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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
//
// 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 <igl/shapeup.h>
#include <igl/min_quad_with_fixed.h>
#include <igl/igl_inline.h>
#include <igl/setdiff.h>
#include <igl/cat.h>
#include <igl/PI.h>
#include <Eigen/Core>
#include <vector>
namespace igl
{
//This projection does nothing but render points into projP. Mostly used for "echoing" the global step
IGL_INLINE bool shapeup_identity_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S, Eigen::PlainObjectBase<Eigen::MatrixXd>& projP){
projP.conservativeResize(SC.rows(), 3*SC.maxCoeff());
for (int i=0;i<S.rows();i++){
Eigen::RowVector3d avgCurrP=Eigen::RowVector3d::Zero();
for (int j=0;j<SC(i);j++)
avgCurrP+=P.row(S(i,j))/(double)(SC(i));
for (int j=0;j<SC(i);j++)
projP.block(i,3*j,1,3)=P.row(S(i,j))-avgCurrP;
}
return true;
}
//the projection assumes that the sets are vertices of polygons in order
IGL_INLINE bool shapeup_regular_face_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S, Eigen::PlainObjectBase<Eigen::MatrixXd>& projP){
projP.conservativeResize(SC.rows(), 3*SC.maxCoeff());
for (int currRow=0;currRow<SC.rows();currRow++){
//computing average
int N=SC(currRow);
const Eigen::RowVectorXi SRow=S.row(currRow);
Eigen::RowVector3d avgCurrP=Eigen::RowVector3d::Zero();
Eigen::MatrixXd targetPolygon(N, 3);
Eigen::MatrixXd sourcePolygon(N, 3);
for (int j=0;j<N;j++)
avgCurrP+=P.row(SRow(j))/(double)(N);
for (int j=0;j<N;j++)
targetPolygon.row(j)=P.row(SRow(j))-avgCurrP;
//creating perfectly regular source polygon
for (int j=0;j<N;j++)
sourcePolygon.row(j)<<cos(2*igl::PI*(double)j/(double(N))), sin(2*igl::PI*(double)j/(double(N))),0.0;
//finding closest similarity transformation between source and target
Eigen::MatrixXd corrMat=sourcePolygon.transpose()*targetPolygon;
Eigen::JacobiSVD<Eigen::Matrix3d> svd(corrMat, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::MatrixXd R=svd.matrixU()*svd.matrixV().transpose();
//getting scale by edge length change average. TODO: by singular values
Eigen::VectorXd sourceEdgeLengths(N);
Eigen::VectorXd targetEdgeLengths(N);
for (int j=0;j<N;j++){
sourceEdgeLengths(j)=(sourcePolygon.row((j+1)%N)-sourcePolygon.row(j)).norm();
targetEdgeLengths(j)=(targetPolygon.row((j+1)%N)-targetPolygon.row(j)).norm();
}
double scale=(targetEdgeLengths.cwiseQuotient(sourceEdgeLengths)).mean();
for (int j=0;j<N;j++)
projP.block(currRow,3*j,1,3)=sourcePolygon.row(j)*R*scale;
}
return true;
}
template <
typename DerivedP,
typename DerivedSC,
typename DerivedS,
typename Derivedw>
IGL_INLINE bool shapeup_precomputation(const Eigen::PlainObjectBase<DerivedP>& P,
const Eigen::PlainObjectBase<DerivedSC>& SC,
const Eigen::PlainObjectBase<DerivedS>& S,
const Eigen::PlainObjectBase<DerivedS>& E,
const Eigen::PlainObjectBase<DerivedSC>& b,
const Eigen::PlainObjectBase<Derivedw>& wShape,
const Eigen::PlainObjectBase<Derivedw>& wSmooth,
ShapeupData & sudata)
{
using namespace std;
using namespace Eigen;
sudata.P=P;
sudata.SC=SC;
sudata.S=S;
sudata.b=b;
typedef typename DerivedP::Scalar Scalar;
//checking for consistency of the input
assert(SC.rows()==S.rows());
assert(SC.rows()==wShape.rows());
assert(E.rows()==wSmooth.rows());
assert(b.rows()!=0); //would lead to matrix becoming SPD
sudata.DShape.conservativeResize(SC.sum(), P.rows()); //Shape matrix (integration);
sudata.DClose.conservativeResize(b.rows(), P.rows()); //Closeness matrix for positional constraints
sudata.DSmooth.conservativeResize(E.rows(), P.rows()); //smoothness matrix
//Building shape matrix
std::vector<Triplet<Scalar> > DShapeTriplets;
int currRow=0;
for (int i=0;i<S.rows();i++){
Scalar avgCoeff=1.0/(Scalar)SC(i);
for (int j=0;j<SC(i);j++){
for (int k=0;k<SC(i);k++){
if (j==k)
DShapeTriplets.push_back(Triplet<Scalar>(currRow+j, S(i,k), (1.0-avgCoeff)));
else
DShapeTriplets.push_back(Triplet<Scalar>(currRow+j, S(i,k), (-avgCoeff)));
}
}
currRow+=SC(i);
}
sudata.DShape.setFromTriplets(DShapeTriplets.begin(), DShapeTriplets.end());
//Building closeness matrix
std::vector<Triplet<Scalar> > DCloseTriplets;
for (int i=0;i<b.size();i++)
DCloseTriplets.push_back(Triplet<Scalar>(i,b(i), 1.0));
sudata.DClose.setFromTriplets(DCloseTriplets.begin(), DCloseTriplets.end());
//Building smoothness matrix
std::vector<Triplet<Scalar> > DSmoothTriplets;
for (int i=0; i<E.rows(); i++) {
DSmoothTriplets.push_back(Triplet<Scalar>(i, E(i, 0), -1));
DSmoothTriplets.push_back(Triplet<Scalar>(i, E(i, 1), 1));
}
SparseMatrix<Scalar> tempMat;
igl::cat(1, sudata.DShape, sudata.DClose, tempMat);
igl::cat(1, tempMat, sudata.DSmooth, sudata.A);
//weight matrix
vector<Triplet<Scalar> > WTriplets;
//one weight per set in S.
currRow=0;
for (int i=0;i<SC.rows();i++){
for (int j=0;j<SC(i);j++)
WTriplets.push_back(Triplet<double>(currRow+j,currRow+j,sudata.shapeCoeff*wShape(i)));
currRow+=SC(i);
}
for (int i=0;i<b.size();i++)
WTriplets.push_back(Triplet<double>(SC.sum()+i, SC.sum()+i, sudata.closeCoeff));
for (int i=0;i<E.rows();i++)
WTriplets.push_back(Triplet<double>(SC.sum()+b.size()+i, SC.sum()+b.size()+i, sudata.smoothCoeff*wSmooth(i)));
sudata.W.conservativeResize(SC.sum()+b.size()+E.rows(), SC.sum()+b.size()+E.rows());
sudata.W.setFromTriplets(WTriplets.begin(), WTriplets.end());
sudata.At=sudata.A.transpose(); //for efficieny, as we use the transpose a lot in the iteration
sudata.Q=sudata.At*sudata.W*sudata.A;
return min_quad_with_fixed_precompute(sudata.Q,VectorXi(),SparseMatrix<double>(),true,sudata.solver_data);
}
template <
typename DerivedP,
typename DerivedSC,
typename DerivedS>
IGL_INLINE bool shapeup_solve(const Eigen::PlainObjectBase<DerivedP>& bc,
const std::function<bool(const Eigen::PlainObjectBase<DerivedP>&, const Eigen::PlainObjectBase<DerivedSC>&, const Eigen::PlainObjectBase<DerivedS>&, Eigen::PlainObjectBase<DerivedP>&)>& local_projection,
const Eigen::PlainObjectBase<DerivedP>& P0,
const ShapeupData & sudata,
const bool quietIterations,
Eigen::PlainObjectBase<DerivedP>& P)
{
using namespace Eigen;
using namespace std;
MatrixXd currP=P0;
MatrixXd prevP=P0;
MatrixXd projP;
assert(bc.rows()==sudata.b.rows());
MatrixXd rhs(sudata.A.rows(), 3); rhs.setZero();
rhs.block(sudata.DShape.rows(), 0, sudata.b.rows(),3)=bc; //this stays constant throughout the iterations
if (!quietIterations){
cout<<"Shapeup Iterations, "<<sudata.DShape.rows()<<" constraints, solution size "<<P0.size()<<endl;
cout<<"**********************************************************************************************"<<endl;
}
projP.conservativeResize(sudata.SC.rows(), 3*sudata.SC.maxCoeff());
for (int iter=0;iter<sudata.maxIterations;iter++){
local_projection(currP, sudata.SC,sudata.S,projP);
//constructing the projection part of the (DShape rows of the) right hand side
int currRow=0;
for (int i=0;i<sudata.S.rows();i++)
for (int j=0;j<sudata.SC(i);j++)
rhs.row(currRow++)=projP.block(i, 3*j, 1,3);
DerivedP lsrhs=-sudata.At*sudata.W*rhs;
MatrixXd Y(0,3), Beq(0,3); //We do not use the min_quad_solver fixed variables mechanism; they are treated with the closeness energy of ShapeUp.
min_quad_with_fixed_solve(sudata.solver_data, lsrhs,Y,Beq,currP);
double currChange=(currP-prevP).lpNorm<Infinity>();
if (!quietIterations)
cout << "Iteration "<<iter<<", integration Linf error: "<<currChange<< endl;
prevP=currP;
if (currChange<sudata.pTolerance){
P=currP;
return true;
}
}
P=currP;
return false; //we went over maxIterations
}
}
#ifdef IGL_STATIC_LIBRARY
template bool igl::shapeup_precomputation< typename Eigen::Matrix<double, -1, -1, 0, -1, -1>, typename Eigen::Matrix<int, -1, 1, 0, -1, 1>, typename Eigen::Matrix<int, -1, -1, 0, -1, -1>, typename Eigen::Matrix<double, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, igl::ShapeupData&);
template bool igl::shapeup_solve<typename Eigen::Matrix<double, -1, -1, 0, -1, -1>, typename Eigen::Matrix<int, -1, 1, 0, -1, 1>, typename Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& bc, const std::function<bool(const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, const Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, const Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& ) >& local_projection, const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& P0, const igl::ShapeupData & sudata, const bool quietIterations, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& P);
#endif
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