Added libigl hessian energy

Former-commit-id: 469c26c5a894ee725bfffd146282d966f157877a

include/igl/hessian_energy.cpp

@@ -0,0 +1,96 @@
+// 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/.
+#include "hessian_energy.h"
+#include <vector>
+
+#include <igl/grad.h>
+#include <igl/doublearea.h>
+#include <igl/massmatrix.h>
+#include <igl/boundary_loop.h>
+#include <igl/repdiag.h>
+
+template <typename DerivedV, typename DerivedF, typename Scalar>
+IGL_INLINE void igl::hessian_energy(
+                               const Eigen::PlainObjectBase<DerivedV> & V,
+                               const Eigen::PlainObjectBase<DerivedF> & F,
+                               Eigen::SparseMatrix<Scalar>& Q)
+{
+    typedef typename DerivedV::Scalar denseScalar;
+    typedef typename Eigen::Matrix<denseScalar, Eigen::Dynamic, 1> VecXd;
+    typedef typename Eigen::SparseMatrix<Scalar> SparseMat;
+    typedef typename Eigen::DiagonalMatrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> DiagMat;
+    
+    int dim = V.cols();
+    assert((dim==2 || dim==3) && "The dimension of the vertices should be 2 or 3");
+
+    SparseMat M;
+    igl::massmatrix(V,F,igl::MASSMATRIX_TYPE_VORONOI,M);
+    
+    //Kill non-interior DOFs
+    VecXd Mint = M.diagonal();
+    std::vector<std::vector<int> > bdryLoop;
+    igl::boundary_loop(F,bdryLoop);
+    for(const std::vector<int>& loop : bdryLoop)
+        for(const int& bdryVert : loop)
+            Mint(bdryVert) = 0.;
+    
+    //Invert Mint
+    for(int i=0; i<Mint.rows(); ++i)
+        if(Mint(i) > 0)
+            Mint(i) = 1./Mint(i);
+    
+    //Repeat Mint to form diaginal matrix
+    DiagMat stackedMinv = Mint.replicate(dim*dim,1).asDiagonal();
+    
+    //Compute squared Hessian
+    SparseMat H;
+    igl::fem_hessian(V,F,H);
+    Q = H.transpose()*stackedMinv*H;
+    
+}
+
+
+template <typename DerivedV, typename DerivedF, typename Scalar>
+IGL_INLINE void igl::fem_hessian(
+                            const Eigen::PlainObjectBase<DerivedV> & V,
+                            const Eigen::PlainObjectBase<DerivedF> & F,
+                            Eigen::SparseMatrix<Scalar>& H)
+{
+    typedef typename DerivedV::Scalar denseScalar;
+    typedef typename Eigen::Matrix<denseScalar, Eigen::Dynamic, 1> VecXd;
+    typedef typename Eigen::SparseMatrix<Scalar> SparseMat;
+    typedef typename Eigen::DiagonalMatrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> DiagMat;
+
+    int dim = V.cols();
+    assert((dim==2 || dim==3) && "The dimension of the vertices should be 2 or 3");
+    
+    //Construct the combined gradient matric
+    SparseMat G;
+    igl::grad(V, F, G, false);
+    SparseMat GG(F.rows(), dim*V.rows());
+    GG.reserve(G.nonZeros());
+    for(int i=0; i<dim; ++i)
+        GG.middleCols(i*G.cols(), G.cols()) = G.middleRows(i*F.rows(), F.rows());
+    SparseMat D;
+    igl::repdiag(GG,dim,D);
+    
+    //Compute area matrix
+    VecXd areas;
+    igl::doublearea(V, F, areas);
+    DiagMat A = (0.5*areas).replicate(dim,1).asDiagonal();
+    
+    //Compute FEM Hessian
+    H = D.transpose()*A*G;
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::hessian_energy<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
+template void igl::fem_hessian<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
+#endif

include/igl/hessian_energy.h

@@ -0,0 +1,60 @@
+// 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
+    //
+    // 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::PlainObjectBase<DerivedV> & V,
+                                   const Eigen::PlainObjectBase<DerivedF> & F,
+                                   Eigen::SparseMatrix<Scalar>& Q);
+    
+    
+    // Constructs the finite element Hessian matrix
+    // as described in https://arxiv.org/abs/1707.04348
+    // The interior vertices are NOT set to zero yet.
+    //
+    // Inputs:
+    //   V  #V by dim list of mesh vertex positions
+    //   F  #F by 3 list of mesh faces (must be triangles)
+    // Outputs:
+    //   H  #V by #V Hessian energy matrix, each column i corresponding to V(i,:)
+    //
+    //
+    //
+    template <typename DerivedV, typename DerivedF, typename Scalar>
+    IGL_INLINE void fem_hessian(
+                                const Eigen::PlainObjectBase<DerivedV> & V,
+                                const Eigen::PlainObjectBase<DerivedF> & F,
+                                Eigen::SparseMatrix<Scalar>& H);
+    
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "hessian_energy.cpp"
+#endif
+
+#endif