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// Copyright (c) 2013-2015 The University of Western Sydney, Australia. // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Cone_spanners_2/include/CGAL/Cone_spanners_2/Less_by_direction_2.h $ // $Id: include/CGAL/Cone_spanners_2/Less_by_direction_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Authors: Weisheng Si, Quincy Tse #ifndef CGAL_LESS_BY_DIRECTION_2_H #define CGAL_LESS_BY_DIRECTION_2_H #include #include #include #include #include #include #include #include #include #include namespace CGAL { /* Function object that orders the vertex_descriptors in a 2D graph based on the order * induced by the direction D described in the book: * * Giri Narasimhan and Michiel Smid, Chapter 4: Spanners based on the Theta graph, Geometric Spanner Networks, * Cambridge University Press, 2007. * * In this implementation, the ties are broken according to the direction of cw90(D). * This way of breaking ties will prevent the overlapping of cone boundaries when this functor * is used to construct Theta and Yao graphs in `CGAL::Construct_theta_graph_2` and * `CGAL::Construct_yao_graph_2`. Resultantly, the cw boundary of a cone will be considered inside this cone, * while the ccw boundary not. On the other hand, if your application requires that * the ccw boundary of a cone belongs to this cone while the cw boundary not, * you can modify the code below to use the direction of ccw90(D) to break the ties. * * This function object utilizes the existing function `CGAL::compare_signed_distance_to_line_2()`, * which orders two points according to their signed distance to a base line. * */ template class Less_by_direction_2 : public CGAL::cpp98::binary_function { public: // typedef for C++11 - doesn't hurt to also have for C++98 typedef typename Graph_::vertex_descriptor first_argument_type; typedef typename Graph_::vertex_descriptor second_argument_type; typedef bool result_type; // typedef for Direction_2 and Line_2 typedef typename Kernel_::Direction_2 Direction_2; typedef typename Kernel_::Line_2 Line_2; typedef typename Kernel_::Point_2 Point_2; typedef typename Kernel_::Aff_transformation_2 Transformation; // constructor Less_by_direction_2(const Graph_& g, const Direction_2& d) : graph(g), base_line(Point_2(0,0), d) {}; bool operator() (const typename Graph_::vertex_descriptor& p, const typename Graph_::vertex_descriptor& q) const { Comparison_result outcome; outcome = compare_signed_distance_to_line(base_line, graph[p], graph[q]); if (outcome == SMALLER) return true; else { if (outcome == LARGER) return false; } /* otherwise, outcome == CGAL::EQUAL, ties will be broken by a second order * according to the cw90(base_line) direction. */ // define a rotation of clockwise 90 Transformation cw90(0, 1, -1, 0); // rotate Line_2 cw90_line = cw90(base_line); outcome = compare_signed_distance_to_line(cw90_line, graph[p], graph[q]); if (outcome == SMALLER) return true; else return false; } private: const Graph_& graph; const Line_2 base_line; }; // class Less_by_direction_2 } // namespace CGAL #endif