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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2020 Oded Stein <oded.stein@columbia.edu>
//
// 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 "curved_hessian_energy.h"
#include "orient_halfedges.h"
#include "doublearea.h"
#include "squared_edge_lengths.h"
#include "cr_vector_laplacian.h"
#include "cr_vector_mass.h"
#include "cr_vector_curvature_correction.h"
#include "scalar_to_cr_vector_gradient.h"
template <typename DerivedV, typename DerivedF, typename ScalarQ>
IGL_INLINE void
igl::curved_hessian_energy(
const Eigen::MatrixBase<DerivedV>& V,
const Eigen::MatrixBase<DerivedF>& F,
Eigen::SparseMatrix<ScalarQ>& Q)
{
Eigen::MatrixXi E, oE;
curved_hessian_energy(V, F, E, oE, Q);
}
template <typename DerivedV, typename DerivedF, typename DerivedE,
typename DerivedOE, typename ScalarQ>
IGL_INLINE void
igl::curved_hessian_energy(
const Eigen::MatrixBase<DerivedV>& V,
const Eigen::MatrixBase<DerivedF>& F,
const Eigen::MatrixBase<DerivedE>& E,
const Eigen::MatrixBase<DerivedOE>& oE,
Eigen::SparseMatrix<ScalarQ>& Q)
{
Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic>
l_sq;
squared_edge_lengths(V, F, l_sq);
curved_hessian_energy_intrinsic(F, l_sq, E, oE, Q);
}
template <typename DerivedV, typename DerivedF, typename DerivedE,
typename DerivedOE, typename ScalarQ>
IGL_INLINE void
igl::curved_hessian_energy(
const Eigen::MatrixBase<DerivedV>& V,
const Eigen::MatrixBase<DerivedF>& F,
Eigen::PlainObjectBase<DerivedE>& E,
Eigen::PlainObjectBase<DerivedOE>& oE,
Eigen::SparseMatrix<ScalarQ>& Q)
{
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;
curved_hessian_energy(V, F, cE, coE, Q);
}
template <typename DerivedF, typename DerivedL_sq, typename DerivedE,
typename DerivedOE, typename ScalarQ>
IGL_INLINE void
igl::curved_hessian_energy_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<ScalarQ>& Q)
{
Eigen::Matrix<typename DerivedL_sq::Scalar, Eigen::Dynamic, Eigen::Dynamic>
dA;
Eigen::Matrix<typename DerivedL_sq::Scalar, Eigen::Dynamic, Eigen::Dynamic>
l_sqrt = l_sq.array().sqrt().matrix();
doublearea(l_sqrt, dA);
curved_hessian_energy_intrinsic(F, l_sq, dA, E, oE, Q);
}
template <typename DerivedF, typename DerivedL_sq, typename DeriveddA,
typename DerivedE, typename DerivedOE, typename ScalarQ>
IGL_INLINE void
igl::curved_hessian_energy_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<ScalarQ>& Q)
{
//Matrices that need to be combined
Eigen::SparseMatrix<ScalarQ> M, D, L, K;
cr_vector_mass_intrinsic(F, l_sq, dA, E, oE, M);
scalar_to_cr_vector_gradient_intrinsic(F, l_sq, dA, E, oE, D);
cr_vector_laplacian_intrinsic(F, l_sq, dA, E, oE, L);
cr_vector_curvature_correction_intrinsic(F, l_sq, E, oE, K);
//Invert M
std::vector<Eigen::Triplet<ScalarQ> > tripletListMi;
for(Eigen::Index k=0; k<M.outerSize(); ++k) {
for(typename Eigen::SparseMatrix<ScalarQ>::InnerIterator it(M,k);
it; ++it) {
if(it.value() > 0) {
tripletListMi.emplace_back(it.row(), it.col(), 1./it.value());
}
}
}
Eigen::SparseMatrix<ScalarQ> Mi(M.rows(), M.cols());
Mi.setFromTriplets(tripletListMi.begin(), tripletListMi.end());
//Hessian energy matrix
Q = D.transpose()*Mi*(L + K)*Mi*D;
}
#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
template void igl::curved_hessian_energy<Eigen::Matrix<double, -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::SparseMatrix<double, 0, int>&);
#endif