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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
// and 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/.
#ifndef IGL_HESSIAN_ENERGY_H
#define IGL_HESSIAN_ENERGY_H
#include "igl_inline.h"
#include <Eigen/Dense>
#include <Eigen/Sparse>
namespace igl
{
// Constructs the Hessian energy matrix using mixed FEM
// as described in https://arxiv.org/abs/1707.04348
// Natural Boundary Conditions for Smoothing in Geometry Processing
// (Oded Stein, Eitan Grinspun, Max Wardetzky, Alec Jacobson)
//
// Inputs:
// V #V by dim list of mesh vertex positions
// F #F by 3 list of mesh faces (must be triangles)
// Outputs:
// Q #V by #V Hessian energy matrix, each row/column i
// corresponding to V(i,:)
//
//
//
template <typename DerivedV, typename DerivedF, typename Scalar>
IGL_INLINE void hessian_energy(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
Eigen::SparseMatrix<Scalar>& Q);
}
#ifndef IGL_STATIC_LIBRARY
# include "hessian_energy.cpp"
#endif
#endif
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