254 lines
6.5 KiB
C++
254 lines
6.5 KiB
C++
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
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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 "arap_linear_block.h"
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#include "verbose.h"
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#include "cotmatrix_entries.h"
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#include <Eigen/Dense>
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void igl::arap_linear_block(
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const MatV & V,
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const MatF & F,
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const int d,
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const igl::ARAPEnergyType energy,
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Eigen::SparseMatrix<Scalar> & Kd)
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{
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switch(energy)
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{
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case ARAP_ENERGY_TYPE_SPOKES:
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return igl::arap_linear_block_spokes(V,F,d,Kd);
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break;
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case ARAP_ENERGY_TYPE_SPOKES_AND_RIMS:
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return igl::arap_linear_block_spokes_and_rims(V,F,d,Kd);
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break;
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case ARAP_ENERGY_TYPE_ELEMENTS:
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return igl::arap_linear_block_elements(V,F,d,Kd);
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break;
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default:
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verbose("Unsupported energy type: %d\n",energy);
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assert(false);
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}
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}
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void igl::arap_linear_block_spokes(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd)
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{
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using namespace std;
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using namespace Eigen;
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// simplex size (3: triangles, 4: tetrahedra)
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int simplex_size = F.cols();
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// Number of elements
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int m = F.rows();
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// Temporary output
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Matrix<int,Dynamic,2> edges;
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Kd.resize(V.rows(), V.rows());
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vector<Triplet<Scalar> > Kd_IJV;
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if(simplex_size == 3)
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{
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// triangles
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Kd.reserve(7*V.rows());
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Kd_IJV.reserve(7*V.rows());
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edges.resize(3,2);
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edges <<
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1,2,
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2,0,
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0,1;
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}else if(simplex_size == 4)
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{
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// tets
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Kd.reserve(17*V.rows());
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Kd_IJV.reserve(17*V.rows());
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edges.resize(6,2);
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edges <<
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1,2,
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2,0,
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0,1,
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3,0,
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3,1,
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3,2;
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}
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// gather cotangent weights
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Matrix<Scalar,Dynamic,Dynamic> C;
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cotmatrix_entries(V,F,C);
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// should have weights for each edge
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assert(C.cols() == edges.rows());
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// loop over elements
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for(int i = 0;i<m;i++)
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{
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// loop over edges of element
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for(int e = 0;e<edges.rows();e++)
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{
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int source = F(i,edges(e,0));
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int dest = F(i,edges(e,1));
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double v = 0.5*C(i,e)*(V(source,d)-V(dest,d));
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Kd_IJV.push_back(Triplet<Scalar>(source,dest,v));
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Kd_IJV.push_back(Triplet<Scalar>(dest,source,-v));
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Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
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Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
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}
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}
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Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
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Kd.makeCompressed();
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}
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void igl::arap_linear_block_spokes_and_rims(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd)
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{
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using namespace std;
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using namespace Eigen;
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// simplex size (3: triangles, 4: tetrahedra)
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int simplex_size = F.cols();
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// Number of elements
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int m = F.rows();
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// Temporary output
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Kd.resize(V.rows(), V.rows());
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vector<Triplet<Scalar> > Kd_IJV;
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Matrix<int,Dynamic,2> edges;
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if(simplex_size == 3)
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{
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// triangles
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Kd.reserve(7*V.rows());
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Kd_IJV.reserve(7*V.rows());
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edges.resize(3,2);
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edges <<
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1,2,
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2,0,
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0,1;
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}else if(simplex_size == 4)
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{
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// tets
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Kd.reserve(17*V.rows());
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Kd_IJV.reserve(17*V.rows());
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edges.resize(6,2);
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edges <<
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1,2,
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2,0,
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0,1,
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3,0,
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3,1,
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3,2;
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// Not implemented yet for tets
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assert(false);
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}
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// gather cotangent weights
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Matrix<Scalar,Dynamic,Dynamic> C;
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cotmatrix_entries(V,F,C);
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// should have weights for each edge
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assert(C.cols() == edges.rows());
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// loop over elements
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for(int i = 0;i<m;i++)
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{
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// loop over edges of element
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for(int e = 0;e<edges.rows();e++)
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{
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int source = F(i,edges(e,0));
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int dest = F(i,edges(e,1));
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double v = C(i,e)*(V(source,d)-V(dest,d))/3.0;
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// loop over edges again
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for(int f = 0;f<edges.rows();f++)
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{
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int Rs = F(i,edges(f,0));
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int Rd = F(i,edges(f,1));
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if(Rs == source && Rd == dest)
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{
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Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,v));
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Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,-v));
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}else if(Rd == source)
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{
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Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,v));
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}else if(Rs == dest)
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{
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Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,-v));
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}
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}
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Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
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Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
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}
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}
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Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
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Kd.makeCompressed();
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}
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template <typename MatV, typename MatF, typename Scalar>
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IGL_INLINE void igl::arap_linear_block_elements(
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const MatV & V,
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const MatF & F,
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const int d,
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Eigen::SparseMatrix<Scalar> & Kd)
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{
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using namespace std;
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using namespace Eigen;
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// simplex size (3: triangles, 4: tetrahedra)
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int simplex_size = F.cols();
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// Number of elements
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int m = F.rows();
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// Temporary output
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Kd.resize(V.rows(), F.rows());
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vector<Triplet<Scalar> > Kd_IJV;
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Matrix<int,Dynamic,2> edges;
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if(simplex_size == 3)
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{
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// triangles
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Kd.reserve(7*V.rows());
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Kd_IJV.reserve(7*V.rows());
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edges.resize(3,2);
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edges <<
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1,2,
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2,0,
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0,1;
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}else if(simplex_size == 4)
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{
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// tets
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Kd.reserve(17*V.rows());
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Kd_IJV.reserve(17*V.rows());
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edges.resize(6,2);
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edges <<
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1,2,
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2,0,
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0,1,
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3,0,
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3,1,
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3,2;
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}
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// gather cotangent weights
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Matrix<Scalar,Dynamic,Dynamic> C;
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cotmatrix_entries(V,F,C);
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// should have weights for each edge
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assert(C.cols() == edges.rows());
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// loop over elements
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for(int i = 0;i<m;i++)
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{
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// loop over edges of element
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for(int e = 0;e<edges.rows();e++)
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{
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int source = F(i,edges(e,0));
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int dest = F(i,edges(e,1));
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double v = C(i,e)*(V(source,d)-V(dest,d));
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Kd_IJV.push_back(Triplet<Scalar>(source,i,v));
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Kd_IJV.push_back(Triplet<Scalar>(dest,i,-v));
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}
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}
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Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
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Kd.makeCompressed();
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template IGL_INLINE void igl::arap_linear_block<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, int, igl::ARAPEnergyType, Eigen::SparseMatrix<double, 0, int>&);
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#endif
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