764 lines
22 KiB
C
764 lines
22 KiB
C
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// Copyright (c) 1998-2004
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Geert-Jan Giezeman
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// Michel Hoffmann <hoffmann@inf.ethz.ch>
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// Andreas Fabri <Andreas.Fabri@geometryfactory.com>
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#ifndef CGAL_SQUARED_DISTANCE_2_1_H
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#define CGAL_SQUARED_DISTANCE_2_1_H
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#include <CGAL/user_classes.h>
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#include <CGAL/kernel_assertions.h>
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#include <CGAL/enum.h>
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#include <CGAL/wmult.h>
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#include <CGAL/squared_distance_utils.h>
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#include <CGAL/Kernel/global_functions_2.h>
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namespace CGAL {
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namespace internal {
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template <class K>
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inline typename K::FT
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squared_distance(const typename K::Point_2 & pt1,
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const typename K::Point_2 & pt2,
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const K& k)
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{
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typename K::Vector_2 vec = k.construct_vector_2_object()(pt2, pt1);
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return (typename K::FT)k.compute_squared_length_2_object()(vec);
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Point_2 &pt,
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const typename K::Line_2 &line,
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const K&,
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const Homogeneous_tag&)
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{
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typedef typename K::RT RT;
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typedef typename K::FT FT;
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const RT & a = line.a();
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const RT & b = line.b();
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const RT & w = pt.hw();
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RT n = a*pt.hx() + b*pt.hy() + w * line.c();
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RT d = (CGAL_NTS square(a) + CGAL_NTS square(b)) * CGAL_NTS square(w);
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return Rational_traits<FT>().make_rational(CGAL_NTS square(n), d);
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Point_2 &pt,
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const typename K::Line_2 &line,
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const K&,
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const Cartesian_tag&)
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{
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typedef typename K::FT FT;
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const FT & a = line.a();
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const FT & b = line.b();
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FT n = a*pt.x() + b*pt.y() + line.c();
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FT d = CGAL_NTS square(a) + CGAL_NTS square(b);
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return CGAL_NTS square(n)/d;
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Point_2 &pt,
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const typename K::Line_2 &line,
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const K& k)
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{
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typedef typename K::Kernel_tag Tag;
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Tag tag;
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return squared_distance(pt, line, k, tag);
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}
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template <class K>
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inline typename K::FT
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squared_distance(const typename K::Line_2 &line,
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const typename K::Point_2 &pt,
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const K& k)
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{
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return internal::squared_distance(pt, line, k);
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Point_2 &pt,
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const typename K::Ray_2 &ray,
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const K& k)
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{
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typedef typename K::Vector_2 Vector_2;
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typename K::Construct_vector_2 construct_vector;
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Vector_2 diff = construct_vector(ray.source(), pt);
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const Vector_2 &dir = ray.direction().vector();
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if (!is_acute_angle(dir,diff, k) )
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return (typename K::FT)k.compute_squared_length_2_object()(diff);
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return internal::squared_distance(pt, ray.supporting_line(), k);
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}
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template <class K>
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inline typename K::FT
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squared_distance(const typename K::Ray_2 &ray,
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const typename K::Point_2 &pt,
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const K& k)
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{
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return internal::squared_distance(pt, ray, k);
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Point_2 &pt,
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const typename K::Segment_2 &seg,
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const K& k)
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{
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typename K::Construct_vector_2 construct_vector;
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typedef typename K::Vector_2 Vector_2;
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typedef typename K::RT RT;
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// assert that the segment is valid (non zero length).
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Vector_2 diff = construct_vector(seg.source(), pt);
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Vector_2 segvec = construct_vector(seg.source(), seg.target());
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RT d = wdot(diff,segvec, k);
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if (d <= (RT)0)
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return (typename K::FT)k.compute_squared_length_2_object()(diff);
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RT e = wdot(segvec,segvec, k);
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if (wmult((K*)0 ,d, segvec.hw()) > wmult((K*)0, e, diff.hw()))
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return internal::squared_distance(pt, seg.target(), k);
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return internal::squared_distance(pt, seg.supporting_line(), k);
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}
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template <class K>
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inline typename K::FT
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squared_distance(const typename K::Segment_2 &seg,
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const typename K::Point_2 &pt,
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const K& k)
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{
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return internal::squared_distance(pt, seg, k);
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}
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template <class K>
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typename K::FT
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squared_distance_parallel(const typename K::Segment_2 &seg1,
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const typename K::Segment_2 &seg2,
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const K& k)
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{
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typedef typename K::Vector_2 Vector_2;
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const Vector_2 &dir1 = seg1.direction().vector();
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const Vector_2 &dir2 = seg2.direction().vector();
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if (same_direction(dir1, dir2, k)) {
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if (!is_acute_angle(seg1.source(), seg1.target(), seg2.source(), k))
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return internal::squared_distance(seg1.target(), seg2.source(), k);
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if (!is_acute_angle(seg1.target(), seg1.source(), seg2.target(), k))
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return internal::squared_distance(seg1.source(), seg2.target(), k);
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} else {
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if (!is_acute_angle(seg1.source(), seg1.target(), seg2.target(), k))
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return internal::squared_distance(seg1.target(), seg2.target(), k);
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if (!is_acute_angle(seg1.target(), seg1.source(), seg2.source(), k))
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return internal::squared_distance(seg1.source(), seg2.source(), k);
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}
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return internal::squared_distance(seg2.source(), seg1.supporting_line(), k);
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}
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template <class K>
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inline typename K::RT
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_distance_measure_sub(const typename K::RT &startwcross,
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const typename K::RT &endwcross,
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const typename K::Point_2 &start,
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const typename K::Point_2 &end)
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{
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return CGAL_NTS abs(wmult((K*)0, startwcross, end.hw())) -
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CGAL_NTS abs(wmult((K*)0, endwcross, start.hw()));
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Segment_2 &seg1,
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const typename K::Segment_2 &seg2,
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const K& k)
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{
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typedef typename K::RT RT;
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typedef typename K::FT FT;
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bool crossing1, crossing2;
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RT c1s, c1e, c2s, c2e;
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if (seg1.source() == seg1.target())
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return internal::squared_distance(seg1.source(), seg2, k);
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if (seg2.source() == seg2.target())
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return internal::squared_distance(seg2.source(), seg1, k);
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c1s = wcross(seg2.source(), seg2.target(), seg1.source(), k);
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c1e = wcross(seg2.source(), seg2.target(), seg1.target(), k);
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c2s = wcross(seg1.source(), seg1.target(), seg2.source(), k);
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c2e = wcross(seg1.source(), seg1.target(), seg2.target(), k);
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if (c1s < RT(0)) {
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crossing1 = (c1e >= RT(0));
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} else {
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if (c1e <= RT(0)) {
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if (c1s == RT(0) && c1e == RT(0))
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return internal::squared_distance_parallel(seg1, seg2, k);
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crossing1 = true;
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} else {
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crossing1 = (c1s == RT(0));
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}
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}
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if (c2s < RT(0)) {
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crossing2 = (c2e >= RT(0));
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} else {
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if (c2e <= RT(0)) {
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if (c2s == RT(0) && c2e == RT(0))
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return internal::squared_distance_parallel(seg1, seg2, k);
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crossing2 = true;
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} else {
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crossing2 = (c2s == RT(0));
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}
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}
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if (crossing1) {
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if (crossing2)
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return (FT)0;
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RT dm;
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dm = _distance_measure_sub<K>(c2s,c2e, seg2.source(), seg2.target());
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if (dm < RT(0)) {
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return internal::squared_distance(seg2.source(), seg1, k);
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} else {
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if (dm > RT(0)) {
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return internal::squared_distance(seg2.target(), seg1, k);
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} else {
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// parallel, should not happen (no crossing)
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return internal::squared_distance_parallel(seg1, seg2, k);
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}
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}
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} else {
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if (crossing2) {
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RT dm;
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dm =
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_distance_measure_sub<K>(c1s, c1e,seg1.source(),seg1.target());
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if (dm < RT(0)) {
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return internal::squared_distance(seg1.source(), seg2, k);
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} else {
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if (dm > RT(0)) {
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return internal::squared_distance(seg1.target(), seg2, k);
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} else {
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// parallel, should not happen (no crossing)
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return internal::squared_distance_parallel(seg1, seg2, k);
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}
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}
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} else {
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FT min1, min2;
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RT dm = _distance_measure_sub<K>(
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c1s, c1e, seg1.source(), seg1.target());
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if (dm == RT(0))
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return internal::squared_distance_parallel(seg1, seg2, k);
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min1 = (dm < RT(0)) ?
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internal::squared_distance(seg1.source(), seg2, k):
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internal::squared_distance(seg1.target(), seg2, k);
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dm = _distance_measure_sub<K>(
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c2s, c2e, seg2.source(), seg2.target());
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if (dm == RT(0)) // should not happen.
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return internal::squared_distance_parallel(seg1, seg2, k);
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min2 = (dm < RT(0)) ?
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internal::squared_distance(seg2.source(), seg1, k):
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internal::squared_distance(seg2.target(), seg1, k);
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return (min1 < min2) ? min1 : min2;
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}
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}
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}
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template <class K>
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inline typename K::RT
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_distance_measure_sub(const typename K::RT &startwcross,
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const typename K::RT &endwcross,
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const typename K::Vector_2 &start,
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const typename K::Vector_2 &end)
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{
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return CGAL_NTS abs(wmult((K*)0, startwcross, end.hw())) -
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CGAL_NTS abs(wmult((K*)0, endwcross, start.hw()));
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}
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template <class K>
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typename K::FT
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squared_distance_parallel(const typename K::Segment_2 &seg,
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const typename K::Ray_2 &ray,
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const K& k)
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{
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typedef typename K::Vector_2 Vector_2;
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const Vector_2 &dir1 = seg.direction().vector();
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const Vector_2 &dir2 = ray.direction().vector();
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if (same_direction(dir1, dir2, k)) {
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if (!is_acute_angle(seg.source(), seg.target(), ray.source(), k))
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return internal::squared_distance(seg.target(), ray.source(), k);
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} else {
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if (!is_acute_angle(seg.target(), seg.source(), ray.source(), k))
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return internal::squared_distance(seg.source(), ray.source(), k);
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}
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return internal::squared_distance(ray.source(), seg.supporting_line(), k);
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}
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template <class K>
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typename K::FT
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squared_distance(const typename K::Segment_2 &seg,
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const typename K::Ray_2 &ray,
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const K& k)
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{
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typename K::Construct_vector_2 construct_vector;
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typedef typename K::RT RT;
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typedef typename K::FT FT;
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typedef typename K::Vector_2 Vector_2;
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const Vector_2 &raydir = ray.direction().vector();
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Vector_2 startvec(construct_vector(ray.source(), seg.source()));
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Vector_2 endvec(construct_vector(ray.source(), seg.target()));
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typename K::Orientation_2 orientation;
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bool crossing1, crossing2;
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RT c1s, c1e;
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if (seg.source() == seg.target())
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return internal::squared_distance(seg.source(), ray, k);
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c1s = wcross(raydir, startvec, k);
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c1e = wcross(raydir, endvec, k);
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if (c1s < RT(0)) {
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crossing1 = (c1e >= RT(0));
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} else {
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if (c1e <= RT(0)) {
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if (c1s == RT(0) && c1e == RT(0))
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return internal::squared_distance_parallel(seg, ray, k);
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crossing1 = true;
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} else {
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crossing1 = (c1s == RT(0));
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}
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}
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|
|
switch (orientation(seg.source(), seg.target(), ray.source())) {
|
||
|
|
case LEFT_TURN:
|
||
|
|
crossing2 = right_turn(construct_vector(seg.source(), seg.target()), raydir, k);
|
||
|
|
break;
|
||
|
|
case RIGHT_TURN:
|
||
|
|
crossing2 = left_turn(construct_vector(seg.source(), seg.target()), raydir, k);
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
crossing2 = true;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (crossing1) {
|
||
|
|
if (crossing2)
|
||
|
|
return FT(0);
|
||
|
|
return internal::squared_distance(ray.source(), seg, k);
|
||
|
|
} else {
|
||
|
|
if (crossing2) {
|
||
|
|
RT dm;
|
||
|
|
dm = _distance_measure_sub<K>(c1s, c1e, startvec, endvec);
|
||
|
|
if (dm < RT(0)) {
|
||
|
|
return internal::squared_distance(seg.source(), ray, k);
|
||
|
|
} else {
|
||
|
|
if (dm > RT(0)) {
|
||
|
|
return internal::squared_distance(seg.target(), ray, k);
|
||
|
|
} else {
|
||
|
|
// parallel, should not happen (no crossing)
|
||
|
|
return internal::squared_distance_parallel(seg, ray, k);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
FT min1, min2;
|
||
|
|
RT dm = _distance_measure_sub<K>(c1s, c1e, startvec, endvec);
|
||
|
|
if (dm == RT(0))
|
||
|
|
return internal::squared_distance_parallel(seg, ray, k);
|
||
|
|
min1 = (dm < RT(0))
|
||
|
|
? internal::squared_distance(seg.source(), ray, k)
|
||
|
|
: internal::squared_distance(seg.target(), ray, k);
|
||
|
|
min2 = internal::squared_distance(ray.source(), seg, k);
|
||
|
|
return (min1 < min2) ? min1 : min2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const typename K::Ray_2 &ray,
|
||
|
|
const typename K::Segment_2 &seg,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, ray, k);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::FT
|
||
|
|
_sqd_to_line(const typename K::Vector_2 &diff,
|
||
|
|
const typename K::RT & wcross,
|
||
|
|
const typename K::Vector_2 &dir )
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
RT numerator = CGAL_NTS square(wcross);
|
||
|
|
RT denominator = wmult((K*)0, RT(wdot(dir,dir, K())),
|
||
|
|
diff.hw(), diff.hw());
|
||
|
|
return Rational_traits<FT>().make_rational(numerator, denominator);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::FT
|
||
|
|
squared_distance(const typename K::Segment_2 &seg,
|
||
|
|
const typename K::Line_2 &line,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typename K::Construct_vector_2 construct_vector;
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
typedef typename K::Vector_2 Vector_2;
|
||
|
|
typedef typename K::Point_2 Point_2;
|
||
|
|
const Vector_2 &linedir = line.direction().vector();
|
||
|
|
const Point_2 &linepoint = line.point();
|
||
|
|
Vector_2 startvec(construct_vector(linepoint, seg.source()));
|
||
|
|
Vector_2 endvec(construct_vector(linepoint, seg.target()));
|
||
|
|
|
||
|
|
bool crossing1;
|
||
|
|
RT c1s, c1e;
|
||
|
|
if (seg.source() == seg.target())
|
||
|
|
return internal::squared_distance(seg.source(), line, k);
|
||
|
|
c1s = wcross(linedir, startvec, k);
|
||
|
|
c1e = wcross(linedir, endvec, k);
|
||
|
|
if (c1s < RT(0)) {
|
||
|
|
crossing1 = (c1e >= RT(0));
|
||
|
|
} else {
|
||
|
|
if (c1e <= RT(0)) {
|
||
|
|
crossing1 = true;
|
||
|
|
} else {
|
||
|
|
crossing1 = (c1s == RT(0));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (crossing1) {
|
||
|
|
return (FT)0;
|
||
|
|
} else {
|
||
|
|
RT dm;
|
||
|
|
dm = _distance_measure_sub<K>(c1s, c1e, startvec, endvec);
|
||
|
|
if (dm <= RT(0)) {
|
||
|
|
return _sqd_to_line<K>(startvec, c1s, linedir);
|
||
|
|
} else {
|
||
|
|
return _sqd_to_line<K>(endvec, c1e, linedir);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const typename K::Line_2 &line,
|
||
|
|
const typename K::Segment_2 &seg,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, line, k);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::FT
|
||
|
|
ray_ray_squared_distance_parallel(
|
||
|
|
const typename K::Vector_2 &ray1dir,
|
||
|
|
const typename K::Vector_2 &ray2dir,
|
||
|
|
const typename K::Vector_2 &from1to2,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::RT RT;
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
if (!is_acute_angle(ray1dir, from1to2, k)) {
|
||
|
|
if (!same_direction(ray1dir, ray2dir, k))
|
||
|
|
return (typename K::FT)k.compute_squared_length_2_object()(from1to2);
|
||
|
|
}
|
||
|
|
RT wcr, w;
|
||
|
|
wcr = wcross(ray1dir, from1to2, k);
|
||
|
|
w = from1to2.hw();
|
||
|
|
return (typename K::FT)(FT(wcr*wcr)
|
||
|
|
/ FT(wmult((K*)0, RT(wdot(ray1dir, ray1dir, k)), w, w)));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::FT
|
||
|
|
squared_distance(const typename K::Ray_2 &ray1,
|
||
|
|
const typename K::Ray_2 &ray2,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typename K::Construct_vector_2 construct_vector;
|
||
|
|
typedef typename K::Vector_2 Vector_2;
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
const Vector_2 &ray1dir = ray1.direction().vector();
|
||
|
|
const Vector_2 &ray2dir = ray2.direction().vector();
|
||
|
|
Vector_2 diffvec(construct_vector(ray1.source(),ray2.source()));
|
||
|
|
|
||
|
|
bool crossing1, crossing2;
|
||
|
|
switch (orientation(ray1dir, ray2dir, k)) {
|
||
|
|
case COUNTERCLOCKWISE:
|
||
|
|
crossing1 = !clockwise(diffvec, ray2dir, k);
|
||
|
|
crossing2 = !counterclockwise(ray1dir, diffvec, k);
|
||
|
|
break;
|
||
|
|
case CLOCKWISE:
|
||
|
|
crossing1 = !counterclockwise(diffvec, ray2dir, k);
|
||
|
|
crossing2 = !clockwise(ray1dir, diffvec, k);
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
return ray_ray_squared_distance_parallel(ray1dir,ray2dir,diffvec,k);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (crossing1) {
|
||
|
|
if (crossing2)
|
||
|
|
return (FT)0;
|
||
|
|
return internal::squared_distance(ray2.source(), ray1, k);
|
||
|
|
} else {
|
||
|
|
if (crossing2) {
|
||
|
|
return internal::squared_distance(ray1.source(), ray2, k);
|
||
|
|
} else {
|
||
|
|
|
||
|
|
FT min1, min2;
|
||
|
|
min1 = internal::squared_distance(ray1.source(), ray2, k);
|
||
|
|
min2 = internal::squared_distance(ray2.source(), ray1, k);
|
||
|
|
return (min1 < min2) ? min1 : min2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
typename K::FT
|
||
|
|
squared_distance(const typename K::Line_2 &line,
|
||
|
|
const typename K::Ray_2 &ray,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typename K::Construct_vector_2 construct_vector;
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
typedef typename K::Vector_2 Vector_2;
|
||
|
|
Vector_2 normalvec(line.a(), line.b());
|
||
|
|
Vector_2 diff = construct_vector(line.point(), ray.source());
|
||
|
|
FT sign_dist = k.compute_scalar_product_2_object()(diff,normalvec);
|
||
|
|
if (sign_dist < FT(0)) {
|
||
|
|
if (is_acute_angle(normalvec, ray.direction().vector(), k) )
|
||
|
|
return (FT)0;
|
||
|
|
} else {
|
||
|
|
if (is_obtuse_angle(normalvec, ray.direction().vector(), k) )
|
||
|
|
return (FT)0;
|
||
|
|
}
|
||
|
|
return (typename K::FT)((sign_dist*sign_dist)/k.compute_squared_length_2_object()(normalvec));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const typename K::Ray_2 &ray,
|
||
|
|
const typename K::Line_2 &line,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(line, ray, k);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const typename K::Line_2 &line1,
|
||
|
|
const typename K::Line_2 &line2,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typedef typename K::FT FT;
|
||
|
|
if (internal::parallel(line1, line2, k))
|
||
|
|
return internal::squared_distance(line1.point(), line2, k);
|
||
|
|
else
|
||
|
|
return (FT)0;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
void
|
||
|
|
distance_index(int &ind,
|
||
|
|
const typename K::Point_2 &pt,
|
||
|
|
const typename K::Ray_2 &ray,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
typename K::Construct_vector_2 construct_vector;
|
||
|
|
if (!is_acute_angle(ray.direction().vector(), construct_vector(ray.source(), pt), k)) {
|
||
|
|
ind = 0;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
ind = -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
void
|
||
|
|
distance_index(int &ind,
|
||
|
|
const typename K::Point_2 &pt,
|
||
|
|
const typename K::Segment_2 &seg,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
if (!is_acute_angle(seg.target(),seg.source(),pt, k)) {
|
||
|
|
ind = 0;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if (!is_acute_angle(seg.source(),seg.target(),pt, k)) {
|
||
|
|
ind = 1;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
ind = -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance_indexed(const typename K::Point_2 &pt,
|
||
|
|
const typename K::Ray_2 &ray,
|
||
|
|
int ind,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
if (ind == 0)
|
||
|
|
return internal::squared_distance(pt, ray.source(), k);
|
||
|
|
return internal::squared_distance(pt, ray.supporting_line(), k);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance_indexed(const typename K::Point_2 &pt,
|
||
|
|
const typename K::Segment_2 &seg,
|
||
|
|
int ind,
|
||
|
|
const K& k)
|
||
|
|
{
|
||
|
|
if (ind == 0)
|
||
|
|
return internal::squared_distance(pt, seg.source(), k);
|
||
|
|
if (ind == 1)
|
||
|
|
return internal::squared_distance(pt, seg.target(), k);
|
||
|
|
return internal::squared_distance(pt, seg.supporting_line(), k);
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Point_2<K> & pt1, const Point_2<K> & pt2)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(pt1, pt2, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Point_2<K> &pt, const Line_2<K> &line)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(pt, line, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Line_2<K> & line, const Point_2<K> & pt)
|
||
|
|
{
|
||
|
|
return squared_distance(pt, line);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Point_2<K> &pt, const Ray_2<K> &ray)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(pt, ray, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Ray_2<K> & ray, const Point_2<K> & pt)
|
||
|
|
{
|
||
|
|
return squared_distance(pt, ray);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Point_2<K> &pt, const Segment_2<K> &seg)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(pt, seg, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Segment_2<K> & seg, const Point_2<K> & pt)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(pt, seg, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Segment_2<K> &seg1, const Segment_2<K> &seg2)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg1, seg2, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Segment_2<K> &seg, const Ray_2<K> &ray)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, ray, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Ray_2<K> & ray, const Segment_2<K> & seg)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, ray, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Segment_2<K> &seg, const Line_2<K> &line)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, line, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
|
||
|
|
inline typename K::FT
|
||
|
|
squared_distance(const Line_2<K> & line, const Segment_2<K> & seg)
|
||
|
|
{
|
||
|
|
return internal::squared_distance(seg, line, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class K>
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inline typename K::FT
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squared_distance(const Ray_2<K> &ray1, const Ray_2<K> &ray2)
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{
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return internal::squared_distance(ray1, ray2, K());
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}
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template <class K>
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inline typename K::FT
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squared_distance(const Line_2<K> &line, const Ray_2<K> &ray)
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{
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return internal::squared_distance(line, ray, K());
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}
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template <class K>
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||
|
|
inline typename K::FT
|
||
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squared_distance(const Ray_2<K> & ray, const Line_2<K> & line)
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||
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|
{
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||
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|
return internal::squared_distance(line, ray, K());
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}
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||
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template <class K>
|
||
|
|
inline typename K::FT
|
||
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|
squared_distance(const Line_2<K> &line1, const Line_2<K> &line2)
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||
|
|
{
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return internal::squared_distance(line1, line2, K());
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}
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} //namespace CGAL
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#endif
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