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// Copyright (c) 1999 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Kernel_23/include/CGAL/Kernel/solve.h $
// $Id: solve.h 28567 2006-02-16 14:30:13Z lsaboret $
//
//
// Author(s) : Andreas Fabri
#ifndef CGAL_SOLVE_H
#define CGAL_SOLVE_H
CGAL_BEGIN_NAMESPACE
template <class FT>
void solve (const FT &a1, const FT &a2, const FT &a3,
const FT &b1, const FT &b2, const FT &b3,
const FT &c1, const FT &c2, const FT &c3,
const FT &d1, const FT &d2, const FT &d3,
FT &x, FT &y, FT &z)
{
FT denom = b2*c1*a3-b1*c2*a3+c3*b1*a2+b3*c2*a1-c1*b3*a2-b2*c3*a1;
x = - (b2*c3*d1-b2*c1*d3+c1*b3*d2+b1*c2*d3-c3*b1*d2-b3*c2*d1)/denom;
z = (b2*d1*a3-b2*a1*d3+b1*a2*d3-b1*d2*a3-d1*b3*a2+a1*b3*d2)/denom;
y = (a2*c3*d1-a2*c1*d3-c2*d1*a3+c2*a1*d3+d2*c1*a3-d2*c3*a1)/denom;
}
// this is for a parabola c1, c2, c3 are equal to 1
template <class FT>
void solve_quadratic (const FT &a1, const FT &a2, const FT &a3,
const FT &b1, const FT &b2, const FT &b3,
const FT &d1, const FT &d2, const FT &d3,
FT &x, FT &y, FT &z)
{
FT denom = b2*a3-b1*a3+b1*a2+b3*a1-b3*a2-b2*a1;
x = - (b2*d1-b2*d3+b3*d2+b1*d3-b1*d2-b3*d1)/denom;
z = (b2*d1*a3-b2*a1*d3+b1*a2*d3-b1*d2*a3-d1*b3*a2+a1*b3*d2)/denom;
y = (a2*d1-a2*d3-d1*a3+a1*d3+d2*a3-d2*a1)/denom;
}
CGAL_END_NAMESPACE
#endif // CGAL_SOLVE_H
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