1182 lines
27 KiB
C++
1182 lines
27 KiB
C++
// 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)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Kernel_23/include/CGAL/Kernel/global_functions_2.h $
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// $Id: global_functions_2.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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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_2_H
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#define CGAL_KERNEL_GLOBAL_FUNCTIONS_2_H
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// Generic functions taking "user classes" as parameters, calling the
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// internal functions (in *_internal*.h, namespace internal) taking a kernel as
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// additional parameter, which themselves call the corresponding kernel
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// functors.
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#include <CGAL/user_classes.h>
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#include <CGAL/Kernel/global_functions_internal_2.h>
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#include <CGAL/Kernel/mpl.h>
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namespace CGAL {
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template < class K >
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typename K::Boolean
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operator==(const Point_2<K> &p, const Origin& o)
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{
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return p == Point_2<K>(o);
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}
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template < class K >
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typename K::Boolean
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operator!=(const Point_2<K> &p, const Origin& o)
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{
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return p != Point_2<K>(o);
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}
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template < class K >
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inline
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Angle
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angle(const Vector_2<K> &u,
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const Vector_2<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 < class K >
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inline
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Angle
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angle(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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 < class K >
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inline
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Angle
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angle(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<K> &r,
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const Point_2<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 < class K >
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inline
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typename K::Boolean
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are_ordered_along_line(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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 < 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_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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::FT
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area(const Point_2<K> &p, const Point_2<K> &q, const Point_2<K> &r)
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{
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return internal::area(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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<K> &p2, const typename K::FT& w2,
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const Point_2<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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<K> &p2, const typename K::FT& w2,
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const Point_2<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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<K> &p2, const typename K::FT& w2,
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const Point_2<K> &p3, const typename K::FT& w3,
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const Point_2<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_2
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barycenter(const Point_2<K> &p1, const typename K::FT& w1,
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const Point_2<K> &p2, const typename K::FT& w2,
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const Point_2<K> &p3, const typename K::FT& w3,
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const Point_2<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::Line_2
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bisector(const Point_2<K> &p, const Point_2<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::Line_2
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bisector(const Line_2<K> &l1, const Line_2<K> &l2)
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{
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return internal::bisector(l1, l2, K());
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}
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template < class K >
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inline
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typename K::Point_2
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centroid(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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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typename K::Point_2
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centroid(const Triangle_2<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_2
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centroid(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<K> &r,
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const Point_2<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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typename K::Point_2
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circumcenter(const Point_2<K> &p,
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const Point_2<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_2
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circumcenter(const Point_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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_2
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circumcenter(const Triangle_2<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_2<K> &p, const Point_2<K> &q, const Point_2<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_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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_2<K> &p,
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const Point_2<K> &q,
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const Point_2<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 < typename K >
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inline
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typename K::Comparison_result
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compare_angle_with_x_axis(const Direction_2<K>& d1,
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const Direction_2<K>& d2)
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{
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return internal::compare_angle_with_x_axis(d1, 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_distance_to_point(const Point_2<K>& p,
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const Point_2<K>& q,
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const Point_2<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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inline
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typename K::Comparison_result
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compare_power_distance(const Point_2<K> &r,
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const Weighted_point_2<K> &p,
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const Weighted_point_2<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
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typename K::Comparison_result
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compare_squared_distance(const Point_2<K>& p,
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const Point_2<K>& q,
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const typename K::FT& d2)
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{
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return internal::compare_squared_distance(p, q, 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_signed_distance_to_line(const Point_2<K>& p,
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const Point_2<K>& q,
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const Point_2<K>& r,
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const Point_2<K>& s)
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{
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return internal::compare_signed_distance_to_line(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::Comparison_result
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compare_signed_distance_to_line(const Line_2<K>& l,
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const Point_2<K>& p,
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const Point_2<K>& q)
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{
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return internal::compare_signed_distance_to_line(l, p, q, K());
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}
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/* FIXME : Undocumented, obsolete...
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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_lexicographically_xy(const Point_2<K> &p,
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const Point_2<K> &q)
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{
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return K().compare_xy_2_object()(p, q);
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}
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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_slope(const Line_2<K> &l1, const Line_2<K> &l2)
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{
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return internal::compare_slope(l1, l2, 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_slope(const Segment_2<K> &s1, const Segment_2<K> &s2)
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{
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return internal::compare_slope(s1, s2, K());
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}
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#ifndef CGAL_NO_DEPRECATED_CODE
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// kept for backward compatibility
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template < class K >
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CGAL_DEPRECATED_MSG("This function is deprecated. CGAL::compare_slope() should be used instead")
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inline
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typename K::Comparison_result
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compare_slopes(const Line_2<K> &l1, const Line_2<K> &l2)
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{
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return internal::compare_slope(l1, l2, K());
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}
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// kept for backward compatibility
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template < class K >
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CGAL_DEPRECATED_MSG("This function is deprecated. CGAL::compare_slope() should be used instead")
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inline
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typename K::Comparison_result
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compare_slopes(const Segment_2<K> &s1, const Segment_2<K> &s2)
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{
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return internal::compare_slope(s1, s2, K());
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}
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#endif
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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_x(const Point_2<K> &p, const Point_2<K> &q)
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{
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return internal::compare_x(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::Comparison_result
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compare_x(const Point_2<K>& p,
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const Line_2<K>& l1,
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const Line_2<K>& l2)
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{
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return internal::compare_x(p, l1, l2, 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_x(const Line_2<K> &l,
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const Line_2<K> &h1,
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const Line_2<K> &h2)
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{
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return internal::compare_x(l, h1, h2, 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_x(const Line_2<K> &l1,
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const Line_2<K> &h1,
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const Line_2<K> &l2,
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const Line_2<K> &h2)
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{
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return internal::compare_x(l1, h1, l2, h2, 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_x_at_y(const Point_2<K>& p, const Line_2<K>& h)
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{
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return internal::compare_x_at_y(p, h, K());
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}
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/* Undocumented
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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_x_at_y(const Point_2<K>& p, const Segment_2<K>& s)
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{
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return internal::compare_x_at_y(p, s, K());
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}
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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_x_at_y(const Point_2<K> &p,
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const Line_2<K> &h1,
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const Line_2<K> &h2)
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{
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return internal::compare_x_at_y(p, h1, h2, 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_x_at_y(const Line_2<K> &l1,
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const Line_2<K> &l2,
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const Line_2<K> &h)
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{
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return internal::compare_x_at_y(l1, l2, h, 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_x_at_y(const Line_2<K> &l1,
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const Line_2<K> &l2,
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const Line_2<K> &h1,
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const Line_2<K> &h2)
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{
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return internal::compare_x_at_y(l1, l2, h1, h2, 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_xy(const Point_2<K> &p, const Point_2<K> &q)
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{
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return internal::compare_xy(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::Comparison_result
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compare_lexicographically(const Point_2<K> &p, const Point_2<K> &q)
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{
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return internal::compare_xy(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::Comparison_result
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compare_y(const Point_2<K> &p, const Point_2<K> &q)
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{
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return internal::compare_y(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::Comparison_result
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compare_y(const Point_2<K> &p,
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const Line_2<K> &l1,
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const Line_2<K> &l2)
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{
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return internal::compare_y(p, l1, l2, 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_y(const Line_2<K> &l1,
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const Line_2<K> &l2,
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const Line_2<K> &h1,
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const Line_2<K> &h2)
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{
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return internal::compare_y(l1, l2, h1, h2, 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_y(const Line_2<K> &l,
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const Line_2<K> &h1,
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const Line_2<K> &h2)
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{
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return internal::compare_y(l, h1, h2, 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_y_at_x(const Point_2<K> &p, const Segment_2<K> &s)
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{
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return internal::compare_y_at_x(p, s, 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_y_at_x(const Point_2<K> &p,
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const Segment_2<K> &s1,
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const Segment_2<K> &s2)
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|
{
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return internal::compare_y_at_x(p, s1, s2, 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_y_at_x(const Point_2<K> &p, const Line_2<K> &h)
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|
{
|
|
return internal::compare_y_at_x(p, h, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const Point_2<K> &p,
|
|
const Line_2<K> &h1,
|
|
const Line_2<K> &h2)
|
|
{
|
|
return internal::compare_y_at_x(p, h1, h2, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const Line_2<K> &l1,
|
|
const Line_2<K> &l2,
|
|
const Line_2<K> &h)
|
|
{
|
|
return internal::compare_y_at_x(l1, l2, h, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const Line_2<K> &l1,
|
|
const Line_2<K> &l2,
|
|
const Line_2<K> &h1,
|
|
const Line_2<K> &h2)
|
|
{
|
|
return internal::compare_y_at_x(l1, l2, h1, h2, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_yx(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::compare_yx(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
determinant(const Vector_2<K> &v0, const Vector_2<K> &v1)
|
|
{
|
|
return internal::determinant(v0, v1, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_distance_to_point(const Point_2<K>& p,
|
|
const Point_2<K>& q,
|
|
const Point_2<K>& r)
|
|
{
|
|
return internal::has_larger_distance_to_point(p, q, r, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_distance_to_point(const Point_2<K>& p,
|
|
const Point_2<K>& q,
|
|
const Point_2<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_line(const Line_2<K>& l,
|
|
const Point_2<K>& p,
|
|
const Point_2<K>& q)
|
|
{
|
|
return internal::has_smaller_signed_distance_to_line(l, p, q, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_line(const Line_2<K>& l,
|
|
const Point_2<K>& p,
|
|
const Point_2<K>& q)
|
|
{
|
|
return internal::has_larger_signed_distance_to_line(l, p, q, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_line(const Point_2<K>& p,
|
|
const Point_2<K>& q,
|
|
const Point_2<K>& r,
|
|
const Point_2<K>& s)
|
|
{
|
|
return internal::has_larger_signed_distance_to_line(p, q, r, s, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_signed_distance_to_line(const Point_2<K>& p,
|
|
const Point_2<K>& q,
|
|
const Point_2<K>& r,
|
|
const Point_2<K>& s)
|
|
{
|
|
return internal::has_smaller_signed_distance_to_line(p, q, r, s, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
left_turn(const Point_2<K> &p, const Point_2<K> &q, const Point_2<K> &r)
|
|
{
|
|
return internal::left_turn(p, q, r, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_x(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::less_x(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_y(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::less_y(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_larger(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_xy_larger(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_larger_or_equal(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_xy_larger_or_equal(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_smaller(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_xy_smaller(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_smaller_or_equal(const Point_2<K> &p,
|
|
const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_xy_smaller_or_equal(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_smaller(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_yx_smaller(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_smaller_or_equal(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_yx_smaller_or_equal(p, q, K());
|
|
}
|
|
|
|
// FIXME : Undocumented
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_larger(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_yx_larger(p, q, K());
|
|
}
|
|
|
|
// FIXME : Undocumented
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_larger_or_equal(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::lexicographically_yx_larger_or_equal(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
typename K::FT
|
|
l_infinity_distance(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::l_infinity_distance(p,q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
midpoint(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::midpoint(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
max_vertex(const Iso_rectangle_2<K> &ir)
|
|
{
|
|
return internal::max_vertex(ir, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
min_vertex(const Iso_rectangle_2<K> &ir)
|
|
{
|
|
return internal::min_vertex(ir, K());
|
|
}
|
|
|
|
// FIXME TODO : What do we do with the operators ?
|
|
// They have no counter part with the kernel argument...
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator<(const Direction_2<K>& d1, const Direction_2<K>& d2)
|
|
{ return compare_angle_with_x_axis(d1, d2) == SMALLER; }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator>(const Direction_2<K>& d1, const Direction_2<K>& d2)
|
|
{ return compare_angle_with_x_axis(d1, d2) == LARGER; }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator>=(const Direction_2<K>& d1, const Direction_2<K>& d2)
|
|
{ return compare_angle_with_x_axis(d1, d2) != SMALLER; }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator<=(const Direction_2<K>& d1, const Direction_2<K>& d2)
|
|
{ return compare_angle_with_x_axis(d1, d2) != LARGER; }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator==(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return K().equal_2_object()(p, q); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator!=(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return ! (p == q); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator<(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return K().less_xy_2_object()(p, q); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator>(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return K().less_xy_2_object()(q, p); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator<=(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return ! K().less_xy_2_object()(q, p); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator>=(const Point_2<K>& p, const Point_2<K>& q)
|
|
{ return ! K().less_xy_2_object()(p, q); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator==(const Vector_2<K>& v, const Vector_2<K>& w)
|
|
{ return K().equal_2_object()(v, w); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
operator!=(const Vector_2<K>& v, const Vector_2<K>& w)
|
|
{ return ! (v == w); }
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator*(const typename K::FT &c, const Vector_2<K> &w)
|
|
{
|
|
return K().construct_scaled_vector_2_object()(w, c);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator*(const Vector_2<K> &w, const typename K::FT &c)
|
|
{
|
|
return K().construct_scaled_vector_2_object()(w, c);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator*(const typename First_if_different<typename K::RT,
|
|
typename K::FT>::Type &c,
|
|
const Vector_2<K> &w)
|
|
{
|
|
return K().construct_scaled_vector_2_object()(w, c);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator*(const Vector_2<K> &w,
|
|
const typename First_if_different<typename K::RT,
|
|
typename K::FT>::Type &c)
|
|
{
|
|
return K().construct_scaled_vector_2_object()(w, c);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
operator*(const Vector_2<K> &v, const Vector_2<K> &w)
|
|
{
|
|
return K().compute_scalar_product_2_object()(v, w);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
operator+(const Point_2<K> &p, const Vector_2<K> &v)
|
|
{
|
|
return K().construct_translated_point_2_object()(p, v);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
operator+(const Origin &o, const Vector_2<K> &v)
|
|
{
|
|
return K().construct_translated_point_2_object()(o, v);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
operator-(const Point_2<K> &p, const Vector_2<K> &v)
|
|
{
|
|
return K().construct_translated_point_2_object()
|
|
(p, K().construct_opposite_vector_2_object()(v));
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
operator-(const Origin &o, const Vector_2<K> &v)
|
|
{
|
|
return K().construct_translated_point_2_object()
|
|
(o, K().construct_opposite_vector_2_object()(v));
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator-(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return K().construct_vector_2_object()(q, p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator-(const Point_2<K> &p, const Origin &o)
|
|
{
|
|
return K().construct_vector_2_object()(o, p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Vector_2
|
|
operator-(const Origin &o, const Point_2<K> &q)
|
|
{
|
|
return K().construct_vector_2_object()(q, o);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const Point_2<K> &p, const Point_2<K> &q, const Point_2<K> &r)
|
|
{
|
|
return internal::orientation(p, q, r, K());
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const Vector_2<K> &u, const Vector_2<K> &v)
|
|
{
|
|
return internal::orientation(u, v, K());
|
|
}
|
|
|
|
// parallel() functions are in global_functions.h
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::FT
|
|
power_product(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q)
|
|
{
|
|
return internal::power_product(p, q, K());
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q)
|
|
{
|
|
return internal::power_side_of_bounded_power_circle(p, q, K());
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r)
|
|
{
|
|
return internal::power_side_of_bounded_power_circle(p, q, r, K());
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r,
|
|
const Weighted_point_2<K> &s)
|
|
{
|
|
return internal::power_side_of_bounded_power_circle(p, q, r, s, K());
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q)
|
|
{
|
|
return internal::power_side_of_oriented_power_circle(p, q, K());
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r)
|
|
{
|
|
return internal::power_side_of_oriented_power_circle(p, q, r, K());
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
power_side_of_oriented_power_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r,
|
|
const Weighted_point_2<K> &s)
|
|
{
|
|
return internal::power_side_of_oriented_power_circle(p, q, r, s, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Line_2
|
|
radical_axis(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q)
|
|
{
|
|
return internal::radical_axis(p, q, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Line_2
|
|
radical_line(const Circle_2<K> &s1,
|
|
const Circle_2<K> &s2)
|
|
{
|
|
return K().construct_radical_line_2_object()(s1,s2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
right_turn(const Point_2<K> &p, const Point_2<K> &q, const Point_2<K> &r)
|
|
{
|
|
return internal::right_turn(p, q, r, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
scalar_product(const Vector_2<K> &v, const Vector_2<K> &w)
|
|
{
|
|
return K().compute_scalar_product_2_object()(v, w);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_circle(const Point_2<K> &p,
|
|
const Point_2<K> &q,
|
|
const Point_2<K> &r,
|
|
const Point_2<K> &t)
|
|
{
|
|
return internal::side_of_bounded_circle(p, q, r, t, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_circle(const Point_2<K> &p,
|
|
const Point_2<K> &q,
|
|
const Point_2<K> &r)
|
|
{
|
|
return internal::side_of_bounded_circle(p, q, r, K());
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Oriented_side
|
|
side_of_oriented_circle(const Point_2<K> &p,
|
|
const Point_2<K> &q,
|
|
const Point_2<K> &r,
|
|
const Point_2<K> &t)
|
|
{
|
|
return internal::side_of_oriented_circle(p, q, r, t, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const Point_2<K> &p)
|
|
{
|
|
return internal::squared_radius(p, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::squared_radius(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
CGAL_KERNEL_INLINE
|
|
typename K::FT
|
|
squared_radius(const Point_2<K>& p, const Point_2<K>& q, const Point_2<K>& r)
|
|
{
|
|
return internal::squared_radius(p, q, r, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const Weighted_point_2<K> &p)
|
|
{
|
|
return internal::squared_radius_smallest_orthogonal_circle(p, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q)
|
|
{
|
|
return internal::squared_radius_smallest_orthogonal_circle(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r)
|
|
{
|
|
return internal::squared_radius_smallest_orthogonal_circle(p, q, r, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
weighted_circumcenter(const Weighted_point_2<K> &p,
|
|
const Weighted_point_2<K> &q,
|
|
const Weighted_point_2<K> &r)
|
|
{
|
|
return internal::weighted_circumcenter(p, q, r, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
x_equal(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::x_equal(p, q, K());
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
y_equal(const Point_2<K> &p, const Point_2<K> &q)
|
|
{
|
|
return internal::y_equal(p, q, K());
|
|
}
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_2_H
|