occurs, Windows sends the error to stdout instead of stderr.
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Use 'TO xxx' to send normal output to xxx
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To improve the command window
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- Double-click the window bar to increase the size of the window
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- Right-click the window bar
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- Select Properties
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- Check QuickEdit Mode
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Select text with right-click or Enter
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Paste text with right-click
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- Change Font to Lucinda Console
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- Change Layout to Screen Buffer Height 999, Window Size Height 55
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- Change Colors to Screen Background White, Screen Text Black
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- Click OK
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- Select 'Modify shortcut that started this window', then OK
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If you use qhull a lot, install a bash shell such as
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MSYS (www.mingw.org/wiki/msys), Road Bash (www.qhull.org/bash),
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or Cygwin (www.cygwin.com).
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-----------------
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Installing Qhull on Unix with gcc
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To build Qhull, static libraries, shared library, and C++ interface
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- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
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- make
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- export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH
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The Makefiles may be edited for other compilers.
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If 'testqset' exits with an error, qhull is broken
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A simple Makefile for Qhull is in src/libqhull and src/libqhull_r.
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To build the Qhull executables and libqhullstatic
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- Extract Qhull from qhull...tgz or qhull...zip
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- cd src/libqhull_r # cd src/libqhull
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- make
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-----------------
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Installing Qhull with CMake 2.6 or later
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See CMakeLists.txt for examples and further build instructions
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To build Qhull, static libraries, shared library, and C++ interface
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- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
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- cd build
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- cmake --help # List build generators
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- make -G "<generator>" .. && cmake ..
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- cmake ..
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- make
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- make install
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The ".." is important. It refers to the parent directory (i.e., qhull/)
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On Windows, CMake installs to C:/Program Files/qhull. 64-bit generators
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have a "Win64" tag.
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If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
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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.
|
||||
32
xs/src/qhull/REGISTER.txt
Normal file
32
xs/src/qhull/REGISTER.txt
Normal file
@ -0,0 +1,32 @@
|
||||
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!
|
||||
935
xs/src/qhull/html/index.htm
Normal file
935
xs/src/qhull/html/index.htm
Normal file
@ -0,0 +1,935 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<meta name="GENERATOR" content="Microsoft FrontPage 2.0">
|
||||
<title>Qhull manual</title>
|
||||
<!-- Navigation links
|
||||
NOTE -- verify all links by 'grep href=' 'grep name=' add # 'sort /+7'
|
||||
index.htm
|
||||
-->
|
||||
</head>
|
||||
|
||||
<body>
|
||||
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b><a
|
||||
href="http://www.qhull.org/news">News</a> about Qhull<br>
|
||||
<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
|
||||
<b>To:</b> <a href="#TOC">Qhull manual: Table of Contents</a>
|
||||
(please wait while loading) <br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html"><img
|
||||
src="qh--rand.gif" alt="[random-fixed]" align="middle"
|
||||
width="100" height="100"></a> Qhull manual </h1>
|
||||
|
||||
<p>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 <a
|
||||
href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html">Fukuda's
|
||||
introduction</a> to convex hulls, Delaunay triangulations,
|
||||
Voronoi diagrams, and linear programming. For a detailed
|
||||
introduction, see O'Rourke [<a href="#orou94">'94</a>], <i>Computational
|
||||
Geometry in C</i>.
|
||||
</p>
|
||||
|
||||
<p>There are six programs. Except for rbox, they use
|
||||
the same code. Each program includes instructions and examples.
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li><a href="qconvex.htm">qconvex</a> -- convex hulls
|
||||
<li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
|
||||
furthest-site Delaunay triangulations
|
||||
<li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
|
||||
<li><a href="qhull.htm">qhull</a> -- all structures with additional options
|
||||
<li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
|
||||
furthest-site Voronoi diagrams
|
||||
<li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>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.
|
||||
|
||||
<p><i>Brad Barber, Arlington, MA</i></p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOP">»</a><a name="TOC">Qhull manual: Table of
|
||||
Contents </a></h2>
|
||||
|
||||
<ul>
|
||||
<li><a href="#when">When</a> to use Qhull
|
||||
<ul>
|
||||
<li><a href="http://www.qhull.org/news">News</a> for Qhull
|
||||
with new features and reported bugs.
|
||||
<li><a href="http://www.qhull.org">Home</a> for Qhull with additional URLs
|
||||
(<a href=index.htm>local copy</a>)
|
||||
<li><a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> for Qhull (<a href="qh-faq.htm">local copy</a>)
|
||||
<li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href=qh-get.htm>local copy</a>)
|
||||
<li><a href="qh-quick.htm#programs">Quick</a> reference for Qhull and its <a href="qh-quick.htm#options">options</a>
|
||||
<p>
|
||||
<li><a href="../COPYING.txt">COPYING.txt</a> - copyright notice<br>
|
||||
<li><a href="../REGISTER.txt">REGISTER.txt</a> - registration<br>
|
||||
<li><a href="../README.txt">README.txt</a> - installation
|
||||
instructions<br>
|
||||
<li><a href="../src/Changes.txt">Changes.txt</a> - change history <br>
|
||||
<li><a href="qhull.txt">qhull.txt</a> - Unix manual page
|
||||
</ul>
|
||||
<p>
|
||||
<li><a href="#description">Description</a> of Qhull
|
||||
<ul>
|
||||
<li><a href="#definition">de</a>finition • <a
|
||||
href="#input">in</a>put • <a href="#output">ou</a>tput
|
||||
• <a href="#algorithm">al</a>gorithm • <a
|
||||
href="#structure">da</a>ta structure </li>
|
||||
<li><a href="qh-impre.htm">Imprecision</a> in Qhull</li>
|
||||
<li><a href="qh-impre.htm#joggle">Merged facets</a> or joggled input
|
||||
<li><a href="qh-eg.htm">Examples</a> of Qhull</li>
|
||||
</ul>
|
||||
<p>
|
||||
<li><a href=qh-quick.htm#programs>Qhull programs</a>, with instructions and examples
|
||||
<ul>
|
||||
<li><a href="qconvex.htm">qconvex</a> -- convex hulls
|
||||
<li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
|
||||
furthest-site Delaunay triangulations
|
||||
<li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
|
||||
<li><a href="qhull.htm">qhull</a> -- all structures with additional options
|
||||
<li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
|
||||
furthest-site Voronoi diagrams
|
||||
<li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
|
||||
</ul>
|
||||
<p>
|
||||
<li><a href="qh-quick.htm#options">Qhull options</a><ul>
|
||||
<li><a href="qh-opto.htm#output">Output</a> formats</li>
|
||||
<li><a href="qh-optf.htm#format">Additional</a> I/O
|
||||
formats</li>
|
||||
<li><a href="qh-optg.htm#geomview">Geomview</a>
|
||||
output options</li>
|
||||
<li><a href="qh-optp.htm#print">Print</a> options</li>
|
||||
<li><a href="qh-optq.htm#qhull">Qhull</a> control
|
||||
options</li>
|
||||
<li><a href="qh-optc.htm#prec">Precision</a> options</li>
|
||||
<li><a href="qh-optt.htm#trace">Trace</a> options</li>
|
||||
</ul>
|
||||
</li>
|
||||
<p>
|
||||
<li><a href="#geomview">Geomview</a>, Qhull's graphical viewer</li>
|
||||
<ul>
|
||||
<li><a href="#geomview-install">Installing Geomview</a></li>
|
||||
<li><a href="#geomview-use">Using Geomview</a></li>
|
||||
<li><a href="#geomview-win">Building Geomview for Windows</a></li>
|
||||
</ul>
|
||||
<p>
|
||||
<li><a href="qh-code.htm">Qhull internals</a><ul>
|
||||
<li><a href="qh-code.htm#reentrant">Reentrant</a> Qhull</li>
|
||||
<li><a href="qh-code.htm#convert">How to convert</a> code to reentrant Qhull</li>
|
||||
<li><a href="qh-code.htm#64bit">Qhull</a> on 64-bit computers</li>
|
||||
<li><a href="qh-code.htm#cpp">Calling</a> Qhull
|
||||
from C++ programs</li>
|
||||
<li><a href="qh-code.htm#library">Calling</a> Qhull
|
||||
from C programs</li>
|
||||
<li><a href="qh-code.htm#performance">Performance</a>
|
||||
of Qhull</li>
|
||||
<li><a href="qh-code.htm#enhance">Enhancements</a> to
|
||||
Qhull</li>
|
||||
<li><a href="../src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and
|
||||
data structures </li>
|
||||
<li><a href="../src/libqhull/index.htm">Qhull</a> functions, macros, and
|
||||
data structures </li>
|
||||
</ul>
|
||||
</li>
|
||||
<p>
|
||||
<li>Related URLs
|
||||
<ul>
|
||||
|
||||
<li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
|
||||
comp.graphics.algorithms
|
||||
<li><a
|
||||
href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a> for computer graphics algorithms and
|
||||
Exaflop's <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures.
|
||||
<li>Amenta's <a href="http://www.geom.uiuc.edu/software/cglist">Directory
|
||||
of Computational Geometry Software </a></li>
|
||||
<li>Erickson's <a
|
||||
href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Computational
|
||||
Geometry Software</a> </li>
|
||||
<li>Fukuda's <a
|
||||
href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html">
|
||||
introduction</a> to convex hulls, Delaunay triangulations,
|
||||
Voronoi diagrams, and linear programming.
|
||||
<li>Stony Brook's <a
|
||||
href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml">Algorithm Repository</a> on computational geometry.
|
||||
</li>
|
||||
</ul>
|
||||
<p>
|
||||
<li><a href="#bugs">What to do</a> if something goes wrong</li>
|
||||
<li><a href="#email">Email</a></li>
|
||||
<li><a href="#authors">Authors</a></li>
|
||||
<li><a href="#ref">References</a></li>
|
||||
<li><a href="#acknowledge">Acknowledgments</a></li>
|
||||
</ul>
|
||||
<h2><a href="#TOC">»</a><a name="when">When to use Qhull</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p>Qhull constructs convex hulls, Delaunay triangulations,
|
||||
halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay
|
||||
triangulations, and furthest-site Voronoi diagrams.</p>
|
||||
|
||||
<p>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 <i>n</i> is the size of
|
||||
the input and <i>d</i> is the dimension (d>=3), the size of the output
|
||||
and execution time
|
||||
grows by <i>n^(floor(d/2)</i>
|
||||
[see <a href=qh-code.htm#performance>Performance</a>]. 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.
|
||||
|
||||
<p>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.
|
||||
|
||||
<!-- duplicated in index.htm and html/index.htm -->
|
||||
<p>Qhull does <i>not</i> support constrained Delaunay
|
||||
triangulations, triangulation of non-convex surfaces, mesh
|
||||
generation of non-convex objects, or medium-sized inputs in 9-D
|
||||
and higher. </p>
|
||||
|
||||
<p>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 <a
|
||||
href="qh-impre.htm">Imprecision in Qhull</a>). </p>
|
||||
|
||||
<p>[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 <a href="../html/qh-impre.htm#limit">Limitations of merged facets</a>
|
||||
|
||||
<p>If you need a short code for convex hull, Delaunay
|
||||
triangulation, or Voronoi volumes consider Clarkson's <a
|
||||
href="http://www.netlib.org/voronoi/hull.html">hull
|
||||
program</a>. If you need 2-d Delaunay triangulations consider
|
||||
Shewchuk's <a href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
|
||||
program</a>. It is much faster than Qhull and it allows
|
||||
constraints. Both programs use exact arithmetic. They are in <a
|
||||
href="http://www.netlib.org/voronoi/">http://www.netlib.org/voronoi/</a>.
|
||||
|
||||
<p>If your input is in general position (i.e., no coplanar or colinear points),
|
||||
<li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href"http://habrahabr.ru/post/245221/"documentation-ru</a/>)
|
||||
or Qhull <a
|
||||
href="http://www.qhull.org/download">version
|
||||
1.0</a> may meet your needs. Both programs detect precision problems,
|
||||
but do not handle them.</p>
|
||||
|
||||
<p><a href=http://www.cgal.org>CGAL</a> 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 <a href="http://doc.cgal.org/latest/Manual/devman_robustness.html">Robustness Issues in CGAL</a>,
|
||||
and <a href+"qh-impre.htm">Imprecision in Qhull</a>.
|
||||
|
||||
|
||||
<p><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a> 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.
|
||||
|
||||
<p>If your problem is in high dimensions with a few,
|
||||
non-simplicial facets, try Fukuda's <a
|
||||
href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">cdd</a>.
|
||||
It is much faster than Qhull for these distributions. </p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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 <a
|
||||
href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
|
||||
Finite Element Mesh Generation</a>.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Qhull is not suitable for the subdivision of arbitrary
|
||||
objects. Use <tt>qdelaunay</tt> to subdivide a convex object.</p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="description">Description of
|
||||
Qhull </a></h2>
|
||||
<blockquote>
|
||||
|
||||
<h3><a href="#TOC">»</a><a name="definition">definition</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The <i>convex hull</i> of a point set <i>P</i> is the smallest
|
||||
convex set that contains <i>P</i>. If <i>P</i> is finite, the
|
||||
convex hull defines a matrix <i>A</i> and a vector <i>b</i> such
|
||||
that for all <i>x</i> in <i>P</i>, <i>Ax+b <= [0,...]</i>. </p>
|
||||
|
||||
<p>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 <i>A</i> and an element of <i>b</i>). </p>
|
||||
|
||||
<p>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 <a href="qh-impre.htm#imprecise">Imprecise
|
||||
convex hulls</a>.</p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="input">input format</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
|
||||
<ul>
|
||||
<li>first line contains the dimension</li>
|
||||
<li>second line contains the number of input points</li>
|
||||
<li>remaining lines contain point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>For example: </p>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<p>Input may be entered by hand. End the input with a control-D
|
||||
(^D) character. </p>
|
||||
|
||||
<p>To input data from a file, use I/O redirection or '<a
|
||||
href="qh-optt.htm#TI">TI file</a>'. The filename may not
|
||||
include spaces or quotes.</p>
|
||||
|
||||
<p>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 <tt>qhull</tt> commands, use option '<a
|
||||
href="qh-optf.htm#FQ">FQ</a>' to place a comment in the output.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="option">option format</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Use options to specify the output formats and control
|
||||
Qhull. The <tt>qhull</tt> program takes all options. The
|
||||
other programs use a subset of the options. They disallow
|
||||
experimental and inappropriate options.
|
||||
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li>
|
||||
qconvex == qhull
|
||||
<li>
|
||||
qdelaunay == qhull d Qbb
|
||||
<li>
|
||||
qhalf == qhull H
|
||||
<li>
|
||||
qvoronoi == qhull v Qbb
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
<p>Single letters are used for output formats and precision
|
||||
constants. The other options are grouped into menus for formats
|
||||
('<a href="qh-optf.htm#format">F</a>'), Geomview ('<a
|
||||
href="qh-optg.htm#geomview">G </a>'), printing ('<a
|
||||
href="qh-optp.htm#print">P</a>'), Qhull control ('<a
|
||||
href="qh-optq.htm#qhull">Q </a>'), and tracing ('<a
|
||||
href="qh-optt.htm#trace">T</a>'). 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 '<a
|
||||
href="qh-optp.htm#PG">PG</a>' and '<a href="qh-optf.htm#format">F</a>'
|
||||
options). Use option '<a href="qh-optf.htm#FO">FO</a>' to print
|
||||
the selected options.</p>
|
||||
|
||||
<p>Qhull uses zero-relative indexing. If there are <i>n</i>
|
||||
points, the index of the first point is <i>0</i> and the index of
|
||||
the last point is <i>n-1</i>.</p>
|
||||
|
||||
<p>The default options are:</p>
|
||||
|
||||
<ul>
|
||||
<li>summary output ('<a href="qh-opto.htm#s">s</a>') </li>
|
||||
<li>merged facets ('<a href="qh-optc.htm#C0">C-0</a>' in 2-d,
|
||||
3-d, 4-d; '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and
|
||||
up)</li>
|
||||
</ul>
|
||||
|
||||
<p>Except for bounding box
|
||||
('<a href="qh-optq.htm#Qbk">Qbk:n</a>', etc.), drop facets
|
||||
('<a href="qh-optp.htm#Pdk">Pdk:n</a>', etc.), and
|
||||
Qhull command ('<a href="qh-optf.htm#FQ">FQ</a>'), 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.
|
||||
|
||||
<p>The Unix <tt>tcsh</tt> and <tt>ksh </tt>shells make it easy to
|
||||
try out different options. In Windows 95, use a command window with <tt>doskey</tt>
|
||||
and a window scroller (e.g., <tt>peruse</tt>). </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="output">output format</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>To write the results to a file, use I/O redirection or '<a
|
||||
href="qh-optt.htm#TO">TO file</a>'. Windows 95 users should use
|
||||
'TO file' or the console. If a filename is surrounded by single quotes,
|
||||
it may include spaces.
|
||||
</p>
|
||||
|
||||
<p>The default output option is a short summary ('<a
|
||||
href="qh-opto.htm#s">s</a>') to <tt>stdout</tt>. There are many
|
||||
others (see <a href="qh-opto.htm">output</a> and <a
|
||||
href="qh-optf.htm">formats</a>). 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 <a href="qh-code.htm#library">Qhull library</a>).</p>
|
||||
|
||||
<p>For example, 'qhull <a href="qh-opto.htm#o">o</a>' lists the
|
||||
vertices and facets of the convex hull. </p>
|
||||
|
||||
<p>Error messages and additional summaries ('<a
|
||||
href="qh-opto.htm#s">s</a>') go to <tt>stderr</tt>. Unless
|
||||
redirected, <tt>stderr</tt> is the console.</p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="algorithm">algorithm</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Qhull implements the Quickhull algorithm for convex hull
|
||||
[Barber et al. <a href="#bar-dob96">'96</a>]. This algorithm
|
||||
combines the 2-d Quickhull algorithm with the <em>n</em>-d
|
||||
beneath-beyond algorithm [c.f., Preparata & Shamos <a
|
||||
href="#pre-sha85">'85</a>]. It is similar to the randomized
|
||||
algorithms of Clarkson and others [Clarkson & Shor <a
|
||||
href="#cla-sho89">'89</a>; Clarkson et al. <a href="#cla-meh93">'93</a>;
|
||||
Mulmuley <a href="#mulm94">'94</a>]. For a demonstration, see <a
|
||||
href="qh-eg.htm#how">How Qhull adds a point</a>. 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. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="structure">data structures</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Qhull produces the following data structures for dimension <i>d</i>:
|
||||
</p>
|
||||
|
||||
<ul>
|
||||
<li>A <em>coordinate</em> is a real number in floating point
|
||||
format. </li>
|
||||
<li>A <em>point</em> is an array of <i>d</i> coordinates.
|
||||
With option '<a href="qh-optq.htm#QJn">QJ</a>', the
|
||||
coordinates are joggled by a small amount. </li>
|
||||
<li>A <em>vertex</em> is an input point. </li>
|
||||
<li>A <em>hyperplane</em> is <i>d</i> normal coefficients and
|
||||
an offset. The length of the normal is one. The
|
||||
hyperplane defines a halfspace. If <i>V</i> is a normal, <i>b</i>
|
||||
is an offset, and <i>x</i> is a point inside the convex
|
||||
hull, then <i>Vx+b <0</i>.</li>
|
||||
<li>An <em>outer plane</em> is a positive
|
||||
offset from a hyperplane. When Qhull is done, all points
|
||||
will be below all outer planes.</li>
|
||||
<li>An <em>inner plane</em> is a negative
|
||||
offset from a hyperplane. When Qhull is done, all
|
||||
vertices will be above the corresponding inner planes.</li>
|
||||
<li>An <em>orientation</em> is either 'top' or 'bottom'. It is the
|
||||
topological equivalent of a hyperplane's geometric
|
||||
orientation. </li>
|
||||
<li>A <em>simplicial facet</em> is a set of
|
||||
<i>d</i> neighboring facets, a set of <i>d</i> vertices, a
|
||||
hyperplane equation, an inner plane, an outer plane, and
|
||||
an orientation. For example in 3-d, a simplicial facet is
|
||||
a triangle. </li>
|
||||
<li>A <em>centrum</em> is a point on a facet's hyperplane. A
|
||||
centrum is the average of a facet's vertices. Neighboring
|
||||
facets are <em>convex</em> if each centrum is below the
|
||||
neighbor facet's hyperplane. </li>
|
||||
<li>A <em>ridge</em> is a set of <i>d-1</i> vertices, two
|
||||
neighboring facets, and an orientation. For example in
|
||||
3-d, a ridge is a line segment. </li>
|
||||
<li>A <em>non-simplicial facet</em> 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. </li>
|
||||
</ul>
|
||||
|
||||
<p>For examples, use option '<a href="qh-opto.htm#f">f</a>'. See <a
|
||||
href="../src/libqhull/qh-poly.htm">polyhedron operations</a> for further
|
||||
design documentation. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a>Imprecision in Qhull</h3>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qh-impre.htm">Imprecision in Qhull</a> and <a href="qh-impre.htm#joggle">Merged facets or joggled input</a></p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a>Examples of Qhull</h3>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qh-eg.htm">Examples of Qhull</a>. Most of these examples require <a href="#geomview">Geomview</a>.
|
||||
Some of the examples have <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures
|
||||
</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a>Options for using Qhull </h2>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qh-quick.htm#options">Options</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a>Qhull internals </h2>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qh-code.htm">Internals</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="geomview">Geomview, Qhull's
|
||||
graphical viewer</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p><a href="http://www.geomview.org">Geomview</a>
|
||||
is an interactive geometry viewing program.
|
||||
Geomview provides a good visualization of Qhull's 2-d and 3-d results.
|
||||
|
||||
<p>Qhull includes <a href="qh-eg.htm">Examples of Qhull</a> that may be viewed with Geomview.
|
||||
|
||||
<p>Geomview can help visulalize a 3-d Delaunay triangulation or the surface of a 4-d convex hull,
|
||||
Use option '<a href="qh-optq.htm#QVn">QVn</a>' to select the 3-D facets adjacent to a vertex.
|
||||
|
||||
<p>You may use Geomview to create movies that animate your objects (c.f., <a href="http://www.geomview.org/FAQ/answers.shtml#mpeg">How can I create a video animation?</a>).
|
||||
Geomview helped create the <a href="http://www.geom.uiuc.edu/video/">mathematical videos</a> "Not Knot", "Outside In", and "The Shape of Space" from the Geometry Center.
|
||||
|
||||
|
||||
<h3><a href="#TOC">»</a><a name="geomview-install">Installing Geomview</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Geomview is an <a href=http://sourceforge.net/projects/geomview>open source project</a>
|
||||
under SourceForge.
|
||||
|
||||
<p>
|
||||
For build instructions see
|
||||
<a href="http://www.geomview.org/download/">Downloading Geomview</a>.
|
||||
Geomview builds under Linux, Unix, Macintosh OS X, and Windows.
|
||||
|
||||
<p>Geomview has <a href="https://packages.debian.org/search?keywords=geomview">installable packages</a> for Debian and Ubuntu.
|
||||
The OS X build needs Xcode, an X11 SDK, and Lesstif or Motif.
|
||||
The Windows build uses Cygwin (see <a href="#geomview-win">Building Geomview</a> below for instructions).
|
||||
|
||||
<p>If using Xforms (e.g., for Geomview's <a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a>), install the 'libXpm-devel' package from cygwin and move the xforms directory into your geomview directory, e.g.,<br><tt>mv xforms-1.2.4 geomview-1.9.5/xforms</tt>
|
||||
|
||||
<p>Geomview's <a href="http://www.geom.uiuc.edu/software/geomview/docs/NDview/manpagehelp.html">ndview<a/> provides multiple views into 4-d and higher objects.
|
||||
This module is out-of-date (<a href="http://sourceforge.net/p/geomview/mailman/message/2004152/">geomview-users: 4dview</a>).
|
||||
Download NDview-sgi.tar.Z at <a href="ftp://www.geom.uiuc.edu/pub/software/geomview/newpieces/sgi">newpieces</a> and 4dview at <a href="https://stuff.mit.edu/afs/sipb/project/3d/arch/sgi_62/lib/Geomview/modules/">Geomview/modules</a>.
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="geomview-use">Using Geomview</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Use Geomview to view <a href="qh-eg.htm">Examples of Qhull</a>. 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.
|
||||
|
||||
<p>Follow these instructions to view 'eg,01.cube' from Examples of Qhull
|
||||
<ol>
|
||||
<li>Launch an XTerm command shell
|
||||
<ul>
|
||||
<li>If needed, start the X terminal server, Use 'xinit' or 'startx' in /usr/X11R6/bin<br><tt>xinit -- -multiwindow -clipboard</tt><br><tt>startx</tt>
|
||||
<li>Start an XTerm command shell. In Windows, click the Cygwin/bash icon on your desktop.
|
||||
<li>Set the DISPLAY variable, e.g.,<br><tt>export DISPLAY=:0</tt><br><tt>export DISPLAY=:0 >>~/.bashenv</tt>
|
||||
</ul>
|
||||
<li>Use Qhull's <a href="qh-optg.htm">Geomview options</a> to create a geomview object
|
||||
<ul>
|
||||
<li><tt>rbox c D3 | qconvex G >eg.01.cube</tt>
|
||||
<li>On windows, convert the output to Unix text format with 'd2u'<br><tt>rbox c D3 | qconvex G | d2u >eg.01.cube</tt><br><tt>d2u eg.*</tt>
|
||||
</ul>
|
||||
<li>Run Geomview
|
||||
<ul>
|
||||
<li>Start Geomview with your example<br><tt>./geomview eg.01.cube</tt>
|
||||
<li>Follow the instructions in <a href="http://www.geomview.org/docs/html/Tutorial.html">Gemoview Tutorial</a>
|
||||
<li>Geomview creates the <i>Geomview control panel</i> with Targets and External Module, the <i>Geomview toolbar</i> with buttons for controlling Geomview, and the <i>Geomview camera window</i> showing a cube.
|
||||
<li>Clear the camera window by selecting your object in the Targets list and 'Edit > Delete' or 'dd'
|
||||
<li>Load the <i>Geomview files panel</i>. Select 'Open' in the 'File' menu.
|
||||
<li>Set 'Filter' in the files panel to your example directory followed by '/*' (e.g., '/usr/local/qhull-2015.2/eg/*')
|
||||
<li>Click 'Filter' in the files panel to view your examples in the 'Files' list.
|
||||
<li>Load another example into the camera window by selecting it and clicking 'OK'.
|
||||
<li>Review the instructions for <a href="http://www.geomview.org/docs/html/Interaction.html">Interacting with Geomview</a>
|
||||
<li>When viewing multiple objects at once, you may want to turn off normalization. In the 'Inspect > Apperance' control panel, set 'Normalize' to 'None'.
|
||||
</ul>
|
||||
</ol>
|
||||
|
||||
<p>Geomview defines GCL (a textual API for controlling Geomview) and OOGL (a textual file format for defining objects).
|
||||
<ul>
|
||||
<li>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.
|
||||
<li><a href="http://www.geomview.org/docs/html/GCL.html">GCL</a> command language for controlling Geomview
|
||||
<li><a href="http://www.geomview.org/docs/html/OOGL-File-Formats.html">OOGL</a> file format for defining objects (<a href="http://www.geomview.org/docs/oogltour.html">tutorial</a>).
|
||||
<li><a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a> for interacting with Geomview via GCL
|
||||
<li>Interact with your objects via <a href="http://www.geomview.org/docs/html/pick.html">pick</a> commands in response to right-mouse double clicks. Enable pick events with the <a href="http://www.geomview.org/docs/html/interest.html">interest</a> command.
|
||||
</ul>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOC">»</a><a name="geomview-win">Building Geomview for Windows</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Compile Geomview under Cygwin. For detailed instructions, see
|
||||
<a href="http://www.ee.surrey.ac.uk/Personal/L.Wood/software/SaVi/building-under-Windows/"
|
||||
>Building Savi and Geomview under Windows</a>. These instructions are somewhat out-of-date. Updated
|
||||
instructions follow.
|
||||
|
||||
<p>How to compile Geomview under 32-bit Cygwin (October 2015)</p>
|
||||
<ol>
|
||||
<li><b>Note:</b> 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.
|
||||
<li>Install 32-bit <a href="http://cygwin.com/">Cygwin</a> as follows.
|
||||
For additional guidance, see Cygwin's <a href="https://cygwin.com/install.html">Installing and Updating Cygwin Packages</a>
|
||||
and <a href="http://www.qhull.org/road/road-faq/xml/cmdline.xml#setup-cygwin">Setup cygwin</a>.
|
||||
<ul>
|
||||
<li>Launch the cygwin installer.
|
||||
<li>Select a mirror from <a href="http://cygwin.com/mirrors.html">Cygwin mirrors</a> (e.g., http://mirrors.kernel.org/sourceware/cygwin/ in California).
|
||||
<li>Select the packages to install. Besides the cygwin packages listed in the Savi/Windows instructions consider adding
|
||||
<ul>
|
||||
<li><b>Default</b> -- libXm-devel (required for /usr/include/Xm/Xm.h)
|
||||
<li><b>Devel</b> -- bashdb, gcc-core (in place of gcc), gdb
|
||||
<li><b>Lib</b> -- libGL-devel, libGLU1 (required, obsolete), libGLU-devel (required, obsolete), libjpeg-devel(XForms), libXext-devel (required), libXpm-devel (Xforms)
|
||||
libGL and lib
|
||||
<li><b>Math</b> -- bc
|
||||
<li><b>Net</b> -- autossh, inetutils, openssh
|
||||
<li><b>System</b> -- chere
|
||||
<li><b>Utils</b> -- dos2unix (required for qhull), keychain
|
||||
<li>If installing perl, ActiveState Perl may be a better choice than cygwin's perl. Perl is not used by Geomview or Qhull.
|
||||
<li><a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a> -- Search for cygwin programs and packages
|
||||
</ul>
|
||||
<li>Click 'Next' to download and install the packages.
|
||||
<li>If the download is incomplete, try again.
|
||||
<li>If you try again after a successful install, cygwin will uninstall and reinstall all modules..
|
||||
<li>Click on the 'Cywin Terminal' icon on the Desktop. It sets up a user directory in /home from /etc/skel/...
|
||||
<li>Mount your disk drives<br>mount c: /c # Ignore the warning /c does not exist
|
||||
</ul>
|
||||
<li>Consider installing the <a href="http://www.qhull.org/bash/doc/road-bash.html">Road Bash</a> scripts (/etc/road-*) from <a href="http://www.qhull.org/road/">Road</a>.
|
||||
They define aliases and functions for Unix command shells (Unix, Linux, Mac OS X, Windows),
|
||||
<ul>
|
||||
<li>Download Road Bash and unzip the downloaded file
|
||||
<li>Copy .../bash/etc/road-* to the Cywin /etc directory (by default, C:\cygwin\etc).
|
||||
<li>Using the cygwin terminal, convert the road scripts to Unix format<br>d2u /etc/road-*
|
||||
<li>Try it<br>source /etc/road-home.bashrc
|
||||
<li>Install it<br>cp /etc/road-home.bashrc ~/.bashrc
|
||||
</ul>
|
||||
<li>Launch the X terminal server from '<tt>Start > All programs > Cygwin-X > Xwin Server</tt>'. Alternatively, run 'startx'
|
||||
<li>Launch an XTerm shell
|
||||
<ul>
|
||||
<li>Right click the Cywin icon on the system tray in the Windows taskbar.
|
||||
<li>Select '<tt>System Tools > XTerm</tt>'
|
||||
</ul>
|
||||
<li>Download and extract Geomview -- <a href="http://www.geomview.org/download/">Downloading Geomview</a>
|
||||
<li>Compile Geomview
|
||||
<ul>
|
||||
<li>./configure
|
||||
<li>make
|
||||
</ul>
|
||||
<li>If './configure' fails, check 'config.log' at the failing step. Look carefully for missing libraries, etc. The <a href="http://www.geomview.org/FAQ/answers.shtml">Geomview FAQ</a> contains suggestions (e.g., "configure claims it can't find OpenGl").
|
||||
<li>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
|
||||
(<a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a>).
|
||||
</ol>
|
||||
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="bugs">What to do if something
|
||||
goes wrong</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p>Please report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
|
||||
</a>. 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.</p>
|
||||
|
||||
<p>If you do not understand something, try a small example. The <a
|
||||
href="rbox.htm">rbox</a> program is an easy way to generate
|
||||
test cases. The <a href="#geomview">Geomview</a> program helps to
|
||||
visualize the output from Qhull.</p>
|
||||
|
||||
<p>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').</p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>If you doubt the output from Qhull, add option '<a
|
||||
href="qh-optt.htm#Tv">Tv</a>'. 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.</p>
|
||||
|
||||
<p>Qhull should work on all inputs. It may report precision
|
||||
errors if you turn off merged facets with option '<a
|
||||
href="qh-optq.htm#Q0">Q0</a>'. 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 <tt>rbox</tt>.</p>
|
||||
|
||||
<p>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 ('<a href="qh-optt.htm#Tn">T4</a>') as
|
||||
a guide. This is especially true if you're incorporating Qhull
|
||||
into your own program. </p>
|
||||
|
||||
<p>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 '<a href="qh-optf.htm#FO">FO</a>', and any
|
||||
messages generated by Qhull. This allows me to see the error for
|
||||
myself. Qhull is maintained part-time. </p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="email">Email</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p>Please send correspondence to Brad Barber at <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
and report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
|
||||
</a>. Let me know how you use Qhull. If you mention it in a
|
||||
paper, please send a reference and abstract.</p>
|
||||
|
||||
<p>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 <a
|
||||
href="http://www.qhull.org/news">qhull-news.html</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="authors">Authors</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<pre>
|
||||
C. Bradford Barber Hannu Huhdanpaa
|
||||
bradb@shore.net hannu@qhull.org
|
||||
</pre>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="acknowledge">Acknowledgments</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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 <a href=http://www.geomtech.com>Geometry Technologies</a>.
|
||||
Mark, Stuart, and Tamara Munzner are the original authors of <a href=http://www.geomview.org>Geomview</a>.
|
||||
|
||||
<p>A special thanks to <a href="http://www.endocardial.com/">Endocardial
|
||||
Solutions, Inc.</a> of St. Paul, Minnesota for their support of the
|
||||
internal documentation (<a href=../src/libqhull/index.htm>src/libqhull/index.htm</a>). They use Qhull to build 3-d models of
|
||||
heart chambers.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
</blockquote>
|
||||
<h2><a href="#TOC">»</a><a name="ref">References</a></h2>
|
||||
<blockquote>
|
||||
|
||||
<p><a name="aure91">Aurenhammer</a>, F., "Voronoi diagrams
|
||||
-- A survey of a fundamental geometric data structure," <i>ACM
|
||||
Computing Surveys</i>, 1991, 23:345-405. </p>
|
||||
|
||||
<p><a name="bar-dob96">Barber</a>, C. B., D.P. Dobkin, and H.T.
|
||||
Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," <i>ACM
|
||||
Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996, www.qhull.org
|
||||
[<a
|
||||
href="http://portal.acm.org/citation.cfm?doid=235815.235821">http://portal.acm.org</a>;
|
||||
<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">http://citeseerx.ist.psu.edu</a>].
|
||||
</p>
|
||||
|
||||
<p><a name="cla-sho89">Clarkson</a>, K.L. and P.W. Shor,
|
||||
"Applications of random sampling in computational geometry,
|
||||
II", <i>Discrete Computational Geometry</i>, 4:387-421, 1989</p>
|
||||
|
||||
<p><a name="cla-meh93">Clarkson</a>, K.L., K. Mehlhorn, and R.
|
||||
Seidel, "Four results on randomized incremental
|
||||
construction," <em>Computational Geometry: Theory and
|
||||
Applications</em>, vol. 3, p. 185-211, 1993.</p>
|
||||
|
||||
<p><a name="devi01">Devillers</a>, et. al.,
|
||||
"Walking in a triangulation," <i>ACM Symposium on
|
||||
Computational Geometry</i>, June 3-5,2001, Medford MA.
|
||||
|
||||
<p><a name="dob-kir90">Dobkin</a>, D.P. and D.G. Kirkpatrick,
|
||||
"Determining the separation of preprocessed polyhedra--a
|
||||
unified approach," in <i>Proc. 17th Inter. Colloq. Automata
|
||||
Lang. Program.</i>, in <i>Lecture Notes in Computer Science</i>,
|
||||
Springer-Verlag, 443:400-413, 1990. </p>
|
||||
|
||||
<p><a name="edel01">Edelsbrunner</a>, H, <i>Geometry and Topology for Mesh Generation</i>,
|
||||
Cambridge University Press, 2001.
|
||||
|
||||
<p><a name=gart99>Gartner, B.</a>, "Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, LNCS 1643.
|
||||
|
||||
<p><a name=golub83>Golub, G.H. and van Loan, C.F.</a>, <i>Matric Computations</i>, Baltimore, Maryland, USA: John Hopkins Press, 1983
|
||||
|
||||
<p><a name="fort93">Fortune, S.</a>, "Computational
|
||||
geometry," in R. Martin, editor, <i>Directions in Geometric
|
||||
Computation</i>, Information Geometers, 47 Stockers Avenue,
|
||||
Winchester, SO22 5LB, UK, ISBN 1-874728-02-X, 1993.</p>
|
||||
|
||||
<p><a name="mile93">Milenkovic, V.</a>, "Robust polygon
|
||||
modeling," Computer-Aided Design, vol. 25, p. 546-566,
|
||||
September 1993. </p>
|
||||
|
||||
<p><a name="muck96">Mucke</a>, E.P., I. Saias, B. Zhu, <i>Fast
|
||||
randomized point location without preprocessing in Two- and
|
||||
Three-dimensional Delaunay Triangulations</i>, ACM Symposium on
|
||||
Computational Geometry, p. 274-283, 1996 [<a
|
||||
href="http://www.geom.uiuc.edu/software/cglist/GeomDir/">GeomDir</a>].
|
||||
</p>
|
||||
|
||||
<p><a name="mulm94">Mulmuley</a>, K., <i>Computational Geometry,
|
||||
An Introduction Through Randomized Algorithms</i>, Prentice-Hall,
|
||||
NJ, 1994.</p>
|
||||
|
||||
<p><a name="orou94">O'Rourke</a>, J., <i>Computational Geometry
|
||||
in C</i>, Cambridge University Press, 1994.</p>
|
||||
|
||||
<p><a name="pre-sha85">Preparata</a>, F. and M. Shamos, <i>Computational
|
||||
Geometry</i>, Springer-Verlag, New York, 1985.</p>
|
||||
|
||||
</blockquote>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b><a
|
||||
href="http://www.qhull.org/news">News</a> about Qhull<br>
|
||||
<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
|
||||
<b>To:</b> <a href="#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>Dn:</b> <a href="qh-impre.htm">Imprecision in Qhull</a><br>
|
||||
<b>Dn:</b> <a href="qh-eg.htm">Description of Qhull examples</a><br>
|
||||
<b>Dn:</b> <a href="qh-code.htm">Qhull internals</a><br>
|
||||
<b>Dn:</b> <a href="../src/libqhull/index.htm">Qhull functions, macros, and data
|
||||
structures</a>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
BIN
xs/src/qhull/html/normal_voronoi_knauss_oesterle.jpg
Normal file
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xs/src/qhull/html/normal_voronoi_knauss_oesterle.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 23 KiB |
630
xs/src/qhull/html/qconvex.htm
Normal file
630
xs/src/qhull/html/qconvex.htm
Normal file
@ -0,0 +1,630 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qconvex -- convex hull</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<a name="TOP"><b>Up</b></a><b>:</b>
|
||||
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> -- Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="qh--cone.gif" alt="[cone]" align="middle" width="100"
|
||||
height="100"></a>qconvex -- convex hull</h1>
|
||||
|
||||
<p>The convex hull of a set of points is the smallest convex set
|
||||
containing the points. See the detailed introduction by O'Rourke
|
||||
[<a href="index.htm#orou94">'94</a>]. See <a
|
||||
href="index.htm#description">Description of Qhull</a> and <a
|
||||
href="qh-eg.htm#how">How Qhull adds a point</a>.</p>
|
||||
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox 10 D3 | qconvex <a
|
||||
href="qh-opto.htm#s">s</a> <a href="qh-opto.htm#o">o</a> <a
|
||||
href="qh-optt.htm#TO">TO result</a></dt>
|
||||
<dd>Compute the 3-d convex hull of 10 random points. Write a
|
||||
summary to the console and the points and facets to
|
||||
'result'.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox c | qconvex <a
|
||||
href="qh-opto.htm#n">n</a></dt>
|
||||
<dd>Print the normals for each facet of a cube.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox c | qconvex <a
|
||||
href="qh-opto.htm#i">i</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>Print the triangulated facets of a cube.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox y 500 W0 | qconvex</dt>
|
||||
<dd>Compute the convex hull of a simplex with 500
|
||||
points on its surface.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox x W1e-12 1000 | qconvex
|
||||
<a href="qh-optq.htm#QR">QR0</a></dt>
|
||||
<dd>Compute the convex hull of 1000 points near the
|
||||
surface of a randomly rotated simplex. Report
|
||||
the maximum thickness of a facet.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox 1000 s | qconvex <a
|
||||
href="qh-opto.htm#s">s</a> <a
|
||||
href="qh-optf.htm#FA">FA</a> </dt>
|
||||
<dd>Compute the convex hull of 1000 cospherical
|
||||
points. Verify the results and print a summary
|
||||
with the total area and volume.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox d D12 | qconvex <a
|
||||
href="qh-optq.htm#QRn">QR0</a> <a
|
||||
href="qh-optf.htm#FA">FA</a></dt>
|
||||
<dd>Compute the convex hull of a 12-d diamond.
|
||||
Randomly rotate the input. Note the large number
|
||||
of facets and the small volume.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox c D7 | qconvex <a
|
||||
href="qh-optf.htm#FA">FA</a> <a
|
||||
href="qh-optt.htm#TFn">TF1000</a></dt>
|
||||
<dd>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. </dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox c d D2 | qconvex <a
|
||||
href="qh-optq.htm#Qc">Qc</a> <a
|
||||
href="qh-opto.htm#s">s</a> <a
|
||||
href="qh-opto.htm#f">f</a> <a
|
||||
href="qh-optf.htm#Fx">Fx</a> | more</dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>Except for rbox, all of the qhull programs compute a convex hull.
|
||||
|
||||
<p>By default, Qhull merges coplanar facets. For example, the convex
|
||||
hull of a cube's vertices has six facets.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (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.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (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 <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>The output for 4-d convex hulls may be confusing if the convex
|
||||
hull contains non-simplicial facets (e.g., a hypercube). See
|
||||
<a href=qh-faq.htm#extra>Why
|
||||
are there extra points in a 4-d or higher convex hull?</a><br>
|
||||
</p>
|
||||
</p>
|
||||
|
||||
<p>The 'qconvex' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull</a>' in 2-d to 4-d, and
|
||||
'<a href=qhull.htm#outputs>qhull</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 5-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>d v H Qbb Qf Qg Qm
|
||||
Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc</i>.
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">qconvex synopsis</a></h3>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="input">qconvex
|
||||
input</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qconvex TI data.txt).
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Here is the input for computing the convex
|
||||
hull of the unit cube. The output is the normals, one
|
||||
per facet.</p>
|
||||
|
||||
<blockquote>
|
||||
<p>rbox c > data </p>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
<p>qconvex s n < data</p>
|
||||
<pre>
|
||||
|
||||
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
|
||||
</pre>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="outputs">qconvex outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of qconvex. They may be used
|
||||
individually or together.</p>
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>Vertices</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fx">Fx</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fv">Fv</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Coordinates</b></dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Ft">Ft</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-opto.htm#p">p</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optq.htm#Qc">Qc</a> <a href="qh-opto.htm#p">p</a></dt>
|
||||
<dd>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 '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> p'
|
||||
to print the coordinates of all points.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Facets</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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 '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> FN'
|
||||
to include coplanar and interior points. </dd>
|
||||
<dt><a href="qh-optf.htm#Fa">Fa</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#FI">FI</a></dt>
|
||||
<dd>list facet IDs. The first line is the number of
|
||||
facets. The IDs follow, one per line.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Coplanar and interior points</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optq.htm#Qi">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#FP">FP</a></dt>
|
||||
<dd>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 '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>
|
||||
<a href="qh-optf.htm#FP">FP</a>' for coplanar and interior points.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Hyperplanes</b></dd>
|
||||
<dt><a href="qh-opto.htm#n">n</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fo">Fo</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fi">Fi</a></dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary for the convex hull. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' and '<a
|
||||
href="qh-optf.htm#FS">FS</a>' if you need numeric data.</dd>
|
||||
<dt><a href="qh-optf.htm#FA">FA</a></dt>
|
||||
<dd>compute total area and volume for '<a
|
||||
href="qh-opto.htm#s">s</a>' and '<a href="qh-optf.htm#FS">FS</a>'</dd>
|
||||
<dt><a href="qh-opto.htm#m">m</a></dt>
|
||||
<dd>Mathematica output for the convex hull in 2-d or 3-d.</dd>
|
||||
<dt><a href="qh-optf.htm#FM">FM</a></dt>
|
||||
<dd>Maple output for the convex hull in 2-d or 3-d.</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for the convex hull in 2-d, 3-d, or 4-d.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Scaling and rotation</b></dd>
|
||||
<dt><a href="qh-optq.htm#Qbk">Qbk:n</a></dt>
|
||||
<dd>scale k'th coordinate to lower bound.</dd>
|
||||
<dt><a href="qh-optq.htm#QBk">QBk:n</a></dt>
|
||||
<dd>scale k'th coordinate to upper bound.</dd>
|
||||
<dt><a href="qh-optq.htm#QbB">QbB</a></dt>
|
||||
<dd>scale input to unit cube centered at the origin.</dd>
|
||||
<dt><a href="qh-optq.htm#QRn">QRn</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
|
||||
<dd>remove k'th coordinate from input. This computes the
|
||||
convex hull in one lower dimension.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="controls">qconvex controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
|
||||
degenerate facets of zero area.</dd>
|
||||
<dt><a href="qh-optq.htm#QJn">QJ</a></dt>
|
||||
<dd>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').</dd>
|
||||
<dt><a href="qh-optq.htm#Qc">Qc</a></dt>
|
||||
<dd>keep coplanar points</dd>
|
||||
<dt><a href="qh-optq.htm#Qi">Qi</a></dt>
|
||||
<dd>keep interior points</dd>
|
||||
<dt><a href="qh-opto.htm#f">f </a></dt>
|
||||
<dd>facet dump. Print the data structure for each facet.</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select facets containing point <em>n</em> as a vertex,</dd>
|
||||
<dt><a href="qh-optq.htm#QGn">QGn</a></dt>
|
||||
<dd>select facets that are visible from point <em>n</em>
|
||||
(marked 'good'). Use <em>-n</em> for the remainder.</dd>
|
||||
<dt><a href="qh-optp.htm#PDk">PDk:0</a></dt>
|
||||
<dd>select facets with a negative coordinate for dimension <i>k</i></dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report progress after constructing <em>n</em> facets</dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optq.htm#Qs">Qs</a></dt>
|
||||
<dd>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 ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
|
||||
If not, use option 'Qs'. It performs an exhaustive search for the
|
||||
best initial simplex. This is expensive is high dimensions.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="graphics">qconvex graphics</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>Display 2-d, 3-d, and 4-d convex hulls with Geomview ('<a
|
||||
href="qh-optg.htm#G">G</a>').</p>
|
||||
|
||||
<p>Display 2-d and 3-d convex hulls with Mathematica ('<a
|
||||
href="qh-opto.htm#m">m</a>').</p>
|
||||
|
||||
<p>To view 4-d convex hulls in 3-d, use '<a
|
||||
href="qh-optp.htm#Pdk">Pd0d1d2d3</a>' to select the positive
|
||||
octant and '<a href="qh-optg.htm#GDn">GrD2</a>' to drop dimension
|
||||
2. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">qconvex notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">qconvex
|
||||
conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The following terminology is used for convex hulls in Qhull.
|
||||
See <a href="index.htm#structure">Qhull's data structures</a>.</p>
|
||||
|
||||
<ul>
|
||||
<li><em>point</em> - <em>d</em> coordinates</li>
|
||||
<li><em>vertex</em> - extreme point of the input set</li>
|
||||
<li><em>ridge</em> - <i>d-1</i> vertices between two
|
||||
neighboring facets</li>
|
||||
<li><em>hyperplane</em> - halfspace defined by a unit normal
|
||||
and offset</li>
|
||||
<li><em>coplanar point</em> - a nearly incident point to a
|
||||
hyperplane</li>
|
||||
<li><em>centrum</em> - a point on the hyperplane for testing
|
||||
convexity</li>
|
||||
<li><em>facet</em> - a facet with vertices, ridges, coplanar
|
||||
points, neighboring facets, and hyperplane</li>
|
||||
<li><em>simplicial facet</em> - a facet with <em>d</em>
|
||||
vertices, <em>d</em> ridges, and <em>d</em> neighbors</li>
|
||||
<li><em>non-simplicial facet</em> - a facet with more than <em>d</em>
|
||||
vertices</li>
|
||||
<li><em>good facet</em> - a facet selected by '<a
|
||||
href="qh-optq.htm#QVn">QVn</a>', etc.</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">qconvex options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
•<a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
416
xs/src/qhull/html/qdelau_f.htm
Normal file
416
xs/src/qhull/html/qdelau_f.htm
Normal file
@ -0,0 +1,416 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qdelaunay Qu -- furthest-site Delaunay triangulation</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<a name="TOP"><b>Up</b></a><b>:</b>
|
||||
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a>qdelaunay Qu -- furthest-site Delaunay triangulation</h1>
|
||||
|
||||
<p>The furthest-site Delaunay triangulation corresponds to the upper facets of the <a href="qdelaun.htm">Delaunay construction</a>.
|
||||
Its vertices are the
|
||||
extreme points of the input sites.
|
||||
It is the dual of the <a
|
||||
href="qvoron_f.htm">furthest-site Voronoi diagram</a>.
|
||||
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
|
||||
href="qh-optq.htm#Qu">Qu</a> <a
|
||||
href="qh-optq.htm#Qt">Qt</a> <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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'.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
|
||||
href="qh-optq.htm#Qu">Qu</a> <a
|
||||
href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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'.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox r y c G1 D2 | qdelaunay <a
|
||||
href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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).
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (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.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (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 <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>The output for 3-d, furthest-site Delaunay triangulations may be confusing if the
|
||||
input contains cospherical data. See the FAQ item
|
||||
<a href=qh-faq.htm#extra>Why
|
||||
are there extra points in a 4-d or higher convex hull?</a>
|
||||
Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
|
||||
joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
</p>
|
||||
|
||||
<p>The 'qdelaunay' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
|
||||
'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 4-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>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</i>.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">furthest-site qdelaunay synopsis</a></h3>
|
||||
<blockquote>
|
||||
|
||||
See <a href="qdelaun.htm#synopsis">qdelaunay synopsis</a>. The same
|
||||
program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
|
||||
for furthest-site Delaunay triangulations.
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="input">furthest-site qdelaunay
|
||||
input</a></h3>
|
||||
|
||||
<blockquote>
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qdelaunay Qu < data.txt), a pipe (e.g., rbox 10 | qdelaunay Qu),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay Qu TI data.txt).
|
||||
|
||||
<p>For example, this is a square containing four random points.
|
||||
Its furthest-site Delaunay
|
||||
triangulation contains one square.
|
||||
<p>
|
||||
<blockquote>
|
||||
<tt>rbox c 4 D2 > data</tt>
|
||||
<blockquote><pre>
|
||||
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
|
||||
</pre></blockquote>
|
||||
|
||||
<p><tt>qdelaunay Qu i < data</tt>
|
||||
<blockquote><pre>
|
||||
|
||||
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
|
||||
</pre></blockquote>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="outputs">furthest-site qdelaunay
|
||||
outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of furthest-site Delaunay triangulations:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dd><b>furthest-site Delaunay regions</b></dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fv">Fv</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Ft">Ft</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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., <em>-1</em>) 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.</dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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., <em>-1</em>) 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 <em>0</em> and three
|
||||
regions outside of the furthest-site Delaunay triangulation.</dd>
|
||||
<dt><a href="qh-optf.htm#Fa">Fa</a></dt>
|
||||
<dd>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. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Input sites</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fx">Fx</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-optf.htm#FA">FA</a></dt>
|
||||
<dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
|
||||
and '<a href="qh-optf.htm#FS">FS</a>'. This is the
|
||||
same as the area of the convex hull.</dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>print upper facets of the corresponding convex hull (a
|
||||
paraboloid)</dd>
|
||||
<dt><a href="qh-opto.htm#m">m</a></dt>
|
||||
<dd>Mathematica output for the upper facets of the paraboloid (2-d triangulations).</dd>
|
||||
<dt><a href="qh-optf.htm#FM">FM</a></dt>
|
||||
<dd>Maple output for the upper facets of the paraboloid (2-d triangulations).</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary for the furthest-site Delaunay triangulation. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' and '<a
|
||||
href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="controls">furthest-site qdelaunay
|
||||
controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qu">Qu</a></dt>
|
||||
<dd>must be used for furthest-site Delaunay triangulation.</dd>
|
||||
<dt><a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
|
||||
degenerate facets of zero area.</dd>
|
||||
<dt><a href="qh-optq.htm#QJn">QJ</a></dt>
|
||||
<dd>joggle the input to avoid cospherical and coincident
|
||||
sites. It is less accurate than triangulated output ('Qt').</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select facets adjacent to input site <em>n</em> (marked
|
||||
'good').</dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report progress after constructing <em>n</em> facets</dd>
|
||||
<dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
|
||||
<dd>include upper and lower facets in the output. Set <em>k</em>
|
||||
to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
|
||||
<dt><a href="qh-opto.htm#f">f</a></dt>
|
||||
<dd>facet dump. Print the data structure for each facet (i.e., furthest-site Delaunay region).</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="graphics">furthest-site qdelaunay
|
||||
graphics</a></h3>
|
||||
<blockquote>
|
||||
|
||||
See <a href="qdelaun.htm#graphics">Delaunay graphics</a>.
|
||||
They are the same except for Mathematica and Maple output.
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">furthest-site
|
||||
qdelaunay notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The furthest-site Delaunay triangulation does not
|
||||
record coincident input sites. Use <tt>qdelaunay</tt> instead.
|
||||
|
||||
<p><tt>qdelaunay Qu</tt> does not work for purely cocircular
|
||||
or cospherical points (e.g., rbox c | qdelaunay Qu). Instead,
|
||||
use <tt>qdelaunay Qz</tt> -- 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.
|
||||
|
||||
<p>A non-simplicial, furthest-site Delaunay region indicates nearly cocircular or
|
||||
cospherical input sites. To avoid non-simplicial regions triangulate
|
||||
the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
|
||||
the input ('<a href="qh-optq.htm#QJn">QJ</a>'). Joggled input
|
||||
is less accurate than triangulated output.
|
||||
You may also triangulate
|
||||
non-simplicial regions with option '<a
|
||||
href="qh-optf.htm#Ft">Ft</a>'. It adds
|
||||
the centrum to non-simplicial regions. Alternatively, use an <a
|
||||
href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
|
||||
|
||||
<p>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 <a href="../src/libqhull/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">furthest-site qdelaunay conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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 <a
|
||||
href="qconvex.htm#conventions">convex hull conventions</a>, <a
|
||||
href="qdelaun.htm#conventions">Delaunay conventions</a>,
|
||||
and <a href="index.htm#structure">Qhull's data structures</a></p>
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li><em>input site</em> - a point in the input (one dimension
|
||||
lower than a point on the convex hull)</li>
|
||||
<li><em>point</em> - <i>d+1</i> coordinates. The last
|
||||
coordinate is the sum of the squares of the input site's
|
||||
coordinates</li>
|
||||
<li><em>vertex</em> - a point on the paraboloid. It
|
||||
corresponds to a unique input site. </li>
|
||||
<li><em>furthest-site Delaunay facet</em> - an upper facet of the
|
||||
paraboloid. The last coefficient of its normal is
|
||||
clearly positive.</li>
|
||||
<li><em>furthest-site Delaunay region</em> - a furthest-site Delaunay
|
||||
facet projected to the input sites</li>
|
||||
<li><em>non-simplicial facet</em> - more than <em>d</em>
|
||||
points are cocircular or cospherical</li>
|
||||
<li><em>good facet</em> - a furthest-site Delaunay facet with optional
|
||||
restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">furthest-site qdelaunay options</a></h3>
|
||||
<blockquote>
|
||||
|
||||
See <a href="qdelaun.htm#options">qdelaunay options</a>. The same
|
||||
program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
|
||||
for furthest-site Delaunay triangulations.
|
||||
|
||||
</blockquote>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
628
xs/src/qhull/html/qdelaun.htm
Normal file
628
xs/src/qhull/html/qdelaun.htm
Normal file
@ -0,0 +1,628 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qdelaunay -- Delaunay triangulation</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<a name="TOP"><b>Up</b></a><b>:</b>
|
||||
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a>qdelaunay -- Delaunay triangulation</h1>
|
||||
|
||||
<p>The Delaunay triangulation is the triangulation with empty
|
||||
circumspheres. It has many useful properties and applications.
|
||||
See the survey article by Aurenhammer [<a
|
||||
href="index.htm#aure91">'91</a>] and the detailed introduction
|
||||
by O'Rourke [<a href="index.htm#orou94">'94</a>]. </p>
|
||||
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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).</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
|
||||
href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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'.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>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 ('<a href=qh-optq.htm#Qbb>Qbb</a>').
|
||||
It computes the convex
|
||||
hull of the lifted sites, and projects the lower convex hull to
|
||||
the input.
|
||||
|
||||
<p>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 <a
|
||||
href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
|
||||
See the examples, <a href="qh-eg.htm#delaunay">Delaunay and
|
||||
Voronoi diagrams</a>.</p>
|
||||
|
||||
<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
|
||||
Voronoi diagram questions.</p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Use option '<a href="qh-optq.htm#Qz">Qz</a>' if the input is circular, cospherical, or
|
||||
nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (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.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (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 <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>The output for 3-d Delaunay triangulations may be confusing if the
|
||||
input contains cospherical data. See the FAQ item
|
||||
<a href=qh-faq.htm#extra>Why
|
||||
are there extra points in a 4-d or higher convex hull?</a>
|
||||
Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
|
||||
joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
</p>
|
||||
|
||||
<p>The 'qdelaunay' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
|
||||
'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 4-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>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</i>.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">qdelaunay synopsis</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="input">qdelaunay
|
||||
input</a></h3>
|
||||
|
||||
<blockquote>
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qdelaunay < data.txt), a pipe (e.g., rbox 10 | qdelaunay),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay TI data.txt).
|
||||
|
||||
<p>For example, this is four cocircular points inside a square. Its Delaunay
|
||||
triangulation contains 8 triangles and one four-sided
|
||||
figure.
|
||||
<p>
|
||||
<blockquote>
|
||||
<tt>rbox s 4 W0 c G1 D2 > data</tt>
|
||||
<blockquote><pre>
|
||||
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
|
||||
</pre></blockquote>
|
||||
|
||||
<p><tt>qdelaunay s i < data</tt>
|
||||
<blockquote><pre>
|
||||
|
||||
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
|
||||
</pre></blockquote>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="outputs">qdelaunay
|
||||
outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of Delaunay triangulations:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dd><b>Delaunay regions</b></dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>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 ('<a href="qh-optq.htm#Qt">Qt</a>') to avoid non-simpicial regions. For the circle-in-square example,
|
||||
eight Delaunay regions are triangular and the ninth has four input sites.</dd>
|
||||
<dt><a href="qh-optf.htm#Fv">Fv</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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., <em>-1</em>) 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.</dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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., <em>-1</em>) indicate regions
|
||||
outside of the Delaunay triangulation.
|
||||
For the circle-in-square example, each point on the circle belongs to four
|
||||
Delaunay regions. Use '<a href="qh-optq.htm#Qc">Qc</a> FN'
|
||||
to include coincident input sites and deleted vertices. </dd>
|
||||
<dt><a href="qh-optf.htm#Fa">Fa</a></dt>
|
||||
<dd>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. </dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Input sites</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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'<a href="qh-optf.htm#Fs">Fs</a>').
|
||||
A coincident site is assigned to one Delaunay
|
||||
region. Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
|
||||
coincident sites.</dd>
|
||||
<dt><a href="qh-optf.htm#FP">FP</a></dt>
|
||||
<dd>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'<a href="qh-optf.htm#Fs">Fs</a>').
|
||||
Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
|
||||
coincident sites.</dd>
|
||||
<dt><a href="qh-optf.htm#Fx">Fx</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-optf.htm#FA">FA</a></dt>
|
||||
<dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
|
||||
and '<a href="qh-optf.htm#FS">FS</a>'</dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>print lower facets of the corresponding convex hull (a
|
||||
paraboloid)</dd>
|
||||
<dt><a href="qh-opto.htm#m">m</a></dt>
|
||||
<dd>Mathematica output for the lower facets of the paraboloid (2-d triangulations).</dd>
|
||||
<dt><a href="qh-optf.htm#FM">FM</a></dt>
|
||||
<dd>Maple output for the lower facets of the paraboloid (2-d triangulations).</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary for the Delaunay triangulation. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' and '<a
|
||||
href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="controls">qdelaunay
|
||||
controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
|
||||
degenerate facets of zero area.</dd>
|
||||
<dt><a href="qh-optq.htm#QJn">QJ</a></dt>
|
||||
<dd>joggle the input to avoid cospherical and coincident
|
||||
sites. It is less accurate than triangulated output ('Qt').</dd>
|
||||
<dt><a href="qh-optq.htm#Qu">Qu</a></dt>
|
||||
<dd>compute the <a href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.</dd>
|
||||
<dt><a href="qh-optq.htm#Qz">Qz</a></dt>
|
||||
<dd>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 '<a href="qh-optf.htm#Ft">Ft</a>' and '<a
|
||||
href="qh-opto.htm#o">o</a>'.</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select facets adjacent to input site <em>n</em> (marked
|
||||
'good').</dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report progress after constructing <em>n</em> facets</dd>
|
||||
<dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
|
||||
<dd>include upper and lower facets in the output. Set <em>k</em>
|
||||
to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
|
||||
<dt><a href="qh-opto.htm#f">f</a></dt>
|
||||
<dd>facet dump. Print the data structure for each facet (i.e., Delaunay region).</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="graphics">qdelaunay
|
||||
graphics</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>For 2-d and 3-d Delaunay triangulations, Geomview ('qdelaunay <a
|
||||
href="qh-optg.htm#G">G</a>') displays the corresponding convex
|
||||
hull (a paraboloid). </p>
|
||||
|
||||
<p>To view a 2-d Delaunay triangulation, use 'qdelaunay <a
|
||||
href="qh-optg.htm#GDn">GrD2</a>' to drop the last dimension. This
|
||||
is the same as viewing the hull without perspective (see
|
||||
Geomview's 'cameras' menu). </p>
|
||||
|
||||
<p>To view a 3-d Delaunay triangulation, use 'qdelaunay <a
|
||||
href="qh-optg.htm#GDn">GrD3</a>' 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 '<a href="qh-optg.htm#Gt">Gt</a>' to make
|
||||
the outer ridges transparent in 3-d. See <a
|
||||
href="qh-eg.htm#delaunay">Delaunay and Voronoi examples</a>.</p>
|
||||
|
||||
<p>For 2-d Delaunay triangulations, Mathematica ('<a
|
||||
href="qh-opto.htm#m">m</a>') and Maple ('<a
|
||||
href="qh-optf.htm#FM">FM</a>') output displays the lower facets of the corresponding convex
|
||||
hull (a paraboloid). </p>
|
||||
|
||||
<p>For 2-d, furthest-site Delaunay triangulations, Maple and Mathematica output ('<a
|
||||
href="qh-optq.htm#Qu">Qu</a> <a
|
||||
href="qh-opto.htm#m">m</a>') displays the upper facets of the corresponding convex
|
||||
hull (a paraboloid). </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">qdelaunay
|
||||
notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>A non-simplicial Delaunay region indicates nearly cocircular or
|
||||
cospherical input sites. To avoid non-simplicial regions either triangulate
|
||||
the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
|
||||
the input ('<a href="qh-optq.htm#QJn">QJ</a>'). Triangulated output
|
||||
is more accurate than joggled input. Alternatively, use an <a
|
||||
href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
|
||||
|
||||
<p>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 <a href="../src/libqhull/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
|
||||
|
||||
<p>See <a href=qh-impre.htm#delaunay>Imprecision issues :: Delaunay triangulations</a>
|
||||
for a discussion of precision issues. Deleted vertices indicate
|
||||
highly degenerate input. They are listed in the summary output and
|
||||
option '<a href="qh-optf.htm#Fs">Fs</a>'.</p>
|
||||
|
||||
<p>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]
|
||||
</p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>With the <a href="qh-code.htm#library">Qhull library</a>, you
|
||||
can use <tt>qh_findbestfacet</tt> in <tt>poly2.c</tt> 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 -- <tt>qh_setdelaunay</tt>). Do not use options
|
||||
'<a href="qh-optq.htm#Qbb">Qbb</a>', '<a href="qh-optq.htm#QbB">QbB</a>',
|
||||
'<a href="qh-optq.htm#Qbk">Qbk:n</a>', or '<a
|
||||
href="qh-optq.htm#QBk">QBk:n</a>' since these scale the last
|
||||
coordinate. </p>
|
||||
|
||||
<p>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:
|
||||
|
||||
<pre>
|
||||
qdelaunay <data s FQ QV0 p | qconvex s Qb3:0B3:0 p
|
||||
</pre>
|
||||
|
||||
<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. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">qdelaunay conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The following terminology is used for Delaunay triangulations
|
||||
in Qhull for dimension <i>d</i>. The underlying structure is the
|
||||
lower facets of a convex hull in dimension <i>d+1</i>. For
|
||||
further information, see <a href="index.htm#structure">data
|
||||
structures</a> and <a href="qconvex.htm#conventions">convex hull
|
||||
conventions</a>.</p>
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li><em>input site</em> - a point in the input (one dimension
|
||||
lower than a point on the convex hull)</li>
|
||||
<li><em>point</em> - a point has <i>d+1</i> coordinates. The
|
||||
last coordinate is the sum of the squares of the input
|
||||
site's coordinates</li>
|
||||
<li><em>coplanar point</em> - a <em>coincident</em>
|
||||
input site or a deleted vertex. Deleted vertices
|
||||
indicate highly degenerate input.</li>
|
||||
<li><em>vertex</em> - a point on the paraboloid. It
|
||||
corresponds to a unique input site. </li>
|
||||
<li><em>point-at-infinity</em> - a point added above the
|
||||
paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
|
||||
<li><em>lower facet</em> - a facet corresponding to a
|
||||
Delaunay region. The last coefficient of its normal is
|
||||
clearly negative.</li>
|
||||
<li><em>upper facet</em> - a facet corresponding to a
|
||||
furthest-site Delaunay region. The last coefficient of
|
||||
its normal is clearly positive. </li>
|
||||
<li><em>Delaunay region</em> - a
|
||||
lower facet projected to the input sites</li>
|
||||
<li><em>upper Delaunay region</em> - an upper facet projected
|
||||
to the input sites</li>
|
||||
<li><em>non-simplicial facet</em> - more than <em>d</em>
|
||||
input sites are cocircular or cospherical</li>
|
||||
<li><em>good facet</em> - a Delaunay region with optional
|
||||
restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">qdelaunay options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
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xs/src/qhull/html/qh-code.htm
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693
xs/src/qhull/html/qh-eg.htm
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xs/src/qhull/html/qh-eg.htm
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@ -0,0 +1,693 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Examples of Qhull</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
|
||||
page</a> for Qhull <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
|
||||
while loading)<br>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
|
||||
src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
|
||||
height="100"></a> Examples of Qhull</h1>
|
||||
|
||||
<p>This section of the Qhull manual will introduce you to Qhull
|
||||
and its options. Each example is a file for viewing with <a
|
||||
href="index.htm#geomview">Geomview</a>. You will need to
|
||||
use a Unix computer with a copy of Geomview.
|
||||
<p>
|
||||
If you are not running Unix, you can view <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures</a>
|
||||
for some of the examples. To understand Qhull without Geomview, try the
|
||||
examples in <a href="qh-quick.htm#programs">Programs</a> and
|
||||
<a href="qh-quick.htm#programs">Programs/input</a>. You can also try small
|
||||
examples that you compute by hand. Use <a href="rbox.htm">rbox</a>
|
||||
to generate examples.
|
||||
<p>
|
||||
To generate the Geomview examples, execute the shell script <tt>eg/q_eg</tt>.
|
||||
It uses <tt>rbox</tt>. The shell script <tt>eg/q_egtest</tt> generates
|
||||
test examples, and <tt>eg/q_test</tt> exercises the code. If you
|
||||
find yourself viewing the inside of a 3-d example, use Geomview's
|
||||
normalization option on the 'obscure' menu.</p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOP">»</a><a name="TOC">Qhull examples: Table of
|
||||
Contents </a></h2>
|
||||
|
||||
<ul>
|
||||
<li><a href="#2d">2-d and 3-d examples</a></li>
|
||||
<li><a href="#how">How Qhull adds a point</a></li>
|
||||
<li><a href="#joggle">Triangulated output or joggled input</a></li>
|
||||
<li><a href="#delaunay">Delaunay and Voronoi diagrams</a></li>
|
||||
<li><a href="#merge">Facet merging for imprecision</a></li>
|
||||
<li><a href="#4d">4-d objects</a></li>
|
||||
<li><a href="#half">Halfspace intersections</a></li>
|
||||
</ul>
|
||||
|
||||
<hr>
|
||||
<ul>
|
||||
<li><a href="#TOC">»</a><a name="2d">2-d and 3-d examples</a><ul>
|
||||
<li><a href="#01">eg.01.cube</a></li>
|
||||
<li><a href="#02">eg.02.diamond.cube</a></li>
|
||||
<li><a href="#03">eg.03.sphere</a></li>
|
||||
<li><a href="#04">eg.04.circle</a></li>
|
||||
<li><a href="#05">eg.05.spiral</a></li>
|
||||
<li><a href="#06">eg.06.merge.square</a></li>
|
||||
<li><a href="#07">eg.07.box</a></li>
|
||||
<li><a href="#08a">eg.08a.cube.sphere</a></li>
|
||||
<li><a href="#08b">eg.08b.diamond.sphere</a></li>
|
||||
<li><a href="#09">eg.09.lens</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#TOC">»</a><a name="how">How Qhull adds a point</a><ul>
|
||||
<li><a href="#10a">eg.10a.sphere.visible</a></li>
|
||||
<li><a href="#10b">eg.10b.sphere.beyond</a></li>
|
||||
<li><a href="#10c">eg.10c.sphere.horizon</a></li>
|
||||
<li><a href="#10d">eg.10d.sphere.cone</a></li>
|
||||
<li><a href="#10e">eg.10e.sphere.new</a></li>
|
||||
<li><a href="#14">eg.14.sphere.corner</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#TOC">»</a> <a name="joggle">Triangulated output or joggled input</a>
|
||||
<ul>
|
||||
<li><a href="#15a">eg.15a.surface</a></li>
|
||||
<li><a href="#15b">eg.15b.triangle</a></li>
|
||||
<li><a href="#15c">eg.15c.joggle</a></li>
|
||||
</ul>
|
||||
<li><a href="#TOC">»</a><a name="delaunay"> Delaunay and
|
||||
Voronoi diagrams</a><ul>
|
||||
<li><a href="#17a">eg.17a.delaunay.2</a></li>
|
||||
<li><a href="#17b">eg.17b.delaunay.2i</a></li>
|
||||
<li><a href="#17c">eg.17c.delaunay.2-3</a></li>
|
||||
<li><a href="#17d">eg.17d.voronoi.2</a></li>
|
||||
<li><a href="#17e">eg.17e.voronoi.2i</a></li>
|
||||
<li><a href="#17f">eg.17f.delaunay.3</a></li>
|
||||
<li><a href="#18a">eg.18a.furthest.2-3</a></li>
|
||||
<li><a href="#18b">eg.18b.furthest-up.2-3</a></li>
|
||||
<li><a href="#18c">eg.18c.furthest.2</a></li>
|
||||
<li><a href="#19">eg.19.voronoi.region.3</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#TOC">»</a><a name="merge">Facet merging for
|
||||
imprecision </a><ul>
|
||||
<li><a href="#20">eg.20.cone</a></li>
|
||||
<li><a href="#21a">eg.21a.roundoff.errors</a></li>
|
||||
<li><a href="#21b">eg.21b.roundoff.fixed</a></li>
|
||||
<li><a href="#22a">eg.22a.merge.sphere.01</a></li>
|
||||
<li><a href="#22b">eg.22b.merge.sphere.-01</a></li>
|
||||
<li><a href="#22c">eg.22c.merge.sphere.05</a></li>
|
||||
<li><a href="#22d">eg.22d.merge.sphere.-05</a></li>
|
||||
<li><a href="#23">eg.23.merge.cube</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#TOC">»</a><a name="4d">4-d objects</a><ul>
|
||||
<li><a href="#24">eg.24.merge.cube.4d-in-3d</a></li>
|
||||
<li><a href="#30">eg.30.4d.merge.cube</a></li>
|
||||
<li><a href="#31">eg.31.4d.delaunay</a></li>
|
||||
<li><a href="#32">eg.32.4d.octant</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#TOC">»</a><a name="half">Halfspace
|
||||
intersections</a><ul>
|
||||
<li><a href="#33a">eg.33a.cone</a></li>
|
||||
<li><a href="#33b">eg.33b.cone.dual</a></li>
|
||||
<li><a href="#33c">eg.33c.cone.halfspace</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOC">»</a>2-d and 3-d examples</h2>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="01">rbox c D3 | qconvex G
|
||||
>eg.01.cube </a></h3>
|
||||
|
||||
<p>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 <tt>rbox</tt>,
|
||||
you can generate hypercubes in any dimension. Above 7-d the
|
||||
number of intermediate facets grows rapidly. Use '<a
|
||||
href="qh-optt.htm#TFn">TFn</a>' to track qconvex's progress. Note
|
||||
that each facet is a square that qconvex merged from coplanar
|
||||
triangles.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="02">rbox c d G3.0 | qconvex G
|
||||
>eg.02.diamond.cube </a></h3>
|
||||
|
||||
<p>The second example is a cube plus a diamond ('d') scaled by <tt>rbox</tt>'s
|
||||
'G' option. In higher dimensions, diamonds are much simpler than
|
||||
hypercubes. </p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="03">rbox s 100 D3 | qconvex G
|
||||
>eg.03.sphere </a></h3>
|
||||
|
||||
<p>The <tt>rbox s</tt> 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.,<i> rbox 1000 s | qconvex
|
||||
A-0.95 p | qconvex G >eg.99</i>.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="04">rbox s 100 D2 | qconvex G
|
||||
>eg.04.circle </a></h3>
|
||||
|
||||
<p>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 <a
|
||||
href="index.htm#pre-sha85">'85</a>]. It was the model for
|
||||
Qhull.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="05">rbox 10 l | qconvex G
|
||||
>eg.05.spiral </a></h3>
|
||||
|
||||
<p>One rotation of a spiral.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="06">rbox 1000 D2 | qconvex C-0.03
|
||||
Qc Gapcv >eg.06.merge.square</a></h3>
|
||||
|
||||
<p>This demonstrates how Qhull handles precision errors. Option '<a
|
||||
href="qh-optc.htm#Cn">C-0.03</a>' requires a clearly convex angle
|
||||
between adjacent facets. Otherwise, Qhull merges the facets. </p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="07">rbox 1000 D3 | qconvex G
|
||||
>eg.07.box </a></h3>
|
||||
|
||||
<p>Here's the same distribution but in 3-d with Qhull handling
|
||||
machine roundoff errors. Note the large number of facets. </p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="08a">rbox c G0.4 s 500 | qconvex G
|
||||
>eg.08a.cube.sphere </a></h3>
|
||||
|
||||
<p>The sphere is just barely poking out of the cube. Try the same
|
||||
distribution with randomization turned on ('<a
|
||||
href="qh-optq.htm#Qr">Qr</a>'). 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.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="08b">rbox d G0.6 s 500 | qconvex G
|
||||
>eg.08b.diamond.sphere </a></h3>
|
||||
|
||||
<p>This is a combination of the diamond distribution and the
|
||||
sphere.</p>
|
||||
|
||||
<h3><a href="#2d">»</a><a name="09">rbox 100 L3 G0.5 s | qconvex
|
||||
G >eg.09.lens </a></h3>
|
||||
|
||||
<p>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 <tt>geom.c</tt>) 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. </p>
|
||||
|
||||
<p>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 <tt>geom2.c</tt>).
|
||||
</p>
|
||||
|
||||
<h2><a href="#TOC">»</a>How Qhull adds a point</h2>
|
||||
|
||||
<h3><a href="#how">»</a><a name="10a">rbox 100 s P0.5,0.5,0.5 |
|
||||
qconvex Ga QG0 >eg.10a.sphere.visible</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#how">»</a><a name="10b">rbox 100 s
|
||||
P0.5,0.5,0.5|qconvex Ga QG-0 >eg.10b.sphere.beyond </a></h3>
|
||||
|
||||
<p>These are the facets that are not visible from the point.
|
||||
Qhull will keep these facets.</p>
|
||||
|
||||
<h3><a href="#how">»</a><a name="10c">rbox 100 s P0.5,0.5,0.5 |
|
||||
qconvex PG Ga QG0 >eg.10c.sphere.horizon </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#how">»</a><a name="10d">rbox 100 s P0.5,0.5,0.5 |
|
||||
qconvex Ga QV0 PgG >eg.10d.sphere.cone </a></h3>
|
||||
|
||||
<p>This is the cone of points from the new point to the horizon
|
||||
facets. Try combining this image with <tt>eg.10c.sphere.horizon</tt>
|
||||
and <tt>eg.10a.sphere.visible</tt>.
|
||||
</p>
|
||||
|
||||
<h3><a href="#how">»</a><a name="10e">rbox 100 s P0.5,0.5,0.5 |
|
||||
qconvex Ga >eg.10e.sphere.new</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#how">»</a><a name="14">rbox 100 s P0.5,0.5,0.5 |
|
||||
qhull Ga QV0g Q0 >eg.14.sphere.corner</a></h3>
|
||||
|
||||
<p>The '<a href="qh-optq.htm#QVn">QVn</a>', '<a
|
||||
href="qh-optq.htm#QGn">QGn </a>' and '<a href="qh-optp.htm#Pdk">Pdk</a>'
|
||||
options define good facets for Qhull. In this case '<a
|
||||
href="qh-optq.htm#QVn">QV0</a>' defines the 0'th point
|
||||
[0.5,0.5,0.5] as the good vertex, and '<a href="qh-optq.htm#Qg">Qg</a>'
|
||||
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.</p>
|
||||
|
||||
<h2><a href="#TOC">»</a>Triangulated output or joggled input</h2>
|
||||
|
||||
<h3><a href="#joggle">»</a><a name="15a">rbox 500 W0 | qconvex QR0 Qc Gvp >eg.15a.surface</a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>If the facets were not merged, Qhull
|
||||
would report precision problems. For example, turn off facet merging
|
||||
with option '<a href="qh-optq.htm#Q0">Q0</a>'. Qhull may report concave
|
||||
facets, flipped facets, or other precision errors:
|
||||
<blockquote>
|
||||
rbox 500 W0 | qhull QR0 Q0
|
||||
</blockquote>
|
||||
|
||||
<p>
|
||||
<h3><a href="#joggle">»</a><a name="15b">rbox 500 W0 | qconvex QR0 Qt Qc Gvp >eg.15b.triangle</a></h3>
|
||||
|
||||
<p>Like the previous examples, this is the convex hull of 500 points on the
|
||||
surface of a cube. Option '<a href="qh-optq.htm#Qt">Qt</a>' triangulates the
|
||||
non-simplicial facets. Triangulated output is
|
||||
particularly helpful for Delaunay triangulations.
|
||||
|
||||
<p>
|
||||
<h3><a href="#joggle">»</a><a name="15c">rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp >eg.15c.joggle</a></h3>
|
||||
|
||||
<p>This is the convex hull of 500 joggled points on the surface of
|
||||
a cube. The option '<a href="qh-optq.htm#QJn">QJ5e-2</a>'
|
||||
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.
|
||||
<p>
|
||||
With option '<a href="qh-optq.htm#QJn">QJ</a>', 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.
|
||||
<p>
|
||||
Joggled input is a simple solution to precision problems in
|
||||
computational geometry. Qhull can also merge facets to handle
|
||||
precision problems. See <a href="qh-impre.htm#joggle">Merged facets or joggled input</a>.
|
||||
|
||||
<h2><a href="#TOC">»</a>Delaunay and Voronoi diagrams</h2>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17a">qdelaunay Qt
|
||||
<eg.data.17 GnraD2 >eg.17a.delaunay.2</a></h3>
|
||||
|
||||
<p>
|
||||
The input file, <tt>eg.data.17</tt>, consists of a square, 15 random
|
||||
points within the outside half of the square, and 6 co-circular
|
||||
points centered on the square.
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qt">Qt</a>'
|
||||
triangulates the co-circular facet.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17b">qdelaunay <eg.data.17
|
||||
GnraD2 >eg.17b.delaunay.2i</a></h3>
|
||||
|
||||
<p>This is the same example without triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>'). qdelaunay
|
||||
merges the non-unique Delaunay triangles into a hexagon.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17c">qdelaunay <eg.data.17
|
||||
Ga >eg.17c.delaunay.2-3 </a></h3>
|
||||
|
||||
<p>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 <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html">object</a>
|
||||
with one of the previous diagrams.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17d">qvoronoi QJ
|
||||
<eg.data.17 Gna >eg.17d.voronoi.2</a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optf.htm#Fo2">Fo</a>'.
|
||||
</p>
|
||||
|
||||
<p>Instead
|
||||
of triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>'), this
|
||||
example uses joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
Normally, you should use neither 'QJ' nor 'Qt' for Voronoi diagrams.
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17e">qvoronoi <eg.data.17
|
||||
Gna >eg.17e.voronoi.2i </a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>This example does not use options 'Qt' or 'QJ'. The cocircular
|
||||
input sites define one Voronoi vertex near the origin. </p>
|
||||
|
||||
<p>Option 'Qt' would triangulate the corresponding Delaunay region into
|
||||
four triangles. Each triangle is assigned the same Voronoi vertex.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="17f"> rbox c G0.1 d |
|
||||
qdelaunay Gt Qz <eg.17f.delaunay.3 </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qz">Qz</a>'
|
||||
to add a point "at infinity". This avoids a degenerate
|
||||
input due to cospherical points.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="18a">rbox 10 D2 d | qdelaunay
|
||||
Qu G >eg.18a.furthest.2-3 </a></h3>
|
||||
|
||||
<p>The furthest-site Voronoi diagram contains Voronoi regions for
|
||||
points that are <i>furthest </i>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 (<a href="#17c">eg.17c.delaunay.2-3</a>).
|
||||
The upper convex hull (blue) generates the furthest-site Delaunay
|
||||
triangulation. </p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="18b">rbox 10 D2 d | qdelaunay
|
||||
Qu Pd2 G >eg.18b.furthest-up.2-3</a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="18c">rbox 10 D2 d | qvoronoi
|
||||
Qu Gv >eg.18c.furthest.2</a></h3>
|
||||
|
||||
<p>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 <a
|
||||
href="qh-opto.htm#o">o</a>'. </p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#delaunay">»</a><a name="19">rbox 10 D3 | qvoronoi QV5
|
||||
p | qconvex G >eg.19.voronoi.region.3 </a></h3>
|
||||
|
||||
<p>This shows the Voronoi region for input site 5 of a 3-d
|
||||
Voronoi diagram.</p>
|
||||
|
||||
<h2><a href="#TOC">»</a>Facet merging for imprecision</h2>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="20">rbox r s 20 Z1 G0.2 |
|
||||
qconvex G >eg.20.cone </a></h3>
|
||||
|
||||
<p>There are two things unusual about this <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html">cone</a>.
|
||||
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 <tt>rbox</tt> 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.</p>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="21a">rbox 200 s | qhull Q0
|
||||
R0.01 Gav Po >eg.21a.roundoff.errors </a></h3>
|
||||
|
||||
<p>This is the convex hull of 200 cospherical points with
|
||||
precision errors ignored ('<a href="qh-optq.htm#Q0">Q0</a>'). To
|
||||
demonstrate the effect of roundoff error, we've added a random
|
||||
perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>') 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. </p>
|
||||
|
||||
<p>Different machines may not produce this picture. If your
|
||||
machine generated a long error message, decrease the number of
|
||||
points or the random perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>').
|
||||
If it did not report flipped facets, increase the number of
|
||||
points or perturbation.</p>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="21b">rbox 200 s | qconvex Qc
|
||||
R0.01 Gpav >eg.21b.roundoff.fixed </a></h3>
|
||||
|
||||
<p>Qhull handles the random perturbations and returns an
|
||||
imprecise <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html">sphere</a>.
|
||||
In this case, the output is a weak approximation to the points.
|
||||
This is because a random perturbation of '<a
|
||||
href="qh-optc.htm#Rn">R0.01 </a>' 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. </p>
|
||||
<p>
|
||||
If you start with a smaller random perturbation, you
|
||||
can use joggle ('<a href="qh-optq.htm#QJn">QJn</a>') to avoid
|
||||
precision problems. You need to set <i>n</i> significantly
|
||||
larger than the random perturbation. For example, try
|
||||
'rbox 200 s | qconvex Qc R1e-4 QJ1e-1'.
|
||||
|
||||
<h3><a href="#merge">»</a><a name="22a">rbox 1000 s| qconvex C0.01
|
||||
Qc Gcrp >eg.22a.merge.sphere.01</a></h3>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="22b">rbox 1000 s| qconvex
|
||||
C-0.01 Qc Gcrp >eg.22b.merge.sphere.-01</a></h3>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="22c">rbox 1000 s| qconvex C0.05
|
||||
Qc Gcrpv >eg.22c.merge.sphere.05</a></h3>
|
||||
|
||||
<h3><a href="#merge">»</a><a name="22d">rbox 1000 s| qconvex
|
||||
C-0.05 Qc Gcrpv >eg.22d.merge.sphere.-05</a></h3>
|
||||
|
||||
<p>The next four examples compare post-merging and pre-merging ('<a
|
||||
href="qh-optc.htm#Cn2">Cn</a>' vs. '<a href="qh-optc.htm#Cn">C-n</a>').
|
||||
Qhull uses '-' as a flag to indicate pre-merging.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<h3><a href="#merge">»</a><a name="23">rbox 1000 | qconvex s
|
||||
Gcprvah C0.1 Qc >eg.23.merge.cube</a></h3>
|
||||
|
||||
<p>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 ('<a href="qh-optc.htm#Cn2">C0.1</a>')
|
||||
instead of pre-merging.
|
||||
|
||||
<h2><a href="#TOC">»</a>4-d objects</h2>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#4d">»</a><a name="24">rbox 5000 D4 | qconvex s GD0v
|
||||
Pd0:0.5 C-0.02 C0.1 >eg.24.merge.cube.4d-in-3d</a></h3>
|
||||
|
||||
<p>Here's one facet of the imprecise cube in 4-d. It's projected
|
||||
into 3-d (the '<a href="qh-optg.htm#GDn">GDn</a>' 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.</p>
|
||||
|
||||
<h3><a href="#4d">»</a><a name="30">rbox 5000 D4 | qconvex s
|
||||
C-0.02 C0.1 Gh >eg.30.4d.merge.cube </a></h3>
|
||||
|
||||
<p><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html">Here</a>
|
||||
is the equivalent in 4-d of the imprecise <a href="#06">square</a>
|
||||
and imprecise <a href="#23">cube</a>. It's the imprecise convex
|
||||
hull of 5000 random points in a hypercube. It's a full 4-d object
|
||||
so Geomview's <tt>ginsu </tt>does not work. If you view it in
|
||||
Geomview, you'll be inside the hypercube. To view 4-d objects
|
||||
directly, either load the <tt>4dview</tt> module or the <tt>ndview
|
||||
</tt>module. For <tt>4dview</tt>, you must have started Geomview
|
||||
in the same directory as the object. For <tt>ndview</tt>,
|
||||
initialize a set of windows with the prefab menu, and load the
|
||||
object through Geomview. The <tt>4dview</tt> 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.</p>
|
||||
|
||||
<p>The '<a href="qh-optg.htm#Gh">Gh</a>' option prints the
|
||||
geometric intersections between adjacent facets. Note the strong
|
||||
convexity constraint for post-merging ('<a href="qh-optc.htm#Cn2">C0.1</a>').
|
||||
It deletes the small facets.</p>
|
||||
|
||||
<h3><a href="#4d">»</a><a name="31">rbox 20 D3 | qdelaunay G
|
||||
>eg.31.4d.delaunay </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Here we see all of the facets together. You can use Geomview's
|
||||
<tt>ndview</tt> 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.</p>
|
||||
|
||||
<p>You can slice the object apart using Geomview's <tt>4dview</tt>.
|
||||
With <tt>4dview</tt>, 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.</p>
|
||||
|
||||
<h3><a href="#4d">»</a><a name="32">rbox 30 s D4 | qconvex s G
|
||||
Pd0d1d2D3</a></h3>
|
||||
|
||||
<p>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 <tt>ndview</tt> on this example.</p>
|
||||
|
||||
<h2><a href="#TOC">»</a>Halfspace intersections</h2>
|
||||
|
||||
<h3><a href="#half">»</a><a name="33a">rbox 10 r s Z1 G0.3 |
|
||||
qconvex G >eg.33a.cone </a></h3>
|
||||
|
||||
<h3><a href="#half">»</a><a name="33b">rbox 10 r s Z1 G0.3 |
|
||||
qconvex FV n | qhalf G >eg.33b.cone.dual</a></h3>
|
||||
|
||||
<h3><a href="#half">»</a><a name="33c">rbox 10 r s Z1 G0.3 |
|
||||
qconvex FV n | qhalf Fp | qconvex G >eg.33c.cone.halfspace</a></h3>
|
||||
|
||||
<p>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 <a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html">both</a>
|
||||
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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home
|
||||
page for Qhull</a> <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
|
||||
while loading)<br>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
1547
xs/src/qhull/html/qh-faq.htm
Normal file
1547
xs/src/qhull/html/qh-faq.htm
Normal file
File diff suppressed because it is too large
Load Diff
106
xs/src/qhull/html/qh-get.htm
Normal file
106
xs/src/qhull/html/qh-get.htm
Normal file
@ -0,0 +1,106 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull Downloads</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org"><i>Qhull Home Page</i></a><br>
|
||||
</p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="../html/qh--cone.gif" alt="[CONE]" align="middle"
|
||||
width="100" height="100"></a> Qhull Downloads</h1>
|
||||
|
||||
<ul>
|
||||
<li><a href="http://www.qhull.org">Qhull Home Page</a> <p>Qhull
|
||||
computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace
|
||||
intersection about a point, furthest-site Delaunay
|
||||
triangulation, and furthest-site Voronoi diagram. It
|
||||
runs in 2-d, 3-d, 4-d, and higher dimensions. It
|
||||
implements the Quickhull algorithm for computing the
|
||||
convex hull. Qhull handles roundoff errors from floating
|
||||
point arithmetic. It can approximate a convex hull. </p>
|
||||
|
||||
<p>Visit <a href="http://www.qhull.org/news">Qhull News</a>
|
||||
for news, bug reports, change history, and users.
|
||||
If you use Qhull 2003.1 or 2009.1, please upgrade to 2015.2 or apply
|
||||
<a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.</p>
|
||||
</li>
|
||||
<li><a
|
||||
href="http://www.qhull.org/download/qhull-2015.2.zip">Download:
|
||||
Qhull 2015.2 for Windows 10, 8, 7, XP, and NT</a> (2.6 MB,
|
||||
<a href="http://www.qhull.org/README.txt">readme</a>,
|
||||
<a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
|
||||
<a href="http://www.qhull.org/download/qhull-2015.2.zip.md5sum">contents</a>)
|
||||
<p>Type: console programs for Windows (32- or 64-bit)</p>
|
||||
<p>Includes 32-bit executables, documentation, and sources files. It runs in a
|
||||
command window. Qhull may be compiled for 64-bits.</p>
|
||||
</li>
|
||||
<li><a href="http://github.com/qhull/qhull/wiki">GitHub Qhull</a> (git@github.com:qhull/qhull.git)
|
||||
<p>Type: git repository for Qhull. See recent <a href="https://github.com/qhull/qhull/blob/master/src/Changes.txt">Changes.txt</a></p>
|
||||
<p>Includes documentation, source files, C++ interface, and test programs. It builds with gcc, mingw,
|
||||
CMake, DevStudio, and Qt Creator.
|
||||
</p>
|
||||
</li>
|
||||
<li><a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz">Download: Qhull 2015.2 for Unix</a> (1.0 MB,
|
||||
<a href="http://www.qhull.org/README.txt">readme</a>,
|
||||
<a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
|
||||
<a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz.md5sum">contents</a>)
|
||||
<p>Type: C/C++ source code for 32-bit and 64-bit architectures. See <a href="http://www.qhull.org/src/Changes.txt">Changes.txt</a></p>
|
||||
<p>Includes documentation, source files, Makefiles, CMakeLists.txt, DevStudio projects, and Qt projects.
|
||||
Includes preliminary C++ support.</p>
|
||||
<p>Download and search sites for pre-built packages include
|
||||
<ul>
|
||||
<li><a href="https://launchpad.net/ubuntu/+source/qhull">https://launchpad.net/ubuntu/+source/qhull</a>
|
||||
<li><a href="http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull">http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull</a>
|
||||
<li><a href="https://www.archlinux.org/packages/extra/i686/qhull/">https://www.archlinux.org/packages/extra/i686/qhull/</a>
|
||||
<li><a href="http://rpmfind.net/linux/rpm2html/search.php?query=qhull">http://rpmfind.net/linux/rpm2html/search.php?query=qhull</a>
|
||||
<li><a href="http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull">http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull</a>
|
||||
</ul></p>
|
||||
</li>
|
||||
|
||||
<li><a
|
||||
href="http://dl.acm.org/author_page.cfm?id=81100129162">Download:
|
||||
Article about Qhull</a> (307K)
|
||||
<p>Type: PDF on ACM Digital Library (from this page only)</p>
|
||||
<p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T.,
|
||||
"The Quickhull algorithm for convex hulls," <i>ACM
|
||||
Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996 [<a
|
||||
href="http://portal.acm.org/citation.cfm?doid=235815.235821">abstract</a>].</p>
|
||||
</li>
|
||||
|
||||
<li><a
|
||||
href="http://www.qhull.org/download/qhull-1.0.tar.gz">Download:
|
||||
Qhull version 1.0</a> (92K) <p>Type: C source code for
|
||||
32-bit architectures </p>
|
||||
<p>Version 1.0 is a fifth the size of version 2.4. It
|
||||
computes convex hulls and Delaunay triangulations. If a
|
||||
precision error occurs, it stops with an error message.
|
||||
It reports an initialization error for inputs made with
|
||||
0/1 coordinates. </p>
|
||||
<p>Version 1.0 compiles on a PC with Borland C++ 4.02 for
|
||||
Win32 and DOS Power Pack. The options for rbox are
|
||||
"bcc32 -WX -w- -O2-e -erbox -lc rbox.c". The
|
||||
options for qhull are the same. [D. Zwick] </p>
|
||||
</li>
|
||||
</ul>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org"><i>Qhull Home Page</i></a><br>
|
||||
<!-- GC common information --></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="../html/qh--geom.gif" alt="[HOME]"
|
||||
align="middle"></a> <i>The Geometry Center Home Page</i> </p>
|
||||
|
||||
<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a><br>
|
||||
</body>
|
||||
</html>
|
||||
826
xs/src/qhull/html/qh-impre.htm
Normal file
826
xs/src/qhull/html/qh-impre.htm
Normal file
@ -0,0 +1,826 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Imprecision in Qhull</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
|
||||
page</a> for Qhull <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
|
||||
Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To: </b><a href="#TOC">Qhull imprecision</a>: Table of Contents
|
||||
(please wait while loading)
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
|
||||
src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
|
||||
height="100"></a> Imprecision in Qhull</h1>
|
||||
|
||||
<p>This section of the Qhull manual discusses the problems caused
|
||||
by coplanar points and why Qhull uses options '<a
|
||||
href="qh-optc.htm#C0">C-0</a>' or '<a href="qh-optq.htm#Qx">Qx</a>'
|
||||
by default. If you ignore precision issues with option '<a
|
||||
href="qh-optq.htm#Q0">Q0</a>', the output from Qhull can be
|
||||
arbitrarily bad. Qhull avoids precision problems if you merge facets (the default) or joggle
|
||||
the input ('<a
|
||||
href="qh-optq.htm#QJn">QJ</a>'). </p>
|
||||
|
||||
<p>Use option '<a href="qh-optt.htm#Tv">Tv</a>' 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. </p>
|
||||
|
||||
<p>Qhull automatically tests for convexity if it detects
|
||||
precision errors while constructing the hull. </p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOP">»</a><a name="TOC">Qhull
|
||||
imprecision: Table of Contents </a></h2>
|
||||
|
||||
<ul>
|
||||
<li><a href="#prec">Precision problems</a></li>
|
||||
<li><a href="#joggle">Merged facets or joggled input</a></li>
|
||||
<li><a href="#delaunay">Delaunay triangulations</a></li>
|
||||
<li><a href="#halfspace">Halfspace intersection/a></li>
|
||||
<li><a href="#imprecise">Merged facets</a></li>
|
||||
<li><a href="#how">How Qhull merges facets</a></li>
|
||||
<li><a href="#limit">Limitations of merged facets</a></li>
|
||||
<li><a href="#injoggle">Joggled input</a></li>
|
||||
<li><a href="#exact">Exact arithmetic</a></li>
|
||||
<li><a href="#approximate">Approximating a convex hull</a></li>
|
||||
</ul>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="prec">Precision problems</a></h2>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>There are several kinds of precision errors:</p>
|
||||
|
||||
<ul>
|
||||
<li>Representation error occurs when there are not enough
|
||||
digits to represent a number, e.g., 1/3.</li>
|
||||
<li>Measurement error occurs when the input coordinates are
|
||||
from measurements. </li>
|
||||
<li>Roundoff error occurs when a calculation is rounded to a
|
||||
fixed number of digits, e.g., a floating point
|
||||
calculation.</li>
|
||||
<li>Approximation error occurs when the user wants an
|
||||
approximate result because the exact result contains too
|
||||
much detail.</li>
|
||||
</ul>
|
||||
|
||||
<p>Under imprecision, calculations may return erroneous results.
|
||||
For example, roundoff error can turn a small, positive number
|
||||
into a small, negative number. See Milenkovic [<a
|
||||
href="index.htm#mile93">'93</a>] for a discussion of <em>strict
|
||||
robust geometry</em>. Qhull does not meet Milenkovic's criterion
|
||||
for accuracy. Qhull's error bound is empirical instead of
|
||||
theoretical.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Qhull 2.4 and later automatically handles errors due to
|
||||
machine round-off. Option '<a href="qh-optc.htm#C0">C-0</a>' or '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>' 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 '<a
|
||||
href="qh-optc.htm#C0">C-0</a>', but then the output may contain
|
||||
wide facets.</p>
|
||||
|
||||
<p>Qhull 2.5 and later provides option '<a href="qh-optq.htm#QJn">QJ</a>'
|
||||
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. </p>
|
||||
|
||||
<p>Qhull 3.1 and later provides option '<a href="qh-optq.htm#Qt">Qt</a>'
|
||||
for triangulated output. This removes the need for
|
||||
joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
Non-simplicial facets are triangulated.
|
||||
The facets may have zero area.
|
||||
Triangulated output is particularly useful for Delaunay triangulations.</p>
|
||||
|
||||
<p>By handling round-off errors, Qhull can provide a variety of
|
||||
output formats. For example, it can return the halfspace that
|
||||
defines each facet ('<a href="qh-opto.htm#n">n</a>'). 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.</p>
|
||||
|
||||
<p>The following pipe implements the identity function for
|
||||
extreme points (with roundoff):
|
||||
<blockquote>
|
||||
qconvex <a href="qh-optf.htm#FV">FV</a> <a
|
||||
href="qh-opto.htm#n">n</a> | qhalf <a href="qh-optf.htm#Fp">Fp</a>
|
||||
</blockquote>
|
||||
|
||||
<p>Bernd Gartner published his
|
||||
<a href=http://www.inf.ethz.ch/personal/gaertner/miniball.html>Miniball</a>
|
||||
algorithm ["Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, 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.
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="joggle">Merged facets or joggled input</a></h2>
|
||||
|
||||
<p>This section discusses the choice between merged facets and joggled input.
|
||||
By default, Qhull uses merged facets to handle
|
||||
precision problems. With option '<a href="qh-optq.htm#QJn">QJ</a>',
|
||||
the input is joggled. See <a href="qh-eg.htm#joggle">examples</a>
|
||||
of joggled input and triangulated output.
|
||||
<ul>
|
||||
<li>Use merged facets (the default)
|
||||
when you want non-simplicial output (e.g., the faces of a cube).
|
||||
<li>Use merged facets and triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') when
|
||||
you want simplicial output and coplanar facets (e.g., triangles for a Delaunay triangulation).
|
||||
<li>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') when you need clearly-convex,
|
||||
simplicial output.
|
||||
</ul>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Most applications should used merged facets
|
||||
with triangulated output. </p>
|
||||
|
||||
<p>Use merged facets (the
|
||||
default, '<a href="qh-optc.htm#C0">C-0</a>')
|
||||
or triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') if </p>
|
||||
|
||||
<ul>
|
||||
<li>Your application supports non-simplicial facets, or
|
||||
it allows degenerate, simplicial facets (option '<a href="qh-optq.htm#Qt">Qt</a>'). </li>
|
||||
<li>You do not want the input modified. </li>
|
||||
<li>You want to set additional options for approximating the
|
||||
hull. </li>
|
||||
<li>You use single precision arithmetic (<a href="../src/libqhull/user.h#realT">realT</a>).
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
<p>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') if </p>
|
||||
|
||||
<ul>
|
||||
<li>Your application needs clearly convex, simplicial output</li>
|
||||
<li>Your application supports perturbed input points and narrow triangles.</li>
|
||||
<li>Seven significant digits is sufficient accuracy.</li>
|
||||
</ul>
|
||||
|
||||
<p>You may use both techniques or combine joggle with
|
||||
post-merging ('<a href="qh-optc.htm#Cn2">Cn</a>'). </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Merged facets ('<a href="qh-optc.htm#C0">C-0</a>') 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. </p>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="delaunay">Delaunay
|
||||
triangulations </a></h2>
|
||||
|
||||
<p>Programs that use Delaunay triangulations traditionally assume
|
||||
a triangulated input. By default, <a href=qdelaun.htm>qdelaunay</a>
|
||||
merges regions with cocircular or cospherical input sites.
|
||||
If you want a simplicial triangulation
|
||||
use triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggled
|
||||
input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
|
||||
<p>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 ('<a href="qh-opto.htm#s">s</a>', '<a href="qh-optf.htm#Fs">Fs</a>'</p>
|
||||
|
||||
<p>You should use option '<a href="qh-optq.htm#Qbb">Qbb</a>' with Delaunay
|
||||
triangulations. It scales the last coordinate and may reduce
|
||||
roundoff error. It is automatically set for <a href=qdelaun.htm>qdelaunay</a>,
|
||||
<a href=qvoronoi.htm>qvoronoi</a>, and option '<a
|
||||
href="qh-optq.htm#QJn">QJ</a>'.</p>
|
||||
|
||||
<p>Edelsbrunner, H, <i>Geometry and Topology for Mesh Generation</i>, 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.
|
||||
|
||||
<p>Veron and Leon published an algorithm for shape preserving polyhedral
|
||||
simplification with bounded error [<i>Computers and Graphics</i>, 22.5:565-585, 1998].
|
||||
It remove nodes using front propagation and multiple remeshing.
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="halfspace">Halfspace intersection</a></h2>
|
||||
|
||||
<p>
|
||||
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]
|
||||
<blockquote>
|
||||
rbox 100 s t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
|
||||
<br>
|
||||
rbox 100 L1e5 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
|
||||
<br>
|
||||
rbox 100 s O10 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
|
||||
</blockquote>
|
||||
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="imprecise">Merged facets </a></h2>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Qhull handles precision problems by merging non-convex facets.
|
||||
The result of merging two facets is a thick facet defined by an <i>inner
|
||||
plane</i> and an <i>outer plane</i>. 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.</p>
|
||||
|
||||
<p>Qhull tests for convexity by computing a point for each facet.
|
||||
This point is called the facet's <i>centrum</i>. It is the
|
||||
arithmetic center of the facet's vertices projected to the
|
||||
facet's hyperplane. For simplicial facets with <em>d</em>
|
||||
vertices, the centrum is equivalent to the centroid or center of
|
||||
gravity. </p>
|
||||
|
||||
<p>Two neighboring facets are convex if each centrum is clearly
|
||||
below the other hyperplane. The '<a href="qh-optc.htm#Cn2">Cn</a>'
|
||||
or '<a href="qh-optc.htm#Cn">C-n</a>' options sets the centrum's
|
||||
radius to <i>n </i>. 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.</p>
|
||||
|
||||
<p>With the '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
|
||||
href="qh-optc.htm#An">A-n </a>' options, Qhull merges non-convex
|
||||
facets while constructing the hull. The remaining facets are
|
||||
clearly convex. With the '<a href="qh-optq.htm#Qx">Qx </a>'
|
||||
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 '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>', coplanar points may be missed, but
|
||||
it appears to be unlikely.</p>
|
||||
|
||||
<p>If the user sets the '<a href="qh-optc.htm#An2">An</a>' or '<a
|
||||
href="qh-optc.htm#An">A-n</a>' option, then all neighboring
|
||||
facets are clearly convex and the maximum (exact) cosine of an
|
||||
angle is <i>n</i>.</p>
|
||||
|
||||
<p>If '<a href="qh-optc.htm#C0">C-0</a>' or '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>' is used without other precision
|
||||
options (default), Qhull tests vertices instead of centrums for
|
||||
adjacent simplices. In 3-d, if simplex <i>abc</i> is adjacent to
|
||||
simplex <i>bcd</i>, Qhull tests that vertex <i>a</i> is clearly
|
||||
below simplex <i>bcd </i>, and vertex <i>d</i> is clearly below
|
||||
simplex <i>abc</i>. When building the hull, Qhull tests vertices
|
||||
if the horizon is simplicial and no merges occur. </p>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="how">How Qhull merges facets</a></h2>
|
||||
|
||||
<p>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 <i>d</i> 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.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Merging two simplicial facets creates a non-simplicial facet
|
||||
of <em>d+1</em> 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).</p>
|
||||
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="limit">Limitations of merged
|
||||
facets</a></h2>
|
||||
|
||||
<ul>
|
||||
<li><b>Uneven dimensions</b> --
|
||||
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 '<a
|
||||
href="qh-optq.htm#QbB">QbB</a>' to scale points to the unit cube.
|
||||
For Delaunay triangulations and Voronoi diagrams, <a href=qdelaun.htm>qdelaunay</a>
|
||||
and <a href=qvoronoi.htm>qvoronoi</a> always set
|
||||
option '<a href="qh-optq.htm#Qbb">Qbb</a>'. It scales the last
|
||||
coordinate to [0,m] where <i>m</i> is the maximum width of the
|
||||
other coordinates. Option '<a href="qh-optq.htm#Qbb">Qbb</a>' is
|
||||
needed for Delaunay triangulations of integer coordinates
|
||||
and nearly cocircular points.
|
||||
|
||||
<p>For example, compare
|
||||
<pre>
|
||||
rbox 1000 W0 t | qconvex Qb2:-1e-14B2:1e-14
|
||||
</pre>
|
||||
with
|
||||
<pre>
|
||||
rbox 1000 W0 t | qconvex
|
||||
</pre>
|
||||
The distributions are the same but the first is compressed to a 2e-14 slab.
|
||||
<p>
|
||||
<li><b>Post-merging of coplanar facets</b> -- In 5-d and higher, option '<a href="qh-optq.htm#Qx">Qx</a>'
|
||||
(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 '<a href="qh-optq.htm#Qx">Qx</a>' for
|
||||
further discussion.</p>
|
||||
|
||||
<p>This is difficult to produce in 5-d and higher. Option '<a href="qh-optq.htm#Q6">Q6</a>' turns off merging of concave
|
||||
facets. This is similar to 'Qx'. It may lead to serious precision errors,
|
||||
for example,
|
||||
<pre>
|
||||
rbox 10000 W1e-13 | qhull Q6 Tv
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
<li><b>Maximum facet width</b> --
|
||||
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 '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>' option, it does a good job in
|
||||
higher dimensions. In 5-d and higher, Qhull does poorly at
|
||||
detecting redundant vertices. </p>
|
||||
|
||||
<p>In the summary ('<a href="qh-opto.htm#s">s</a>'), 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.
|
||||
|
||||
<p>For example, if special processing for narrow distributions is
|
||||
turned off ('<a href="qh-optq.htm#Q10">Q10</a>'), qhull may produce
|
||||
a wide facet:</p>
|
||||
<pre>
|
||||
rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
<li><b>Narrow distribution</b> -- In 3-d, a narrow distribution may result in a poor
|
||||
approximation. For example, if you do not use qdelaunay nor option
|
||||
'<a href="qh-optq.htm#Qbb">Qbb</a>', the furthest-site
|
||||
Delaunay triangulation of nearly cocircular points may produce a poor
|
||||
approximation:
|
||||
<pre>
|
||||
rbox s 5000 W1e-13 D2 t1002151341 | qhull d Qt
|
||||
rbox 1000 s W1e-13 t1002231672 | qhull d Tv
|
||||
</pre>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qbb">Qbb</a>'
|
||||
(it scales the last coordinate). Option '<a href="qh-optq.htm#Qbb">Qbb</a>'
|
||||
is automatically set for <a href=qdelaun.htm>qdelaunay</a> and <a href=qvoronoi.htm>qvoronoi</a>.
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Q10">Q10</a>' to try Qhull without
|
||||
special processing for narrow distributions.
|
||||
For example, special processing is needed for:
|
||||
<pre>
|
||||
rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
|
||||
</pre>
|
||||
|
||||
<p>You may turn off the warning message by reducing
|
||||
qh_WARNnarrow in <tt>user.h</tt> or by setting option
|
||||
'<a href="qh-optp.htm#Pp">Pp</a>'. </p>
|
||||
|
||||
<p>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 ('<a href="qh-optt.htm#Tv">Tv</a>').
|
||||
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.
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
<li><b>Quadratic running time</b> -- 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, <tt>rbox 1000 s W1e-13 c G2 | qhull d</tt> 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 '<a href="qh-optq.htm#Qbb">Qbb</a>',
|
||||
or add the origin ('P0') to the input.
|
||||
<p>
|
||||
<li><b>Nearly coincident points within 1e-13</b> --
|
||||
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).
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Q12">Q12</a>'.
|
||||
|
||||
<p>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.
|
||||
<pre>
|
||||
rbox 1000 C1,1e-13 D4 s t | qhull
|
||||
rbox 75 C1,1e-13 t | qhull d
|
||||
</pre>
|
||||
For Delaunay triangulations, a bounding box may alleviate this error (e.g., <tt>rbox 500 C1,1E-13 t c G1 | qhull d</tt>).
|
||||
A later release of qhull will avoid pinched horizons by merging duplicate subridges. A subridge is
|
||||
merged by merging adjacent vertices.
|
||||
<p>
|
||||
<li><b>Facet with zero-area</b> --
|
||||
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. </p>
|
||||
|
||||
<p>
|
||||
<li><b>No more facets</b> -- Qhull reports an error if there are <em>d+1</em> 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 '<a href="qh-optc.htm#Cn">C-n</a>'.</p>
|
||||
|
||||
<p>
|
||||
<li><b>Deleted cone</b> -- 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.
|
||||
|
||||
<p>
|
||||
<li><b>Triangulated output leads to precision problems</b> -- 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 ('<a href="qh-optq.htm#Qt">Qt</a>')
|
||||
will fail since two facets have the same vertex set. Furthermore,
|
||||
a triangulated facet may have flipped orientation compared to its
|
||||
neighbors.</li>
|
||||
|
||||
<p>The triangulation process detects degenerate facets with
|
||||
only two neighbors. These are marked degenerate. They have
|
||||
zero area.
|
||||
|
||||
<p>
|
||||
<li><b>Coplanar points</b> --
|
||||
Option '<a href="qh-optq.htm#Qc">Qc</a>' 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 <tt>user.h.</tt>
|
||||
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 '<a
|
||||
href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>') or
|
||||
make qh_RATIOnearInside sufficiently large.</p>
|
||||
|
||||
<p>
|
||||
<li><b>Maximum roundoff error</b> -- 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 '<a href="qh-optc.htm#Cn">C-n</a>'.
|
||||
|
||||
<p>
|
||||
<li><b>All flipped or upper Delaunay</b> -- 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:
|
||||
<pre>
|
||||
rbox 1000 s t993602376 | qdelaunay C-1e-3
|
||||
</pre>
|
||||
|
||||
</ul>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="injoggle">Joggled input</a></h2>
|
||||
|
||||
<p>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
|
||||
<i>jostled input</i> or <i>random perturbation</i>.
|
||||
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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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 ('<a href="qh-optt.htm#TRn">TRn</a>') . For example, consider
|
||||
computing the convex hull of the unit cube centered on the
|
||||
origin. The arithmetic has 16 significant decimal digits. </p>
|
||||
|
||||
<blockquote>
|
||||
<p><b>Convex hull of unit cube</b> </p>
|
||||
<table border="1">
|
||||
<tr>
|
||||
<th align="left">joggle</th>
|
||||
<th align="right">error prob. </th>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.0e-15</td>
|
||||
<td align="center">0.983 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">2.0e-15</td>
|
||||
<td align="center">0.830 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">4.0e-15</td>
|
||||
<td align="center">0.561 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">8.0e-15</td>
|
||||
<td align="center">0.325 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.6e-14</td>
|
||||
<td align="center">0.185 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">3.2e-14</td>
|
||||
<td align="center">0.099 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">6.4e-14</td>
|
||||
<td align="center">0.051 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.3e-13</td>
|
||||
<td align="center">0.025 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">2.6e-13</td>
|
||||
<td align="center">0.010 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">5.1e-13</td>
|
||||
<td align="center">0.004 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.0e-12</td>
|
||||
<td align="center">0.002 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">2.0e-12</td>
|
||||
<td align="center">0.001 </td>
|
||||
</tr>
|
||||
</table>
|
||||
</blockquote>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<blockquote>
|
||||
<p><b>Convex hull of 1000 points on unit cube</b> </p>
|
||||
<table border="1">
|
||||
<tr>
|
||||
<th align="left">joggle</th>
|
||||
<th align="right">error prob. </th>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.0e-12</td>
|
||||
<td align="center">0.870 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">2.0e-12</td>
|
||||
<td align="center">0.700 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">4.0e-12</td>
|
||||
<td align="center">0.450 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">8.0e-12</td>
|
||||
<td align="center">0.250 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.6e-11</td>
|
||||
<td align="center">0.110 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">3.2e-11</td>
|
||||
<td align="center">0.065 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">6.4e-11</td>
|
||||
<td align="center">0.030 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">1.3e-10</td>
|
||||
<td align="center">0.010 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">2.6e-10</td>
|
||||
<td align="center">0.008 </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">5.1e-09</td>
|
||||
<td align="center">0.003 </td>
|
||||
</tr>
|
||||
</table>
|
||||
</blockquote>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="exact">Exact arithmetic</a></h2>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Clarkson's <a
|
||||
href="http://www.netlib.org/voronoi/hull.html">hull
|
||||
program</a> and Shewchuk's <a
|
||||
href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
|
||||
program</a> are practical implementations of exact arithmetic.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h2><a href="#TOC">»</a><a name="approximate">Approximating a
|
||||
convex hull</a></h2>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qx">Qx</a> <a
|
||||
href="qh-optc.htm#Cn">C-n</a>' to merge facets as the hull is
|
||||
being constructed. Then use '<a href="qh-optc.htm#Cn2">Cn</a>'
|
||||
and/or '<a href="qh-optc.htm#An2">An</a>' to merge small facets
|
||||
during post-processing. You can print the <i>n</i> largest facets
|
||||
with option '<a href="qh-optp.htm#PAn">PAn</a>'. You can print
|
||||
facets whose area is at least <i>n</i> with option '<a
|
||||
href="qh-optp.htm#PFn">PFn</a>'. You can output the outer planes
|
||||
and an interior point with '<a href="qh-optf.htm#FV">FV</a> <a
|
||||
href="qh-optf.htm#Fo">Fo</a>' and then compute their intersection
|
||||
with 'qhalf'. </p>
|
||||
|
||||
<p>To approximate a convex hull in 6-d and higher, use
|
||||
post-merging with '<a href="qh-optc.htm#Wn">Wn</a>' (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 '<a href="qh-optq.htm#QbB">QbB</a>'
|
||||
may help to spread out the data.</p>
|
||||
|
||||
<p>You will need to experiment to determine a satisfactory set of
|
||||
options. Use <a href="rbox.htm">rbox</a> to generate test sets
|
||||
quickly and <a href="index.htm#geomview">Geomview</a> 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.</p>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home
|
||||
page</a> for Qhull <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
|
||||
Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#TOC">Qhull imprecision: Table of Contents</a>
|
||||
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
292
xs/src/qhull/html/qh-optc.htm
Normal file
292
xs/src/qhull/html/qh-optc.htm
Normal file
@ -0,0 +1,292 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull precision options</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull precision options</h1>
|
||||
|
||||
This section lists the precision options for Qhull. These options are
|
||||
indicated by an upper-case letter followed by a number.
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="prec">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Precision options</h2>
|
||||
|
||||
<p>Most users will not need to set these options. They are best
|
||||
used for <a href="qh-impre.htm#approximate">approximating</a> a
|
||||
convex hull. They may also be used for testing Qhull's handling
|
||||
of precision errors.</p>
|
||||
|
||||
<p>By default, Qhull uses options '<a href="#C0">C-0</a>' for
|
||||
2-d, 3-d and 4-d, and '<a href="qh-optq.htm#Qx">Qx</a>' for 5-d
|
||||
and higher. These options use facet merging to handle precision
|
||||
errors. You may also use joggled input '<a href="qh-optq.htm#QJn">QJ</a>'
|
||||
to avoid precision problems.
|
||||
For more information see <a
|
||||
href="qh-impre.htm">Imprecision in Qhull</a>.</p>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="#Cn2">Cn</a></dt>
|
||||
<dd>centrum radius for post-merging</dd>
|
||||
<dt><a href="#Cn">C-n</a></dt>
|
||||
<dd>centrum radius for pre-merging</dd>
|
||||
<dt><a href="#An2">An</a></dt>
|
||||
<dd>cosine of maximum angle for post-merging</dd>
|
||||
<dt><a href="#An">A-n</a></dt>
|
||||
<dd>cosine of maximum angle for pre-merging</dd>
|
||||
<dt><a href="qh-optq.htm#Qx">Qx</a></dt>
|
||||
<dd>exact pre-merges (allows coplanar facets)</dd>
|
||||
<dt><a href="#C0">C-0</a></dt>
|
||||
<dd>handle all precision errors</dd>
|
||||
<dt><a href="#Wn">Wn</a></dt>
|
||||
<dd>min distance above plane for outside points</dd>
|
||||
</dl>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>Experimental</b></dd>
|
||||
<dt><a href="#Un">Un</a></dt>
|
||||
<dd>max distance below plane for a new, coplanar point</dd>
|
||||
<dt><a href="#En">En</a></dt>
|
||||
<dd>max roundoff error for distance computation</dd>
|
||||
<dt><a href="#Vn">Vn</a></dt>
|
||||
<dd>min distance above plane for a visible facet</dd>
|
||||
<dt><a href="#Rn">Rn</a></dt>
|
||||
<dd>randomly perturb computations by a factor of [1-n,1+n]</dd>
|
||||
</dl>
|
||||
|
||||
<dl compact>
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="An">A-n - cosine of maximum
|
||||
angle for pre-merging.</a></h3>
|
||||
|
||||
<p>Pre-merging occurs while Qhull constructs the hull. It is
|
||||
indicated by '<a href="#Cn">C-n</a>', 'A-n', or '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>'.</p>
|
||||
|
||||
<p>If the angle between a pair of facet normals is greater than <i>n</i>,
|
||||
Qhull merges one of the facets into a neighbor. It selects the
|
||||
facet that is closest to a neighboring facet.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>If 'A-n' is set without '<a href="#Cn">C-n</a>', then '<a
|
||||
href="#C0">C-0</a>' is automatically set. </p>
|
||||
|
||||
<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
|
||||
along with 'A-n'. It skips merges of coplanar facets until after
|
||||
the hull is constructed and before '<a href="#An2">An</a>' and '<a
|
||||
href="#Cn2">Cn</a>' are checked. </p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="An2">An - cosine of maximum angle for
|
||||
post-merging.</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>If 'An' is set without '<a href="#Cn2">Cn</a>', then '<a
|
||||
href="#Cn2">C0</a>' is automatically set. </p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="C0">C-0 - handle all precision
|
||||
errors </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and higher.
|
||||
Use '<a href="qh-optq.htm#QJn">QJ</a>' to joggle the input
|
||||
instead of merging facets.
|
||||
Use '<a
|
||||
href="qh-optq.htm#Q0">Q0</a>' to turn both options off.</p>
|
||||
|
||||
<p>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 <a href="qh-impre.htm">How
|
||||
Qhull handles imprecision</a>.</p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Cn">C-n - centrum radius for
|
||||
pre-merging</a></h3>
|
||||
|
||||
<p>Pre-merging occurs while Qhull constructs the hull. It is
|
||||
indicated by 'C-n', '<a href="#An">A-n</a>', or '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>'.</p>
|
||||
|
||||
<p>The <i>centrum</i> 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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>For option 'C-n', <i>n</i> 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.</p>
|
||||
|
||||
<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
|
||||
along with 'C-n'. It skips merges of coplanar facets until after
|
||||
the hull is constructed and before '<a href="#An2">An</a>' and '<a
|
||||
href="#Cn2">Cn</a>' are checked. </p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Cn2">Cn - centrum radius for
|
||||
post-merging</a></h3>
|
||||
|
||||
<p>Post-merging occurs after Qhull constructs the hull. It is
|
||||
indicated by '<a href="#Cn2">Cn</a>' or '<a href="#An2">An</a>'. </p>
|
||||
|
||||
<p>For option '<a href="#Cn2">Cn</a>', <i>n</i> 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.</p>
|
||||
|
||||
<p>Both pre-merging and post-merging may be defined. If only
|
||||
post-merging is used ('<a href="qh-optq.htm#Q0">Q0</a>' with
|
||||
'Cn'), Qhull may fail to produce a hull due to precision errors
|
||||
during the hull's construction.</p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="En">En - max roundoff error
|
||||
for distance computations</a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optt.htm#Ts">Ts</a>') is a
|
||||
reasonable upper bound for the actual roundoff error. </p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Rn">Rn - randomly perturb
|
||||
computations </a></h3>
|
||||
|
||||
<p>This option perturbs every distance, hyperplane, and angle
|
||||
computation by up to <i>(+/- n * max_coord)</i>. It simulates the
|
||||
effect of roundoff errors. Unless '<a href="#En">En</a>' is
|
||||
explicitly set, it is adjusted for 'Rn'. The command 'qhull Rn'
|
||||
will generate a convex hull despite the perturbations. See the <a
|
||||
href="qh-eg.htm#merge">Examples </a>section for an example.</p>
|
||||
|
||||
<p>Options 'Rn C-n' have the effect of '<a href="#Wn">W2n</a>'
|
||||
and '<a href="#Cn">C-2n</a>'. To use time as the random number
|
||||
seed, use option '<a href="qh-optq.htm#QRn">QR-1</a>'.</p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Un">Un - max distance for a
|
||||
new, coplanar point </a></h3>
|
||||
|
||||
<p>This allows the user to set coplanarity. When pre-merging ('<a
|
||||
href="#Cn">C-n </a>', '<a href="#An">A-n</a>' or '<a
|
||||
href="qh-optq.htm#Qx">Qx</a>'), Qhull merges a new point into any
|
||||
coplanar facets. The default value for 'Un' is '<a href="#Vn">Vn</a>'.</p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Vn">Vn - min distance for a
|
||||
visible facet </a></h3>
|
||||
|
||||
<p>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'.</p>
|
||||
|
||||
<p>Without merging, the default value for 'Vn' is the roundoff
|
||||
error ('<a href="#En">En</a>'). With merging, the default value
|
||||
is the pre-merge centrum ('<a href="#Cn">C-n</a>') in 2-d or 3-d,
|
||||
or three times that in other dimensions. If the outside width is
|
||||
specified with option '<a href="#Wn">Wn </a>', the maximum,
|
||||
default value for 'Vn' is '<a href="#Wn">Wn</a>'.</p>
|
||||
|
||||
<p>Qhull warns if 'Vn' is greater than '<a href="#Wn">Wn</a>' and
|
||||
furthest outside ('<a href="qh-optq.htm#Qf">Qf</a>') is not
|
||||
selected; this combination usually results in flipped facets
|
||||
(i.e., reversed normals).</p>
|
||||
|
||||
<h3><a href="#prec">»</a><a name="Wn">Wn - min distance above
|
||||
plane for outside points</a></h3>
|
||||
|
||||
<p>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 '<a href="#En">En </a>'. If the user
|
||||
specifies pre-merging and does not set 'Wn', than 'Wn' is set to
|
||||
the maximum of '<a href="#Cn">C-n</a>' and <i>maxcoord*(1 - </i><a
|
||||
href="#An"><i>A-n</i></a><i>)</i>.</p>
|
||||
|
||||
<p>This option is good for <a href="qh-impre.htm#approximate">approximating</a>
|
||||
a convex hull.</p>
|
||||
|
||||
<p>Options '<a href="qh-optq.htm#Qc">Qc</a>' and '<a
|
||||
href="qh-optq.htm#Qi">Qi</a>' use the minimum vertex to
|
||||
distinguish coplanar points from interior points.</p>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
736
xs/src/qhull/html/qh-optf.htm
Normal file
736
xs/src/qhull/html/qh-optf.htm
Normal file
@ -0,0 +1,736 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull format options (F)</title>
|
||||
</head>
|
||||
|
||||
<body><!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><IMG
|
||||
align=middle alt=[delaunay] height=100
|
||||
src="qh--dt.gif" width=100 ></a> Qhull format options (F)</h1>
|
||||
|
||||
<p>This section lists the format options for Qhull. These options
|
||||
are indicated by 'F' followed by a letter. See <A
|
||||
href="qh-opto.htm#output" >Output</a>, <a href="qh-optp.htm#print">Print</a>,
|
||||
and <a href="qh-optg.htm#geomview">Geomview</a> for other output
|
||||
options. </p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="format">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Additional input & output formats</h2>
|
||||
|
||||
<p>These options allow for automatic processing of Qhull output.
|
||||
Options '<a href="qh-opto.htm#i">i</a>', '<a href="qh-opto.htm#o">o</a>',
|
||||
'<a href="qh-opto.htm#n">n</a>', and '<a href="qh-opto.htm#p">p</a>'
|
||||
may also be used.</p>
|
||||
|
||||
<dl compact>
|
||||
<dt>
|
||||
<dd><b>Summary and control</b>
|
||||
<dt><a href="#FA">FA</a>
|
||||
<dd>compute total area and volume for option '<A
|
||||
href="qh-opto.htm#s">s</a>'
|
||||
|
||||
<dt><a href="#FV">FV</a>
|
||||
<dd>print average vertex (interior point for '<A
|
||||
href="qhalf.htm">qhalf</a>')
|
||||
<dt><a href="#FQ">FQ</a>
|
||||
<dd>print command for qhull and input
|
||||
<dt><a href="#FO">FO</a>
|
||||
<dd>print options to stderr or stdout
|
||||
<dt><a href="#FS">FS</a>
|
||||
<dd>print sizes: total area and volume
|
||||
<dt><a href="#Fs">Fs</a>
|
||||
<dd>print summary: dim, #points, total vertices and
|
||||
facets, #vertices, #facets, max outer and inner plane
|
||||
<dt><a href="#Fd">Fd</a>
|
||||
<dd>use format for input (offset first)
|
||||
<dt><a href="#FD">FD</a>
|
||||
<dd>use cdd format for normals (offset first)
|
||||
<dt><a href="#FM">FM</a>
|
||||
<dd>print Maple output (2-d and 3-d)
|
||||
<dt>
|
||||
<dt>
|
||||
<dd><b>Facets, points, and vertices</b>
|
||||
<dt><a href="#Fa">Fa</a>
|
||||
<dd>print area for each facet
|
||||
<dt><a href="#FC">FC</a>
|
||||
<dd>print centrum for each facet
|
||||
<dt><a href="#Fc">Fc</a>
|
||||
<dd>print coplanar points for each facet
|
||||
<dt><a href="#Fx">Fx</a>
|
||||
<dd>print extreme points (i.e., vertices) of convex hull.
|
||||
|
||||
<dt><a href="#FF">FF</a>
|
||||
<dd>print facets w/o ridges
|
||||
<dt><a href="#FI">FI</a>
|
||||
<dd>print ID for each facet
|
||||
<dt><a href="#Fi">Fi</a>
|
||||
<dd>print inner planes for each facet
|
||||
<dt><a href="#Fm">Fm</a>
|
||||
<dd>print merge count for each facet (511 max)
|
||||
<dt><a href="#FP">FP</a>
|
||||
<dd>print nearest vertex for coplanar points
|
||||
<dt><a href="#Fn">Fn</a>
|
||||
<dd>print neighboring facets for each facet
|
||||
<dt><a href="#FN">FN</a>
|
||||
<dd>print neighboring facets for each point
|
||||
<dt><a href="#Fo">Fo</a>
|
||||
<dd>print outer planes for each facet
|
||||
<dt><a href="#Ft">Ft</a>
|
||||
<dd>print triangulation with added points
|
||||
<dt><a href="#Fv">Fv</a>
|
||||
<dd>print vertices for each facet
|
||||
<dt>
|
||||
<dt>
|
||||
<dd><b>Delaunay, Voronoi, and halfspace</b>
|
||||
<dt><a href="#Fx">Fx</a>
|
||||
<dd>print extreme input sites of Delaunay triangulation
|
||||
or Voronoi diagram.
|
||||
<dt><a href="#Fp">Fp</a>
|
||||
<dd>print points at halfspace intersections
|
||||
<dt><a href="#Fi2">Fi</a>
|
||||
<dd>print separating hyperplanes for inner, bounded
|
||||
Voronoi regions
|
||||
<dt><a href="#Fo2">Fo</a>
|
||||
<dd>print separating hyperplanes for outer, unbounded
|
||||
Voronoi regions
|
||||
<dt><a href="#Fv2">Fv</a>
|
||||
<dd>print Voronoi diagram as ridges for each input pair
|
||||
<dt><a href="#FC">FC</a>
|
||||
<dd>print Voronoi vertex ("center") for each facet</dd>
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fa">Fa - print area for each
|
||||
facet </a></h3>
|
||||
|
||||
<p>The first line is the number of facets. The remaining lines
|
||||
are the area for each facet, one facet per line. See '<A
|
||||
href="#FA" >FA</a>' and '<a href="#FS">FS</a>' for computing the total area and volume.</p>
|
||||
|
||||
<p>Use '<a href="qh-optp.htm#PAn">PAn</a>' for printing the n
|
||||
largest facets. Use option '<a href="qh-optp.htm#PFn">PFn</a>'
|
||||
for printing facets larger than <i>n</i>.</p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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 <tt>user.h</tt>),
|
||||
the corresponding triangles are ignored.</p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FA">FA - compute total area
|
||||
and volume for option 's' </a></h3>
|
||||
|
||||
<p>With option 'FA', Qhull includes the total area and volume in
|
||||
the summary ('<a href="qh-opto.htm#s">s</a>'). Option '<a href="#FS">FS</a>' also includes the total area and volume.
|
||||
If facets are
|
||||
merged, the area and volume are approximations. Option 'FA' is
|
||||
automatically set for options '<a href="#Fa">Fa</a>', '<A
|
||||
href="qh-optp.htm#PAn" >PAn</a>', and '<a href="qh-optp.htm#PFn">PFn</a>'.
|
||||
</p>
|
||||
|
||||
<p>With '<a href="qdelaun.htm">qdelaunay</a> <A
|
||||
href="qh-opto.htm#s" >s</a> FA', Qhull computes the total area of
|
||||
the Delaunay triangulation. This equals the volume of the convex
|
||||
hull of the data points. With options '<a href="qdelau_f.htm">qdelaunay Qu</a>
|
||||
<a href="qh-opto.htm#s">s</a> FA', Qhull computes the
|
||||
total area of the furthest-site Delaunay triangulation. This
|
||||
equals of the total area of the Delaunay triangulation. </p>
|
||||
|
||||
<p>See '<a href="#Fa">Fa</a>' for further details. Option '<a href="#FS">FS</a>' also computes the total area and volume.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fc">Fc - print coplanar
|
||||
points for each facet </a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>By default, option 'Fc' reports coplanar points
|
||||
('<a href="qh-optq.htm#Qc">Qc</a>'). You may also use
|
||||
option '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qi Fc' prints
|
||||
interior points while 'Qci Fc' prints both coplanar and interior
|
||||
points.
|
||||
|
||||
<p>Each coplanar point or interior point is assigned to the
|
||||
facet it is furthest above (resp., least below). </p>
|
||||
|
||||
<p>Use 'Qc <a href="qh-opto.htm#p">p</a>' to print vertex and
|
||||
coplanar point coordinates. Use '<a href="qh-optf.htm#Fv">Fv</a>'
|
||||
to print vertices. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FC">FC - print centrum or
|
||||
Voronoi vertex for each facet </a></h3>
|
||||
|
||||
<p>The output starts with the dimension followed by the number of
|
||||
facets. Then each facet centrum is printed, one per line. For
|
||||
<a href="qvoronoi.htm">qvoronoi</a>, Voronoi vertices are
|
||||
printed instead. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fd">Fd - use cdd format for
|
||||
input </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>For halfspaces ('<a href="qhalf.htm">qhalf</a> 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 '<a href="#FV">FV</a>' format.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FD">FD - use cdd format for
|
||||
normals </a></h3>
|
||||
|
||||
<p>Option 'FD' prints normals ('<a href="qh-opto.htm#n">n</a>', '<A
|
||||
href="#Fo" >Fo</a>', '<a href="#Fi">Fi</a>') or points ('<A
|
||||
href="qh-opto.htm#p" >p</a>') 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.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FF">FF - print facets w/o
|
||||
ridges </a></h3>
|
||||
|
||||
<p>Option 'FF' prints all fields of all facets (as in '<A
|
||||
href="qh-opto.htm#f" >f</a>') without printing the ridges. This is
|
||||
useful in higher dimensions where a facet may have many ridges.
|
||||
For simplicial facets, options 'FF' and '<a href="qh-opto.htm#f">f
|
||||
</a>' are equivalent.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fi">Fi - print inner planes
|
||||
for each facet </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-opto.htm#n">n</a>'.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Note that the inner planes for Geomview output ('<A
|
||||
href="qh-optg.htm#Gi" >Gi</a>') include an additional offset for
|
||||
vertex visualization and roundoff error. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fi2">Fi - print separating
|
||||
hyperplanes for inner, bounded Voronoi regions</a></h3>
|
||||
|
||||
<p>With <a href="qvoronoi.htm" >qvoronoi</a>, '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 <i>d</i> floats are the
|
||||
normalized coefficients for the hyperplane, and the last float is
|
||||
the offset. The hyperplane is oriented toward '<A
|
||||
href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
|
||||
site of the pair. </p>
|
||||
|
||||
<p>Use '<a href="qh-optf.htm#Fo2">Fo</a>' for unbounded regions,
|
||||
and '<a href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
|
||||
Voronoi vertices. </p>
|
||||
|
||||
<p>Use '<a href="qh-optt.htm#Tv">Tv</a>' 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. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FI">FI - print ID for each
|
||||
facet </a></h3>
|
||||
|
||||
<p>Print facet identifiers. These are used internally and listed
|
||||
with options '<a href="qh-opto.htm#f">f</a>' and '<a href="#FF">FF</a>'.
|
||||
Options '<a href="#Fn">Fn </a>' and '<a href="#FN">FN</a>' use
|
||||
facet identifiers for negative indices. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fm">Fm - print merge count
|
||||
for each facet </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optp.htm#PMn">PMn</a>'
|
||||
for printing the facets with the most merges. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FM">FM - print Maple
|
||||
output </a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p><i>Warning</i>: This option has not been tested in Maple.
|
||||
|
||||
<p>[From T. K. Abraham with help from M. R. Feinberg and N. Platinova.]
|
||||
The following steps apply while working within the
|
||||
Maple worksheet environment :
|
||||
<ol>
|
||||
<li>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]
|
||||
<p>
|
||||
<li>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.)
|
||||
<p>
|
||||
>data:=[seq([x[i],y[i],z[i]],i=1..n)]:# here n is the number of data points
|
||||
|
||||
<li>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 :
|
||||
<p>
|
||||
>system("del c:\\qhull3.1\\datafile.txt");#To erase any previous versions of the file
|
||||
<br>>writedata("c:\\qhull3.1\\datafile.txt ",[3, nops(data)]);#writing in qhull format
|
||||
<br>>writedata[APPEND]("c:\\ qhull3.1\\datafile.txt ", data);#writing the data points
|
||||
<li>
|
||||
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)
|
||||
<p>
|
||||
qconvex s FM <datafile.txt >dataplot.mpl
|
||||
|
||||
<li>
|
||||
To read 3-d output in Maple, we use the 'read' command followed by
|
||||
a 'display3d' command. For example (in Maple environment):
|
||||
<p>
|
||||
>with (plots):
|
||||
<br>>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)
|
||||
<br>> qhullplot:=%:
|
||||
<br>> display3d(qhullplot);
|
||||
</ol>
|
||||
|
||||
<p>For Delaunay triangulation orthogonal projection is better.
|
||||
|
||||
<p>For halfspace intersections, Qhull produces the dual
|
||||
convex hull.
|
||||
|
||||
<p>See <a href="qh-faq.htm#math">Is Qhull available for Maple?</a>
|
||||
for other URLs.
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fn">Fn - print neighboring
|
||||
facets for each facet </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>For simplicial facets, each neighbor is opposite
|
||||
the corresponding vertex (option '<a href="#Fv">Fv</a>').
|
||||
Do not compare to option '<a href="qh-opto.htm#i">i</a>'. Option 'i'
|
||||
orients facets by reversing the order of two vertices. For non-simplicial facets,
|
||||
the neighbors are unordered.
|
||||
|
||||
<p>A negative index indicates an unprinted facet due to printing
|
||||
only good facets ('<a href="qh-optp.htm#Pg">Pg</a>', <a href="qdelaun.htm" >qdelaunay</a>,
|
||||
<a href="qvoronoi.htm" >qvoronoi</a>). It
|
||||
is the negation of the facet's ID (option '<a href="#FI">FI</a>').
|
||||
For example, negative indices are used for facets "at
|
||||
infinity" in the Delaunay triangulation.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FN">FN - print neighboring
|
||||
facets for each point </a></h3>
|
||||
|
||||
<p>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 ('<a href="qh-optq.htm#Qc">Qc</a>'), the line is
|
||||
"1" followed by the index of the facet that is furthest
|
||||
below the point. For assigned interior points ('<A
|
||||
href="qh-optq.htm#Qi" >Qi</a>'), 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"</p>
|
||||
|
||||
<p>For vertices of good facets, the line is the number of
|
||||
neighboring facets followed by the facet indices. The indices
|
||||
correspond to the other '<a href="#format">F</a>' formats. In 4-d
|
||||
and higher, the facets are sorted by index. In 3-d, the facets
|
||||
are in adjacency order (not oriented).</p>
|
||||
|
||||
<p>A negative index indicates an unprinted facet due to printing
|
||||
only good facets (<a href="qdelaun.htm" >qdelaunay</a>,
|
||||
<a href="qvoronoi.htm" >qvoronoi</a>, '<a href="qh-optp.htm#Pdk">Pdk</a>',
|
||||
'<a href="qh-optp.htm#Pg">Pg</a>'). It is the negation of the
|
||||
facet's ID ('<a href="#FI"> FI</a>'). For example, negative
|
||||
indices are used for facets "at infinity" in the
|
||||
Delaunay triangulation.</p>
|
||||
|
||||
<p>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 '<a href="qh-opto.htm#o">o</a>'. To convert from 'FN' to '<A
|
||||
href="qh-opto.htm#o" >o</a>', replace negative indices with zero
|
||||
and increment non-negative indices by one. </p>
|
||||
|
||||
<p>If you are using the <a href="qh-code.htm#library">Qhull
|
||||
library</a> or <a href="qh-code.htm#cpp">C++ interface</a>, option 'FN' has the side effect of reordering the
|
||||
neighbors for a vertex </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fo">Fo - print outer planes
|
||||
for each facet </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-opto.htm#n">n</a>'.</p>
|
||||
|
||||
<p>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., '<a href="qh-optt.htm#Tv">Tv</a>'), another roundoff error
|
||||
should be added for the tested point.</p>
|
||||
|
||||
<p>If outer planes are not checked ('<a href="qh-optq.htm#Q5">Q5</a>')
|
||||
or not computed (!qh_MAXoutside), the maximum, computed outside
|
||||
distance is used instead. This can be much larger than the actual
|
||||
outer planes.</p>
|
||||
|
||||
<p>Note that the outer planes for Geomview output ('<A
|
||||
href="qh-optg.htm#G" >G</a>') include an additional offset for
|
||||
vertex/point visualization, 'lines closer,' and roundoff error.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fo2">Fo - print separating
|
||||
hyperplanes for outer, unbounded Voronoi regions</a></h3>
|
||||
|
||||
<p>With <a href="qvoronoi.htm" >qvoronoi</a>, '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 <i>d</i> floats are the
|
||||
normalized coefficients for the hyperplane, and the last float is
|
||||
the offset. The hyperplane is oriented toward '<A
|
||||
href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
|
||||
site of the pair. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Use '<a href="qh-optf.htm#Fi2">Fi</a>' for bounded regions,
|
||||
and '<a href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
|
||||
Voronoi vertices. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify
|
||||
that the corresponding Voronoi vertices lie on the hyperplane. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FO">FO - print list of
|
||||
selected options </a></h3>
|
||||
|
||||
<p>Lists selected options and default values to stderr.
|
||||
Additional 'FO's are printed to stdout. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fp">Fp - print points at
|
||||
halfspace intersections</a></h3>
|
||||
|
||||
<p>The first line is the number of intersection points. The
|
||||
remainder is one intersection point per line. A intersection
|
||||
point is the intersection of <i>d</i> or more halfspaces from
|
||||
'<a href="qhalf.htm">qhalf</a>'. It corresponds to a
|
||||
facet of the dual polytope. The "infinity" point
|
||||
[-10.101,-10.101,...] indicates an unbounded intersection.</p>
|
||||
|
||||
<p>If [x,y,z] are the dual facet's normal coefficients and <i>b<0</i>
|
||||
is its offset, the halfspace intersection occurs at
|
||||
[x/-b,y/-b,z/-b] plus the interior point. If <i>b>=0</i>, the
|
||||
halfspace intersection is unbounded. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FP">FP - print nearest
|
||||
vertex for coplanar points </a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Use options '<a href="qh-optq.htm#Qc">Qc</a>' and/or '<A
|
||||
href="qh-optq.htm#Qi" >Qi</a>' 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.
|
||||
|
||||
<p>For Delaunay triangulations (<a href="qdelaun.htm" >qdelaunay</a>
|
||||
or <a href="qvoronoi.htm" >qvoronoi</a>), a coplanar point is nearly
|
||||
incident to a vertex. The distance is the distance in the
|
||||
original point set.</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>If there are many coplanar or coincident points and non-simplicial
|
||||
facets are triangulated ('<a href="qh-optq.htm#Qt">Qt</a>'), option
|
||||
'FP' may be inefficient. It redetermines the original vertex set
|
||||
for each coplanar point.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FQ">FQ - print command for
|
||||
qhull and input </a></h3>
|
||||
|
||||
<p>Prints qhull and input command, e.g., "rbox 10 s | qhull
|
||||
FQ". Option 'FQ' may be repeated multiple times.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fs">Fs - print summary</a></h3>
|
||||
|
||||
<p>The first line consists of number of integers ("10")
|
||||
followed by the:
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points
|
||||
<li>number of vertices
|
||||
<li>number of facets
|
||||
<li>number of vertices selected for output
|
||||
<li>number of facets selected for output
|
||||
<li>number of coplanar points for selected facets
|
||||
<li>number of nonsimplicial or merged facets selected for
|
||||
output
|
||||
<LI>number of deleted vertices</LI>
|
||||
<LI>number of triangulated facets ('<a href="qh-optq.htm#Qt">Qt</a>')</LI>
|
||||
</ul>
|
||||
|
||||
<p>The second line consists of the number of reals
|
||||
("2") followed by the:
|
||||
<ul>
|
||||
<li>maximum offset to an outer plane
|
||||
<li>minimum offset to an inner plane.</li>
|
||||
</ul>
|
||||
Roundoff and joggle are included.
|
||||
<P></P>
|
||||
|
||||
<p>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, <tt>'RBOX 1000 s W1e-13 t995138628 | QHULL d Qbb'</tt> reports
|
||||
deleted vertices; the input is nearly cospherical.</p>
|
||||
|
||||
<P>Later versions of Qhull may produce additional integers or reals.</P>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FS">FS - print sizes</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>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 '<a href="#Fa">Fa </a>' for
|
||||
further notes. Option '<a href="#FA">FA </a>' also computes the total area and volume. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Ft">Ft - print triangulation</a></h3>
|
||||
|
||||
<p>Prints a triangulation with added points for non-simplicial
|
||||
facets. The output is </p>
|
||||
|
||||
<ul>
|
||||
<li>The first line is the dimension
|
||||
<li>The second line is the number of points, the number
|
||||
of facets, and the number of ridges.
|
||||
<li>All of the input points follow, one per line.
|
||||
<li>The centrums follow, one per non-simplicial facet
|
||||
<li>Then the facets follow as a list of point indices
|
||||
preceded by the number of points. The simplices are
|
||||
oriented. </li>
|
||||
</ul>
|
||||
|
||||
<p>For convex hulls with simplicial facets, the output is the
|
||||
same as option '<a href="qh-opto.htm#o">o</a>'.</p>
|
||||
|
||||
<p>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 <a href="qh-impre.htm">Precision issues</a>.
|
||||
</p>
|
||||
|
||||
<p>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 ('<A
|
||||
href="qh-optq.htm#Qt">Qt</a>') for Delaunay triangulations.
|
||||
|
||||
<p>For Delaunay triangulations with simplicial facets, the output is the
|
||||
same as option '<a href="qh-opto.htm#o">o</a>' 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 ('<a href="qh-optq.htm#QJn" >QJ</a>') or triangulated output ('<A
|
||||
href="qh-optq.htm#Qt" >Qt</a>'), for example, rbox 10 c G 0.01 | qhull d QJ Ft</p>
|
||||
|
||||
<p>If you add a point-at-infinity with '<a href="qh-optq.htm#Qz">Qz</a>',
|
||||
it is printed after the input sites and before any centrums. It
|
||||
will not be used in a Delaunay facet.</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fv">Fv - print vertices for
|
||||
each facet</a></h3>
|
||||
|
||||
<p>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).
|
||||
</p>
|
||||
<p>Option '<a href="qh-opto.htm#i">i</a>' 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.
|
||||
</p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fv2">Fv - print Voronoi
|
||||
diagram</a></h3>
|
||||
|
||||
<p>With <a href="qvoronoi.htm" >qvoronoi</a>, '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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Use '<a href="qh-optf.htm#Fo2">Fo</a>' for separating
|
||||
hyperplanes of outer, unbounded regions. Use '<A
|
||||
href="qh-optf.htm#Fi2" >Fi</a>' for separating hyperplanes of
|
||||
inner, bounded regions. </p>
|
||||
|
||||
<p>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 <A
|
||||
href="mailto:qhull@qhull.org" >qhull@qhull.org</a>. </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="FV">FV - print average
|
||||
vertex </a></h3>
|
||||
|
||||
<p>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,</p>
|
||||
|
||||
<blockquote>
|
||||
<p>qconvex FV <A
|
||||
href="qh-opto.htm#n">n</a> | qhalf <a href="#Fp">Fp</a></p>
|
||||
</blockquote>
|
||||
|
||||
<p>prints the extreme points of the original point set (roundoff
|
||||
included). </p>
|
||||
|
||||
<h3><a href="#format">»</a><a name="Fx">Fx - print extreme
|
||||
points (vertices) of convex hulls and Delaunay triangulations</a></h3>
|
||||
|
||||
<p>The first line is the number of points. The following lines
|
||||
give the index of the corresponding points. The first point is
|
||||
'0'. </p>
|
||||
|
||||
<p>In 2-d, the extreme points (vertices) are listed in
|
||||
counterclockwise order (by qh_ORIENTclock in user.h). </p>
|
||||
|
||||
<p>In 3-d and higher convex hulls, the extreme points (vertices)
|
||||
are sorted by index. This is the same order as option '<A
|
||||
href="qh-opto.htm#p" >p</a>' when it doesn't include coplanar or
|
||||
interior points. </p>
|
||||
|
||||
<p>For Delaunay triangulations, 'Fx' lists the extreme
|
||||
points of the input sites (i.e., the vertices of their convex hull). The points
|
||||
are unordered. <!-- Navigation links --> </p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p><!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><IMG align=middle
|
||||
height=40 src="qh--geom.gif" width=40 ></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created:
|
||||
Sept. 25, 1995 --- <!-- hhmts start -->Last modified: see top
|
||||
<!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
274
xs/src/qhull/html/qh-optg.htm
Normal file
274
xs/src/qhull/html/qh-optg.htm
Normal file
@ -0,0 +1,274 @@
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull Geomview options (G)</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull Geomview options (G)</h1>
|
||||
|
||||
This section lists the Geomview options for Qhull. These options are
|
||||
indicated by 'G' followed by a letter. See
|
||||
<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>,
|
||||
and <a href="qh-optf.htm#format">Format</a> for other output options.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="geomview">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Geomview output options</h2>
|
||||
|
||||
<p><a href="http://www.geomview.org">Geomview</a> is the graphical
|
||||
viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="#G">G</a></dt>
|
||||
<dd>display Geomview output</dd>
|
||||
<dt><a href="#Gt">Gt</a></dt>
|
||||
<dd>display transparent 3-d Delaunay triangulation</dd>
|
||||
<dt><a href="#GDn">GDn</a></dt>
|
||||
<dd>drop dimension n in 3-d and 4-d output </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Specific</b></dd>
|
||||
<dt><a href="#Ga">Ga</a></dt>
|
||||
<dd>display all points as dots</dd>
|
||||
<dt><a href="#Gc">Gc</a></dt>
|
||||
<dd>display centrums (2-d, 3-d)</dd>
|
||||
<dt><a href="#Gp">Gp</a></dt>
|
||||
<dd>display coplanar points and vertices as radii</dd>
|
||||
<dt><a href="#Gh">Gh</a></dt>
|
||||
<dd>display hyperplane intersections</dd>
|
||||
<dt><a href="#Gi">Gi</a></dt>
|
||||
<dd>display inner planes only (2-d, 3-d)</dd>
|
||||
<dt><a href="#Go">Go</a></dt>
|
||||
<dd>display outer planes only (2-d, 3-d)</dd>
|
||||
<dt><a href="#Gr">Gr</a></dt>
|
||||
<dd>display ridges (3-d)</dd>
|
||||
<dt><a href="#Gv">Gv</a></dt>
|
||||
<dd>display vertices as spheres</dd>
|
||||
<dt><a href="#Gn">Gn</a></dt>
|
||||
<dd>do not display planes</dd>
|
||||
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="G">G - produce output for
|
||||
viewing with Geomview</a></h3>
|
||||
|
||||
<p>By default, option 'G' displays edges in 2-d, outer planes in
|
||||
3-d, and ridges in 4-d.</p>
|
||||
|
||||
<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-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.</p>
|
||||
|
||||
<p>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 '<a
|
||||
href="#Gh">Gh</a>' to project ridges to the intersection of both
|
||||
hyperplanes. This usually results in a cleaner display. </p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Ga">Ga - display all
|
||||
points as dots </a></h3>
|
||||
|
||||
<p>Each input point is displayed as a green dot.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gc">Gc - display centrums
|
||||
(3-d) </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
|
||||
href="qh-optc.htm#Cn2">Cn</a>'.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="GDn">GDn - drop dimension
|
||||
n in 3-d and 4-d output </a></h3>
|
||||
|
||||
<p>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 '<a
|
||||
href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>'
|
||||
'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>'
|
||||
and '<a href="qh-optq.htm#QVn">QVn</a>' 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 <tt>ginsu</tt>
|
||||
module to view the interior</p>
|
||||
|
||||
<p>To view multiple 4-d dimensions at once, output the object
|
||||
without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you
|
||||
rotate the object in one set of dimensions, you can see how it
|
||||
changes in other sets of dimensions.</p>
|
||||
|
||||
<p>For additional control over 4-d objects, output the object
|
||||
without 'GDn' and read it with Geomview's <tt>4dview</tt>. 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.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gh">Gh - display
|
||||
hyperplane intersections (3-d, 4-d)</a></h3>
|
||||
|
||||
<p>In 3-d, the intersection is a black line. It lies on two
|
||||
neighboring hyperplanes, c.f., the blue squares associated with
|
||||
centrums ('<a href="#Gc">Gc </a>'). 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.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gi">Gi - display inner
|
||||
planes only (2-d, 3-d)</a></h3>
|
||||
|
||||
<p>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., <i>[1-r,1-g,1-b] </i>.
|
||||
Its edges are determined by the vertices.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gn">Gn - do not display
|
||||
planes </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Go">Go - display outer
|
||||
planes only (2-d, 3-d)</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gp">Gp - display coplanar
|
||||
points and vertices as radii </a></h3>
|
||||
|
||||
<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior
|
||||
points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a
|
||||
href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'),
|
||||
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 <i>maxcoord * (1 -
|
||||
</i><a href="qh-optc.htm#An"><i>A-n</i></a><i>)</i>. It is at
|
||||
least 1/20'th of the maximum coordinate, and ignores post merging
|
||||
if pre-merging is done.</p>
|
||||
|
||||
<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as
|
||||
spheres) is also selected, option 'Gp' displays coplanar
|
||||
points as radii. Select options <a href="qh-optq.htm#Qc">Qc</a>'
|
||||
and/or '<a href="qh-optq.htm#Qi">Qi</a>'. 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'.
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gr">Gr - display ridges
|
||||
(3-d) </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gt">Gt - transparent 3-d
|
||||
Delaunay </a></h3>
|
||||
|
||||
<p>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 '<a
|
||||
href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a
|
||||
href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p>
|
||||
|
||||
<h3><a href="#geomview">»</a><a name="Gv">Gv - display vertices
|
||||
as spheres (2-d, 3-d)</a></h3>
|
||||
|
||||
<p>The radius of the sphere corresponds to the imprecision of the
|
||||
data. See '<a href="#Gp">Gp</a>' for determining the radius.</p>
|
||||
|
||||
<!-- Navigation links -->
|
||||
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
353
xs/src/qhull/html/qh-opto.htm
Normal file
353
xs/src/qhull/html/qh-opto.htm
Normal file
@ -0,0 +1,353 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull output options</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull output options</h1>
|
||||
|
||||
<p>This section lists the output options for Qhull. These options
|
||||
are indicated by lower case characters. See <a
|
||||
href="qh-optf.htm#format">Formats</a>, <a
|
||||
href="qh-optp.htm#print">Print</a>, and <a
|
||||
href="qh-optg.htm#geomview">Geomview</a> for other output
|
||||
options. </p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="output">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Output options</h2>
|
||||
|
||||
<p>Qhull prints its output to standard out. All output is printed
|
||||
text. The default output is a summary (option '<a href="#s">s</a>').
|
||||
Other outputs may be specified as follows. </p>
|
||||
|
||||
<dl compact>
|
||||
<dt><a href="#f">f</a></dt>
|
||||
<dd>print all fields of all facets</dd>
|
||||
<dt><a href="#n">n</a></dt>
|
||||
<dd>print hyperplane normals with offsets</dd>
|
||||
<dt><a href="#m">m</a></dt>
|
||||
<dd>print Mathematica output (2-d and 3-d)</dd>
|
||||
<dt><a href="#o">o</a></dt>
|
||||
<dd>print OFF file format (dim, points and facets)</dd>
|
||||
<dt><a href="#s">s</a></dt>
|
||||
<dd>print summary to stderr</dd>
|
||||
<dt><a href="#p">p</a></dt>
|
||||
<dd>print vertex and point coordinates</dd>
|
||||
<dt><a href="#i">i</a></dt>
|
||||
<dd>print vertices incident to each facet </dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Related options</b></dd>
|
||||
<dt><a href="qh-optf.htm#format">F</a></dt>
|
||||
<dd>additional input/output formats</dd>
|
||||
<dt><a href="qh-optg.htm#geomview">G</a></dt>
|
||||
<dd>Geomview output</dd>
|
||||
<dt><a href="qh-optp.htm#print">P</a></dt>
|
||||
<dd>Print options</dd>
|
||||
<dt><a href="qh-optf.htm#Ft">Ft</a></dt>
|
||||
<dd>print triangulation with added points</dd>
|
||||
<dt> </dt>
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#output">»</a><a name="f">f - print all fields of
|
||||
all facets </a></h3>
|
||||
|
||||
<p>Print <a href=../src/libqhull.h#facetT>all fields</a> of all facets.
|
||||
The facet is the primary <a href=index.htm#structure>data structure</a> for
|
||||
Qhull.
|
||||
|
||||
<p>Option 'f' is for
|
||||
debugging. Most of the fields are available via the '<a
|
||||
href="qh-optf.htm#format">F</a>' options. If you need specialized
|
||||
information from Qhull, you can use the <a
|
||||
href="qh-code.htm#library">Qhull library</a> or <a
|
||||
href="qh-code.htm#cpp">C++ interface</a>.</p>
|
||||
|
||||
<p>Use the '<a href="qh-optf.htm#FF">FF</a>' option to print the
|
||||
facets but not the ridges. </p>
|
||||
|
||||
<h3><a href="#output">»</a><a name="i">i - print vertices
|
||||
incident to each facet </a></h3>
|
||||
|
||||
<p>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 '<a href="qh-optf.htm#Fv">Fv</a>'
|
||||
displays an unoriented list of vertices with a vertex count per
|
||||
line. Options '<a href="qh-opto.htm#o">o</a>' and '<a
|
||||
href="qh-optf.htm#Ft">Ft</a>' displays coordinates for each
|
||||
vertex prior to the vertices for each facet. </p>
|
||||
|
||||
<p>Simplicial facets (e.g., triangles in 3-d) consist of <i>d</i>
|
||||
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 '<a href="qh-optq.htm#Qt">Qt</a>' to triangulate non-simplicial facets.</p>
|
||||
|
||||
<p>For 4-d and higher convex hulls and 3-d and higher Delaunay
|
||||
triangulations, <i>d</i> 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 '<a href="qh-optf.htm#Fv">Fv</a>' to list the vertices
|
||||
of non-simplicial facets as is. Use option '<a
|
||||
href="qh-optf.htm#Ft">Ft</a>' to print the coordinates of the
|
||||
centrums as well as those of the input points. </p>
|
||||
|
||||
<h3><a href="#output">»</a><a name="m">m - print Mathematica
|
||||
output </a></h3>
|
||||
|
||||
<p>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: "<tt>list= << <outputfilename> </tt>".
|
||||
If the object is 2-d, it can be visualized by "<tt>Show[Graphics[list]]
|
||||
</tt>". For 3-d objects the command is "<tt>Show[Graphics3D[list]]
|
||||
</tt>". Now the object can be manipulated by commands of the
|
||||
form <tt>"Show[%, <parametername> ->
|
||||
<newvalue>]</tt>". </p>
|
||||
|
||||
<p>For Delaunay triangulation orthogonal projection is better.
|
||||
This can be specified, for example, by "<tt>BoxRatios:
|
||||
Show[%, BoxRatios -> {1, 1, 1e-8}]</tt>". To see the
|
||||
meaningful side of the 3-d object used to visualize 2-d Delaunay,
|
||||
you need to change the viewpoint: "<tt>Show[%, ViewPoint
|
||||
-> {0, 0, -1}]</tt>". By specifying different viewpoints
|
||||
you can slowly rotate objects. </p>
|
||||
|
||||
<p>For halfspace intersections, Qhull produces the dual
|
||||
convex hull.
|
||||
|
||||
<p>See <a href="qh-faq.htm#math">Is Qhull available for Mathematica?</a>
|
||||
for URLs.
|
||||
|
||||
<h3><a href="#output">»</a><a name="n">n - print hyperplane
|
||||
normals with offsets </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>The normals point outward, i.e., the convex hull satisfies <i>Ax
|
||||
<= -b </i>where <i>A</i> is the matrix of coefficients and <i>b</i>
|
||||
is the vector of offsets.</p>
|
||||
|
||||
<p>A point is <i>inside</i> or <i>below</i> a hyperplane if its distance
|
||||
to the hyperplane is negative. A point is <i>outside</i> or <i>above</i> a hyperplane
|
||||
if its distance to the hyperplane is positive. Otherwise a point is <i>on</i> or
|
||||
<i>coplanar to</i> the hyperplane.
|
||||
|
||||
<p>If cdd output is specified ('<a href="qh-optf.htm#FD">FD</a>'),
|
||||
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". </p>
|
||||
|
||||
<h3><a href="#output">»</a><a name="o">o - print OFF file format
|
||||
</a></h3>
|
||||
|
||||
<p>The output is: </p>
|
||||
|
||||
<ul>
|
||||
<li>The first line is the dimension </li>
|
||||
<li>The second line is the number of points, the number of
|
||||
facets, and the number of ridges. </li>
|
||||
<li>All of the input points follow, one per line. </li>
|
||||
<li>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. </li>
|
||||
</ul>
|
||||
|
||||
<p>Option '<a href="qh-optf.htm#Ft">Ft</a>' prints the same
|
||||
information with added points for non-simplicial facets.</p>
|
||||
|
||||
<p>Option '<a href="qh-opto.htm#i">i</a>' displays vertices
|
||||
without the point coordinates. Option '<a href="qh-opto.htm#p">p</a>'
|
||||
displays the point coordinates without vertex and facet information.</p>
|
||||
|
||||
<p>In 3-d, Geomview can load the file directly if you delete the
|
||||
first line (e.g., by piping through '<tt>tail +2</tt>').</p>
|
||||
|
||||
<p>For Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>), 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 '<a
|
||||
href="qh-optf.htm#FN">FN</a>' option for listing Voronoi regions
|
||||
without listing Voronoi vertices.</p>
|
||||
|
||||
<p>If you are using the Qhull library, options 'v o' have the
|
||||
side effect of reordering the neighbors for a vertex.</p>
|
||||
|
||||
<h3><a href="#output">»</a><a name="p">p - print vertex and
|
||||
point coordinates </a></h3>
|
||||
|
||||
<p>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</p>
|
||||
|
||||
<p>With the '<a href="qh-optg.htm#Gc">Gc</a>' and '<a
|
||||
href="qh-optg.htm#Gi">Gi</a>' options, option 'p' also prints
|
||||
coplanar and interior points respectively.</p>
|
||||
|
||||
<p>For <a href=qvoronoi.htm>qvoronoi</a>, it prints the
|
||||
coordinates of each Voronoi vertex.</p>
|
||||
|
||||
<p>For <a href=qdelaun.htm>qdelaunay</a>, it prints the
|
||||
input sites as lifted to a paraboloid. For <a href=qhalf.htm>qhalf</a>
|
||||
it prints the dual points. For both, option 'p' is the same as the first
|
||||
section of option '<a href="qh-opto.htm#o">o</a>'.</p>
|
||||
|
||||
<p>Use '<a href="qh-optf.htm#Fx">Fx</a>' to list the point ids of
|
||||
the extreme points (i.e., vertices). </p>
|
||||
|
||||
<p>If a subset of the facets is selected ('<a
|
||||
href="qh-optp.htm#Pdk">Pdk</a>', '<a href="qh-optp.htm#PDk">PDk</a>',
|
||||
'<a href="qh-optp.htm#Pg">Pg</a>' options), option 'p' only
|
||||
prints vertices and points associated with those facets.</p>
|
||||
|
||||
<p>If cdd-output format is selected ('<a href="qh-optf.htm#FD">FD</a>'),
|
||||
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". </p>
|
||||
|
||||
<h3><a href="#output">»</a><a name="s">s - print summary to
|
||||
stderr </a></h3>
|
||||
|
||||
<p>The default output of Qhull is a summary to stderr. Options '<a
|
||||
href="qh-optf.htm#FS">FS</a>' and '<a href="qh-optf.htm#Fs">Fs</a>'
|
||||
produce the same information for programs. <b>Note</b>: Windows 95 and 98
|
||||
treats stderr the same as stdout. Use option '<a href="qh-optt.htm#TO">TO file</a>' to separate
|
||||
stderr and stdout.</p>
|
||||
|
||||
<p>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 '<a href="qh-optp.htm#Pg">Pg</a>',
|
||||
'<a href="qh-optp.htm#Pdk">Pdk</a>', <a href=qdelaun.htm>qdelaunay</a>,
|
||||
or <a href=qvoronoi.htm>qvoronoi</a> (Delaunay triangulations only
|
||||
use the lower half of a convex hull). It lists the number of
|
||||
coplanar points. For Delaunay triangulations without '<a
|
||||
href="qh-optq.htm#Qc">Qc</a>', it lists the total number of
|
||||
coplanar points. It lists the number of simplicial facets in
|
||||
the output.</p>
|
||||
|
||||
<p>The terminology depends on the output structure. </p>
|
||||
|
||||
<p>The summary lists these statistics:</p>
|
||||
|
||||
<ul>
|
||||
<li>number of points processed by Qhull </li>
|
||||
<li>number of hyperplanes created</li>
|
||||
<li>number of distance tests (not counting statistics,
|
||||
summary, and checking) </li>
|
||||
<li>number of merged facets (if any)</li>
|
||||
<li>number of distance tests for merging (if any)</li>
|
||||
<li>CPU seconds to compute the hull</li>
|
||||
<li>the maximum joggle for '<a href="qh-optq.htm#QJn">QJ</a>'<br>
|
||||
or, the probability of precision errors for '<a
|
||||
href="qh-optq.htm#QJn">QJ</a> <a href="qh-optt.htm#TRn">TRn</a>'
|
||||
</li>
|
||||
<li>total area and volume (if computed, see '<a
|
||||
href="qh-optf.htm#FS">FS</a>' '<a href="qh-optf.htm#FA">FA</a>'
|
||||
'<a href="qh-optf.htm#Fa">Fa</a>' '<a
|
||||
href="qh-optp.htm#PAn">PAn</a>')</li>
|
||||
<li>max. distance of a point above a facet (if non-zero)</li>
|
||||
<li>max. distance of a vertex below a facet (if non-zero)</li>
|
||||
</ul>
|
||||
|
||||
<p>The statistics include intermediate hulls. For example 'rbox d
|
||||
D4 | qhull' reports merged facets even though the final hull is
|
||||
simplicial. </p>
|
||||
|
||||
<p>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 <tt>libqhull.c</tt>. If the number of CPU
|
||||
seconds is clearly wrong, check qh_SECticks in <tt>user.h</tt>. </p>
|
||||
|
||||
<p>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 '<a href="qh-optc.htm#Rn">Rn</a>').
|
||||
Use '<a href="qh-optf.htm#Fs">Fs</a>' to report the maximum outer
|
||||
and inner plane. </p>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qx">Qx</a>'. It is not printed if less
|
||||
than 0.05. </p>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
253
xs/src/qhull/html/qh-optp.htm
Normal file
253
xs/src/qhull/html/qh-optp.htm
Normal file
@ -0,0 +1,253 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull print options (P)</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull print options (P)</h1>
|
||||
|
||||
This section lists the print options for Qhull. These options are
|
||||
indicated by 'P' followed by a letter. See
|
||||
<a href="qh-opto.htm#output">Output</a>, <a href="qh-optg.htm#geomview">Geomview</a>,
|
||||
and <a href="qh-optf.htm#format">Format</a> for other output options.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="format">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Print options</h2>
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="#Pp">Pp</a></dt>
|
||||
<dd>do not report precision problems </dd>
|
||||
<dt><a href="#Po">Po</a></dt>
|
||||
<dd>force output despite precision problems</dd>
|
||||
<dt><a href="#Po2">Po</a></dt>
|
||||
<dd>if error, output neighborhood of facet</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Select</b></dd>
|
||||
<dt><a href="#Pdk">Pdk:n</a></dt>
|
||||
<dd>print facets with normal[k] >= n (default 0.0)</dd>
|
||||
<dt><a href="#PDk">PDk:n</a></dt>
|
||||
<dd>print facets with normal[k] <= n </dd>
|
||||
<dt><a href="#PFn">PFn</a></dt>
|
||||
<dd>print facets whose area is at least n</dd>
|
||||
<dt><a href="#Pg">Pg</a></dt>
|
||||
<dd>print good facets only (needs '<a href="qh-optq.htm#QGn">QGn</a>'
|
||||
or '<a href="qh-optq.htm#QVn">QVn </a>')</dd>
|
||||
<dt><a href="#PMn">PMn</a></dt>
|
||||
<dd>print n facets with most merges</dd>
|
||||
<dt><a href="#PAn">PAn</a></dt>
|
||||
<dd>print n largest facets by area</dd>
|
||||
<dt><a href="#PG">PG</a></dt>
|
||||
<dd>print neighbors of good facets</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
<hr>
|
||||
|
||||
<h3><a href="#print">»</a><a name="PAn">PAn - keep n largest
|
||||
facets by area</a></h3>
|
||||
|
||||
<p>The <i>n</i> largest facets are marked good for printing. This
|
||||
may be useful for <a href="qh-impre.htm#approximate">approximating
|
||||
a hull</a>. Unless '<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>'
|
||||
is automatically set. </p>
|
||||
|
||||
<h3><a href="#print">»</a><a name="Pdk">Pdk:n - print facet if
|
||||
normal[k] >= n </a></h3>
|
||||
|
||||
<p>For a given output, print only those facets with <i>normal[k] >= n</i>
|
||||
and <i>drop</i> the others. For example, 'Pd0:0.5' prints facets with <i>normal[0]
|
||||
>= 0.5 </i>. The default value of <i>n</i> is zero. For
|
||||
example in 3-d, 'Pd0d1d2' prints facets in the positive octant.
|
||||
<p>
|
||||
If no facets match, the closest facet is returned.</p>
|
||||
<p>
|
||||
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'.
|
||||
|
||||
<h3><a href="#print">»</a><a name="PDk">PDk:n - print facet if
|
||||
normal[k] <= n</a></h3>
|
||||
|
||||
<p>For a given output, print only those facets with <i>normal[k] <= n</i>
|
||||
and <i>drop</i> the others.
|
||||
For example, 'PD0:0.5' prints facets with <i>normal[0]
|
||||
<= 0.5 </i>. The default value of <i>n</i> is zero. For
|
||||
example in 3-d, 'PD0D1D2' displays facets in the negative octant.
|
||||
<p>
|
||||
If no facets match, the closest facet is returned.</p>
|
||||
|
||||
<p>In 2-d, 'd G PD2' displays the Delaunay triangulation instead
|
||||
of the corresponding paraboloid. </p>
|
||||
|
||||
<p>Be careful of placing 'Dk' or 'dk' immediately after a real
|
||||
number. Some compilers treat the 'D' as a double precision
|
||||
exponent. </p>
|
||||
|
||||
<h3><a href="#print">»</a><a name="PFn">PFn - keep facets whose
|
||||
area is at least n</a></h3>
|
||||
|
||||
<p>The facets with area at least <i>n</i> are marked good for
|
||||
printing. This may be useful for <a
|
||||
href="qh-impre.htm#approximate">approximating a hull</a>. Unless
|
||||
'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
|
||||
automatically set. </p>
|
||||
|
||||
<h3><a href="#print">»</a><a name="Pg">Pg - print good facets </a></h3>
|
||||
|
||||
<p>Qhull can mark facets as "good". This is used to</p>
|
||||
|
||||
<ul>
|
||||
<li>mark the lower convex hull for Delaunay triangulations
|
||||
and Voronoi diagrams</li>
|
||||
<li>mark the facets that are visible from a point (the '<a
|
||||
href="qh-optq.htm#QGn">QGn </a>' option)</li>
|
||||
<li>mark the facets that contain a point (the '<a
|
||||
href="qh-optq.htm#QVn">QVn</a>' option).</li>
|
||||
<li>indicate facets with a large enough area (options '<a
|
||||
href="#PAn">PAn</a>' and '<a href="#PFn">PFn</a>')</li>
|
||||
</ul>
|
||||
|
||||
<p>Option '<a href="#Pg">Pg</a>' only prints good facets that
|
||||
also meet '<a href="#Pdk">Pdk</a>' and '<a href="#PDk">PDk</a>'
|
||||
options. It is automatically set for options '<a href="#PAn">PAn</a>',
|
||||
'<a href="#PFn">PFn </a>', '<a href="qh-optq.htm#QGn">QGn</a>',
|
||||
and '<a href="qh-optq.htm#QVn">QVn</a>'.</p>
|
||||
|
||||
<h3><a href="#print">»</a><a name="PG">PG - print neighbors of
|
||||
good facets</a></h3>
|
||||
|
||||
<p>Option 'PG' can be used with or without option '<a href="#Pg">Pg</a>'
|
||||
to print the neighbors of good facets. For example, options '<a
|
||||
href="qh-optq.htm#QGn">QGn</a>' and '<a href="qh-optq.htm#QVn">QVn</a>'
|
||||
print the horizon facets for point <i>n. </i></p>
|
||||
|
||||
<h3><a href="#print">»</a><a name="PMn">PMn - keep n facets with
|
||||
most merges</a></h3>
|
||||
|
||||
<p>The n facets with the most merges are marked good for
|
||||
printing. This may be useful for <a
|
||||
href="qh-impre.htm#approximate">approximating a hull</a>. Unless
|
||||
'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
|
||||
automatically set. </p>
|
||||
|
||||
<p>Use option '<a href="qh-optf.htm#Fm">Fm</a>' to print merges
|
||||
per facet.
|
||||
|
||||
<h3><a href="#print">»</a><a name="Po">Po - force output despite
|
||||
precision problems</a></h3>
|
||||
|
||||
<p>Use options 'Po' and '<a href="qh-optq.htm#Q0">Q0</a>' if you
|
||||
can not merge facets, triangulate the output ('<a href="qh-optq.htm#Qt">Qt</a>'),
|
||||
or joggle the input (<a href="qh-optq.htm#QJn">QJ</a>).
|
||||
|
||||
<p>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 <a
|
||||
href="qh-impre.htm#exact">exact arithmetic</a> are better.</p>
|
||||
|
||||
<p>If you need a simplicial Delaunay triangulation, use
|
||||
joggled input '<a href="qh-optq.htm#QJn">QJ</a>' or triangulated
|
||||
output '<a
|
||||
href="qh-optf.htm#Ft">Ft</a>'.
|
||||
|
||||
<p>Option 'Po' may be used without '<a href="qh-optq.htm#Q0">Q0</a>'
|
||||
to remove some steps from Qhull or to output the neighborhood of
|
||||
an error.</p>
|
||||
|
||||
<p>Option 'Po' may be used with option '<a href="qh-optq.htm#Q5">Q5</a>')
|
||||
to skip qh_check_maxout (i.e., do not determine the maximum outside distance).
|
||||
This can save a significant amount of time.
|
||||
|
||||
<p>If option 'Po' is used,</p>
|
||||
|
||||
<ul>
|
||||
<li>most precision errors allow Qhull to continue. </li>
|
||||
<li>verify ('<a href="qh-optt.htm#Tv">Tv</a>') does not check
|
||||
coplanar points.</li>
|
||||
<li>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. </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="#print">»</a><a name="Po2">Po - if error, output
|
||||
neighborhood of facet</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>See '<a href="qh-optp.htm#Po">Po</a>' - force output despite
|
||||
precision problems.
|
||||
|
||||
<h3><a href="#print">»</a><a name="Pp">Pp - do not report
|
||||
precision problems </a></h3>
|
||||
|
||||
<p>With option 'Pp', Qhull does not print statistics about
|
||||
precision problems, and it removes some of the warnings. It
|
||||
removes the narrow hull warning.</p>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
731
xs/src/qhull/html/qh-optq.htm
Normal file
731
xs/src/qhull/html/qh-optq.htm
Normal file
@ -0,0 +1,731 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull control options (Q)</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull control options (Q)</h1>
|
||||
|
||||
<p>This section lists the control options for Qhull. These
|
||||
options are indicated by 'Q' followed by a letter. </p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="qhull">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Qhull control options</h2>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="#Qu">Qu</a></dt>
|
||||
<dd>compute upper hull for furthest-site Delaunay
|
||||
triangulation </dd>
|
||||
<dt><a href="#Qc">Qc</a></dt>
|
||||
<dd>keep coplanar points with nearest facet</dd>
|
||||
<dt><a href="#Qi">Qi</a></dt>
|
||||
<dd>keep interior points with nearest facet</dd>
|
||||
<dt><a href="#QJn">QJ</a></dt>
|
||||
<dd>joggled input to avoid precision problems</dd>
|
||||
<dt><a href="#Qt">Qt</a></dt>
|
||||
<dd>triangulated output</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Precision handling</b></dd>
|
||||
<dt><a href="#Qz">Qz</a></dt>
|
||||
<dd>add a point-at-infinity for Delaunay triangulations</dd>
|
||||
<dt><a href="#Qx">Qx</a></dt>
|
||||
<dd>exact pre-merges (allows coplanar facets)</dd>
|
||||
<dt><a href="#Qs">Qs</a></dt>
|
||||
<dd>search all points for the initial simplex</dd>
|
||||
<dt><a href="#Qbb">Qbb</a></dt>
|
||||
<dd>scale last coordinate to [0,m] for Delaunay</dd>
|
||||
<dt><a href="#Qv">Qv</a></dt>
|
||||
<dd>test vertex neighbors for convexity</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Transform input</b></dd>
|
||||
<dt><a href="#Qb0">Qbk:0Bk:0</a></dt>
|
||||
<dd>drop dimension k from input</dd>
|
||||
<dt><a href="#QRn">QRn</a></dt>
|
||||
<dd>random rotation (n=seed, n=0 time, n=-1 time/no rotate)</dd>
|
||||
<dt><a href="#Qbk">Qbk:n</a></dt>
|
||||
<dd>scale coord[k] to low bound of n (default -0.5)</dd>
|
||||
<dt><a href="#QBk">QBk:n</a></dt>
|
||||
<dd>scale coord[k] to upper bound of n (default 0.5)</dd>
|
||||
<dt><a href="#QbB">QbB</a></dt>
|
||||
<dd>scale input to fit the unit cube</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Select facets</b></dd>
|
||||
<dt><a href="#QVn">QVn</a></dt>
|
||||
<dd>good facet if it includes point n, -n if not</dd>
|
||||
<dt><a href="#QGn">QGn</a></dt>
|
||||
<dd>good facet if visible from point n, -n for not visible</dd>
|
||||
<dt><a href="#Qg">Qg</a></dt>
|
||||
<dd>only build good facets (needs '<a href="#QGn">QGn</a>', '<a
|
||||
href="#QVn">QVn </a>', or '<a href="qh-optp.htm#Pdk">Pdk</a>')</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Experimental</b></dd>
|
||||
<dt><a href="#Q4">Q4</a></dt>
|
||||
<dd>avoid merging old facets into new facets</dd>
|
||||
<dt><a href="#Q5">Q5</a></dt>
|
||||
<dd>do not correct outer planes at end of qhull</dd>
|
||||
<dt><a href="#Q3">Q3</a></dt>
|
||||
<dd>do not merge redundant vertices</dd>
|
||||
<dt><a href="#Q6">Q6</a></dt>
|
||||
<dd>do not pre-merge concave or coplanar facets</dd>
|
||||
<dt><a href="#Q0">Q0</a></dt>
|
||||
<dd>do not pre-merge facets with 'C-0' or 'Qx'</dd>
|
||||
<dt><a href="#Q8">Q8</a></dt>
|
||||
<dd>ignore near-interior points</dd>
|
||||
<dt><a href="#Q2">Q2</a></dt>
|
||||
<dd>merge all non-convex at once instead of independent sets</dd>
|
||||
<dt><a href="#Qf">Qf</a></dt>
|
||||
<dd>partition point to furthest outside facet</dd>
|
||||
<dt><a href="#Q7">Q7</a></dt>
|
||||
<dd>process facets depth-first instead of breadth-first</dd>
|
||||
<dt><a href="#Q9">Q9</a></dt>
|
||||
<dd>process furthest of furthest points</dd>
|
||||
<dt><a href="#Q10">Q10</a></dt>
|
||||
<dd>no special processing for narrow distributions</dd>
|
||||
<dt><a href="#Q11">Q11</a></dt>
|
||||
<dd>copy normals and recompute centrums for tricoplanar facets</dd>
|
||||
<dt><a href="#Q12">Q12</a></dt>
|
||||
<dd>do not error on wide merge due to duplicate ridge and nearly coincident points</dd>
|
||||
<dt><a href="#Qm">Qm</a></dt>
|
||||
<dd>process points only if they would increase the max. outer
|
||||
plane </dd>
|
||||
<dt><a href="#Qr">Qr</a></dt>
|
||||
<dd>process random outside points instead of furthest one</dd>
|
||||
<dt><a href="#Q1">Q1</a></dt>
|
||||
<dd>sort merges by type instead of angle</dd>
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qbb">Qbb - scale the last
|
||||
coordinate to [0,m] for Delaunay</a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Option 'Qbb' is automatically set for <a href=qdelaun.htm>qdelaunay</a>
|
||||
and <a href=qvoronoi.htm>qvoronoi</a>. Option 'Qbb' is automatically set for joggled input '<a
|
||||
href="qh-optq.htm#QJn">QJ</a>'. </p>
|
||||
|
||||
<p>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, <tt>rbox 10000 D2 B1e8 | qhull d</tt> has precision
|
||||
problems while <tt>rbox 10000 D2 B1e8 | qhull d Qbb</tt> is OK. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QbB">QbB - scale the input to
|
||||
fit the unit cube</a></h3>
|
||||
|
||||
<p>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 <tt>user.h</tt> (0.5 is best for <a
|
||||
href="index.htm#geomview">Geomview</a>).</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qbk">Qbk:n - scale coord[k]
|
||||
to low bound</a></h3>
|
||||
|
||||
<p>After scaling, the lower bound for dimension k of the input
|
||||
points will be n. 'Qbk' scales coord[k] to -0.5. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QBk">QBk:n - scale coord[k]
|
||||
to upper bound </a></h3>
|
||||
|
||||
<p>After scaling, the upper bound for dimension k of the input
|
||||
points will be n. 'QBk' scales coord[k] to 0.5. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qb0">Qbk:0Bk:0 - drop
|
||||
dimension k from the input points</a></h3>
|
||||
|
||||
<p>Drop dimension<em> k </em>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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qc">Qc - keep coplanar points
|
||||
with nearest facet </a></h3>
|
||||
|
||||
<p>During construction of the hull, a point is coplanar if it is
|
||||
between '<a href="qh-optc.htm#Wn">Wn</a>' above and '<a
|
||||
href="qh-optc.htm#Un">Un</a>' below a facet's hyperplane. A
|
||||
different definition is used for output from Qhull. </p>
|
||||
|
||||
<p>For output, a coplanar point is above the minimum vertex
|
||||
(i.e., above the inner plane). With joggle ('<a
|
||||
href="qh-optq.htm#QJn">QJ</a>'), a coplanar point includes points
|
||||
within one joggle of the inner plane. </p>
|
||||
|
||||
<p>With option 'Qc', output formats '<a href="qh-opto.htm#p">p </a>',
|
||||
'<a href="qh-opto.htm#f">f</a>', '<a href="qh-optg.htm#Gp">Gp</a>',
|
||||
'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
|
||||
and '<a href="qh-optf.htm#FP">FP</a>' will print the coplanar
|
||||
points. With options 'Qc <a href="#Qi">Qi</a>' these outputs
|
||||
include the interior points.</p>
|
||||
|
||||
<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>
|
||||
or <a href=qvoronoi.htm>qvoronoi</a>), a coplanar point is a point
|
||||
that is nearly incident to a vertex. All input points are either
|
||||
vertices of the triangulation or coplanar.</p>
|
||||
|
||||
<p>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 '<a href="#Q5">Q5</a> <a href="#Q8">Q8</a>' are set, a
|
||||
coplanar point may be missed in the output (see <a
|
||||
href="qh-impre.htm#limit">Qhull limitations</a>).</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qf">Qf - partition point to
|
||||
furthest outside facet </a></h3>
|
||||
|
||||
<p>After adding a new point to the convex hull, Qhull partitions
|
||||
the outside points and coplanar points of the old, visible
|
||||
facets. Without the '<a href="qh-opto.htm#f">f </a>' option and
|
||||
merging, it assigns a point to the first facet that it is outside
|
||||
('<a href="qh-optc.htm#Wn">Wn</a>'). When merging, it assigns a
|
||||
point to the first facet that is more than several times outside
|
||||
(see qh_DISToutside in user.h).</p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Option '<a href="#Q9">Q9</a>' processes the furthest of all
|
||||
furthest points.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qg">Qg - only build good
|
||||
facets (needs 'QGn' 'QVn' or 'Pdk') </a></h3>
|
||||
|
||||
<p>Qhull has several options for defining and printing good
|
||||
facets. With the '<a href="#Qg">Qg</a>' 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 (<a href=qdelau_f.htm>qdelaunay Qu</a>,
|
||||
invoke with 'qhull d Qbb <a href="#Qu">Qu</a> 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.</p>
|
||||
|
||||
<p>See '<a href="#QGn">QGn</a>', '<a href="#QVn">QVn</a>', and '<a
|
||||
href="qh-optp.htm#Pdk">Pdk</a>' for defining good facets, and '<a
|
||||
href="qh-optp.htm#Pg">Pg</a>' and '<a href="qh-optp.htm#PG">PG</a>'
|
||||
for printing good facets and their neighbors. If pre-merging ('<a
|
||||
href="qh-optc.htm#Cn">C-n</a>') is not used and there are
|
||||
coplanar facets, then 'Qg Pg' may produce a different result than
|
||||
'<a href="qh-optp.htm#Pg">Pg</a>'. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QGn">QGn - good facet if
|
||||
visible from point n, -n for not visible </a></h3>
|
||||
|
||||
<p>With option 'QGn', a facet is good (see '<a href="#Qg">Qg</a>'
|
||||
and '<a href="qh-optp.htm#Pg">Pg</a>') if it is visible from
|
||||
point n. If <i>n < 0</i>, a facet is good if it is not visible
|
||||
from point n. Point n is not added to the hull (unless '<a
|
||||
href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TPn">TPn</a>').</p>
|
||||
|
||||
<p>With <a href="rbox.htm">rbox</a>, use the 'Pn,m,r' option
|
||||
to define your point; it will be point 0 ('QG0'). </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qi">Qi - keep interior points
|
||||
with nearest facet </a></h3>
|
||||
|
||||
<p>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 '<a href="#Qc">Qc </a>' as well. </p>
|
||||
|
||||
<p>Option 'Qi' is automatically set for '<a href=qdelaun.htm>qdelaunay</a>
|
||||
<a href="#Qc">Qc</a>' and '<a href=qvoronoi.htm>qvoronoi</a>
|
||||
<a href="#Qc">Qc</a>'. If you use
|
||||
'<a href=qdelaun.htm>qdelaunay</a> Qi' or '<a href=qvoronoi.htm>qvoronoi</a>
|
||||
Qi', option '<a href="qh-opto.htm#s">s</a>' reports all nearly
|
||||
incident points while option '<a href="qh-optf.htm#Fs">Fs</a>'
|
||||
reports the number of interior points (should always be zero).</p>
|
||||
|
||||
<p>With option 'Qi', output formats '<a href="qh-opto.htm#p">p</a>',
|
||||
'<a href="qh-opto.htm#f">f</a>','<a href="qh-optg.htm#Gp">Gp</a>',
|
||||
'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
|
||||
and '<a href="qh-optf.htm#FP">FP</a>' include interior points. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QJ">QJ</a> or <a name="QJn">QJn</a> - joggled
|
||||
input to avoid precision errors</a></h3>
|
||||
|
||||
<p>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 <i>n</i>
|
||||
ten-fold and tries again. The maximum value for increasing <i>n</i>
|
||||
is 0.01 times the maximum width of the input. Option 'QJ' selects
|
||||
a default value for <i>n</i>. <a href="../src/user.h#JOGGLEdefault">User.h</a>
|
||||
defines these parameters and a maximum number of retries. See <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>Users of joggled input should consider converting to
|
||||
triangulated output ('<a href="../html/qh-optq.htm#Qt">Qt</a>'). Triangulated output is
|
||||
approximately 1000 times more accurate than joggled input.
|
||||
|
||||
<p>Option 'QJ' also sets '<a href="qh-optq.htm#Qbb">Qbb</a>' for
|
||||
Delaunay triangulations and Voronoi diagrams. It does not set
|
||||
'Qbb' if '<a href="qh-optq.htm#Qbk">Qbk:n</a>' or '<a
|
||||
href="qh-optq.htm#QBk">QBk:n</a>' are set. </p>
|
||||
|
||||
<p>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
|
||||
('<a href="qh-optq.htm#Qt">Qt</a>') or Option '<a href="qh-optf.htm#Ft">Ft</a>'.
|
||||
|
||||
<p>Qhull adjusts the outer and inner planes for 'QJn' ('<a
|
||||
href="qh-optf.htm#Fs">Fs</a>'). They are increased by <i>sqrt(d)*n</i>
|
||||
to account for the maximum distance between a joggled point and
|
||||
the corresponding input point. Coplanar points ('<a
|
||||
href="qh-optq.htm#Qc">Qc</a>') require an additional <i>sqrt(d)*n</i>
|
||||
since vertices and coplanar points may be joggled in opposite
|
||||
directions. </p>
|
||||
|
||||
<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>), joggle
|
||||
happens before lifting the input sites to a paraboloid. Instead of
|
||||
'QJ', you may use triangulated output ('<a
|
||||
href="qh-optq.htm#Qt">Qt</a>')</p>
|
||||
|
||||
<p>This option is deprecated for Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>).
|
||||
It triangulates cospherical points, leading to duplicated Voronoi vertices.</p>
|
||||
|
||||
<p>By default, 'QJn' uses a fixed random number seed. To use time
|
||||
as the random number seed, select '<a href="qh-optq.htm#QRn">QR-1</a>'.
|
||||
The summary ('<a href="qh-opto.htm#s">s</a>') will show the
|
||||
selected seed as 'QR-n'.
|
||||
|
||||
<p>With 'QJn', Qhull does not error on degenerate hyperplane
|
||||
computations. Except for Delaunay and Voronoi computations, Qhull
|
||||
does not error on coplanar points. </p>
|
||||
|
||||
<p>Use option '<a href="qh-optf.htm#FO">FO</a>' to display the
|
||||
selected options. Option 'FO' displays the joggle and the joggle
|
||||
seed. If Qhull restarts, it will redisplay the options. </p>
|
||||
|
||||
<p>Use option '<a href="qh-optt.htm#TRn">TRn</a>' to estimate the
|
||||
probability that Qhull will fail for a given 'QJn'.
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qm">Qm - only process points
|
||||
that increase the maximum outer plane </a></h3>
|
||||
|
||||
<p>Qhull reports the maximum outer plane in its summary ('<a
|
||||
href="qh-opto.htm#s">s</a>'). With option 'Qm', Qhull does not
|
||||
process points that are below the current, maximum outer plane.
|
||||
This is equivalent to always adjusting '<a href="qh-optc.htm#Wn">Wn
|
||||
</a>' 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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qr">Qr - process random
|
||||
outside points instead of furthest ones </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>The original randomization algorithm by Clarkson and Shor [<a
|
||||
href="index.htm#cla-sho89">'89</a>] used a conflict list which
|
||||
is equivalent to Qhull's outside set. Later randomized algorithms
|
||||
retained the previously constructed facets. </p>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QRn">QRn - random rotation </a></h3>
|
||||
|
||||
<p>Option 'QRn' randomly rotates the input. For Delaunay
|
||||
triangulations (<a href=qdelaun.htm>qdelaunay</a> or <a href=qvoronoi.htm>qvoronoi</a>),
|
||||
it rotates the lifted points about
|
||||
the last axis. </p>
|
||||
|
||||
<p>If <em>n=0</em>, use time as the random number seed. If <em>n>0</em>,
|
||||
use n as the random number seed. If <em>n=-1</em>, don't rotate
|
||||
but use time as the random number seed. If <em>n<-1</em>,
|
||||
don't rotate but use <em>n</em> as the random number seed. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qs">Qs - search all points
|
||||
for the initial simplex </a></h3>
|
||||
|
||||
<p>Qhull constructs an initial simplex from <i>d+1</i> 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 <tt>poly2.c </tt>).
|
||||
It rejects points with nearly zero determinants. This should work
|
||||
for almost all input sets.</p>
|
||||
|
||||
<p>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 ('<a href="#Qb0">Qbk:0Bk:0</a>').
|
||||
If not, use option 'Qs'. It performs an exhaustive search for the
|
||||
best initial simplex. This is expensive is high dimensions. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qt">Qt - triangulated output</a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Use option 'Qt' to triangulate all non-simplicial facets before generating
|
||||
results. Alternatively, use joggled input ('<a href="#QJn">QJ</a>') to
|
||||
prevent non-simplical facets. Unless '<a href="qh-optp.htm#Pp">Pp</a>' is set,
|
||||
qhull produces a warning if 'QJ' and 'Qt' are used together.
|
||||
|
||||
<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>), triangulation
|
||||
occurs after lifting the input sites to a paraboloid and computing the convex hull.
|
||||
</p>
|
||||
|
||||
<p>Option 'Qt' is deprecated for Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>).
|
||||
It triangulates cospherical points, leading to duplicated Voronoi vertices.</p>
|
||||
|
||||
<p>Option 'Qt' may produce degenerate facets with zero area.</p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>With sufficient merging, the ridges of a non-simplicial facet may share more than two neighboring facets. If so, their triangulation ('<a href="#Qt">Qt</a>') will fail since two facets have the same vertex set. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qu">Qu - compute upper hull
|
||||
for furthest-site Delaunay triangulation </a></h3>
|
||||
|
||||
<p>When computing a Delaunay triangulation (<a href=qdelaun.htm>qdelaunay</a>
|
||||
or <a href=qvoronoi.htm>qvoronoi</a>),
|
||||
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 <a
|
||||
href="qdelau_f.htm">furthest-site Delaunay triangulation</a>
|
||||
and the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</p>
|
||||
|
||||
<p>Option 'qhull d Qbb Qu <a href="#Qg">Qg</a>' 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.,
|
||||
'<a href="qh-optf.htm#FV">FV</a>', the average of <em>d</em> extreme points); 4) run
|
||||
'qhull d Qbb Qu' or 'qhull v Qbb Qu' on these points.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qv">Qv - test vertex
|
||||
neighbors for convexity </a></h3>
|
||||
|
||||
<p>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.. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="QVn">QVn - good facet if it
|
||||
includes point n, -n if not </a></h3>
|
||||
|
||||
<p>With option 'QVn', a facet is good ('<a href="#Qg">Qg</a>',
|
||||
'<a href="qh-optp.htm#Pg">Pg</a>') if one of its vertices is
|
||||
point n. If <i>n<0</i>, a good facet does not include point n.
|
||||
|
||||
<p>If options '<a href="qh-optp.htm#PG">PG</a>'
|
||||
and '<a href="#Qg">Qg</a>' are not set, option '<a href="qh-optp.htm#Pg">Pg</a>'
|
||||
(print only good)
|
||||
is automatically set.
|
||||
</p>
|
||||
|
||||
<p>Option 'QVn' behaves oddly with options '<a href="qh-optf.htm#Fx">Fx</a>'
|
||||
and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fv2">Fv</a>'.
|
||||
|
||||
<p>If used with option '<a href="#Qg">Qg</a>' (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 '<a href="#QJn">QJ</a>' or
|
||||
'<a href="#Q0">Q0</a>' (no merging).</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qx">Qx - exact pre-merges
|
||||
(allows coplanar facets) </a></h3>
|
||||
|
||||
<p>Option 'Qx' performs exact merges while building the hull.
|
||||
Option 'Qx' is set by default in 5-d and higher. Use option '<a
|
||||
href="#Q0">Q0</a>' to not use 'Qx' by default. Unless otherwise
|
||||
specified, option 'Qx' sets option '<a href="qh-optc.htm#C0">C-0</a>'.
|
||||
</p>
|
||||
|
||||
<p>The "exact" merges are merging a point into a
|
||||
coplanar facet (defined by '<a href="qh-optc.htm#Vn">Vn </a>', '<a
|
||||
href="qh-optc.htm#Un">Un</a>', and '<a href="qh-optc.htm#Cn">C-n</a>'),
|
||||
merging concave facets, merging duplicate ridges, and merging
|
||||
flipped facets. Coplanar merges and angle coplanar merges ('<a
|
||||
href="qh-optc.htm#An">A-n</a>') are not performed. Concavity
|
||||
testing is delayed until a merge occurs.</p>
|
||||
|
||||
<p>After the hull is built, all coplanar merges are performed
|
||||
(defined by '<a href="qh-optc.htm#Cn">C-n</a>' and '<a
|
||||
href="qh-optc.htm#An">A-n</a>'), then post-merges are performed
|
||||
(defined by '<a href="qh-optc.htm#Cn2">Cn</a>' and '<a
|
||||
href="qh-optc.htm#An2">An</a>'). If facet progress is logged ('<a
|
||||
href="qh-optt.htm#TFn">TFn</a>'), Qhull reports each phase and
|
||||
prints intermediate summaries and statistics ('<a
|
||||
href="qh-optt.htm#Ts">Ts</a>'). </p>
|
||||
|
||||
<p>Without 'Qx' in 5-d and higher, options '<a
|
||||
href="qh-optc.htm#Cn">C-n</a>' and '<a href="qh-optc.htm#An">A-n</a>'
|
||||
may merge too many facets. Since redundant vertices are not
|
||||
removed effectively, facets become increasingly wide. </p>
|
||||
|
||||
<p>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 '<a href="#Q6">Q6</a>'
|
||||
which doesn't pre-merge concave facets. A concave facet makes a
|
||||
large dent in the intermediate hull.</p>
|
||||
|
||||
<p>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 <tt>poly2.c </tt>. 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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Qz">Qz - add a
|
||||
point-at-infinity for Delaunay triangulations</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q0">Q0 - no merging with C-0
|
||||
and Qx</a></h3>
|
||||
|
||||
<p>Turn off default merge options '<a href="qh-optc.htm#C0">C-0</a>'
|
||||
and '<a href="#Qx">Qx</a>'. </p>
|
||||
|
||||
<p>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 <a href="qh-impre.htm">Precision issues</a>.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q1">Q1 - sort merges by type
|
||||
instead of angle </a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q2">Q2 - merge all non-convex
|
||||
at once instead of independent sets </a></h3>
|
||||
|
||||
<p>With 'Q2', Qhull merges all facets at once instead of
|
||||
performing merges in independent sets. This may make the facets
|
||||
wider. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q3">Q3 - do not merge
|
||||
redundant vertices </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q4">Q4 - avoid merging </a>old
|
||||
facets into new facets</h3>
|
||||
|
||||
<p>With 'Q4', Qhull avoids merges of an old facet into a new
|
||||
facet. This sometimes improves facet width and sometimes makes it
|
||||
worse. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q5">Q5 - do not correct outer
|
||||
planes at end of qhull </a></h3>
|
||||
|
||||
<p>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 <tt>geom.c</tt>).
|
||||
It includes points that are just inside the hull. </p>
|
||||
|
||||
<p>With options 'Q5' or '<a href="qh-optp.htm#Po">Po</a>', Qhull
|
||||
does not test outer planes. The maximum outer plane is used
|
||||
instead. Coplanar points ('<a href="#Qc">Qc</a>') are defined by
|
||||
'<a href="qh-optc.htm#Un">Un</a>'. An input point may be outside
|
||||
of the maximum outer plane (this appears to be unlikely). An
|
||||
interior point may be above '<a href="qh-optc.htm#Un">Un</a>'
|
||||
from a hyperplane.</p>
|
||||
|
||||
<p>Option 'Q5' may be used if outer planes are not needed. Outer
|
||||
planes are needed for options '<a href="qh-opto.htm#s">s</a>', '<a
|
||||
href="qh-optg.htm#G">G</a>', '<a href="qh-optg.htm#Go">Go </a>',
|
||||
'<a href="qh-optf.htm#Fs">Fs</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
|
||||
'<a href="qh-optf.htm#FF">FF</a>', and '<a href="qh-opto.htm#f">f</a>'.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q6">Q6 - do not pre-merge
|
||||
concave or coplanar facets </a></h3>
|
||||
|
||||
<p>With 'Q6', Qhull does not pre-merge concave or coplanar
|
||||
facets. This demonstrates the effect of "dents" when
|
||||
using '<a href="#Qx">Qx</a>'. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q7">Q7 - depth-first
|
||||
processing instead of breadth-first </a></h3>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Under 'Q7', Qhull runs slower and the facets may be wider. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q8">Q8 - ignore near-interior
|
||||
points </a></h3>
|
||||
|
||||
<p>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 <a
|
||||
href="#Qc">Qc</a>' may be sufficient. </p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q9">Q9 - process furthest of
|
||||
furthest points </a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q10">Q10 - no special processing
|
||||
for narrow distributions</a></h3>
|
||||
|
||||
<p>With 'Q10', Qhull does not special-case narrow distributions.
|
||||
See <a href=qh-impre.htm#limit>Limitations of merged facets</a> for
|
||||
more information.
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q11">Q11 - copy normals and recompute
|
||||
centrums for
|
||||
tricoplanar facets</a></h3>
|
||||
|
||||
Option '<a href="#Qt">Qt</a>' 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.
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>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.
|
||||
|
||||
<h3><a href="#qhull">»</a><a name="Q12">Q12 - do not error
|
||||
on wide merge due to duplicate ridge and nearly coincident points</a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Use option 'Q12' to log a warning instead of throwing an error.
|
||||
|
||||
<p>For Delaunay triangulations, a bounding box may alleviate this error (e.g., <tt>rbox 500 C1,1E-13 t c G1 | qhull d</tt>).
|
||||
This avoids the ill-defined edge between upper and lower convex hulls.
|
||||
The problem will be fixed in a future release of Qhull.
|
||||
|
||||
<p>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 <a href="qh-impre.htm#limit"</a>Nearly coincident points on an edge</a>.
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
278
xs/src/qhull/html/qh-optt.htm
Normal file
278
xs/src/qhull/html/qh-optt.htm
Normal file
@ -0,0 +1,278 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull trace options (T)</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a> Qhull trace options (T)</h1>
|
||||
|
||||
This section lists the trace options for Qhull. These options are
|
||||
indicated by 'T' followed by a letter.
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
<a name="trace">•</a> <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<h2>Trace options</h2>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="#Tz">Tz</a></dt>
|
||||
<dd>output error information to stdout instead of stderr</dd>
|
||||
<dt><a href="#TI">TI file</a></dt>
|
||||
<dd>input data from a file</dd>
|
||||
<dt><a href="#TO">TO file</a></dt>
|
||||
<dd>output results to a file</dd>
|
||||
<dt><a href="#Ts">Ts</a></dt>
|
||||
<dd>print statistics</dd>
|
||||
<dt><a href="#TFn">TFn</a></dt>
|
||||
<dd>report progress whenever n or more facets created</dd>
|
||||
<dt><a href="#TRn">TRn</a></dt>
|
||||
<dd>rerun qhull n times</dd>
|
||||
<dt><a href="#Tv">Tv</a></dt>
|
||||
<dd>verify result: structure, convexity, and point inclusion</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Debugging</b></dd>
|
||||
<dt><a href="#Tc">Tc</a></dt>
|
||||
<dd>check frequently during execution</dd>
|
||||
<dt><a href="#TVn2">TVn</a></dt>
|
||||
<dd>stop qhull after adding point n </dd>
|
||||
<dt><a href="#TCn">TCn</a></dt>
|
||||
<dd>stop qhull after building cone for point n</dd>
|
||||
<dt><a href="#TVn">TV-n</a></dt>
|
||||
<dd>stop qhull before adding point n</dd>
|
||||
<dt><a href="#Tn">T4</a></dt>
|
||||
<dd>trace at level n, 4=all, 5=mem/gauss, -1= events</dd>
|
||||
<dt><a href="#TWn">TWn</a></dt>
|
||||
<dd>trace merge facets when width > n</dd>
|
||||
<dt><a href="#TMn">TMn</a></dt>
|
||||
<dd>turn on tracing at merge n</dd>
|
||||
<dt><a href="#TPn">TPn</a></dt>
|
||||
<dd>turn on tracing when point n added to hull</dd>
|
||||
</dl>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="Tc">Tc - check frequently
|
||||
during execution </a></h3>
|
||||
|
||||
<p>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 '<a href="#Tv">Tv</a>'
|
||||
performs the same checks after the hull is constructed.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TCn">TCn - stop qhull after
|
||||
building cone for point n</a></h3>
|
||||
|
||||
<p>Qhull builds a cone from the point to its horizon facets.
|
||||
Option 'TCn' stops Qhull just after building the cone. The output
|
||||
for '<a href="qh-opto.htm#f">f</a>' includes the cone and the old
|
||||
hull.'. </p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TFn">TFn - report summary
|
||||
whenever n or more facets created </a></h3>
|
||||
|
||||
<p>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
|
||||
<i>n/2</i> merges. </p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TI">TI file - input data from file</a></h3>
|
||||
|
||||
<p>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').</P>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TMn">TMn - turn on tracing at
|
||||
merge n </a></h3>
|
||||
|
||||
<p>Turn on tracing at n'th merge. </p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="Tn">Tn - trace at level n</a></h3>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>Option 'Tn' can produce large amounts of output. Use options '<a
|
||||
href="#TPn">TPn</a>', '<a href="#TWn">TWn</a>', and '<a href="#TMn">TMn</a>' to selectively
|
||||
turn on tracing. Since all errors report the last processed
|
||||
point, option '<a href="#TPn">TPn</a>' is particularly useful.</p>
|
||||
|
||||
<p>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.
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TO">TO file - output results to file</a></h3>
|
||||
|
||||
<p>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').</P>
|
||||
<p>
|
||||
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)</p>
|
||||
<p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TPn">TPn - turn on tracing
|
||||
when point n added to hull </a></h3>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>Use options 'TPn <a href="qh-optt.htm#TVn">TVn</a>' to
|
||||
trace the addition of point n to the convex hull and stop when done.</p>
|
||||
|
||||
<p>If used with option '<a href="qh-optt.htm#TWn">TWn</a>',
|
||||
'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.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TRn">TRn - rerun qhull n times</a></h3>
|
||||
|
||||
<p>Option 'TRn' reruns Qhull n times. It is usually used
|
||||
with '<a href="qh-optq.htm#QJn">QJn</a>' to determine the probability
|
||||
that a given joggle will fail. The summary
|
||||
('<a href="qh-opto.htm#s">s</a>') lists the failure
|
||||
rate and the precision errors that occurred.
|
||||
Option '<a href="#Ts">Ts</a>' will report statistics for
|
||||
all of the runs. Trace and output options only apply to the last
|
||||
run. An event trace, '<a href="#Tn">T-1</a>' reports events for all runs.
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="Ts">Ts - print statistics </a></h3>
|
||||
|
||||
<p>Option 'Ts' collects statistics and prints them to stderr. For
|
||||
Delaunay triangulations, the angle statistics are restricted to
|
||||
the lower or upper envelope.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="Tv">Tv - verify result:
|
||||
structure, convexity, and point inclusion </a></h3>
|
||||
|
||||
<p>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 '<a
|
||||
href="qh-optp.htm#Po">Po</a>', or if '<a href="qh-optq.htm#Q5">Q5</a>'
|
||||
is set. </p>
|
||||
|
||||
<p>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 '<a
|
||||
href="qh-optc.htm#C0">C-0</a>' (default), use 'C-1e-30' instead. </p>
|
||||
|
||||
<p>Point inclusion testing occurs after producing output. It
|
||||
prints a message to stderr unless option '<a
|
||||
href="qh-optp.htm#Pp">Pp</a>' is used. This allows the user to
|
||||
interrupt Qhull without changing the output. </p>
|
||||
|
||||
<p>With '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fi2">Fi</a>'
|
||||
and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fo2">Fo</a>',
|
||||
option 'Tv' collects statistics that verify all Voronoi vertices lie
|
||||
on the separating hyperplane, and for bounded regions, all
|
||||
separating hyperplanes are perpendicular bisectors.
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TVn">TV-n - stop qhull before
|
||||
adding point n</a></h3>
|
||||
|
||||
<p>Qhull adds one point at a time to the convex hull. See <a
|
||||
href="qh-eg.htm#how">how Qhull adds a point</a>. Option 'TV-n'
|
||||
stops Qhull just before adding a new point. Output shows the hull
|
||||
at this time.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TVn2">TVn - stop qhull after
|
||||
adding point n</a></h3>
|
||||
|
||||
<p>Option 'TVn' stops Qhull after it has added point n. Output
|
||||
shows the hull at this time.</p>
|
||||
|
||||
<h3><a href="#trace">»</a><a name="TWn">TWn - trace merge facets
|
||||
when width > n </a></h3>
|
||||
|
||||
<p>Along with TMn, this option allows the user to determine the
|
||||
cause of a wide merge.</p>
|
||||
<h3><a href="#trace">»</a><a name="Tz">Tz - send all output to
|
||||
stdout </a></h3>
|
||||
|
||||
<p>Redirect stderr to stdout. </p>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
495
xs/src/qhull/html/qh-quick.htm
Normal file
495
xs/src/qhull/html/qh-quick.htm
Normal file
@ -0,0 +1,495 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull quick reference</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOC"><b>Up:</b></a> <a href="http://www.qhull.org">Home
|
||||
page for Qhull</a> <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> <br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="qh-code.htm#TOC">Qhull internals</a><br>
|
||||
<b>To:</b> <a href="../src/libqhull/index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="../src/libqhull/index.htm#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="../src/libqhull/qh-geom.htm">Geom</a> • <a href="../src/libqhull/qh-globa.htm">Global</a>
|
||||
• <a href="../src/libqhull/qh-io.htm">Io</a> • <a href="../src/libqhull/qh-mem.htm">Mem</a>
|
||||
• <a href="../src/libqhull/qh-merge.htm">Merge</a> • <a href="../src/libqhull/qh-poly.htm">Poly</a>
|
||||
• <a href="../src/libqhull/qh-qhull.htm">Qhull</a> • <a href="../src/libqhull/qh-set.htm">Set</a>
|
||||
• <a href="../src/libqhull/qh-stat.htm">Stat</a> • <a href="../src/libqhull/qh-user.htm">User</a>
|
||||
</p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="qh--cone.gif" alt="[cone]" align="middle" width="100"
|
||||
height="100"></a> Qhull quick reference</h1>
|
||||
|
||||
This section lists all programs and options in Qhull.
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<p>
|
||||
<a name="programs"> </a>
|
||||
<hr>
|
||||
<b>Qhull programs</b>
|
||||
<p><a href="#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<dl>
|
||||
<dt><a href="qconvex.htm">qconvex</a> -- convex hull</dt>
|
||||
<dd><a href="qconvex.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qconvex.htm#input">in</a>put • <a
|
||||
href="qconvex.htm#outputs">ou</a>tputs • <a
|
||||
href="qconvex.htm#controls">co</a>ntrols • <a
|
||||
href="qconvex.htm#graphics">gr</a>aphics • <a
|
||||
href="qconvex.htm#notes">no</a>tes • <a
|
||||
href="qconvex.htm#conventions">co</a>nventions • <a
|
||||
href="qconvex.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulation</dt>
|
||||
<dd><a href="qdelaun.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qdelaun.htm#input">in</a>put • <a
|
||||
href="qdelaun.htm#outputs">ou</a>tputs • <a
|
||||
href="qdelaun.htm#controls">co</a>ntrols • <a
|
||||
href="qdelaun.htm#graphics">gr</a>aphics • <a
|
||||
href="qdelaun.htm#notes">no</a>tes • <a
|
||||
href="qdelaun.htm#conventions">co</a>nventions • <a
|
||||
href="qdelaun.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qdelau_f.htm">qdelaunay Qu</a> -- furthest-site Delaunay triangulation</dt>
|
||||
<dd><a href="qdelau_f.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qdelau_f.htm#input">in</a>put • <a
|
||||
href="qdelau_f.htm#outputs">ou</a>tputs • <a
|
||||
href="qdelau_f.htm#controls">co</a>ntrols • <a
|
||||
href="qdelau_f.htm#graphics">gr</a>aphics • <a
|
||||
href="qdelau_f.htm#notes">no</a>tes • <a
|
||||
href="qdelau_f.htm#conventions">co</a>nventions • <a
|
||||
href="qdelau_f.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qhalf.htm">qhalf</a> -- halfspace intersection about a point</dt>
|
||||
<dd><a href="qhalf.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qhalf.htm#input">in</a>put • <a
|
||||
href="qhalf.htm#outputs">ou</a>tputs • <a
|
||||
href="qhalf.htm#controls">co</a>ntrols • <a
|
||||
href="qhalf.htm#graphics">gr</a>aphics • <a
|
||||
href="qhalf.htm#notes">no</a>tes • <a
|
||||
href="qhalf.htm#conventions">co</a>nventions • <a
|
||||
href="qhalf.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagram</dt>
|
||||
<dd><a href="qvoronoi.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qvoronoi.htm#input">in</a>put • <a
|
||||
href="qvoronoi.htm#outputs">ou</a>tputs •
|
||||
<a href="qvoronoi.htm#controls">co</a>ntrols • <a
|
||||
href="qvoronoi.htm#graphics">gr</a>aphics • <a
|
||||
href="qvoronoi.htm#notes">no</a>tes • <a
|
||||
href="qvoronoi.htm#conventions">co</a>nventions • <a
|
||||
href="qvoronoi.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qvoron_f.htm">qvoronoi Qu</a> -- furthest-site Voronoi diagram</dt>
|
||||
<dd><a href="qvoron_f.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qvoron_f.htm#input">in</a>put • <a
|
||||
href="qvoron_f.htm#outputs">ou</a>tputs • <a
|
||||
href="qvoron_f.htm#controls">co</a>ntrols • <a
|
||||
href="qvoron_f.htm#graphics">gr</a>aphics • <a
|
||||
href="qvoron_f.htm#notes">no</a>tes • <a
|
||||
href="qvoron_f.htm#conventions">co</a>nventions • <a
|
||||
href="qvoron_f.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="rbox.htm">rbox</a> -- generate point distributions for qhull</dt>
|
||||
<dd><a href="rbox.htm#synopsis">sy</a>nopsis • <a
|
||||
href="rbox.htm#outputs">ou</a>tputs • <a
|
||||
href="rbox.htm#examples">ex</a>amples • <a
|
||||
href="rbox.htm#notes">no</a>tes • <a
|
||||
href="rbox.htm#options">op</a>tions</dd>
|
||||
<dt> </dt>
|
||||
<dt><a href="qhull.htm">qhull</a> -- convex hull and related structures</dt>
|
||||
<dd><a href="qhull.htm#synopsis">sy</a>nopsis • <a
|
||||
href="qhull.htm#input">in</a>put • <a
|
||||
href="qhull.htm#outputs">ou</a>tputs • <a
|
||||
href="qhull.htm#controls">co</a>ntrols • <a
|
||||
href="qhull.htm#options">op</a>tions</dd>
|
||||
</dl>
|
||||
<a name="options"> </a>
|
||||
<hr>
|
||||
<b>Qhull options</b>
|
||||
|
||||
<p><a href="#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a></p>
|
||||
|
||||
<p><table>
|
||||
<!-- Note: keep all lines the same for easy reorganization -->
|
||||
<tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fa>Fa</a>'
|
||||
Farea
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fa>FA</a>'
|
||||
FArea-total
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fc>Fc</a>'
|
||||
Fcoplanars
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FC>FC</a>'
|
||||
FCentrums
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fd>Fd</a>'
|
||||
Fd-cdd-in
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FD>FD</a>'
|
||||
FD-cdd-out
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FF>FF</a>'
|
||||
FF-dump-xridge
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fi>Fi</a>'
|
||||
Finner
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fi2>Fi</a>'
|
||||
Finner_bounded
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FI>FI</a>'
|
||||
FIDs
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fm>Fm</a>'
|
||||
Fmerges
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FM>FM</a>'
|
||||
FMaple
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fn>Fn</a>'
|
||||
Fneighbors
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FN>FN</a>'
|
||||
FNeigh-vertex
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo>Fo</a>'
|
||||
Fouter
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo2>Fo</a>'
|
||||
Fouter_unbounded
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#FO>FO</a>'
|
||||
FOptions
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fp>Fp</a>'
|
||||
Fpoint-intersect
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FP>FP</a>'
|
||||
FPoint_near
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FQ>FQ</a>'
|
||||
FQhull
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fs>Fs</a>'
|
||||
Fsummary
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FS>FS</a>'
|
||||
FSize
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Ft>Ft</a>'
|
||||
Ftriangles
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fv>Fv</a>'
|
||||
Fvertices
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optf.htm#Fv2>Fv</a>'
|
||||
Fvoronoi
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#FV>FV</a>'
|
||||
FVertex-ave
|
||||
</nobr></td><td><nobr>'<a href=qh-optf.htm#Fx>Fx</a>'
|
||||
Fxtremes
|
||||
</nobr></td><td colspan=2><nobr>
|
||||
<a href=qh-impre.htm#joggle>Merged facets or joggled input</a>
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optp.htm#PAn>PAn</a>'
|
||||
PArea-keep
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#Pdk>Pdk:n</a>'
|
||||
Pdrop_low
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#PDk>PDk:n</a>'
|
||||
Pdrop_high
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#Pg>Pg</a>'
|
||||
Pgood
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optp.htm#PFn>PFn</a>'
|
||||
PFacet_area_keep
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#PG>PG</a>'
|
||||
PGood_neighbors
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#PMn>PMn</a>'
|
||||
PMerge-keep
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#Po>Po</a>'
|
||||
Poutput_forced
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optp.htm#Po2>Po</a>'
|
||||
Poutput_error
|
||||
</nobr></td><td><nobr>'<a href=qh-optp.htm#Pp>Pp</a>'
|
||||
Pprecision_not
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qhull.htm#outputs>d</a>'
|
||||
delaunay
|
||||
</nobr></td><td><nobr>'<a href=qhull.htm#outputs>v</a>'
|
||||
voronoi
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm>G</a>'
|
||||
Geomview
|
||||
</nobr></td><td><nobr>'<a href=qhull.htm#outputs>H</a>'
|
||||
Halfspace
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-opto.htm#f>f</a>'
|
||||
facet_dump
|
||||
</nobr></td><td><nobr>'<a href=qh-opto.htm#i>i</a>'
|
||||
incidences
|
||||
</nobr></td><td><nobr>'<a href=qh-opto.htm#m>m</a>'
|
||||
mathematica
|
||||
</nobr></td><td><nobr>'<a href=qh-opto.htm#n>n</a>'
|
||||
normals
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-opto.htm#o>o</a>'
|
||||
OFF_format
|
||||
</nobr></td><td><nobr>'<a href=qh-opto.htm#p>p</a>'
|
||||
points
|
||||
</nobr></td><td><nobr>'<a href=qh-opto.htm#s>s</a>'
|
||||
summary
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optg.htm#Gv>Gv</a>'
|
||||
Gvertices
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gp>Gp</a>'
|
||||
Gpoints
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Ga>Ga</a>'
|
||||
Gall_points
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gn>Gn</a>'
|
||||
Gno_planes
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optg.htm#Gi>Gi</a>'
|
||||
Ginner
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gc>Gc</a>'
|
||||
Gcentrums
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gh>Gh</a>'
|
||||
Ghyperplanes
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gr>Gr</a>'
|
||||
Gridges
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optg.htm#Go>Go</a>'
|
||||
Gouter
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#GDn>GDn</a>'
|
||||
GDrop_dim
|
||||
</nobr></td><td><nobr>'<a href=qh-optg.htm#Gt>Gt</a>'
|
||||
Gtransparent
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optt.htm#Tn>T4</a>'
|
||||
T4_trace
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#Tc>Tc</a>'
|
||||
Tcheck_often
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#Ts>Ts</a>'
|
||||
Tstatistics
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#Tv>Tv</a>'
|
||||
Tverify
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optt.htm#Tz>Tz</a>'
|
||||
Tz_stdout
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TFn>TFn</a>'
|
||||
TFacet_log
|
||||
<td><nobr>'<a href=qh-optt.htm#TI>TI file</a>'
|
||||
TInput_file
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TPn>TPn</a>'
|
||||
TPoint_trace
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optt.htm#TMn>TMn</a>'
|
||||
TMerge_trace
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TO>TO file</a>'
|
||||
TOutput_file
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TRn>TRn</a>'
|
||||
TRerun
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TWn>TWn</a>'
|
||||
TWide_trace
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optt.htm#TVn>TV-n</a>'
|
||||
TVertex_stop_before
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optt.htm#TVn2>TVn</a>'
|
||||
TVertex_stop_after
|
||||
</nobr></td><td><nobr>'<a href=qh-optt.htm#TCn>TCn</a>'
|
||||
TCone_stop_after
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optc.htm#An>A-n</a>'
|
||||
Angle_max_pre
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#An2>An</a>'
|
||||
Angle_max_post
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#C0>C-0</a>'
|
||||
Centrum_roundoff
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#Cn>C-n</a>'
|
||||
Centrum_size_pre
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optc.htm#Cn2>Cn</a>'
|
||||
Centrum_size_post
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#En>En</a>'
|
||||
Error_round
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#Rn>Rn</a>'
|
||||
Random_dist
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#Vn>Vn</a>'
|
||||
Visible_min
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optc.htm#Un>Un</a>'
|
||||
Ucoplanar_max
|
||||
</nobr></td><td><nobr>'<a href=qh-optc.htm#Wn>Wn</a>'
|
||||
Wide_outside
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Qbk>Qbk:n</a>'
|
||||
Qbound_low
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#QBk>QBk:n</a>'
|
||||
QBound_high
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qb0>Qbk:0Bk:0</a>'
|
||||
Qbound_drop
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#QbB>QbB</a>'
|
||||
QbB-scale-box
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Qbb>Qbb</a>'
|
||||
Qbb-scale-last
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qc>Qc</a>'
|
||||
Qcoplanar
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qf>Qf</a>'
|
||||
Qfurthest
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qg>Qg</a>'
|
||||
Qgood_only
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#QGn>QGn</a>'
|
||||
QGood_point
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qi>Qi</a>'
|
||||
Qinterior
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qm>Qm</a>'
|
||||
Qmax_out
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#QJn>QJn</a>'
|
||||
QJoggle
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Qr>Qr</a>'
|
||||
Qrandom
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#QRn>QRn</a>'
|
||||
QRotate
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qs>Qs</a>'
|
||||
Qsearch_1st
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qt>Qt</a>'
|
||||
Qtriangulate
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Qu>Qu</a>'
|
||||
QupperDelaunay
|
||||
</nobr><td><nobr>'<a href=qh-optq.htm#QVn>QVn</a>'
|
||||
QVertex_good
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qv>Qv</a>'
|
||||
Qvneighbors
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Qx>Qx</a>'
|
||||
Qxact_merge
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Qz>Qz</a>'
|
||||
Qzinfinite
|
||||
|
||||
</nobr></td></tr>
|
||||
<tr><td> </td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Q0>Q0</a>'
|
||||
Q0_no_premerge
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q1>Q1</a>'
|
||||
Q1_no_angle
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q2>Q2</a>'
|
||||
Q2_no_independ
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q3>Q3</a>'
|
||||
Q3_no_redundant
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Q4>Q4</a>'
|
||||
Q4_no_old
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q5>Q5</a>'
|
||||
Q5_no_check_out
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q6>Q6</a>'
|
||||
Q6_no_concave
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q7>Q7</a>'
|
||||
Q7_depth_first
|
||||
|
||||
</nobr></td></tr><tr>
|
||||
<td><nobr>'<a href=qh-optq.htm#Q8>Q8</a>'
|
||||
Q8_no_near_in
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q9>Q9</a>'
|
||||
Q9_pick_furthest
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q10>Q10</a>'
|
||||
Q10_no_narrow
|
||||
</nobr></td><td><nobr>'<a href=qh-optq.htm#Q11>Q11</a>'
|
||||
Q11_trinormals
|
||||
</td></tr></table>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home
|
||||
page for Qhull</a> <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> <br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="qh-code.htm#TOC">Qhull internals</a><br>
|
||||
<b>To:</b> <a href="../src/libqhull/index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="../src/libqhull/index.htm#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="../src/libqhull/qh-geom.htm">Geom</a> • <a href="../src/libqhull/qh-globa.htm">Global</a>
|
||||
• <a href="../src/libqhull/qh-io.htm">Io</a> • <a href="../src/libqhull/qh-mem.htm">Mem</a>
|
||||
• <a href="../src/libqhull/qh-merge.htm">Merge</a> • <a href="../src/libqhull/qh-poly.htm">Poly</a>
|
||||
• <a href="../src/libqhull/qh-qhull.htm">Qhull</a> • <a href="../src/libqhull/qh-set.htm">Set</a>
|
||||
• <a href="../src/libqhull/qh-stat.htm">Stat</a> • <a href="../src/libqhull/qh-user.htm">User</a><br>
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
626
xs/src/qhull/html/qhalf.htm
Normal file
626
xs/src/qhull/html/qhalf.htm
Normal file
@ -0,0 +1,626 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qhalf -- halfspace intersection about a point</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up</b></a><b>:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
|
||||
src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
|
||||
height="100"></a>qhalf -- halfspace intersection about a point</h1>
|
||||
|
||||
<p>The intersection of a set of halfspaces is a polytope. The
|
||||
polytope may be unbounded. See Preparata & Shamos [<a
|
||||
href="index.htm#pre-sha85">'85</a>] for a discussion. In low
|
||||
dimensions, halfspace intersection may be used for linear
|
||||
programming.
|
||||
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt><p><b>Example:</b> rbox c | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
|
||||
<a href="qh-opto.htm#n">n</a> | qhalf <a
|
||||
href="qh-optf.htm#Fp">Fp</a></dt>
|
||||
<dd>Print the intersection of the facets of a cube. <tt>rbox c</tt>
|
||||
generates the vertices of a cube. <tt>qconvex FV n</tt> returns of average
|
||||
of the cube's vertices (in this case, the origin) and the halfspaces
|
||||
that define the cube. <tt>qhalf Fp</tt> computes the intersection of
|
||||
the halfspaces about the origin. The intersection is the vertices
|
||||
of the original cube.</dd>
|
||||
|
||||
<dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
|
||||
<a href="qh-opto.htm#n">n</a> | qhalf <a
|
||||
href="qh-optf.htm#Fp">Fp</a></dt>
|
||||
<dd>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.
|
||||
</dd>
|
||||
|
||||
<dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
|
||||
<a href="qh-opto.htm#n">n</a> | qhalf <a
|
||||
href="qh-optf.htm#Fp">Fp</a>
|
||||
<a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>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.
|
||||
</dd>
|
||||
|
||||
<dt><p><b>Example:</b> rbox 10 s t10 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
|
||||
<a href="qh-opto.htm#n">n</a> | qhalf <a
|
||||
href="qh-optf.htm#Fp">Fp</a> <a
|
||||
href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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.
|
||||
</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>In Qhull, a <i>halfspace</i> 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.
|
||||
|
||||
<p>Qhull computes a halfspace intersection by the geometric
|
||||
duality between points and halfspaces.
|
||||
See <a href="qh-eg.htm#half">halfspace examples</a>,
|
||||
<a href="#notes">qhalf notes</a>, and
|
||||
option 'p' of <a href="#outputs">qhalf outputs</a>. </p>
|
||||
|
||||
<p>Qhalf's <a href="#outputs">outputs</a> are the intersection
|
||||
points (<a href="qh-optf.htm#Fp">Fp</a>) and
|
||||
the neighboring intersection points (<a href="qh-optf.htm#Fn">Fn</a>).
|
||||
For random inputs, halfspace
|
||||
intersections are usually defined by more than <i>d</i> halfspaces. See the sphere example.
|
||||
|
||||
<p>You can try triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') and joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
|
||||
It demonstrates that triangulated output is more accurate than joggled input.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (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.</p>
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (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 <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>The 'qhalf' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull H</a>' in 2-d to 4-d, and
|
||||
'<a href=qhull.htm#outputs>qhull H</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 5-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>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</i>.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">qhalf synopsis</a></h3>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="input">qhalf input</a></h3>
|
||||
|
||||
<blockquote>
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>[optional] interior point
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>1
|
||||
<li>coordinates of interior point
|
||||
</ul>
|
||||
<li>dimension + 1
|
||||
<li>number of halfspaces</li>
|
||||
<li>halfspace coefficients followed by offset</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qhalf < data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhalf TI data.txt).
|
||||
|
||||
<p>Qhull needs an interior point to compute the halfspace
|
||||
intersection. An interior point is clearly inside all of the halfspaces.
|
||||
A point is <i>inside</i> a halfspace if its distance to the corresponding hyperplane is negative.
|
||||
|
||||
<p>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 <em>0</em> is the default coordinate (e.g.,
|
||||
'H0' is the origin). Use linear programming if you do not know
|
||||
the interior point (see <a href="#notes">halfspace notes</a>),</p>
|
||||
|
||||
<p>The input to qhalf is a set of halfspaces that are defined by their hyperplanes.
|
||||
Each halfspace is defined by
|
||||
<em>d</em> 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.</p>
|
||||
|
||||
<p>The halfspace format is the same as Qhull's output options '<a
|
||||
href="qh-opto.htm#n">n</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
|
||||
and '<a href="qh-optf.htm#Fi">Fi</a>'. Use option '<a
|
||||
href="qh-optf.htm#Fd">Fd</a>' to use cdd format for the
|
||||
halfspaces.</p>
|
||||
|
||||
<p>For example, here is the input for computing the intersection
|
||||
of halfplanes that form a cube.</p>
|
||||
|
||||
<blockquote>
|
||||
<p>rbox c | qconvex FQ FV n TO data </p>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
<p>qhalf s Fp < data </p>
|
||||
<pre>
|
||||
|
||||
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
|
||||
</pre>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="outputs">qhalf outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The following options control the output for halfspace
|
||||
intersection.</p>
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>Intersections</b></dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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.
|
||||
<p>
|
||||
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 '<a href="qh-optq.htm#Qt">Qt</a>' produces three
|
||||
neighboring intersections per intersection by duplicating the intersection
|
||||
points. Option <a href="qh-optq.htm#QJn">QJ</a>' produces three
|
||||
neighboring intersections per intersection by joggling the hyperplanes and
|
||||
hence their intersections.
|
||||
</dd>
|
||||
<dt><a href="qh-optf.htm#Fp">Fp</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#FI">FI</a></dt>
|
||||
<dd>list intersection IDs. The first line is the number of
|
||||
intersections. The IDs follow, one per line.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Halfspaces</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fx">Fx</a></dt>
|
||||
<dd>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 <i>non-redundant</i> if it
|
||||
defines a facet of the intersection. Redundant halfspaces are ignored. For
|
||||
the cube example, all of the halfspaces are non-redundant.
|
||||
</dd>
|
||||
<dt><a href="qh-optf.htm#Fv">Fv</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>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.
|
||||
</dd>
|
||||
<dt><a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optq.htm#Qc">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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 '<a href="qh-optq.htm#Qc">Qc</a> Qi Fc' to list
|
||||
coplanar and redundant halfspaces.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary for the halfspace intersection. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' if you need numeric data.</dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-opto.htm#p">p</a></dt>
|
||||
<dd>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 <a href="qh-optq.htm#Qc">Qc</a>' includes coplanar halfspaces.
|
||||
Options 'p <a href="qh-optq.htm#Qi">Qi</a>' includes redundant halfspaces.</dd>
|
||||
<dt><a href="qh-opto.htm#m">m</a></dt>
|
||||
<dd>Mathematica output for the dual convex hull in 2-d or 3-d.</dd>
|
||||
<dt><a href="qh-optf.htm#FM">FM</a></dt>
|
||||
<dd>Maple output for the dual convex hull in 2-d or 3-d.</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="controls">qhalf controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qt">Qt</a></dt>
|
||||
<dd>triangulated output. If a 3-d intersection is defined by more than
|
||||
three hyperplanes, Qhull produces duplicate intersections -- one for
|
||||
each extra hyperplane.</dd>
|
||||
<dt><a href="qh-optq.htm#QJn">QJ</a></dt>
|
||||
<dd>joggle the input instead of merging facets. In 3-d, this guarantees that
|
||||
each intersection is defined by three hyperplanes.</dd>
|
||||
<dt><a href="qh-opto.htm#f">f </a></dt>
|
||||
<dd>facet dump. Print the data structure for each intersection (i.e.,
|
||||
facet)</dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report summary after constructing <em>n</em>
|
||||
intersections</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select intersection points for halfspace <em>n</em>
|
||||
(marked 'good')</dd>
|
||||
<dt><a href="qh-optq.htm#QGn">QGn</a></dt>
|
||||
<dd>select intersection points that are visible to halfspace <em>n</em>
|
||||
(marked 'good'). Use <em>-n</em> for the remainder.</dd>
|
||||
<dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
|
||||
<dd>remove the k-th coordinate from the input. This computes the
|
||||
halfspace intersection in one lower dimension.</dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optq.htm#Qs">Qs</a></dt>
|
||||
<dd>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 ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
|
||||
If not, use option 'Qs'. It performs an exhaustive search for the
|
||||
best initial simplex. This is expensive is high dimensions.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="graphics">qhalf graphics</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>To view the results with Geomview, compute the convex hull of
|
||||
the intersection points ('qhull FQ H0 Fp | qhull G'). See <a
|
||||
href="qh-eg.htm#half">Halfspace examples</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">qhalf notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qh-impre.htm#halfspace">halfspace intersection</a> for precision issues related to qhalf.</p>
|
||||
|
||||
<p>If you do not know an interior point for the halfspaces, use
|
||||
linear programming to find one. Assume, <em>n</em> halfspaces
|
||||
defined by: <em>aj*x1+bj*x2+cj*x3+dj<=0, j=1..n</em>. Perform
|
||||
the following linear program: </p>
|
||||
|
||||
<blockquote>
|
||||
<p>max(x5) aj*x1+bj*x2+cj*x3+dj*x4+x5<=0, j=1..n</p>
|
||||
</blockquote>
|
||||
|
||||
<p>Then, if <em>[x1,x2,x3,x4,x5]</em> is an optimal solution with
|
||||
<em>x4>0</em> and <em>x5>0</em> we get: </p>
|
||||
|
||||
<blockquote>
|
||||
<p>aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj<=(-x5/x4) j=1..n and (-x5/x4)<0,
|
||||
</p>
|
||||
</blockquote>
|
||||
|
||||
<p>and conclude that the point <em>[x1/x4,x2/x4,x3/x4]</em> is in
|
||||
the interior of all the halfspaces. Since <em>x5</em> is
|
||||
optimal, this point is "way in" the interior (good
|
||||
for precision errors).</p>
|
||||
|
||||
<p>After finding an interior point, the rest of the intersection
|
||||
algorithm is from Preparata & Shamos [<a
|
||||
href="index.htm#pre-sha85">'85</a>, 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 <em>d</em>
|
||||
from the origin are dual to vertices at distance <em>1/d</em>).
|
||||
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].</p>
|
||||
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">qhalf
|
||||
conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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 <a href="#conventions">convex hull
|
||||
conventions</a> and <a href="index.htm#structure">Qhull's data structures</a>.</p>
|
||||
|
||||
<ul>
|
||||
<li><em>interior point</em> - a point in the intersection of
|
||||
the halfspaces. Qhull needs an interior point to compute
|
||||
the intersection. See <a href="#input">halfspace input</a>.</li>
|
||||
<li><em>halfspace</em> - <em>d</em> coordinates for the
|
||||
normal and a signed offset. The distance to an interior
|
||||
point is negative.</li>
|
||||
<li><em>non-redundant halfspace</em> - a halfspace that
|
||||
defines an output facet</li>
|
||||
<li><em>vertex</em> - a dual vertex in the convex hull
|
||||
corresponding to a non-redundant halfspace</li>
|
||||
<li><em>coplanar point</em> - the dual point corresponding to
|
||||
a similar halfspace</li>
|
||||
<li><em>interior point</em> - the dual point corresponding to
|
||||
a redundant halfspace</li>
|
||||
<li><em>intersection point</em>- the intersection of <em>d</em>
|
||||
or more non-redundant halfspaces</li>
|
||||
<li><em>facet</em> - a dual facet in the convex hull
|
||||
corresponding to an intersection point</li>
|
||||
<li><em>non-simplicial facet</em> - more than <em>d</em>
|
||||
halfspaces intersect at a point</li>
|
||||
<li><em>good facet</em> - an intersection point that
|
||||
satisfies restriction '<a href="qh-optq.htm#QVn">QVn</a>',
|
||||
etc.</li>
|
||||
</ul>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">qhalf options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
214
xs/src/qhull/html/qhull-cpp.xml
Normal file
214
xs/src/qhull/html/qhull-cpp.xml
Normal file
@ -0,0 +1,214 @@
|
||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
<?xml-stylesheet type="text/xsl" href="../../road-faq/xsl/road-faq.xsl"?>
|
||||
|
||||
<rf:topic xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
|
||||
xsi:schemaLocation="http://schemas.roadintranet.org/road-faq-1 /road/road-faq/xsl/road-faq.xsd"
|
||||
xmlns:rf="http://schemas.roadintranet.org/road-faq-1"
|
||||
title=" C++ interface to Qhull"
|
||||
file="qhull-cpp.xml"
|
||||
fileid="$Id: //main/2015/qhull/html/qhull-cpp.xml#2 $$Change: 2027 $"
|
||||
fileChange="$DateTime: 2015/11/09 23:18:11 $$Author: bbarber $">
|
||||
<div><h4>Qhull C++ -- C++ interface to Qhull</h4></div>
|
||||
<rf:copyright>
|
||||
<a href="../cpp/COPYING.txt">Copyright</a> (c) 2009-2015, C.B. Barber
|
||||
</rf:copyright>
|
||||
<rf:section id="cpp-cpp-links" title="Useful Links for Qhull C++">
|
||||
<div>
|
||||
<p> This draft
|
||||
document records some of the design decisions for Qhull C++. Convert it to HTML by road-faq.xsl from <a href="http://www.qhull.org/road/road-faq/road-faq.html">road-faq</a>.
|
||||
|
||||
Please send comments and suggestions to <a
|
||||
href="mailto:bradb@shore.net">bradb@shore.net</a>
|
||||
</p>
|
||||
</div>
|
||||
<div class="twocol">
|
||||
<div class="col leftcol">
|
||||
Help
|
||||
<ul><li>
|
||||
</li><li>
|
||||
</li><li>
|
||||
</li></ul>
|
||||
</div>
|
||||
<div class="col rightcol">
|
||||
<ul><li>
|
||||
</li><li>
|
||||
</li></ul>
|
||||
</div>
|
||||
</div>
|
||||
<div>
|
||||
. <!-- clear the two column display -->
|
||||
</div>
|
||||
|
||||
</rf:section>
|
||||
<rf:section id="qhull-api" title="Qhull's collection classes">
|
||||
|
||||
<rf:item id="collection-api" title="API for Qhull collections" date="Feb 2009" author="bbarber">
|
||||
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.
|
||||
|
||||
<p>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 <rf:iref item="cpp-collection-api"/>.
|
||||
</p>
|
||||
|
||||
|
||||
Qhull's collection API (where applicable). For documentation, see Qt's QList, QMap, QListIterator, QMapIterator, QMutableListIterator, and QMutableMapIterator
|
||||
<ul><li>
|
||||
STL types [list, qlinkedlist, qlist, qvector, vector] -- const_iterator, iterator
|
||||
</li><li>
|
||||
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>)
|
||||
</li><li>
|
||||
const_iterator, iterator types -- difference_type, iterator_category, pointer, reference, value_type
|
||||
</li><li>
|
||||
Qt types [qlinkedlist, qlist, qvector] -- ConstIterator, Iterator, QhullclassIterator, MutableQhullclassIterator.
|
||||
Qt's foreach requires const_iterator.
|
||||
</li><li>
|
||||
Types for sets/maps [hash_map, QHash] -- key_compare, key_type, mapped_type
|
||||
</li><li>
|
||||
Constructor -- default constructor, copy constructor, assignment operator, destructor
|
||||
</li><li>
|
||||
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)
|
||||
</li><li>
|
||||
Get/set -- configuration options for class
|
||||
</li><li>
|
||||
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.
|
||||
</li><li>
|
||||
Java-style iterator [qiterator.h] - countRemaining, findNext, findPrevious, hasNext, hasPrevious, next, peekNext, peekPrevious, previous, toBack, toFront, = Coordinates
|
||||
</li><li>
|
||||
Mutable Java-style iterator adds - insert, remove, setValue, value
|
||||
</li><li>
|
||||
Element access -- back, first, front, last
|
||||
</li><li>
|
||||
Element access w/ index -- [], at (const& only), constData, data, mid, value
|
||||
</li><li>
|
||||
Read-only - (int)count, empty, isEmpty, (size_t)size. Count() and size() may be filtered. If so, they may be zero when !empty().
|
||||
</li><li>
|
||||
Read-only for sets/maps - capacity, key, keys, reserve, resize, values
|
||||
</li><li>
|
||||
Operator - ==, !=, +, +=, <<
|
||||
</li><li>
|
||||
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
|
||||
</li><li>
|
||||
Read-write for sets/maps -- insertMulti, squeeze, take, unite
|
||||
</li><li>
|
||||
Search -- contains(const T &), count(const T &), indexOf, lastIndexOf
|
||||
</li><li>
|
||||
Search for sets/maps -- constFind, lowerBound, upperBound
|
||||
</li><li>
|
||||
Stream I/O -- stream <<
|
||||
</li></ul>
|
||||
|
||||
STL list and vector -- For unfiltered access to each element.
|
||||
<ul><li>
|
||||
<a href="http://stdcxx.apache.org/doc/stdlibug/16-3.html">Apache: Creating your own containers</a> -- requirements for STL containers. Iterators should define the types from 'iterator_traits'.
|
||||
</li><li>
|
||||
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
|
||||
</li><li>
|
||||
STL constructors -- MyType(), MyType(count), MyType(count, value), MyType(first, last),
|
||||
MyType(MyType&),
|
||||
</li><li>
|
||||
STL getter/setters -- at (random_access only), back, begin, capacity, end, front, rbegin, rend, size, max_size
|
||||
</li><li>
|
||||
STL predicates -- empty
|
||||
</li><li>
|
||||
STL iterator types -- const_pointer, const_reference, difference_type, iterator_category, pointer, reference, value_type
|
||||
</li><li>
|
||||
STL iterator operators -- *, -<, ++, --, +=, -=, +, -, [], ==, !=, <, >, >=, <=
|
||||
</li><li>
|
||||
STL operators -- =, [] (random_access only), ==, !=, <, >, <=, >=
|
||||
</li><li>
|
||||
STL modifiers -- assign, clear, erase, insert, pop_back, push_back, reserve, resize, swap
|
||||
</li><li>
|
||||
</li></ul>
|
||||
|
||||
Qt Qlist -- For unfiltered access to each element
|
||||
<ul><li>
|
||||
</li><li>
|
||||
Additional Qt types -- ConstIterator, Iterator, QListIterator, QMutableListIterator
|
||||
</li><li>
|
||||
Additional Qt get/set -- constBegin, constEnd, count, first, last, value (random_access only)
|
||||
</li><li>
|
||||
Additional Qt predicates -- isEmpty
|
||||
</li><li>
|
||||
Additional Qt -- mid (random_access only)
|
||||
</li><li>
|
||||
Additional Qt search -- contains, count(T&), indexOf (random_access only), lastIndeOf (random_access only)
|
||||
</li><li>
|
||||
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
|
||||
</li><li>
|
||||
Additional Qt operators -- +, <<, +=,
|
||||
stream << and >>
|
||||
</li><li>
|
||||
Unsupported types by Qt -- allocator_type, const_reverse_iterator, reverse_iterator
|
||||
</li><li>
|
||||
Unsupported accessors by Qt -- max_size, rbegin, rend
|
||||
</li><li>
|
||||
Unsupported constructors by Qt -- multi-value constructors
|
||||
</li><li>
|
||||
unsupported modifiers by Qt -- assign, muli-value inserts, STL's swaps
|
||||
</li><li>
|
||||
</li></ul>
|
||||
|
||||
STL map and Qt QMap. These use nearly the same API as list and vector classes. They add the following.
|
||||
<ul><li>
|
||||
STL types -- key_compare, key_type, mapped_type
|
||||
</li><li>
|
||||
STL search -- equal_range, find, lower_bound, upper_bound
|
||||
</li><li>
|
||||
Qt removes -- equal_range, key_compare
|
||||
</li><li>
|
||||
Qt renames -- lowerBound, upperBound
|
||||
</li><li>
|
||||
Qt adds -- constFind, insertMulti, key, keys, take, uniqueKeys, unite, values
|
||||
</li><li>
|
||||
Not applicable to map and QMap -- at, back, pop_back, pop_front, push_back, push_front, swap
|
||||
</li><li>
|
||||
Not applicable to QMap -- append, first, last, lastIndexOf, mid, move, prepend, removeAll, removeAt, removeFirst, removeLast, replace, squeeze, takeAt, takeFirst, takeLast
|
||||
</li><li>
|
||||
Not applicable to map -- assign
|
||||
</li></ul>
|
||||
|
||||
Qt QHash. STL extensions provide similar classes, e.g., Microsoft's stdext::hash_set. THey are nearly the same as QMap
|
||||
<ul><li>
|
||||
</li><li>
|
||||
</li><li>
|
||||
Not applicable to Qhash -- lowerBound, unite, upperBound,
|
||||
</li><li>
|
||||
Qt adds -- squeeze
|
||||
</li></ul>
|
||||
</rf:item>
|
||||
<rf:item id="class-api" title="API for Qhull collections" date="Feb 2009" author="bbarber">
|
||||
<ul><li>
|
||||
check... -- Throw error on failure
|
||||
</li><li>
|
||||
try... -- Return false on failure. Do not throw errors.
|
||||
</li><li>
|
||||
...Temporarily -- lifetime depends on source. e.g., toByteArrayTemporarily
|
||||
</li><li>
|
||||
...p -- indicates pointer-to.
|
||||
</li><li>
|
||||
end... -- points to one beyond the last available
|
||||
</li><li>
|
||||
private functions -- No syntactic indication. They may become public later on.
|
||||
</li><li>
|
||||
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: ..."
|
||||
</li><li>
|
||||
parameter order -- qhRunId, dimension, coordinates, count.
|
||||
</li><li>
|
||||
toClass -- Convert into a Class object (makes a deep copy)
|
||||
</li><li>
|
||||
qRunId -- Requires Qh installed. Some routines allow 0 for limited info (e.g., operator<<)
|
||||
</li><li>
|
||||
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).
|
||||
</li><li>
|
||||
Constructor order -- default constructor, other constructors, copy constructor, copy assignment, destructor
|
||||
</li></ul>
|
||||
</rf:item>
|
||||
</rf:section>
|
||||
</rf:topic>
|
||||
473
xs/src/qhull/html/qhull.htm
Normal file
473
xs/src/qhull/html/qhull.htm
Normal file
@ -0,0 +1,473 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qhull -- convex hull and related structures</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b><a name="TOP">Up</a></b><b>:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#input">in</a>put
|
||||
• <a href="#outputs">ou</a>tputs • <a href="#controls">co</a>ntrols
|
||||
• <a href="#options">op</a>tions
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="qh--cone.gif" alt="[cone]" align="middle" width="100"
|
||||
height="100"></a>qhull -- convex hull and related structures</h1>
|
||||
|
||||
<p>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.
|
||||
|
||||
<p>The <tt>qhull</tt> program provides options to build these
|
||||
structures and to experiment with the process. Use the
|
||||
<a href=qconvex.htm>qconvex</a>,
|
||||
<a href=qdelaun.htm>qdelaunay</a>, <a href=qhalf.htm>qhalf</a>,
|
||||
and <a href=qvoronoi.htm>qvoronoi</a> programs
|
||||
to build specific structures. You may use <tt>qhull</tt> instead.
|
||||
It takes the same options and uses the same code.
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox 1000 D3 | qhull
|
||||
<a href="qh-optc.htm#Cn">C-1e-4</a>
|
||||
<a href="qh-optf.htm#FO">FO</a>
|
||||
<a href="qh-optt.htm#Ts">Ts</a>
|
||||
</dt>
|
||||
<dd>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.</dd>
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox 1000 D3 | qhull <a href=qhull.htm#outputs>d</a>
|
||||
<a href="qh-optq.htm#Qbb">Qbb</a>
|
||||
<a href="qh-optc.htm#Rn">R1e-4</a>
|
||||
<a href="qh-optq.htm#Q0">Q0</a></dt>
|
||||
<dd>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.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
<p>Use the following equivalences when calling <tt>qhull</tt> in 2-d to 4-d (a 3-d
|
||||
Delaunay triangulation is a 4-d convex hull):
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="qconvex.htm">qconvex</a> == qhull
|
||||
<li>
|
||||
<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a>
|
||||
<li>
|
||||
<a href=qhalf.htm>qhalf</a> == qhull H
|
||||
<li>
|
||||
<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a>
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
<p>Use the following equivalences when calling <tt>qhull</tt> in 5-d and higher (a 4-d
|
||||
Delaunay triangulation is a 5-d convex hull):
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="qconvex.htm">qconvex</a> == qhull <a href="qh-optq.htm#Qx">Qx</a>
|
||||
<li>
|
||||
<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
|
||||
<li>
|
||||
<a href=qhalf.htm>qhalf</a> == qhull H <a href="qh-optq.htm#Qx">Qx</a>
|
||||
<li>
|
||||
<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
|
||||
<p>By default, Qhull merges coplanar facets. For example, the convex
|
||||
hull of a cube's vertices has six facets.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (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.
|
||||
|
||||
<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
|
||||
all facets will be simplicial. The corresponding vertices will be
|
||||
slightly perturbed. Joggled input is less accurate that triangulated
|
||||
output.See <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
<p>The output for 4-d convex hulls may be confusing if the convex
|
||||
hull contains non-simplicial facets (e.g., a hypercube). See
|
||||
<a href=qh-faq.htm#extra>Why
|
||||
are there extra points in a 4-d or higher convex hull?</a><br>
|
||||
</p>
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">qhull synopsis</a></h3>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="input">qhull input</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qhull < data.txt), a pipe (e.g., rbox 10 | qhull),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhull TI data.txt).
|
||||
|
||||
<p>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 <a href=qhalf.htm#input>qhalf input</a>).
|
||||
|
||||
<p>Here is the input for computing the convex
|
||||
hull of the unit cube. The output is the normals, one
|
||||
per facet.</p>
|
||||
|
||||
<blockquote>
|
||||
<p>rbox c > data </p>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
<p>qhull s n < data</p>
|
||||
<pre>
|
||||
|
||||
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
|
||||
</pre>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="outputs">qhull outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of qhull. They may be used
|
||||
individually or together.</p>
|
||||
<blockquote>
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a>qhull</a></dt>
|
||||
<dd>compute the convex hull of the input points.
|
||||
See <a href=qconvex.htm>qconvex</a>.</dd>
|
||||
<dt><a name="d">qhull d Qbb</a></dt>
|
||||
<dd>compute the Delaunay triangulation by lifting the points
|
||||
to a paraboloid. Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
|
||||
to scale the paraboloid and improve numeric precision.
|
||||
See <a href=qdelaun.htm>qdelaunay</a>.</dd>
|
||||
<dt><a name="v">qhull v Qbb</a></dt>
|
||||
<dd>compute the Voronoi diagram by computing the Delaunay
|
||||
triangulation. Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
|
||||
to scale the paraboloid and improve numeric precision.
|
||||
See <a href=qvoronoi.htm>qvoronoi</a>.</dd>
|
||||
<dt><a name="H">qhull H</a></dt>
|
||||
<dd>compute the halfspace intersection about a point via polar
|
||||
duality. The point is below the hyperplane that defines the halfspace.
|
||||
See <a href=qhalf.htm>qhalf</a>.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>For a full list of output options see
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li><a href="qh-opto.htm#output">Output</a> formats</li>
|
||||
<li><a href="qh-optf.htm#format">Additional</a> I/O
|
||||
formats</li>
|
||||
<li><a href="qh-optg.htm#geomview">Geomview</a>
|
||||
output options</li>
|
||||
<li><a href="qh-optp.htm#print">Print</a> options</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="controls">qhull controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>For a full list of control options see
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li><a href="qh-optq.htm#qhull">Qhull</a> control
|
||||
options</li>
|
||||
<li><a href="qh-optc.htm#prec">Precision</a> options</li>
|
||||
<li><a href="qh-optt.htm#trace">Trace</a> options</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">qhull options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#input">in</a>put
|
||||
• <a href="#outputs">ou</a>tputs • <a href="#controls">co</a>ntrols
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
1008
xs/src/qhull/html/qhull.man
Normal file
1008
xs/src/qhull/html/qhull.man
Normal file
File diff suppressed because it is too large
Load Diff
1263
xs/src/qhull/html/qhull.txt
Normal file
1263
xs/src/qhull/html/qhull.txt
Normal file
File diff suppressed because it is too large
Load Diff
396
xs/src/qhull/html/qvoron_f.htm
Normal file
396
xs/src/qhull/html/qvoron_f.htm
Normal file
@ -0,0 +1,396 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qvoronoi Qu -- furthest-site Voronoi diagram</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<a name="TOP"><b>Up</b></a><b>:</b>
|
||||
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
|
||||
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
|
||||
height="100"></a>qvoronoi Qu -- furthest-site Voronoi diagram</h1>
|
||||
|
||||
<p>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 [<a href="index.htm#aure91">'91</a>]
|
||||
and the brief introduction by O'Rourke [<a
|
||||
href="index.htm#orou94">'94</a>]. The furthest-site Voronoi diagram is the dual of the <a
|
||||
href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
|
||||
</p>
|
||||
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox 10 D2 | qvoronoi <a
|
||||
href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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.</dd>
|
||||
</dl>
|
||||
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox r y c G1 D2 | qvoronoi <a
|
||||
href="qh-optq.htm#Qu">Qu</a>
|
||||
<a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-optf.htm#Fn">Fn</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>
|
||||
Qhull computes the furthest-site Voronoi diagram via the <a href="qdelau_f.htm">
|
||||
furthest-site Delaunay triangulation</a>.
|
||||
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).</p>
|
||||
|
||||
<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
|
||||
Voronoi diagram questions.</p>
|
||||
|
||||
<p>The 'qvonoroi' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
|
||||
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 4-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>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</i>.
|
||||
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">furthest-site qvoronoi synopsis</a></h3>
|
||||
<blockquote>
|
||||
|
||||
See <a href="qvoronoi.htm#synopsis">qvoronoi synopsis</a>. The same
|
||||
program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
|
||||
for furthest-site Voronoi diagrams.
|
||||
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="input">furthest-site qvoronoi
|
||||
input</a></h3>
|
||||
<blockquote>
|
||||
<p>The input data on <tt>stdin</tt> consists of:</p>
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qvoronoi Qu < data.txt), a pipe (e.g., rbox 10 | qvoronoi Qu),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt Qu).
|
||||
|
||||
<p>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)
|
||||
<p>
|
||||
<blockquote>
|
||||
<tt>rbox c 4 D2 > data</tt>
|
||||
<blockquote><pre>
|
||||
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
|
||||
</pre></blockquote>
|
||||
|
||||
<p><tt>qvoronoi Qu s Fo < data</tt>
|
||||
<blockquote><pre>
|
||||
|
||||
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
|
||||
</pre></blockquote>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="outputs">furthest-site qvoronoi
|
||||
outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of furthest-site Voronoi diagrams.</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>furthest-site Voronoi vertices</b></dd>
|
||||
<dt><a href="qh-opto.htm#p">p</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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., <em>-1</em>) indicate vertices
|
||||
outside of the Voronoi diagram. In the points-in-square example, the
|
||||
Voronoi vertex at the origin has four neighbors-at-infinity.</dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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., <em>-1</em>) indicate vertices
|
||||
outside of the Voronoi diagram.
|
||||
In the points-in-square example, all regions share the Voronoi vertex
|
||||
at the origin.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>furthest-site Voronoi regions</b></dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>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 <em>0</em> indicate
|
||||
interior input sites. </dd>
|
||||
<dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
|
||||
<dd>print separating hyperplanes for inner, bounded furthest-site Voronoi
|
||||
regions. The first number is the number of separating
|
||||
hyperplanes. Each remaining line starts with <i>3+dim</i>. The
|
||||
next two numbers are adjacent input sites. The next <i>dim</i>
|
||||
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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
|
||||
<dd>print separating hyperplanes for outer, unbounded furthest-site Voronoi
|
||||
regions. The first number is the number of separating
|
||||
hyperplanes. Each remaining line starts with <i>3+dim</i>. The
|
||||
next two numbers are adjacent input sites on the convex hull. The
|
||||
next <i>dim</i>
|
||||
numbers are the coefficients of the separating hyperplane. The
|
||||
last number is its offset. The points-in-square example has four
|
||||
unbounded, separating hyperplanes.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Input sites</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
|
||||
<dd>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 <em>0</em> 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.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary of the furthest-site Voronoi diagram. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>list input sites for each <a href=qdelau_f.htm>furthest-site Delaunay region</a>. Use option '<a href="qh-optp.htm#Pp">Pp</a>'
|
||||
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.
|
||||
</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for 2-d furthest-site Voronoi diagrams.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="controls">furthest-site qvoronoi
|
||||
controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qu">Qu</a></dt>
|
||||
<dd>must be used.</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select furthest-site Voronoi vertices for input site <em>n</em> </dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report progress after constructing <em>n</em> facets</dd>
|
||||
<dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
|
||||
<dd>include upper and lower facets in the output. Set <em>k</em>
|
||||
to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
|
||||
<dt><a href="qh-opto.htm#f">f </a></dt>
|
||||
<dd>facet dump. Print the data structure for each facet (i.e.,
|
||||
furthest-site Voronoi vertex).</dd>
|
||||
</dl>
|
||||
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="graphics">furthest-site qvoronoi
|
||||
graphics</a></h3>
|
||||
<blockquote>
|
||||
<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
|
||||
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.</p>
|
||||
|
||||
<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
|
||||
examples</a> 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. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">furthest-site qvoronoi
|
||||
notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>See <a href="qvoronoi.htm#notes">Voronoi notes</a>.</p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">furthest-site qvoronoi conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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 <a
|
||||
href="qconvex.htm#conventions">qconvex conventions</a>, <a
|
||||
href="qdelau_f.htm#conventions">furthest-site delaunay
|
||||
conventions</a>, and <a href="index.htm#structure">Qhull's data structures</a>.</p>
|
||||
|
||||
<ul>
|
||||
<li><em>input site</em> - a point in the input (one dimension
|
||||
lower than a point on the convex hull)</li>
|
||||
<li><em>point</em> - a point has <i>d+1</i> coordinates. The
|
||||
last coordinate is the sum of the squares of the input
|
||||
site's coordinates</li>
|
||||
<li><em>vertex</em> - a point on the upper facets of the
|
||||
paraboloid. It corresponds to a unique input site. </li>
|
||||
<li><em>furthest-site Delaunay facet</em> - an upper facet of the
|
||||
paraboloid. The last coefficient of its normal is
|
||||
clearly positive.</li>
|
||||
<li><em>furthest-site Voronoi vertex</em> - the circumcenter
|
||||
of a furthest-site Delaunay facet</li>
|
||||
<li><em>furthest-site Voronoi region</em> - 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.</li>
|
||||
<li><em>furthest-site Voronoi diagram</em> - the graph of the
|
||||
furthest-site Voronoi regions with the ridges (edges)
|
||||
between the regions.</li>
|
||||
<li><em>infinity vertex</em> - the Voronoi vertex for
|
||||
unbounded furthest-site Voronoi regions in '<a
|
||||
href="qh-opto.htm#o">o</a>' output format. Its
|
||||
coordinates are <em>-10.101</em>.</li>
|
||||
<li><em>good facet</em> - an furthest-site Voronoi vertex with
|
||||
optional restrictions by '<a href="qh-optq.htm#QVn">QVn</a>',
|
||||
etc.</li>
|
||||
</ul>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">furthest-site qvoronoi options</a></h3>
|
||||
<blockquote>
|
||||
|
||||
See <a href="qvoronoi.htm#options">qvoronoi options</a>. The same
|
||||
program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
|
||||
for furthest-site Voronoi diagrams.
|
||||
</blockquote>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
667
xs/src/qhull/html/qvoronoi.htm
Normal file
667
xs/src/qhull/html/qvoronoi.htm
Normal file
@ -0,0 +1,667 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>qvoronoi -- Voronoi diagram</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<a name="TOP"><b>Up</b></a><b>:</b>
|
||||
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.archinect.com/gallery/displayimage.php?pos=-4658"><img
|
||||
src="normal_voronoi_knauss_oesterle.jpg" alt="[voronoi]" align="middle"
|
||||
height="100"></a>qvoronoi -- Voronoi diagram</h1>
|
||||
|
||||
<p>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 [<a href="index.htm#aure91">'91</a>]
|
||||
and the detailed introduction by O'Rourke [<a
|
||||
href="index.htm#orou94">'94</a>]. The Voronoi diagram is the
|
||||
dual of the <a href=qdelaun.htm>Delaunay triangulation</a>. </p>
|
||||
|
||||
<blockquote>
|
||||
<dl>
|
||||
<dt><b>Example:</b> rbox 10 D3 | qvoronoi <a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi
|
||||
<a href="qh-opto.htm#s">s</a>
|
||||
<a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
|
||||
result</a></dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fv2">Fv</a>
|
||||
<a href="qh-optt.htm#TO">TO result</a></dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fi2">Fi</a></dt>
|
||||
<dd>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.
|
||||
</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
<p>Qhull computes the Voronoi diagram via the <a href="qdelaun.htm">Delaunay
|
||||
triangulation</a>. 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. </p>
|
||||
|
||||
<p>Qhull outputs the Voronoi vertices for each Voronoi region. With
|
||||
option '<a href="qh-optf.htm#Fv2">Fv</a>',
|
||||
it lists all ridges of the Voronoi diagram with the corresponding
|
||||
pairs of input sites. With
|
||||
options '<a href="qh-optf.htm#Fi2">Fi</a>' and '<a href="qh-optf.htm#Fo2">Fo</a>',
|
||||
it lists the bounded and unbounded separating hyperplanes.
|
||||
You can also output a single Voronoi region
|
||||
for further processing [see <a href="#graphics">graphics</a>].</p>
|
||||
|
||||
<p>Use option '<a href="qh-optq.htm#Qz">Qz</a>' if the input is circular, cospherical, or
|
||||
nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid.
|
||||
|
||||
<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
|
||||
Voronoi diagram questions.</p>
|
||||
|
||||
<p>The 'qvonoroi' program is equivalent to
|
||||
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
|
||||
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
|
||||
in 4-d and higher. It disables the following Qhull
|
||||
<a href=qh-quick.htm#options>options</a>: <i>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</i>.
|
||||
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
|
||||
<p>Voronoi image by KOOK Architecture, Silvan Oesterle and Michael Knauss.
|
||||
|
||||
<hr>
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">qvoronoi synopsis</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="input">qvoronoi input</a></h3>
|
||||
<blockquote>
|
||||
The input data on <tt>stdin</tt> consists of:
|
||||
<ul>
|
||||
<li>dimension
|
||||
<li>number of points</li>
|
||||
<li>point coordinates</li>
|
||||
</ul>
|
||||
|
||||
<p>Use I/O redirection (e.g., qvoronoi < data.txt), a pipe (e.g., rbox 10 | qvoronoi),
|
||||
or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt).
|
||||
|
||||
<p>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.
|
||||
<p>
|
||||
<blockquote>
|
||||
<tt>rbox s 4 W0 c G1 D2 > data</tt>
|
||||
<blockquote><pre>
|
||||
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
|
||||
</pre></blockquote>
|
||||
|
||||
<p><tt>qvoronoi s p < data</tt>
|
||||
<blockquote><pre>
|
||||
|
||||
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
|
||||
</pre></blockquote>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="outputs">qvoronoi
|
||||
outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options control the output of Voronoi diagrams.</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt> </dt>
|
||||
<dd><b>Voronoi vertices</b></dd>
|
||||
<dt><a href="qh-opto.htm#p">p</a></dt>
|
||||
<dd>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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
|
||||
<dd>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., <em>-1</em>) indicate vertices
|
||||
outside of the Voronoi diagram.
|
||||
In the circle-in-box example, the
|
||||
Voronoi vertex at the origin has four neighbors.</dd>
|
||||
<dt><a href="qh-optf.htm#FN">FN</a></dt>
|
||||
<dd>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., <em>-1</em>) indicate vertices
|
||||
outside of the Voronoi diagram.
|
||||
In the circle-in-box example, the four bounded regions are defined by four
|
||||
Voronoi vertices.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Voronoi regions</b></dd>
|
||||
<dt><a href="qh-opto.htm#o">o</a></dt>
|
||||
<dd>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 <em>0</em> indicate
|
||||
coplanar input sites or '<a href="qh-optq.htm#Qz">Qz</a>'. </dd>
|
||||
<dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
|
||||
<dd>print separating hyperplanes for inner, bounded Voronoi
|
||||
regions. The first number is the number of separating
|
||||
hyperplanes. Each remaining line starts with <i>3+dim</i>. The
|
||||
next two numbers are adjacent input sites. The next <i>dim</i>
|
||||
numbers are the coefficients of the separating hyperplane. The
|
||||
last number is its offset. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
|
||||
hyperplanes are perpendicular bisectors. It will list relevant
|
||||
statistics to stderr. </dd>
|
||||
<dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
|
||||
<dd>print separating hyperplanes for outer, unbounded Voronoi
|
||||
regions. The first number is the number of separating
|
||||
hyperplanes. Each remaining line starts with <i>3+dim</i>. The
|
||||
next two numbers are adjacent input sites on the convex hull. The
|
||||
next <i>dim</i>
|
||||
numbers are the coefficients of the separating hyperplane. The
|
||||
last number is its offset. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
|
||||
hyperplanes are perpendicular bisectors. It will list relevant
|
||||
statistics to stderr,</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>Input sites</b></dd>
|
||||
<dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
|
||||
<dd>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 <em>0</em> 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.</dd>
|
||||
<dt><a href="qh-optf.htm#Fc">Fc</a></dt>
|
||||
<dd>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'<a href="qh-optf.htm#Fs">Fs</a>').
|
||||
A coincident site is assigned to one Voronoi
|
||||
vertex. Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
|
||||
coincident sites.</dd>
|
||||
<dt><a href="qh-optf.htm#FP">FP</a></dt>
|
||||
<dd>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'<a href="qh-optf.htm#Fs">Fs</a>').
|
||||
Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
|
||||
coincident sites.</dd>
|
||||
<dt> </dt>
|
||||
<dt> </dt>
|
||||
<dd><b>General</b></dd>
|
||||
<dt><a href="qh-opto.htm#s">s</a></dt>
|
||||
<dd>print summary of the Voronoi diagram. Use '<a
|
||||
href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
|
||||
<dt><a href="qh-opto.htm#i">i</a></dt>
|
||||
<dd>list input sites for each <a href=qdelaun.htm>Delaunay region</a>. Use option '<a href="qh-optp.htm#Pp">Pp</a>'
|
||||
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.
|
||||
</dd>
|
||||
<dt><a href="qh-optg.htm#G">G</a></dt>
|
||||
<dd>Geomview output for 2-d Voronoi diagrams.</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="controls">qvoronoi
|
||||
controls</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>These options provide additional control:</p>
|
||||
<blockquote>
|
||||
|
||||
<dl compact>
|
||||
<dt><a href="qh-optq.htm#Qu">Qu</a></dt>
|
||||
<dd>compute the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</dd>
|
||||
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
||||
<dd>select Voronoi vertices for input site <em>n</em> </dd>
|
||||
<dt><a href="qh-optq.htm#Qz">Qz</a></dt>
|
||||
<dd>add a point above the paraboloid to reduce precision
|
||||
errors. Use it for nearly cocircular/cospherical input
|
||||
(e.g., 'rbox c | qvoronoi Qz').</dd>
|
||||
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
||||
<dd>verify result</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
||||
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
||||
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
||||
<dd>output results to file. Use single quotes if the filename
|
||||
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
||||
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
||||
<dd>report progress after constructing <em>n</em> facets</dd>
|
||||
<dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
|
||||
<dd>include upper and lower facets in the output. Set <em>k</em>
|
||||
to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
|
||||
<dt><a href="qh-opto.htm#f">f </a></dt>
|
||||
<dd>facet dump. Print the data structure for each facet (i.e.,
|
||||
Voronoi vertex).</dd>
|
||||
</dl>
|
||||
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a> <a name="graphics">qvoronoi
|
||||
graphics</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
|
||||
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.</p>
|
||||
|
||||
<p>You can also view <i>individual</i> Voronoi regions in 3-d. To
|
||||
view the Voronoi region for site 3 in Geomview, execute</p>
|
||||
|
||||
<blockquote>
|
||||
<p>qvoronoi <data <a href="qh-optq.htm#QVn">QV3</a> <a
|
||||
href="qh-opto.htm#p">p</a> | qconvex s G >output</p>
|
||||
</blockquote>
|
||||
|
||||
<p>The <tt>qvoronoi</tt> command returns the Voronoi vertices
|
||||
for input site 3. The <tt>qconvex</tt> 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 '<a href="qh-optf.htm#Fi">Fi</a>'
|
||||
and '<a href="qh-optf.htm#Fo">Fo</a>' (up to roundoff error).
|
||||
|
||||
<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
|
||||
examples</a> 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. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="notes">qvoronoi
|
||||
notes</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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.</p>
|
||||
|
||||
<p>See <a href="#graphics">Voronoi graphics</a> for computing
|
||||
the convex hull of a Voronoi region. </p>
|
||||
|
||||
<p>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 <a href="../src/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
|
||||
|
||||
<p>Unbounded regions can be confusing. For example, '<tt>rbox c |
|
||||
qvoronoi Qz o</tt>' produces the Voronoi regions for the vertices
|
||||
of a cube centered at the origin. All regions are unbounded. The
|
||||
output is </p>
|
||||
|
||||
<blockquote>
|
||||
<pre>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
|
||||
</pre>
|
||||
</blockquote>
|
||||
|
||||
<p>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 '<a href="qh-optq.htm#Qz">Qz</a>'. The next two lines
|
||||
lists the Voronoi vertices. The first vertex is the infinity
|
||||
vertex. It is indicate by the coordinates <em>-10.101</em>. 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. </p>
|
||||
|
||||
<p>To use option '<a href="qh-optf.htm#Fv">Fv</a>', add an
|
||||
interior point. For example, </p>
|
||||
|
||||
<blockquote>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
</blockquote>
|
||||
|
||||
<p>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. </p>
|
||||
|
||||
<p>Options '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output)
|
||||
and '<a href="qh-optq.htm#QJn">QJ</a>' (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 <a
|
||||
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="conventions">qvoronoi conventions</a></h3>
|
||||
<blockquote>
|
||||
|
||||
<p>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 <a
|
||||
href="qconvex.htm#conventions">convex hull conventions</a>, <a
|
||||
href="qdelaun.htm#conventions">Delaunay conventions</a>, and
|
||||
<a href="index.htm#structure">Qhull's data structures</a>.</p>
|
||||
<blockquote>
|
||||
|
||||
<ul>
|
||||
<li><em>input site</em> - a point in the input (one dimension
|
||||
lower than a point on the convex hull)</li>
|
||||
<li><em>point</em> - a point has <i>d+1</i> coordinates. The
|
||||
last coordinate is the sum of the squares of the input
|
||||
site's coordinates</li>
|
||||
<li><em>coplanar point</em> - a <em>nearly incident</em>
|
||||
input site</li>
|
||||
<li><em>vertex</em> - a point on the paraboloid. It
|
||||
corresponds to a unique input site. </li>
|
||||
<li><em>point-at-infinity</em> - a point added above the
|
||||
paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
|
||||
<li><em>Delaunay facet</em> - a lower facet of the
|
||||
paraboloid. The last coefficient of its normal is
|
||||
clearly negative.</li>
|
||||
<li><em>Voronoi vertex</em> - the circumcenter of a Delaunay
|
||||
facet</li>
|
||||
<li><em>Voronoi region</em> - the Voronoi vertices for an
|
||||
input site. The region of Euclidean space nearest to an
|
||||
input site.</li>
|
||||
<li><em>Voronoi diagram</em> - the graph of the Voronoi
|
||||
regions. It includes the ridges (i.e., edges) between the
|
||||
regions.</li>
|
||||
<li><em>vertex-at-infinity</em> - the Voronoi vertex that
|
||||
indicates unbounded Voronoi regions in '<a
|
||||
href="qh-opto.htm#o">o</a>' output format. Its
|
||||
coordinates are <em>-10.101</em>.</li>
|
||||
<li><em>good facet</em> - a Voronoi vertex with optional
|
||||
restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
|
||||
</ul>
|
||||
|
||||
</blockquote>
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">qvoronoi options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis
|
||||
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
|
||||
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
277
xs/src/qhull/html/rbox.htm
Normal file
277
xs/src/qhull/html/rbox.htm
Normal file
@ -0,0 +1,277 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>rbox -- generate point distributions</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><b><a name="TOP">Up:</a></b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
|
||||
• <a href="#options">op</a>tions
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<h1><a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="qh--cone.gif" alt="[CONE]" align="middle" width="100"
|
||||
height="100"></a>rbox -- generate point distributions</h1>
|
||||
|
||||
<blockquote>
|
||||
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.
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="synopsis">rbox synopsis</a></h3>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="outputs">rbox outputs</a></h3>
|
||||
<blockquote>
|
||||
|
||||
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.
|
||||
|
||||
<p>For example, <tt>rbox c 10 D2</tt> generates
|
||||
<blockquote>
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="examples">rbox examples</a></h3>
|
||||
|
||||
<pre>
|
||||
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.
|
||||
</pre>
|
||||
|
||||
<h3><a href="#TOP">»</a><a name="notes">rbox notes</a></h3>
|
||||
<blockquote>
|
||||
Some combinations of arguments generate odd results.
|
||||
|
||||
</blockquote>
|
||||
<h3><a href="#TOP">»</a><a name="options">rbox options</a></h3>
|
||||
|
||||
<pre>
|
||||
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
|
||||
</pre>
|
||||
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
|
||||
<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
|
||||
• <a href="qh-quick.htm#options">Options</a>
|
||||
• <a href="qh-opto.htm#output">Output</a>
|
||||
• <a href="qh-optf.htm#format">Formats</a>
|
||||
• <a href="qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="qh-optp.htm#print">Print</a>
|
||||
• <a href="qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="qh-optc.htm#prec">Precision</a>
|
||||
• <a href="qh-optt.htm#trace">Trace</a>
|
||||
• <a href="../src/libqhull_r/index.htm">Functions</a><br>
|
||||
<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
|
||||
• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
|
||||
• <a href="#options">op</a>tions
|
||||
<!-- GC common information -->
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
|
||||
align="middle" width="40" height="40"></a><i>The Geometry Center
|
||||
Home Page </i></p>
|
||||
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
<br>
|
||||
Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: August 12, 1998 <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
176
xs/src/qhull/html/rbox.man
Normal file
176
xs/src/qhull/html/rbox.man
Normal file
@ -0,0 +1,176 @@
|
||||
.\" 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
|
||||
|
||||
195
xs/src/qhull/html/rbox.txt
Normal file
195
xs/src/qhull/html/rbox.txt
Normal file
@ -0,0 +1,195 @@
|
||||
|
||||
|
||||
|
||||
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
|
||||
|
||||
|
||||
284
xs/src/qhull/index.htm
Normal file
284
xs/src/qhull/index.htm
Normal file
@ -0,0 +1,284 @@
|
||||
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
|
||||
<html>
|
||||
|
||||
<head>
|
||||
<title>Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
|
||||
<br><b>To:</b>
|
||||
<a href="http://www.qhull.org/news">News</a>
|
||||
• <a href="http://www.qhull.org/download">Download</a>
|
||||
• <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
|
||||
• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
|
||||
• <a href="html/index.htm#TOC">Manual</a>
|
||||
• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
|
||||
• <a href="html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="html/qh-quick.htm#options">Options</a>
|
||||
</p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document -->
|
||||
<table>
|
||||
<tr><td valign=top>
|
||||
<h1>Qhull</h1>
|
||||
<a
|
||||
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
|
||||
src="html/qh--cone.gif" alt="[CONE]" align="middle" width="100"
|
||||
height="100"></a>
|
||||
</td><td>
|
||||
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.</p>
|
||||
|
||||
<!-- duplicated in index.htm and html/index.htm -->
|
||||
<p>Qhull does <i>not</i> 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, </p>
|
||||
|
||||
<p>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 <a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.
|
||||
</p>
|
||||
</td></tr></table>
|
||||
|
||||
<hr>
|
||||
<form method=get action=http://www.google.com/search>
|
||||
<input type=hidden name=sitesearch value=www.qhull.org>
|
||||
<input type=hidden name=num value=100>
|
||||
<ul>
|
||||
<li><a href="http://www.qhull.org/news">News</a> and
|
||||
<a href="http://www.qhull.org/news/qhull-news.html#bugs">Bugs</a>
|
||||
about Qhull 2015.2 2016/01/18</li>
|
||||
<li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href="http://www.qhull.org/src/Changes.txt">changes</a>)</li>
|
||||
<li><a href=http://github.com/qhull/qhull/wiki>GitHub</a> C++ interface to Qhull
|
||||
<li><a href="html/index.htm">Manual</a> for Qhull and rbox
|
||||
<li><a href="html/index.htm#geomview">Geomview</a> for 3-D and 4-D visualization of Qhull output
|
||||
<li><input name=as_q size=10 value="">
|
||||
<input type="submit" value="Search">
|
||||
www.qhull.org
|
||||
<p>
|
||||
<li><a href="http://www.qhull.org/news/qhull-news.html#users">How</a> is Qhull used?</li>
|
||||
<li><a href="http://scholar.google.com/scholar?cites=13151392091060773178&as_sdt=40000005">Google Scholar</a>,
|
||||
<a href="http://libra.msra.cn/Publication/232063/the-quickhull-algorithm-for-convex-hulls">Microsoft Academic</a>,
|
||||
and <a href="http://citeseerx.ist.psu.edu/showciting?doi=10.1.1.117.405&sort=cite">CiteSeer</a>
|
||||
references to Qhull
|
||||
<li>
|
||||
<a href=http://www.google.com/search?as_q=qhull+-debian+-cvs+-gentoo+-pool+-mirrors&num=100>Google</a> Qhull,
|
||||
<a href="http://images.google.com/images?q=qhull&num=100">Images</a>,
|
||||
<a href="http://www.google.com/#q=qhull&tbm=bks">Books</a>,
|
||||
<a href="http://www.google.com/search?q=qhull&tbm=pts">Patents</a>,
|
||||
<a href="http://groups.google.com/groups?as_q=qhull&num=100&as_scoring=d">Newsgroups</a>,
|
||||
<a href="http://www.google.com/search?q=qhull&tbm=blg">Blogs</a>,
|
||||
and <a href=http://www.googlism.com/who_is/q/qhull/>Who is</a> Qhull?
|
||||
|
||||
|
||||
<p>
|
||||
<li><a href=http://www.mathworks.com/>MATLAB</a> uses Qhull for their n-d computational geometry functions:
|
||||
<a href=http://www.mathworks.com/help/techdoc/ref/convhulln.html>convhulln</a>
|
||||
<a href=http://www.mathworks.com/help/techdoc/ref/delaunayn.html>delaunayn</a>
|
||||
<a href=http://www.mathworks.com/help/techdoc/ref/griddatan.html>griddatan</a>
|
||||
<a href=http://www.mathworks.com/help/techdoc/ref/voronoin.html>voronoin</a>.
|
||||
</li>
|
||||
<li>The <a href="http://cran.r-project.org/web/packages/geometry/geometry.pdf">geometry</a> package of <a href="http://www.r-project.org/">R</a> provides <a href="http://geometry.r-forge.r-project.org/">Qhull in R</a>.
|
||||
<li>The <a href="http://packages.debian.org/sid/octave3.2">Debian build</a> of
|
||||
<a href=http://www.octave.org/>GNU Octave</a> includes Qhull for <a href="http://www.gnu.org/software/octave/doc/interpreter/Geometry.html">computational geometry<a>.
|
||||
<li><a href=http://www.wolfram.com/products/mathematica/>Mathematica</a>'s Delaunay interface <a href=http://library.wolfram.com/infocenter/MathSource/1160/>qh-math</a>
|
||||
and <a href="http://portal.uni-freiburg.de/imteksimulation/downloads/ims">QHullInterface</a>
|
||||
<li>The <a href="http://docs.scipy.org/doc/scipy/reference/tutorial/spatial.html">scipy.spatial</a> of <a href="http://scipy.org/">SciPy</a> is implemented with Qhull. It includes
|
||||
support for Delaunay triangulations,
|
||||
</ul>
|
||||
</form>
|
||||
|
||||
<p><b>Introduction</b>
|
||||
<ul>
|
||||
<li><a
|
||||
href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html"
|
||||
>Fukuda's introduction</a> to convex hulls, Delaunay
|
||||
triangulations, Voronoi diagrams, and linear programming</li>
|
||||
<li><a
|
||||
href="http://www.cse.unsw.edu.au/~lambert/java/3d/hull.html"
|
||||
>Lambert's Java</a> visualization of convex hull algorithms </li>
|
||||
<li><a
|
||||
href="http://www.algorithmic-solutions.info/leda_guide/geometryalgorithms.html"
|
||||
>LEDA Guide</a> to geometry algorithms
|
||||
<li><a
|
||||
href="http://mathworld.wolfram.com/ComputationalGeometry.html"
|
||||
>MathWorld's</a> Computational Geometry from Wolfram Research
|
||||
<li><a
|
||||
href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
|
||||
>Skiena's</a> Computational Geometry from his <i>Algorithm Design Manual</i>.
|
||||
<li><a
|
||||
href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
|
||||
>Stony Brook</a> Algorithm Repository, computational geometry</li>
|
||||
</ul>
|
||||
|
||||
<p><b>Qhull Documentation and Support</b>
|
||||
<ul>
|
||||
<li><a href="html/index.htm">Manual</a> for Qhull and rbox
|
||||
<table><tr><td>
|
||||
<ul>
|
||||
<li><a href="html/index.htm#description">Description</a> of Qhull
|
||||
<li><a href="html/qh-impre.htm">Imprecision</a> in Qhull
|
||||
<li><a href="html/qh-quick.htm#programs">Programs</a> and <a href="html/qh-quick.htm#options">Options</a>
|
||||
quick reference
|
||||
<li><a href="html/qconvex.htm">qconvex</a> -- convex hull
|
||||
<li><a href="html/qdelaun.htm">qdelaunay</a> -- Delaunay triangulation
|
||||
<li><a href="html/qvoronoi.htm">qvoronoi</a> -- Voronoi diagram
|
||||
<li><a href="html/qhalf.htm">qhalf</a> -- halfspace intersection about a point
|
||||
<li><a href="html/rbox.htm">rbox</a> -- generate point distributions
|
||||
</ul></td><td><ul>
|
||||
<li><a href="http://www.qhull.org/html/qh-faq.htm">Frequently</a> asked
|
||||
questions about Qhull</li>
|
||||
<li><a href="html/index.htm#geomview">Geomview</a> for visualizing Qhull
|
||||
<li><a href="COPYING.txt">COPYING.txt</a> - copyright notice<br>
|
||||
<li><a href="REGISTER.txt">REGISTER.txt</a> - registration<br>
|
||||
<li><a href="README.txt">README.txt</a> - installation
|
||||
instructions<br>
|
||||
<li><a href="src/Changes.txt">Changes.txt</a> - change history <br>
|
||||
<li><a href="html/qh-code.htm">Calling Qhull</a> from your program
|
||||
<li><a href="src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and data structures with source
|
||||
</ul>
|
||||
</td></tr></table>
|
||||
<li>Send e-mail to <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> </li>
|
||||
<li>Report bugs to <a
|
||||
href="mailto:qhull_bug@qhull.org">qhull_bug@qhull.org</a>
|
||||
</ul>
|
||||
|
||||
<p><b>Related URLs</b>
|
||||
<ul>
|
||||
<li><a href="http://www.geom.uiuc.edu/software/cglist">Amenta's directory</a> of
|
||||
computational geometry software </li>
|
||||
|
||||
<li><a href=http://www.boost.org/libs/graph/doc/table_of_contents.html>BGL</a>
|
||||
Boost Graph Library provides C++ classes for graph data structures
|
||||
and algorithms,
|
||||
<li><a
|
||||
href="http://www.netlib.org/voronoi/hull.html">Clarkson's
|
||||
hull </a>program with exact arithmetic for convex hulls, Delaunay triangulations,
|
||||
Voronoi volumes, and alpha shapes. </li>
|
||||
<li><a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/compgeom.html">Erickson's
|
||||
Computational</a> Geometry Pages and
|
||||
<a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Software</a>
|
||||
<li><a
|
||||
href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">Fukuda's
|
||||
cdd</a> program for halfspace intersection and convex hulls (<a
|
||||
href="http://www.csb.ethz.ch/tools/polco">Polco/Java</a>)</li>
|
||||
<li><a href="http://www.inf.ethz.ch/personal/gaertner/miniball.html">Gartner's
|
||||
Miniball</a> for fast and robust smallest enclosing balls (up to 20-d)
|
||||
|
||||
<li><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a>
|
||||
and <a href=http://www.cgal.org/>CGAL</a> libraries for writing computational
|
||||
geometry programs and other combinatorial algorithms
|
||||
<li><a href=http://www.mathtools.net/>Mathtools.net</a> of scientific and engineering
|
||||
software
|
||||
<li><a href="http://www.imr.sandia.gov/papers/topics.html">Owen's International Meshing</a> Roundtable
|
||||
<li><a
|
||||
href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
|
||||
Finite Element</a> Mesh Generation page</li>
|
||||
<li><a href="http://www.cs.cmu.edu/~quake/triangle.html">Shewchuk's
|
||||
triangle </a>program for 2-d Delaunay</li>
|
||||
<li><a href=http://www.voronoi.com>Voronoi Web Site</a> for all things Voronoi
|
||||
<li>Young's <a href="http://homepage.usask.ca/~ijm451/finite/fe_resources/">Internet Finite Element Resources</a>
|
||||
<li><a href="http://www.uic.nnov.ru/~zny/skeleton/">Zolotykh's Skeleton</a> generates all extreme rays of a polyhedral cone using the Double Description Method</li>
|
||||
<li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href="http://habrahabr.ru/post/245221/">doc-ru</a>) implements the Quickhull algorithm for points in general position.
|
||||
</ul>
|
||||
|
||||
<p><b>FAQs and Newsgroups</b>
|
||||
<ul>
|
||||
<li><a
|
||||
href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a>
|
||||
for computer graphics algorithms
|
||||
(Exaflop.org: <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures)
|
||||
</li>
|
||||
<li><a
|
||||
href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html">FAQ
|
||||
</a>for linear programming </li>
|
||||
<li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
|
||||
comp.graphics.algorithms </li>
|
||||
<li><a href="news:comp.soft-sys.matlab">Newsgroup</a>:
|
||||
comp.soft-sys.matlab</li>
|
||||
<li><a href="news:sci.math.num-analysis">Newsgroup</a>:
|
||||
sci.math.num-analysis </li>
|
||||
<li><a href="news:sci.op-research">Newsgroup</a>:
|
||||
sci.op-research </li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<hr>
|
||||
|
||||
<p>The program includes options for input transformations,
|
||||
randomization, tracing, multiple output formats, and execution
|
||||
statistics. The program can be called from within your
|
||||
application. </p>
|
||||
|
||||
<p>You can view the results in 2-d, 3-d and 4-d with <a
|
||||
href="http://www.geomview.org">Geomview</a>. An alternative
|
||||
is <a href=http://www.vtk.org/>VTK</a>.</p>
|
||||
|
||||
<p>For an article about Qhull, download from
|
||||
<a href="http://dl.acm.org/authorize?89250">ACM</a> or <a
|
||||
href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>:
|
||||
</p>
|
||||
|
||||
<blockquote>
|
||||
<p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The
|
||||
Quickhull algorithm for convex hulls," <i>ACM Trans. on
|
||||
Mathematical Software</i>, 22(4):469-483, Dec 1996, http://www.qhull.org</p>
|
||||
</blockquote>
|
||||
|
||||
<p>Abstract: </p>
|
||||
|
||||
<blockquote>
|
||||
<p>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. </p>
|
||||
<p>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. </p>
|
||||
</blockquote>
|
||||
<!-- Navigation links -->
|
||||
<hr>
|
||||
|
||||
<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/past-projects.html"><i>Past Software
|
||||
Projects of the Geometry Center</i></a> <br>
|
||||
<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
|
||||
<br><b>To:</b>
|
||||
<a href="http://www.qhull.org/news">News</a>
|
||||
• <a href="http://www.qhull.org/download">Download</a>
|
||||
• <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
|
||||
• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
|
||||
• <a href="html/index.htm#TOC">Manual</a>
|
||||
• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
|
||||
• <a href="html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="html/qh-quick.htm#options">Options</a>
|
||||
<!-- GC common information --></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img src="html/qh--geom.gif" alt="[HOME]"
|
||||
align="middle"></a> <i>The Geometry Center Home Page</i> </p>
|
||||
|
||||
<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a>
|
||||
<br>
|
||||
Created: May 17 1995 --- <!-- hhmts start -->
|
||||
</body>
|
||||
</html>
|
||||
426
xs/src/qhull/origCMakeLists.txt
Normal file
426
xs/src/qhull/origCMakeLists.txt
Normal file
@ -0,0 +1,426 @@
|
||||
# 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 <build/install_manifest.txt
|
||||
#
|
||||
# To build Qhull with Visual Studio projects, run cmake twice
|
||||
# To install bin/doc/include/lib in the current directory
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
|
||||
# To install into Program Files/qhull
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake ..
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake ..
|
||||
# To build for Visual Studio 2005 and install into Program Files/qhull
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005" .. && cmake ..
|
||||
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005 Win64" .. && cmake ..
|
||||
# Double click build-cmake/qhull-all.sln
|
||||
# Build INSTALL to copy files into C:/Program Files/qhull
|
||||
#
|
||||
# Additional build targets
|
||||
# qhullp -- Same as qhull using qh_QHpointer and deprecated libqhull_p
|
||||
# user_egp -- Same as user_eg using qh_QHpointer and deprecated libqhull_p
|
||||
#
|
||||
# Notes on Visual Studio projects
|
||||
# You may need to copy bin/msvcr80.dll into C:/Program Files/qhull/bin
|
||||
# If using library debug targets, please rename with '_d' (e.g., qhullstatic_d.lib)
|
||||
#
|
||||
# Troubleshooting
|
||||
# "No CMAKE_C_COMPILER could be found"
|
||||
# cmake was not able to find the build environment specified (e.g., Visual Studio 11)
|
||||
#
|
||||
# To uninstall on Windows
|
||||
# Delete C:/Program Files/qhull
|
||||
#
|
||||
# If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
|
||||
#
|
||||
# For qhulltest, use the Qt build (src/qhull-all.pro)
|
||||
#
|
||||
# Qhull ships with cmake-derived sln and proj files for DevStudio 8 2005
|
||||
# See eg/make-vcproj.sh
|
||||
# Change to relative paths
|
||||
# Remove ZERO_CHECK, ALL_BUILD, and INSTALL projects
|
||||
# Change targets to bin/ and lib/ directories
|
||||
# Disable incremental linking and ilk files (LinkIncremental="1")
|
||||
# Disable Run-Time Type Info (rtti)
|
||||
# Remove src/libqhullcpp from most of the AdditionalIncludeDirectories
|
||||
# Remove CMAKE_INTDIR from PreprocessorDefinitions
|
||||
# Adjust target names and destinations (e.g., lib/libqhullstatic_rd.a)
|
||||
#
|
||||
# $Id: //main/2015/qhull/CMakeLists.txt#8 $$Change: 2066 $
|
||||
# $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
|
||||
|
||||
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
|
||||
|
||||
# SOVERSION -- qhull 2003 = empty, 2009 = 5, 2010-2012 = 6, 2015 (reentrant) = 7
|
||||
set(qhull_SOVERSION 7) # For SOVERSION
|
||||
|
||||
include(CMakeModules/CheckLFS.cmake)
|
||||
option(WITH_LFS "Enable Large File Support" ON)
|
||||
check_lfs(WITH_LFS)
|
||||
|
||||
if(INCLUDE_INSTALL_DIR)
|
||||
else()
|
||||
set(INCLUDE_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/include)
|
||||
endif()
|
||||
if(LIB_INSTALL_DIR)
|
||||
else()
|
||||
set(LIB_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/lib)
|
||||
endif()
|
||||
if(BIN_INSTALL_DIR)
|
||||
else()
|
||||
set(BIN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/bin)
|
||||
endif()
|
||||
if(MAN_INSTALL_DIR)
|
||||
else()
|
||||
if(WIN32)
|
||||
set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/man/man1)
|
||||
else()
|
||||
set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/man/man1)
|
||||
endif()
|
||||
endif()
|
||||
if(DOC_INSTALL_DIR)
|
||||
else()
|
||||
if(WIN32)
|
||||
set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/doc)
|
||||
else()
|
||||
set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/doc/qhull)
|
||||
endif()
|
||||
endif()
|
||||
message(STATUS)
|
||||
message(STATUS "========== qhull Build Information ==========")
|
||||
message(STATUS "Build Version: ${qhull_VERSION}")
|
||||
message(STATUS "Install Prefix (CMAKE_INSTALL_PREFIX): ${CMAKE_INSTALL_PREFIX}")
|
||||
message(STATUS "Binary Directory (BIN_INSTALL_DIR): ${BIN_INSTALL_DIR}")
|
||||
message(STATUS "Library Directory (LIB_INSTALL_DIR): ${LIB_INSTALL_DIR}")
|
||||
message(STATUS "Include Directory (INCLUDE_INSTALL_DIR): ${INCLUDE_INSTALL_DIR}")
|
||||
message(STATUS "Documentation Directory (DOC_INSTALL_DIR): ${DOC_INSTALL_DIR}")
|
||||
message(STATUS "Man Pages Directory (MAN_INSTALL_DIR): ${MAN_INSTALL_DIR}")
|
||||
message(STATUS "Build Type (CMAKE_BUILD_TYPE): ${CMAKE_BUILD_TYPE}")
|
||||
message(STATUS "To override these options, add -D{OPTION_NAME}=... to the cmake command")
|
||||
message(STATUS " Build the debug targets -DCMAKE_BUILD_TYPE=Debug")
|
||||
message(STATUS)
|
||||
message(STATUS "To build and install qhull, enter \"make\" and \"make install\"")
|
||||
message(STATUS "To smoketest qhull, enter \"ctest\"")
|
||||
message(STATUS)
|
||||
|
||||
|
||||
# ---------------------------------------
|
||||
# Define library source files and variables
|
||||
#
|
||||
# Files for individual targets are defined with the target
|
||||
# ---------------------------------------
|
||||
|
||||
# Order libqhull object files by frequency of execution. Small files at end.
|
||||
|
||||
# Non-reentrant Qhull
|
||||
set(
|
||||
libqhull_HEADERS
|
||||
src/libqhull/libqhull.h
|
||||
src/libqhull/geom.h
|
||||
src/libqhull/io.h
|
||||
src/libqhull/mem.h
|
||||
src/libqhull/merge.h
|
||||
src/libqhull/poly.h
|
||||
src/libqhull/qhull_a.h
|
||||
src/libqhull/qset.h
|
||||
src/libqhull/random.h
|
||||
src/libqhull/stat.h
|
||||
src/libqhull/user.h
|
||||
)
|
||||
set(
|
||||
libqhull_SOURCES
|
||||
src/libqhull/global.c
|
||||
src/libqhull/stat.c
|
||||
src/libqhull/geom2.c
|
||||
src/libqhull/poly2.c
|
||||
src/libqhull/merge.c
|
||||
src/libqhull/libqhull.c
|
||||
src/libqhull/geom.c
|
||||
src/libqhull/poly.c
|
||||
src/libqhull/qset.c
|
||||
src/libqhull/mem.c
|
||||
src/libqhull/random.c
|
||||
src/libqhull/usermem.c
|
||||
src/libqhull/userprintf.c
|
||||
src/libqhull/io.c
|
||||
src/libqhull/user.c
|
||||
src/libqhull/rboxlib.c
|
||||
src/libqhull/userprintf_rbox.c
|
||||
${libqhull_HEADERS}
|
||||
)
|
||||
|
||||
set(
|
||||
libqhull_DOC
|
||||
src/libqhull/index.htm
|
||||
src/libqhull/qh-geom.htm
|
||||
src/libqhull/qh-globa.htm
|
||||
src/libqhull/qh-io.htm
|
||||
src/libqhull/qh-mem.htm
|
||||
src/libqhull/qh-merge.htm
|
||||
src/libqhull/qh-poly.htm
|
||||
src/libqhull/qh-qhull.htm
|
||||
src/libqhull/qh-set.htm
|
||||
src/libqhull/qh-stat.htm
|
||||
src/libqhull/qh-user.htm
|
||||
src/libqhull/DEPRECATED.txt
|
||||
)
|
||||
|
||||
set(
|
||||
testqset_HEADERS
|
||||
src/libqhull/mem.h
|
||||
src/libqhull/qset.h
|
||||
)
|
||||
set(
|
||||
testqset_SOURCES
|
||||
src/libqhull/qset.c
|
||||
src/libqhull/mem.c
|
||||
src/libqhull/usermem.c
|
||||
src/testqset/testqset.c
|
||||
${testqset_HEADERS}
|
||||
)
|
||||
|
||||
# Reeentrant Qhull
|
||||
|
||||
set(
|
||||
libqhullr_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
|
||||
)
|
||||
set(
|
||||
libqhullr_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/userprintf_r.c
|
||||
src/libqhull_r/io_r.c
|
||||
src/libqhull_r/user_r.c
|
||||
src/libqhull_r/rboxlib_r.c
|
||||
src/libqhull_r/userprintf_rbox_r.c
|
||||
${libqhullr_HEADERS}
|
||||
)
|
||||
|
||||
set(
|
||||
libqhullr_DOC
|
||||
src/libqhull_r/index.htm
|
||||
src/libqhull_r/qh-geom_r.htm
|
||||
src/libqhull_r/qh-globa_r.htm
|
||||
src/libqhull_r/qh-io_r.htm
|
||||
src/libqhull_r/qh-mem_r.htm
|
||||
src/libqhull_r/qh-merge_r.htm
|
||||
src/libqhull_r/qh-poly_r.htm
|
||||
src/libqhull_r/qh-qhull_r.htm
|
||||
src/libqhull_r/qh-set_r.htm
|
||||
src/libqhull_r/qh-stat_r.htm
|
||||
src/libqhull_r/qh-user_r.htm
|
||||
)
|
||||
|
||||
set(
|
||||
testqsetr_HEADERS
|
||||
src/libqhull_r/mem_r.h
|
||||
src/libqhull_r/qset_r.h
|
||||
)
|
||||
set(
|
||||
testqsetr_SOURCES
|
||||
src/libqhull_r/qset_r.c
|
||||
src/libqhull_r/mem_r.c
|
||||
src/libqhull_r/usermem_r.c
|
||||
src/testqset_r/testqset_r.c
|
||||
${testqsetr_HEADERS}
|
||||
)
|
||||
|
||||
# C++ interface to reentrant Qhull
|
||||
|
||||
set(
|
||||
libqhullcpp_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(
|
||||
libqhullcpp_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
|
||||
${libqhullcpp_HEADERS}
|
||||
)
|
||||
|
||||
# Documentation files (index.htm refers to html/...)
|
||||
|
||||
set(
|
||||
doc_FILES
|
||||
README.txt
|
||||
REGISTER.txt
|
||||
Announce.txt
|
||||
COPYING.txt
|
||||
index.htm
|
||||
)
|
||||
|
||||
include_directories(${CMAKE_SOURCE_DIR}/src)
|
||||
|
||||
if(CMAKE_BUILD_TYPE MATCHES "[dD]ebug")
|
||||
set(qhull_CPP qhullcpp_d)
|
||||
set(qhull_SHARED qhull_d)
|
||||
set(qhull_SHAREDP qhull_pd)
|
||||
set(qhull_SHAREDR qhull_rd)
|
||||
set(qhull_STATIC qhullstatic_d)
|
||||
set(qhull_STATICR qhullstatic_rd)
|
||||
else()
|
||||
set(qhull_CPP qhullcpp)
|
||||
set(qhull_SHARED libqhull) # Temporarily avoid name conflict with qhull executable
|
||||
set(qhull_SHAREDP qhull_p)
|
||||
set(qhull_SHAREDR qhull_r)
|
||||
set(qhull_STATIC qhullstatic)
|
||||
set(qhull_STATICR qhullstatic_r)
|
||||
endif()
|
||||
|
||||
|
||||
|
||||
# ---------------------------------------
|
||||
# Define static libraries qhullstatic (non-reentrant) and qhullstatic_r (reentrant)
|
||||
# ---------------------------------------
|
||||
|
||||
add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES})
|
||||
set_target_properties(${qhull_STATIC} PROPERTIES
|
||||
VERSION ${qhull_VERSION})
|
||||
|
||||
add_library(${qhull_STATICR} STATIC ${libqhullr_SOURCES})
|
||||
set_target_properties(${qhull_STATICR} PROPERTIES
|
||||
VERSION ${qhull_VERSION})
|
||||
|
||||
if(UNIX)
|
||||
target_link_libraries(${qhull_STATIC} m)
|
||||
target_link_libraries(${qhull_STATICR} m)
|
||||
endif(UNIX)
|
||||
|
||||
# ---------------------------------------
|
||||
# Define C++ static library qhullcpp
|
||||
# Do not create libqhullcpp as a shared library. Qhull C++ classes may change layout and size.
|
||||
# ---------------------------------------
|
||||
|
||||
add_library(${qhull_CPP} STATIC ${libqhullcpp_SOURCES})
|
||||
set_target_properties(${qhull_CPP} PROPERTIES
|
||||
VERSION ${qhull_VERSION})
|
||||
|
||||
# ---------------------------------------
|
||||
# Define qhull executables linked to qhullstatic library
|
||||
# qhull is linked to reentrant qhull (more flexible)
|
||||
# the others are linked to non-reentrant qhull (somewhat faster)
|
||||
# ---------------------------------------
|
||||
|
||||
set(qhull_SOURCES src/qhull/unix_r.c)
|
||||
set(rbox_SOURCES src/rbox/rbox.c)
|
||||
set(qconvex_SOURCES src/qconvex/qconvex.c)
|
||||
set(qdelaunay_SOURCES src/qdelaunay/qdelaun.c)
|
||||
set(qvoronoi_SOURCES src/qvoronoi/qvoronoi.c)
|
||||
set(qhalf_SOURCES src/qhalf/qhalf.c)
|
||||
|
||||
add_executable(qhull ${qhull_SOURCES})
|
||||
target_link_libraries(qhull ${qhull_STATICR})
|
||||
|
||||
add_executable(rbox ${rbox_SOURCES})
|
||||
target_link_libraries(rbox ${qhull_STATIC})
|
||||
|
||||
add_executable(qconvex ${qconvex_SOURCES})
|
||||
target_link_libraries(qconvex ${qhull_STATIC})
|
||||
|
||||
add_executable(qdelaunay ${qdelaunay_SOURCES})
|
||||
target_link_libraries(qdelaunay ${qhull_STATIC})
|
||||
|
||||
add_executable(qvoronoi ${qvoronoi_SOURCES})
|
||||
target_link_libraries(qvoronoi ${qhull_STATIC})
|
||||
|
||||
add_executable(qhalf ${qhalf_SOURCES})
|
||||
target_link_libraries(qhalf ${qhull_STATIC})
|
||||
|
||||
|
||||
# ---------------------------------------
|
||||
# Define install
|
||||
# ---------------------------------------
|
||||
|
||||
install(TARGETS ${qhull_TARGETS_INSTALL}
|
||||
RUNTIME DESTINATION ${BIN_INSTALL_DIR}
|
||||
LIBRARY DESTINATION ${LIB_INSTALL_DIR}
|
||||
ARCHIVE DESTINATION ${LIB_INSTALL_DIR})
|
||||
|
||||
install(FILES ${libqhull_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
|
||||
install(FILES ${libqhull_DOC} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
|
||||
install(FILES ${libqhullr_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
|
||||
install(FILES ${libqhullr_DOC} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
|
||||
install(FILES ${libqhullcpp_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhullcpp)
|
||||
install(FILES html/qhull.man DESTINATION ${MAN_INSTALL_DIR} RENAME qhull.1)
|
||||
install(FILES html/rbox.man DESTINATION ${MAN_INSTALL_DIR} RENAME rbox.1)
|
||||
install(FILES ${doc_FILES} DESTINATION ${DOC_INSTALL_DIR})
|
||||
install(DIRECTORY html/ DESTINATION ${DOC_INSTALL_DIR})
|
||||
2129
xs/src/qhull/src/Changes.txt
Normal file
2129
xs/src/qhull/src/Changes.txt
Normal file
File diff suppressed because it is too large
Load Diff
29
xs/src/qhull/src/libqhull/DEPRECATED.txt
Normal file
29
xs/src/qhull/src/libqhull/DEPRECATED.txt
Normal file
@ -0,0 +1,29 @@
|
||||
|
||||
qhull/src/libqhull
|
||||
|
||||
This directory contains the non-reentrant version of qhull, libqhull.
|
||||
|
||||
New code should use the reentrant version of qhull (libqhull_r).
|
||||
It allows multiple instances of qhull to run at the same time. On
|
||||
modern architectures, it is nearly as fast as libqhull.
|
||||
|
||||
Qhull programs may be built with either library. Each program has a
|
||||
reentrant version (e.g., qconvex_r.c) and a non-reentrant
|
||||
version (qconvex.c). The programs, rbox, qconvex, qdelaunay, qhalf,
|
||||
and qvoronoi, are built with libqhull. The qhull program is built
|
||||
with libqhull_r.
|
||||
|
||||
Qhull's C++ interface requires libqhull_r. If you previously used the
|
||||
C++ interface, you will need to update your code. See Changes.txt for
|
||||
suggestions.
|
||||
|
||||
The C code in libqhull looks unusual because of the 'qh' macro. The 'qh'
|
||||
macro controls access to Qhull's global data structure, qhT. If
|
||||
'qh_QHpointer' is defined, 'qh' is 'qh_qh->' and 'qh_qh' is defined as
|
||||
'qhT *qh_qh', otherwise 'qh' is 'qh_qh.' and 'qh_qh' is defined as
|
||||
'qhT qh_qh'.
|
||||
|
||||
libqhull will be supported indefinitely. The qh_QHpointer variation
|
||||
of libqhull will be not be retested each release. It is replaced by
|
||||
libqhull_r.
|
||||
|
||||
240
xs/src/qhull/src/libqhull/Makefile
Normal file
240
xs/src/qhull/src/libqhull/Makefile
Normal file
@ -0,0 +1,240 @@
|
||||
# Simple gcc Makefile for non-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 non-reentrant qhull
|
||||
# testqset_r Standalone test of non-reentrant qset_r.c with mem_r.c
|
||||
# user_eg An example of using qhull (non-reentrant)
|
||||
# user_eg2 An example of using qhull (non-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/Makefile#8 $
|
||||
|
||||
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.c unix.c qdelaun.c qhalf.c qvoronoi.c rbox.c
|
||||
rm -f user_eg.c user_eg2.c testqset.c
|
||||
|
||||
cleanall: clean
|
||||
rm -f qconvex qdelaunay qhalf qvoronoi qhull *.exe
|
||||
rm -f core user_eg user_eg2 testqset libqhullstatic.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.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
|
||||
|
||||
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.o stat.o geom2.o poly2.o merge.o \
|
||||
libqhull.o geom.o poly.o qset.o mem.o random.o
|
||||
|
||||
LIBQHULLS_OBJS_2= $(LIBQHULLS_OBJS_1) usermem.o userprintf.o io.o user.o
|
||||
|
||||
LIBQHULLS_OBJS= $(LIBQHULLS_OBJS_2) rboxlib.o userprintf_rbox.o
|
||||
|
||||
LIBQHULL_HDRS= user.h libqhull.h qhull_a.h geom.h \
|
||||
io.h mem.h merge.h poly.h random.h \
|
||||
qset.h stat.h
|
||||
|
||||
# CFILES ordered alphabetically after libqhull.c
|
||||
CFILES= ../qhull/unix.c libqhull.c geom.c geom2.c global.c io.c \
|
||||
mem.c merge.c poly.c poly2.c random.c rboxlib.c \
|
||||
qset.c stat.c user.c usermem.c userprintf.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.c ] || ln -s ../qconvex/qconvex.c
|
||||
[ -f qdelaun.c ] || ln -s ../qdelaunay/qdelaun.c
|
||||
[ -f qhalf.c ] || ln -s ../qhalf/qhalf.c
|
||||
[ -f qvoronoi.c ] || ln -s ../qvoronoi/qvoronoi.c
|
||||
[ -f rbox.c ] || ln -s ../rbox/rbox.c
|
||||
[ -f testqset.c ] || ln -s ../testqset/testqset.c
|
||||
[ -f unix.c ] || ln -s ../qhull/unix.c
|
||||
[ -f user_eg.c ] || ln -s ../user_eg/user_eg.c
|
||||
[ -f user_eg2.c ] || ln -s ../user_eg2/user_eg2.c
|
||||
|
||||
# compile qhull without using bin/libqhullstatic.a
|
||||
qhull_all: qconvex.o qdelaun.o qhalf.o qvoronoi.o unix.o user_eg.o user_eg2.o rbox.o testqset.o $(LIBQHULLS_OBJS)
|
||||
$(CC) -o qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qconvex.o
|
||||
$(CC) -o qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qdelaun.o
|
||||
$(CC) -o qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qhalf.o
|
||||
$(CC) -o qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qvoronoi.o
|
||||
$(CC) -o qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) unix.o
|
||||
$(CC) -o rbox $(CC_OPTS2) -lm $(LIBQHULLS_OBJS) rbox.o
|
||||
$(CC) -o user_eg $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) user_eg.o
|
||||
$(CC) -o user_eg2 $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_1) user_eg2.o usermem.o userprintf.o io.o
|
||||
$(CC) -o testqset $(CC_OPTS2) -lm mem.o qset.o usermem.o testqset.o
|
||||
-ar -rs libqhullstatic.a $(LIBQHULLS_OBJS)
|
||||
#libqhullstatic.a is not needed for qhull
|
||||
#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
|
||||
#ranlib libqhullstatic.a
|
||||
|
||||
qtest:
|
||||
@echo ============================================
|
||||
@echo == make qtest ==============================
|
||||
@echo ============================================
|
||||
@echo -n "== "
|
||||
@date
|
||||
@echo
|
||||
@echo Testing qset.c and mem.c with testqset
|
||||
./testqset 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
|
||||
206
xs/src/qhull/src/libqhull/Mborland
Normal file
206
xs/src/qhull/src/libqhull/Mborland
Normal file
@ -0,0 +1,206 @@
|
||||
#########################################################################
|
||||
# Borland C++ 4.02 for Win32 and DOS Power Pack #
|
||||
# Makefile for qhull and rbox #
|
||||
# #
|
||||
# make -fMborland all to produce qconvex, qhull, and rbox #
|
||||
# make -fMborland user_eg to produce user_eg #
|
||||
# make -fMborland user_eg2 to produce user_eg2 #
|
||||
# make -fMborland new to rebuild qhull and rbox from source #
|
||||
# make -fMborland clean to remove object files #
|
||||
# make -fMborland cleanall to remove all generated files #
|
||||
# make -fMborland test to test rbox and qhull #
|
||||
# #
|
||||
# Author: D. Zwick of Germany, C.B. Barber #
|
||||
#########################################################################
|
||||
|
||||
CC = bcc32 # 32 bit compiler for DOS
|
||||
# bcc32i - Intel's compiler
|
||||
LINKER = $(CC) # bcc calls tlink32 with needed options
|
||||
CFLAGS = -w- -A -O2
|
||||
# -w- no warnings, bcc doesn't handle assigns in conditions
|
||||
# -A Ansi standard
|
||||
# -X no auto-dependency outputs
|
||||
# -v debugging, use CCOPTS for both
|
||||
# -O2 optimization
|
||||
!if $d(_DPMI)
|
||||
LFLAGS = -WX -w- # -WX loads DPMI library
|
||||
!else
|
||||
LFLAGS = -lap -lx -lc
|
||||
# -lap 32-bit console application
|
||||
# -lx no map file
|
||||
# -lc case is significant
|
||||
!endif
|
||||
|
||||
EXERB = rbox
|
||||
EXEQH = qhull
|
||||
EXEQC = qconvex
|
||||
EXEQD = qdelaunay
|
||||
EXEQV = qvoronoi
|
||||
EXEQF = qhalf
|
||||
EXEEG = user_eg
|
||||
EXEEG2 = user_eg2
|
||||
|
||||
TMPFILE = BCC32tmp.cfg
|
||||
|
||||
OBJS1 = global.obj stat.obj geom2.obj poly2.obj merge.obj
|
||||
OBJS2 = libqhull.obj geom.obj poly.obj qset.obj mem.obj
|
||||
OBJS3 = random.obj usermem.obj userprintf.obj io.obj user.obj
|
||||
OBJS4 = rboxlib.obj random.obj usermem.obj userprintf_rbox.obj
|
||||
|
||||
HFILES1 = libqhull.h stat.h qhull_a.h user.h
|
||||
|
||||
|
||||
# General rules
|
||||
|
||||
.c.obj:
|
||||
$(CC) -c $(CFLAGS) $<
|
||||
|
||||
# Default
|
||||
|
||||
all: $(EXERB) $(EXEQH) $(EXEQC) $(EXEQD) $(EXEQV) $(EXEQF) test
|
||||
|
||||
help:
|
||||
@echo USAGE:
|
||||
@echo "make all to produce qhull, rbox, qconvex, qdelaun, qvoronoi, qhalf"
|
||||
@echo "make user_eg to produce user_eg"
|
||||
@echo "make user_eg2 to produce user_eg2"
|
||||
@echo "make new to rebuild qhull and rbox from source"
|
||||
@echo "make clean to remove object files"
|
||||
@echo "make cleanall to remove all generated file"
|
||||
@echo "make test to test rbox and qhull"
|
||||
@echo OPTIONS (default is 32-bit console app):
|
||||
@echo "-D_DPMI for C++ 4.01 and DOS Power Pack"
|
||||
|
||||
# Executables
|
||||
|
||||
$(EXEQH): ..\..\bin\$(EXEQH).exe
|
||||
@echo Made ..\..\bin\$(EXEQH).exe
|
||||
|
||||
unix.obj: ..\qhull\unix.c
|
||||
..\..\bin\$(EXEQH).exe: unix.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo unix.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEQC): ..\..\bin\$(EXEQC).exe
|
||||
@echo Made ..\..\bin\$(EXEQC).exe
|
||||
|
||||
qconvex.obj: ..\qconvex\qconvex.c
|
||||
..\..\bin\$(EXEQC).exe: qconvex.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo qconvex.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEQD): ..\..\bin\$(EXEQD).exe
|
||||
@echo Made ..\..\bin\$(EXEQD).exe
|
||||
|
||||
qdelaun.obj: ..\qdelaunay\qdelaun.c
|
||||
..\..\bin\$(EXEQD).exe: qdelaun.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo qdelaun.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEQV): ..\..\bin\$(EXEQV).exe
|
||||
@echo Made ..\..\bin\$(EXEQV).exe
|
||||
|
||||
qvoronoi.obj: ..\qvoronoi\qvoronoi.c
|
||||
..\..\bin\$(EXEQV).exe: qvoronoi.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo qvoronoi.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEQF): ..\..\bin\$(EXEQF).exe
|
||||
@echo Made ..\..\bin\$(EXEQF).exe
|
||||
|
||||
qhalf.obj: ..\qhalf\qhalf.c
|
||||
..\..\bin\$(EXEQF).exe: qhalf.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo qhalf.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEEG): ..\..\bin\$(EXEEG).exe
|
||||
@echo Made ..\..\bin\$(EXEEG).exe
|
||||
|
||||
user_eg.obj: ..\user_eg\user_eg.c
|
||||
..\..\bin\$(EXEEG).exe: user_eg.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo user_eg.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXEEG2): ..\..\bin\$(EXEEG2).exe
|
||||
@echo Made ..\..\bin\$(EXEEG2).exe
|
||||
|
||||
user_eg2.obj: ..\user_eg2\user_eg2.c
|
||||
..\..\bin\$(EXEEG2).exe: user_eg2.obj $(OBJS1) $(OBJS2) $(OBJS3)
|
||||
@echo user_eg2.obj > $(TMPFILE)
|
||||
@echo $(OBJS1) >> $(TMPFILE)
|
||||
@echo $(OBJS2) >> $(TMPFILE)
|
||||
@echo $(OBJS3) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
$(EXERB): ..\..\bin\$(EXERB).exe
|
||||
@echo Made ..\..\bin\$(EXERB).exe
|
||||
|
||||
rbox.obj: ..\rbox\rbox.c
|
||||
..\..\bin\$(EXERB).exe: rbox.obj $(OBJS4)
|
||||
@echo rbox.obj > $(TMPFILE)
|
||||
@echo $(OBJS4) >> $(TMPFILE)
|
||||
$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
|
||||
|
||||
# Test rbox and qhull
|
||||
|
||||
test:
|
||||
@..\..\bin\rbox D4 > test.x
|
||||
@..\..\bin\qhull <test.x
|
||||
@del test.x
|
||||
|
||||
# Clean up
|
||||
|
||||
clean:
|
||||
@del *.obj
|
||||
@del $(TMPFILE)
|
||||
|
||||
cleanall: clean
|
||||
@del ..\..\bin\$(EXERB).exe
|
||||
@del ..\..\bin\$(EXEQC).exe
|
||||
@del ..\..\bin\$(EXEQD).exe
|
||||
@del ..\..\bin\$(EXEQF).exe
|
||||
@del ..\..\bin\$(EXEQH).exe
|
||||
@del ..\..\bin\$(EXEQV).exe
|
||||
@del ..\..\bin\$(EXEEG).exe
|
||||
@del ..\..\bin\$(EXEEG2).exe
|
||||
@del ..\q_test.x
|
||||
@del ..\q_test.log.1
|
||||
|
||||
# Clean up and rebuild all
|
||||
|
||||
new: cleanall all
|
||||
|
||||
# Header file dependencies
|
||||
|
||||
libqhull.obj stat.obj user.obj global.obj usermem.obj userprintf.obj: $(HFILES1)
|
||||
random.obj: libqhull.h random.h
|
||||
geom.obj geom2.obj: $(HFILES1) geom.h
|
||||
poly.obj poly2.obj: $(HFILES1) poly.h
|
||||
io.obj: $(HFILES1) io.h
|
||||
merge.obj: $(HFILES1) merge.h
|
||||
mem.obj: mem.h
|
||||
qset.obj: qset.h mem.h
|
||||
unix.obj: libqhull.h user.h
|
||||
qconvex.obj: libqhull.h user.h
|
||||
qdelaun.obj: libqhull.h user.h
|
||||
qhalf.obj: libqhull.h user.h
|
||||
qvoronoi.obj: libqhull.h user.h
|
||||
rbox.obj: user.h
|
||||
1234
xs/src/qhull/src/libqhull/geom.c
Normal file
1234
xs/src/qhull/src/libqhull/geom.c
Normal file
File diff suppressed because it is too large
Load Diff
176
xs/src/qhull/src/libqhull/geom.h
Normal file
176
xs/src/qhull/src/libqhull/geom.h
Normal file
@ -0,0 +1,176 @@
|
||||
/*<html><pre> -<a href="qh-geom.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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- ======================== */
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="fabs_">-</a>
|
||||
|
||||
fabs_(a)
|
||||
returns the absolute value of a
|
||||
*/
|
||||
#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="fmax_">-</a>
|
||||
|
||||
fmax_(a,b)
|
||||
returns the maximum value of a and b
|
||||
*/
|
||||
#define fmax_( a,b ) ( ( a ) < ( b ) ? ( b ) : ( a ) )
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="fmin_">-</a>
|
||||
|
||||
fmin_(a,b)
|
||||
returns the minimum value of a and b
|
||||
*/
|
||||
#define fmin_( a,b ) ( ( a ) > ( b ) ? ( b ) : ( a ) )
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="maximize_">-</a>
|
||||
|
||||
maximize_(maxval, val)
|
||||
set maxval to val if val is greater than maxval
|
||||
*/
|
||||
#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="minimize_">-</a>
|
||||
|
||||
minimize_(minval, val)
|
||||
set minval to val if val is less than minval
|
||||
*/
|
||||
#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="det2_">-</a>
|
||||
|
||||
det2_(a1, a2,
|
||||
b1, b2)
|
||||
|
||||
compute a 2-d determinate
|
||||
*/
|
||||
#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="det3_">-</a>
|
||||
|
||||
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 ) )
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="dX">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
|
||||
2094
xs/src/qhull/src/libqhull/geom2.c
Normal file
2094
xs/src/qhull/src/libqhull/geom2.c
Normal file
File diff suppressed because it is too large
Load Diff
2217
xs/src/qhull/src/libqhull/global.c
Normal file
2217
xs/src/qhull/src/libqhull/global.c
Normal file
File diff suppressed because it is too large
Load Diff
264
xs/src/qhull/src/libqhull/index.htm
Normal file
264
xs/src/qhull/src/libqhull/index.htm
Normal file
@ -0,0 +1,264 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>Qhull functions, macros, and data structures</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code</a><br>
|
||||
<b>To:</b> <a href="#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document. -->
|
||||
|
||||
<h1>Qhull functions, macros, and data structures</h1>
|
||||
<blockquote>
|
||||
<p>The following sections provide an overview and index to
|
||||
Qhull's functions, macros, and data structures.
|
||||
Each section starts with an introduction.
|
||||
See also <a href=../../html/qh-code.htm#library>Calling
|
||||
Qhull from C programs</a> and <a href="../../html/qh-code.htm#cpp">Calling Qhull from C++ programs</a>.</p>
|
||||
|
||||
<p>Qhull uses the following conventions:</p>
|
||||
<blockquote>
|
||||
|
||||
<ul>
|
||||
<li>in code, global variables start with "qh "
|
||||
<li>in documentation, global variables start with 'qh.'
|
||||
<li>constants start with an upper case word
|
||||
<li>important globals include an '_'
|
||||
<li>functions, macros, and constants start with "qh_"</li>
|
||||
<li>data types end in "T"</li>
|
||||
<li>macros with arguments end in "_"</li>
|
||||
<li>iterators are macros that use local variables</li>
|
||||
<li>iterators for sets start with "FOREACH"</li>
|
||||
<li>iterators for lists start with "FORALL"</li>
|
||||
<li>qhull options are in single quotes (e.g., 'Pdn')</li>
|
||||
<li>lists are sorted alphabetically</li>
|
||||
<li>preprocessor directives on left margin for older compilers</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<p>
|
||||
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().
|
||||
<p>
|
||||
When reading code with an editor, a search for
|
||||
'<i>"function</i>'
|
||||
will locate the header of <i>qh_function</i>. A search for '<i>* function</i>'
|
||||
will locate the tail of <i>qh_function</i>.
|
||||
|
||||
<p>A useful starting point is <a href="libqhull.h">libqhull.h</a>. It defines most
|
||||
of Qhull data structures and top-level functions. Search for <i>'PFn'</i> to
|
||||
determine the corresponding constant in Qhull. Search for <i>'Fp'</i> to
|
||||
determine the corresponding <a href="libqhull.h#qh_PRINT">qh_PRINT...</a> constant.
|
||||
Search <a href="io.c">io.c</a> to learn how the print function is implemented.</p>
|
||||
|
||||
<p>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.
|
||||
<ul>
|
||||
<li>In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
|
||||
<li>Opera 12.10
|
||||
<ol>
|
||||
<li>In Tools > Preferences > Advanced > Downloads
|
||||
<li>Uncheck 'Hide file types opened with Opera'
|
||||
<li>Quick find 'html'
|
||||
<li>Select 'text/html' > Edit
|
||||
<li>Add File extensions 'c,h,'
|
||||
<li>Click 'OK'
|
||||
</ol>
|
||||
<li>Internet Explorer -- Mime types are not available from 'Internet Options'. Is there a registry key for these settings?
|
||||
<li>Firefox -- Mime types are not available from 'Preferences'. Is there an add-on to change the file extensions for a mime type?
|
||||
<li>Chrome -- Can Chrome be configured?
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
Please report documentation and link errors
|
||||
to <a href="mailto:qhull-bug@qhull.org">qhull-bug@qhull.org</a>.
|
||||
</blockquote>
|
||||
|
||||
<p><b>Copyright © 1997-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOP">»</a><a name="TOC">Qhull files</a> </h2>
|
||||
<blockquote>
|
||||
|
||||
<p>This sections lists the .c and .h files for Qhull. Please
|
||||
refer to these files for detailed information.</p>
|
||||
<blockquote>
|
||||
|
||||
<dl>
|
||||
<dt><a href="../../Makefile"><b>Makefile</b></a><b>, </b><a href="../../CMakeLists.txt"><b>CMakeLists.txt</b></a></dt>
|
||||
<dd><tt>Makefile</tt> is preconfigured for gcc. <tt>CMakeLists.txt</tt> supports multiple
|
||||
platforms with <a href=http://www.cmake.org/>CMake</a>.
|
||||
Qhull includes project files for Visual Studio and Qt.
|
||||
</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="libqhull.h"><b>libqhull.h</b></a> </dt>
|
||||
<dd>Include file for the Qhull library (<tt>libqhull.so</tt>, <tt>qhull.dll</tt>, <tt>libqhullstatic.a</tt>).
|
||||
Data structures are documented under <a href="qh-poly.htm">Poly</a>.
|
||||
Global variables are documented under <a href="qh-globa.htm">Global</a>.
|
||||
Other data structures and variables are documented under
|
||||
<a href="qh-qhull.htm#TOC">Qhull</a> or <a href="qh-geom.htm"><b>Geom</b></a><b>.</b></dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-geom.htm"><b>Geom</b></a><b>, </b>
|
||||
<a href="geom.h"><b>geom.h</b></a><b>, </b>
|
||||
<a href="geom.c"><b>geom.c</b></a><b>, </b>
|
||||
<a href="geom2.c"><b>geom2.c</b></a><b>, </b>
|
||||
<a href="random.c"><b>random.c</b></a><b>, </b>
|
||||
<a href="random.h"><b>random.h</b></a></dt>
|
||||
<dd>Geometric routines. These routines implement mathematical
|
||||
functions such as Gaussian elimination and geometric
|
||||
routines needed for Qhull. Frequently used routines are
|
||||
in <tt>geom.c</tt> while infrequent ones are in <tt>geom2.c</tt>.
|
||||
</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-globa.htm"><b>Global</b></a><b>, </b>
|
||||
<a href="global.c"><b>global.c</b></a><b>, </b>
|
||||
<a href="libqhull.h"><b>libqhull.h</b></a> </dt>
|
||||
<dd>Global routines. Qhull uses a global data structure, <tt>qh</tt>,
|
||||
to store globally defined constants, lists, sets, and
|
||||
variables.
|
||||
<tt>global.c</tt> initializes and frees these
|
||||
structures. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-io.htm"><b>Io</b></a><b>, </b><a href="io.h"><b>io.h</b></a><b>,
|
||||
</b><a href="io.c"><b>io.c</b></a> </dt>
|
||||
<dd>Input and output routines. Qhull provides a wide range of
|
||||
input and output options.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-mem.htm"><b>Mem</b></a><b>, </b>
|
||||
<a href="mem.h"><b>mem.h</b></a><b>, </b>
|
||||
<a href="mem.c"><b>mem.c</b></a> </dt>
|
||||
<dd>Memory routines. Qhull provides memory allocation and
|
||||
deallocation. It uses quick-fit allocation.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-merge.htm"><b>Merge</b></a><b>, </b>
|
||||
<a href="merge.h"><b>merge.h</b></a><b>, </b>
|
||||
<a href="merge.c"><b>merge.c</b></a> </dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-poly.htm"><b>Poly</b></a><b>, </b>
|
||||
<a href="poly.h"><b>poly.h</b></a><b>, </b>
|
||||
<a href="poly.c"><b>poly.c</b></a><b>, </b>
|
||||
<a href="poly2.c"><b>poly2.c</b></a><b>, </b>
|
||||
<a href="libqhull.h"><b>libqhull.h</b></a> </dt>
|
||||
<dd>Polyhedral routines. Qhull produces a polyhedron as a
|
||||
list of facets with vertices, neighbors, ridges, and
|
||||
geometric information. <tt>libqhull.h</tt> defines the main
|
||||
data structures. Frequently used routines are in <tt>poly.c</tt>
|
||||
while infrequent ones are in <tt>poly2.c</tt>.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-qhull.htm#TOC"><b>Qhull</b></a><b>, </b>
|
||||
<a href="libqhull.c"><b>libqhull.c</b></a><b>, </b>
|
||||
<a href="libqhull.h"><b>libqhull.h</b></a><b>, </b>
|
||||
<a href="qhull_a.h"><b>qhull_a.h</b></a><b>, </b>
|
||||
<a href="../qhullo/unix.c"><b>unix.c</b></a> <b>, </b>
|
||||
<a href="../qconvex/qconvex.c"><b>qconvex.c</b></a> <b>, </b>
|
||||
<a href="../qdelaunay/qdelaun.c"><b>qdelaun.c</b></a> <b>, </b>
|
||||
<a href="../qhalf/qhalf.c"><b>qhalf.c</b></a> <b>, </b>
|
||||
<a href="../qvoronoi/qvoronoi.c"><b>qvoronoi.c</b></a> </dt>
|
||||
<dd>Top-level routines. The Quickhull algorithm is
|
||||
implemented by <tt>libqhull.c</tt>. <tt>qhull_a.h</tt>
|
||||
includes all header files. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-set.htm"><b>Set</b></a><b>, </b>
|
||||
<a href="qset.h"><b>qset.h</b></a><b>, </b>
|
||||
<a href="qset.c"><b>qset.c</b></a> </dt>
|
||||
<dd>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. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-stat.htm"><b>Stat</b></a><b>, </b>
|
||||
<a href="stat.h"><b>stat.h</b></a><b>, </b>
|
||||
<a href="stat.c"><b>stat.c</b></a> </dt>
|
||||
<dd>Statistical routines. Qhull maintains statistics about
|
||||
its implementation. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-user.htm"><b>User</b></a><b>, </b>
|
||||
<a href="user.h"><b>user.h</b></a><b>, </b>
|
||||
<a href="user.c"><b>user.c</b></a><b>, </b>
|
||||
<a href="../user_eg/user_eg.c"><b>user_eg.c</b></a><b>, </b>
|
||||
<a href="../user_eg2/user_eg2.c"><b>user_eg2.c</b></a><b>, </b>
|
||||
</dt>
|
||||
<dd>User-defined routines. Qhull allows the user to configure
|
||||
the code with defined constants and specialized routines.
|
||||
</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
4062
xs/src/qhull/src/libqhull/io.c
Normal file
4062
xs/src/qhull/src/libqhull/io.c
Normal file
File diff suppressed because it is too large
Load Diff
159
xs/src/qhull/src/libqhull/io.h
Normal file
159
xs/src/qhull/src/libqhull/io.h
Normal file
@ -0,0 +1,159 @@
|
||||
/*<html><pre> -<a href="qh-io.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 ==================*/
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_MAXfirst">-</a>
|
||||
|
||||
qh_MAXfirst
|
||||
maximum length of first two lines of stdin
|
||||
*/
|
||||
#define qh_MAXfirst 200
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_MINradius">-</a>
|
||||
|
||||
qh_MINradius
|
||||
min radius for Gp and Gv, fraction of maxcoord
|
||||
*/
|
||||
#define qh_MINradius 0.02
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_GEOMepsilon">-</a>
|
||||
|
||||
qh_GEOMepsilon
|
||||
adjust outer planes for 'lines closer' and geomview roundoff.
|
||||
This prevents bleed through.
|
||||
*/
|
||||
#define qh_GEOMepsilon 2e-3
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_WHITESPACE">-</a>
|
||||
|
||||
qh_WHITESPACE
|
||||
possible values of white space
|
||||
*/
|
||||
#define qh_WHITESPACE " \n\t\v\r\f"
|
||||
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="RIDGE">-</a>
|
||||
|
||||
qh_RIDGE
|
||||
to select which ridges to print in qh_eachvoronoi
|
||||
*/
|
||||
typedef enum
|
||||
{
|
||||
qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
|
||||
}
|
||||
qh_RIDGE;
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>--------------------------------</a><a name="printvridgeT">-</a>
|
||||
|
||||
printvridgeT
|
||||
prints results of qh_printvdiagram
|
||||
|
||||
see:
|
||||
<a href="io.c#printvridge">qh_printvridge</a> 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 */
|
||||
1403
xs/src/qhull/src/libqhull/libqhull.c
Normal file
1403
xs/src/qhull/src/libqhull/libqhull.c
Normal file
File diff suppressed because it is too large
Load Diff
1140
xs/src/qhull/src/libqhull/libqhull.h
Normal file
1140
xs/src/qhull/src/libqhull/libqhull.h
Normal file
File diff suppressed because it is too large
Load Diff
67
xs/src/qhull/src/libqhull/libqhull.pro
Normal file
67
xs/src/qhull/src/libqhull/libqhull.pro
Normal file
@ -0,0 +1,67 @@
|
||||
# -------------------------------------------------
|
||||
# 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
|
||||
576
xs/src/qhull/src/libqhull/mem.c
Normal file
576
xs/src/qhull/src/libqhull/mem.c
Normal file
@ -0,0 +1,576 @@
|
||||
/*<html><pre> -<a href="qh-mem.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <string.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#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 ======== */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="intcompare">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="memalloc">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="memcheck">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="memfree">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="memfreeshort">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="meminit">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="meminitbuffers">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="memsetup">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="memsize">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="memstatistics">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="NOmem">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="memtotlong">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
222
xs/src/qhull/src/libqhull/mem.h
Normal file
222
xs/src/qhull/src/libqhull/mem.h
Normal file
@ -0,0 +1,222 @@
|
||||
/*<html><pre> -<a href="qh-mem.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdio.h>
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="NOmem">-</a>
|
||||
|
||||
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
|
||||
*/
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>-------------------------------</a><a name="TRACEshort">-</a>
|
||||
|
||||
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 <a href="user.h#MEMalign">qh_MEMalign</a> 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 */
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="ptr_intT">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="qhmemT">-</a>
|
||||
|
||||
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 ====================*/
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="memalloc_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-mem.htm#TOC"
|
||||
>--------------------------------</a><a name="memfree_">-</a>
|
||||
|
||||
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 */
|
||||
3628
xs/src/qhull/src/libqhull/merge.c
Normal file
3628
xs/src/qhull/src/libqhull/merge.c
Normal file
File diff suppressed because it is too large
Load Diff
178
xs/src/qhull/src/libqhull/merge.h
Normal file
178
xs/src/qhull/src/libqhull/merge.h
Normal file
@ -0,0 +1,178 @@
|
||||
/*<html><pre> -<a href="qh-merge.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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- ==============*/
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_ANGLEredundant">-</a>
|
||||
|
||||
qh_ANGLEredundant
|
||||
indicates redundant merge in mergeT->angle
|
||||
*/
|
||||
#define qh_ANGLEredundant 6.0
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_ANGLEdegen">-</a>
|
||||
|
||||
qh_ANGLEdegen
|
||||
indicates degenerate facet in mergeT->angle
|
||||
*/
|
||||
#define qh_ANGLEdegen 5.0
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_ANGLEconcave">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="MRG">-</a>
|
||||
|
||||
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;
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_MERGEapex">-</a>
|
||||
|
||||
qh_MERGEapex
|
||||
flag for qh_mergefacet() to indicate an apex merge
|
||||
*/
|
||||
#define qh_MERGEapex True
|
||||
|
||||
/*============ -structures- ====================*/
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="mergeT">-</a>
|
||||
|
||||
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- =========================*/
|
||||
|
||||
/*-<a href="qh-merge.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHmerge_">-</a>
|
||||
|
||||
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 <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#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 */
|
||||
1205
xs/src/qhull/src/libqhull/poly.c
Normal file
1205
xs/src/qhull/src/libqhull/poly.c
Normal file
File diff suppressed because it is too large
Load Diff
296
xs/src/qhull/src/libqhull/poly.h
Normal file
296
xs/src/qhull/src/libqhull/poly.h
Normal file
@ -0,0 +1,296 @@
|
||||
/*<html><pre> -<a href="qh-poly.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 ========================== */
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>--------------------------------</a><a name="ALGORITHMfault">-</a>
|
||||
|
||||
ALGORITHMfault
|
||||
use as argument to checkconvex() to report errors during buildhull
|
||||
*/
|
||||
#define qh_ALGORITHMfault 0
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="DATAfault">-</a>
|
||||
|
||||
DATAfault
|
||||
use as argument to checkconvex() to report errors during initialhull
|
||||
*/
|
||||
#define qh_DATAfault 1
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="DUPLICATEridge">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="MERGEridge">-</a>
|
||||
|
||||
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- =========================*/
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLfacet_">-</a>
|
||||
|
||||
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 )
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLnew_facets">-</a>
|
||||
|
||||
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 )
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLvertex_">-</a>
|
||||
|
||||
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 )
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLvisible_facets">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLsame_">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FORALLsame_cycle_">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHneighborA_">-</a>
|
||||
|
||||
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:
|
||||
<a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#define FOREACHneighborA_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighborA)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHvisible_">-</a>
|
||||
|
||||
FOREACHvisible_( facets ) { ... }
|
||||
assign 'visible' to each facet in facets
|
||||
|
||||
notes:
|
||||
uses 'facetT *facet, *facetp;'
|
||||
see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHnewfacet_">-</a>
|
||||
|
||||
FOREACHnewfacet_( facets ) { ... }
|
||||
assign 'newfacet' to each facet in facets
|
||||
|
||||
notes:
|
||||
uses 'facetT *newfacet, *newfacetp;'
|
||||
see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHvertexA_">-</a>
|
||||
|
||||
FOREACHvertexA_( vertices ) { ... }
|
||||
assign 'vertexA' to each vertex in vertices
|
||||
|
||||
notes:
|
||||
uses 'vertexT *vertexA, *vertexAp;'
|
||||
see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
|
||||
|
||||
/*-<a href="qh-poly.htm#TOC"
|
||||
>--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
|
||||
|
||||
FOREACHvertexreverse12_( vertices ) { ... }
|
||||
assign 'vertex' to each vertex in vertices
|
||||
reverse order of first two vertices
|
||||
|
||||
notes:
|
||||
uses 'vertexT *vertex, *vertexp;'
|
||||
see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
*/
|
||||
#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 */
|
||||
3222
xs/src/qhull/src/libqhull/poly2.c
Normal file
3222
xs/src/qhull/src/libqhull/poly2.c
Normal file
File diff suppressed because it is too large
Load Diff
295
xs/src/qhull/src/libqhull/qh-geom.htm
Normal file
295
xs/src/qhull/src/libqhull/qh-geom.htm
Normal file
@ -0,0 +1,295 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>geom.c, geom2.c -- geometric and floating point routines</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm#TOC">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document. -->
|
||||
|
||||
<h2>geom.c, geom2.c, random.c -- geometric and floating point routines</h2>
|
||||
<blockquote>
|
||||
<p>Geometrically, a vertex is a point with <em>d</em> coordinates
|
||||
and a facet is a halfspace. A <em>halfspace</em> is defined by an
|
||||
oriented hyperplane through the facet's vertices. A <em>hyperplane</em>
|
||||
is defined by <em>d</em> normalized coefficients and an offset. A
|
||||
point is <em>above</em> a facet if its distance to the facet is
|
||||
positive.</p>
|
||||
|
||||
<p>Qhull uses floating point coordinates for input points,
|
||||
vertices, halfspace equations, centrums, and an interior point.</p>
|
||||
|
||||
<p>Qhull may be configured for single precision or double
|
||||
precision floating point arithmetic (see <a href="user.h#realT">realT</a>
|
||||
). </p>
|
||||
|
||||
<p>Each floating point operation may incur round-off error (see
|
||||
<a href="qh-merge.htm#TOC">Merge</a>). 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. </p>
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <b>Geom</b>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
|
||||
<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
|
||||
<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a> •
|
||||
<a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a> •
|
||||
<a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a> </p>
|
||||
|
||||
<h3>Index to <a href="geom.c">geom.c</a>,
|
||||
<a href="geom2.c">geom2.c</a>, <a href="geom.h">geom.h</a>,
|
||||
<a href="random.c">random.c</a>, <a href="random.h">random.h</a>
|
||||
</h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="#gtype">geometric data types and constants</a> </li>
|
||||
<li><a href="#gmacro">mathematical macros</a>
|
||||
</li>
|
||||
<li><a href="#gmath">mathematical functions</a> </li>
|
||||
<li><a href="#gcomp">computational geometry functions</a> </li>
|
||||
<li><a href="#gpoint">point array functions</a> </li>
|
||||
<li><a href="#gfacet">geometric facet functions</a> </li>
|
||||
<li><a href="#ground">geometric roundoff functions</a></li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gtype">geometric data types
|
||||
and constants</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="libqhull.h#coordT">coordT</a> coordinates and
|
||||
coefficients are stored as realT</li>
|
||||
<li><a href="libqhull.h#pointT">pointT</a> a point is an array
|
||||
of <tt>DIM3</tt> coordinates </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gmacro">mathematical macros</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="geom.h#fabs_">fabs_</a> returns the absolute
|
||||
value of a </li>
|
||||
<li><a href="geom.h#fmax_">fmax_</a> returns the maximum
|
||||
value of a and b </li>
|
||||
<li><a href="geom.h#fmin_">fmin_</a> returns the minimum
|
||||
value of a and b </li>
|
||||
<li><a href="geom.h#maximize_">maximize_</a> maximize a value
|
||||
</li>
|
||||
<li><a href="geom.h#minimize_">minimize_</a> minimize a value
|
||||
</li>
|
||||
<li><a href="geom.h#det2_">det2_</a> compute a 2-d
|
||||
determinate </li>
|
||||
<li><a href="geom.h#det3_">det3_</a> compute a 3-d
|
||||
determinate </li>
|
||||
<li><a href="geom.h#dX">dX, dY, dZ</a> compute the difference
|
||||
between two coordinates </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gmath">mathematical functions</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="geom.c#backnormal">qh_backnormal</a> solve for
|
||||
normal using back substitution </li>
|
||||
<li><a href="geom2.c#crossproduct">qh_crossproduct</a>
|
||||
compute the cross product of two 3-d vectors </li>
|
||||
<li><a href="geom2.c#determinant">qh_determinant</a> compute
|
||||
the determinant of a square matrix </li>
|
||||
<li><a href="geom.c#gausselim">qh_gausselim</a> Gaussian
|
||||
elimination with partial pivoting </li>
|
||||
<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
|
||||
implements Gram-Schmidt orthogonalization by rows </li>
|
||||
<li><a href="geom2.c#maxabsval">qh_maxabsval</a> return max
|
||||
absolute value of a vector </li>
|
||||
<li><a href="geom2.c#minabsval">qh_minabsval</a> return min
|
||||
absolute value of a dim vector </li>
|
||||
<li><a href="geom2.c#mindiff">qh_mindiff</a> return index of
|
||||
min absolute difference of two vectors </li>
|
||||
<li><a href="geom.c#normalize">qh_normalize</a> normalize a
|
||||
vector </li>
|
||||
<li><a href="geom.c#normalize2">qh_normalize2</a> normalize a
|
||||
vector and report if too small </li>
|
||||
<li><a href="geom2.c#printmatrix">qh_printmatrix</a> print
|
||||
matrix given by row vectors </li>
|
||||
<li><a href="random.c#rand">qh_rand/srand</a> generate random
|
||||
numbers </li>
|
||||
<li><a href="random.c#randomfactor">qh_randomfactor</a> return
|
||||
a random factor near 1.0 </li>
|
||||
<li><a href="random.c#randommatrix">qh_randommatrix</a>
|
||||
generate a random dimXdim matrix in range (-1,1) </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gcomp">computational geometry functions</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="geom2.c#detsimplex">qh_detsimplex</a> compute
|
||||
determinate of a simplex of points </li>
|
||||
<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
|
||||
<li><a href="geom2.c#distnorm">qh_distnorm</a> compute
|
||||
distance from point to hyperplane as defined by normal and offset</li>
|
||||
<li><a href="geom2.c#facetarea_simplex">qh_facetarea_simplex</a>
|
||||
return area of a simplex</li>
|
||||
<li><a href="geom.c#getangle">qh_getangle</a> return cosine
|
||||
of angle (i.e., dot product) </li>
|
||||
<li><a href="geom.c#getcenter">qh_getcenter</a> return
|
||||
arithmetic center for a set of vertices </li>
|
||||
<li><a href="geom2.c#pointdist">qh_pointdist</a> return
|
||||
distance between two points </li>
|
||||
<li><a href="geom2.c#rotatepoints">qh_rotatepoints</a> rotate
|
||||
numpoints points by a row matrix </li>
|
||||
<li><a href="geom2.c#sethalfspace">qh_sethalfspace</a> set
|
||||
coords to dual of halfspace relative to an interior point </li>
|
||||
<li><a href="geom.c#sethyperplane_det">qh_sethyperplane_det</a>
|
||||
return hyperplane for oriented simplex using determinates
|
||||
</li>
|
||||
<li><a href="geom.c#sethyperplane_gauss">qh_sethyperplane_gauss</a>
|
||||
return hyperplane for oriented simplex using Gaussian
|
||||
elimination </li>
|
||||
<li><a href="geom2.c#voronoi_center">qh_voronoi_center</a>
|
||||
return Voronoi center for a set of points </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gpoint">point array functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="geom2.c#copypoints">qh_copypoints</a> return
|
||||
malloc'd copy of points</li>
|
||||
<li><a href="geom2.c#joggleinput">qh_joggleinput</a> joggle
|
||||
input points by qh.JOGGLEmax </li>
|
||||
<li><a href="geom2.c#maxmin">qh_maxmin</a> return max/min
|
||||
points for each dimension</li>
|
||||
<li><a href="geom2.c#maxsimplex">qh_maxsimplex</a> determines
|
||||
maximum simplex for a set of points </li>
|
||||
<li><a href="geom2.c#printpoints">qh_printpoints</a> print ids for a
|
||||
set of points </li>
|
||||
<li><a href="geom2.c#projectinput">qh_projectinput</a> project
|
||||
input using qh DELAUNAY and qh low_bound/high_bound </li>
|
||||
<li><a href="geom2.c#projectpoints">qh_projectpoints</a>
|
||||
project points along one or more dimensions </li>
|
||||
<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
|
||||
input points using row matrix </li>
|
||||
<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
|
||||
input points using qh low_bound/high_bound </li>
|
||||
<li><a href="geom2.c#scalelast">qh_scalelast</a> scale last
|
||||
coordinate to [0,m] for Delaunay triangulations </li>
|
||||
<li><a href="geom2.c#scalepoints">qh_scalepoints</a> scale
|
||||
points to new lowbound and highbound </li>
|
||||
<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
|
||||
points to paraboloid for Delaunay triangulation </li>
|
||||
<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
|
||||
generate dual for halfspace intersection with interior
|
||||
point </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="gfacet">geometric facet functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="geom.c#distplane">qh_distplane</a> return
|
||||
distance from point to facet </li>
|
||||
<li><a href="geom2.c#facetarea">qh_facetarea</a> return area
|
||||
of a facet </li>
|
||||
<li><a href="geom2.c#facetcenter">qh_facetcenter</a> return
|
||||
Voronoi center for a facet's vertices </li>
|
||||
<li><a href="geom.c#findbest">qh_findbest</a> find visible
|
||||
facet or best facet for a point </li>
|
||||
<li><a href="geom.c#findbesthorizon">qh_findbesthorizon</a>
|
||||
update best new facet with horizon facets</li>
|
||||
<li><a href="geom.c#findbestnew">qh_findbestnew</a> find best
|
||||
new facet for point </li>
|
||||
<li><a href="geom2.c#getarea">qh_getarea</a> get area of all
|
||||
facets in facetlist, collect statistics </li>
|
||||
<li><a href="geom.c#getcentrum">qh_getcentrum</a> return
|
||||
centrum for a facet </li>
|
||||
<li><a href="geom.c#getdistance">qh_getdistance</a> returns
|
||||
the max and min distance of a facet's vertices to a
|
||||
neighboring facet</li>
|
||||
<li><a href="geom2.c#findgooddist">qh_findgooddist</a> find
|
||||
best good facet visible for point from facet </li>
|
||||
<li><a href="geom2.c#inthresholds">qh_inthresholds</a> return
|
||||
True if facet normal within 'Pdn' and 'PDn'</li>
|
||||
<li><a href="geom2.c#orientoutside">qh_orientoutside</a>
|
||||
orient facet so that <tt>qh.interior_point</tt> is inside</li>
|
||||
<li><a href="geom.c#projectpoint">qh_projectpoint</a> project
|
||||
point onto a facet </li>
|
||||
<li><a href="geom.c#setfacetplane">qh_setfacetplane</a> sets
|
||||
the hyperplane for a facet </li>
|
||||
<li><a href="geom2.c#sharpnewfacets">qh_sharpnewfacets</a> true
|
||||
if new facets contains a sharp corner</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-geom.htm#TOC">»</a><a name="ground">geometric roundoff functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="geom2.c#detjoggle">qh_detjoggle</a> determine
|
||||
default joggle for points and distance roundoff error</li>
|
||||
<li><a href="geom2.c#detroundoff">qh_detroundoff</a>
|
||||
determine maximum roundoff error and other precision constants</li>
|
||||
<li><a href="geom2.c#distround">qh_distround</a> compute
|
||||
maximum roundoff error due to a distance computation to a
|
||||
normalized hyperplane</li>
|
||||
<li><a href="geom2.c#divzero">qh_divzero</a> divide by a
|
||||
number that is nearly zero </li>
|
||||
<li><a href="geom2.c#maxouter">qh_maxouter</a> return maximum outer
|
||||
plane</li>
|
||||
<li><a href="geom2.c#outerinner">qh_outerinner</a> return actual
|
||||
outer and inner planes
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
|
||||
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
165
xs/src/qhull/src/libqhull/qh-globa.htm
Normal file
165
xs/src/qhull/src/libqhull/qh-globa.htm
Normal file
@ -0,0 +1,165 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>global.c -- global variables and their functions</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document. -->
|
||||
|
||||
<h2>global.c -- global variables and their functions</h2>
|
||||
<blockquote>
|
||||
<p>Qhull uses a global data structure, <tt>qh</tt>, 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
|
||||
<a href="user.h#QHpointer">QHpointer</a>.
|
||||
</p>
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <b>Global</b> •
|
||||
<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
|
||||
<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a> •
|
||||
<a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a> •
|
||||
<a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a> </p>
|
||||
|
||||
<h3>Index to <a href="global.c">global.c</a> and
|
||||
<a href="libqhull.h">libqhull.h</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="#ovar">Qhull's global variables</a> </li>
|
||||
<li><a href="#ofunc">Global variable and initialization
|
||||
routines</a> </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-globa.htm#TOC">»</a><a name="ovar">Qhull's global
|
||||
variables</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href=global.c#qh_version>qh_version</a> version string
|
||||
<li><a href="libqhull.h#qh">qh</a> all global variables for
|
||||
qhull are in <tt>qh,qhmem</tt>, and <tt>qhstat</tt></li>
|
||||
<li><a href="libqhull_r.h#qh">QHULL_LIB_CHECK</a> Check for compatible library</li>
|
||||
<li><a href="libqhull.h#qh-const">qh constants</a> configuration
|
||||
flags and constants for Qhull </li>
|
||||
<li><a href="libqhull.h#qh-prec">qh precision constants</a>
|
||||
precision constants for Qhull </li>
|
||||
<li><a href="libqhull.h#qh-codetern">qh internal constants</a>
|
||||
internal constants for Qhull </li>
|
||||
<li><a href="libqhull.h#qh-lists">qh facet and vertex lists</a>
|
||||
lists of facets and vertices </li>
|
||||
<li><a href="libqhull.h#qh-var">qh global variables</a> minimum
|
||||
and maximum distances, next visit ids, several flags, and
|
||||
other global variables. </li>
|
||||
<li><a href="libqhull.h#qh-set">qh global sets</a> global sets
|
||||
for merging, hashing, input, etc. </li>
|
||||
<li><a href="libqhull.h#qh-buf">qh global buffers</a> buffers
|
||||
for matrix operations and input </li>
|
||||
<li><a href="libqhull.h#qh-static">qh static variables</a>
|
||||
static variables for individual functions </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-globa.htm#TOC">»</a><a name="ofunc">Global variable and
|
||||
initialization routines</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="global.c#appendprint">qh_appendprint</a> append
|
||||
output format to <tt>qh.PRINTout</tt> </li>
|
||||
<li><a href="global.c#freebuffers">qh_freebuffers</a> free
|
||||
global memory buffers </li>
|
||||
<li><a href="global.c#freeqhull">qh_freeqhull</a> free memory
|
||||
used by qhull </li>
|
||||
<li><a href="global.c#init_A">qh_init_A</a> called before
|
||||
error handling initialized </li>
|
||||
<li><a href="global.c#init_B">qh_init_B</a> called after
|
||||
points are defined </li>
|
||||
<li><a href="global.c#init_qhull_command">qh_init_qhull_command</a>
|
||||
build <tt>qh.qhull_command</tt> from <tt>argc/argv</tt></li>
|
||||
<li><a href="global.c#initflags">qh_initflags</a> set flags
|
||||
and constants from command line </li>
|
||||
<li><a href="global.c#initqhull_buffers">qh_initqhull_buffers</a>
|
||||
initialize global memory buffers </li>
|
||||
<li><a href="global.c#initqhull_globals">qh_initqhull_globals</a>
|
||||
initialize global variables </li>
|
||||
<li><a href="global.c#initqhull_mem">qh_initqhull_mem</a>
|
||||
initialize Qhull memory management </li>
|
||||
<li><a href="global.c#initqhull_start">qh_initqhull_start</a>
|
||||
allocate qh_qh and call qh_initqhull_start2()
|
||||
<li><a href="global.c#initqhull_start2">qh_initqhull_start2</a>
|
||||
initialize default values at Qhull startup </li>
|
||||
<li><a href="global.c#initthresholds">qh_initthresholds</a>
|
||||
initialize 'Pdn' and 'PDn' thresholds </li>
|
||||
<li><a href="global.c#lib_check">qh_lib_check</a> check for compatible Qhull library. Invoked by QHULL_LIB_CHECK at start of each program.</li>
|
||||
<li><a href="global.c#option">qh_option</a> append option
|
||||
description to <tt>qh.global_options</tt> </li>
|
||||
<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
|
||||
restores a previously saved qhull </li>
|
||||
<li><a href="global.c#save_qhull">qh_save_qhull</a> saves
|
||||
qhull for a later qh_restore_qhull() </li>
|
||||
<li><a href="global.c#strtol">qh_strtol</a> duplicates
|
||||
strtod() and strtol() </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
305
xs/src/qhull/src/libqhull/qh-io.htm
Normal file
305
xs/src/qhull/src/libqhull/qh-io.htm
Normal file
@ -0,0 +1,305 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>io.c -- input and output operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>io.c -- input and output operations</h2>
|
||||
<blockquote>
|
||||
|
||||
<p>Qhull provides a wide range of input
|
||||
and output options. To organize the code, most output formats use
|
||||
the same driver: </p>
|
||||
|
||||
<pre>
|
||||
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 );
|
||||
</pre>
|
||||
|
||||
<p>Note the 'printall' flag. It selects whether or not
|
||||
qh_skipfacet() is tested. </p>
|
||||
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a> <a name="TOC">•</a>
|
||||
<a href="qh-globa.htm#TOC">Global</a> • <b>Io</b> •
|
||||
<a href="qh-mem.htm#TOC">Mem</a> • <a href="qh-merge.htm#TOC">Merge</a> •
|
||||
<a href="qh-poly.htm#TOC">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a> •
|
||||
<a href="qh-set.htm#TOC">Set</a> • <a href="qh-stat.htm#TOC">Stat</a> •
|
||||
<a href="qh-user.htm#TOC">User</a> </p>
|
||||
|
||||
<h3>Index to <a href="io.c">io.c</a> and <a href="io.h">io.h</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="#iconst">io.h constants and types</a> </li>
|
||||
<li><a href="#ilevel">User level functions</a> </li>
|
||||
<li><a href="#iprint">Print functions for all output formats</a></li>
|
||||
<li><a href="#itext">Text output functions</a> </li>
|
||||
<li><a href="#iutil">Text utility functions</a></li>
|
||||
<li><a href="#igeom">Geomview output functions</a> </li>
|
||||
<li><a href="#iview">Geomview utility functions</a></li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="iconst">io.h constants and types</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="io.h#qh_MAXfirst">qh_MAXfirst</a> maximum length
|
||||
of first two lines of stdin </li>
|
||||
<li><a href="io.h#qh_WHITESPACE">qh_WHITESPACE</a> possible
|
||||
values of white space </li>
|
||||
<li><a href="io.h#printvridgeT">printvridgeT</a> function to
|
||||
print results of qh_printvdiagram or qh_eachvoronoi</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="ilevel">User level functions</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="io.c#copyfilename">qh_copyfilename</a>
|
||||
copy filename identified by qh_skipfilename
|
||||
<li><a href="io.c#eachvoronoi_all">qh_eachvoronoi_all</a>
|
||||
visit each Voronoi ridge of the Voronoi diagram
|
||||
<li><a href="io.c#prepare_output">qh_prepare_output</a>
|
||||
prepare Qhull for output (called by qh_produce_output())
|
||||
<li><a href="io.c#printhelp_degenerate">qh_printhelp_degenerate</a>
|
||||
prints descriptive message for precision error </li>
|
||||
<li><a href="io.c#printhelp_singular">qh_printhelp_singular</a>
|
||||
print help message for singular data </li>
|
||||
<li><a href="libqhull.c#printsummary">qh_printsummary</a> print
|
||||
summary ('s')</li>
|
||||
<li><a href="io.c#produce_output">qh_produce_output</a>
|
||||
prints out the result of qhull()</li>
|
||||
<li><a href="io.c#produce_output">qh_produce_output2</a>
|
||||
prints out the result of qhull() without calling qh_prepare_output()</li>
|
||||
<li><a href="io.c#readfeasible">qh_readfeasible</a> read
|
||||
interior point from remainder and qh fin ('H')</li>
|
||||
<li><a href="io.c#readpoints">qh_readpoints</a> read input
|
||||
points </li>
|
||||
<li><a href="io.c#setfeasible">qh_setfeasible</a> set
|
||||
interior point from qh feasible_string ('Hn,n,n')</li>
|
||||
<li><a href="io.c#skipfilename">qh_skipfilename</a>
|
||||
skip filename in string
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="iprint">Print functions for all
|
||||
output formats</a></h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="io.c#countfacets">qh_countfacets</a> count good
|
||||
facets for printing and set visitid </li>
|
||||
<li><a href="io.c#markkeep">qh_markkeep</a> mark good facets
|
||||
that meet qh.KEEParea ('PAn'), qh.KEEPmerge ('PMn'), and qh.KEEPminArea ('PFn')</li>
|
||||
<li><a href="io.c#order_vertexneighbors">qh_order_vertexneighbors</a>
|
||||
order neighbors for a 3-d vertex by adjacency ('i', 'o')</li>
|
||||
<li><a href="io.c#printafacet">qh_printafacet</a> print facet
|
||||
in an output format </li>
|
||||
<li><a href="io.c#printbegin">qh_printbegin</a> print header
|
||||
for an output format </li>
|
||||
<li><a href="io.c#printend">qh_printend</a> print trailer for
|
||||
an output format </li>
|
||||
<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
|
||||
print facets in a facetlist</li>
|
||||
<li><a href="io.c#printfacets">qh_printfacets</a> print
|
||||
facetlist and/or facet set in an output format </li>
|
||||
<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
|
||||
print neighborhood of one or two facets ('Po')</li>
|
||||
<li><a href="io.c#produce_output">qh_produce_output</a>
|
||||
print the results of qh_qhull() </li>
|
||||
<li><a href="io.c#skipfacet">qh_skipfacet</a> True if not
|
||||
printing this facet ('Pdk:n', 'QVn', 'QGn')</li>
|
||||
<li><a href="io.c#facetvertices">qh_facetvertices</a> return
|
||||
vertices in a set of facets ('p')</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="itext">Text output functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="io.c#eachvoronoi">qh_eachvoronoi</a>
|
||||
print or visit each Voronoi ridge for an input site of the Voronoi diagram
|
||||
<li><a href="io.c#printextremes">qh_printextremes</a> print
|
||||
extreme points by point ID (vertices of convex hull) ('Fx')</li>
|
||||
<li><a href="io.c#printextremes_2d">qh_printextremes_2d</a> print
|
||||
2-d extreme points by point ID ('Fx')</li>
|
||||
<li><a href="io.c#printextremes_d">qh_printextremes_d</a> print
|
||||
extreme points of input sites for Delaunay triangulations ('Fx')</li>
|
||||
<li><a href="io.c#printfacet">qh_printfacet</a> print all
|
||||
fields of a facet ('f')</li>
|
||||
<li><a href="io.c#printfacet2math">qh_printfacet2math</a> print
|
||||
2-d Maple or Mathematica output for a facet ('FM' or 'm')</li>
|
||||
<li><a href="io.c#printfacet3math">qh_printfacet3math</a>
|
||||
print 3-d Maple or Mathematica facet ('FM' or 'm')</li>
|
||||
<li><a href="io.c#printfacet3vertex">qh_printfacet3vertex</a>
|
||||
print vertices for a 3-d facet ('i', 'o')</li>
|
||||
<li><a href="io.c#printfacetheader">qh_printfacetheader</a>
|
||||
prints header fields of a facet ('f')</li>
|
||||
<li><a href="io.c#printfacetNvertex_nonsimplicial">qh_printfacetNvertex_nonsimplicial</a>
|
||||
print vertices for an N-d non-simplicial facet ('i', 'Ft')</li>
|
||||
<li><a href="io.c#printfacetNvertex_simplicial">qh_printfacetNvertex_simplicial</a>
|
||||
print vertices for an N-d simplicial facet ('i', 'o', 'Ft')</li>
|
||||
<li><a href="io.c#printfacetridges">qh_printfacetridges</a>
|
||||
prints ridges of a facet ('f')</li>
|
||||
<li><a href="io.c#printpoints_out">qh_printpoints_out</a> prints
|
||||
vertices for facets by their point coordinates ('p')</li>
|
||||
<li><a href="io.c#printridge">qh_printridge</a> print all
|
||||
fields for a ridge ('f')</li>
|
||||
<li><a href="io.c#printvdiagram">qh_printvdiagram</a> print
|
||||
voronoi diagram as Voronoi vertices for each input pair</li>
|
||||
<li><a href="io.c#printvertex">qh_printvertex</a> print all
|
||||
fields for a vertex ('f')</li>
|
||||
<li><a href="io.c#printvertexlist">qh_printvertexlist</a>
|
||||
print vertices used by a list or set of facets ('f')</li>
|
||||
<li><a href="io.c#printvertices">qh_printvertices</a> print a
|
||||
set of vertices ('f')</li>
|
||||
<li><a href="io.c#printvneighbors">qh_printvneighbors</a>
|
||||
print vertex neighbors of vertices ('FN')</li>
|
||||
<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
|
||||
voronoi diagram in 'o' or 'G' format</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="iutil">Text utility functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="io.c#dfacet">dfacet</a> print facet by ID </li>
|
||||
<li><a href="io.c#dvertex">dvertex</a> print vertex by ID </li>
|
||||
<li><a href="io.c#compare_facetarea">qh_compare_facetarea</a>
|
||||
used by qsort() to order facets by area </li>
|
||||
<li><a href="io.c#compare_facetmerge">qh_compare_facetmerge</a>
|
||||
used by qsort() to order facets by number of merges </li>
|
||||
<li><a href="io.c#compare_facetvisit">qh_compare_facetvisit</a>
|
||||
used by qsort() to order facets by visit ID or ID </li>
|
||||
<li><a href="io.c#compare_vertexpoint">qh_compare_vertexpoint</a>
|
||||
used by qsort() to order vertices by point ID </li>
|
||||
<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
|
||||
<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
|
||||
ridge for an input site
|
||||
<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
|
||||
ridge for an input site
|
||||
<li><a href="io.c#facet2point">qh_facet2point</a> return two
|
||||
projected temporary vertices for a 2-d facet ('m', 'G')</li>
|
||||
<li><a href="io.c#markvoronoi">qh_markvoronoi</a> mark Voronoi
|
||||
vertices for printing
|
||||
<li><a href="io.c#printcenter">qh_printcenter</a> print
|
||||
facet->center as centrum or Voronoi center ('Ft', 'v p', 'FC', 'f') </li>
|
||||
<li><a href="io.c#printpoint">qh_printpoint</a>, qh_printpointid, print
|
||||
coordinates of a point ('p', 'o', 'Fp', 'G', 'f')</li>
|
||||
<li><a href="io.c#printpoint3">qh_printpoint3</a> prints 2-d,
|
||||
3-d, or 4-d point as 3-d coordinates ('G')</li>
|
||||
<li><a href="io.c#printvdiagram2">qh_printvdiagram2</a> print
|
||||
voronoi diagram for each ridge of each vertex from qh_markvoronoi</li>
|
||||
<li><a href="io.c#printvnorm">qh_printvnorm</a> print
|
||||
separating plane of the Voronoi diagram for a pair of input sites</li>
|
||||
<li><a href="io.c#printvridge">qh_printvridge</a> print
|
||||
ridge of the Voronoi diagram for a pair of input sites</li>
|
||||
<li><a href="io.c#projectdim3">qh_projectdim3</a> project 2-d
|
||||
3-d or 4-d point to a 3-d point ('G')</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="igeom">Geomview output functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="io.c#printfacet2geom">qh_printfacet2geom</a>
|
||||
print facet as a 2-d VECT object </li>
|
||||
<li><a href="io.c#printfacet2geom_points">qh_printfacet2geom_points</a>
|
||||
print points as a 2-d VECT object with offset </li>
|
||||
<li><a href="io.c#printfacet3geom_nonsimplicial">qh_printfacet3geom_nonsimplicial</a>
|
||||
print Geomview OFF for a 3-d nonsimplicial facet. </li>
|
||||
<li><a href="io.c#printfacet3geom_points">qh_printfacet3geom_points</a>
|
||||
prints a 3-d facet as OFF Geomview object. </li>
|
||||
<li><a href="io.c#printfacet3geom_simplicial">qh_printfacet3geom_simplicial</a>
|
||||
print Geomview OFF for a 3-d simplicial facet. </li>
|
||||
<li><a href="io.c#printfacet4geom_nonsimplicial">qh_printfacet4geom_nonsimplicial</a>
|
||||
print Geomview 4OFF file for a 4d nonsimplicial facet </li>
|
||||
<li><a href="io.c#printfacet4geom_simplicial">qh_printfacet4geom_simplicial</a>
|
||||
print Geomview 4OFF file for a 4d simplicial facet </li>
|
||||
<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
|
||||
print hyperplane intersection as OFF or 4OFF </li>
|
||||
<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
|
||||
voronoi diagram in 'o' or 'G' format</li>
|
||||
</ul>
|
||||
<h3><a href="qh-io.htm#TOC">»</a><a name="iview">Geomview utility functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="io.c#geomplanes">qh_geomplanes</a>
|
||||
return outer and inner planes for Geomview</li>
|
||||
<li><a href="io.c#printcentrum">qh_printcentrum</a> print
|
||||
centrum for a facet in OOGL format </li>
|
||||
<li><a href="io.c#printend4geom">qh_printend4geom</a> helper
|
||||
function for qh_printbegin/printend </li>
|
||||
<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
|
||||
print Geomview OFF or 4OFF for the intersection of two
|
||||
hyperplanes in 3-d or 4-d </li>
|
||||
<li><a href="io.c#printline3geom">qh_printline3geom</a> prints a
|
||||
line as a VECT </li>
|
||||
<li><a href="io.c#printpointvect">qh_printpointvect</a>
|
||||
prints a 2-d or 3-d point as 3-d VECT's </li>
|
||||
<li><a href="io.c#printpointvect2">qh_printpointvect2</a>
|
||||
prints a 2-d or 3-d point as 2 3-d VECT's </li>
|
||||
<li><a href="io.c#printspheres">qh_printspheres</a> prints 3-d
|
||||
vertices as OFF spheres </li>
|
||||
</ul>
|
||||
<p>
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
145
xs/src/qhull/src/libqhull/qh-mem.htm
Normal file
145
xs/src/qhull/src/libqhull/qh-mem.htm
Normal file
@ -0,0 +1,145 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>mem.c -- memory operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>mem.c -- memory operations</h2>
|
||||
<blockquote>
|
||||
<p>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. </p>
|
||||
<p>Use 'T5' to trace memory allocations.</p>
|
||||
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
|
||||
<a href="qh-io.htm#TOC">Io</a> • <b>Mem</b>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="mem.c">mem.c</a> and
|
||||
<a href="mem.h">mem.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#etype">mem.h data types</a> </li>
|
||||
<li><a href="#emacro">mem.h macros</a> </li>
|
||||
<li><a href="#efunc">User level functions</a> </li>
|
||||
</ul>
|
||||
<h3><a href="qh-mem.htm#TOC">»</a><a name="etype">mem.h data types and constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="mem.h#ptr_intT">ptr_intT</a> for casting
|
||||
a void* to an integer-type </li>
|
||||
<li><a href="mem.h#qhmemT">qhmemT</a> global memory
|
||||
structure for mem.c </li>
|
||||
<li><a href="mem.h#NOmem">qh_NOmem</a> disable memory allocation</li>
|
||||
</ul>
|
||||
<h3><a href="qh-mem.htm#TOC">»</a><a name="emacro">mem.h macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="mem.h#memalloc_">qh_memalloc_</a>
|
||||
allocate memory</li>
|
||||
<li><a href="mem.h#memfree_">qh_memfree_</a> free
|
||||
memory</li>
|
||||
</ul>
|
||||
<h3><a href="qh-mem.htm#TOC">»</a><a name="efunc">User level
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="mem.c#memalloc">qh_memalloc</a> allocate
|
||||
memory </li>
|
||||
<li><a href="mem.c#memcheck">qh_memcheck</a>
|
||||
quick check of memory for internal consistency</li>
|
||||
<li><a href="mem.c#memfree">qh_memfree</a> free
|
||||
memory </li>
|
||||
<li><a href="mem.c#meminit">qh_meminit</a> initialize
|
||||
memory </li>
|
||||
<li><a href="mem.c#memstatistics">qh_memstatistics</a>
|
||||
print memory statistics </li>
|
||||
<li><a href="mem.c#meminit">qh_memtotlong</a> return total, allocated long memory</li>
|
||||
<li><a href="mem.c#NOmem">qh_NOmem</a> allocation routines with malloc() and free()
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-mem.htm#TOC">»</a><a name="m">Initialization and
|
||||
termination functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="mem.c#intcompare">qh_intcompare</a> used by
|
||||
qsort and bsearch to compare two integers </li>
|
||||
<li><a href="mem.c#memfreeshort">qh_memfreeshort</a>
|
||||
frees up all short and qhmem memory allocations </li>
|
||||
<li><a href="mem.c#meminit">qh_meminit</a> initialize
|
||||
memory </li>
|
||||
<li><a href="mem.c#meminitbuffers">qh_meminitbuffers</a>
|
||||
initialize qhmem </li>
|
||||
<li><a href="mem.c#memsetup">qh_memsetup</a> set up
|
||||
memory after running memsize() </li>
|
||||
<li><a href="mem.c#memsize">qh_memsize</a> define a free
|
||||
list for this size </li>
|
||||
<li><a href="mem.c#memstatistics">qh_memstatistics</a>
|
||||
print out memory statistics </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
366
xs/src/qhull/src/libqhull/qh-merge.htm
Normal file
366
xs/src/qhull/src/libqhull/qh-merge.htm
Normal file
@ -0,0 +1,366 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>merge.c -- facet merge operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>merge.c -- facet merge operations</h2>
|
||||
<blockquote>
|
||||
<p>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 <a href="../../html/qh-impre.htm">Imprecision in Qhull</a>
|
||||
for further information. </p>
|
||||
<p>Users may joggle the input ('<a href="../../html/qh-optq.htm#QJn">QJn</a>')
|
||||
instead of merging facets. </p>
|
||||
<p>Qhull detects and corrects the following problems: </p>
|
||||
<ul>
|
||||
<li><b>More than two facets meeting at a ridge. </b>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 <em>duplicate
|
||||
ridge</em>. In 2-d, a duplicate ridge would
|
||||
create a loop of facets. </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>A facet contained in another facet. </b>Facet
|
||||
merging may leave all vertices of one facet as a
|
||||
subset of the vertices of another facet. This is
|
||||
called a <em>redundant facet</em>. </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>A facet with fewer than three neighbors. </b>Facet
|
||||
merging may leave a facet with one or two
|
||||
neighbors. This is called a <em>degenerate facet</em>.
|
||||
</li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>A facet with flipped orientation. </b>A
|
||||
facet's hyperplane may define a halfspace that
|
||||
does not include the interior point.This is
|
||||
called a <em>flipped facet</em>. </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><strong>A coplanar horizon facet.</strong> 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 <em>samecycle</em>.
|
||||
The new facet or samecycle is merged into the
|
||||
horizon facet. </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>Concave facets. </b>A facet's centrum may be
|
||||
above a neighboring facet. If so, the facets meet
|
||||
at a concave angle. </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>Coplanar facets. </b>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.</li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><b>Redundant vertex. </b>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 <em>redundant vertex</em>.
|
||||
</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <b>Merge</b> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="merge.c">merge.c</a> and
|
||||
<a href="merge.h">merge.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#mtype">merge.h data types, macros, and
|
||||
global sets</a> </li>
|
||||
<li><a href="#mconst">merge.h constants</a> </li>
|
||||
</ul>
|
||||
<ul>
|
||||
<li><a href="#mtop">top-level merge functions</a> </li>
|
||||
<li><a href="#mset">functions for identifying merges</a></li>
|
||||
<li><a href="#mbest">functions for determining the
|
||||
best merge</a> </li>
|
||||
<li><a href="#mmerge">functions for merging facets</a>
|
||||
</li>
|
||||
<li><a href="#mcycle">functions for merging a cycle
|
||||
of facets</a> </li>
|
||||
<li><a href="#mrename">functions for renaming a
|
||||
vertex</a> </li>
|
||||
<li><a href="#mvertex">functions for identifying
|
||||
vertices for renaming</a> </li>
|
||||
<li><a href="#mcheck">functions for check and trace</a> </li>
|
||||
</ul>
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mtype">merge.h data
|
||||
types, macros, and global sets</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.h#mergeT">mergeT</a> structure to
|
||||
identify a merge of two facets</li>
|
||||
<li><a href="merge.h#FOREACHmerge_">FOREACHmerge_</a>
|
||||
assign 'merge' to each merge in merges </li>
|
||||
<li><a href="libqhull.h#qh-set">qh global sets</a>
|
||||
qh.facet_mergeset contains non-convex merges
|
||||
while qh.degen_mergeset contains degenerate and
|
||||
redundant facets</li>
|
||||
</ul>
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mconst">merge.h
|
||||
constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#qh-prec">qh precision constants</a>
|
||||
precision constants for Qhull </li>
|
||||
<li><a href="merge.h#MRG">MRG...</a> indicates the
|
||||
type of a merge (mergeT->type)</li>
|
||||
<li><a href="merge.h#qh_ANGLEredundant">qh_ANGLEredundant</a>
|
||||
indicates redundant merge in mergeT->angle </li>
|
||||
<li><a href="merge.h#qh_ANGLEdegen">qh_ANGLEdegen</a>
|
||||
indicates degenerate facet in mergeT->angle </li>
|
||||
<li><a href="merge.h#qh_ANGLEconcave">qh_ANGLEconcave</a>
|
||||
offset to indicate concave facets in
|
||||
mergeT->angle </li>
|
||||
<li><a href="merge.h#qh_MERGEapex">qh_MERGEapex</a>
|
||||
flag for qh_mergefacet() to indicate an apex
|
||||
merge </li>
|
||||
</ul>
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mtop">top-level merge
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#all_merges">qh_all_merges</a>
|
||||
merge all non-convex facets </li>
|
||||
<li><a href="merge.c#checkzero">qh_checkzero</a>
|
||||
check that facets are clearly convex </li>
|
||||
<li><a href="merge.c#flippedmerges">qh_flippedmerges</a>
|
||||
merge flipped facets into best neighbor </li>
|
||||
<li><a href="merge.c#forcedmerges">qh_forcedmerges</a>
|
||||
merge all duplicate ridges </li>
|
||||
<li><a href="merge.c#merge_degenredundant">qh_merge_degenredundant</a>
|
||||
merge degenerate and redundant facets </li>
|
||||
<li><a href="merge.c#merge_nonconvex">qh_merge_nonconvex</a>
|
||||
merge a non-convex ridge </li>
|
||||
<li><a href="merge.c#premerge">qh_premerge</a>
|
||||
pre-merge non-convex facets </li>
|
||||
<li><a href="merge.c#postmerge">qh_postmerge</a>
|
||||
post-merge nonconvex facets as defined by
|
||||
maxcentrum/maxangle </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mset">functions for
|
||||
identifying merges</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#appendmergeset">qh_appendmergeset</a>
|
||||
appends an entry to qh.facet_mergeset</li>
|
||||
<li><a href="merge.c#compareangle">qh_compareangle</a>
|
||||
used by qsort() to order merges </li>
|
||||
<li><a href="merge.c#comparemerge">qh_comparemerge</a>
|
||||
used by qsort() to order merges </li>
|
||||
<li><a href="merge.c#degen_redundant_facet">qh_degen_redundant_facet</a>
|
||||
check for a degenerate and redundant facet</li>
|
||||
<li><a href="merge.c#degen_redundant_neighbors">qh_degen_redundant_neighbors</a>
|
||||
append degenerate and redundant neighbors to
|
||||
qh.degen_mergeset </li>
|
||||
<li><a href="merge.c#getmergeset_initial">qh_getmergeset_initial</a>
|
||||
build initial qh.facet_mergeset </li>
|
||||
<li><a href="merge.c#getmergeset">qh_getmergeset</a>
|
||||
update qh.facet_mergeset </li>
|
||||
<li><a href="merge.c#mark_dupridges">qh_mark_dupridges</a>
|
||||
add duplicated ridges to qh.facet_mergeset</li>
|
||||
<li><a href="merge.c#maydropneighbor">qh_maydropneighbor</a>
|
||||
drop neighbor relationship if no ridge between
|
||||
facet and neighbor </li>
|
||||
<li><a href="merge.c#test_appendmerge">qh_test_appendmerge</a>
|
||||
test a pair of facets for convexity and append to
|
||||
qh.facet_mergeset if non-convex </li>
|
||||
<li><a href="merge.c#test_vneighbors">qh_test_vneighbors</a>
|
||||
test vertex neighbors for convexity </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mbest">functions for
|
||||
determining the best merge</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#findbest_test">qh_findbest_test</a>
|
||||
test neighbor for best merge </li>
|
||||
<li><a href="merge.c#findbestneighbor">qh_findbestneighbor</a>
|
||||
finds best neighbor of a facet for merging (i.e.,
|
||||
closest hyperplane) </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mmerge">functions for
|
||||
merging facets</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#copynonconvex">qh_copynonconvex</a>
|
||||
copy non-convex flag to another ridge for the
|
||||
same neighbor </li>
|
||||
<li><a href="merge.c#makeridges">qh_makeridges</a>
|
||||
creates explicit ridges between simplicial facets
|
||||
</li>
|
||||
<li><a href="merge.c#mergefacet">qh_mergefacet</a>
|
||||
merges one facet into another facet</li>
|
||||
<li><a href="merge.c#mergeneighbors">qh_mergeneighbors</a>
|
||||
merges the neighbors of two facets </li>
|
||||
<li><a href="merge.c#mergeridges">qh_mergeridges</a>
|
||||
merges the ridge sets of two facets </li>
|
||||
<li><a href="merge.c#mergesimplex">qh_mergesimplex</a>
|
||||
merge a simplicial facet into another simplicial
|
||||
facet </li>
|
||||
<li><a href="merge.c#mergevertex_del">qh_mergevertex_del</a>
|
||||
delete a vertex due to merging one facet into
|
||||
another facet </li>
|
||||
<li><a href="merge.c#mergevertex_neighbors">qh_mergevertex_neighbors</a>
|
||||
merge the vertex neighbors of two facets </li>
|
||||
<li><a href="merge.c#mergevertices">qh_mergevertices</a>
|
||||
merge the vertex sets of two facets </li>
|
||||
<li><a href="merge.c#newvertices">qh_newvertices</a>
|
||||
register all vertices as new vertices </li>
|
||||
<li><a href="merge.c#updatetested">qh_updatetested</a>
|
||||
clear tested flags and centrums involved in a
|
||||
merge </li>
|
||||
<li><a href="merge.c#willdelete">qh_willdelete</a>
|
||||
moves facet to qh.visible_list; sets replacement
|
||||
or NULL </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mcycle">functions for
|
||||
merging a cycle of facets</a></h3>
|
||||
<p>If a point is coplanar with an horizon facet, the
|
||||
corresponding new facets are linked together (a <em>samecycle</em>)
|
||||
for merging.</p>
|
||||
<ul>
|
||||
<li><a href="merge.c#basevertices">qh_basevertices</a>
|
||||
return temporary set of base vertices for a
|
||||
samecycle </li>
|
||||
<li><a href="merge.c#mergecycle">qh_mergecycle</a>
|
||||
merge a samecycle into a horizon facet </li>
|
||||
<li><a href="merge.c#mergecycle_all">qh_mergecycle_all</a>
|
||||
merge all samecycles into horizon facets</li>
|
||||
<li><a href="merge.c#mergecycle_facets">qh_mergecycle_facets</a>
|
||||
finish merge of samecycle </li>
|
||||
<li><a href="merge.c#mergecycle_neighbors">qh_mergecycle_neighbors</a>
|
||||
merge neighbor sets for samecycle </li>
|
||||
<li><a href="merge.c#mergecycle_ridges">qh_mergecycle_ridges</a>
|
||||
merge ridge sets for samecycle </li>
|
||||
<li><a href="merge.c#mergecycle_vneighbors">qh_mergecycle_vneighbors</a>
|
||||
merge vertex neighbor sets for samecycle </li>
|
||||
</ul>
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mrename">functions
|
||||
for renaming a vertex</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#comparevisit">qh_comparevisit</a>
|
||||
used by qsort() to order vertices by visitid</li>
|
||||
<li><a href="merge.c#reducevertices">qh_reducevertices</a>
|
||||
reduce vertex sets </li>
|
||||
<li><a href="merge.c#redundant_vertex">qh_redundant_vertex</a>
|
||||
returns true if detect and rename redundant
|
||||
vertex </li>
|
||||
<li><a href="merge.c#rename_sharedvertex">qh_rename_sharedvertex</a>
|
||||
detect and rename a shared vertex </li>
|
||||
<li><a href="merge.c#renameridgevertex">qh_renameridgevertex</a>
|
||||
rename oldvertex to newvertex in a ridge </li>
|
||||
<li><a href="merge.c#renamevertex">qh_renamevertex</a>
|
||||
rename oldvertex to newvertex in ridges </li>
|
||||
<li><a href="merge.c#remove_extravertices">qh_remove_extravertices</a>
|
||||
remove extra vertices in non-simplicial facets </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mvertex">functions
|
||||
for identifying vertices for renaming</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#find_newvertex">qh_find_newvertex</a>
|
||||
locate new vertex for renaming old vertex </li>
|
||||
<li><a href="merge.c#hashridge">qh_hashridge</a> add
|
||||
ridge to hashtable </li>
|
||||
<li><a href="merge.c#hashridge_find">qh_hashridge_find</a>
|
||||
returns matching ridge in hashtable</li>
|
||||
<li><a href="merge.c#neighbor_intersections">qh_neighbor_intersections</a>
|
||||
return intersection of vertex sets for
|
||||
neighboring facets </li>
|
||||
<li><a href="merge.c#vertexridges">qh_vertexridges</a>
|
||||
return temporary set of ridges adjacent to a
|
||||
vertex </li>
|
||||
<li><a href="merge.c#vertexridges_facet">qh_vertexridges_facet</a>
|
||||
add adjacent ridges for a vertex in facet </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-merge.htm#TOC">»</a><a name="mcheck">functions for check and
|
||||
trace</a></h3>
|
||||
<ul>
|
||||
<li><a href="merge.c#checkconnect">qh_checkconnect</a>
|
||||
check that new facets are connected </li>
|
||||
<li><a href="merge.c#tracemerge">qh_tracemerge</a>
|
||||
print trace message after merge </li>
|
||||
<li><a href="merge.c#tracemerging">qh_tracemerging</a>
|
||||
print trace message during post-merging </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
485
xs/src/qhull/src/libqhull/qh-poly.htm
Normal file
485
xs/src/qhull/src/libqhull/qh-poly.htm
Normal file
@ -0,0 +1,485 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>poly.c, poly2.c -- polyhedron operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>poly.c, poly2.c -- polyhedron operations</h2>
|
||||
<blockquote>
|
||||
|
||||
<p>Qhull uses dimension-free terminology. Qhull builds a
|
||||
polyhedron in dimension <em>d. </em>A <em>polyhedron</em> is a
|
||||
simplicial complex of faces with geometric information for the
|
||||
top and bottom-level faces. A (<em>d-1</em>)-face is a <em>facet</em>,
|
||||
a (<em>d-2</em>)-face is a <em>ridge</em>, and a <em>0</em>-face
|
||||
is a <em>vertex</em>. For example in 3-d, a facet is a polygon
|
||||
and a ridge is an edge. A facet is built from a ridge (the <em>base</em>)
|
||||
and a vertex (the <em>apex</em>). See
|
||||
<a href="../../html/index.htm#structure">Qhull's data structures</a>.</p>
|
||||
|
||||
<p>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 <em>a, b, c, d</em>, and its facets
|
||||
are <em>1, 2, 3, 4,</em> the tetrahedron is </p>
|
||||
<blockquote>
|
||||
<ul>
|
||||
<li>facet 1 <ul>
|
||||
<li>vertices: b c d </li>
|
||||
<li>neighbors: 2 3 4 </li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>facet 2 <ul>
|
||||
<li>vertices: a c d </li>
|
||||
<li>neighbors: 1 3 4 </li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>facet 3 <ul>
|
||||
<li>vertices: a b d </li>
|
||||
<li>neighbors: 1 2 4 </li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>facet 4 <ul>
|
||||
<li>vertices: a b c </li>
|
||||
<li>neighbors: 1 2 3 </li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<p>A facet may be simplicial or non-simplicial. In 3-d, a
|
||||
<i>simplicial facet</i> has three vertices and three
|
||||
neighbors. A <i>nonsimplicial facet</i> has more than
|
||||
three vertices and more than three neighbors. A
|
||||
nonsimplicial facet has a set of ridges and a centrum. </p>
|
||||
<p>
|
||||
A simplicial facet has an orientation. An <i>orientation</i>
|
||||
is either <i>top</i> or <i>bottom</i>.
|
||||
The flag, <tt>facet->toporient,</tt>
|
||||
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.
|
||||
|
||||
<p>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, <tt>facet->toporient,</tt>is
|
||||
ignored. </p>
|
||||
<p>A nonsimplicial facet has a centrum for testing
|
||||
convexity. A <i>centrum</i> 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. </p>
|
||||
<p>A nonsimplicial facet is an approximation that is
|
||||
defined by offsets from the facet's hyperplane. When
|
||||
Qhull finishes, the <i>outer plane</i> is above all
|
||||
points while the <i>inner plane</i> 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 <tt>facet->maxoutside</tt> while
|
||||
the inner plane is computed from the facet's vertices.</p>
|
||||
|
||||
<p>Qhull 3.1 includes triangulation of non-simplicial facets
|
||||
('<a href="../../html/qh-optq.htm#Qt">Qt</a>').
|
||||
These facets,
|
||||
called <i>tricoplanar</i>, 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.
|
||||
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <b>Poly</b>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="poly.c">poly.c</a>,
|
||||
<a href="poly2.c">poly2.c</a>, <a href="poly.h">poly.h</a>,
|
||||
and <a href="libqhull.h">libqhull.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#ptype">Data types and global
|
||||
lists for polyhedrons</a> </li>
|
||||
<li><a href="#pconst">poly.h constants</a> </li>
|
||||
<li><a href="#pgall">Global FORALL macros</a> </li>
|
||||
<li><a href="#pall">FORALL macros</a> </li>
|
||||
<li><a href="#peach">FOREACH macros</a> </li>
|
||||
<li><a href="#pieach">Indexed FOREACH macros</a> </li>
|
||||
<li><a href="#pmacro">Other macros for polyhedrons</a><p> </li>
|
||||
<li><a href="#plist">Facetlist functions</a> </li>
|
||||
<li><a href="#pfacet">Facet functions</a> </li>
|
||||
<li><a href="#pvertex">Vertex, ridge, and point
|
||||
functions</a> </li>
|
||||
<li><a href="#phash">Hashtable functions</a> </li>
|
||||
<li><a href="#pnew">Allocation and deallocation
|
||||
functions</a> </li>
|
||||
<li><a href="#pcheck">Check functions</a> </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="ptype">Data
|
||||
types and global lists for polyhedrons</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#facetT">facetT</a> defines a
|
||||
facet </li>
|
||||
<li><a href="libqhull.h#ridgeT">ridgeT</a> defines a
|
||||
ridge </li>
|
||||
<li><a href="libqhull.h#vertexT">vertexT</a> defines a
|
||||
vertex </li>
|
||||
<li><a href="libqhull.h#qh-lists">qh facet and vertex
|
||||
lists</a> lists of facets and vertices </li>
|
||||
<li><a href="libqhull.h#qh-set">qh global sets</a>
|
||||
global sets for merging, hashing, input, etc. </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pconst">poly.h constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly.h#ALGORITHMfault">ALGORITHMfault</a>
|
||||
flag to not report errors in qh_checkconvex() </li>
|
||||
<li><a href="poly.h#DATAfault">DATAfault</a> flag to
|
||||
report errors in qh_checkconvex() </li>
|
||||
<li><a href="poly.h#DUPLICATEridge">DUPLICATEridge</a>
|
||||
special value for facet->neighbor to indicate
|
||||
a duplicate ridge </li>
|
||||
<li><a href="poly.h#MERGEridge">MERGEridge</a>
|
||||
special value for facet->neighbor to indicate
|
||||
a merged ridge </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pgall">Global FORALL
|
||||
macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#FORALLfacets">FORALLfacets</a>
|
||||
assign 'facet' to each facet in qh.facet_list </li>
|
||||
<li><a href="poly.h#FORALLnew_facets">FORALLnew_facets</a>
|
||||
assign 'facet' to each facet in qh.newfacet_list </li>
|
||||
<li><a href="poly.h#FORALLvisible_facets">FORALLvisible_facets</a>
|
||||
assign 'visible' to each visible facet in
|
||||
qh.visible_list </li>
|
||||
<li><a href="libqhull.h#FORALLpoints">FORALLpoints</a>
|
||||
assign 'point' to each point in qh.first_point,
|
||||
qh.num_points </li>
|
||||
<li><a href="libqhull.h#FORALLvertices">FORALLvertices</a>
|
||||
assign 'vertex' to each vertex in qh.vertex_list </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pall">FORALL macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly.h#FORALLfacet_">FORALLfacet_</a>
|
||||
assign 'facet' to each facet in facetlist </li>
|
||||
<li><a href="libqhull.h#FORALLpoint_">FORALLpoint_</a>
|
||||
assign 'point' to each point in points array</li>
|
||||
<li><a href="poly.h#FORALLsame_">FORALLsame_</a>
|
||||
assign 'same' to each facet in samecycle</li>
|
||||
<li><a href="poly.h#FORALLsame_cycle_">FORALLsame_cycle_</a>
|
||||
assign 'same' to each facet in samecycle</li>
|
||||
<li><a href="poly.h#FORALLvertex_">FORALLvertex_</a>
|
||||
assign 'vertex' to each vertex in vertexlist </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="peach">FOREACH macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#FOREACHfacet_">FOREACHfacet_</a>
|
||||
assign 'facet' to each facet in facets </li>
|
||||
<li><a href="libqhull.h#FOREACHneighbor_">FOREACHneighbor_</a>
|
||||
assign 'neighbor' to each facet in
|
||||
facet->neighbors or vertex->neighbors</li>
|
||||
<li><a href="poly.h#FOREACHnewfacet_">FOREACHnewfacet_</a>
|
||||
assign 'newfacet' to each facet in facet set </li>
|
||||
<li><a href="libqhull.h#FOREACHpoint_">FOREACHpoint_</a>
|
||||
assign 'point' to each point in points set </li>
|
||||
<li><a href="libqhull.h#FOREACHridge_">FOREACHridge_</a>
|
||||
assign 'ridge' to each ridge in ridge set </li>
|
||||
<li><a href="libqhull.h#FOREACHvertex_">FOREACHvertex_</a>
|
||||
assign 'vertex' to each vertex in vertex set </li>
|
||||
<li><a href="poly.h#FOREACHvertexA_">FOREACHvertexA_</a>
|
||||
assign 'vertexA' to each vertex in vertex set</li>
|
||||
<li><a href="poly.h#FOREACHvisible_">FOREACHvisible_</a>
|
||||
assign 'visible' to each facet in facet set </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pieach">Indexed
|
||||
FOREACH macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#FOREACHfacet_i_">FOREACHfacet_i_</a>
|
||||
assign 'facet' and 'facet_i' to each facet in
|
||||
facet set </li>
|
||||
<li><a href="libqhull.h#FOREACHneighbor_i_">FOREACHneighbor_i_</a>
|
||||
assign 'neighbor' and 'neighbor_i' to each facet
|
||||
in facet->neighbors or vertex->neighbors</li>
|
||||
<li><a href="libqhull.h#FOREACHpoint_i_">FOREACHpoint_i_</a>
|
||||
assign 'point' and 'point_i' to each point in
|
||||
points set </li>
|
||||
<li><a href="libqhull.h#FOREACHridge_i_">FOREACHridge_i_</a>
|
||||
assign 'ridge' and 'ridge_i' to each ridge in
|
||||
ridges set </li>
|
||||
<li><a href="libqhull.h#FOREACHvertex_i_">FOREACHvertex_i_</a>
|
||||
assign 'vertex' and 'vertex_i' to each vertex in
|
||||
vertices set </li>
|
||||
<li><a href="poly.h#FOREACHvertexreverse12_">FOREACHvertexreverse12_</a>
|
||||
assign 'vertex' to each vertex in vertex set;
|
||||
reverse the order of first two vertices </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pmacro">Other macros for polyhedrons</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#getid_">getid_</a> return ID for
|
||||
a facet, ridge, or vertex </li>
|
||||
<li><a href="libqhull.h#otherfacet_">otherfacet_</a>
|
||||
return neighboring facet for a ridge in a facet </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="plist">Facetlist
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly.c#appendfacet">qh_appendfacet</a>
|
||||
appends facet to end of qh.facet_list</li>
|
||||
<li><a href="poly.c#attachnewfacets">qh_attachnewfacets</a>
|
||||
attach new facets in qh.newfacet_list to the
|
||||
horizon </li>
|
||||
<li><a href="poly2.c#findgood">qh_findgood</a>
|
||||
identify good facets for qh.PRINTgood </li>
|
||||
<li><a href="poly2.c#findgood_all">qh_findgood_all</a>
|
||||
identify more good facets for qh.PRINTgood </li>
|
||||
<li><a href="poly2.c#furthestnext">qh_furthestnext</a>
|
||||
move facet with furthest of furthest points to
|
||||
facet_next </li>
|
||||
<li><a href="poly2.c#initialhull">qh_initialhull</a>
|
||||
construct the initial hull as a simplex of
|
||||
vertices </li>
|
||||
<li><a href="poly2.c#nearcoplanar">qh_nearcoplanar</a>
|
||||
remove near-inside points from coplanar sets</li>
|
||||
<li><a href="poly2.c#prependfacet">qh_prependfacet</a>
|
||||
prepends facet to start of facetlist </li>
|
||||
<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
|
||||
print facets in a facetlist</li>
|
||||
<li><a href="poly2.c#printlists">qh_printlists</a>
|
||||
print out facet list for debugging </li>
|
||||
<li><a href="poly.c#removefacet">qh_removefacet</a>
|
||||
unlinks facet from qh.facet_list</li>
|
||||
<li><a href="poly2.c#resetlists">qh_resetlists</a>
|
||||
reset qh.newvertex_list, qh.newfacet_list, and
|
||||
qh.visible_list </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pfacet">Facet
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly2.c#createsimplex">qh_createsimplex</a>
|
||||
create a simplex of facets from a set of vertices
|
||||
</li>
|
||||
<li><a href="poly2.c#findbestlower">qh_findbestlower</a> find best
|
||||
non-upper, non-flipped facet for point at upperfacet</li>
|
||||
<li><a href="poly2.c#furthestout">qh_furthestout</a>
|
||||
make furthest outside point the last point of a
|
||||
facet's outside set </li>
|
||||
<li><a href="poly.c#makenew_nonsimplicial">qh_makenew_nonsimplicial</a>
|
||||
make new facets from ridges of visible facets </li>
|
||||
<li><a href="poly.c#makenew_simplicial">qh_makenew_simplicial</a>
|
||||
make new facets for horizon neighbors </li>
|
||||
<li><a href="poly.c#makenewfacet">qh_makenewfacet</a>
|
||||
create a facet from vertices and apex </li>
|
||||
<li><a href="poly2.c#makenewfacets">qh_makenewfacets</a>
|
||||
make new facets from vertex, horizon facets, and
|
||||
visible facets </li>
|
||||
<li><a href="poly.c#makenewplanes">qh_makenewplanes</a>
|
||||
make new hyperplanes for facets </li>
|
||||
<li><a href="poly2.c#outcoplanar">qh_outcoplanar</a>
|
||||
move points from outside set to coplanar set </li>
|
||||
<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
|
||||
compute Voronoi centers for all facets </li>
|
||||
<li><a href="poly2.c#triangulate">qh_triangulate</a>
|
||||
triangulate non-simplicial facets</li>
|
||||
<li><a href="poly2.c#triangulate_facet">qh_triangulate_facet</a>
|
||||
triangulate a non-simplicial facet</li>
|
||||
<li><a href="poly2.c#triangulate_link">qh_triangulate_link</a>
|
||||
link facets together from qh_triangulate</li>
|
||||
<li><a href="poly2.c#triangulate_mirror">qh_triangulate_mirror</a>
|
||||
delete mirrored facets from qh_triangulate</li>
|
||||
<li><a href="poly2.c#triangulate_null">qh_triangulate_null</a>
|
||||
delete null facet from qh_triangulate</li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pvertex">Vertex,
|
||||
ridge, and point functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly.c#appendvertex">qh_appendvertex</a>
|
||||
append vertex to end of qh.vertex_list, </li>
|
||||
<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
|
||||
ridge for an input site
|
||||
<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
|
||||
ridge for an input site
|
||||
<li><a href="poly2.c#facet3vertex">qh_facet3vertex</a>
|
||||
return an oriented vertex set for a 3-d facet </li>
|
||||
<li><a href="poly.c#facetintersect">qh_facetintersect</a>
|
||||
return intersection of simplicial facets </li>
|
||||
<li><a href="poly2.c#initialvertices">qh_initialvertices</a>
|
||||
return non-singular set of initial vertices </li>
|
||||
<li><a href="poly2.c#isvertex">qh_isvertex</a> true
|
||||
if point is in a vertex set </li>
|
||||
<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
|
||||
return nearest vertex to point </li>
|
||||
<li><a href="poly2.c#nextridge3d">qh_nextridge3d</a>
|
||||
iterate over each ridge and vertex for a 3-d
|
||||
facet </li>
|
||||
<li><a href="poly2.c#point">qh_point</a> return point
|
||||
for a point ID </li>
|
||||
<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
|
||||
return temporary set of facets indexed by point
|
||||
ID </li>
|
||||
<li><a href="poly.c#pointid">qh_pointid</a> return ID
|
||||
for a point</li>
|
||||
<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
|
||||
return temporary set of vertices indexed by point
|
||||
ID </li>
|
||||
<li><a href="poly.c#removevertex">qh_removevertex</a>
|
||||
unlink vertex from qh.vertex_list, </li>
|
||||
<li><a href="poly.c#updatevertices">qh_updatevertices</a>
|
||||
update vertex neighbors and delete interior
|
||||
vertices </li>
|
||||
<li><a href="poly2.c#vertexintersect">qh_vertexintersect</a>
|
||||
intersect two vertex sets </li>
|
||||
<li><a href="poly2.c#vertexintersect_new">qh_vertexintersect_new</a>
|
||||
return intersection of two vertex sets </li>
|
||||
<li><a href="poly2.c#vertexneighbors">qh_vertexneighbors</a>
|
||||
for each vertex in hull, determine facet
|
||||
neighbors </li>
|
||||
<li><a href="poly2.c#vertexsubset">qh_vertexsubset</a>
|
||||
returns True if vertexsetA is a subset of
|
||||
vertexsetB </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="phash">Hashtable functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly2.c#addhash">qh_addhash</a> add hash
|
||||
element to linear hash table</li>
|
||||
<li><a href="poly.c#gethash">qh_gethash</a> return
|
||||
hash value for a set</li>
|
||||
<li><a href="poly2.c#matchduplicates">qh_matchduplicates</a>
|
||||
match duplicate ridges in hash table </li>
|
||||
<li><a href="poly.c#matchneighbor">qh_matchneighbor</a>
|
||||
try to match subridge of new facet with a
|
||||
neighbor </li>
|
||||
<li><a href="poly.c#matchnewfacets">qh_matchnewfacets</a>
|
||||
match new facets with their new facet neighbors </li>
|
||||
<li><a href="poly.c#matchvertices">qh_matchvertices</a>
|
||||
tests whether a facet and hash entry match at a
|
||||
ridge </li>
|
||||
<li><a href="poly2.c#newhashtable">qh_newhashtable</a>
|
||||
allocate a new qh.hash_table </li>
|
||||
<li><a href="poly2.c#printhashtable">qh_printhashtable</a>
|
||||
print hash table </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pnew">Allocation and
|
||||
deallocation functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly2.c#clearcenters">qh_clearcenters</a>
|
||||
clear old data from facet->center </li>
|
||||
<li><a href="poly.c#deletevisible">qh_deletevisible</a>
|
||||
delete visible facets and vertices </li>
|
||||
<li><a href="poly.c#delfacet">qh_delfacet</a> free up
|
||||
the memory occupied by a facet </li>
|
||||
<li><a href="poly2.c#delridge">qh_delridge</a> delete
|
||||
ridge</li>
|
||||
<li><a href="poly2.c#delvertex">qh_delvertex</a>
|
||||
delete vertex </li>
|
||||
<li><a href="poly.c#newfacet">qh_newfacet</a> create
|
||||
and allocate space for a facet </li>
|
||||
<li><a href="poly.c#newridge">qh_newridge</a> create
|
||||
and allocate space for a ridge </li>
|
||||
<li><a href="poly2.c#newvertex">qh_newvertex</a>
|
||||
create and allocate space for a vertex </li>
|
||||
</ul>
|
||||
<h3><a href="qh-poly.htm#TOC">»</a><a name="pcheck">Check
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="poly2.c#check_bestdist">qh_check_bestdist</a>
|
||||
check that points are not outside of facets </li>
|
||||
<li><a href="poly2.c#check_dupridge">qh_check_dupridge</a>
|
||||
check duplicate ridge between facet1 and facet2 for wide merge </li>
|
||||
<li><a href="poly2.c#check_maxout">qh_check_maxout</a>
|
||||
updates qh.max_outside and checks all points
|
||||
against bestfacet </li>
|
||||
<li><a href="poly2.c#check_output">qh_check_output</a>
|
||||
check topological and geometric output</li>
|
||||
<li><a href="poly2.c#check_point">qh_check_point</a>
|
||||
check that point is not outside of facet </li>
|
||||
<li><a href="poly2.c#check_points">qh_check_points</a>
|
||||
check that all points are inside all facets </li>
|
||||
<li><a href="poly2.c#checkconvex">qh_checkconvex</a>
|
||||
check that each ridge in facetlist is convex </li>
|
||||
<li><a href="poly2.c#checkfacet">qh_checkfacet</a>
|
||||
check for consistency errors in facet </li>
|
||||
<li><a href="poly.c#checkflipped">qh_checkflipped</a>
|
||||
check facet orientation to the interior point </li>
|
||||
<li><a href="poly2.c#checkflipped_all">qh_checkflipped_all</a>
|
||||
check facet orientation for a facet list </li>
|
||||
<li><a href="poly2.c#checkpolygon">qh_checkpolygon</a>
|
||||
check topological structure </li>
|
||||
<li><a href="poly2.c#checkvertex">qh_checkvertex</a>
|
||||
check vertex for consistency </li>
|
||||
<li><a href="poly2.c#infiniteloop">qh_infiniteloop</a>
|
||||
report error for a loop of facets </li>
|
||||
<li><a href="poly2.c#printlists">qh_printlists</a>
|
||||
print out facet list for debugging </li>
|
||||
</ul>
|
||||
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
279
xs/src/qhull/src/libqhull/qh-qhull.htm
Normal file
279
xs/src/qhull/src/libqhull/qh-qhull.htm
Normal file
@ -0,0 +1,279 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>libqhull.c -- top-level functions and basic data types</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>libqhull.c -- top-level functions and basic data types</h2>
|
||||
<blockquote>
|
||||
<p>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
|
||||
<a href="../../html/index.htm#description">Description of Qhull</a>. </p>
|
||||
<p>This section provides an index to the top-level
|
||||
functions and base data types. The top-level header file, <tt>libqhull.h</tt>,
|
||||
contains prototypes for these functions.</p>
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <b>Qhull</b> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="libqhull.c">libqhull.c</a>,
|
||||
<a href="libqhull.h">libqhull.h</a>, and
|
||||
<a href="../qhull/unix.c">unix.c</a></h3>
|
||||
<ul>
|
||||
<li><a href="#qtype">libqhull.h and unix.c data types and
|
||||
constants</a> </li>
|
||||
<li><a href="#qmacro">libqhull.h other macros</a> </li>
|
||||
<li><a href="#qfunc">Quickhull routines in call order</a> </li>
|
||||
<li><a href="#qinit">Top-level routines for initializing and terminating Qhull</a></li>
|
||||
<li><a href="#qin">Top-level routines for reading and modifying the input</a></li>
|
||||
<li><a href="#qcall">Top-level routines for calling Qhull</a></li>
|
||||
<li><a href="#qout">Top-level routines for returning results</a></li>
|
||||
<li><a href="#qtest">Top-level routines for testing and debugging</a></li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qtype">libqhull.h and unix.c
|
||||
data types and constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.h#flagT">flagT</a> Boolean flag as
|
||||
a bit </li>
|
||||
<li><a href="libqhull.h#boolT">boolT</a> boolean value,
|
||||
either True or False </li>
|
||||
<li><a href="libqhull.h#CENTERtype">CENTERtype</a> to
|
||||
distinguish facet->center </li>
|
||||
<li><a href="libqhull.h#qh_PRINT">qh_PRINT</a> output
|
||||
formats for printing (qh.PRINTout) </li>
|
||||
<li><a href="libqhull.h#qh_ALL">qh_ALL</a> argument flag
|
||||
for selecting everything </li>
|
||||
<li><a href="libqhull.h#qh_ERR">qh_ERR</a> Qhull exit
|
||||
codes for indicating errors </li>
|
||||
<li><a href="libqhull.h#qh_FILEstderr">qh_FILEstderr</a> Fake stderr
|
||||
to distinguish error output from normal output [C++ only]</li>
|
||||
<li><a href="../qhull/unix.c#prompt">qh_prompt</a> version and long prompt for Qhull</li>
|
||||
<li><a href="../qhull/unix.c#prompt2">qh_prompt2</a> synopsis for Qhull</li>
|
||||
<li><a href="../qhull/unix.c#prompt3">qh_prompt3</a> concise prompt for Qhull</li>
|
||||
<li><a href="global.c#qh_version">qh_version</a> version stamp</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qmacro">libqhull.h other
|
||||
macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="qhull_a.h#traceN">traceN</a> print trace
|
||||
message if <em>qh.IStracing >= N</em>. </li>
|
||||
<li><a href="qhull_a.h#QHULL_UNUSED">QHULL_UNUSED</a> declare an
|
||||
unused variable to avoid warnings. </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qfunc">Quickhull
|
||||
routines in call order</a></h3>
|
||||
<ul>
|
||||
<li><a href="../qhull/unix.c#main">main</a> processes the
|
||||
command line, calls qhull() to do the work, and
|
||||
exits </li>
|
||||
<li><a href="libqhull.c#qhull">qh_qhull</a> construct
|
||||
the convex hull of a set of points </li>
|
||||
<li><a href="libqhull.c#build_withrestart">qh_build_withrestart</a>
|
||||
allow restarts while calling qh_buildhull</li>
|
||||
<li><a href="poly2.c#initbuild">qh_initbuild</a>
|
||||
initialize hull and outside sets with point array</li>
|
||||
<li><a href="libqhull.c#partitionall">qh_partitionall</a>
|
||||
partition all points into outside sets </li>
|
||||
<li><a href="libqhull.c#buildhull">qh_buildhull</a>
|
||||
construct a convex hull by adding points one at a
|
||||
time </li>
|
||||
<li><a href="libqhull.c#nextfurthest">qh_nextfurthest</a>
|
||||
return next furthest point for processing </li>
|
||||
<li><a href="libqhull.c#buildtracing">qh_buildtracing</a>
|
||||
trace an iteration of buildhull </li>
|
||||
<li><a href="libqhull.c#addpoint">qh_addpoint</a> add a
|
||||
point to the convex hull </li>
|
||||
<li><a href="libqhull.c#findhorizon">qh_findhorizon</a>
|
||||
find the horizon and visible facets for a point </li>
|
||||
<li><a href="libqhull.c#partitionvisible">qh_partitionvisible</a>
|
||||
partition points from facets in qh.visible_list
|
||||
to facets in qh.newfacet_list </li>
|
||||
<li><a href="libqhull.c#partitionpoint">qh_partitionpoint</a>
|
||||
partition a point as inside, coplanar with, or
|
||||
outside a facet </li>
|
||||
<li><a href="libqhull.c#partitioncoplanar">qh_partitioncoplanar</a>
|
||||
partition coplanar point into a facet </li>
|
||||
<li><a href="libqhull.c#precision">qh_precision</a> restart on precision errors if not merging and if 'QJn'</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qinit">Top-level routines for initializing and terminating Qhull (in other modules)</a></h3>
|
||||
<ul>
|
||||
<li><a href="global.c#freebuild">qh_freebuild</a>
|
||||
free memory used by qh_initbuild and qh_buildhull
|
||||
</li>
|
||||
<li><a href="global.c#checkflags">qh_checkflags</a>
|
||||
check flags for multiple frontends to qhull
|
||||
<li><a href="global.c#freeqhull">qh_freeqhull</a>
|
||||
free memory used by qhull </li>
|
||||
<li><a href="global.c#init_A">qh_init_A</a> called
|
||||
before error handling initialized </li>
|
||||
<li><a href="global.c#init_B">qh_init_B</a> called
|
||||
after points are defined </li>
|
||||
<li><a href="global.c#initflags">qh_initflags</a> set
|
||||
flags and constants from command line </li>
|
||||
<li><a href="rboxlib.c#rboxpoints">qh_rboxpoints</a>
|
||||
generate points for qhull </li>
|
||||
<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
|
||||
restores a saved qhull </li>
|
||||
<li><a href="global.c#save_qhull">qh_save_qhull</a>
|
||||
saves qhull for later restoring </li>
|
||||
<li><a href="user.c#user_memsizes">qh_user_memsizes</a>
|
||||
define additional quick allocation sizes
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qin">Top-level routines for reading and modifying the input (in other modules)</a></h3>
|
||||
<ul>
|
||||
<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
|
||||
implements Gram-Schmidt orthogonalization by rows </li>
|
||||
<li><a href="geom2.c#projectinput">qh_projectinput</a>
|
||||
project input along one or more dimensions +
|
||||
Delaunay projection </li>
|
||||
<li><a href="geom2.c#randommatrix">qh_randommatrix</a>
|
||||
generate a random dimXdim matrix in range (-1,1) </li>
|
||||
<li><a href="io.c#readpoints">qh_readpoints</a> read
|
||||
points from input </li>
|
||||
<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
|
||||
input points using row matrix </li>
|
||||
<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
|
||||
input points using qh low_bound/high_bound </li>
|
||||
<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
|
||||
points to paraboloid for Delaunay triangulation </li>
|
||||
<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
|
||||
generate dual for halfspace intersection with interior
|
||||
point </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qcall">Top-level routines for calling Qhull (in other modules)</a></h3>
|
||||
<ul>
|
||||
<li><a href="libqhull.c#addpoint">qh_addpoint</a> add
|
||||
point to convex hull </li>
|
||||
<li><a href="poly2.c#findbestfacet">qh_findbestfacet</a>
|
||||
find facet that is furthest below a point </li>
|
||||
<li><a href="poly2.c#findfacet_all">qh_findfacet_all</a>
|
||||
exhaustive search for facet below a point </li>
|
||||
<li><a href="libqhull.c#qhull">qh_qhull</a> construct
|
||||
the convex hull of a set of points </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qout">Top-level routines for returning results (in other modules)</a></h3>
|
||||
<ul>
|
||||
<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
|
||||
collect statistics for qh.facet_list </li>
|
||||
<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
|
||||
return nearest vertex to point </li>
|
||||
<li><a href="poly2.c#point">qh_point</a> return point
|
||||
for a point ID </li>
|
||||
<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
|
||||
return temporary set of facets indexed by point
|
||||
ID </li>
|
||||
<li><a href="poly.c#pointid">qh_pointid</a> return ID
|
||||
for a point</li>
|
||||
<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
|
||||
return vertices (if any) for all points</li>
|
||||
<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
|
||||
print all statistics </li>
|
||||
<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
|
||||
print neighborhood of one or two facets </li>
|
||||
<li><a href="libqhull.c#printsummary">qh_printsummary</a>
|
||||
print summary </li>
|
||||
<li><a href="io.c#produce_output">qh_produce_output</a>
|
||||
print the results of qh_qhull() </li>
|
||||
<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
|
||||
compute Voronoi centers for all facets </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-qhull.htm#TOC">»</a><a name="qtest">Top-level routines for testing and debugging (in other modules)</a></h3>
|
||||
<ul>
|
||||
<li><a href="io.c#dfacet">dfacet</a> print facet by
|
||||
ID from debugger </li>
|
||||
<li><a href="io.c#dvertex">dvertex</a> print vertex
|
||||
by ID from debugger </li>
|
||||
<li><a href="poly2.c#check_output">qh_check_output</a>
|
||||
check output </li>
|
||||
<li><a href="poly2.c#check_points">qh_check_points</a>
|
||||
verify that all points are inside the convex hull
|
||||
</li>
|
||||
<li><a href="user.c#errexit">qh_errexit</a> report
|
||||
error with a facet and a ridge</li>
|
||||
<li><a href="libqhull.c#errexit2">qh_errexit2</a> report
|
||||
error with two facets </li>
|
||||
<li><a href="user.c#errprint">qh_errprint</a> print
|
||||
erroneous facets, ridge, and vertex </li>
|
||||
<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
|
||||
print all fields for a list of facets </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
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• <a href="../../html/qh-optf.htm#format">Formats</a>
|
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• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
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• <a href="../../html/qh-optp.htm#print">Print</a>
|
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• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
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<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
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<b>To:</b> <a href="qh-geom.htm">Geom</a> •
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<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
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• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
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• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
308
xs/src/qhull/src/libqhull/qh-set.htm
Normal file
308
xs/src/qhull/src/libqhull/qh-set.htm
Normal file
@ -0,0 +1,308 @@
|
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<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>qset.c -- set data type and operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
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<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
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• <a href="../../html/qh-quick.htm#options">Options</a>
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• <a href="../../html/qh-optp.htm#print">Print</a>
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• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
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• <a href="../../html/qh-optc.htm#prec">Precision</a>
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• <a href="../../html/qh-optt.htm#trace">Trace</a>
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• <a href="index.htm">Functions</a><br>
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||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
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<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
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<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
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• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
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• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>qset.c -- set data type and operations</h2>
|
||||
<blockquote>
|
||||
<p>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. </p>
|
||||
<p>In Qhull, a <i>set</i> is represented by an unordered
|
||||
array of pointers with a maximum size and a NULL
|
||||
terminator (<a href="qset.h#setT">setT</a>).
|
||||
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. </p>
|
||||
<p>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'. </p>
|
||||
<p>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. </p>
|
||||
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
|
||||
<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
|
||||
<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <b>Set</b>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="qset.c">qset.c</a> and
|
||||
<a href="qset.h">qset.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#stype">Data types and constants</a> </li>
|
||||
<li><a href="#seach">FOREACH macros</a> </li>
|
||||
<li><a href="#saccess">access and size macros</a> </li>
|
||||
<li><a href="#sint">internal macros</a> </li>
|
||||
<li><a href="#saddr">address macros</a><p> </li>
|
||||
|
||||
<li><a href="#snew">Allocation and deallocation functions</a> </li>
|
||||
<li><a href="#spred">Access and predicate functions</a>
|
||||
</li>
|
||||
<li><a href="#sadd">Add functions</a> </li>
|
||||
<li><a href="#scheck">Check and print functions</a></li>
|
||||
<li><a href="#scopy">Copy, compact, and zero functions</a></li>
|
||||
<li><a href="#sdel">Delete functions</a> </li>
|
||||
<li><a href="#stemp">Temporary set functions</a> </li>
|
||||
</ul>
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="stype">Data types and
|
||||
constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.h#SETelemsize">SETelemsize</a> size
|
||||
of a set element in bytes </li>
|
||||
<li><a href="qset.h#setT">setT</a> a set with a
|
||||
maximum size and a current size</li>
|
||||
<li><a href="libqhull.h#qh-set">qh global sets</a>
|
||||
global sets for temporary sets, etc. </li>
|
||||
</ul>
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="seach">FOREACH macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.h#FOREACHelem_">FOREACHelem_</a>
|
||||
assign 'elem' to each element in a set </li>
|
||||
<li><a href="qset.h#FOREACHset_">FOREACHset_</a>
|
||||
assign 'set' to each set in a set of sets </li>
|
||||
<li><a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
|
||||
define a FOREACH iterator </li>
|
||||
<li><a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
|
||||
define an indexed FOREACH iterator </li>
|
||||
<li><a href="qset.h#FOREACHsetelementreverse_">FOREACHsetelementreverse_</a>
|
||||
define a reversed FOREACH iterator </li>
|
||||
<li><a href="qset.h#FOREACHsetelementreverse12_">FOREACHsetelementreverse12_</a>
|
||||
define a FOREACH iterator with e[1] and e[0]
|
||||
reversed </li>
|
||||
</ul>
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="saccess">Access and
|
||||
size macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.h#SETelem_">SETelem_</a> return the
|
||||
n'th element of set </li>
|
||||
<li><a href="qset.h#SETelemt_">SETelemt_</a> return
|
||||
the n'th element of set as a type</li>
|
||||
<li><a href="qset.h#SETempty_">SETempty_</a> return
|
||||
true (1) if set is empty </li>
|
||||
<li><a href="qset.h#SETfirst_">SETfirst_</a> return
|
||||
first element of set </li>
|
||||
<li><a href="qset.h#SETfirstt_">SETfirstt_</a> return
|
||||
first element of set as a type</li>
|
||||
<li><a href="qset.h#SETindex_">SETindex_</a> return
|
||||
index of elem in set </li>
|
||||
<li><a href="qset.h#SETreturnsize_">SETreturnsize_</a>
|
||||
return size of a set (normally use <a href="qset.c#setsize">qh_setsize</a>) </li>
|
||||
<li><a href="qset.h#SETsecond_">SETsecond_</a> return
|
||||
second element of set </li>
|
||||
<li><a href="qset.h#SETsecondt_">SETsecondt_</a>
|
||||
return second element of set as a type</li>
|
||||
<li><a href="qset.h#SETtruncate_">SETtruncate_</a>
|
||||
truncate set to size, i.e., qh_settruncate()</li>
|
||||
</ul>
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="sint">Internal macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#SETsizeaddr_">SETsizeaddr_</a>
|
||||
return pointer to end element of a set (indicates
|
||||
current size) </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="saddr">address macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.h#SETaddr_">SETaddr_</a> return
|
||||
address of a set's elements </li>
|
||||
<li><a href="qset.h#SETelemaddr_">SETelemaddr_</a>
|
||||
return address of the n'th element of a set </li>
|
||||
<li><a href="qset.h#SETref_">SETref_</a> l.h.s. for
|
||||
modifying the current element in a FOREACH
|
||||
iteration </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="snew">Allocation and
|
||||
deallocation functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setfree">qh_setfree</a> free the
|
||||
space occupied by a set </li>
|
||||
<li><a href="qset.c#setfree2">qh_setfree2</a> free a
|
||||
set and its elements </li>
|
||||
<li><a href="qset.c#setfreelong">qh_setfreelong</a>
|
||||
free a set only if it is in long memory </li>
|
||||
<li><a href="qset.c#setnew">qh_setnew</a> create a new
|
||||
set </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="spred">Access and
|
||||
predicate functions </a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setendpointer">qh_setendpointer</a> return
|
||||
pointer to NULL terminator of a set</li>
|
||||
<li><a href="qset.c#setequal">qh_setequal</a> return 1
|
||||
if two sorted sets are equal </li>
|
||||
<li><a href="qset.c#setequal_except">qh_setequal_except</a>
|
||||
return 1 if two sorted sets are equal except for
|
||||
an element </li>
|
||||
<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
|
||||
return 1 if two sorted sets are equal except for
|
||||
a pair of skipped elements </li>
|
||||
<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
|
||||
return 1 if two sorted sets are equal except for
|
||||
a pair of skipped elements </li>
|
||||
<li><a href="qset.c#setin">qh_setin</a> return 1 if an
|
||||
element is in a set </li>
|
||||
<li><a href="qset.c#setindex">qh_setindex</a> return
|
||||
the index of an element in a set </li>
|
||||
<li><a href="qset.c#setlast">qh_setlast</a> return
|
||||
last element of a set</li>
|
||||
<li><a href="qset.c#setsize">qh_setsize</a> returns
|
||||
the size of a set </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="sadd">Add functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setaddnth">qh_setaddnth</a> add a
|
||||
element as n'th element of sorted or unsorted set
|
||||
</li>
|
||||
<li><a href="qset.c#setaddsorted">qh_setaddsorted</a>
|
||||
add an element to a sorted set </li>
|
||||
<li><a href="qset.c#setappend">qh_setappend</a> append
|
||||
an element to a set </li>
|
||||
<li><a href="qset.c#setappend_set">qh_setappend_set</a>
|
||||
append a set of elements to a set </li>
|
||||
<li><a href="qset.c#setappend2ndlast">qh_setappend2ndlast</a>
|
||||
add an element as the next to the last element in
|
||||
a set </li>
|
||||
<li><a href="qset.c#setlarger">qh_setlarger</a> return
|
||||
a larger set with the same elements</li>
|
||||
<li><a href="qset.c#setreplace">qh_setreplace</a>
|
||||
replace one element with another in a set</li>
|
||||
<li><a href="qset.c#setunique">qh_setunique</a> add an
|
||||
element if it is not already in a set </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="scheck">Check and print functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setcheck">qh_setcheck</a> check a
|
||||
set for validity </li>
|
||||
<li><a href="qset.c#setprint">qh_setprint</a> print a
|
||||
set's elements to fp </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="scopy">Copy, compact, and zero functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setcompact">qh_setcompact</a>
|
||||
compact NULLs from an unsorted set </li>
|
||||
<li><a href="qset.c#setcopy">qh_setcopy</a> make a
|
||||
copy of a sorted or unsorted set </li>
|
||||
<li><a href="qset.c#setduplicate">qh_setduplicate</a>
|
||||
duplicate a set and its elements </li>
|
||||
<li><a href="qset.c#settruncate">qh_settruncate</a>
|
||||
truncate a set to size elements </li>
|
||||
<li><a href="qset.c#setzero">qh_setzero</a> zero the
|
||||
remainder of a set </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="sdel">Delete functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#setdel">qh_setdel</a> delete an
|
||||
element from an unsorted set. </li>
|
||||
<li><a href="qset.c#setdellast">qh_setdellast</a>
|
||||
delete and return last element from a set</li>
|
||||
<li><a href="qset.c#setdelnth">qh_setdelnth</a> delete
|
||||
and return nth element from an unsorted set </li>
|
||||
<li><a href="qset.c#setdelnthsorted">qh_setdelnthsorted</a>
|
||||
delete and return nth element from a sorted set </li>
|
||||
<li><a href="qset.c#setdelsorted">qh_setdelsorted</a>
|
||||
delete an element from a sorted set </li>
|
||||
<li><a href="qset.c#setnew_delnthsorted">qh_setnew_delnthsorted</a>
|
||||
create a sorted set not containing the nth
|
||||
element </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-set.htm#TOC">»</a><a name="stemp">Temporary set functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="qset.c#settemp">qh_settemp</a> return a
|
||||
temporary set and append it qhmem.tempstack</li>
|
||||
<li><a href="qset.c#settempfree">qh_settempfree</a>
|
||||
free and pop a set from qhmem.tempstack</li>
|
||||
<li><a href="qset.c#settempfree_all">qh_settempfree_all</a>
|
||||
free all sets in qhmem.tempstack </li>
|
||||
<li><a href="qset.c#settemppop">qh_settemppop</a> pop
|
||||
a set from qhmem.tempstack (makes it permanent) </li>
|
||||
<li><a href="qset.c#settemppush">qh_settemppush</a>
|
||||
push a set unto qhmem.tempstack (makes it
|
||||
temporary) </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
163
xs/src/qhull/src/libqhull/qh-stat.htm
Normal file
163
xs/src/qhull/src/libqhull/qh-stat.htm
Normal file
@ -0,0 +1,163 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>stat.c -- statistical operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
|
||||
<h2>stat.c -- statistical operations</h2>
|
||||
<blockquote>
|
||||
<p>Qhull records many statistics. These functions and
|
||||
macros make it inexpensive to add a statistic.
|
||||
<p>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.</p>
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <b>Stat</b> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<h3>Index to <a href="stat.c">stat.c</a> and
|
||||
<a href="stat.h">stat.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#ttype">stat.h types</a> </li>
|
||||
<li><a href="#tconst">stat.h constants</a> </li>
|
||||
<li><a href="#tmacro">stat.h macros</a> </li>
|
||||
<li><a href="#tfunc">stat.c functions</a> </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-stat.htm#TOC">»</a><a name="ttype">stat.h types</a></h3>
|
||||
<ul>
|
||||
<li><a href="stat.h#intrealT">intrealT</a> union of
|
||||
integer and real</li>
|
||||
<li><a href="stat.h#qhstat">qhstat</a> global data
|
||||
structure for statistics </li>
|
||||
</ul>
|
||||
<h3><a href="qh-stat.htm#TOC">»</a><a name="tconst">stat.h
|
||||
constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="stat.h#KEEPstatistics">qh_KEEPstatistics</a> 0 turns off most statistics</li>
|
||||
<li><a href="stat.h#statistics">Z..., W...</a> integer (Z) and real (W) statistics
|
||||
</li>
|
||||
<li><a href="stat.h#ZZstat">ZZstat</a> Z.../W... statistics that
|
||||
remain defined if qh_KEEPstatistics=0
|
||||
</li>
|
||||
<li><a href="stat.h#ztype">ztype</a> zdoc, zinc, etc.
|
||||
for definining statistics </li>
|
||||
</ul>
|
||||
<h3><a href="qh-stat.htm#TOC">»</a><a name="tmacro">stat.h macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="stat.h#MAYdebugx">MAYdebugx</a> called
|
||||
frequently for error trapping </li>
|
||||
<li><a href="stat.h#zadd_">zadd_/wadd_</a> add value
|
||||
to an integer or real statistic </li>
|
||||
<li><a href="stat.h#zdef_">zdef_</a> define a
|
||||
statistic </li>
|
||||
<li><a href="stat.h#zinc_">zinc_</a> increment an
|
||||
integer statistic </li>
|
||||
<li><a href="stat.h#zmax_">zmax_/wmax_</a> update
|
||||
integer or real maximum statistic </li>
|
||||
<li><a href="stat.h#zmin_">zmin_/wmin_</a> update
|
||||
integer or real minimum statistic </li>
|
||||
<li><a href="stat.h#zval_">zval_/wval_</a> set or
|
||||
return value of a statistic </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-stat.htm#TOC">»</a><a name="tfunc">stat.c
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="stat.c#allstatA">qh_allstatA</a> define
|
||||
statistics in groups of 20 </li>
|
||||
<li><a href="stat.c#allstatistics">qh_allstatistics</a>
|
||||
reset printed flag for all statistics </li>
|
||||
<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
|
||||
collect statistics for qh.facet_list </li>
|
||||
<li><a href="stat.c#freestatistics">qh_freestatistics</a>
|
||||
free memory used for statistics </li>
|
||||
<li><a href="stat.c#initstatistics">qh_initstatistics</a>
|
||||
allocate and initialize statistics </li>
|
||||
<li><a href="stat.c#newstats">qh_newstats</a> returns
|
||||
True if statistics for zdoc </li>
|
||||
<li><a href="stat.c#nostatistic">qh_nostatistic</a>
|
||||
true if no statistic to print </li>
|
||||
<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
|
||||
print all statistics </li>
|
||||
<li><a href="stat.c#printstatistics">qh_printstatistics</a>
|
||||
print statistics to a file </li>
|
||||
<li><a href="stat.c#printstatlevel">qh_printstatlevel</a>
|
||||
print level information for a statistic </li>
|
||||
<li><a href="stat.c#printstats">qh_printstats</a>
|
||||
print statistics for a zdoc group </li>
|
||||
<li><a href="stat.c#stddev">qh_stddev</a> compute the
|
||||
standard deviation and average from statistics </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
271
xs/src/qhull/src/libqhull/qh-user.htm
Normal file
271
xs/src/qhull/src/libqhull/qh-user.htm
Normal file
@ -0,0 +1,271 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>user.c -- user-definable operations</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
|
||||
• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
|
||||
• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
|
||||
• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
|
||||
• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm#TOC">User</a>
|
||||
</p>
|
||||
<hr>
|
||||
<h2>user.c -- user-definable operations</h2>
|
||||
<blockquote>
|
||||
<p>This section contains functions and constants that the
|
||||
user may want to change. </p>
|
||||
|
||||
</blockquote>
|
||||
<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
|
||||
<hr>
|
||||
<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
|
||||
<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
|
||||
• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
|
||||
• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
|
||||
• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
|
||||
• <a href="qh-stat.htm#TOC">Stat</a> • <b>User</b>
|
||||
</p>
|
||||
<h3>Index to <a href="user.c">user.c</a>, <a href="usermem.c">usermem.c</a>, <a href="userprintf.c">userprintf.c</a>, <a href="userprintf_rbox.c">userprintf_rbox.c</a> and
|
||||
<a href="user.h">user.h</a></h3>
|
||||
<ul>
|
||||
<li><a href="#qulllib">qhull library constants</a></li>
|
||||
<li><a href="#utype">user.h data types and
|
||||
configuration macros</a> </li>
|
||||
<li><a href="#ujoggle">joggle constants</a></li>
|
||||
<li><a href="#uperform">performance related constants</a></li>
|
||||
<li><a href="#umemory">memory constants</a></li>
|
||||
<li><a href="#ucond">conditional compilation</a></li>
|
||||
<li><a href="#umerge">merge constants</a> </li>
|
||||
<li><a href="#ufunc">user.c functions</a> </li>
|
||||
<li><a href="#u2func">usermem.c functions</a> </li>
|
||||
<li><a href="#u3func">userprintf.c functions</a> </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="qulllib">Qhull library constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#filenamelen">FILENAMElen</a> -- max length of TI or TO filename </li>
|
||||
<li><a href="user.h#msgcode">msgcode</a> -- unique message codes for qh_fprintf </li>
|
||||
<li><a href="user.h#qh_OPTIONline">qh_OPTIONline</a> -- max length of option line ('FO')</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="utype">user.h data
|
||||
types and configuration macros</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#realT">realT, qh_REAL...</a> size
|
||||
of floating point numbers </li>
|
||||
<li><a href="user.h#countT">countT, COUNTmax</a> size
|
||||
of counts and identifiers, typically 'int' or 'long long' </li>
|
||||
<li><a href="user.h#CPUclock">qh_CPUclock</a> clock()
|
||||
function for reporting the total time spent by
|
||||
Qhull </li>
|
||||
<li><a href="user.h#RANDOM">qh_RANDOM...</a> random
|
||||
number generator </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="udef">definition constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#DEFAULTbox">qh_DEFAULTbox</a>
|
||||
define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) </li>
|
||||
<li><a href="user.h#INFINITE">qh_INFINITE</a> on
|
||||
output, indicates Voronoi center at infinity </li>
|
||||
<li><a href="user.h#ORIENTclock">qh_ORIENTclock</a>
|
||||
define convention for orienting facets</li>
|
||||
<li><a href="user.h#ZEROdelaunay">qh_ZEROdelaunay</a>
|
||||
define facets that are ignored in Delaunay triangulations</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="ujoggle">joggle constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#JOGGLEagain">qh_JOGGLEagain</a>
|
||||
how often to retry before using qh_JOGGLEmaxincrease
|
||||
again </li>
|
||||
<li><a href="user.h#JOGGLEdefault">qh_JOGGLEdefault</a>
|
||||
default value for qh.JOGGLEmax for 'QP' </li>
|
||||
<li><a href="user.h#JOGGLEincrease">qh_JOGGLEincrease</a>
|
||||
factor to increase qh.JOGGLEmax on retrys for
|
||||
'QPn' </li>
|
||||
<li><a href="user.h#JOGGLEmaxincrease">qh_JOGGLEmaxincrease</a> max
|
||||
for increasing qh.JOGGLEmax relative to
|
||||
qh.MAXwidth </li>
|
||||
<li><a href="user.h#JOGGLEretry">qh_JOGGLEmaxretry</a>
|
||||
report error if this many retries </li>
|
||||
<li><a href="user.h#JOGGLEretry">qh_JOGGLEretry</a>
|
||||
how often to retry before using qh_JOGGLEmax </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="uperform">performance
|
||||
related constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#HASHfactor">qh_HASHfactor</a>
|
||||
total/used hash slots </li>
|
||||
<li><a href="user.h#INITIALmax">qh_INITIALmax</a> if
|
||||
dim >= qh_INITIALmax, use min/max coordinate
|
||||
points for initial simplex </li>
|
||||
<li><a href="user.h#INITIALsearch">qh_INITIALsearch</a>
|
||||
if qh.INITIALmax, search points up to this
|
||||
dimension </li>
|
||||
<li><a href="user.h#NOtrace">qh_NOtrace</a> disallow
|
||||
tracing </li>
|
||||
<li><a href="user.h#VERIFYdirect">qh_VERIFYdirect</a>
|
||||
'Tv' verifies all <em>points X facets</em> if op
|
||||
count is smaller </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="umemory">memory constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#MEMalign">qh_MEMalign</a> memory
|
||||
alignment for qh_meminitbuffers() in global.c </li>
|
||||
<li><a href="user.h#MEMbufsize">qh_MEMbufsize</a>
|
||||
size of additional memory buffers </li>
|
||||
<li><a href="user.h#MEMinitbuf">qh_MEMinitbuf</a>
|
||||
size of initial memory buffer </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="ucond">conditional compilation</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#compiler">compiler</a> defined symbols,
|
||||
e.g., _STDC_ and _cplusplus
|
||||
|
||||
<li><a href="user.h#COMPUTEfurthest">qh_COMPUTEfurthest</a>
|
||||
compute furthest distance to an outside point instead of storing it with the facet
|
||||
<li><a href="user.h#KEEPstatistics">qh_KEEPstatistics</a>
|
||||
enable statistic gathering and reporting with option 'Ts'
|
||||
<li><a href="user.h#MAXoutside">qh_MAXoutside</a>
|
||||
record outer plane for each facet
|
||||
<li><a href="user.h#NOmerge">qh_NOmerge</a>
|
||||
disable facet merging
|
||||
<li><a href="user.h#NOtrace">qh_NOtrace</a>
|
||||
disable tracing with option 'T4'
|
||||
<li><a href="user.h#QHpointer">qh_QHpointer</a>
|
||||
access global data with pointer or static structure
|
||||
<li><a href="user.h#QUICKhelp">qh_QUICKhelp</a>
|
||||
use abbreviated help messages, e.g., for degenerate inputs
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="umerge">merge
|
||||
constants</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.h#BESTcentrum">qh_BESTcentrum</a>
|
||||
when does qh_findbestneighbor() test centrums? </li>
|
||||
<li><a href="user.h#BESTnonconvex">qh_BESTnonconvex</a>
|
||||
when does qh_findbestneighbor() test nonconvex
|
||||
ridges only? </li>
|
||||
<li><a href="user.h#COPLANARratio">qh_COPLANARratio</a>
|
||||
what is qh.MINvisible? </li>
|
||||
<li><a href="user.h#DIMreduceBuild">qh_DIMreduceBuild</a>
|
||||
max dimension for vertex reduction </li>
|
||||
<li><a href="user.h#DIMmergeVertex">qh_DIMmergeVertex</a>
|
||||
max dimension for vertex merging </li>
|
||||
<li><a href="user.h#DISToutside">qh_DISToutside</a>
|
||||
when is a point clearly outside of a facet for qh_findbestnew and qh_partitionall</li>
|
||||
<li><a href="user.h#MAXnarrow">qh_MAXnarrow</a> max.
|
||||
cosine for qh.NARROWhull </li>
|
||||
<li><a href="user.h#MAXnewcentrum">qh_MAXnewcentrum</a>
|
||||
when does qh_reducevertices_centrum() reset the
|
||||
centrum? </li>
|
||||
<li><a href="user.h#MAXnewmerges">qh_MAXnewmerges</a>
|
||||
when does qh_merge_nonconvex() call
|
||||
qh_reducevertices_centrums? </li>
|
||||
<li><a href="user.h#RATIOnearinside">qh_RATIOnearinside</a>
|
||||
ratio for retaining inside points for
|
||||
qh_check_maxout() </li>
|
||||
<li><a href="user.h#SEARCHdist">qh_SEARCHdist</a>
|
||||
when is facet coplanar with the best facet for qh_findbesthorizon</li>
|
||||
<li><a href="user.h#USEfindbestnew">qh_USEfindbestnew</a>
|
||||
when to use qh_findbestnew for qh_partitionpoint()</li>
|
||||
<li><a href="user.h#WARNnarrow">qh_WARNnarrow</a>
|
||||
max. cosine to warn about qh.NARROWhull </li>
|
||||
<li><a href="user.h#WIDEcoplanar">qh_WIDEcoplanar</a>
|
||||
what is a wide facet? </li>
|
||||
<li><a href="user.h#WIDEduplicate">qh_WIDEduplicate</a>
|
||||
what is a wide ratio on merging duplicate ridges? </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="ufunc">user.c
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="user.c#qhull_template">Qhull template</a> for calling qh_new_qhull from your program</li>
|
||||
<li><a href="user.c#errexit">qh_errexit</a> report
|
||||
error and exit qhull()</li>
|
||||
<li><a href="user.c#errprint">qh_errprint</a> print
|
||||
information about facets and ridges </li>
|
||||
<li><a href="user.c#new_qhull">qh_new_qhull</a> call qhull on an array
|
||||
of points</li>
|
||||
<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
|
||||
print all fields of all facets </li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="u2func">usermem.c
|
||||
functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="usermem.c#qh_exit">qh_exit</a> exit program, same as exit(). May be redefined as throw "QH10003.." by libqhullcpp/usermem_r-cpp.cpp</li>
|
||||
<li><a href="usermem.c#qh_fprintf_stderr">qh_fprintf_stderr</a> print to stderr when qh.ferr is not defined.</li>
|
||||
<li><a href="usermem.c#qh_free">qh_free</a> free memory, same as free().</li>
|
||||
<li><a href="usermem.c#qh_malloc">qh_malloc</a> allocate memory, same as malloc()</li>
|
||||
</ul>
|
||||
|
||||
<h3><a href="qh-user.htm#TOC">»</a><a name="u3func">userprintf.c
|
||||
and userprintf_rbox,c functions</a></h3>
|
||||
<ul>
|
||||
<li><a href="userprintf.c#qh_fprintf">qh_fprintf</a> print
|
||||
information from Qhull, sames as fprintf(). </li>
|
||||
<li><a href="userprintf_rbox.c#qh_fprintf_rbox">qh_fprintf_rbox</a> print
|
||||
information from Rbox, sames as fprintf(). </li>
|
||||
</ul>
|
||||
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
|
||||
<b>To:</b> <a href="qh-geom.htm">Geom</a> •
|
||||
<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
|
||||
• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
|
||||
• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
|
||||
• <a href="qh-user.htm">User</a><br>
|
||||
</p>
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
417
xs/src/qhull/src/libqhull/qhull-exports.def
Normal file
417
xs/src/qhull/src/libqhull/qhull-exports.def
Normal file
@ -0,0 +1,417 @@
|
||||
; 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
|
||||
150
xs/src/qhull/src/libqhull/qhull_a.h
Normal file
150
xs/src/qhull/src/libqhull/qhull_a.h
Normal file
@ -0,0 +1,150 @@
|
||||
/*<html><pre> -<a href="qh-qhull.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <setjmp.h>
|
||||
#include <string.h>
|
||||
#include <math.h>
|
||||
#include <float.h> /* some compilers will not need float.h */
|
||||
#include <limits.h>
|
||||
#include <time.h>
|
||||
#include <ctype.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
/*** uncomment here and qset.c
|
||||
if string.h does not define memcpy()
|
||||
#include <memory.h>
|
||||
*/
|
||||
|
||||
#if qh_CLOCKtype == 2 /* defined in user.h from libqhull.h */
|
||||
#include <sys/types.h>
|
||||
#include <sys/times.h>
|
||||
#include <unistd.h>
|
||||
#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- =========== */
|
||||
|
||||
/*-<a href="qh-qhull.htm#TOC"
|
||||
>--------------------------------</a><a name="traceN">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-qhull.htm#TOC"
|
||||
>--------------------------------</a><a name="QHULL_UNUSED">-</a>
|
||||
|
||||
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 <typename T>
|
||||
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 */
|
||||
418
xs/src/qhull/src/libqhull/qhull_p-exports.def
Normal file
418
xs/src/qhull/src/libqhull/qhull_p-exports.def
Normal file
@ -0,0 +1,418 @@
|
||||
; 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
|
||||
1340
xs/src/qhull/src/libqhull/qset.c
Normal file
1340
xs/src/qhull/src/libqhull/qset.c
Normal file
File diff suppressed because it is too large
Load Diff
490
xs/src/qhull/src/libqhull/qset.h
Normal file
490
xs/src/qhull/src/libqhull/qset.h
Normal file
@ -0,0 +1,490 @@
|
||||
/*<html><pre> -<a href="qh-set.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdio.h>
|
||||
|
||||
/*================= -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 */
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>----------------------------------------</a><a name="setT">-</a>
|
||||
|
||||
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- =========================*/
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------</a><a name="SETelemsize">-</a>
|
||||
|
||||
SETelemsize
|
||||
size of a set element in bytes
|
||||
*/
|
||||
#define SETelemsize ((int)sizeof(setelemT))
|
||||
|
||||
|
||||
/*=========== -macros- =========================*/
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------</a><a name="FOREACHsetelement_">-</a>
|
||||
|
||||
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++);)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>----------------------------------------</a><a name="FOREACHsetelement_i_">-</a>
|
||||
|
||||
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) )
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>--------------------------------------</a><a name="FOREACHsetelementreverse_">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------</a><a name="FOREACHsetelementreverse12_">-</a>
|
||||
|
||||
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++))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------</a><a name="FOREACHelem_">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------</a><a name="FOREACHset_">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-----------------------------------------</a><a name="SETindex_">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETref_">-</a>
|
||||
|
||||
SETref_( elem )
|
||||
l.h.s. for modifying the current element in a FOREACH iteration
|
||||
|
||||
example:
|
||||
SETref_(ridge)= anotherridge;
|
||||
*/
|
||||
#define SETref_(elem) (elem##p[-1])
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETelem_">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETelemt_">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETelemaddr_">-</a>
|
||||
|
||||
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)))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETfirst_">-</a>
|
||||
|
||||
SETfirst_(set)
|
||||
return first element of set
|
||||
|
||||
*/
|
||||
#define SETfirst_(set) ((set)->e[0].p)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETfirstt_">-</a>
|
||||
|
||||
SETfirstt_(set, type)
|
||||
return first element of set as a type
|
||||
|
||||
*/
|
||||
#define SETfirstt_(set, type) ((type*)((set)->e[0].p))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETsecond_">-</a>
|
||||
|
||||
SETsecond_(set)
|
||||
return second element of set
|
||||
|
||||
*/
|
||||
#define SETsecond_(set) ((set)->e[1].p)
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETsecondt_">-</a>
|
||||
|
||||
SETsecondt_(set, type)
|
||||
return second element of set as a type
|
||||
*/
|
||||
#define SETsecondt_(set, type) ((type*)((set)->e[1].p))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETaddr_">-</a>
|
||||
|
||||
SETaddr_(set, type)
|
||||
return address of set's elements
|
||||
*/
|
||||
#define SETaddr_(set,type) ((type **)(&((set)->e[0].p)))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETreturnsize_">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETempty_">-</a>
|
||||
|
||||
SETempty_(set)
|
||||
return true(1) if set is empty
|
||||
|
||||
notes:
|
||||
set may be NULL
|
||||
*/
|
||||
#define SETempty_(set) (!set || (SETfirst_(set) ? 0 : 1))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>-------------------------------<a name="SETsizeaddr_">-</a>
|
||||
|
||||
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]))
|
||||
|
||||
/*-<a href="qh-set.htm#TOC"
|
||||
>---------------------------------------</a><a name="SETtruncate_">-</a>
|
||||
|
||||
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 */
|
||||
245
xs/src/qhull/src/libqhull/random.c
Normal file
245
xs/src/qhull/src/libqhull/random.c
Normal file
@ -0,0 +1,245 @@
|
||||
/*<html><pre> -<a href="index.htm#TOC"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <string.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#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
|
||||
|
||||
/*-<a href="qh-globa.htm#TOC"
|
||||
>-------------------------------</a><a name="argv_to_command">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-globa.htm#TOC"
|
||||
>-------------------------------</a><a name="argv_to_command_size">-</a>
|
||||
|
||||
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; i<argc; i++){
|
||||
count += (int)strlen(argv[i]) + 1; /* WARN64 */
|
||||
if (i>0 && strchr(argv[i], ' ')) {
|
||||
count += 2; /* quote delimiters */
|
||||
for (s=argv[i]; *s; s++) {
|
||||
if (*s == '"') {
|
||||
count++;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return count;
|
||||
} /* argv_to_command_size */
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>-------------------------------</a><a name="rand">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>-------------------------------</a><a name="randomfactor">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-geom.htm#TOC"
|
||||
>-------------------------------</a><a name="randommatrix">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-globa.htm#TOC"
|
||||
>-------------------------------</a><a name="strtol">-</a>
|
||||
|
||||
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 */
|
||||
34
xs/src/qhull/src/libqhull/random.h
Normal file
34
xs/src/qhull/src/libqhull/random.h
Normal file
@ -0,0 +1,34 @@
|
||||
/*<html><pre> -<a href="qh-geom.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
|
||||
870
xs/src/qhull/src/libqhull/rboxlib.c
Normal file
870
xs/src/qhull/src/libqhull/rboxlib.c
Normal file
@ -0,0 +1,870 @@
|
||||
/*<html><pre> -<a href="index.htm#TOC"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <ctype.h>
|
||||
#include <limits.h>
|
||||
#include <math.h>
|
||||
#include <setjmp.h>
|
||||
#include <string.h>
|
||||
#include <time.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#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;
|
||||
|
||||
/*-<a href="qh-qhull.htm#TOC"
|
||||
>-------------------------------</a><a name="rboxpoints">-</a>
|
||||
|
||||
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<dim; i++) {
|
||||
for (k=0; k<dim; k++)
|
||||
*(simplexp++)= i==k ? 1.0 : 0.0;
|
||||
}
|
||||
for (k=0; k<dim; k++)
|
||||
*(simplexp++)= -1.0;
|
||||
}else {
|
||||
for (i=0; i<dim+1; i++) {
|
||||
for (k=0; k<dim; k++) {
|
||||
randr= qh_RANDOMint;
|
||||
*(simplexp++)= 2.0 * randr/randmax - 1.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
if (issimplex2) {
|
||||
simplexp= simplex;
|
||||
for (i=0; i<dim+1; i++) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
for (k=0; k<dim; k++)
|
||||
qh_out1( *(simplexp++) * box);
|
||||
qh_fprintf_rbox(rbox.fout, 9395, "\n");
|
||||
}
|
||||
}
|
||||
for (j=0; j<numpoints; j++) {
|
||||
if (iswidth)
|
||||
apex= qh_RANDOMint % (dim+1);
|
||||
else
|
||||
apex= -1;
|
||||
for (k=0; k<dim; k++)
|
||||
coord[k]= 0.0;
|
||||
norm= 0.0;
|
||||
for (i=0; i<dim+1; i++) {
|
||||
randr= qh_RANDOMint;
|
||||
factor= randr/randmax;
|
||||
if (i == apex)
|
||||
factor *= width;
|
||||
norm += factor;
|
||||
for (k=0; k<dim; k++) {
|
||||
simplexp= simplex + i*dim + k;
|
||||
coord[k] += factor * (*simplexp);
|
||||
}
|
||||
}
|
||||
for (k=0; k<dim; k++)
|
||||
coord[k] *= box/norm;
|
||||
qh_outcoord(iscdd, coord, dim);
|
||||
if(coincidentcount++ < coincidenttotal)
|
||||
qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
|
||||
}
|
||||
isregular= 0; /* continue with isbox */
|
||||
numpoints= 0;
|
||||
}
|
||||
|
||||
/* ============= mesh distribution =============== */
|
||||
if (ismesh) {
|
||||
nthroot= (int)(pow((double)numpoints, 1.0/dim) + 0.99999);
|
||||
for (k=dim; k--; )
|
||||
mult[k]= 0;
|
||||
for (i=0; i < numpoints; i++) {
|
||||
coordp= coord;
|
||||
for (k=0; k < dim; k++) {
|
||||
if (k == 0)
|
||||
*(coordp++)= mult[0] * meshn + mult[1] * (-meshm);
|
||||
else if (k == 1)
|
||||
*(coordp++)= mult[0] * meshm + mult[1] * meshn;
|
||||
else
|
||||
*(coordp++)= mult[k] * meshr;
|
||||
}
|
||||
qh_outcoord(iscdd, coord, dim);
|
||||
if(coincidentcount++ < coincidenttotal)
|
||||
qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
|
||||
for (k=0; k < dim; k++) {
|
||||
if (++mult[k] < nthroot)
|
||||
break;
|
||||
mult[k]= 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
/* ============= regular points for 's' =============== */
|
||||
else if (isregular && !islens) {
|
||||
if (dim != 2 && dim != 3) {
|
||||
qh_free(simplex);
|
||||
qh_fprintf_rbox(rbox.ferr, 6197, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
|
||||
qh_errexit_rbox(qh_ERRinput);
|
||||
}
|
||||
if (!isaxis || radius == 0.0) {
|
||||
isaxis= 1;
|
||||
radius= 1.0;
|
||||
}
|
||||
if (dim == 3) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out3n( 0.0, 0.0, -box);
|
||||
if (!isgap) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out3n( 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( 1.0);
|
||||
qh_out2n( x*box, y*box);
|
||||
}else {
|
||||
norm= sqrt(1.0 + x*x + y*y);
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out3n( 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( 1.0);
|
||||
qh_out3n( 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( 1.0);
|
||||
qh_out2n( x*box, y*box);
|
||||
if (i != 0 && i != numpoints - 1) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out2n( 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(rbox.ferr, 6198, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
|
||||
qh_errexit_rbox(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( 1.0);
|
||||
qh_out3n( box*x, box*y, 0.0);
|
||||
x *= 1-gap;
|
||||
y *= 1-gap;
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out3n( box*x, box*y, box * offset);
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
qh_out3n( box*x, box*y, -box * offset);
|
||||
}
|
||||
}
|
||||
/* ============= apex of 'Zn' distribution + gendim =============== */
|
||||
else {
|
||||
if (isaxis) {
|
||||
gendim= dim-1;
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
for (j=0; j < gendim; j++)
|
||||
qh_out1( 0.0);
|
||||
qh_out1( -box);
|
||||
qh_fprintf_rbox(rbox.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; j<gendim; j++)
|
||||
coord[j]= factor * coord[j];
|
||||
/* ============= dim-1 point of 'Ln s' distribution =========== */
|
||||
}else if (islens && issphere) {
|
||||
if (!isgap) {
|
||||
isgap= 1;
|
||||
gap= 1.0;
|
||||
}
|
||||
randr= qh_RANDOMint;
|
||||
rangap= 1.0 - gap * randr/randmax;
|
||||
factor= rangap / norm;
|
||||
for (j=0; j<gendim; j++)
|
||||
coord[j]= factor * coord[j];
|
||||
/* ============= dim-1 point of 'Ln' distribution ========== */
|
||||
}else if (islens && !issphere) {
|
||||
if (!isgap) {
|
||||
isgap= 1;
|
||||
gap= 1.0;
|
||||
}
|
||||
j= qh_RANDOMint % gendim;
|
||||
if (coord[j] < 0)
|
||||
coord[j]= -1.0 - coord[j] * gap;
|
||||
else
|
||||
coord[j]= 1.0 - coord[j] * gap;
|
||||
/* ============= point of 'l' distribution =============== */
|
||||
}else if (isspiral) {
|
||||
if (dim != 3) {
|
||||
qh_free(simplex);
|
||||
qh_fprintf_rbox(rbox.ferr, 6199, "rbox error: spiral distribution is available only in 3d\n\n");
|
||||
qh_errexit_rbox(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<dim; j++)
|
||||
coord[j]= factor * coord[j];
|
||||
}
|
||||
/* ============= project 'Zn s' point in to sphere =============== */
|
||||
if (isaxis && issphere) {
|
||||
coord[dim-1]= 1.0;
|
||||
norm= 1.0;
|
||||
for (j=0; j<gendim; j++)
|
||||
norm += coord[j] * coord[j];
|
||||
norm= sqrt(norm);
|
||||
for (j=0; j<dim; j++)
|
||||
coord[j]= coord[j] / norm;
|
||||
if (iswidth) {
|
||||
randr= qh_RANDOMint;
|
||||
coord[dim-1] *= 1 - width * randr/randmax;
|
||||
}
|
||||
/* ============= project 'Zn' point onto cube =============== */
|
||||
}else if (isaxis && !issphere) { /* not very interesting */
|
||||
randr= qh_RANDOMint;
|
||||
coord[dim-1]= 2.0 * randr/randmax - 1.0;
|
||||
/* ============= project 'Ln' point out to sphere =============== */
|
||||
}else if (islens) {
|
||||
coord[dim-1]= lensbase;
|
||||
for (j=0, norm= 0; j<dim; j++)
|
||||
norm += coord[j] * coord[j];
|
||||
norm= sqrt(norm);
|
||||
for (j=0; j<dim; j++)
|
||||
coord[j]= coord[j] * radius/ norm;
|
||||
coord[dim-1] -= lensbase;
|
||||
if (iswidth) {
|
||||
randr= qh_RANDOMint;
|
||||
coord[dim-1] *= 1 - width * randr/randmax;
|
||||
}
|
||||
if (qh_RANDOMint > 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<dim; k++)
|
||||
coord[k]= coord[k] * box;
|
||||
|
||||
/* ============= write output =============== */
|
||||
qh_outcoord(iscdd, coord, dim);
|
||||
if(coincidentcount++ < coincidenttotal)
|
||||
qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
|
||||
}
|
||||
}
|
||||
|
||||
/* ============= write cube vertices =============== */
|
||||
if (addcube) {
|
||||
for (j=0; j<cubesize; j++) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
for (k=dim-1; 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<diamondsize; j++) {
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
for (k=dim-1; k>=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<coincidentpoints; i++) {
|
||||
p= coord;
|
||||
if (iscdd)
|
||||
qh_out1( 1.0);
|
||||
for (k=0; k < dim; k++) {
|
||||
randr= qh_RANDOMint;
|
||||
delta= 2.0 * randr/randmax - 1.0; /* -1..+1 */
|
||||
delta *= radius;
|
||||
qh_out1(*(p++) + delta);
|
||||
}
|
||||
qh_fprintf_rbox(rbox.fout, 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(int exitcode)
|
||||
{
|
||||
longjmp(rbox.errexit, exitcode);
|
||||
} /* qh_errexit_rbox */
|
||||
|
||||
717
xs/src/qhull/src/libqhull/stat.c
Normal file
717
xs/src/qhull/src/libqhull/stat.c
Normal file
@ -0,0 +1,717 @@
|
||||
/*<html><pre> -<a href="qh-stat.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 ================*/
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="allstatA">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="allstatistics">-</a>
|
||||
|
||||
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
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="collectstatistics">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="freestatistics">-</a>
|
||||
|
||||
qh_freestatistics( )
|
||||
free memory used for statistics
|
||||
*/
|
||||
void qh_freestatistics(void) {
|
||||
|
||||
#if qh_QHpointer
|
||||
qh_free(qh_qhstat);
|
||||
qh_qhstat= NULL;
|
||||
#endif
|
||||
} /* freestatistics */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="initstatistics">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="newstats">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="nostatistic">-</a>
|
||||
|
||||
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
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="printallstatistics">-</a>
|
||||
|
||||
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);
|
||||
}
|
||||
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="printstatistics">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="printstatlevel">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="printstats">-</a>
|
||||
|
||||
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<nexti; j++)
|
||||
qh_printstatlevel(fp, qhstat id[j]);
|
||||
}
|
||||
if (nextindex)
|
||||
*nextindex= nexti;
|
||||
} /* printstats */
|
||||
|
||||
#if qh_KEEPstatistics
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="stddev">-</a>
|
||||
|
||||
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
|
||||
|
||||
543
xs/src/qhull/src/libqhull/stat.h
Normal file
543
xs/src/qhull/src/libqhull/stat.h
Normal file
@ -0,0 +1,543 @@
|
||||
/*<html><pre> -<a href="qh-stat.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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"
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="KEEPstatistics">-</a>
|
||||
|
||||
qh_KEEPstatistics
|
||||
0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
|
||||
*/
|
||||
#ifndef qh_KEEPstatistics
|
||||
#define qh_KEEPstatistics 1
|
||||
#endif
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="statistics">-</a>
|
||||
|
||||
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">-</a>
|
||||
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};
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="ZZstat">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>-------------------------------</a><a name="ztype">-</a>
|
||||
|
||||
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 =============*/
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="MAYdebugx">-</a>
|
||||
|
||||
MAYdebugx
|
||||
define as maydebug() to be called frequently for error trapping
|
||||
*/
|
||||
#define MAYdebugx
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zdef_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zinc_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zadd_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zval_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zmax_">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="zmin_">-</a>
|
||||
|
||||
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 ==============*/
|
||||
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="intrealT">-</a>
|
||||
|
||||
intrealT
|
||||
union of integer and real, used for statistics
|
||||
*/
|
||||
typedef union intrealT intrealT; /* union of int and realT */
|
||||
union intrealT {
|
||||
int i;
|
||||
realT r;
|
||||
};
|
||||
|
||||
/*-<a href="qh-stat.htm#TOC"
|
||||
>--------------------------------</a><a name="qhstat">-</a>
|
||||
|
||||
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 */
|
||||
538
xs/src/qhull/src/libqhull/user.c
Normal file
538
xs/src/qhull/src/libqhull/user.c
Normal file
@ -0,0 +1,538 @@
|
||||
/*<html><pre> -<a href="qh-user.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdarg.h>
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qhull_template">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="new_qhull">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="errexit">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="errprint">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="printfacetlist">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>-------------------------------</a><a name="printhelp_degenerate">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-globa.htm#TOC"
|
||||
>-------------------------------</a><a name="printhelp_narrowhull">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-io.htm#TOC"
|
||||
>-------------------------------</a><a name="printhelp_singular">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-globa.htm#TOC"
|
||||
>-------------------------------</a><a name="user_memsizes">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
909
xs/src/qhull/src/libqhull/user.h
Normal file
909
xs/src/qhull/src/libqhull/user.h
Normal file
@ -0,0 +1,909 @@
|
||||
/*<html><pre> -<a href="qh-user.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <time.h>
|
||||
|
||||
#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 ======================*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="filenamelen">-</a>
|
||||
|
||||
FILENAMElen -- max length for TI and TO filenames
|
||||
|
||||
*/
|
||||
|
||||
#define qh_FILENAMElen 500
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="msgcode">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_OPTIONline">-</a>
|
||||
|
||||
qh_OPTIONline -- max length of an option line 'FO'
|
||||
*/
|
||||
#define qh_OPTIONline 80
|
||||
|
||||
/*============================================================*/
|
||||
/*============= data types and configuration macros ==========*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="realT">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="CPUclock">-</a>
|
||||
|
||||
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,
|
||||
<time.h> 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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="RANDOM">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="ORIENTclock">-</a>
|
||||
|
||||
qh_ORIENTclock
|
||||
0 for inward pointing normals by Geomview convention
|
||||
*/
|
||||
#define qh_ORIENTclock 0
|
||||
|
||||
|
||||
/*============================================================*/
|
||||
/*============= joggle constants =============================*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEdefault">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEincrease">-</a>
|
||||
|
||||
qh_JOGGLEincrease
|
||||
factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
|
||||
*/
|
||||
#define qh_JOGGLEincrease 10.0
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEretry">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEagain">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="JOGGLEmaxretry">-</a>
|
||||
|
||||
qh_JOGGLEmaxretry
|
||||
stop after qh_JOGGLEmaxretry attempts
|
||||
*/
|
||||
#define qh_JOGGLEmaxretry 100
|
||||
|
||||
/*============================================================*/
|
||||
/*============= performance related constants ================*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="HASHfactor">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="VERIFYdirect">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="INITIALsearch">-</a>
|
||||
|
||||
qh_INITIALsearch
|
||||
if qh_INITIALmax, search points up to this dimension
|
||||
*/
|
||||
#define qh_INITIALsearch 6
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="INITIALmax">-</a>
|
||||
|
||||
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 =============================*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MEMalign">-</a>
|
||||
|
||||
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 *))))
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MEMbufsize">-</a>
|
||||
|
||||
qh_MEMbufsize
|
||||
size of additional memory buffers
|
||||
|
||||
notes:
|
||||
used for qh_meminitbuffers() in global.c
|
||||
*/
|
||||
#define qh_MEMbufsize 0x10000 /* allocate 64K memory buffers */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MEMinitbuf">-</a>
|
||||
|
||||
qh_MEMinitbuf
|
||||
size of initial memory buffer
|
||||
|
||||
notes:
|
||||
use for qh_meminitbuffers() in global.c
|
||||
*/
|
||||
#define qh_MEMinitbuf 0x20000 /* initially allocate 128K buffer */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="INFINITE">-</a>
|
||||
|
||||
qh_INFINITE
|
||||
on output, indicates Voronoi center at infinity
|
||||
*/
|
||||
#define qh_INFINITE -10.101
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="DEFAULTbox">-</a>
|
||||
|
||||
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 ======================*/
|
||||
/*============================================================*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="compiler">-</a>
|
||||
|
||||
__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
|
||||
*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="COMPUTEfurthest">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="KEEPstatistics">-</a>
|
||||
|
||||
qh_KEEPstatistics
|
||||
=0 removes most of statistic gathering and reporting
|
||||
|
||||
notes:
|
||||
if 0, code size is reduced by about 4%.
|
||||
*/
|
||||
#define qh_KEEPstatistics 1
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MAXoutside">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="NOmerge">-</a>
|
||||
|
||||
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:
|
||||
<a href="mem.h#NOmem">qh_NOmem</a> in mem.c
|
||||
|
||||
see user.c/user_eg.c for removing io.o
|
||||
*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="NOtrace">-</a>
|
||||
|
||||
qh_NOtrace
|
||||
no tracing if defined
|
||||
|
||||
notes:
|
||||
This saves about 5% space.
|
||||
|
||||
#define qh_NOtrace
|
||||
*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="QHpointer">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="QUICKhelp">-</a>
|
||||
|
||||
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.
|
||||
*/
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="DIMmergeVertex">-</a>
|
||||
|
||||
qh_DIMmergeVertex
|
||||
max dimension for vertex merging (it is not effective in high-d)
|
||||
*/
|
||||
#define qh_DIMmergeVertex 6
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="DIMreduceBuild">-</a>
|
||||
|
||||
qh_DIMreduceBuild
|
||||
max dimension for vertex reduction during build (slow in high-d)
|
||||
*/
|
||||
#define qh_DIMreduceBuild 5
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="BESTcentrum">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="BESTnonconvex">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MAXnewmerges">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MAXnewcentrum">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="COPLANARratio">-</a>
|
||||
|
||||
qh_COPLANARratio
|
||||
for 3-d+ merging, qh.MINvisible is n*premerge_centrum
|
||||
|
||||
notes:
|
||||
for non-merging, it's DISTround
|
||||
*/
|
||||
#define qh_COPLANARratio 3
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="DISToutside">-</a>
|
||||
|
||||
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))
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="RATIOnearinside">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="SEARCHdist">-</a>
|
||||
|
||||
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)));
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="USEfindbestnew">-</a>
|
||||
|
||||
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)
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="WIDEcoplanar">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="WIDEduplicate">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="MAXnarrow">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="WARNnarrow">-</a>
|
||||
|
||||
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
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>--------------------------------</a><a name="ZEROdelaunay">-</a>
|
||||
|
||||
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 <stdlib.h>
|
||||
#include <crtdbg.h>
|
||||
#endif
|
||||
#endif /* qh_DEFuser */
|
||||
|
||||
|
||||
|
||||
94
xs/src/qhull/src/libqhull/usermem.c
Normal file
94
xs/src/qhull/src/libqhull/usermem.c
Normal file
@ -0,0 +1,94 @@
|
||||
/*<html><pre> -<a href="qh-user.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdarg.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_exit">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_fprintf_stderr">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_free">-</a>
|
||||
|
||||
qh_free( mem )
|
||||
free memory
|
||||
|
||||
notes:
|
||||
same as free()
|
||||
No calls to qh_errexit()
|
||||
*/
|
||||
void qh_free(void *mem) {
|
||||
free(mem);
|
||||
} /* free */
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_malloc">-</a>
|
||||
|
||||
qh_malloc( mem )
|
||||
allocate memory
|
||||
|
||||
notes:
|
||||
same as malloc()
|
||||
*/
|
||||
void *qh_malloc(size_t size) {
|
||||
return malloc(size);
|
||||
} /* malloc */
|
||||
|
||||
|
||||
66
xs/src/qhull/src/libqhull/userprintf.c
Normal file
66
xs/src/qhull/src/libqhull/userprintf.c
Normal file
@ -0,0 +1,66 @@
|
||||
/*<html><pre> -<a href="qh-user.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdarg.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_fprintf">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
53
xs/src/qhull/src/libqhull/userprintf_rbox.c
Normal file
53
xs/src/qhull/src/libqhull/userprintf_rbox.c
Normal file
@ -0,0 +1,53 @@
|
||||
/*<html><pre> -<a href="qh-user.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <stdarg.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
/*-<a href="qh-user.htm#TOC"
|
||||
>-------------------------------</a><a name="qh_fprintf_rbox">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
240
xs/src/qhull/src/libqhull_r/Makefile
Normal file
240
xs/src/qhull/src/libqhull_r/Makefile
Normal file
@ -0,0 +1,240 @@
|
||||
# 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
|
||||
2096
xs/src/qhull/src/libqhull_r/geom2_r.c
Normal file
2096
xs/src/qhull/src/libqhull_r/geom2_r.c
Normal file
File diff suppressed because it is too large
Load Diff
1234
xs/src/qhull/src/libqhull_r/geom_r.c
Normal file
1234
xs/src/qhull/src/libqhull_r/geom_r.c
Normal file
File diff suppressed because it is too large
Load Diff
184
xs/src/qhull/src/libqhull_r/geom_r.h
Normal file
184
xs/src/qhull/src/libqhull_r/geom_r.h
Normal file
@ -0,0 +1,184 @@
|
||||
/*<html><pre> -<a href="qh-geom_r.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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- ======================== */
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="fabs_">-</a>
|
||||
|
||||
fabs_(a)
|
||||
returns the absolute value of a
|
||||
*/
|
||||
#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="fmax_">-</a>
|
||||
|
||||
fmax_(a,b)
|
||||
returns the maximum value of a and b
|
||||
*/
|
||||
#define fmax_( a,b ) ( ( a ) < ( b ) ? ( b ) : ( a ) )
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="fmin_">-</a>
|
||||
|
||||
fmin_(a,b)
|
||||
returns the minimum value of a and b
|
||||
*/
|
||||
#define fmin_( a,b ) ( ( a ) > ( b ) ? ( b ) : ( a ) )
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="maximize_">-</a>
|
||||
|
||||
maximize_(maxval, val)
|
||||
set maxval to val if val is greater than maxval
|
||||
*/
|
||||
#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="minimize_">-</a>
|
||||
|
||||
minimize_(minval, val)
|
||||
set minval to val if val is less than minval
|
||||
*/
|
||||
#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="det2_">-</a>
|
||||
|
||||
det2_(a1, a2,
|
||||
b1, b2)
|
||||
|
||||
compute a 2-d determinate
|
||||
*/
|
||||
#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="det3_">-</a>
|
||||
|
||||
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 ) )
|
||||
|
||||
/*-<a href="qh-geom_r.htm#TOC"
|
||||
>--------------------------------</a><a name="dX">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
|
||||
2100
xs/src/qhull/src/libqhull_r/global_r.c
Normal file
2100
xs/src/qhull/src/libqhull_r/global_r.c
Normal file
File diff suppressed because it is too large
Load Diff
266
xs/src/qhull/src/libqhull_r/index.htm
Normal file
266
xs/src/qhull/src/libqhull_r/index.htm
Normal file
@ -0,0 +1,266 @@
|
||||
<!-- Do not edit with Front Page, it adds too many spaces -->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type"
|
||||
content="text/html; charset=iso-8859-1">
|
||||
<title>Reentrant Qhull functions, macros, and data structures</title>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<!-- Navigation links -->
|
||||
<p><a name="TOP"><b>Up:</b></a> <a
|
||||
href="http://www.qhull.org">Home page</a> for Qhull<br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code</a><br>
|
||||
<b>To:</b> <a href="#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="qh-geom_r.htm">Geom</a> • <a href="qh-globa_r.htm">Global</a>
|
||||
• <a href="qh-io_r.htm">Io</a> • <a href="qh-mem_r.htm">Mem</a>
|
||||
• <a href="qh-merge_r.htm">Merge</a> • <a href="qh-poly_r.htm">Poly</a>
|
||||
• <a href="qh-qhull_r.htm">Qhull</a> • <a href="qh-set_r.htm">Set</a>
|
||||
• <a href="qh-stat_r.htm">Stat</a> • <a href="qh-user_r.htm">User</a>
|
||||
|
||||
<hr>
|
||||
<!-- Main text of document. -->
|
||||
|
||||
<h1>Reentrant Qhull functions, macros, and data structures</h1>
|
||||
<blockquote>
|
||||
<p>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 <a href=../../html/qh-code.htm#library>Calling
|
||||
Qhull from C programs</a> and <a href="../../html/qh-code.htm#cpp">Calling Qhull from C++ programs</a>.</p>
|
||||
|
||||
<p>Qhull uses the following conventions:</p>
|
||||
<blockquote>
|
||||
|
||||
<ul>
|
||||
<li>in code, global variables start with "qh "
|
||||
<li>in documentation, global variables start with 'qh.'
|
||||
<li>constants start with an upper case word
|
||||
<li>important globals include an '_'
|
||||
<li>functions, macros, and constants start with "qh_"</li>
|
||||
<li>data types end in "T"</li>
|
||||
<li>macros with arguments end in "_"</li>
|
||||
<li>iterators are macros that use local variables</li>
|
||||
<li>iterators for sets start with "FOREACH"</li>
|
||||
<li>iterators for lists start with "FORALL"</li>
|
||||
<li>qhull options are in single quotes (e.g., 'Pdn')</li>
|
||||
<li>lists are sorted alphabetically</li>
|
||||
<li>preprocessor directives on left margin for older compilers</li>
|
||||
</ul>
|
||||
</blockquote>
|
||||
<p>
|
||||
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.).
|
||||
<p>
|
||||
When reading code with an editor, a search for
|
||||
'<i>"function</i>'
|
||||
will locate the header of <i>qh_function</i>. A search for '<i>* function</i>'
|
||||
will locate the tail of <i>qh_function</i>.
|
||||
|
||||
<p>A useful starting point is <a href="libqhull_r.h">libqhull_r.h</a>. It defines most
|
||||
of Qhull data structures and top-level functions. Search for <i>'PFn'</i> to
|
||||
determine the corresponding constant in Qhull. Search for <i>'Fp'</i> to
|
||||
determine the corresponding <a href="libqhull_r.h#qh_PRINT">qh_PRINT...</a> constant.
|
||||
Search <a href="io_r.c">io_r.c</a> to learn how the print function is implemented.</p>
|
||||
|
||||
<p>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.
|
||||
<ul>
|
||||
<li>In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
|
||||
<li>Opera 12.10
|
||||
<ol>
|
||||
<li>In Tools > Preferences > Advanced > Downloads
|
||||
<li>Uncheck 'Hide file types opened with Opera'
|
||||
<li>Quick find 'html'
|
||||
<li>Select 'text/html' > Edit
|
||||
<li>Add File extensions 'c,h,'
|
||||
<li>Click 'OK'
|
||||
</ol>
|
||||
<li>Internet Explorer -- Mime types are not available from 'Internet Options'. Is there a registry key for these settings?
|
||||
<li>Firefox -- Mime types are not available from 'Preferences'. Is there an add-on to change the file extensions for a mime type?
|
||||
<li>Chrome -- Can Chrome be configured?
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
Please report documentation and link errors
|
||||
to <a href="mailto:qhull-bug@qhull.org">qhull-bug@qhull.org</a>.
|
||||
</blockquote>
|
||||
|
||||
<p><b>Copyright © 1997-2015 C.B. Barber</b></p>
|
||||
|
||||
<hr>
|
||||
|
||||
<h2><a href="#TOP">»</a><a name="TOC">Qhull files</a> </h2>
|
||||
<blockquote>
|
||||
|
||||
<p>This sections lists the .c and .h files for Qhull. Please
|
||||
refer to these files for detailed information.</p>
|
||||
<blockquote>
|
||||
|
||||
<dl>
|
||||
<dt><a href="../../Makefile"><b>Makefile</b></a><b>, </b><a href="../../CMakeLists.txt"><b>CMakeLists.txt</b></a></dt>
|
||||
<dd><tt>Makefile</tt> is preconfigured for gcc. <tt>CMakeLists.txt</tt> supports multiple
|
||||
platforms with <a href=http://www.cmake.org/>CMake</a>.
|
||||
Qhull includes project files for Visual Studio and Qt.
|
||||
</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
|
||||
<dd>Include file for the Qhull library (<tt>libqhull.so</tt>, <tt>qhull.dll</tt>, <tt>libqhullstatic.a</tt>).
|
||||
Data structures are documented under <a href="qh-poly_r.htm">Poly</a>.
|
||||
Global variables are documented under <a href="qh-globa_r.htm">Global</a>.
|
||||
Other data structures and variables are documented under
|
||||
<a href="qh-qhull_r.htm#TOC">Qhull</a> or <a href="qh-geom_r.htm"><b>Geom</b></a><b>.</b></dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-geom_r.htm"><b>Geom</b></a><b>, </b>
|
||||
<a href="geom_r.h"><b>geom_r.h</b></a><b>, </b>
|
||||
<a href="geom_r.c"><b>geom_r.c</b></a><b>, </b>
|
||||
<a href="geom2_r.c"><b>geom2_r.c</b></a><b>, </b>
|
||||
<a href="random_r.c"><b>random_r.c</b></a><b>, </b>
|
||||
<a href="random_r.h"><b>random_r.h</b></a></dt>
|
||||
<dd>Geometric routines. These routines implement mathematical
|
||||
functions such as Gaussian elimination and geometric
|
||||
routines needed for Qhull. Frequently used routines are
|
||||
in <tt>geom_r.c</tt> while infrequent ones are in <tt>geom2_r.c</tt>.
|
||||
</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-globa_r.htm"><b>Global</b></a><b>, </b>
|
||||
<a href="global_r.c"><b>global_r.c</b></a><b>, </b>
|
||||
<a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
|
||||
<dd>Global routines. Qhull uses a global data structure, <tt>qh</tt>,
|
||||
to store globally defined constants, lists, sets, and
|
||||
variables.
|
||||
<tt>global_r.c</tt> initializes and frees these
|
||||
structures. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-io_r.htm"><b>Io</b></a><b>, </b><a href="io_r.h"><b>io_r.h</b></a><b>,
|
||||
</b><a href="io_r.c"><b>io_r.c</b></a> </dt>
|
||||
<dd>Input and output routines. Qhull provides a wide range of
|
||||
input and output options.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-mem_r.htm"><b>Mem</b></a><b>, </b>
|
||||
<a href="mem_r.h"><b>mem_r.h</b></a><b>, </b>
|
||||
<a href="mem_r.c"><b>mem_r.c</b></a> </dt>
|
||||
<dd>Memory routines. Qhull provides memory allocation and
|
||||
deallocation. It uses quick-fit allocation.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-merge_r.htm"><b>Merge</b></a><b>, </b>
|
||||
<a href="merge_r.h"><b>merge_r.h</b></a><b>, </b>
|
||||
<a href="merge_r.c"><b>merge_r.c</b></a> </dt>
|
||||
<dd>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.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-poly_r.htm"><b>Poly</b></a><b>, </b>
|
||||
<a href="poly_r.h"><b>poly_r.h</b></a><b>, </b>
|
||||
<a href="poly_r.c"><b>poly_r.c</b></a><b>, </b>
|
||||
<a href="poly2_r.c"><b>poly2_r.c</b></a><b>, </b>
|
||||
<a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
|
||||
<dd>Polyhedral routines. Qhull produces a polyhedron as a
|
||||
list of facets with vertices, neighbors, ridges, and
|
||||
geometric information. <tt>libqhull_r.h</tt> defines the main
|
||||
data structures. Frequently used routines are in <tt>poly_r.c</tt>
|
||||
while infrequent ones are in <tt>poly2_r.c</tt>.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-qhull_r.htm#TOC"><b>Qhull</b></a><b>, </b>
|
||||
<a href="libqhull_r.c"><b>libqhull_r.c</b></a><b>, </b>
|
||||
<a href="libqhull_r.h"><b>libqhull_r.h</b></a><b>, </b>
|
||||
<a href="qhull_ra.h"><b>qhull_ra.h</b></a><b>, </b>
|
||||
<a href="../qhull/unix_r.c"><b>unix_r.c</b></a> <b>, </b>
|
||||
<a href="../qconvex/qconvex_r.c"><b>qconvex_r.c</b></a> <b>, </b>
|
||||
<a href="../qdelaunay/qdelaun_r.c"><b>qdelaun_r.c</b></a> <b>, </b>
|
||||
<a href="../qhalf/qhalf_r.c"><b>qhalf_r.c</b></a> <b>, </b>
|
||||
<a href="../qvoronoi/qvoronoi_r.c"><b>qvoronoi_r.c</b></a> </dt>
|
||||
<dd>Top-level routines. The Quickhull algorithm is
|
||||
implemented by <tt>libqhull_r.c</tt>. <tt>qhull_ra.h</tt>
|
||||
includes all header files. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-set_r.htm"><b>Set</b></a><b>, </b>
|
||||
<a href="qset_r.h"><b>qset_r.h</b></a><b>, </b>
|
||||
<a href="qset_r.c"><b>qset_r.c</b></a> </dt>
|
||||
<dd>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. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-stat_r.htm"><b>Stat</b></a><b>, </b>
|
||||
<a href="stat_r.h"><b>stat_r.h</b></a><b>, </b>
|
||||
<a href="stat_r.c"><b>stat_r.c</b></a> </dt>
|
||||
<dd>Statistical routines. Qhull maintains statistics about
|
||||
its implementation. </dd>
|
||||
|
||||
<dt> </dt>
|
||||
<dt><a href="qh-user_r.htm"><b>User</b></a><b>, </b>
|
||||
<a href="user_r.h"><b>user_r.h</b></a><b>, </b>
|
||||
<a href="user_r.c"><b>user_r.c</b></a><b>, </b>
|
||||
<a href="../user_eg/user_eg_r.c"><b>user_eg_r.c</b></a><b>, </b>
|
||||
<a href="../user_eg2/user_eg2_r.c"><b>user_eg2_r.c</b></a><b>, </b>
|
||||
<a href="../user_eg3/user_eg3_r.cpp"><b>user_eg3_r.cpp</b></a><b>, </b>
|
||||
</dt>
|
||||
<dd>User-defined routines. Qhull allows the user to configure
|
||||
the code with defined constants and specialized routines.
|
||||
</dd>
|
||||
</dl>
|
||||
</blockquote>
|
||||
|
||||
</blockquote>
|
||||
<p><!-- Navigation links --> </p>
|
||||
<hr>
|
||||
<p><b>Up:</b>
|
||||
<a href="http://www.qhull.org">Home page for
|
||||
Qhull</a> <br>
|
||||
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
|
||||
<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
|
||||
• <a href="../../html/qh-quick.htm#options">Options</a>
|
||||
• <a href="../../html/qh-opto.htm#output">Output</a>
|
||||
• <a href="../../html/qh-optf.htm#format">Formats</a>
|
||||
• <a href="../../html/qh-optg.htm#geomview">Geomview</a>
|
||||
• <a href="../../html/qh-optp.htm#print">Print</a>
|
||||
• <a href="../../html/qh-optq.htm#qhull">Qhull</a>
|
||||
• <a href="../../html/qh-optc.htm#prec">Precision</a>
|
||||
• <a href="../../html/qh-optt.htm#trace">Trace</a>
|
||||
• <a href="index.htm">Functions</a><br>
|
||||
<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
|
||||
<b>To:</b> <a href="#TOC">Qhull files</a><br>
|
||||
<b>To:</b> <a href="qh-geom_r.htm">Geom</a> •
|
||||
<a href="qh-globa_r.htm">Global</a> • <a href="qh-io_r.htm">Io</a>
|
||||
• <a href="qh-mem_r.htm">Mem</a> • <a href="qh-merge_r.htm">Merge</a>
|
||||
• <a href="qh-poly_r.htm">Poly</a> • <a href="qh-qhull_r.htm#TOC">Qhull</a>
|
||||
• <a href="qh-set_r.htm">Set</a> • <a href="qh-stat_r.htm">Stat</a>
|
||||
• <a href="qh-user_r.htm">User</a><br>
|
||||
|
||||
<p><!-- GC common information --> </p>
|
||||
<hr>
|
||||
<p><a href="http://www.geom.uiuc.edu/"><img
|
||||
src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
|
||||
Geometry Center Home Page </i></p>
|
||||
<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
|
||||
</a><br>
|
||||
Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
||||
</body>
|
||||
</html>
|
||||
4062
xs/src/qhull/src/libqhull_r/io_r.c
Normal file
4062
xs/src/qhull/src/libqhull_r/io_r.c
Normal file
File diff suppressed because it is too large
Load Diff
167
xs/src/qhull/src/libqhull_r/io_r.h
Normal file
167
xs/src/qhull/src/libqhull_r/io_r.h
Normal file
@ -0,0 +1,167 @@
|
||||
/*<html><pre> -<a href="qh-io_r.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 ==================*/
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_MAXfirst">-</a>
|
||||
|
||||
qh_MAXfirst
|
||||
maximum length of first two lines of stdin
|
||||
*/
|
||||
#define qh_MAXfirst 200
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_MINradius">-</a>
|
||||
|
||||
qh_MINradius
|
||||
min radius for Gp and Gv, fraction of maxcoord
|
||||
*/
|
||||
#define qh_MINradius 0.02
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_GEOMepsilon">-</a>
|
||||
|
||||
qh_GEOMepsilon
|
||||
adjust outer planes for 'lines closer' and geomview roundoff.
|
||||
This prevents bleed through.
|
||||
*/
|
||||
#define qh_GEOMepsilon 2e-3
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="qh_WHITESPACE">-</a>
|
||||
|
||||
qh_WHITESPACE
|
||||
possible values of white space
|
||||
*/
|
||||
#define qh_WHITESPACE " \n\t\v\r\f"
|
||||
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="RIDGE">-</a>
|
||||
|
||||
qh_RIDGE
|
||||
to select which ridges to print in qh_eachvoronoi
|
||||
*/
|
||||
typedef enum
|
||||
{
|
||||
qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
|
||||
}
|
||||
qh_RIDGE;
|
||||
|
||||
/*-<a href="qh-io_r.htm#TOC"
|
||||
>--------------------------------</a><a name="printvridgeT">-</a>
|
||||
|
||||
printvridgeT
|
||||
prints results of qh_printvdiagram
|
||||
|
||||
see:
|
||||
<a href="io_r.c#printvridge">qh_printvridge</a> 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 */
|
||||
1403
xs/src/qhull/src/libqhull_r/libqhull_r.c
Normal file
1403
xs/src/qhull/src/libqhull_r/libqhull_r.c
Normal file
File diff suppressed because it is too large
Load Diff
1134
xs/src/qhull/src/libqhull_r/libqhull_r.h
Normal file
1134
xs/src/qhull/src/libqhull_r/libqhull_r.h
Normal file
File diff suppressed because it is too large
Load Diff
67
xs/src/qhull/src/libqhull_r/libqhull_r.pro
Normal file
67
xs/src/qhull/src/libqhull_r/libqhull_r.pro
Normal file
@ -0,0 +1,67 @@
|
||||
# -------------------------------------------------
|
||||
# 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
|
||||
562
xs/src/qhull/src/libqhull_r/mem_r.c
Normal file
562
xs/src/qhull/src/libqhull_r/mem_r.c
Normal file
@ -0,0 +1,562 @@
|
||||
/*<html><pre> -<a href="qh-mem_r.htm"
|
||||
>-------------------------------</a><a name="TOP">-</a>
|
||||
|
||||
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 <string.h>
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#ifndef qh_NOmem
|
||||
|
||||
/*============= internal functions ==============*/
|
||||
|
||||
static int qh_intcompare(const void *i, const void *j);
|
||||
|
||||
/*========== functions in alphabetical order ======== */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="intcompare">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>--------------------------------</a><a name="memalloc">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>--------------------------------</a><a name="memcheck">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>--------------------------------</a><a name="memfree">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="memfreeshort">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>--------------------------------</a><a name="meminit">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="meminitbuffers">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="memsetup">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="memsize">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="memstatistics">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="NOmem">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
/*-<a href="qh-mem_r.htm#TOC"
|
||||
>-------------------------------</a><a name="memtotlong">-</a>
|
||||
|
||||
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 */
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue
Block a user