105 lines
4.1 KiB
C++
105 lines
4.1 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef IGL_DOUBLEAREA_H
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#define IGL_DOUBLEAREA_H
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#include "igl_inline.h"
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#include <Eigen/Dense>
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namespace igl
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{
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// DOUBLEAREA computes twice the area for each input triangle[quad]
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//
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// Templates:
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// DerivedV derived type of eigen matrix for V (e.g. derived from
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// MatrixXd)
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// DerivedF derived type of eigen matrix for F (e.g. derived from
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// MatrixXi)
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// DeriveddblA derived type of eigen matrix for dblA (e.g. derived from
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// MatrixXd)
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// Inputs:
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// V #V by dim list of mesh vertex positions
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// F #F by simplex_size list of mesh faces (must be triangles or quads)
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// Outputs:
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// dblA #F list of triangle[quad] double areas (SIGNED only for 2D input)
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//
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// Known bug: For dim==3 complexity is O(#V + #F)!! Not just O(#F). This is a big deal
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// if you have 1million unreferenced vertices and 1 face
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template <typename DerivedV, typename DerivedF, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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// Stream of triangles, computes signed area...
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template <
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typename DerivedA,
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typename DerivedB,
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typename DerivedC,
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typename DerivedD>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<DerivedA> & A,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedC> & C,
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Eigen::PlainObjectBase<DerivedD> & D);
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// Single triangle in 2D!
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//
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// This should handle streams of corners not just single corners
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template <
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typename DerivedA,
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typename DerivedB,
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typename DerivedC>
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IGL_INLINE typename DerivedA::Scalar doublearea_single(
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const Eigen::MatrixBase<DerivedA> & A,
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const Eigen::MatrixBase<DerivedB> & B,
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const Eigen::MatrixBase<DerivedC> & C);
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// Same as above but use instrinsic edge lengths rather than (V,F) mesh. This
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//
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// Inputs:
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// l #F by dim list of edge lengths using
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// for triangles, columns correspond to edges 23,31,12
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// nan_replacement what value should be used for triangles whose given
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// edge lengths do not obey the triangle inequality. These may be very
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// wrong (e.g., [100 1 1]) or may be nearly degenerate triangles whose
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// floating point side length computation leads to breach of the triangle
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// inequality. One may wish to set this parameter to 0 if side lengths l
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// are _known_ to come from a valid embedding (e.g., some mesh (V,F)). In
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// that case, the only circumstance the triangle inequality is broken is
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// when the triangle is nearly degenerate and floating point error
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// dominates: hence replacing with zero is reasonable.
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// Outputs:
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// dblA #F list of triangle double areas
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template <typename Derivedl, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<Derivedl> & l,
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const typename Derivedl::Scalar nan_replacement,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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// default behavior is to assert on NaNs and leave them in place
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template <typename Derivedl, typename DeriveddblA>
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IGL_INLINE void doublearea(
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const Eigen::MatrixBase<Derivedl> & l,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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// DOUBLEAREA_QUAD computes twice the area for each input quadrilateral
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//
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// Inputs:
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// V #V by dim list of mesh vertex positions
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// F #F by simplex_size list of mesh faces (must be quadrilaterals)
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// Outputs:
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// dblA #F list of quadrilateral double areas
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//
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template <typename DerivedV, typename DerivedF, typename DeriveddblA>
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IGL_INLINE void doublearea_quad(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::PlainObjectBase<DeriveddblA> & dblA);
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}
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#ifndef IGL_STATIC_LIBRARY
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# include "doublearea.cpp"
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#endif
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#endif
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