90 lines
2.5 KiB
C++
Executable File
90 lines
2.5 KiB
C++
Executable File
// Copyright (c) 1999
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). 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; either version 3 of the License,
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// or (at your option) any later version.
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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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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Andreas Fabri
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#ifndef CGAL_SOLVE_H
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#define CGAL_SOLVE_H
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namespace CGAL {
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template <class FT>
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void solve (const FT &a1, const FT &a2, const FT &a3,
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const FT &b1, const FT &b2, const FT &b3,
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const FT &c1, const FT &c2, const FT &c3,
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const FT &d1, const FT &d2, const FT &d3,
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FT &x, FT &y, FT &z)
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{
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#if 0
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FT denom = CGAL::determinant(a1, a2, a3, b1, b2, b3, c1, c2, c3);
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x = CGAL::determinant(b1, b2, b3, c1, c2, c3, d1, d2, d3)/denom;
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y = - CGAL::determinant(a1, a2, a3, c1, c2, c3, d1, d2, d3)/denom;
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z = CGAL::determinant(a1, a2, a3, b1, b2, b3, d1, d2, d3)/denom;
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#else
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// Same as above, but expanded to factorize 6 internal 2x2 minors.
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FT ab23 = a3*b2 - a2*b3;
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FT ab13 = a3*b1 - a1*b3;
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FT ab12 = a2*b1 - a1*b2;
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FT denom = ab23*c1 - ab13*c2 + ab12*c3;
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FT cd23 = c3*d2 - c2*d3;
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FT cd13 = c3*d1 - c1*d3;
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FT cd12 = c2*d1 - c1*d2;
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x = (b3*cd12 - b2*cd13 + b1*cd23)/denom;
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y = (a2*cd13 - cd12*a3 - cd23*a1)/denom;
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z = (ab23*d1 + ab12*d3 - ab13*d2)/denom;
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#endif
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}
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// this is for a parabola c1, c2, c3 are equal to 1
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template <class FT>
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void solve_quadratic (const FT &a1, const FT &a2, const FT &a3,
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const FT &b1, const FT &b2, const FT &b3,
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const FT &d1, const FT &d2, const FT &d3,
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FT &x, FT &y, FT &z)
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{
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FT denom = b2*a3-b1*a3+b1*a2+b3*a1-b3*a2-b2*a1;
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x = - (b2*d1-b2*d3+b3*d2+b1*d3-b1*d2-b3*d1)/denom;
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z = (b2*d1*a3-b2*a1*d3+b1*a2*d3-b1*d2*a3-d1*b3*a2+a1*b3*d2)/denom;
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y = (a2*d1-a2*d3-d1*a3+a1*d3+d2*a3-d2*a1)/denom;
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}
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} //namespace CGAL
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#endif // CGAL_SOLVE_H
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