libigl/include/igl/cr_vector_laplacian.cpp

// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2020 Oded Stein <[email protected]>
//
// 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 "cr_vector_laplacian.h"

#include <vector>

#include "orient_halfedges.h"

#include "doublearea.h"
#include "squared_edge_lengths.h"


template <typename DerivedV, typename DerivedF, typename DerivedE,
typename DerivedOE, typename ScalarL>
IGL_INLINE void
igl::cr_vector_laplacian(
  const Eigen::MatrixBase<DerivedV>& V,
  const Eigen::MatrixBase<DerivedF>& F,
  const Eigen::MatrixBase<DerivedE>& E,
  const Eigen::MatrixBase<DerivedOE>& oE,
  Eigen::SparseMatrix<ScalarL>& L)
{
  Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic>
  l_sq;
  squared_edge_lengths(V, F, l_sq);
  cr_vector_laplacian_intrinsic(F, l_sq, E, oE, L);
}


template <typename DerivedV, typename DerivedF, typename DerivedE,
typename DerivedOE, typename ScalarL>
IGL_INLINE void
igl::cr_vector_laplacian(
  const Eigen::MatrixBase<DerivedV>& V,
  const Eigen::MatrixBase<DerivedF>& F,
  Eigen::PlainObjectBase<DerivedE>& E,
  Eigen::PlainObjectBase<DerivedOE>& oE,
  Eigen::SparseMatrix<ScalarL>& L)
{
  if(E.rows()!=F.rows() || E.cols()!=F.cols() || oE.rows()!=F.rows() ||
   oE.cols()!=F.cols()) {
    orient_halfedges(F, E, oE);
  }

  const Eigen::PlainObjectBase<DerivedE>& cE = E;
  const Eigen::PlainObjectBase<DerivedOE>& coE = oE;
  cr_vector_laplacian(V, F, cE, coE, L);
}


template <typename DerivedF, typename DerivedL_sq, typename DerivedE,
typename DerivedOE, typename ScalarL>
IGL_INLINE void
igl::cr_vector_laplacian_intrinsic(
  const Eigen::MatrixBase<DerivedF>& F,
  const Eigen::MatrixBase<DerivedL_sq>& l_sq,
  const Eigen::MatrixBase<DerivedE>& E,
  const Eigen::MatrixBase<DerivedOE>& oE,
  Eigen::SparseMatrix<ScalarL>& L)
{
  Eigen::Matrix<typename DerivedL_sq::Scalar, Eigen::Dynamic, Eigen::Dynamic>
  dA;
  DerivedL_sq l_sqrt = l_sq.array().sqrt().matrix();
  doublearea(l_sqrt, dA);
  cr_vector_laplacian_intrinsic(F, l_sq, dA, E, oE, L);
}


template <typename DerivedF, typename DerivedL_sq, typename DeriveddA,
typename DerivedE, typename DerivedOE, typename ScalarL>
IGL_INLINE void
igl::cr_vector_laplacian_intrinsic(
  const Eigen::MatrixBase<DerivedF>& F,
  const Eigen::MatrixBase<DerivedL_sq>& l_sq,
  const Eigen::MatrixBase<DeriveddA>& dA,
  const Eigen::MatrixBase<DerivedE>& E,
  const Eigen::MatrixBase<DerivedOE>& oE,
  Eigen::SparseMatrix<ScalarL>& L)
{
  assert(F.cols()==3 && "Faces have three vertices");
  assert(E.rows()==F.rows() && E.cols()==F.cols() && oE.rows()==F.rows() &&
   oE.cols()==F.cols() && "Wrong dimension in edge vectors");
  assert(l_sq.rows()==F.rows() && l_sq.cols()==3 && "l_sq dimensions wrong");
  assert(dA.size()==F.rows() && "dA dimensions wrong");

  const Eigen::Index m = F.rows();
  const typename DerivedE::Scalar nE = E.maxCoeff() + 1;

  std::vector<Eigen::Triplet<ScalarL> > tripletList;
  tripletList.reserve(10*3*m);
  for(Eigen::Index f=0; f<m; ++f) {
    for(int e=0; e<3; ++e) {
      const ScalarL eij=l_sq(f,e), ejk=l_sq(f,(e+1)%3),
      eki=l_sq(f,(e+2)%3); //These are squared quantities.
      const ScalarL lens = sqrt(eij*eki);
      const ScalarL o = oE(f,e)*oE(f,(e+2)%3);
      
      tripletList.emplace_back(E(f,e), E(f,e), 2./dA(f) * eij);
      tripletList.emplace_back(E(f,e)+nE, E(f,e)+nE, 2./dA(f) * eij);
      
      const ScalarL Dijki = o * pow(eij-ejk+eki,2)/(2.*lens*dA(f));
      tripletList.emplace_back(E(f,e), E(f,(e+2)%3), Dijki);
      tripletList.emplace_back(E(f,(e+2)%3), E(f,e), Dijki);
      tripletList.emplace_back(E(f,e)+nE, E(f,(e+2)%3)+nE, Dijki);
      tripletList.emplace_back(E(f,(e+2)%3)+nE, E(f,e)+nE, Dijki);
      
      const ScalarL Dijkiperp = -o * (eij-ejk+eki)/lens;
      tripletList.emplace_back(E(f,e), E(f,(e+2)%3)+nE, Dijkiperp);
      tripletList.emplace_back(E(f,(e+2)%3)+nE, E(f,e), Dijkiperp);
      tripletList.emplace_back(E(f,e)+nE, E(f,(e+2)%3), -Dijkiperp);
      tripletList.emplace_back(E(f,(e+2)%3), E(f,e)+nE, -Dijkiperp);
    }
  }
  L.resize(2*nE, 2*nE);
  L.setFromTriplets(tripletList.begin(), tripletList.end());
}


#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
template void igl::cr_vector_laplacian<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(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<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::SparseMatrix<double, 0, int>&);
template void igl::cr_vector_laplacian_intrinsic<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
#endif