148 lines
7.1 KiB
C++
148 lines
7.1 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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// Copyright (C) 2018 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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#include "cotmatrix_entries.h"
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#include "doublearea.h"
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#include "squared_edge_lengths.h"
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#include "edge_lengths.h"
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#include "face_areas.h"
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#include "volume.h"
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#include "dihedral_angles.h"
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#include "verbose.h"
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template <typename DerivedV, typename DerivedF, typename DerivedC>
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IGL_INLINE void igl::cotmatrix_entries(
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const Eigen::MatrixBase<DerivedV>& V,
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const Eigen::MatrixBase<DerivedF>& F,
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Eigen::PlainObjectBase<DerivedC>& C)
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{
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using namespace std;
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using namespace Eigen;
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// simplex size (3: triangles, 4: tetrahedra)
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int simplex_size = F.cols();
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// Number of elements
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int m = F.rows();
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// Law of cosines + law of sines
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switch(simplex_size)
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{
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case 3:
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{
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// Triangles
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//Compute Squared Edge lengths
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Matrix<typename DerivedC::Scalar,Dynamic,3> l2;
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igl::squared_edge_lengths(V,F,l2);
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//Compute Edge lengths
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Matrix<typename DerivedC::Scalar,Dynamic,3> l;
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l = l2.array().sqrt();
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// double area
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Matrix<typename DerivedC::Scalar,Dynamic,1> dblA;
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doublearea(l,0.,dblA);
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// cotangents and diagonal entries for element matrices
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// correctly divided by 4 (alec 2010)
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C.resize(m,3);
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for(int i = 0;i<m;i++)
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{
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// Alec: I'm doubtful that using l2 here is actually improving numerics.
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C(i,0) = (l2(i,1) + l2(i,2) - l2(i,0))/dblA(i)/4.0;
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C(i,1) = (l2(i,2) + l2(i,0) - l2(i,1))/dblA(i)/4.0;
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C(i,2) = (l2(i,0) + l2(i,1) - l2(i,2))/dblA(i)/4.0;
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}
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break;
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}
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case 4:
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{
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// edge lengths numbered same as opposite vertices
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Matrix<typename DerivedC::Scalar,Dynamic,6> l;
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edge_lengths(V,F,l);
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Matrix<typename DerivedC::Scalar,Dynamic,4> s;
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face_areas(l,s);
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Matrix<typename DerivedC::Scalar,Dynamic,6> cos_theta,theta;
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dihedral_angles_intrinsic(l,s,theta,cos_theta);
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// volume
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Matrix<typename DerivedC::Scalar,Dynamic,1> vol;
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volume(l,vol);
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// Law of sines
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// http://mathworld.wolfram.com/Tetrahedron.html
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Matrix<typename DerivedC::Scalar,Dynamic,6> sin_theta(m,6);
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sin_theta.col(0) = vol.array() / ((2./(3.*l.col(0).array())).array() * s.col(1).array() * s.col(2).array());
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sin_theta.col(1) = vol.array() / ((2./(3.*l.col(1).array())).array() * s.col(2).array() * s.col(0).array());
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sin_theta.col(2) = vol.array() / ((2./(3.*l.col(2).array())).array() * s.col(0).array() * s.col(1).array());
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sin_theta.col(3) = vol.array() / ((2./(3.*l.col(3).array())).array() * s.col(3).array() * s.col(0).array());
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sin_theta.col(4) = vol.array() / ((2./(3.*l.col(4).array())).array() * s.col(3).array() * s.col(1).array());
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sin_theta.col(5) = vol.array() / ((2./(3.*l.col(5).array())).array() * s.col(3).array() * s.col(2).array());
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// http://arxiv.org/pdf/1208.0354.pdf Page 18
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C = (1./6.) * l.array() * cos_theta.array() / sin_theta.array();
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break;
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}
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default:
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{
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fprintf(stderr,
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"cotmatrix_entries.h: Error: Simplex size (%d) not supported\n", simplex_size);
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assert(false);
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}
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}
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}
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template <typename Derivedl, typename DerivedC>
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IGL_INLINE void igl::cotmatrix_entries(
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const Eigen::MatrixBase<Derivedl>& l,
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Eigen::PlainObjectBase<DerivedC>& C)
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{
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using namespace Eigen;
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const int m = l.rows();
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assert(l.cols() == 3 && "Only triangles accepted");
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//Compute squared Edge lengths
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Matrix<typename DerivedC::Scalar,Dynamic,3> l2;
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l2 = l.array().square();
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// Alec: It's a little annoying that there's duplicate code here. The
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// "extrinic" version above is first computing squared edge lengths, taking
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// the square root and calling this. We can't have a cotmatrix_entries(l,l2,C)
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// overload because it will confuse Eigen with the cotmatrix_entries(V,F,C)
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// overload. In the end, I'd like to be convinced that using l2 directly above
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// is actually better numerically (or significantly faster) than just calling
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// edge_lengths and this cotmatrix_entries(l,C);
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//
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// double area
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Matrix<typename DerivedC::Scalar,Dynamic,1> dblA;
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doublearea(l,0.,dblA);
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// cotangents and diagonal entries for element matrices
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// correctly divided by 4 (alec 2010)
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C.resize(m,3);
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for(int i = 0;i<m;i++)
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{
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// Alec: I'm doubtful that using l2 here is actually improving numerics.
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C(i,0) = (l2(i,1) + l2(i,2) - l2(i,0))/dblA(i)/4.0;
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C(i,1) = (l2(i,2) + l2(i,0) - l2(i,1))/dblA(i)/4.0;
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C(i,2) = (l2(i,0) + l2(i,1) - l2(i,2))/dblA(i)/4.0;
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}
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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// generated by autoexplicit.sh
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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// generated by autoexplicit.sh
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 4, 0, -1, 4>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 4, 0, -1, 4> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::cotmatrix_entries<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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#endif
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