polar_decomposition.h

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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                           |      *
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* for more details.                                                         *
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****************************************************************************/
#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{

        /* @{ */
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