1399 lines
34 KiB
C
1399 lines
34 KiB
C
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// Copyright (c) 2003-2004
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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) : Sylvain Pion
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#ifndef CGAL_KERNEL_GLOBAL_FUNCTIONS_3_H
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#define CGAL_KERNEL_GLOBAL_FUNCTIONS_3_H
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#include <CGAL/user_classes.h>
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#include <CGAL/Kernel/global_functions_internal_3.h>
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#include <CGAL/Kernel/mpl.h>
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// Generic functions calling the kernel functor.
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// See comments in CGAL/Kernel/global_functions_2.h.
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namespace CGAL {
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template <typename K>
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inline
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Angle
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angle(const Vector_3<K> &u, const Vector_3<K> &v)
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{
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return internal::angle(u, v, K());
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}
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template <typename K>
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inline
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Angle
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angle(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
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{
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return internal::angle(p, q, r, K());
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}
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template <typename K>
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inline
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Angle
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angle(const Point_3<K> &p, const Point_3<K> &q,
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const Point_3<K> &r, const Point_3<K> &s)
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{
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return internal::angle(p, q, r, s, K());
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}
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template <typename K>
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inline
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Angle
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angle(const Point_3<K> &p, const Point_3<K> &q,
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const Point_3<K> &r, const Vector_3<K> &v)
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{
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return internal::angle(p, q, r, v, K());
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}
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template < class K >
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inline
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typename K::FT
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approximate_dihedral_angle(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r,
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const Point_3<K> &s)
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{
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return internal::approximate_dihedral_angle(p, q, r, s, K());
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}
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template < typename K >
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inline
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typename K::Boolean
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are_negative_oriented(const Point_3<K>& p, const Point_3<K>& q,
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const Point_3<K>& r, const Point_3<K>& s)
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{
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return internal::are_negative_oriented(p, q, r, s, K());
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}
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template < class K >
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inline
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typename K::Boolean
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are_ordered_along_line(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::are_ordered_along_line(p, q, r, K());
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}
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template < typename K >
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inline
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typename K::Boolean
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are_positive_oriented(const Point_3<K>& p, const Point_3<K>& q,
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const Point_3<K>& r, const Point_3<K>& s)
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{
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return internal::are_positive_oriented(p, q, r, s, K());
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}
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template < class K >
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inline
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typename K::Boolean
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are_strictly_ordered_along_line(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::are_strictly_ordered_along_line(p, q, r, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2)
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{
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return internal::barycenter(p1, w1, p2, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2, const typename K::FT& w2)
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{
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return internal::barycenter(p1, w1, p2, w2, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2, const typename K::FT& w2,
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const Point_3<K> &p3)
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{
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return internal::barycenter(p1, w1, p2, w2, p3, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2, const typename K::FT& w2,
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const Point_3<K> &p3, const typename K::FT& w3)
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{
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return internal::barycenter(p1, w1, p2, w2, p3, w3, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2, const typename K::FT& w2,
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const Point_3<K> &p3, const typename K::FT& w3,
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const Point_3<K> &p4)
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{
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return internal::barycenter(p1, w1, p2, w2, p3, w3, p4, K());
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}
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template < class K >
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inline
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typename K::Point_3
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barycenter(const Point_3<K> &p1, const typename K::FT& w1,
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const Point_3<K> &p2, const typename K::FT& w2,
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const Point_3<K> &p3, const typename K::FT& w3,
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const Point_3<K> &p4, const typename K::FT& w4)
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{
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return internal::barycenter(p1, w1, p2, w2, p3, w3, p4, w4, K());
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}
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template <typename K>
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inline
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typename K::Plane_3
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bisector(const Point_3<K> &p, const Point_3<K> &q)
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{
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return internal::bisector(p, q, K());
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}
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template <typename K>
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inline
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typename K::Plane_3
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bisector(const Plane_3<K> &h1, const Plane_3<K> &h2)
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{
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return internal::bisector(h1, h2, K());
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}
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template < class K >
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inline
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Point_3<K>
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centroid(const Point_3<K> &p, const Point_3<K> &q,
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const Point_3<K> &r, const Point_3<K> &s)
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{
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return internal::centroid(p, q, r, s, K());
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}
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template < class K >
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inline
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Point_3<K>
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centroid(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
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{
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return internal::centroid(p, q, r, K());
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}
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template < class K >
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inline
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Point_3<K>
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centroid(const Tetrahedron_3<K> &t)
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{
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return internal::centroid(t, K());
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}
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template < class K >
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inline
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Point_3<K>
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centroid(const Triangle_3<K> &t)
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{
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return internal::centroid(t, K());
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}
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template < class K >
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inline
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typename K::Point_3
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circumcenter(const Point_3<K> &p,
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const Point_3<K> &q)
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{
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return internal::circumcenter(p, q, K());
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}
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template < class K >
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inline
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typename K::Point_3
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circumcenter(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::circumcenter(p, q, r, K());
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}
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template < class K >
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inline
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typename K::Point_3
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circumcenter(const Point_3<K> &p, const Point_3<K> &q,
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const Point_3<K> &r, const Point_3<K> &s)
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{
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return internal::circumcenter(p, q, r, s, K());
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}
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template < class K >
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inline
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typename K::Point_3
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circumcenter(const Tetrahedron_3<K> &t)
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{
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return internal::circumcenter(t, K());
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}
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template < class K >
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inline
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typename K::Point_3
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circumcenter(const Triangle_3<K> &t)
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{
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return internal::circumcenter(t, K());
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}
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template < class K >
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inline
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typename K::Boolean
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collinear(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
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{
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return internal::collinear(p, q, r, K());
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}
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template < class K >
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inline
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typename K::Boolean
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collinear_are_ordered_along_line(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::collinear_are_ordered_along_line(p, q, r, K());
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}
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template < class K >
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inline
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typename K::Boolean
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collinear_are_strictly_ordered_along_line(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::collinear_are_strictly_ordered_along_line(p, q, r, K());
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}
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template < class K >
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inline
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typename K::Comparison_result
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compare_dihedral_angle(const Point_3<K>& a1, const Point_3<K>& b1,
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const Point_3<K>& c1, const Point_3<K>& d1,
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const Point_3<K>& a2, const Point_3<K>& b2,
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const Point_3<K>& c2, const Point_3<K>& d2)
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{
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return internal::compare_dihedral_angle(a1, b1, c1, d1, a2, b2, c2, d2, K());
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}
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template < class K >
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inline
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typename K::Comparison_result
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compare_dihedral_angle(const Point_3<K>& a1, const Point_3<K>& b1,
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const Point_3<K>& c1, const Point_3<K>& d1,
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const typename K::FT& cosine)
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{
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return internal::compare_dihedral_angle(a1, b1, c1, d1, cosine, K());
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}
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template < class K >
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inline
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typename K::Comparison_result
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compare_dihedral_angle(const Vector_3<K>& ab1,
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const Vector_3<K>& ac1,
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const Vector_3<K>& ad1,
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const Vector_3<K>& ab2,
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const Vector_3<K>& ac2,
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const Vector_3<K>& ad2)
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{
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return internal::compare_dihedral_angle(ab1, ac1, ad1, ab2, ac2, ad2, K());
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}
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template < class K >
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inline
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typename K::Comparison_result
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compare_dihedral_angle(const Vector_3<K>& ab1,
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const Vector_3<K>& ac1,
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const Vector_3<K>& ad1,
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const typename K::FT& cosine)
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{
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return internal::compare_dihedral_angle(ab1, ac1, ad1, cosine, K());
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}
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template < class K >
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inline
|
||
|
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typename K::Comparison_result
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compare_distance_to_point(const Point_3<K> &p,
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const Point_3<K> &q,
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const Point_3<K> &r)
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{
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return internal::compare_distance_to_point(p, q, r, K());
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}
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template < class K >
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||
|
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inline
|
||
|
|
typename K::Comparison_result
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||
|
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compare_power_distance(const Point_3<K> &r,
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||
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const Weighted_point_3<K> &p,
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|
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const Weighted_point_3<K> &q)
|
||
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{
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return internal::compare_power_distance(r, p, q, K());
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}
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template < class K >
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||
|
|
inline
|
||
|
|
typename K::Comparison_result
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||
|
|
compare_slope(const Point_3<K> &p,
|
||
|
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const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s)
|
||
|
|
{
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|
return internal::compare_slope(p, q, r, s, K());
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}
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|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_squared_distance(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const typename K::FT &d2)
|
||
|
|
{
|
||
|
|
return internal::compare_squared_distance(p, q, d2, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_squared_radius(const Point_3<K> &p,
|
||
|
|
const typename K::FT &sr)
|
||
|
|
{
|
||
|
|
return internal::compare_squared_radius(p, sr, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_squared_radius(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const typename K::FT &sr)
|
||
|
|
{
|
||
|
|
return internal::compare_squared_radius(p, q, sr, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_squared_radius(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const typename K::FT &sr)
|
||
|
|
{
|
||
|
|
return internal::compare_squared_radius(p, q, r, sr, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_squared_radius(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s,
|
||
|
|
const typename K::FT &sr)
|
||
|
|
{
|
||
|
|
return internal::compare_squared_radius(p, q, r, s, sr, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_lexicographically_xyz(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_lexicographically_xyz(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_lexicographically(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_lexicographically_xyz(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_signed_distance_to_plane(const Plane_3<K> &h,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_signed_distance_to_plane(h, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_signed_distance_to_plane(const Point_3<K> &hp,
|
||
|
|
const Point_3<K> &hq,
|
||
|
|
const Point_3<K> &hr,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_signed_distance_to_plane(hp, hq, hr, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_weighted_squared_radius(const Weighted_point_3<K> &p,
|
||
|
|
const typename K::FT &w)
|
||
|
|
{
|
||
|
|
return internal::compare_weighted_squared_radius(p, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_weighted_squared_radius(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const typename K::FT &w)
|
||
|
|
{
|
||
|
|
return internal::compare_weighted_squared_radius(p, q, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_weighted_squared_radius(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const typename K::FT &w)
|
||
|
|
{
|
||
|
|
return internal::compare_weighted_squared_radius(p, q, r, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_weighted_squared_radius(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s,
|
||
|
|
const typename K::FT &w)
|
||
|
|
{
|
||
|
|
return internal::compare_weighted_squared_radius(p, q, r, s, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_x(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_x(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_y(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_y(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_z(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_z(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Comparison_result
|
||
|
|
compare_xyz(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::compare_xyz(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
coplanar(const Point_3<K> &p, const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r, const Point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::coplanar(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Orientation
|
||
|
|
coplanar_orientation(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::coplanar_orientation(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Orientation
|
||
|
|
coplanar_orientation(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::coplanar_orientation(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
coplanar_side_of_bounded_circle(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &t)
|
||
|
|
{
|
||
|
|
return internal::coplanar_side_of_bounded_circle(p, q, r, t, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
cross_product(const Vector_3<K> &v, const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return internal::cross_product(v, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
determinant(const Vector_3<K> &v0, const Vector_3<K> &v1,
|
||
|
|
const Vector_3<K> &v2)
|
||
|
|
{
|
||
|
|
return internal::determinant(v0, v1, v2, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Line_3
|
||
|
|
equidistant_line(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::equidistant_line(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_larger_distance_to_point(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::has_larger_distance_to_point(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_larger_signed_distance_to_plane(const Point_3<K> &hp,
|
||
|
|
const Point_3<K> &hq,
|
||
|
|
const Point_3<K> &hr,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::has_larger_signed_distance_to_plane(hp, hq, hr, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_larger_signed_distance_to_plane(const Plane_3<K> &h,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::has_larger_signed_distance_to_plane(h, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_smaller_distance_to_point(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::has_smaller_distance_to_point(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_smaller_signed_distance_to_plane(const Point_3<K> &hp,
|
||
|
|
const Point_3<K> &hq,
|
||
|
|
const Point_3<K> &hr,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::has_smaller_signed_distance_to_plane(hp, hq, hr, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
has_smaller_signed_distance_to_plane(const Plane_3<K> &h,
|
||
|
|
const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::has_smaller_signed_distance_to_plane(h, p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
less_x(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::less_x(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
less_y(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::less_y(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
less_z(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::less_z(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
lexicographically_xyz_smaller(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::lexicographically_xyz_smaller(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
lexicographically_xyz_smaller_or_equal(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::lexicographically_xyz_smaller_or_equal(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
typename K::FT
|
||
|
|
l_infinity_distance(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::l_infinity_distance(p,q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
midpoint(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::midpoint(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
max_vertex(const Iso_cuboid_3<K> &ic)
|
||
|
|
{
|
||
|
|
return internal::max_vertex(ic, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
min_vertex(const Iso_cuboid_3<K> &ic)
|
||
|
|
{
|
||
|
|
return internal::min_vertex(ic, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
normal(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::normal(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
// FIXME TODO : what to do with the operators ?
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Point_3<K>& p, const Origin& o)
|
||
|
|
{ return K().equal_3_object()(p, Point_3<K>(o)); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Point_3<K>& p, const Origin& o)
|
||
|
|
{ return ! (p == o); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Iso_cuboid_3<K>& p, const Iso_cuboid_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Iso_cuboid_3<K>& p, const Iso_cuboid_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Plane_3<K>& p, const Plane_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Plane_3<K>& p, const Plane_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Segment_3<K>& p, const Segment_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Segment_3<K>& p, const Segment_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Line_3<K>& p, const Line_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Line_3<K>& p, const Line_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Ray_3<K>& p, const Ray_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Ray_3<K>& p, const Ray_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Triangle_3<K>& p, const Triangle_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Triangle_3<K>& p, const Triangle_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Tetrahedron_3<K>& p, const Tetrahedron_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Tetrahedron_3<K>& p, const Tetrahedron_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Direction_3<K>& p, const Direction_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Direction_3<K>& p, const Direction_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Sphere_3<K>& p, const Sphere_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Sphere_3<K>& p, const Sphere_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Vector_3<K>& p, const Vector_3<K>& q)
|
||
|
|
{ return K().equal_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Vector_3<K>& p, const Vector_3<K>& q)
|
||
|
|
{ return ! (p == q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator==(const Vector_3<K>& p, const Null_vector& o)
|
||
|
|
{ return K().equal_3_object()(p, Vector_3<K>(o)); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator!=(const Vector_3<K>& p, const Null_vector& o)
|
||
|
|
{ return ! (p == o); }
|
||
|
|
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator<(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return K().less_xyz_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator>(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return K().less_xyz_3_object()(q, p); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator<=(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return ! K().less_xyz_3_object()(q, p); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
operator>=(const Point_3<K>& p, const Point_3<K>& q)
|
||
|
|
{ return ! K().less_xyz_3_object()(p, q); }
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator*(const typename K::FT &c, const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return K().construct_scaled_vector_3_object()(w, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator*(const Vector_3<K> &w, const typename K::FT &c)
|
||
|
|
{
|
||
|
|
return K().construct_scaled_vector_3_object()(w, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator*(const typename First_if_different<typename K::RT,
|
||
|
|
typename K::FT>::Type &c,
|
||
|
|
const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return K().construct_scaled_vector_3_object()(w, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator*(const Vector_3<K> &w,
|
||
|
|
const typename First_if_different<typename K::RT,
|
||
|
|
typename K::FT>::Type &c)
|
||
|
|
{
|
||
|
|
return K().construct_scaled_vector_3_object()(w, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
operator*(const Vector_3<K> &v, const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return K().compute_scalar_product_3_object()(v, w);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
operator+(const Point_3<K> &p, const Vector_3<K> &v)
|
||
|
|
{
|
||
|
|
return K().construct_translated_point_3_object()(p, v);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
operator+(const Origin &o, const Vector_3<K> &v)
|
||
|
|
{
|
||
|
|
return K().construct_translated_point_3_object()(o, v);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
operator-(const Point_3<K> &p, const Vector_3<K> &v)
|
||
|
|
{
|
||
|
|
return K().construct_translated_point_3_object()
|
||
|
|
(p, K().construct_opposite_vector_3_object()(v));
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
operator-(const Origin &o, const Vector_3<K> &v)
|
||
|
|
{
|
||
|
|
return K().construct_translated_point_3_object()
|
||
|
|
(o, K().construct_opposite_vector_3_object()(v));
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator-(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return K().construct_vector_3_object()(q, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator-(const Point_3<K> &p, const Origin &o)
|
||
|
|
{
|
||
|
|
return K().construct_vector_3_object()(o, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
operator-(const Origin &o, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return K().construct_vector_3_object()(q, o);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Orientation
|
||
|
|
orientation(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::orientation(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Orientation
|
||
|
|
orientation(const Vector_3<K> &u, const Vector_3<K> &v, const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return internal::orientation(u, v, w, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
orthogonal_vector(const Point_3<K>& p,
|
||
|
|
const Point_3<K>& q,
|
||
|
|
const Point_3<K>& r)
|
||
|
|
{
|
||
|
|
return internal::orthogonal_vector(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
orthogonal_vector(const Plane_3<K>& p)
|
||
|
|
{
|
||
|
|
return internal::orthogonal_vector(p, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
// parallel() functions are in Kernel/global_functions.h
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
power_distance_to_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s,
|
||
|
|
const Weighted_point_3<K> &t)
|
||
|
|
{
|
||
|
|
return internal::power_distance_to_power_sphere(p, q, r, s, t, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
power_product(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::power_product(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_bounded_power_sphere(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_bounded_power_sphere(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_bounded_power_sphere(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
power_side_of_bounded_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s,
|
||
|
|
const Weighted_point_3<K> &t)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_bounded_power_sphere(p, q, r, s, t, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Oriented_side
|
||
|
|
power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_oriented_power_sphere(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Oriented_side
|
||
|
|
power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_oriented_power_sphere(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Oriented_side
|
||
|
|
power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_oriented_power_sphere(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Oriented_side
|
||
|
|
power_side_of_oriented_power_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s,
|
||
|
|
const Weighted_point_3<K> &t)
|
||
|
|
{
|
||
|
|
return internal::power_side_of_oriented_power_sphere(p, q, r, s, t, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline
|
||
|
|
typename K::Plane_3
|
||
|
|
radical_plane(const Sphere_3<K> &s1,
|
||
|
|
const Sphere_3<K> &s2)
|
||
|
|
{
|
||
|
|
return K().construct_radical_plane_3_object()(s1,s2);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
scalar_product(const Vector_3<K> &v, const Vector_3<K> &w)
|
||
|
|
{
|
||
|
|
return K().compute_scalar_product_3_object()(v, w);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
side_of_bounded_sphere(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &test)
|
||
|
|
{
|
||
|
|
return internal::side_of_bounded_sphere(p, q, test, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
side_of_bounded_sphere(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &test)
|
||
|
|
{
|
||
|
|
return internal::side_of_bounded_sphere(p, q, r, test, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Bounded_side
|
||
|
|
side_of_bounded_sphere(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s,
|
||
|
|
const Point_3<K> &test)
|
||
|
|
{
|
||
|
|
return internal::side_of_bounded_sphere(p, q, r, s, test, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K >
|
||
|
|
inline
|
||
|
|
typename K::Oriented_side
|
||
|
|
side_of_oriented_sphere(const Point_3<K> &p,
|
||
|
|
const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r,
|
||
|
|
const Point_3<K> &s,
|
||
|
|
const Point_3<K> &test)
|
||
|
|
{
|
||
|
|
return internal::side_of_oriented_sphere(p, q, r, s, test, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename K>
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_area(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::squared_area(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius(const Point_3<K> &p, const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r, const Point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::squared_radius(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::squared_radius(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::squared_radius(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius(const Point_3<K> &p)
|
||
|
|
{
|
||
|
|
return internal::squared_radius(p, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p)
|
||
|
|
{
|
||
|
|
return internal::squared_radius_smallest_orthogonal_sphere(p, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::squared_radius_smallest_orthogonal_sphere(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::squared_radius_smallest_orthogonal_sphere(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
squared_radius_smallest_orthogonal_sphere(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::squared_radius_smallest_orthogonal_sphere(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Vector_3
|
||
|
|
unit_normal(const Point_3<K> &p, const Point_3<K> &q, const Point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::unit_normal(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::FT
|
||
|
|
volume(const Point_3<K> &p, const Point_3<K> &q,
|
||
|
|
const Point_3<K> &r, const Point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::volume(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
weighted_circumcenter(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::weighted_circumcenter(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
weighted_circumcenter(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r)
|
||
|
|
{
|
||
|
|
return internal::weighted_circumcenter(p, q, r, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Point_3
|
||
|
|
weighted_circumcenter(const Weighted_point_3<K> &p,
|
||
|
|
const Weighted_point_3<K> &q,
|
||
|
|
const Weighted_point_3<K> &r,
|
||
|
|
const Weighted_point_3<K> &s)
|
||
|
|
{
|
||
|
|
return internal::weighted_circumcenter(p, q, r, s, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
x_equal(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::x_equal(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
y_equal(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::y_equal(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class K >
|
||
|
|
inline
|
||
|
|
typename K::Boolean
|
||
|
|
z_equal(const Point_3<K> &p, const Point_3<K> &q)
|
||
|
|
{
|
||
|
|
return internal::z_equal(p, q, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_3_H
|