mirror of https://github.com/CGAL/cgal
82 lines
2.3 KiB
C++
82 lines
2.3 KiB
C++
// Copyright (c) 2006 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 may redistribute it under
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// the terms of the Q Public License version 1.0.
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// See the file LICENSE.QPL 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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// $Id$
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//
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//
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// Author(s) : Laurent RINEAU
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#ifndef CGAL_RADIUS_RATIO_H
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#define CGAL_RADIUS_RATIO_H
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#include <CGAL/Point_3.h>
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namespace CGAL {
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template <typename K>
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typename K::FT
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radius_ratio(const typename K::Point_3& p0,
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const typename K::Point_3& p1,
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const typename K::Point_3& p2,
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const typename K::Point_3& p3,
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K k = K())
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{
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typedef typename K::FT FT;
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typedef typename K::Point_3 Point_3;
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typename K::Compute_squared_distance_3 sq_distance =
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k.compute_squared_distance_3_object();
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typename K::Construct_circumcenter_3 circumcenter =
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k.construct_circumcenter_3_object();
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typename K::Compute_volume_3 volume =
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k.compute_volume_3_object();
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typename K::Compute_area_3 area =
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k.compute_area_3_object();
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const Point_3 center = circumcenter(p0,
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p1,
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p2,
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p3);
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const FT sq_circumradius = sq_distance(center, p0);
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CGAL_assertion(sq_circumradius != FT(0));
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FT triangles_area = FT(0);
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triangles_area += area(p0, p1, p2);
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triangles_area += area(p1, p2, p3);
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triangles_area += area(p2, p3, p0);
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triangles_area += area(p3, p0, p1);
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CGAL_assertion(triangles_area != FT(0));
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const FT cell_volume = volume(p0,
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p1,
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p2,
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p3);
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const FT inradius =
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3 * CGAL::abs(cell_volume) / triangles_area;
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const FT result = FT(3) * inradius / CGAL::sqrt(sq_circumradius);
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CGAL_assertion(result >= FT(0));
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CGAL_assertion(result <= FT(1));
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return result;
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}
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} // end namespace CGAL
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#endif // end CGAL_RADIUS_RATIO_H
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