98 lines
3.5 KiB
C++
98 lines
3.5 KiB
C++
// 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 "polar_dec.h"
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#include "polar_svd.h"
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#ifdef _WIN32
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#else
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# include <fenv.h>
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#endif
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#include <cmath>
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#include <Eigen/Eigenvalues>
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#include <iostream>
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#include <cfenv>
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// From Olga's CGAL mentee's ARAP code
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template <
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typename DerivedA,
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typename DerivedR,
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typename DerivedT,
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typename DerivedU,
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typename DerivedS,
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typename DerivedV>
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IGL_INLINE void igl::polar_dec(
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const Eigen::PlainObjectBase<DerivedA> & A,
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Eigen::PlainObjectBase<DerivedR> & R,
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Eigen::PlainObjectBase<DerivedT> & T,
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Eigen::PlainObjectBase<DerivedU> & U,
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Eigen::PlainObjectBase<DerivedS> & S,
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Eigen::PlainObjectBase<DerivedV> & V)
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{
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using namespace std;
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using namespace Eigen;
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typedef typename DerivedA::Scalar Scalar;
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const Scalar th = std::sqrt(Eigen::NumTraits<Scalar>::dummy_precision());
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Eigen::SelfAdjointEigenSolver<DerivedA> eig;
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feclearexcept(FE_UNDERFLOW);
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eig.computeDirect(A.transpose()*A);
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if(fetestexcept(FE_UNDERFLOW) || eig.eigenvalues()(0)/eig.eigenvalues()(2)<th)
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{
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cout<<"resorting to svd 1..."<<endl;
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return polar_svd(A,R,T,U,S,V);
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}
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S = eig.eigenvalues().cwiseSqrt();
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V = eig.eigenvectors();
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U = A * V;
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R = U * S.asDiagonal().inverse() * V.transpose();
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T = V * S.asDiagonal() * V.transpose();
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S = S.reverse().eval();
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V = V.rowwise().reverse().eval();
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U = U.rowwise().reverse().eval() * S.asDiagonal().inverse();
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if(R.determinant() < 0)
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{
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// Annoyingly the .eval() is necessary
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auto W = V.eval();
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const auto & SVT = S.asDiagonal() * V.adjoint();
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W.col(V.cols()-1) *= -1.;
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R = U*W.transpose();
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T = W*SVT;
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}
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if(std::fabs(R.squaredNorm()-3.) > th)
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{
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cout<<"resorting to svd 2..."<<endl;
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return polar_svd(A,R,T,U,S,V);
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}
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}
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template <
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typename DerivedA,
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typename DerivedR,
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typename DerivedT>
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IGL_INLINE void igl::polar_dec(
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const Eigen::PlainObjectBase<DerivedA> & A,
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Eigen::PlainObjectBase<DerivedR> & R,
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Eigen::PlainObjectBase<DerivedT> & T)
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{
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DerivedA U;
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DerivedA V;
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Eigen::Matrix<typename DerivedA::Scalar,DerivedA::RowsAtCompileTime,1> S;
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return igl::polar_dec(A,R,T,U,S,V);
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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::polar_dec<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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template void igl::polar_dec<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, 2, 2, 0, 2, 2>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 2, 2, 0, 2, 2> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
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#endif
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