mirror of https://github.com/CGAL/cgal
1081 lines
28 KiB
C++
1081 lines
28 KiB
C++
// Copyright (c) 2003-2010
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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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// $URL$
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// $Id$
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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_INTERNAL_2_H
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#define CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_2_H
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// Generic functions calling the kernel functor, taking the kernel as
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// parameter.
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// These functions are not documented for now, but could be as some point.
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#include <CGAL/basic.h>
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#include <CGAL/Dimension.h>
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#include "boost/mpl/equal_to.hpp"
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#include <boost/mpl/int.hpp>
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#include <boost/mpl/integral_c.hpp>
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#include <type_traits>
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namespace CGAL {
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namespace internal {
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template < class K >
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inline
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typename K::Angle
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angle(const typename K::Vector_2 &u,
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const typename K::Vector_2 &v, const K& k)
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{
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return k.angle_2_object()(u, v);
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}
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template < class K >
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inline
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typename K::Angle
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angle(const typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.angle_2_object()(p, q, r);
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}
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template < class K >
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inline
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typename K::Angle
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angle(const typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r,
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const typename K::Point_2 &s, const K& k)
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{
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return k.angle_2_object()(p, q, r, s);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.are_ordered_along_line_2_object()(p, q, r);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r,
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const K& k)
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{
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return k.are_strictly_ordered_along_line_2_object()(p, q, r);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r,
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const K& k)
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{
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return k.compute_area_2_object()(p, q, r);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const typename K::FT& w2, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2, w2);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const typename K::FT& w2,
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const typename K::Point_2 &p3, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2, w2, p3);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const typename K::FT& w2,
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const typename K::Point_2 &p3, const typename K::FT& w3, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2, w2, p3, w3);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const typename K::FT& w2,
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const typename K::Point_2 &p3, const typename K::FT& w3,
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const typename K::Point_2 &p4, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2, w2, p3, w3, p4);
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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 typename K::Point_2 &p1, const typename K::FT& w1,
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const typename K::Point_2 &p2, const typename K::FT& w2,
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const typename K::Point_2 &p3, const typename K::FT& w3,
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const typename K::Point_2 &p4, const typename K::FT& w4, const K& k)
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{
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return k.construct_barycenter_2_object()(p1, w1, p2, w2, p3, w3, p4, w4);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q, const K &k)
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{
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return k.construct_bisector_2_object()(p, q);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &l2, const K &k)
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{
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return k.construct_bisector_2_object()(l1, l2);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.construct_centroid_2_object()(p, q, r);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r,
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const typename K::Point_2 &s, const K& k)
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{
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return k.construct_centroid_2_object()(p, q, r, s);
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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 typename K::Triangle_2 &t, const K& k)
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{
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return k.construct_centroid_2_object()(t);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q, const K& k)
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{
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return k.construct_circumcenter_2_object()(p, q);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.construct_circumcenter_2_object()(p, q, r);
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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 typename K::Triangle_2 &t, const K& k)
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{
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return k.construct_circumcenter_2_object()(t);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.collinear_2_object()(p, q, r);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r,
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const K& k)
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{
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return k.collinear_are_ordered_along_line_2_object()(p, q, r);
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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(
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const typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.collinear_are_strictly_ordered_along_line_2_object()(p, q, r);
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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 typename K::Direction_2& d1,
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const typename K::Direction_2& d2,
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const K& k)
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{
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return k.compare_angle_with_x_axis_2_object()(d1, d2);
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}
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template <class K, class T1, class T2, class T3>
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inline
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std::enable_if_t<
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boost::mpl::equal_to<boost::mpl::integral_c<int,
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Ambient_dimension<T1>::type::value>,
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boost::mpl::integral_c<int, 2> >::value,
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typename K::Comparison_result>
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compare_distance(const T1 &o1,
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const T2 &o2,
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const T3 &o3, const K& k)
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{
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return k.compare_distance_2_object()(o1, o2, o3);
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}
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template <class K, class T1, class T2, class T3, class T4>
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inline
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std::enable_if_t<
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boost::mpl::equal_to<boost::mpl::integral_c<int,
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Ambient_dimension<T1>::type::value>,
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boost::mpl::integral_c<int, 2> >::value,
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typename K::Comparison_result>
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compare_distance(const T1 &o1,
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const T2 &o2,
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const T3 &o3,
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const T4 &o4, const K& k)
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{
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return k.compare_distance_2_object()(o1, o2, o3, o4);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::Point_2 &r, const K& k)
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{
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return k.compare_distance_2_object()(p, q, r);
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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 typename K::Point_2 &r,
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const typename K::Weighted_point_2 &p,
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const typename K::Weighted_point_2 &q, const K& k)
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{
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return k.compare_power_distance_2_object()(r, p, q);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q,
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const typename K::FT &d2, const K& k)
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{
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return k.compare_squared_distance_2_object()(p, q, d2);
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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 typename K::Point_2& p,
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const typename K::Point_2& q,
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const typename K::Point_2& r,
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const typename K::Point_2& s,
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const K& k)
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{
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return k.compare_signed_distance_to_line_2_object()(p, q, r, s);
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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 typename K::Line_2& l,
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const typename K::Point_2& p,
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const typename K::Point_2& q,
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const K& k)
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{
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return k.compare_signed_distance_to_line_2_object()(l, p, q);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &l2, const K& k)
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{
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return k.compare_slope_2_object()(l1, l2);
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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 typename K::Segment_2 &s1,
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const typename K::Segment_2 &s2, const K& k)
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{
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return k.compare_slope_2_object()(s1, s2);
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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 typename K::Point_2 &s1s,
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const typename K::Point_2 &s1t,
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const typename K::Point_2 &s2s,
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const typename K::Point_2 &s2t,const K& k)
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{
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return k.compare_slope_2_object()(s1s, s1t, s2s, s2t);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q, const K& k)
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{
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return k.compare_x_2_object()(p, q);
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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 typename K::Point_2 &p,
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const typename K::Line_2 &l1,
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const typename K::Line_2 &l2, const K& k)
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{
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return k.compare_x_2_object()(p, l1, l2);
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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 typename K::Line_2 &l,
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const typename K::Line_2 &h1,
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const typename K::Line_2 &h2, const K& k)
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{
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return k.compare_x_2_object()(l, h1, h2);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &h1,
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const typename K::Line_2 &l2,
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const typename K::Line_2 &h2, const K& k)
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{
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return k.compare_x_2_object()(l1, h1, l2, h2);
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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 typename K::Point_2& p,
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const typename K::Line_2& h, const K& k)
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{
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return k.compare_x_at_y_2_object()(p, h);
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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_y_at_x(const typename K::Point_2 &p,
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const typename K::Segment_2 &s, const K& k)
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{
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return k.compare_y_at_x_2_object()(p, s);
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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 typename K::Point_2 &p,
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const typename K::Line_2 &h1,
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const typename K::Line_2 &h2, const K& k)
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{
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return k.compare_x_at_y_2_object()(p, h1, h2);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &l2,
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const typename K::Line_2 &h, const K& k)
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{
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return k.compare_x_at_y_2_object()(l1, l2, h);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &l2,
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const typename K::Line_2 &h1,
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const typename K::Line_2 &h2, const K& k)
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{
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return k.compare_x_at_y_2_object()(l1, l2, h1, h2);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q, const K& k)
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{
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return k.compare_xy_2_object()(p, q);
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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_yx(const typename K::Point_2 &p,
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const typename K::Point_2 &q, const K& k)
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{
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return k.compare_yx_2_object()(p, q);
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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 typename K::Point_2 &p,
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const typename K::Point_2 &q, const K& k)
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{
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return k.compare_y_2_object()(p, q);
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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 typename K::Point_2 &p,
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const typename K::Line_2 &l1,
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const typename K::Line_2 &l2, const K& k)
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{
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return k.compare_y_2_object()(p, l1, l2);
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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 typename K::Line_2 &l1,
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const typename K::Line_2 &l2,
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const typename K::Line_2 &h1,
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|
const typename K::Line_2 &h2, const K& k)
|
|
{
|
|
return k.compare_y_2_object()(l1, l2, h1, h2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y(const typename K::Line_2 &l,
|
|
const typename K::Line_2 &h1,
|
|
const typename K::Line_2 &h2, const K& k)
|
|
{
|
|
return k.compare_y_2_object()(l, h1, h2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Point_2 &p,
|
|
const typename K::Segment_2 &s, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(p, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Point_2 &p,
|
|
const typename K::Segment_2 &s1,
|
|
const typename K::Segment_2 &s2, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(p, s1, s2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Point_2 &p,
|
|
const typename K::Line_2 &l, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(p, l);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Point_2 &p,
|
|
const typename K::Line_2 &h1,
|
|
const typename K::Line_2 &h2, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(p, h1, h2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Line_2 &l1,
|
|
const typename K::Line_2 &l2,
|
|
const typename K::Line_2 &h, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(l1, l2, h);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Comparison_result
|
|
compare_y_at_x(const typename K::Line_2 &l1,
|
|
const typename K::Line_2 &l2,
|
|
const typename K::Line_2 &h1,
|
|
const typename K::Line_2 &h2, const K& k)
|
|
{
|
|
return k.compare_y_at_x_2_object()(l1, l2, h1, h2);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
determinant(const typename K::Vector_2 &v0,
|
|
const typename K::Vector_2 &v1, const K &k)
|
|
{
|
|
return k.compute_determinant_2_object()(v0, v1);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_distance_to_point(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r,
|
|
const K& k)
|
|
{
|
|
return k.less_distance_to_point_2_object()(p, r, q);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_distance_to_point(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r,
|
|
const K& k)
|
|
{
|
|
return k.less_distance_to_point_2_object()(p, q, r);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_signed_distance_to_line(const typename K::Line_2& l,
|
|
const typename K::Point_2& p,
|
|
const typename K::Point_2& q,
|
|
const K& k)
|
|
{
|
|
return k.less_signed_distance_to_line_2_object()(l, p, q);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_line(const typename K::Line_2& l,
|
|
const typename K::Point_2& p,
|
|
const typename K::Point_2& q,
|
|
const K& k)
|
|
{
|
|
return k.less_signed_distance_to_line_2_object()(l, q, p);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_larger_signed_distance_to_line(const typename K::Point_2& p,
|
|
const typename K::Point_2& q,
|
|
const typename K::Point_2& r,
|
|
const typename K::Point_2& s,
|
|
const K& k)
|
|
{
|
|
return k.less_signed_distance_to_line_2_object()(p, q, s, r);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Boolean
|
|
has_smaller_signed_distance_to_line(const typename K::Point_2& p,
|
|
const typename K::Point_2& q,
|
|
const typename K::Point_2& r,
|
|
const typename K::Point_2& s,
|
|
const K& k)
|
|
{
|
|
return k.less_signed_distance_to_line_2_object()(p, q, r, s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
left_turn(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r, const K& k)
|
|
{
|
|
return k.left_turn_2_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_x(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K& k)
|
|
{
|
|
return k.less_x_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
less_y(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K& k)
|
|
{
|
|
return k.less_y_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_larger(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.compare_xy_2_object()(p, q) == LARGER;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_larger_or_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.compare_xy_2_object()(p, q) != SMALLER;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_smaller(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.less_xy_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_xy_smaller_or_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.compare_xy_2_object()(p, q) != LARGER;
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_smaller(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.less_yx_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_smaller_or_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return !k.less_yx_2_object()(q, p);
|
|
}
|
|
|
|
// FIXME : Undocumented
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_larger(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.less_yx_2_object()(q, p);
|
|
}
|
|
|
|
// FIXME : Undocumented
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
lexicographically_yx_larger_or_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return !k.less_yx_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
l_infinity_distance(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const K& k)
|
|
{
|
|
return k.compute_L_infinity_distance_2_object()(p, q);
|
|
}
|
|
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
midpoint(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K &k)
|
|
{
|
|
return k.construct_midpoint_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
midpoint(const typename K::Segment_2 &s, const K &k)
|
|
{
|
|
return k.construct_midpoint_2_object()(s);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
max_vertex(const typename K::Iso_rectangle_2 &ir, const K &k)
|
|
{
|
|
return k.construct_max_vertex_2_object()(ir);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
min_vertex(const typename K::Iso_rectangle_2 &ir, const K &k)
|
|
{
|
|
return k.construct_min_vertex_2_object()(ir);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r, const K &k)
|
|
{
|
|
return k.orientation_2_object()(p, q, r);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Orientation
|
|
orientation(const typename K::Vector_2 &u,
|
|
const typename K::Vector_2 &v, const K &k)
|
|
{
|
|
return k.orientation_2_object()(u, v);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Line_2 &l1,
|
|
const typename K::Line_2 &l2, const K &k)
|
|
{
|
|
return k.are_parallel_2_object()(l1, l2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Ray_2 &r1,
|
|
const typename K::Ray_2 &r2, const K &k)
|
|
{
|
|
return k.are_parallel_2_object()(r1, r2);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
parallel(const typename K::Segment_2 &s1,
|
|
const typename K::Segment_2 &s2, const K &k)
|
|
{
|
|
return k.are_parallel_2_object()(s1, s2);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::FT
|
|
power_product(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q, const K &k)
|
|
{
|
|
return k.compute_power_product_2_object()(p, q);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_circle_2_object()(p, q);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_circle_2_object()(p, q, r);
|
|
}
|
|
|
|
template <class K >
|
|
inline
|
|
typename K::Bounded_side
|
|
power_side_of_bounded_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r,
|
|
const typename K::Weighted_point_2 &s, const K &k)
|
|
{
|
|
return k.power_side_of_bounded_power_circle_2_object()(p, q, r, s);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_circle_2_object()(p, q);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_circle_2_object()(p, q, r);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Oriented_side
|
|
power_side_of_oriented_power_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r,
|
|
const typename K::Weighted_point_2 &t, const K &k)
|
|
{
|
|
return k.power_side_of_oriented_power_circle_2_object()(p, q, r, t);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Line_2
|
|
radical_axis(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q, const K &k)
|
|
{
|
|
return k.construct_radical_axis_2_object()(p, q);
|
|
}
|
|
|
|
template <typename K>
|
|
inline
|
|
typename K::Boolean
|
|
right_turn(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r, const K &k)
|
|
{
|
|
return internal::orientation(p, q, r, k) == RIGHT_TURN;
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_circle(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r,
|
|
const typename K::Point_2 &t, const K &k)
|
|
{
|
|
return k.side_of_bounded_circle_2_object()(p, q, r, t);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Bounded_side
|
|
side_of_bounded_circle(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r, const K &k)
|
|
{
|
|
return k.side_of_bounded_circle_2_object()(p, q, r);
|
|
}
|
|
|
|
template <class K>
|
|
inline
|
|
typename K::Oriented_side
|
|
side_of_oriented_circle(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r,
|
|
const typename K::Point_2 &t, const K &k)
|
|
{
|
|
return k.side_of_oriented_circle_2_object()(p, q, r, t);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_2 &p, const K &k)
|
|
{
|
|
return k.compute_squared_radius_2_object()(p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K &k)
|
|
{
|
|
return k.compute_squared_radius_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q,
|
|
const typename K::Point_2 &r, const K &k)
|
|
{
|
|
return k.compute_squared_radius_2_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const typename K::Weighted_point_2 &p,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_circle_2_object()(p);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_circle_2_object()(p, q);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::FT
|
|
squared_radius_smallest_orthogonal_circle(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r,
|
|
const K &k)
|
|
{
|
|
return k.compute_squared_radius_smallest_orthogonal_circle_2_object()(p, q, r);
|
|
}
|
|
|
|
template < class K >
|
|
inline
|
|
typename K::Point_2
|
|
weighted_circumcenter(const typename K::Weighted_point_2 &p,
|
|
const typename K::Weighted_point_2 &q,
|
|
const typename K::Weighted_point_2 &r, const K &k)
|
|
{
|
|
return k.construct_weighted_circumcenter_2_object()(p, q, r);
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}
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|
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template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
x_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K &k)
|
|
{
|
|
return k.equal_x_2_object()(p, q);
|
|
}
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|
|
|
template < class K >
|
|
inline
|
|
typename K::Boolean
|
|
y_equal(const typename K::Point_2 &p,
|
|
const typename K::Point_2 &q, const K &k)
|
|
{
|
|
return k.equal_y_2_object()(p, q);
|
|
}
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|
|
|
} // namespace internal
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|
|
|
} //namespace CGAL
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|
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#endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_2_H
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