// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // You can redistribute it and/or modify it under the terms of the GNU // General Public License as published by the Free Software Foundation, // either version 3 of the License, or (at your option) any later version. // // Licensees holding a valid commercial license may use this file in // accordance with the commercial license agreement provided with the software. // // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. // // $URL$ // $Id$ // SPDX-License-Identifier: GPL-3.0+ // // // Author(s) : Ron Wein // Efi Fogel // (based on old version by Eyal Flato) #ifndef CGAL_ARRANGEMENT_ZONE_2_H #define CGAL_ARRANGEMENT_ZONE_2_H #include #include /*! \file * Defintion of the Arrangement_zone_2 class. */ #include #include #include #include #include #include #include namespace CGAL { /*! \class * A class for computing the zone of a given $x$-monotone curve in a given * arrangement. * The arrangement parameter corresponds to the underlying arrangement, and * the zone-visitor parameter corresponds to a visitor class which is capable * of receiving notifications on the arrangment features the query curve * traverses. The visitor has to support the following functions: * - init(), for initializing the visitor with a given arrangement. * - found_subcurve(), called when a non-intersecting x-monotone curve is * computed and located in the arrangement. * - found_overlap(), called when an x-monotone curve overlaps an existing * halfedge in the arrangement. * Both the second and the third functions return pair, * where the halfedge handle corresponds to the halfedge created or modified * by the visitor (if valid), and the Boolean value indicates whether we * should halt the zone-computation process. */ template class Arrangement_zone_2 { public: typedef Arrangement_ Arrangement_2; typedef typename Arrangement_2::Geometry_traits_2 Geometry_traits_2; typedef typename Arrangement_2::Topology_traits Topology_traits; protected: typedef Arr_traits_adaptor_2 Traits_adaptor_2; typedef typename Traits_adaptor_2::Left_side_category Left_side_category; typedef typename Traits_adaptor_2::Bottom_side_category Bottom_side_category; typedef typename Traits_adaptor_2::Top_side_category Top_side_category; typedef typename Traits_adaptor_2::Right_side_category Right_side_category; BOOST_MPL_ASSERT( (typename Arr_sane_identified_tagging< Left_side_category, Bottom_side_category, Top_side_category, Right_side_category >::result) ); public: typedef ZoneVisitor_ Visitor; typedef typename Arrangement_2::Vertex_handle Vertex_handle; typedef typename Arrangement_2::Halfedge_handle Halfedge_handle; typedef typename Arrangement_2::Face_handle Face_handle; typedef std::pair Visitor_result; typedef typename Geometry_traits_2::Point_2 Point_2; typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2; typedef typename Geometry_traits_2::Multiplicity Multiplicity; protected: typedef typename Arr_are_all_sides_oblivious_tag< Left_side_category, Bottom_side_category, Top_side_category, Right_side_category >::result Are_all_sides_oblivious_category; typedef typename Arrangement_2::Vertex_const_handle Vertex_const_handle; typedef typename Arrangement_2::Halfedge_const_handle Halfedge_const_handle; typedef typename Arrangement_2::Face_const_handle Face_const_handle; // Types used for caching intersection points: typedef std::pair Intersect_point_2; typedef std::list Intersect_list; typedef std::map Intersect_map; typedef typename Intersect_map::iterator Intersect_map_iterator; typedef std::set Curves_set; typedef typename Curves_set::iterator Curves_set_iterator; // Data members: Arrangement_2& arr; // The associated arrangement. const Traits_adaptor_2 * m_geom_traits; // Its associated geometry traits. Arr_accessor arr_access; // An accessor for the arrangement. Visitor *visitor; // The zone visitor. Intersect_map inter_map; // Stores all computed intersections. const Vertex_handle invalid_v; // An invalid vertex handle. const Halfedge_handle invalid_he; // An invalid halfedge handle. X_monotone_curve_2 cv; // The current portion of the // inserted curve. CGAL::Object obj; // The location of the left endpoint. bool has_left_pt; // Is the left end of the curve // bounded. bool left_on_boundary; // Is the left point on the boundary. Point_2 left_pt; // Its current left endpoint. bool has_right_pt; // Is the right end of the curve // bounded. bool right_on_boundary;// Is the right point on the boundary. Point_2 right_pt; // Its right endpoint (if bounded). Vertex_handle left_v; // The arrangement vertex associated // with the current left_pt (if any). Halfedge_handle left_he; // If left_v is valid, left_he is the // predecessor for cv around this // vertex. Otherwise, if it is valid, // it is the halfedge that contains // the left endpoint it its interior. Vertex_handle right_v; // The arrangement vertex associated // with the current right_pt (if any). Halfedge_handle right_he; // If right_v is valid, left_he is the // predecessor for cv around this // vertex. Otherwise, if it is valid, // it is the halfedge that contains // the right endpoint it its interior. Point_2 intersect_p; // The next intersection point. unsigned int ip_mult; // Its multiplicity // (0 in case of an overlap). bool found_intersect; // Have we found an intersection // (or an overlap). X_monotone_curve_2 overlap_cv; // The currently discovered overlap. bool found_overlap; // Have we found an overlap. bool found_iso_vert; // Check if an isolated vertex induces // the next intersection. Vertex_handle intersect_v; // The vertex that intersects cv. Halfedge_handle intersect_he; // The halfedge that intersects cv // (or overlaps it). X_monotone_curve_2 sub_cv1; // Auxiliary variable (for curve split). X_monotone_curve_2 sub_cv2; // Auxiliary variable (for curve split). public: /*! * Constructor. * \param _arr The arrangement for which we compute the zone. * \param _visitor A pointer to a zone-visitor object. */ Arrangement_zone_2 (Arrangement_2& _arr, Visitor *_visitor) : arr (_arr), arr_access (_arr), visitor (_visitor), invalid_v (), invalid_he () { m_geom_traits = static_cast (arr.geometry_traits()); CGAL_assertion (visitor != NULL); // Initialize the visitor. visitor->init (&arr); } /*! * Initialize the zone-computation process with a given curve. * \param _cv The query curve. * \param pl A point-location object associated with the arrangement. */ template void init (const X_monotone_curve_2& _cv, const PointLocation& pl) { // Set the curve and check whether its left end has boundary conditions. cv = _cv; const Arr_parameter_space bx1 = m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MIN_END); const Arr_parameter_space by1 = m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MIN_END); if (bx1 == ARR_INTERIOR && by1 == ARR_INTERIOR) { // The curve has a finite left endpoint with no boundary conditions: // locate it in the arrangement. has_left_pt = true; left_on_boundary = (bx1 != ARR_INTERIOR || by1 != ARR_INTERIOR); left_pt = m_geom_traits->construct_min_vertex_2_object() (cv); obj = pl.locate (left_pt); } else { // The left end of the curve has boundary conditions: use the topology // traits use the arrangement accessor to locate it. // Note that if the curve-end is unbounded, left_pt does not exist. // Note that if the curve-end is unbounded, left_pt does not exist. has_left_pt = m_geom_traits->is_closed_2_object()(cv, ARR_MIN_END); left_on_boundary = true; if (has_left_pt) left_pt = m_geom_traits->construct_min_vertex_2_object() (cv); obj = arr_access.locate_curve_end (cv, ARR_MIN_END, bx1, by1); } // Check the boundary conditions of th right curve end. if (m_geom_traits->is_closed_2_object()(cv, ARR_MAX_END)) { const Arr_parameter_space bx2 = m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MAX_END); const Arr_parameter_space by2 = m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MAX_END); // The right endpoint is valid. has_right_pt = true; right_pt = m_geom_traits->construct_max_vertex_2_object() (cv); right_on_boundary = (bx2 != ARR_INTERIOR) || (by2 != ARR_INTERIOR); } else { // The right end of the curve lies at infinity. has_right_pt = false; right_on_boundary = true; } return; } /*! * Initialize the zone-computation process with a given curve and an object * that wraps the location of the curve's left end. * \param _cv The query curve. * \param _obj An object that represents the location of the left end * of the curve. */ void init_with_hint (const X_monotone_curve_2& _cv, const Object& _obj); /*! * Compute the zone of the given curve and issue the apporpriate * notifications for the visitor. */ void compute_zone (); private: /*! * Find a face containing the query curve cv around the given vertex. * In case an overlap occurs, sets intersect_he to be the overlapping edge. * \param v The query vertex. * \param he Output: The predecessor of cv around the vertex. * \return (true) if cv overlaps with the curve associated with he; * (false) if there is no overlap. */ bool _find_prev_around_vertex (Vertex_handle v, Halfedge_handle& he); /*! * Direct the halfedge for the location of the given subcurve around a split * point that occurs in the interior of a given edge, when the subcurve lies * to the right of the split point. * In case of overlaps, it sets also found_overlap and intersect_he. * \param cv_ins The curve to be inserted, whose left endpoint coincides * with the edge to be split. * \param cv_left_pt The left endpoint of cv_ins. * \param query_he The edge that intersects cv_ins. * \pre The left endpoint of cv_ins lies in the interior of the curve * associated with query_he. * \return The halfedge whose incident face contains cv_ins * (either query_he or its twin). */ Halfedge_handle _direct_intersecting_edge_to_right(const X_monotone_curve_2& cv_ins, const Point_2& cv_left_pt, Halfedge_handle query_he); /*! * Direct the halfedge for the location of the given subcurve around a split * point that occurs in the interior of a given edge, when the subcurve lies * to the left of the split point. * \param cv_ins The curve to be inserted, whose right endpoint coincides * with the edge to be split. * \param query_he The edge that intersects cv_ins. * \pre The right endpoint of cv_ins lies in the interior of the curve * associated with query_he. * \return The halfedge whose incident face contains cv_ins * (either query_he or its twin). */ Halfedge_handle _direct_intersecting_edge_to_left(const X_monotone_curve_2& cv_ins, Halfedge_handle query_he); /*! * Get the next intersection of cv with the given halfedge. * \param he A handle to the halfedge. * \param skip_first_point Should we skip the first intersection point. * \param intersect_on_right_boundary Output: If an intersetion point is * computed, marks whether this * point coincides with the right * curve-end, which lies on the * surface boundary. * \return An object representing the next intersection: Intersect_point_2 * in case of a simple intersection point, X_monotone_curve_2 in * case of an overlap, and an empty object if there is no * intersection. */ CGAL::Object _compute_next_intersection (Halfedge_handle he, bool skip_first_point, bool& intersect_on_right_boundary); /*! * Remove the next intersection of cv with the given halfedge from the map. * \param he A handle to the halfedge. * \pre The list of intersections with the curve of he has already been * computed, and it is not empty. */ void _remove_next_intersection (Halfedge_handle he); /*! * Check if the given point lies completely to the left of the given egde. * \param p The point. * \param he The halfedge. * \pre he is not a fictitious edge. * \return Whether p lies entirely to the left of the edge. */ bool _is_to_left(const Point_2& p, Halfedge_handle he) const { return (_is_to_left_impl(p, he, Are_all_sides_oblivious_category())); } bool _is_to_left_impl(const Point_2& p, Halfedge_handle he, Arr_all_sides_oblivious_tag) const { return ((he->direction() == ARR_LEFT_TO_RIGHT && m_geom_traits->compare_xy_2_object() (p, he->source()->point()) == SMALLER) || (he->direction() == ARR_RIGHT_TO_LEFT && m_geom_traits->compare_xy_2_object() (p, he->target()->point()) == SMALLER)); } bool _is_to_left_impl(const Point_2& p, Halfedge_handle he, Arr_not_all_sides_oblivious_tag) const; /*! * Check if the given point lies completely to the right of the given egde. * \param p The point. * \param he The halfedge. * \pre he is not a fictitious edge. * \return Whether p lies entirely to the right of the edge. */ bool _is_to_right(const Point_2& p, Halfedge_handle he) const { return (_is_to_right_impl(p, he, Are_all_sides_oblivious_category())); } bool _is_to_right_impl(const Point_2& p, Halfedge_handle he, Arr_all_sides_oblivious_tag) const { return ((he->direction() == ARR_LEFT_TO_RIGHT && m_geom_traits->compare_xy_2_object() (p, he->target()->point()) == LARGER) || (he->direction() == ARR_RIGHT_TO_LEFT && m_geom_traits->compare_xy_2_object() (p, he->source()->point()) == LARGER)); } bool _is_to_right_impl(const Point_2& p, Halfedge_handle he, Arr_not_all_sides_oblivious_tag) const; /*! * Compute the (lexicographically) leftmost intersection of the query * curve with the boundary of a given face in the arrangement. * The function computes sets intersect_p, intersect_he (or alternatively * overlap_cv and intersect_he) and set the flags found_intersect and * found_overlap accordingly. * \param face A handle to the face. * \param on_boundary Specifies whether the left endpoint of the curve lies * on the face boundary. */ void _leftmost_intersection_with_face_boundary (Face_handle face, bool on_boundary); /*! * Compute the zone of an x-monotone curve in a given arrangement face. * The left endpoint of the curve either lies in the face interior or on * the boundary of the face. * This function updates cv and its left endpoint and also sets left_v * and left_he for the remaining portion of the curve. * In case of overlaps, it sets also overlap_cv and intersect_he. * \param face The given face. * \param on_boundary Specifies whether the left endpoint of the curve lies * on the face boundary. * \pre If on_boundary is (true) then left_he must be valid; if it is (false) * then both left_v anf left_he must be invalid. * \return (true) if we are done with the zone-computation process; * (false) if we still have a remaining portion of cv to continue * with. */ bool _zone_in_face (Face_handle face, bool on_boundary); /*! * Compute the zone of an overlapping subcurve overlap_cv of cv and the * curve currently associated with intersect_he. * This function updates cv and its left endpoint and also sets left_v * and left_he for the remaining portion of the curve. * \return (true) if we are done with the zone-computation process; * (false) if we still have a remaining portion of cv to continue * with. */ bool _zone_in_overlap (); }; } //namespace CGAL // The function definitions can be found under: #include #include #endif