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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/Construct_yao_graph_2.h $ // $Id: include/CGAL/Construct_yao_graph_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Authors: Weisheng Si, Quincy Tse, Frédérik Paradis /*! \file Construct_yao_graph_2.h * * This header implements the functor for constructing Yao graphs. */ #ifndef CGAL_CONSTRUCT_YAO_GRAPH_2_H #define CGAL_CONSTRUCT_YAO_GRAPH_2_H #include #include #include #include #include #include #include #include #include namespace CGAL { /*! \ingroup PkgConeSpanners2Ref \brief A template functor for constructing Yao graphs with a given set of 2D points and a given initial direction for the cone boundaries. \tparam Traits_ Must be either `CGAL::Exact_predicates_exact_constructions_kernel_with_root_of` or `CGAL::Exact_predicates_inexact_constructions_kernel`. \tparam Graph_ The graph type to store the constructed cone based spanner. It must be `boost::adjacency_list` with `Traits_::Point_2` as `VertexProperties` */ template class Construct_yao_graph_2 { public: /*! the geometric traits class. */ typedef Traits_ Traits; /*! the specific type of `boost::adjacency_list`. */ typedef Graph_ Graph; /*! the point type */ typedef typename Traits::Point_2 Point_2; /*! the direction type */ typedef typename Traits::Direction_2 Direction_2; private: typedef typename Traits::Line_2 Line_2; typedef Less_by_direction_2 Less_by_direction; // a type for the set to store vertices sorted by a direction typedef std::set Point_set; /* Store the number of cones. */ unsigned int cone_number; /* Store whether even, odd or all cones are selected to construct graph. */ Cones_selected cones_choice; /* Store the directions of the rays dividing the plane. The initial direction will be stored in rays[0]. */ std::vector rays; public: /*! \brief Constructor. \param k Number of cones to divide space into \param initial_direction A direction denoting one of the rays dividing the cones. This allows arbitrary rotations of the rays that divide the plane. (default: positive x-axis) \param cones_selected Indicates whether even, odd or all cones are selected to construct graph. */ Construct_yao_graph_2 (unsigned int k, Direction_2 initial_direction = Direction_2(1,0), Cones_selected cones_selected = ALL_CONES ): cone_number(k), cones_choice(cones_selected), rays(std::vector(k)) { if (k<2) { std::cout << "The number of cones must be larger than 1!" << std::endl; CGAL_assertion(false); } /* Initialize a functor, specialization will happen here depending on the kernel type to compute the cone boundaries either exactly or inexactly */ Compute_cone_boundaries_2 compute_cones; // compute the rays using the functor compute_cones(k, initial_direction, rays.begin()); } /*! \brief Function operator to construct a Yao graph. \details For the details of this algorithm, please refer to the User Manual. \tparam PointInputIterator an `InputIterator` with value type `Point_2`. \param[in] start An iterator pointing to the first vertex of the input. \param[in] end An iterator pointing to the past-the-end location of the input. \param[out] g The constructed graph object. */ template Graph_& operator()(const PointInputIterator& start, const PointInputIterator& end, Graph_& g) { // add vertices into the graph for (PointInputIterator curr = start; curr != end; ++curr) { g[boost::add_vertex(g)] = *curr; } unsigned int i; // ray index of the cw ray unsigned int j; // index of the ccw ray // add edges into the graph for every cone int new_start = cones_choice != ALL_CONES ? cones_choice : 0; int increment = cones_choice != ALL_CONES ? 2 : 1; for (i = new_start; i < cone_number; i += increment) { j = (i+1) % cone_number; add_edges_in_cone(rays[i], rays[j], g); } return g; } /*! \brief returns the number of cones. */ unsigned int number_of_cones() const { return cone_number; } /*! \brief outputs the set of directions to the iterator `result`. \tparam DirectionOutputIterator an `OutputIterator` with value type `Direction_2`. \return `result` */ template DirectionOutputIterator directions(DirectionOutputIterator result) { typename std::vector::iterator it; for (it=rays.begin(); it!=rays.end(); it++) { *result++ = *it; } return result; } protected: /* Construct edges in one cone bounded by two directions. \param cwBound The direction of the clockwise boundary of the cone. \param ccwBound The direction of the counterclockwise boundary. \param g The Yao graph to be built. */ void add_edges_in_cone(const Direction_2& cwBound, const Direction_2& ccwBound, Graph_& g) { if (ccwBound == cwBound) { // Degenerate case, not allowed. throw std::out_of_range("The cw boundary and the ccw boundary shouldn't be same!"); } // Ordering // here D1 is the reverse of D1 in the book, we find this is easier to implement const Less_by_direction orderD1 (g, ccwBound); const Less_by_direction orderD2 (g, cwBound); typename Graph_::vertex_iterator vit, ve; std::tie(vit, ve) = boost::vertices(g); // Step 1: Sort S according to order induced by D1 std::vector S(vit, ve); std::sort(S.begin (), S.end (), orderD1); // Step 2: initialize an empty set to store vertices sorted by orderD2 Point_set pst(orderD2); // Step 3: visit S in orderD1 // insert 'it' into pst // search the min in pst for (typename std::vector::const_iterator it = S.begin(); it != S.end(); ++it) { Less_euclidean_distance comp(g[*it], g); pst.insert(*it); // Find the last added node - O(logn) typename Point_set::iterator it2 = pst.find(*it); // Find minimum in pst from last ended node - O(n) typename Point_set::iterator min = std::min_element(++it2, pst.end(), comp); // add an edge if (min != pst.end()) { typename Graph_::edge_descriptor existing_e; bool existing; // check whether the edge already exists std::tie(existing_e, existing)=boost::edge(*it, *min, g); if (!existing) boost::add_edge(*it, *min, g); } } // end of for }; // end of add edges in cone /* Functor for comparing Euclidean distances of two vertices in a graph g to a given vertex. It is implemented by encapsulating the CGAL::has_smaller_distance_to_point() function. */ struct Less_euclidean_distance { const Point_2& p; const Graph_& g; // constructor Less_euclidean_distance(const Point_2&p, const Graph_& g) : p(p), g(g) {} // operator bool operator() (const typename Point_set::iterator::value_type& i, const typename Point_set::iterator::value_type& j) { const Point_2& p1 = g[i]; const Point_2& p2 = g[j]; return has_smaller_distance_to_point(p, p1, p2); } }; }; // class Construct_yao_graph_2 } // namespace CGAL #endif