94 lines
2.4 KiB
C
94 lines
2.4 KiB
C
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// 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).
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Mesh_3/include/CGAL/Mesh_3/radius_ratio.h $
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// $Id: radius_ratio.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Laurent RINEAU
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#ifndef CGAL_MESH_3_RADIUS_RATIO_H
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#define CGAL_MESH_3_RADIUS_RATIO_H
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#include <CGAL/license/Mesh_3.h>
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namespace CGAL {
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namespace Mesh_3 {
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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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typename K::Compute_squared_distance_3 sq_distance =
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k.compute_squared_distance_3_object();
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typename K::Compute_squared_radius_3 comp_sq_circumradius =
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k.compute_squared_radius_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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typename K::Coplanar_3 are_coplanar =
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k.coplanar_3_object();
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if(are_coplanar(p0, p1, p2, p3))
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return FT(0.);
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const FT sq_circumradius = comp_sq_circumradius(p0,
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p1,
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p2,
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p3);
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CGAL_assertion(sq_circumradius != FT(0));
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const FT triangles_area =
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area(p0, p1, p2)
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+ area(p1, p2, p3)
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+ area(p2, p3, p0)
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+ area(p3, p0, p1);
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CGAL_assertion(triangles_area != FT(0));
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const FT cell_volume = volume(p0, p1, p2, 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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template <typename K>
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typename K::FT
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radius_ratio(const typename K::Tetrahedron_3& t, K k = K())
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{
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return radius_ratio(t[0], t[1], t[2], t[3], k);
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}
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template <typename Tetrahedron_3>
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typename Kernel_traits<Tetrahedron_3>::Kernel::FT
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radius_ratio(const Tetrahedron_3& t)
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{
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return radius_ratio(t, typename Kernel_traits<Tetrahedron_3>::Kernel());
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}
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} // end namespace Mesh_3
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} // end namespace CGAL
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#endif // end CGAL_MESH_3_RADIUS_RATIO_H
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