dust3d/third_party/libigl/include/igl/cotmatrix_entries.cpp

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
// Copyright (C) 2018 Alec Jacobson <alecjacobson@gmail.com>
// 
// This Source Code Form is subject to the terms of the Mozilla Public License 
// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
// obtain one at http://mozilla.org/MPL/2.0/.
#include "cotmatrix_entries.h"
#include "doublearea.h"
#include "squared_edge_lengths.h"
#include "edge_lengths.h"
#include "face_areas.h"
#include "volume.h"
#include "dihedral_angles.h"

#include "verbose.h"


template <typename DerivedV, typename DerivedF, typename DerivedC>
IGL_INLINE void igl::cotmatrix_entries(
  const Eigen::MatrixBase<DerivedV>& V,
  const Eigen::MatrixBase<DerivedF>& F,
  Eigen::PlainObjectBase<DerivedC>& C)
{
  using namespace std;
  using namespace Eigen;
  // simplex size (3: triangles, 4: tetrahedra)
  int simplex_size = F.cols();
  // Number of elements
  int m = F.rows();

  // Law of cosines + law of sines
  switch(simplex_size)
  {
    case 3:
    {
      // Triangles
      //Compute Squared Edge lengths 
      Matrix<typename DerivedC::Scalar,Dynamic,3> l2;
      igl::squared_edge_lengths(V,F,l2);
      //Compute Edge lengths 
      Matrix<typename DerivedC::Scalar,Dynamic,3> l;
      l = l2.array().sqrt();
      
      // double area
      Matrix<typename DerivedC::Scalar,Dynamic,1> dblA;
      doublearea(l,0.,dblA);
      // cotangents and diagonal entries for element matrices
      // correctly divided by 4 (alec 2010)
      C.resize(m,3);
      for(int i = 0;i<m;i++)
      {
        // Alec: I'm doubtful that using l2 here is actually improving numerics.
        C(i,0) = (l2(i,1) + l2(i,2) - l2(i,0))/dblA(i)/4.0;
        C(i,1) = (l2(i,2) + l2(i,0) - l2(i,1))/dblA(i)/4.0;
        C(i,2) = (l2(i,0) + l2(i,1) - l2(i,2))/dblA(i)/4.0;
      }
      break;
    }
    case 4:
    {

      // edge lengths numbered same as opposite vertices
      Matrix<typename DerivedC::Scalar,Dynamic,6> l;
      edge_lengths(V,F,l);
      Matrix<typename DerivedC::Scalar,Dynamic,4> s;
      face_areas(l,s);
      Matrix<typename DerivedC::Scalar,Dynamic,6> cos_theta,theta;
      dihedral_angles_intrinsic(l,s,theta,cos_theta);

      // volume
      Matrix<typename DerivedC::Scalar,Dynamic,1> vol;
      volume(l,vol);


      // Law of sines
      // http://mathworld.wolfram.com/Tetrahedron.html
      Matrix<typename DerivedC::Scalar,Dynamic,6> sin_theta(m,6);
      sin_theta.col(0) = vol.array() / ((2./(3.*l.col(0).array())).array() * s.col(1).array() * s.col(2).array());
      sin_theta.col(1) = vol.array() / ((2./(3.*l.col(1).array())).array() * s.col(2).array() * s.col(0).array());
      sin_theta.col(2) = vol.array() / ((2./(3.*l.col(2).array())).array() * s.col(0).array() * s.col(1).array());
      sin_theta.col(3) = vol.array() / ((2./(3.*l.col(3).array())).array() * s.col(3).array() * s.col(0).array());
      sin_theta.col(4) = vol.array() / ((2./(3.*l.col(4).array())).array() * s.col(3).array() * s.col(1).array());
      sin_theta.col(5) = vol.array() / ((2./(3.*l.col(5).array())).array() * s.col(3).array() * s.col(2).array());


      // http://arxiv.org/pdf/1208.0354.pdf Page 18
      C = (1./6.) * l.array() * cos_theta.array() / sin_theta.array();

      break;
    }
    default:
    {
      fprintf(stderr,
          "cotmatrix_entries.h: Error: Simplex size (%d) not supported\n", simplex_size);
      assert(false);
    }
  }
}

template <typename Derivedl, typename DerivedC>
IGL_INLINE void igl::cotmatrix_entries(
  const Eigen::MatrixBase<Derivedl>& l,
  Eigen::PlainObjectBase<DerivedC>& C)
{
  using namespace Eigen;
  const int m = l.rows();
  assert(l.cols() == 3 && "Only triangles accepted");
  //Compute squared Edge lengths 
  Matrix<typename DerivedC::Scalar,Dynamic,3> l2;
  l2 = l.array().square();
  // Alec: It's a little annoying that there's duplicate code here. The
  // "extrinic" version above is first computing squared edge lengths, taking
  // the square root and calling this. We can't have a cotmatrix_entries(l,l2,C)
  // overload because it will confuse Eigen with the cotmatrix_entries(V,F,C)
  // overload. In the end, I'd like to be convinced that using l2 directly above
  // is actually better numerically (or significantly faster) than just calling
  // edge_lengths and this cotmatrix_entries(l,C);
  //
  // double area
  Matrix<typename DerivedC::Scalar,Dynamic,1> dblA;
  doublearea(l,0.,dblA);
  // cotangents and diagonal entries for element matrices
  // correctly divided by 4 (alec 2010)
  C.resize(m,3);
  for(int i = 0;i<m;i++)
  {
    // Alec: I'm doubtful that using l2 here is actually improving numerics.
    C(i,0) = (l2(i,1) + l2(i,2) - l2(i,0))/dblA(i)/4.0;
    C(i,1) = (l2(i,2) + l2(i,0) - l2(i,1))/dblA(i)/4.0;
    C(i,2) = (l2(i,0) + l2(i,1) - l2(i,2))/dblA(i)/4.0;
  }
}

#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
// generated by autoexplicit.sh
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> >&);
// generated by autoexplicit.sh
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> >&);
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> >&);
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> >&);
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> >&);
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> >&);
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> >&);
#endif