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// Copyright (c) 1998-2004 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Distance_2/include/CGAL/Distance_2/Segment_2_Segment_2.h $ // $Id: include/CGAL/Distance_2/Segment_2_Segment_2.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Geert-Jan Giezeman // Michel Hoffmann // Andreas Fabri #ifndef CGAL_DISTANCE_2_SEGMENT_2_SEGMENT_2_H #define CGAL_DISTANCE_2_SEGMENT_2_SEGMENT_2_H #include #include #include #include #include #include #include namespace CGAL { namespace internal { template typename K::FT squared_distance_parallel(const typename K::Segment_2& seg1, const typename K::Segment_2& seg2, const K& k) { typedef typename K::Vector_2 Vector_2; typename K::Compute_squared_distance_2 sq_dist = k.compute_squared_distance_2_object(); const Vector_2 dir1 = seg1.direction().vector(); const Vector_2 dir2 = seg2.direction().vector(); if(same_direction(dir1, dir2, k)) { if(!is_acute_angle(seg1.source(), seg1.target(), seg2.source(), k)) return sq_dist(seg1.target(), seg2.source()); if(!is_acute_angle(seg1.target(), seg1.source(), seg2.target(), k)) return sq_dist(seg1.source(), seg2.target()); } else { if(!is_acute_angle(seg1.source(), seg1.target(), seg2.target(), k)) return sq_dist(seg1.target(), seg2.target()); if(!is_acute_angle(seg1.target(), seg1.source(), seg2.source(), k)) return sq_dist(seg1.source(), seg2.source()); } return sq_dist(seg2.source(), seg1.supporting_line()); } template inline typename K::RT _distance_measure_sub(const typename K::RT& startwcross, const typename K::RT& endwcross, const typename K::Point_2& start, const typename K::Point_2& end) { return CGAL_NTS abs(wmult((K*)0, startwcross, end.hw())) - CGAL_NTS abs(wmult((K*)0, endwcross, start.hw())); } template typename K::FT squared_distance(const typename K::Segment_2& seg1, const typename K::Segment_2& seg2, const K& k, const Cartesian_tag&) { typedef typename K::RT RT; typedef typename K::FT FT; typename K::Orientation_2 orientation = k.orientation_2_object(); typename K::Compute_squared_distance_2 sq_dist = k.compute_squared_distance_2_object(); if(seg1.source() == seg1.target()) return sq_dist(seg1.source(), seg2); if(seg2.source() == seg2.target()) return sq_dist(seg2.source(), seg1); const Orientation o1s = orientation(seg2.source(), seg2.target(), seg1.source()); const Orientation o1e = orientation(seg2.source(), seg2.target(), seg1.target()); bool crossing1, crossing2; if(o1s == RIGHT_TURN) { crossing1 = (o1e != RIGHT_TURN); } else { if(o1e != LEFT_TURN) { if(o1s == COLLINEAR && o1e == COLLINEAR) return internal::squared_distance_parallel(seg1, seg2, k); crossing1 = true; } else { crossing1 = (o1s == COLLINEAR); } } const Orientation o2s = orientation(seg1.source(), seg1.target(), seg2.source()); const Orientation o2e = orientation(seg1.source(), seg1.target(), seg2.target()); if(o2s == RIGHT_TURN) { crossing2 = (o2e != RIGHT_TURN); } else { if(o2e != LEFT_TURN) { if(o2s == COLLINEAR && o2e == COLLINEAR) return internal::squared_distance_parallel(seg1, seg2, k); crossing2 = true; } else { crossing2 = (o2s == COLLINEAR); } } if(crossing1) { if(crossing2) return (FT)0; const RT c2s = CGAL_NTS abs(wcross(seg1.source(), seg1.target(), seg2.source(), k)); const RT c2e = CGAL_NTS abs(wcross(seg1.source(), seg1.target(), seg2.target(), k)); Comparison_result dm = CGAL_NTS compare(c2s, c2e); if(dm == SMALLER) { return sq_dist(seg2.source(), seg1); } else { if(dm == LARGER) { return sq_dist(seg2.target(), seg1); } else { // parallel, should not happen (no crossing) return internal::squared_distance_parallel(seg1, seg2, k); } } } else { const RT c1s = CGAL_NTS abs(wcross(seg2.source(), seg2.target(), seg1.source(), k)); const RT c1e = CGAL_NTS abs(wcross(seg2.source(), seg2.target(), seg1.target(), k)); Comparison_result dm = CGAL_NTS compare(c1s, c1e); if(crossing2) { if(dm == SMALLER) { return sq_dist(seg1.source(), seg2); } else { if(dm == LARGER) return sq_dist(seg1.target(), seg2); else // parallel, should not happen (no crossing) return internal::squared_distance_parallel(seg1, seg2, k); } } else { if(dm == EQUAL) return internal::squared_distance_parallel(seg1, seg2, k); FT min1 = (dm == SMALLER) ? sq_dist(seg1.source(), seg2): sq_dist(seg1.target(), seg2); const RT c2s = CGAL_NTS abs(wcross(seg1.source(), seg1.target(), seg2.source(), k)); const RT c2e = CGAL_NTS abs(wcross(seg1.source(), seg1.target(), seg2.target(), k)); dm = CGAL_NTS compare(c2s,c2e); if(dm == EQUAL) // should not happen. return internal::squared_distance_parallel(seg1, seg2, k); FT min2 = (dm == SMALLER) ? sq_dist(seg2.source(), seg1): sq_dist(seg2.target(), seg1); return (min1 < min2) ? min1 : min2; } } } template typename K::FT squared_distance(const typename K::Segment_2& seg1, const typename K::Segment_2& seg2, const K& k, const Homogeneous_tag&) { typedef typename K::RT RT; typedef typename K::FT FT; typename K::Compute_squared_distance_2 sq_dist = k.compute_squared_distance_2_object(); if(seg1.source() == seg1.target()) return sq_dist(seg1.source(), seg2); if(seg2.source() == seg2.target()) return sq_dist(seg2.source(), seg1); const RT c1s = wcross(seg2.source(), seg2.target(), seg1.source(), k); const RT c1e = wcross(seg2.source(), seg2.target(), seg1.target(), k); const RT c2s = wcross(seg1.source(), seg1.target(), seg2.source(), k); const RT c2e = wcross(seg1.source(), seg1.target(), seg2.target(), k); bool crossing1, crossing2; if(c1s < RT(0)) { crossing1 = (c1e >= RT(0)); } else { if(c1e <= RT(0)) { if(c1s == RT(0) && c1e == RT(0)) return internal::squared_distance_parallel(seg1, seg2, k); crossing1 = true; } else { crossing1 = (c1s == RT(0)); } } if(c2s < RT(0)) { crossing2 = (c2e >= RT(0)); } else { if(c2e <= RT(0)) { if(c2s == RT(0) && c2e == RT(0)) return internal::squared_distance_parallel(seg1, seg2, k); crossing2 = true; } else { crossing2 = (c2s == RT(0)); } } if(crossing1) { if(crossing2) return (FT)0; const RT dm = _distance_measure_sub(c2s,c2e, seg2.source(), seg2.target()); if(dm < RT(0)) { return sq_dist(seg2.source(), seg1); } else { if(dm > RT(0)) return sq_dist(seg2.target(), seg1); else // parallel, should not happen (no crossing) return internal::squared_distance_parallel(seg1, seg2, k); } } else { if(crossing2) { const RT dm = _distance_measure_sub(c1s, c1e,seg1.source(),seg1.target()); if(dm < RT(0)) { return sq_dist(seg1.source(), seg2); } else { if(dm > RT(0)) return sq_dist(seg1.target(), seg2); else // parallel, should not happen (no crossing) return internal::squared_distance_parallel(seg1, seg2, k); } } else { RT dm = _distance_measure_sub(c1s, c1e, seg1.source(), seg1.target()); if(dm == RT(0)) return internal::squared_distance_parallel(seg1, seg2, k); FT min1 = (dm < RT(0)) ? sq_dist(seg1.source(), seg2): sq_dist(seg1.target(), seg2); dm = _distance_measure_sub(c2s, c2e, seg2.source(), seg2.target()); if(dm == RT(0)) // should not happen. return internal::squared_distance_parallel(seg1, seg2, k); FT min2 = (dm < RT(0)) ? sq_dist(seg2.source(), seg1): sq_dist(seg2.target(), seg1); return (min1 < min2) ? min1 : min2; } } } template inline typename K::FT squared_distance(const Segment_2& seg1, const Segment_2& seg2, const K& k) { typedef typename K::Kernel_tag Tag; return squared_distance(seg1, seg2, k, Tag()); } } // namespace internal template inline typename K::FT squared_distance(const Segment_2& seg1, const Segment_2& seg2) { return K().compute_squared_distance_2_object()(seg1, seg2); } } // namespace CGAL #endif // CGAL_DISTANCE_2_SEGMENT_2_SEGMENT_2_H