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// Copyright (c) 1998-2021 // 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_3/include/CGAL/Distance_3/Segment_3_Ray_3.h $ // $Id: include/CGAL/Distance_3/Segment_3_Ray_3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Geert-Jan Giezeman, Andreas Fabri #ifndef CGAL_DISTANCE_3_SEGMENT_3_RAY_3_H #define CGAL_DISTANCE_3_SEGMENT_3_RAY_3_H #include #include #include namespace CGAL { namespace internal { template typename K::FT squared_distance_parallel(const typename K::Segment_3& seg, const typename K::Ray_3& ray, const K& k) { typedef typename K::Vector_3 Vector_3; const Vector_3 dir1 = seg.direction().vector(); const Vector_3 dir2 = ray.direction().vector(); bool same_direction; if(CGAL_NTS abs(dir1.hx()) > CGAL_NTS abs(dir1.hy())) same_direction = (CGAL_NTS sign(dir1.hx()) == CGAL_NTS sign(dir2.hx())); else same_direction = (CGAL_NTS sign(dir1.hy()) == CGAL_NTS sign(dir2.hy())); if(same_direction) { if(!is_acute_angle(seg.source(), seg.target(), ray.source(), k)) return squared_distance(seg.target(), ray.source(), k); } else { if(!is_acute_angle(seg.target(), seg.source(), ray.source(), k)) return squared_distance(seg.source(), ray.source(), k); } return squared_distance(ray.source(), seg.supporting_line(), k); } template typename K::FT squared_distance(const typename K::Segment_3& seg, const typename K::Ray_3& ray, const K& k) { typedef typename K::RT RT; typedef typename K::FT FT; typedef typename K::Point_3 Point_3; typedef typename K::Vector_3 Vector_3; typename K::Construct_vector_3 vector = k.construct_vector_3_object(); typename K::Compute_squared_distance_3 sq_dist = k.compute_squared_distance_3_object(); const Point_3& ss = seg.source(); const Point_3& se = seg.target(); //TODO This seems complicated compared to Segment_3_Segment_3.h. Consider improving by adapting Lumelsky's method for segment-segment intersection. if(ss == se) return sq_dist(ss, ray); const Vector_3 raydir = ray.direction().vector(); const Vector_3 segdir = seg.direction().vector(); const Vector_3 normal = wcross(segdir, raydir, k); if(is_null(normal, k)) return squared_distance_parallel(seg, ray, k); bool crossing1, crossing2; const Vector_3 perpend2seg = wcross(segdir, normal, k); const Vector_3 perpend2ray = wcross(raydir, normal, k); const Vector_3 ss_min_rs = vector(ray.source(), ss); const Vector_3 se_min_rs = vector(ray.source(), se); const RT sdm_ss2r = wdot(perpend2ray, ss_min_rs, k); const RT sdm_se2r = wdot(perpend2ray, se_min_rs, k); if(sdm_ss2r < RT(0)) { crossing1 = (sdm_se2r >= RT(0)); } else { if(sdm_se2r <= RT(0)) crossing1 = true; else crossing1 = (sdm_ss2r == RT(0)); } const RT sdm_rs2s = - wdot(perpend2seg, ss_min_rs, k); const RT sdm_re2s = wdot(perpend2seg, raydir, k); if(sdm_rs2s < RT(0)) { crossing2 = (sdm_re2s >= RT(0)); } else { if(sdm_re2s <= RT(0)) crossing2 = true; else crossing2 = (sdm_rs2s == RT(0)); } if(crossing1) { if(crossing2) return squared_distance_to_plane(normal, ss_min_rs, k); return sq_dist(ray.source(), seg); } else { if(crossing2) { const RT dm = distance_measure_sub(sdm_ss2r, sdm_se2r, ss_min_rs, se_min_rs, k); if(dm < RT(0)) { return sq_dist(ss, ray); } else { if(dm > RT(0)) return sq_dist(se, ray); else // parallel, should not happen (no crossing) return squared_distance_parallel(seg, ray, k); } } else { const RT dm = distance_measure_sub(sdm_ss2r, sdm_se2r, ss_min_rs, se_min_rs, k); if(dm == RT(0)) return squared_distance_parallel(seg, ray, k); const FT min1 = (dm < RT(0)) ? sq_dist(ss, ray) : sq_dist(se, ray); const FT min2 = sq_dist(ray.source(), seg); return (min1 < min2) ? min1 : min2; } } } template typename K::FT squared_distance(const typename K::Ray_3& ray, const typename K::Segment_3& seg, const K& k) { return squared_distance(seg, ray, k); } template typename K::Comparison_result compare_squared_distance(const typename K::Ray_3& ray, const typename K::Segment_3& seg, const K& k, const typename K::FT& d2) { return ::CGAL::compare(squared_distance(ray, seg, k), d2); } template typename K::Comparison_result compare_squared_distance(const typename K::Segment_3& seg, const typename K::Ray_3& ray, const K& k, const typename K::FT& d2) { return compare_squared_distance(ray, seg, k, d2); } } // namespace internal template inline typename K::FT squared_distance_parallel(const Segment_3& seg, const Ray_3& ray) { return internal::squared_distance_parallel(ray, seg, K()); } } // namespace CGAL #endif // CGAL_DISTANCE_3_SEGMENT_3_RAY_3_H