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// Copyright (c) 2005 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/Envelope_3/include/CGAL/Envelope_3/Env_plane_traits_3_functions.h $ // $Id: include/CGAL/Envelope_3/Env_plane_traits_3_functions.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Baruch Zukerman #ifndef CGAL_ENV_PLANE_TRAITE_3_FUNCTIONS_H #define CGAL_ENV_PLANE_TRAITE_3_FUNCTIONS_H #include #include #include namespace CGAL { template std::optional< std::variant > plane_half_plane_proj_intersection(const typename K::Plane_3 &h1, const typename K::Plane_3 &h2, const typename K::Line_2 &l, const K& k) { typedef typename K::Line_3 Line_3; typedef typename K::Line_2 Line_2; typedef typename K::Plane_3 Plane_3; // intersect the two planes auto h_obj = k.intersect_3_object()(h1, h2); if(h_obj == std::nullopt) return std::nullopt; // no intersection at all (parallel planes) Plane_3 p; if(std::get_if(&(*h_obj))==nullptr) return std::nullopt; // if two planes are not parallel they must intersect at a 3D line const Line_3* l3 = std::get_if(&(*h_obj)); CGAL_assertion(l3!=nullptr); const Line_2& proj_inter_line = project_xy(*l3, k); return line_under_linear_constraint(proj_inter_line, l, k); //LR } template std::optional< std::variant > half_plane_half_plane_proj_intersection(const typename K::Plane_3 &h1, const typename K::Line_2 &l1, const typename K::Plane_3 &h2, const typename K::Line_2 &l2, const K& k) { typedef typename K::Ray_2 Ray_2; typedef typename K::Line_2 Line_2; auto obj = plane_half_plane_proj_intersection(h1, h2, l2, k); if(obj == std::nullopt) return std::nullopt; if(const Line_2* line = std::get_if(&(*obj))) return line_under_linear_constraint(*line, l1, k); if(const Ray_2* ray = std::get_if(&(*obj))) return ray_under_linear_constraint(*ray, l1, k); CGAL_error(); // doesn't suppose to reach here return std::nullopt; } template typename K::Line_2 project_xy(const typename K::Line_3& l, const K& k) { typedef typename K::Vector_3 Vector_3; typedef typename K::Vector_2 Vector_2; typedef typename K::Point_3 Point_3; typedef typename K::Point_2 Point_2; Vector_3 vec3 = k.construct_vector_3_object()(l); Vector_2 vec2(vec3.x(), vec3.y()); Point_3 p3 = k.construct_point_on_3_object()(l, 0); Point_2 p2(p3.x(), p3.y()); return k.construct_line_2_object()(p2, vec2); } // l1 is a line, l2 is a linear constraint (determined by the direction // of the line). template std::optional< std::variant > line_under_linear_constraint(const typename K::Line_2& l1, const typename K::Line_2& l2, const K& k) { typedef typename K::Ray_2 Ray_2; typedef typename K::Vector_2 Vector_2; typedef typename K::Point_2 Point_2; auto obj = k.intersect_2_object()(l1, l2); if(obj == std::nullopt)// the two lines are parallel { const Point_2& s = k.construct_point_on_2_object()(l1, 0); Oriented_side side = k.oriented_side_2_object()(l2, s); if(side == ON_NEGATIVE_SIDE) return std::nullopt; CGAL_assertion(side == ON_POSITIVE_SIDE); // the two lines are parallel return l1; } if(const Point_2* p = std::get_if(&(*obj))) { const Vector_2& vec = k.construct_vector_2_object()(l1); const Point_2& s = k.construct_translated_point_2_object()(*p, vec); const Ray_2& ray = k.construct_ray_2_object()(*p, s); Oriented_side side = k.oriented_side_2_object()(l2, s); if(side == ON_NEGATIVE_SIDE) { return k.construct_opposite_ray_2_object()(ray); } CGAL_assertion(side == ON_POSITIVE_SIDE); //the two lines are not parallel return ray; } // the two lines overlap return l1; } template std::optional< std::variant > ray_under_linear_constraint(const typename K::Ray_2& ray, const typename K::Line_2& l, const K& k) { typedef typename K::Vector_2 Vector_2; typedef typename K::Point_2 Point_2; const Point_2& s = k.construct_point_on_2_object()(ray, 0); Oriented_side side = k.oriented_side_2_object()(l, s); auto obj = k.intersect_2_object()(ray, l); if(obj == std::nullopt) { if(side == ON_NEGATIVE_SIDE) return std::nullopt; CGAL_assertion(side == ON_POSITIVE_SIDE); return ray; } if(const Point_2* p = std::get_if(&(*obj))) { if(side == ON_POSITIVE_SIDE) return k.construct_segment_2_object()(s, *p); Vector_2 vec = k.construct_vector_2_object()(ray); if(side == ON_NEGATIVE_SIDE) return k.construct_ray_2_object()(*p, vec); CGAL_assertion(side == ON_ORIENTED_BOUNDARY); const Vector_2& vec_of_l = k.construct_vector_2_object()(l); Orientation orient = k.orientation_2_object()(vec_of_l, vec); if(orient == LEFT_TURN) return ray; CGAL_assertion(orient == RIGHT_TURN); return s; } // the ray and the line overlap return ray; } } //namespace CGAL #endif