From 43b85e9405fd78915431d3ae204edd52884f8328 Mon Sep 17 00:00:00 2001
From: ganovelli <fabio.ganovelli@isti.cnr.it>
Date: Fri, 18 Nov 2005 14:46:23 +0000
Subject: [PATCH] created

---
 vcg/math/polar_decomposition.h | 80 ++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 vcg/math/polar_decomposition.h

diff --git a/vcg/math/polar_decomposition.h b/vcg/math/polar_decomposition.h
new file mode 100644
index 00000000..053cdf30
--- /dev/null
+++ b/vcg/math/polar_decomposition.h
@@ -0,0 +1,80 @@
+/****************************************************************************
+* 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.                                                         *
+*                                                                           *
+****************************************************************************/
+/****************************************************************************
+  History
+
+$Log: not supported by cvs2svn $
+
+
+****************************************************************************/
+#ifndef POLAR_DECOMPOSITION_VCG
+#define POLAR_DECOMPOSITION_VCG
+
+
+#include <vcg/math/matrix33.h>
+#include <vcg/math/matrix44.h>
+#include <vcg/math/lin_algebra.h>
+
+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 ){
+
+	vcg::Matrix33<S> tmp,s;
+
+	r.SetZero();
+	s.SetZero();
+
+	tmp= m;
+	tmp.Transpose();
+	tmp = m*tmp;
+
+	Matrix33<S> res;
+	Point3<S> e;
+
+	bool ss = SingularValueDecomposition<vcg::Matrix33<S> >(tmp,&e[0],res);
+
+	res.Transpose();
+	e[0]=math::Sqrt(e[0]);
+	e[1]=math::Sqrt(e[1]);
+	e[2]=math::Sqrt(e[2]);
+	tmp = tmp*Matrix33Diag<S>(e)*res;
+
+	bool s1 = SingularValueDecomposition<vcg::Matrix33<S> >(tmp,&e[0],res);
+	tmp.Transpose();
+	e[0]=1/e[0];
+	e[1]=1/e[1];
+	e[2]=1/e[2];
+
+	tmp = res*Matrix33Diag<S>(e)*tmp;
+
+	r = m*tmp;
+}
+
+/*! @} */
+};
+#endif