mirror of https://github.com/CGAL/cgal
88 lines
2.7 KiB
C++
88 lines
2.7 KiB
C++
// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; version 2.1 of the License.
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// See the file LICENSE.LGPL distributed with CGAL.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$ $Date$
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//
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//
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// Author(s) : Pierre Alliez
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#ifndef CGAL_EIGEN_2_H
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#define CGAL_EIGEN_2_H
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CGAL_BEGIN_NAMESPACE
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namespace CGALi {
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// extract eigenvalues and eigenvectors from a 2x2 symmetric matrix.
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// Note: involves a square root.
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// Matrix numbering:
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// a b
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// b c
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// Eigen values and vectors are sorted in descendent order.
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template <typename K>
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void eigen_symmetric_2(const typename K::FT *matrix, // a b c
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std::pair<typename K::Vector_2,
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typename K::Vector_2>& eigen_vectors,
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std::pair<typename K::FT,
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typename K::FT>& eigen_values)
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{
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// types
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typedef typename K::FT FT;
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typedef typename K::Vector_2 Vector;
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// for better reading
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FT a = matrix[0];
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FT b = matrix[1];
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FT c = matrix[2];
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FT p = c*c - 2*a*c + 4*b*b + a*a;
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// degenerate or isotropic case
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if(p == 0.0 || p == 0.0)
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{
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// unit eigen values by default
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eigen_values.first = eigen_values.second = (FT)1.0;
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// any vector is eigen vector
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// the 2D canonical frame is set by default
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eigen_vectors.first = Vector((FT)1.0,(FT)0.0);
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eigen_vectors.second = Vector((FT)0.0,(FT)1.0);
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}
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else // generic case
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{
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FT l1 = 0.5 * ( -std::sqrt(p) + c + a);
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FT l2 = 0.5 * ( std::sqrt(p) + c + a);
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// sort eigen values and vectors in descendent order.
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if(l1 >= l2)
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{
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eigen_values.first = l1;
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eigen_values.second = l2;
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eigen_vectors.first = Vector((FT)1.0, -(std::sqrt(p)-c+a) / (2*b));
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eigen_vectors.second = Vector((FT)1.0, (std::sqrt(p)+c-a) / (2*b));
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}
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else
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{
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eigen_values.first = l2;
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eigen_values.second = l1;
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eigen_vectors.first = Vector((FT)1.0, (std::sqrt(p)+c-a) / (2*b));
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eigen_vectors.second = Vector((FT)1.0, -(std::sqrt(p)-c+a) / (2*b));
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}
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} // end generic case
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} // end eigen_symmetric_2
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} // end namespace CGALi
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CGAL_END_NAMESPACE
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#endif // CGAL_EIGEN_2_H
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