496 lines
18 KiB
C++
496 lines
18 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004-2016 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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#ifndef __VCG_IMPLICIT_TETRA_SMOOTHER
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#define __VCG_IMPLICIT_TETRA_SMOOTHER
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#include <Eigen/Sparse>
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#include <vcg/complex/algorithms/mesh_to_matrix.h>
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#include <vcg/complex/algorithms/update/quality.h>
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#include <vcg/complex/algorithms/smooth.h>
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#define PENALTY 10000
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namespace vcg
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{
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template <class MeshType>
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class ImplicitTetraSmoother
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{
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typedef typename MeshType::FaceType FaceType;
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typedef typename MeshType::VertexType VertexType;
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typedef typename MeshType::TetraType TetraType;
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typedef typename MeshType::CoordType CoordType;
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typedef typename MeshType::ScalarType ScalarType;
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typedef typename Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic> MatrixXm;
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public:
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struct FaceConstraint
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{
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int numF;
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std::vector<ScalarType> BarycentricW;
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CoordType TargetPos;
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FaceConstraint()
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{
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numF = -1;
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}
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FaceConstraint(int _numF,
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const std::vector<ScalarType> &_BarycentricW,
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const CoordType &_TargetPos)
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{
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numF = _numF;
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BarycentricW = std::vector<ScalarType>(_BarycentricW.begin(), _BarycentricW.end());
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TargetPos = _TargetPos;
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}
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};
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struct Parameter
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{
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//the amount of smoothness, useful only if we set the mass matrix
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ScalarType lambda;
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//the use of mass matrix to keep the mesh close to its original position
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//(weighted per area distributed on vertices)
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bool useMassMatrix;
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//this bool is used to fix the border vertices of the mesh or not
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bool fixBorder;
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//this bool is used to set if cotangent weight is used, this flag to false means uniform laplacian
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bool useCotWeight;
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//use this weight for the laplacian when the cotangent one is not used
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ScalarType lapWeight;
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//the set of fixed vertices
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std::vector<int> FixedV;
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//the set of faces for barycentric constraints
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std::vector<FaceConstraint> ConstrainedF;
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//the degree of laplacian
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int degree;
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//this is to say if we smooth the positions or the quality
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bool SmoothQ;
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Parameter()
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{
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degree = 2;
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lambda = 0.05;
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useMassMatrix = true;
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fixBorder = true;
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useCotWeight = false;
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lapWeight = 1;
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SmoothQ = false;
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}
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};
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private:
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static void InitSparse(const std::vector<std::pair<int, int>> &Index,
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const std::vector<ScalarType> &Values,
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const int m,
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const int n,
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Eigen::SparseMatrix<ScalarType> &X)
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{
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assert(Index.size() == Values.size());
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std::vector<Eigen::Triplet<ScalarType>> IJV;
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IJV.reserve(Index.size());
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for (size_t i = 0; i < Index.size(); i++)
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{
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int row = Index[i].first;
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int col = Index[i].second;
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ScalarType val = Values[i];
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assert(row < m);
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assert(col < n);
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IJV.push_back(Eigen::Triplet<ScalarType>(row, col, val));
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}
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X.resize(m, n);
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X.setFromTriplets(IJV.begin(), IJV.end());
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}
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static void CollectHardConstraints(MeshType &mesh, const Parameter &SParam,
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std::vector<std::pair<int, int>> &IndexC,
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std::vector<ScalarType> &WeightC,
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bool SmoothQ = false)
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{
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std::vector<int> To_Fix;
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//collect fixed vert
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if (SParam.fixBorder)
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{
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//add penalization constra
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for (size_t i = 0; i < mesh.vert.size(); i++)
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{
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if (!mesh.vert[i].IsB())
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continue;
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To_Fix.push_back(i);
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}
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}
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//add additional fixed vertices constraint
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To_Fix.insert(To_Fix.end(), SParam.FixedV.begin(), SParam.FixedV.end());
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//sort and make them unique
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std::sort(To_Fix.begin(), To_Fix.end());
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typename std::vector<int>::iterator it = std::unique(To_Fix.begin(), To_Fix.end());
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To_Fix.resize(std::distance(To_Fix.begin(), it));
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for (size_t i = 0; i < To_Fix.size(); i++)
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{
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if (!SmoothQ)
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{
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for (int j = 0; j < 3; j++)
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{
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int IndexV = (To_Fix[i] * 3) + j;
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IndexC.push_back(std::pair<int, int>(IndexV, IndexV));
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WeightC.push_back((ScalarType)PENALTY);
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}
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}
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else
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{
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int IndexV = To_Fix[i];
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IndexC.push_back(std::pair<int, int>(IndexV, IndexV));
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WeightC.push_back((ScalarType)PENALTY);
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}
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}
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}
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static void CollectBarycentricConstraints(MeshType &mesh,
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const Parameter &SParam,
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std::vector<std::pair<int, int>> &IndexC,
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std::vector<ScalarType> &WeightC,
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std::vector<int> &IndexRhs,
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std::vector<ScalarType> &ValueRhs)
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{
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ScalarType penalty;
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int baseIndex = mesh.vert.size();
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for (size_t i = 0; i < SParam.ConstrainedF.size(); i++)
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{
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//get the index of the current constraint
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int IndexConstraint = baseIndex + i;
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//add one hard constraint
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int FaceN = SParam.ConstrainedF[i].numF;
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assert(FaceN >= 0);
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assert(FaceN < (int)mesh.face.size());
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assert(mesh.face[FaceN].VN() == (int)SParam.ConstrainedF[i].BarycentricW.size());
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penalty = ScalarType(1) - SParam.lapWeight;
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assert(penalty > ScalarType(0) && penalty < ScalarType(1));
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//then add all the weights to impose the constraint
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for (int j = 0; j < mesh.face[FaceN].VN(); j++)
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{
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//get the current weight
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ScalarType currW = SParam.ConstrainedF[i].BarycentricW[j];
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//get the index of the current vertex
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int FaceVert = vcg::tri::Index(mesh, mesh.face[FaceN].V(j));
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//then add the constraints componentwise
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for (int k = 0; k < 3; k++)
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{
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//multiply times 3 per component
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int IndexV = (FaceVert * 3) + k;
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//get the index of the current constraint
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int ComponentConstraint = (IndexConstraint * 3) + k;
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IndexC.push_back(std::pair<int, int>(ComponentConstraint, IndexV));
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WeightC.push_back(currW * penalty);
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IndexC.push_back(std::pair<int, int>(IndexV, ComponentConstraint));
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WeightC.push_back(currW * penalty);
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//this to avoid the 1 on diagonal last entry of mass matrix
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IndexC.push_back(std::pair<int, int>(ComponentConstraint, ComponentConstraint));
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WeightC.push_back(-1);
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}
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}
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for (int j = 0; j < 3; j++)
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{
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//get the index of the current constraint
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int ComponentConstraint = (IndexConstraint * 3) + j;
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//get per component value
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ScalarType ComponentV = SParam.ConstrainedF[i].TargetPos.V(j);
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//add the diagonal value
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IndexRhs.push_back(ComponentConstraint);
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ValueRhs.push_back(ComponentV * penalty);
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}
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}
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}
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static void MassMatrixEntry(MeshType &m,
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std::vector<std::pair<int, int>> &index,
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std::vector<ScalarType> &entry,
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bool vertexCoord = true)
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{
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tri::RequireCompactness(m);
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typename MeshType::template PerVertexAttributeHandle<ScalarType> h =
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tri::Allocator<MeshType>::template GetPerVertexAttribute<ScalarType>(m, "volume");
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for (int i = 0; i < m.vn; ++i)
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h[i] = 0;
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ForEachTetra(m, [&](TetraType &t) {
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ScalarType v = Tetra::ComputeVolume(t);
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for (int i = 0; i < 4; ++i)
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h[tri::Index(m, t.V(i))] += v;
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});
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ScalarType maxV = 0;
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for (int i = 0; i < m.vn; ++i)
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maxV = max(maxV, h[i]);
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for (int i = 0; i < m.vn; ++i)
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{
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int currI = i;
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index.push_back(std::pair<int, int>(currI, currI));
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entry.push_back(h[i] / maxV);
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}
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tri::Allocator<MeshType>::template DeletePerVertexAttribute<ScalarType>(m, h);
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}
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static ScalarType ComputeCotangentWeight(TetraType &t, const int i)
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{
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//i is the edge in the tetra
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tetra::Pos<TetraType> pp(&t, Tetra::FofE(i, 0), i, Tetra::VofE(i, 0));
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tetra::Pos<TetraType> pt(&t, Tetra::FofE(i, 0), i, Tetra::VofE(i, 0));
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ScalarType weight = 0;
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do
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{
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CoordType po0 = t.V(Tetra::VofE(5 - pt.E(), 0))->cP();
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CoordType po1 = t.V(Tetra::VofE(5 - pt.E(), 1))->cP();
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ScalarType length = vcg::Distance(po0, po1);
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ScalarType cot = std::tan((M_PI / 2.) - Tetra::DihedralAngle(*pt.T(), 5 - pt.E()));
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weight = (length / 6.) * cot;
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pt.FlipT();
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pt.FlipF();
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} while (pp != pt);
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return weight;
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}
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static void GetLaplacianEntry(MeshType &mesh,
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TetraType &t,
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std::vector<std::pair<int, int>> &index,
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std::vector<ScalarType> &entry,
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bool cotangent,
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ScalarType weight = 1,
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bool vertexCoord = true)
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{
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// if (cotangent)
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// vcg::tri::MeshAssert<MeshType>::OnlyT(mesh);
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//iterate on edges
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for (int i = 0; i < 6; ++i)
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{
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weight = 1;//ComputeCotangentWeight(t, i);
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int indexV0 = Index(mesh, t.V(Tetra::VofE(i, 0)));
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int indexV1 = Index(mesh, t.V(Tetra::VofE(i, 1)));
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for (int j = 0; j < 3; j++)
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{
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//multiply by 3 and add the component
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int currI0 = (indexV0 * 3) + j;
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int currI1 = (indexV1 * 3) + j;
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index.push_back(std::pair<int, int>(currI0, currI0));
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entry.push_back(weight);
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index.push_back(std::pair<int, int>(currI0, currI1));
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entry.push_back(-weight);
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index.push_back(std::pair<int, int>(currI1, currI1));
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entry.push_back(weight);
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index.push_back(std::pair<int, int>(currI1, currI0));
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entry.push_back(-weight);
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}
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}
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}
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static void GetLaplacianMatrix(MeshType &mesh,
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std::vector<std::pair<int, int>> &index,
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std::vector<ScalarType> &entry,
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bool cotangent,
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ScalarType weight = 1,
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bool vertexCoord = true)
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{
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//store the index and the scalar for the sparse matrix
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ForEachTetra(mesh, [&](TetraType &t) {
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GetLaplacianEntry(mesh, t, index, entry, cotangent, weight);
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});
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}
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public:
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static void Compute(MeshType &mesh, Parameter &SParam)
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{
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//calculate the size of the system
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int matr_size = mesh.vert.size() + SParam.ConstrainedF.size();
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//the laplacian and the mass matrix
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Eigen::SparseMatrix<ScalarType> L, M, B;
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//initialize the mass matrix
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std::vector<std::pair<int, int>> IndexM;
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std::vector<ScalarType> ValuesM;
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//add the entries for mass matrix
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if (SParam.useMassMatrix)
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MassMatrixEntry(mesh, IndexM, ValuesM, !SParam.SmoothQ);
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//then add entries for lagrange mult due to barycentric constraints
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for (size_t i = 0; i < SParam.ConstrainedF.size(); i++)
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{
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int baseIndex = (mesh.vert.size() + i) * 3;
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if (SParam.SmoothQ)
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baseIndex = (mesh.vert.size() + i);
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if (SParam.SmoothQ)
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{
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IndexM.push_back(std::pair<int, int>(baseIndex, baseIndex));
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ValuesM.push_back(1);
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}
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else
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{
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for (int j = 0; j < 3; j++)
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{
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IndexM.push_back(std::pair<int, int>(baseIndex + j, baseIndex + j));
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ValuesM.push_back(1);
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}
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}
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}
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//add the hard constraints
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CollectHardConstraints(mesh, SParam, IndexM, ValuesM, SParam.SmoothQ);
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//initialize sparse mass matrix
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if (!SParam.SmoothQ)
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InitSparse(IndexM, ValuesM, matr_size * 3, matr_size * 3, M);
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else
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InitSparse(IndexM, ValuesM, matr_size, matr_size, M);
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//initialize the barycentric matrix
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std::vector<std::pair<int, int>> IndexB;
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std::vector<ScalarType> ValuesB;
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std::vector<int> IndexRhs;
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std::vector<ScalarType> ValuesRhs;
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//then also collect hard constraints
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if (!SParam.SmoothQ)
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{
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CollectBarycentricConstraints(mesh, SParam, IndexB, ValuesB, IndexRhs, ValuesRhs);
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//initialize sparse constraint matrix
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InitSparse(IndexB, ValuesB, matr_size * 3, matr_size * 3, B);
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}
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else
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InitSparse(IndexB, ValuesB, matr_size, matr_size, B);
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//get the entries for laplacian matrix
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std::vector<std::pair<int, int>> IndexL;
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std::vector<ScalarType> ValuesL;
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GetLaplacianMatrix(mesh, IndexL, ValuesL, SParam.useCotWeight, SParam.lapWeight, !SParam.SmoothQ);
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//initialize sparse laplacian matrix
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if (!SParam.SmoothQ)
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InitSparse(IndexL, ValuesL, matr_size * 3, matr_size * 3, L);
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else
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InitSparse(IndexL, ValuesL, matr_size, matr_size, L);
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for (int i = 0; i < (SParam.degree - 1); i++)
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L = L * L;
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//then solve the system
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Eigen::SparseMatrix<ScalarType> S = (M + B + SParam.lambda * L);
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//SimplicialLDLT
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Eigen::SimplicialCholesky<Eigen::SparseMatrix<ScalarType>> solver(S);
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assert(solver.info() == Eigen::Success);
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MatrixXm V;
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if (!SParam.SmoothQ)
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V = MatrixXm(matr_size * 3, 1);
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else
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V = MatrixXm(matr_size, 1);
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//set the first part of the matrix with vertex values
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if (!SParam.SmoothQ)
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{
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for (size_t i = 0; i < mesh.vert.size(); i++)
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{
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int index = i * 3;
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V(index, 0) = mesh.vert[i].P().X();
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V(index + 1, 0) = mesh.vert[i].P().Y();
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V(index + 2, 0) = mesh.vert[i].P().Z();
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}
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}
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else
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{
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for (size_t i = 0; i < mesh.vert.size(); i++)
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{
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int index = i;
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V(index, 0) = mesh.vert[i].Q();
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}
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}
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//then set the second part by considering RHS gien by barycentric constraint
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for (size_t i = 0; i < IndexRhs.size(); i++)
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{
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int index = IndexRhs[i];
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ScalarType val = ValuesRhs[i];
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V(index, 0) = val;
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}
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//solve the system
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V = solver.solve(M * V).eval();
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//then copy back values
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if (!SParam.SmoothQ)
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{
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for (size_t i = 0; i < mesh.vert.size(); i++)
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{
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int index = i * 3;
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mesh.vert[i].P().X() = V(index, 0);
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mesh.vert[i].P().Y() = V(index + 1, 0);
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mesh.vert[i].P().Z() = V(index + 2, 0);
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}
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}
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else
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{
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for (size_t i = 0; i < mesh.vert.size(); i++)
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{
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int index = i;
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mesh.vert[i].Q() = V(index, 0);
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}
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}
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}
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};
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} //end namespace vcg
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#endif
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