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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
#ifndef POLAR_DECOMPOSITION_VCG
#define POLAR_DECOMPOSITION_VCG
#include <vcg/math/matrix33.h>
#include <vcg/math/matrix44.h>
#include <eigenlib/Eigen/Dense>
#include <eigenlib/Eigen/SVD>
namespace vcg{
/** \addtogroup math */
/* @{ */
/// Extract the rotational part of a matrix by polar decomposition
/// m = R*S. Polar decomposition is computed by taking r = m * sqrt(m^t*m)^{-1}
template <class S>
void RotationalPartByPolarDecomposition( const vcg::Matrix33<S> & m, vcg::Matrix33<S> &r ){
Eigen::Matrix<S,3,3> tmp,s;
r.setZero();
s.setZero();
tmp = m*m.transpose();
Eigen::Matrix<S,3,3> res;
Eigen::Matrix<S,3,3> e;
bool ss = SingularValueDecomposition<vcg::Matrix33<S> >(tmp,&e[0],res);
Eigen::JacobiSVD<Eigen::MatrixXd> svd(A);
sol=svd.solve(b);
e[0]=math::Sqrt(e[0]);
e[1]=math::Sqrt(e[1]);
e[2]=math::Sqrt(e[2]);
tmp = tmp*e.asDiagonal()*res.transpose();
bool s1 = SingularValueDecomposition<vcg::Matrix33<S> >(tmp,&e[0],res.transpose());
e[0]=1/e[0];
e[1]=1/e[1];
e[2]=1/e[2];
tmp = res*e.asDiagonal()*tmp.transpose();
r = m*tmp;
}
/*! @} */
};
#endif
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