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60 lines
2.1 KiB
C++
60 lines
2.1 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
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// and Oded Stein <oded.stein@columbia.edu>
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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 "hessian.h"
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#include <vector>
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#include "grad.h"
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#include "igl/doublearea.h"
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#include "igl/repdiag.h"
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template <typename DerivedV, typename DerivedF, typename Scalar>
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IGL_INLINE void igl::hessian(
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const Eigen::MatrixBase<DerivedV> & V,
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const Eigen::MatrixBase<DerivedF> & F,
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Eigen::SparseMatrix<Scalar>& H)
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{
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typedef typename DerivedV::Scalar denseScalar;
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typedef typename Eigen::Matrix<denseScalar, Eigen::Dynamic, 1> VecXd;
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typedef typename Eigen::SparseMatrix<Scalar> SparseMat;
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typedef typename Eigen::DiagonalMatrix
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<Scalar, Eigen::Dynamic, Eigen::Dynamic> DiagMat;
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int dim = V.cols();
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assert((dim==2 || dim==3) &&
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"The dimension of the vertices should be 2 or 3");
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//Construct the combined gradient matric
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SparseMat G;
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igl::grad(DerivedV(V),
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DerivedF(F),
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G, false);
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SparseMat GG(F.rows(), dim*V.rows());
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GG.reserve(G.nonZeros());
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for(int i=0; i<dim; ++i)
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GG.middleCols(i*G.cols(),G.cols()) = G.middleRows(i*F.rows(),F.rows());
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SparseMat D;
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igl::repdiag(GG,dim,D);
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//Compute area matrix
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VecXd areas;
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igl::doublearea(V, F, areas);
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DiagMat A = (0.5*areas).replicate(dim,1).asDiagonal();
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//Compute FEM Hessian
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H = D.transpose()*A*G;
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template void igl::hessian<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>&);
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#endif
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