451 lines
19 KiB
C
451 lines
19 KiB
C
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// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: GPL-3.0+
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//
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//
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// Author(s) : Ron Wein <wein@post.tau.ac.il>
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// Efi Fogel <efif@post.tau.ac.il>
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// (based on old version by Eyal Flato)
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#ifndef CGAL_ARRANGEMENT_ZONE_2_H
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#define CGAL_ARRANGEMENT_ZONE_2_H
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#include <CGAL/license/Arrangement_on_surface_2.h>
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#include <CGAL/disable_warnings.h>
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/*! \file
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* Defintion of the Arrangement_zone_2 class.
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*/
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#include <boost/mpl/assert.hpp>
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#include <CGAL/Arr_tags.h>
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#include <CGAL/Arr_accessor.h>
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#include <CGAL/Arrangement_2/Arr_traits_adaptor_2.h>
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#include <list>
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#include <map>
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#include <set>
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namespace CGAL {
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/*! \class
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* A class for computing the zone of a given $x$-monotone curve in a given
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* arrangement.
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* The arrangement parameter corresponds to the underlying arrangement, and
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* the zone-visitor parameter corresponds to a visitor class which is capable
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* of receiving notifications on the arrangment features the query curve
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* traverses. The visitor has to support the following functions:
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* - init(), for initializing the visitor with a given arrangement.
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* - found_subcurve(), called when a non-intersecting x-monotone curve is
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* computed and located in the arrangement.
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* - found_overlap(), called when an x-monotone curve overlaps an existing
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* halfedge in the arrangement.
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* Both the second and the third functions return pair<Halfedge_handle, bool>,
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* where the halfedge handle corresponds to the halfedge created or modified
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* by the visitor (if valid), and the Boolean value indicates whether we
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* should halt the zone-computation process.
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*/
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template <class Arrangement_, class ZoneVisitor_>
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class Arrangement_zone_2
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{
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public:
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typedef Arrangement_ Arrangement_2;
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typedef typename Arrangement_2::Geometry_traits_2 Geometry_traits_2;
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typedef typename Arrangement_2::Topology_traits Topology_traits;
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protected:
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typedef Arr_traits_adaptor_2<Geometry_traits_2> Traits_adaptor_2;
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typedef typename Traits_adaptor_2::Left_side_category Left_side_category;
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typedef typename Traits_adaptor_2::Bottom_side_category Bottom_side_category;
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typedef typename Traits_adaptor_2::Top_side_category Top_side_category;
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typedef typename Traits_adaptor_2::Right_side_category Right_side_category;
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BOOST_MPL_ASSERT(
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(typename
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Arr_sane_identified_tagging< Left_side_category, Bottom_side_category,
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Top_side_category, Right_side_category >::result)
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);
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public:
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typedef ZoneVisitor_ Visitor;
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typedef typename Arrangement_2::Vertex_handle Vertex_handle;
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typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
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typedef typename Arrangement_2::Face_handle Face_handle;
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typedef std::pair<Halfedge_handle, bool> Visitor_result;
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typedef typename Geometry_traits_2::Point_2 Point_2;
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typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2;
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typedef typename Geometry_traits_2::Multiplicity Multiplicity;
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protected:
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typedef typename Arr_are_all_sides_oblivious_tag<
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Left_side_category, Bottom_side_category,
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Top_side_category, Right_side_category >::result
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Are_all_sides_oblivious_category;
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typedef typename Arrangement_2::Vertex_const_handle Vertex_const_handle;
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typedef typename Arrangement_2::Halfedge_const_handle Halfedge_const_handle;
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typedef typename Arrangement_2::Face_const_handle Face_const_handle;
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// Types used for caching intersection points:
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typedef std::pair<Point_2,Multiplicity> Intersect_point_2;
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typedef std::list<CGAL::Object> Intersect_list;
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typedef std::map<const X_monotone_curve_2*,
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Intersect_list> Intersect_map;
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typedef typename Intersect_map::iterator Intersect_map_iterator;
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typedef std::set<const X_monotone_curve_2*> Curves_set;
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typedef typename Curves_set::iterator Curves_set_iterator;
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// Data members:
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Arrangement_2& arr; // The associated arrangement.
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const Traits_adaptor_2 * m_geom_traits; // Its associated geometry traits.
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Arr_accessor<Arrangement_2> arr_access; // An accessor for the arrangement.
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Visitor *visitor; // The zone visitor.
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Intersect_map inter_map; // Stores all computed intersections.
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const Vertex_handle invalid_v; // An invalid vertex handle.
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const Halfedge_handle invalid_he; // An invalid halfedge handle.
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X_monotone_curve_2 cv; // The current portion of the
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// inserted curve.
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CGAL::Object obj; // The location of the left endpoint.
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bool has_left_pt; // Is the left end of the curve
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// bounded.
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bool left_on_boundary; // Is the left point on the boundary.
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Point_2 left_pt; // Its current left endpoint.
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bool has_right_pt; // Is the right end of the curve
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// bounded.
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bool right_on_boundary;// Is the right point on the boundary.
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Point_2 right_pt; // Its right endpoint (if bounded).
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Vertex_handle left_v; // The arrangement vertex associated
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// with the current left_pt (if any).
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Halfedge_handle left_he; // If left_v is valid, left_he is the
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// predecessor for cv around this
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// vertex. Otherwise, if it is valid,
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// it is the halfedge that contains
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// the left endpoint it its interior.
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Vertex_handle right_v; // The arrangement vertex associated
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// with the current right_pt (if any).
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Halfedge_handle right_he; // If right_v is valid, left_he is the
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// predecessor for cv around this
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// vertex. Otherwise, if it is valid,
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// it is the halfedge that contains
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// the right endpoint it its interior.
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Point_2 intersect_p; // The next intersection point.
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unsigned int ip_mult; // Its multiplicity
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// (0 in case of an overlap).
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bool found_intersect; // Have we found an intersection
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// (or an overlap).
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X_monotone_curve_2 overlap_cv; // The currently discovered overlap.
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bool found_overlap; // Have we found an overlap.
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bool found_iso_vert; // Check if an isolated vertex induces
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// the next intersection.
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Vertex_handle intersect_v; // The vertex that intersects cv.
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Halfedge_handle intersect_he; // The halfedge that intersects cv
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// (or overlaps it).
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X_monotone_curve_2 sub_cv1; // Auxiliary variable (for curve split).
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X_monotone_curve_2 sub_cv2; // Auxiliary variable (for curve split).
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public:
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/*!
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* Constructor.
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* \param _arr The arrangement for which we compute the zone.
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* \param _visitor A pointer to a zone-visitor object.
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*/
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Arrangement_zone_2 (Arrangement_2& _arr, Visitor *_visitor) :
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arr (_arr),
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arr_access (_arr),
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visitor (_visitor),
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invalid_v (),
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invalid_he ()
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{
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m_geom_traits = static_cast<const Traits_adaptor_2*> (arr.geometry_traits());
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CGAL_assertion (visitor != NULL);
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// Initialize the visitor.
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visitor->init (&arr);
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}
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/*!
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* Initialize the zone-computation process with a given curve.
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* \param _cv The query curve.
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* \param pl A point-location object associated with the arrangement.
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*/
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template <class PointLocation>
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void init (const X_monotone_curve_2& _cv, const PointLocation& pl)
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{
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// Set the curve and check whether its left end has boundary conditions.
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cv = _cv;
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const Arr_parameter_space bx1 =
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m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MIN_END);
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const Arr_parameter_space by1 =
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m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MIN_END);
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if (bx1 == ARR_INTERIOR && by1 == ARR_INTERIOR) {
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// The curve has a finite left endpoint with no boundary conditions:
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// locate it in the arrangement.
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has_left_pt = true;
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left_on_boundary = (bx1 != ARR_INTERIOR || by1 != ARR_INTERIOR);
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left_pt = m_geom_traits->construct_min_vertex_2_object() (cv);
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obj = pl.locate (left_pt);
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}
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else {
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// The left end of the curve has boundary conditions: use the topology
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// traits use the arrangement accessor to locate it.
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// Note that if the curve-end is unbounded, left_pt does not exist.
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// Note that if the curve-end is unbounded, left_pt does not exist.
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has_left_pt = m_geom_traits->is_closed_2_object()(cv, ARR_MIN_END);
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left_on_boundary = true;
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if (has_left_pt)
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left_pt = m_geom_traits->construct_min_vertex_2_object() (cv);
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obj = arr_access.locate_curve_end (cv, ARR_MIN_END, bx1, by1);
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}
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// Check the boundary conditions of th right curve end.
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if (m_geom_traits->is_closed_2_object()(cv, ARR_MAX_END)) {
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const Arr_parameter_space bx2 =
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m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MAX_END);
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const Arr_parameter_space by2 =
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m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MAX_END);
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// The right endpoint is valid.
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has_right_pt = true;
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right_pt = m_geom_traits->construct_max_vertex_2_object() (cv);
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right_on_boundary = (bx2 != ARR_INTERIOR) || (by2 != ARR_INTERIOR);
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}
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else {
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// The right end of the curve lies at infinity.
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has_right_pt = false;
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right_on_boundary = true;
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}
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return;
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}
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/*!
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* Initialize the zone-computation process with a given curve and an object
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* that wraps the location of the curve's left end.
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* \param _cv The query curve.
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* \param _obj An object that represents the location of the left end
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* of the curve.
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*/
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void init_with_hint (const X_monotone_curve_2& _cv, const Object& _obj);
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/*!
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* Compute the zone of the given curve and issue the apporpriate
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* notifications for the visitor.
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*/
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void compute_zone ();
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private:
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/*!
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* Find a face containing the query curve cv around the given vertex.
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* In case an overlap occurs, sets intersect_he to be the overlapping edge.
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* \param v The query vertex.
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* \param he Output: The predecessor of cv around the vertex.
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* \return (true) if cv overlaps with the curve associated with he;
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* (false) if there is no overlap.
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*/
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bool _find_prev_around_vertex (Vertex_handle v, Halfedge_handle& he);
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/*!
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* Direct the halfedge for the location of the given subcurve around a split
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* point that occurs in the interior of a given edge, when the subcurve lies
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* to the right of the split point.
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* In case of overlaps, it sets also found_overlap and intersect_he.
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* \param cv_ins The curve to be inserted, whose left endpoint coincides
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* with the edge to be split.
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* \param cv_left_pt The left endpoint of cv_ins.
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* \param query_he The edge that intersects cv_ins.
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* \pre The left endpoint of cv_ins lies in the interior of the curve
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* associated with query_he.
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* \return The halfedge whose incident face contains cv_ins
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* (either query_he or its twin).
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*/
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Halfedge_handle
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_direct_intersecting_edge_to_right(const X_monotone_curve_2& cv_ins,
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const Point_2& cv_left_pt,
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Halfedge_handle query_he);
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/*!
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* Direct the halfedge for the location of the given subcurve around a split
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* point that occurs in the interior of a given edge, when the subcurve lies
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* to the left of the split point.
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* \param cv_ins The curve to be inserted, whose right endpoint coincides
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* with the edge to be split.
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* \param query_he The edge that intersects cv_ins.
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* \pre The right endpoint of cv_ins lies in the interior of the curve
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* associated with query_he.
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* \return The halfedge whose incident face contains cv_ins
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* (either query_he or its twin).
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*/
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Halfedge_handle
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_direct_intersecting_edge_to_left(const X_monotone_curve_2& cv_ins,
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Halfedge_handle query_he);
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/*!
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* Get the next intersection of cv with the given halfedge.
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* \param he A handle to the halfedge.
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* \param skip_first_point Should we skip the first intersection point.
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* \param intersect_on_right_boundary Output: If an intersetion point is
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* computed, marks whether this
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* point coincides with the right
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* curve-end, which lies on the
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* surface boundary.
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* \return An object representing the next intersection: Intersect_point_2
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* in case of a simple intersection point, X_monotone_curve_2 in
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* case of an overlap, and an empty object if there is no
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* intersection.
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*/
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CGAL::Object _compute_next_intersection (Halfedge_handle he,
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bool skip_first_point,
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bool& intersect_on_right_boundary);
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/*!
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* Remove the next intersection of cv with the given halfedge from the map.
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* \param he A handle to the halfedge.
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* \pre The list of intersections with the curve of he has already been
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* computed, and it is not empty.
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*/
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void _remove_next_intersection (Halfedge_handle he);
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/*!
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* 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 <CGAL/Arrangement_2/Arrangement_zone_2_impl.h>
|
||
|
|
|
||
|
|
#include <CGAL/enable_warnings.h>
|
||
|
|
|
||
|
|
#endif
|