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// Copyright (c) 2000 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Partition_2/include/CGAL/Partition_2/partition_y_monotone_2.h $ // $Id: include/CGAL/Partition_2/partition_y_monotone_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Susan Hert // // Implementation of the algorithm from pp 49--55 of "Computational Geometry // Algorithms and Applications" by de Berg, van Kreveld, Overmars, and // Schwarzkopf for producing a partitioning of a polygon into y-monotone // pieces. // // NOTE: e_i = (v_i, v_{i+1}) // // TREE: // "Therefore we store the edges of P intersecting the sweep line in the // leaves of a dynamic binary search tree T. The left-to-right order of // the leaves of T corresponds to the left-to-right order of the edges. // Because we are only interested in edges to the left of split and merge // vertices we only need to store edges in T that have the interior of P // to their right. With each edge in T we store its helper." // // #ifndef CGAL_PARTITION_Y_MONOTONE_H #define CGAL_PARTITION_Y_MONOTONE_H #include #include #include #include #include #include #include #include #include #include namespace CGAL { enum Partition_y_mono_vertex_type {PARTITION_Y_MONO_START_VERTEX, PARTITION_Y_MONO_SPLIT_VERTEX, PARTITION_Y_MONO_REGULAR_VERTEX, PARTITION_Y_MONO_COLLINEAR_VERTEX, PARTITION_Y_MONO_MERGE_VERTEX, PARTITION_Y_MONO_END_VERTEX}; // // assumes CCW orientation of vertices // template Partition_y_mono_vertex_type partition_y_mono_vertex_type( BidirectionalCirculator c, const Traits& traits) { typedef typename Traits::Point_2 Point_2; BidirectionalCirculator previous = c; previous--; BidirectionalCirculator next = c; next++; #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono__vertex_type: previous " << *previous << " c " << *c << " next " << *next << std::endl; #endif typename Traits::Compare_y_2 compare_y_2 = traits.compare_y_2_object(); if (compare_y_2(Point_2(*previous), Point_2(*c)) == EQUAL && compare_y_2(Point_2(*next), Point_2(*c)) == EQUAL) return PARTITION_Y_MONO_COLLINEAR_VERTEX; typename Traits::Less_yx_2 less_yx = traits.less_yx_2_object(); typename Traits::Left_turn_2 left_turn = traits.left_turn_2_object(); if(less_yx(Point_2(*previous), Point_2(*c))) { if(less_yx(Point_2(*next), Point_2(*c))) // previous and next both less_yx if(left_turn(Point_2(*previous), Point_2(*c), Point_2(*next))) // interior angle less than pi return PARTITION_Y_MONO_START_VERTEX; else // interior angle greater than pi return PARTITION_Y_MONO_SPLIT_VERTEX; else // previous less_yx and next not return PARTITION_Y_MONO_REGULAR_VERTEX; } else { if(less_yx(Point_2(*c), Point_2(*next))) // previous and next both not less_yx if(left_turn(Point_2(*previous), Point_2(*c), Point_2(*next))) // interior angle less than pi return PARTITION_Y_MONO_END_VERTEX; else // interior angle greater than pi return PARTITION_Y_MONO_MERGE_VERTEX; else // next less_yx and previous not return PARTITION_Y_MONO_REGULAR_VERTEX; } } template void partition_y_mono_print_tree(Tree tree) { typedef typename Tree::iterator iterator; iterator it = tree.begin(); for (; it != tree.end(); it++) { std::cout << "edge node " << *(*it).first << " helper " << *(*it).second << std::endl; } std::cout << std::endl; } template void partition_y_mono_handle_start_vertex(BidirectionalCirculator c, Tree& tree) { typedef typename Tree::value_type ValuePair; #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is a start vertex " << std::endl; #endif tree.insert(ValuePair(c, c)); #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_handle_start_vertex: after insert tree is " << std::endl; partition_y_mono_print_tree(tree); #endif // insert e_i (edge from *c to *++c) into "tree" with helper(e_i) = v_i } template void partition_y_mono_handle_end_vertex(BidirectionalCirculator c, Tree& tree, Partition_Poly& partition_poly, const Traits& traits ) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is an end vertex " << std::endl; #endif typedef typename Tree::iterator tree_iterator; tree_iterator it; BidirectionalCirculator previous = c; previous--; #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_end_vertex: previous " << *previous << std::endl; #endif it = tree.find(previous); CGAL_assertion (it != tree.end()); if (partition_y_mono_vertex_type((*it).second, traits) == PARTITION_Y_MONO_MERGE_VERTEX) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_end_vertex: diagonal " << *(*it).second << " to " << *c << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); } tree.erase(it); #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_end_vertex: after erase tree is " << std::endl; partition_y_mono_print_tree(tree); #endif // if helper(e_{i-1}) is a merge vertex // insert diagonal connecting v_i to helper(e_{i-1}) // delete e_{i-1} from tree } template inline void partition_y_mono_edge_directly_left(BidirectionalCirculator c, Tree& tree, Iterator& it) { it = tree.lower_bound(c); // edge directly to the left of v_i since the // items in the tree are sorted from right to // left #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG if (it != tree.end()) std::cout << "partition_y_mono_edge_directly_left: lower_bound edge node: " << *((*it).first) << " helper " << *((*it).second) << std::endl; #endif } template void partition_y_mono_handle_split_vertex(BidirectionalCirculator c, Tree& tree, Partition_Poly& partition_poly) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is a split vertex " << std::endl; #endif typedef typename Tree::iterator tree_iterator; typedef typename Tree::value_type ValuePair; tree_iterator it; partition_y_mono_edge_directly_left(c, tree, it); if (it != tree.end()) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_split_vertex: diagonal " << *(*it).second << " to " << *c << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); BidirectionalCirculator ej = (*it).first; tree.erase(it); tree.insert(ValuePair(ej, c)); } tree.insert(ValuePair(c, c)); #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_split_vertex: " << "after erase and inserts tree is" << std::endl; partition_y_mono_print_tree(tree); #endif // 1. find the edge e_j in tree directly to the left of v_i // 2. insert the diagonal connecting v_i to helper(e_j) // 3. helper(e_j) = v_i // 4. Insert e_i in tree and set helper(e_i) to v_i } template void partition_y_mono_handle_merge_vertex(BidirectionalCirculator c, Tree& tree, Partition_Poly& partition_poly, const Traits& traits) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is a merge vertex " << std::endl; #endif typedef typename Tree::iterator tree_iterator; typedef typename Tree::value_type ValuePair; BidirectionalCirculator prev = c; prev--; tree_iterator it = tree.find(prev); CGAL_assertion (it != tree.end()); if (partition_y_mono_vertex_type((*it).second,traits) == PARTITION_Y_MONO_MERGE_VERTEX) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_merge_vertex 1: diagonal " << *(*it).second << " to " << *c << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); } tree.erase(it); partition_y_mono_edge_directly_left(c, tree, it); if (it != tree.end()) { if (partition_y_mono_vertex_type((*it).second,traits) == PARTITION_Y_MONO_MERGE_VERTEX) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_merge_vertex 2: diagonal " << *(*it).second << " to " << *c << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); } BidirectionalCirculator ej = (*it).first; tree.erase(it); tree.insert(ValuePair(ej,c)); } #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_merge_vertex: after erase(s) tree is " << std::endl; partition_y_mono_print_tree(tree); #endif // 1. if helper(e_{i-1}) is a merge vertex // insert the diagonal connecting v_i to helper(e_{i-1}) // 2. delete e_{i-1} from tree // 3. find the edge e_j in tree directly to the left of v_i // 4. if helper(e_j) is a merge vertex // insert diagonal connecting v_i to helper(e_j) in polygon // 5. helper(e_j) = v_i } template bool partition_y_mono_interior_to_right(BidirectionalCirculator c, const Traits& traits) { typedef typename Traits::Point_2 Point_2; typename Traits::Compare_y_2 compare_y_2 = traits.compare_y_2_object(); BidirectionalCirculator previous = c; previous--; Comparison_result cmp_y = compare_y_2(Point_2(*previous), Point_2(*c)); if (cmp_y == LARGER) return true; BidirectionalCirculator next = c; next++; if (cmp_y == EQUAL && compare_y_2(Point_2(*next), Point_2(*c)) == SMALLER) return true; return false; } template void partition_y_mono_handle_regular_vertex(BidirectionalCirculator c, Tree& tree, Partition_Poly& partition_poly, const Traits& traits ) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is a regular vertex " << std::endl; #endif typedef typename Tree::iterator tree_iterator; typedef typename Tree::value_type ValuePair; tree_iterator it; BidirectionalCirculator previous = c; previous--; if (partition_y_mono_interior_to_right(c, traits)) { it = tree.find(previous); CGAL_assertion( it != tree.end() ); if (partition_y_mono_vertex_type((*it).second, traits) == PARTITION_Y_MONO_MERGE_VERTEX) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_regular_vertex 1: diagonal " << *(*it).second << " to " << *c << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); } tree.erase(it); tree.insert(ValuePair(c,c)); } else { partition_y_mono_edge_directly_left(c, tree, it); CGAL_assertion (it != tree.end()); if (partition_y_mono_vertex_type((*it).second, traits) == PARTITION_Y_MONO_MERGE_VERTEX) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_regular_vertex 2: diagonal " << *c << " to " << *(*it).second << std::endl; #endif partition_poly.insert_diagonal(c, (*it).second); } BidirectionalCirculator ej = (*it).first; tree.erase(it); tree.insert(ValuePair(ej,c)); } #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_regular_vertex: " << "after erase and insert tree is" << std::endl; partition_y_mono_print_tree(tree); #endif // if interior of polygon lies to the right of v_i // if helper(e_{i-1}) is a merge vertex // insert diagonal connecting v_i to helper(e_{i-1}) in polygon // delete e_{i-1} from tree // insert e_i in tree and set helper(e_i) to v_i // else // find the edge e_j in tree directly left of v_i // if helper(e_j) is a merge vertex // insert diagonal connecting v_i to helper(e_j) in D // helper(e_j) = v_i } template void partition_y_mono_handle_collinear_vertex(BidirectionalCirculator c, Tree& tree) { typedef typename Tree::iterator tree_iterator; typedef typename Tree::value_type ValuePair; #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *c << " is a collinear vertex " << std::endl; #endif tree_iterator it; BidirectionalCirculator previous = c; previous--; #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << *previous << " is the previous vertex " << std::endl; #endif it = tree.find(previous); if ( it != tree.end() ) { #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "partition_y_mono_handle_collinear_vertex : removing " << *(*it).first << std::endl; #endif tree.erase(it); } tree.insert(ValuePair(c,c)); } template OutputIterator partition_y_monotone_2(InputIterator first, InputIterator beyond, OutputIterator result, const Traits& traits) { if (first == beyond) return result; typedef Partitioned_polygon_2< Traits > P_Polygon_2; typedef typename P_Polygon_2::iterator I; typedef Circulator_from_iterator Circulator; #if defined(CGAL_PARTITION_NO_POSTCONDITIONS) || \ defined(CGAL_NO_POSTCONDITIONS) OutputIterator res(result); #else typedef typename Traits::Polygon_2 Polygon_2; Tee_for_output_iterator res(result); #endif // no postcondition P_Polygon_2 polygon(first, beyond, traits); CGAL_precondition( orientation_2(polygon.begin(), polygon.end(), traits) == COUNTERCLOCKWISE); Circulator circ(polygon.begin(), polygon.end()), done = circ; std::vector circulators; CGAL_For_all(circ, done){ circulators.push_back(circ); } std::sort(circulators.begin(), circulators.end(), Indirect_not_less_yx_2(traits)); #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG std::cout << "Initial vertex list: "<< circulators << std::endl; for(std::vector::const_iterator it = circulators.begin(); it != circulators.end(); it++){ std::cout << **it << " " ; } std::cout << std::endl; #endif typedef Indirect_edge_compare Cmp; typedef std::map Tree; Cmp cmp(traits); Tree tree(cmp); typename std::vector::iterator it = circulators.begin(); for (; it != circulators.end(); it++) { switch (partition_y_mono_vertex_type(*it, traits)) { case PARTITION_Y_MONO_START_VERTEX: partition_y_mono_handle_start_vertex(*it, tree); break; case PARTITION_Y_MONO_SPLIT_VERTEX: partition_y_mono_handle_split_vertex(*it, tree, polygon); break; case PARTITION_Y_MONO_END_VERTEX: partition_y_mono_handle_end_vertex(*it, tree, polygon, traits); break; case PARTITION_Y_MONO_MERGE_VERTEX: partition_y_mono_handle_merge_vertex(*it, tree, polygon, traits); break; case PARTITION_Y_MONO_REGULAR_VERTEX: partition_y_mono_handle_regular_vertex(*it, tree, polygon, traits); break; case PARTITION_Y_MONO_COLLINEAR_VERTEX: partition_y_mono_handle_collinear_vertex(*it, tree); break; } } #ifdef CGAL_PARTITION_Y_MONOTONE_DEBUG I v_it; for (v_it = polygon.begin(); v_it != polygon.end(); v_it++) { (*v_it).print_diagonals(); } #endif polygon.partition(res, 0); CGAL_postcondition( y_monotone_partition_is_valid_2(polygon.begin(), polygon.end(), res.output_so_far_begin(), res.output_so_far_end(), traits)); #if defined(CGAL_PARTITION_NO_POSTCONDITIONS) || \ defined(CGAL_NO_POSTCONDITIONS) return res; #else return res.to_output_iterator(); #endif // no postconditions } template inline OutputIterator partition_y_monotone_2(InputIterator first, InputIterator beyond, OutputIterator result) { typedef typename std::iterator_traits::value_type Point_2; typedef typename Kernel_traits::Kernel K; return partition_y_monotone_2(first, beyond, result, Partition_traits_2()); } } #endif // CGAL_PARTITION_Y_MONOTONE_H