993 lines
30 KiB
C
993 lines
30 KiB
C
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// Copyright (c) 1997 INRIA Sophia-Antipolis (France).
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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) : Mariette Yvinec, Jean Daniel Boissonnat
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#ifndef CGAL_CONSTRAINED_DELAUNAY_TRIANGULATION_2_H
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#define CGAL_CONSTRAINED_DELAUNAY_TRIANGULATION_2_H
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#include <CGAL/license/Triangulation_2.h>
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#include <CGAL/triangulation_assertions.h>
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#include <CGAL/Constrained_triangulation_2.h>
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#include <CGAL/Triangulation_2/insert_constraints.h>
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#ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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#include <CGAL/Spatial_sort_traits_adapter_2.h>
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#include <CGAL/internal/info_check.h>
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#include <CGAL/is_iterator.h>
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#include <boost/iterator/zip_iterator.hpp>
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#include <boost/mpl/and.hpp>
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namespace CGAL {
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namespace internal{
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template <class T,bool has_info=is_iterator<T>::value>
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struct Get_iterator_value_type{
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struct type{};
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};
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template <class T>
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struct Get_iterator_value_type<T,true>{
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typedef typename std::iterator_traits<T>::value_type type;
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};
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} } //namespace CGAL::internal
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#endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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namespace CGAL {
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template <class Gt,
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class Tds_ = Default ,
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class Itag_ = Default>
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class Constrained_Delaunay_triangulation_2
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: public Constrained_triangulation_2<Gt, Tds_, Itag_>
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{
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public:
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typedef Constrained_triangulation_2<Gt,Tds_,Itag_> Ctr;
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typedef typename Ctr::Tds Tds;
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typedef typename Ctr::Itag Itag;
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typedef Constrained_Delaunay_triangulation_2<Gt,Tds_,Itag_> CDt;
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typedef typename Ctr::Geom_traits Geom_traits;
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typedef typename Ctr::Intersection_tag Intersection_tag;
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typedef typename Ctr::Constraint Constraint;
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typedef typename Ctr::Vertex_handle Vertex_handle;
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typedef typename Ctr::Face_handle Face_handle;
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typedef typename Ctr::Edge Edge;
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typedef typename Ctr::Finite_faces_iterator Finite_faces_iterator;
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typedef typename Ctr::Constrained_edges_iterator Constrained_edges_iterator;
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typedef typename Ctr::Face_circulator Face_circulator;
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typedef typename Ctr::size_type size_type;
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typedef typename Ctr::Locate_type Locate_type;
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typedef typename Ctr::List_edges List_edges;
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typedef typename Ctr::List_faces List_faces;
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typedef typename Ctr::List_vertices List_vertices;
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typedef typename Ctr::List_constraints List_constraints;
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typedef typename Ctr::Less_edge less_edge;
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typedef typename Ctr::Edge_set Edge_set;
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//Tag to distinguish Delaunay from regular triangulations
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typedef Tag_false Weighted_tag;
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// Tag to distinguish periodic triangulations from others
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typedef Tag_false Periodic_tag;
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#ifndef CGAL_CFG_USING_BASE_MEMBER_BUG_2
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using Ctr::geom_traits;
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using Ctr::number_of_vertices;
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using Ctr::finite_faces_begin;
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using Ctr::finite_faces_end;
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using Ctr::dimension;
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using Ctr::cw;
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using Ctr::ccw;
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using Ctr::infinite_vertex;
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using Ctr::side_of_oriented_circle;
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using Ctr::is_infinite;
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using Ctr::collinear_between;
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using Ctr::are_there_incident_constraints;
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using Ctr::make_hole;
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// The next using statement makes trouble for VC++ with the version
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// of the method that is templated with PointIterator
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// VC++ cannot disambiguate between this method and the method of the base class
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// using Ctr::insert_constraint;
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using Ctr::locate;
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using Ctr::test_dim_down;
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using Ctr::fill_hole_delaunay;
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using Ctr::update_constraints;
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using Ctr::delete_vertex;
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using Ctr::push_back;
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#endif
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typedef typename Geom_traits::Point_2 Point;
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Constrained_Delaunay_triangulation_2(const Geom_traits& gt=Geom_traits())
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: Ctr(gt) { }
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Constrained_Delaunay_triangulation_2(const CDt& cdt)
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: Ctr(cdt) {}
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Constrained_Delaunay_triangulation_2(const List_constraints& lc,
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const Geom_traits& gt=Geom_traits())
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: Ctr(gt)
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{
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insert_constraints(lc.begin(), lc.end());
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CGAL_triangulation_postcondition( is_valid() );
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}
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template<class InputIterator>
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Constrained_Delaunay_triangulation_2(InputIterator it,
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InputIterator last,
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const Geom_traits& gt=Geom_traits() )
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: Ctr(gt)
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{
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insert_constraints(it, last);
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CGAL_triangulation_postcondition( is_valid() );
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}
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virtual ~Constrained_Delaunay_triangulation_2() {}
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// FLIPS
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bool is_flipable(Face_handle f, int i, bool perturb = true) const;
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void flip(Face_handle& f, int i);
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void flip_around(Vertex_handle va);
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void flip_around(List_vertices & new_vertices);
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#ifndef CGAL_CDT2_USE_RECURSIVE_PROPAGATING_FLIP
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void non_recursive_propagating_flip(Face_handle f,int i);
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void propagating_flip(Face_handle f,int i, int depth=0);
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#else
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void propagating_flip(Face_handle f,int i);
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#endif
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void propagating_flip(List_edges & edges);
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// CONFLICTS
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bool test_conflict(Face_handle fh, const Point& p) const; //deprecated
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bool test_conflict(const Point& p, Face_handle fh) const;
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void find_conflicts(const Point& p, std::list<Edge>& le, //deprecated
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Face_handle hint= Face_handle()) const;
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// //template member functions, declared and defined at the end
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// template <class OutputItFaces, class OutputItBoundaryEdges>
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// std::pair<OutputItFaces,OutputItBoundaryEdges>
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// get_conflicts_and_boundary(const Point &p,
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// OutputItFaces fit,
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// OutputItBoundaryEdges eit,
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// Face_handle start) const;
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// template <class OutputItFaces>
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// OutputItFaces
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// get_conflicts (const Point &p,
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// OutputItFaces fit,
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// Face_handle start ) const;
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// template <class OutputItBoundaryEdges>
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// OutputItBoundaryEdges
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// get_boundary_of_conflicts(const Point &p,
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// OutputItBoundaryEdges eit,
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// Face_handle start ) const;
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// INSERTION-REMOVAL
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Vertex_handle insert(const Point & a, Face_handle start = Face_handle());
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Vertex_handle insert(const Point& p,
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Locate_type lt,
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Face_handle loc, int li );
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Vertex_handle push_back(const Point& a);
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// template < class InputIterator >
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// std::ptrdiff_t insert(InputIterator first, InputIterator last);
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void remove(Vertex_handle v);
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void remove_incident_constraints(Vertex_handle v);
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void remove_constrained_edge(Face_handle f, int i);
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// template <class OutputItFaces>
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// OutputItFaces
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// remove_constrained_edge(Face_handle f, int i, OutputItFaces out)
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//for backward compatibility
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void insert(Point a, Point b) { insert_constraint(a, b);}
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void insert(Vertex_handle va, Vertex_handle vb) {insert_constraint(va,vb);}
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void insert_constraint(Vertex_handle va, Vertex_handle vb)
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{
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((Ctr*)this)->insert_constraint(va,vb);
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}
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void
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insert_constraint(const Point& a, const Point& b)
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{
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((Ctr*)this)->insert_constraint(a,b);
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}
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template <class PointIterator>
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void insert_constraint(PointIterator first, PointIterator last, bool close=false)
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{
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if(first == last){
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return;
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}
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const Point& p0 = *first;
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Point p = p0;
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Vertex_handle v0 = insert(p0), v(v0), w(v0);
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++first;
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for(; first!=last; ++first){
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const Point& q = *first;
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if(p != q){
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w = insert(q);
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insert_constraint(v,w);
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v = w;
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p = q;
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}
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}
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if(close && (p != p0)){
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insert(w,v0);
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}
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}
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void remove_constraint(Face_handle f, int i){remove_constrained_edge(f,i);}
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// CHECK
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bool is_valid(bool verbose = false, int level = 0) const;
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protected:
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virtual Vertex_handle virtual_insert(const Point & a,
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Face_handle start = Face_handle());
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virtual Vertex_handle virtual_insert(const Point& a,
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Locate_type lt,
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Face_handle loc,
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int li );
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//Vertex_handle special_insert_in_edge(const Point & a, Face_handle f, int i);
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void remove_2D(Vertex_handle v );
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virtual void triangulate_hole(List_faces& intersected_faces,
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List_edges& conflict_boundary_ab,
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List_edges& conflict_boundary_ba);
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public:
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// MESHING
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// suppressed meshing functions from here
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//template member functions
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public:
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template < class InputIterator >
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#ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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std::ptrdiff_t
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insert( InputIterator first, InputIterator last,
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typename boost::enable_if<
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boost::is_convertible<
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typename internal::Get_iterator_value_type< InputIterator >::type,
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Point
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>
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>::type* = NULL
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)
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#else
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#if defined(_MSC_VER)
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std::ptrdiff_t insert(InputIterator first, InputIterator last, int i = 0)
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#else
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std::ptrdiff_t insert(InputIterator first, InputIterator last)
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#endif
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#endif
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{
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size_type n = number_of_vertices();
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std::vector<Point> points (first, last);
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spatial_sort (points.begin(), points.end(), geom_traits());
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Face_handle f;
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for (typename std::vector<Point>::const_iterator p = points.begin(), end = points.end();
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p != end; ++p)
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f = insert (*p, f)->face();
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return number_of_vertices() - n;
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}
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#ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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private:
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//top stands for tuple-or-pair
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template <class Info>
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const Point& top_get_first(const std::pair<Point,Info>& pair) const { return pair.first; }
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template <class Info>
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const Info& top_get_second(const std::pair<Point,Info>& pair) const { return pair.second; }
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template <class Info>
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const Point& top_get_first(const boost::tuple<Point,Info>& tuple) const { return boost::get<0>(tuple); }
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template <class Info>
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const Info& top_get_second(const boost::tuple<Point,Info>& tuple) const { return boost::get<1>(tuple); }
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template <class Tuple_or_pair,class InputIterator>
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std::ptrdiff_t insert_with_info(InputIterator first,InputIterator last)
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{
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size_type n = this->number_of_vertices();
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std::vector<std::size_t> indices;
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std::vector<Point> points;
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std::vector<typename Tds::Vertex::Info> infos;
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std::size_t index=0;
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for (InputIterator it=first;it!=last;++it){
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Tuple_or_pair value=*it;
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points.push_back( top_get_first(value) );
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infos.push_back ( top_get_second(value) );
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indices.push_back(index++);
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}
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typedef typename Pointer_property_map<Point>::type Pmap;
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typedef Spatial_sort_traits_adapter_2<Geom_traits,Pmap> Search_traits;
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spatial_sort(indices.begin(),
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indices.end(),
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Search_traits(make_property_map(points),geom_traits()));
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Vertex_handle v_hint;
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Face_handle hint;
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for (typename std::vector<std::size_t>::const_iterator
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it = indices.begin(), end = indices.end();
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it != end; ++it){
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v_hint = insert(points[*it], hint);
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if (v_hint!=Vertex_handle()){
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v_hint->info()=infos[*it];
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hint=v_hint->face();
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}
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}
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return this->number_of_vertices() - n;
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}
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public:
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template < class InputIterator >
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std::ptrdiff_t
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insert( InputIterator first,
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InputIterator last,
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typename boost::enable_if<
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boost::is_convertible<
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typename internal::Get_iterator_value_type< InputIterator >::type,
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|
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std::pair<Point,typename internal::Info_check<typename Tds::Vertex>::type>
|
||
|
|
>
|
||
|
|
>::type* =NULL
|
||
|
|
)
|
||
|
|
{
|
||
|
|
return insert_with_info< std::pair<Point,typename internal::Info_check<typename Tds::Vertex>::type> >(first,last);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class InputIterator_1,class InputIterator_2>
|
||
|
|
std::ptrdiff_t
|
||
|
|
insert( boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > first,
|
||
|
|
boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > last,
|
||
|
|
typename boost::enable_if<
|
||
|
|
boost::mpl::and_<
|
||
|
|
boost::is_convertible< typename std::iterator_traits<InputIterator_1>::value_type, Point >,
|
||
|
|
boost::is_convertible< typename std::iterator_traits<InputIterator_2>::value_type, typename internal::Info_check<typename Tds::Vertex>::type >
|
||
|
|
>
|
||
|
|
>::type* =NULL
|
||
|
|
)
|
||
|
|
{
|
||
|
|
return insert_with_info< boost::tuple<Point,typename internal::Info_check<typename Tds::Vertex>::type> >(first,last);
|
||
|
|
}
|
||
|
|
#endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
|
||
|
|
|
||
|
|
|
||
|
|
template <class PointIterator, class IndicesIterator>
|
||
|
|
std::size_t insert_constraints(PointIterator points_first,
|
||
|
|
PointIterator points_beyond,
|
||
|
|
IndicesIterator indices_first,
|
||
|
|
IndicesIterator indices_beyond)
|
||
|
|
{
|
||
|
|
std::vector<Point> points(points_first, points_beyond);
|
||
|
|
return internal::insert_constraints(*this,points, indices_first, indices_beyond);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class ConstraintIterator>
|
||
|
|
std::size_t insert_constraints(ConstraintIterator first,
|
||
|
|
ConstraintIterator beyond)
|
||
|
|
{
|
||
|
|
return internal::insert_constraints(*this,first,beyond);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
||
|
|
get_conflicts_and_boundary(const Point &p,
|
||
|
|
OutputItFaces fit,
|
||
|
|
OutputItBoundaryEdges eit,
|
||
|
|
Face_handle start = Face_handle()) const {
|
||
|
|
CGAL_triangulation_precondition( dimension() == 2);
|
||
|
|
int li;
|
||
|
|
Locate_type lt;
|
||
|
|
Face_handle fh = locate(p,lt,li, start);
|
||
|
|
switch(lt) {
|
||
|
|
case Ctr::OUTSIDE_AFFINE_HULL:
|
||
|
|
case Ctr::VERTEX:
|
||
|
|
return std::make_pair(fit,eit);
|
||
|
|
case Ctr::FACE:
|
||
|
|
case Ctr::EDGE:
|
||
|
|
case Ctr::OUTSIDE_CONVEX_HULL:
|
||
|
|
*fit++ = fh; //put fh in OutputItFaces
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
||
|
|
pit = std::make_pair(fit,eit);
|
||
|
|
pit = propagate_conflicts(p,fh,0,pit);
|
||
|
|
pit = propagate_conflicts(p,fh,1,pit);
|
||
|
|
pit = propagate_conflicts(p,fh,2,pit);
|
||
|
|
return pit;
|
||
|
|
}
|
||
|
|
CGAL_triangulation_assertion(false);
|
||
|
|
return std::make_pair(fit,eit);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class OutputItFaces>
|
||
|
|
OutputItFaces
|
||
|
|
get_conflicts (const Point &p,
|
||
|
|
OutputItFaces fit,
|
||
|
|
Face_handle start= Face_handle()) const {
|
||
|
|
std::pair<OutputItFaces,Emptyset_iterator> pp =
|
||
|
|
get_conflicts_and_boundary(p,fit,Emptyset_iterator(),start);
|
||
|
|
return pp.first;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class OutputItBoundaryEdges>
|
||
|
|
OutputItBoundaryEdges
|
||
|
|
get_boundary_of_conflicts(const Point &p,
|
||
|
|
OutputItBoundaryEdges eit,
|
||
|
|
Face_handle start= Face_handle()) const {
|
||
|
|
std::pair<Emptyset_iterator, OutputItBoundaryEdges> pp =
|
||
|
|
get_conflicts_and_boundary(p,Emptyset_iterator(),eit,start);
|
||
|
|
return pp.second;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
public:
|
||
|
|
// made public for the need of Mesh_2
|
||
|
|
// but not documented
|
||
|
|
#ifdef CGAL_CDT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
||
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
||
|
|
propagate_conflicts (const Point &p,
|
||
|
|
Face_handle fh,
|
||
|
|
int i,
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges> pit) const
|
||
|
|
{
|
||
|
|
Face_handle fn = fh->neighbor(i);
|
||
|
|
|
||
|
|
if ( fh->is_constrained(i) || ! test_conflict(p,fn)) {
|
||
|
|
*(pit.second)++ = Edge(fn, fn->index(fh));
|
||
|
|
} else {
|
||
|
|
*(pit.first)++ = fn;
|
||
|
|
int j = fn->index(fh);
|
||
|
|
pit = propagate_conflicts(p,fn,ccw(j),pit);
|
||
|
|
pit = propagate_conflicts(p,fn,cw(j), pit);
|
||
|
|
}
|
||
|
|
return pit;
|
||
|
|
}
|
||
|
|
#else // NO CGAL_CDT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
||
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
||
|
|
non_recursive_propagate_conflicts (const Point &p,
|
||
|
|
Face_handle fh,
|
||
|
|
int i,
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges> pit) const
|
||
|
|
{
|
||
|
|
std::stack<std::pair<Face_handle, int> > stack;
|
||
|
|
stack.push(std::make_pair(fh, i));
|
||
|
|
while(!stack.empty()) {
|
||
|
|
const Face_handle fh = stack.top().first;
|
||
|
|
const int i = stack.top().second;
|
||
|
|
stack.pop();
|
||
|
|
const Face_handle fn = fh->neighbor(i);
|
||
|
|
if ( fh->is_constrained(i) || ! test_conflict(p,fn)) {
|
||
|
|
*(pit.second)++ = Edge(fn, fn->index(fh));
|
||
|
|
} else {
|
||
|
|
*(pit.first)++ = fn;
|
||
|
|
int j = fn->index(fh);
|
||
|
|
stack.push(std::make_pair(fn, cw(j)));
|
||
|
|
stack.push(std::make_pair(fn,ccw(j)));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return pit;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
||
|
|
propagate_conflicts (const Point &p,
|
||
|
|
Face_handle fh,
|
||
|
|
int i,
|
||
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges> pit,
|
||
|
|
int depth=0) const
|
||
|
|
{
|
||
|
|
if ( depth==100) return non_recursive_propagate_conflicts(p,fh,i,pit);
|
||
|
|
Face_handle fn = fh->neighbor(i);
|
||
|
|
|
||
|
|
if ( fh->is_constrained(i) || ! test_conflict(p,fn)) {
|
||
|
|
*(pit.second)++ = Edge(fn, fn->index(fh));
|
||
|
|
} else {
|
||
|
|
*(pit.first)++ = fn;
|
||
|
|
int j = fn->index(fh);
|
||
|
|
pit = propagate_conflicts(p,fn,ccw(j),pit,depth+1);
|
||
|
|
pit = propagate_conflicts(p,fn,cw(j), pit,depth+1);
|
||
|
|
}
|
||
|
|
return pit;
|
||
|
|
}
|
||
|
|
#endif // NO CGAL_CDT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
public:
|
||
|
|
template <class OutputItFaces>
|
||
|
|
OutputItFaces
|
||
|
|
propagating_flip(List_edges & edges,
|
||
|
|
OutputItFaces out = Emptyset_iterator()) {
|
||
|
|
// makes the triangulation Delaunay by flipping
|
||
|
|
// List edges contains an initial list of edges to be flipped
|
||
|
|
// Precondition : the output triangulation is Delaunay if the list
|
||
|
|
// edges contains all edges of the input triangulation that need to be
|
||
|
|
// flipped (plus possibly others)
|
||
|
|
int i, ii, indf, indn;
|
||
|
|
Face_handle ni, f,ff;
|
||
|
|
Edge ei,eni;
|
||
|
|
typename Ctr::Edge_set edge_set;
|
||
|
|
typename Ctr::Less_edge less_edge;
|
||
|
|
Edge e[4];
|
||
|
|
typename List_edges::iterator itedge=edges.begin();
|
||
|
|
|
||
|
|
// initialization of the set of edges to be flip
|
||
|
|
while (itedge != edges.end()) {
|
||
|
|
f=(*itedge).first;
|
||
|
|
i=(*itedge).second;
|
||
|
|
if (is_flipable(f,i)) {
|
||
|
|
eni=Edge(f->neighbor(i),this->mirror_index(f,i));
|
||
|
|
if (less_edge(*itedge,eni)) edge_set.insert(*itedge);
|
||
|
|
else edge_set.insert(eni);
|
||
|
|
}
|
||
|
|
++itedge;
|
||
|
|
}
|
||
|
|
|
||
|
|
// flip edges and updates the set of edges to be flipped
|
||
|
|
while (!(edge_set.empty())) {
|
||
|
|
f=(*(edge_set.begin())).first;
|
||
|
|
indf=(*(edge_set.begin())).second;
|
||
|
|
|
||
|
|
// erase from edge_set the 4 edges of the wing of the edge to be
|
||
|
|
// flipped (edge_set.begin) , i.e. the edges of the faces f and
|
||
|
|
// f->neighbor(indf) that are distinct from the edge to be flipped
|
||
|
|
|
||
|
|
ni = f->neighbor(indf);
|
||
|
|
indn=this->mirror_index(f,indf);
|
||
|
|
ei= Edge(f,indf);
|
||
|
|
edge_set.erase(ei);
|
||
|
|
e[0]= Edge(f,cw(indf));
|
||
|
|
e[1]= Edge(f,ccw(indf));
|
||
|
|
e[2]= Edge(ni,cw(indn));
|
||
|
|
e[3]= Edge(ni,ccw(indn));
|
||
|
|
|
||
|
|
for(i=0;i<4;i++) {
|
||
|
|
ff=e[i].first;
|
||
|
|
ii=e[i].second;
|
||
|
|
eni=Edge(ff->neighbor(ii),this->mirror_index(ff,ii));
|
||
|
|
if (less_edge(e[i],eni)) {edge_set.erase(e[i]);}
|
||
|
|
else { edge_set.erase(eni);}
|
||
|
|
}
|
||
|
|
|
||
|
|
// here is the flip
|
||
|
|
*out++ = f;
|
||
|
|
*out++ = f->neighbor(indf);
|
||
|
|
flip(f, indf);
|
||
|
|
|
||
|
|
|
||
|
|
//insert in edge_set the 4 edges of the wing of the edge that
|
||
|
|
//have been flipped
|
||
|
|
e[0]= Edge(f,indf);
|
||
|
|
e[1]= Edge(f,cw(indf));
|
||
|
|
e[2]= Edge(ni,indn);
|
||
|
|
e[3]= Edge(ni,cw(indn));
|
||
|
|
|
||
|
|
for(i=0;i<4;i++) {
|
||
|
|
ff=e[i].first;
|
||
|
|
ii=e[i].second;
|
||
|
|
if (is_flipable(ff,ii)) {
|
||
|
|
eni=Edge(ff->neighbor(ii),this->mirror_index(ff,ii));
|
||
|
|
if (less_edge(e[i],eni)) {
|
||
|
|
edge_set.insert(e[i]);}
|
||
|
|
else {
|
||
|
|
edge_set.insert(eni);}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class OutputItFaces>
|
||
|
|
OutputItFaces
|
||
|
|
remove_constrained_edge(Face_handle f, int i, OutputItFaces out) {
|
||
|
|
Ctr::remove_constrained_edge(f,i);
|
||
|
|
if(dimension() == 2) {
|
||
|
|
List_edges le;
|
||
|
|
le.push_back(Edge(f,i));
|
||
|
|
propagating_flip(le,out);
|
||
|
|
}
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
bool
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
is_flipable(Face_handle f, int i, bool perturb /* = true */) const
|
||
|
|
// determines if edge (f,i) can be flipped
|
||
|
|
{
|
||
|
|
Face_handle ni = f->neighbor(i);
|
||
|
|
if (is_infinite(f) || is_infinite(ni)) return false;
|
||
|
|
if (f->is_constrained(i)) return false;
|
||
|
|
return (side_of_oriented_circle(ni, f->vertex(i)->point(), perturb)
|
||
|
|
== ON_POSITIVE_SIDE);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
flip (Face_handle& f, int i)
|
||
|
|
{
|
||
|
|
Face_handle g = f->neighbor(i);
|
||
|
|
int j = this->mirror_index(f,i);
|
||
|
|
|
||
|
|
// save wings neighbors to be able to restore contraint status
|
||
|
|
Face_handle f1 = f->neighbor(cw(i));
|
||
|
|
int i1 = this->mirror_index(f,cw(i));
|
||
|
|
Face_handle f2 = f->neighbor(ccw(i));
|
||
|
|
int i2 = this->mirror_index(f,ccw(i));
|
||
|
|
Face_handle f3 = g->neighbor(cw(j));
|
||
|
|
int i3 = this->mirror_index(g,cw(j));
|
||
|
|
Face_handle f4 = g->neighbor(ccw(j));
|
||
|
|
int i4 = this->mirror_index(g,ccw(j));
|
||
|
|
|
||
|
|
// The following precondition prevents the test suit
|
||
|
|
// of triangulation to work on constrained Delaunay triangulation
|
||
|
|
//CGAL_triangulation_precondition(is_flipable(f,i));
|
||
|
|
this->_tds.flip(f, i);
|
||
|
|
|
||
|
|
// restore constraint status
|
||
|
|
f->set_constraint(f->index(g), false);
|
||
|
|
g->set_constraint(g->index(f), false);
|
||
|
|
f1->neighbor(i1)->set_constraint(this->mirror_index(f1,i1),
|
||
|
|
f1->is_constrained(i1));
|
||
|
|
f2->neighbor(i2)->set_constraint(this->mirror_index(f2,i2),
|
||
|
|
f2->is_constrained(i2));
|
||
|
|
f3->neighbor(i3)->set_constraint(this->mirror_index(f3,i3),
|
||
|
|
f3->is_constrained(i3));
|
||
|
|
f4->neighbor(i4)->set_constraint(this->mirror_index(f4,i4),
|
||
|
|
f4->is_constrained(i4));
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
flip_around(Vertex_handle va)
|
||
|
|
// makes the triangles incident to vertex va Delaunay using flips
|
||
|
|
{
|
||
|
|
if (dimension() <= 1) return;
|
||
|
|
Face_handle f=va->face();
|
||
|
|
Face_handle next;
|
||
|
|
Face_handle start(f);
|
||
|
|
int i;
|
||
|
|
do {
|
||
|
|
i = f->index(va); // FRAGILE : DIM 1
|
||
|
|
next = f->neighbor(ccw(i)); // turns ccw around a
|
||
|
|
propagating_flip(f,i);
|
||
|
|
f=next;
|
||
|
|
} while(next != start);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
flip_around(List_vertices& new_vertices)
|
||
|
|
{
|
||
|
|
typename List_vertices::iterator itv=new_vertices.begin();
|
||
|
|
for( ; itv != new_vertices.end(); itv++) {
|
||
|
|
flip_around(*itv);
|
||
|
|
}
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
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#ifndef CGAL_CDT2_USE_RECURSIVE_PROPAGATING_FLIP
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template <class Gt, class Tds, class Itag >
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void
|
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Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
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non_recursive_propagating_flip(Face_handle f , int i)
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{
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std::stack<Edge> edges;
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const Vertex_handle& vp = f->vertex(i);
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edges.push(Edge(f,i));
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while(! edges.empty()){
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const Edge& e = edges.top();
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f = e.first;
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i = e.second;
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Face_handle ni = f->neighbor(i);
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flip(f,i);
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if ( !is_flipable(f,i) ) edges.pop();
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i = ni->index(vp);
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if ( is_flipable(ni,i) ) edges.push( Edge(ni,i) );
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}
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}
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template <class Gt, class Tds, class Itag >
|
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|
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void
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Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
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propagating_flip(Face_handle f,int i, int depth)
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{
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if (!is_flipable(f,i)) return;
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#ifdef CGAL_CDT2_IMMEDIATELY_NON_RECURSIVE_PROPAGATING_FLIP
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non_recursive_propagating_flip(f,i);
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#else
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int max_depth = 100;
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if(depth==max_depth){
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non_recursive_propagating_flip(f,i);
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return;
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}
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Face_handle ni = f->neighbor(i);
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flip(f, i); // flip for constrained triangulations
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propagating_flip(f,i, depth+1);
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i = ni->index(f->vertex(i));
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propagating_flip(ni,i, depth+1);
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#endif
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}
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#else
|
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template < class Gt, class Tds, class Itag >
|
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|
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void
|
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Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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propagating_flip(Face_handle f,int i)
|
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|
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// similar to the corresponding function in Delaunay_triangulation_2.h
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{
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if (!is_flipable(f,i)) return;
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Face_handle ni = f->neighbor(i);
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flip(f, i); // flip for constrained triangulations
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propagating_flip(f,i);
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i = ni->index(f->vertex(i));
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propagating_flip(ni,i);
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}
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#endif
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|
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template < class Gt, class Tds, class Itag >
|
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|
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void
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|
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Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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|
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propagating_flip(List_edges & edges) {
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propagating_flip(edges,Emptyset_iterator());
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}
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|
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|
|
|
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|
|
template < class Gt, class Tds, class Itag >
|
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|
|
inline bool
|
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|
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Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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|
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test_conflict(const Point& p, Face_handle fh) const
|
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// true if point P lies inside the circle circumscribing face fh
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|
|
{
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|
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// return true if P is inside the circumcircle of fh
|
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|
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// if fh is infinite, return true when p is in the positive
|
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|
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// halfspace or on the boundary and in the finite edge of fh
|
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|
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Oriented_side os = side_of_oriented_circle(fh,p,true);
|
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|
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if (os == ON_POSITIVE_SIDE) return true;
|
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|
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|
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|
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if (os == ON_ORIENTED_BOUNDARY && is_infinite(fh)) {
|
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|
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int i = fh->index(infinite_vertex());
|
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|
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return collinear_between(fh->vertex(cw(i))->point(), p,
|
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|
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fh->vertex(ccw(i))->point() );
|
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|
|
}
|
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|
|
|
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|
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return false;
|
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|
|
}
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|
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|
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|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline bool
|
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|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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|
|
test_conflict(Face_handle fh, const Point& p) const
|
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|
|
// true if point P lies inside the circle circumscribing face fh
|
||
|
|
{
|
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|
|
return test_conflict(p,fh);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
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|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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|
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find_conflicts(const Point& p, std::list<Edge>& le, Face_handle hint) const
|
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|
|
{
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||
|
|
// sets in le the counterclocwise list of the edges of the boundary of the
|
||
|
|
// union of the faces in conflict with p
|
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|
|
// an edge is represented by the incident face that is not in conflict with p
|
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|
|
get_boundary_of_conflicts(p, std::back_inserter(le), hint);
|
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}
|
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|
|
|
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|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline
|
||
|
|
typename Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
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|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
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|
|
virtual_insert(const Point & a, Face_handle start)
|
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|
|
// virtual version of the insertion
|
||
|
|
{
|
||
|
|
return insert(a,start);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline
|
||
|
|
typename Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
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|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
virtual_insert(const Point& a,
|
||
|
|
Locate_type lt,
|
||
|
|
Face_handle loc,
|
||
|
|
int li )
|
||
|
|
// virtual version of insert
|
||
|
|
{
|
||
|
|
return insert(a,lt,loc,li);
|
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|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline
|
||
|
|
typename Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
insert(const Point & a, Face_handle start)
|
||
|
|
// inserts a in the triangulation
|
||
|
|
// constrained edges are updated
|
||
|
|
// Delaunay property is restored
|
||
|
|
{
|
||
|
|
Vertex_handle va= Ctr::insert(a, start);
|
||
|
|
flip_around(va);
|
||
|
|
return va;
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
typename Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
insert(const Point& a, Locate_type lt, Face_handle loc, int li)
|
||
|
|
// insert a point p, whose localisation is known (lt, f, i)
|
||
|
|
// constrained edges are updated
|
||
|
|
// Delaunay property is restored
|
||
|
|
{
|
||
|
|
Vertex_handle va= Ctr::insert(a,lt,loc,li);
|
||
|
|
flip_around(va);
|
||
|
|
return va;
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline
|
||
|
|
typename Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
push_back(const Point &p)
|
||
|
|
{
|
||
|
|
return insert(p);
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
triangulate_hole(List_faces& intersected_faces,
|
||
|
|
List_edges& conflict_boundary_ab,
|
||
|
|
List_edges& conflict_boundary_ba)
|
||
|
|
{
|
||
|
|
List_edges new_edges;
|
||
|
|
Ctr::triangulate_hole(intersected_faces,
|
||
|
|
conflict_boundary_ab,
|
||
|
|
conflict_boundary_ba,
|
||
|
|
new_edges);
|
||
|
|
propagating_flip(new_edges);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
inline void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
remove(Vertex_handle v)
|
||
|
|
// remove a vertex and updates the constrained edges of the new faces
|
||
|
|
// precondition : there is no incident constraints
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition( v != Vertex_handle() );
|
||
|
|
CGAL_triangulation_precondition( ! is_infinite(v));
|
||
|
|
CGAL_triangulation_precondition( ! are_there_incident_constraints(v));
|
||
|
|
if (dimension() <= 1) Ctr::remove(v);
|
||
|
|
else remove_2D(v);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
// template < class Gt, class Tds, class Itag >
|
||
|
|
// typename
|
||
|
|
// Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::Vertex_handle
|
||
|
|
// Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
// special_insert_in_edge(const Point & a, Face_handle f, int i)
|
||
|
|
// // insert point p in edge(f,i)
|
||
|
|
// // bypass the precondition for point a to be in edge(f,i)
|
||
|
|
// // update constrained status
|
||
|
|
// // this member fonction is not robust with exact predicates
|
||
|
|
// // and approximate construction. Should be removed
|
||
|
|
// {
|
||
|
|
// Vertex_handle vh=Ctr::special_insert_in_edge(a,f,i);
|
||
|
|
// flip_around(vh);
|
||
|
|
// return vh;
|
||
|
|
// }
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
remove_2D(Vertex_handle v)
|
||
|
|
{
|
||
|
|
if (test_dim_down(v)) { this->_tds.remove_dim_down(v); }
|
||
|
|
else {
|
||
|
|
std::list<Edge> hole;
|
||
|
|
make_hole(v, hole);
|
||
|
|
std::list<Edge> shell=hole; //because hole will be emptied by fill_hole
|
||
|
|
fill_hole_delaunay(hole);
|
||
|
|
update_constraints(shell);
|
||
|
|
delete_vertex(v);
|
||
|
|
}
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
remove_incident_constraints(Vertex_handle v)
|
||
|
|
{
|
||
|
|
List_edges iconstraints;
|
||
|
|
if (are_there_incident_constraints(v,
|
||
|
|
std::back_inserter(iconstraints))) {
|
||
|
|
Ctr::remove_incident_constraints(v);
|
||
|
|
if (dimension()==2) propagating_flip(iconstraints);
|
||
|
|
}
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
void
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
remove_constrained_edge(Face_handle f, int i)
|
||
|
|
{
|
||
|
|
remove_constrained_edge(f,i,Emptyset_iterator());
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template < class Gt, class Tds, class Itag >
|
||
|
|
bool
|
||
|
|
Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>::
|
||
|
|
is_valid(bool verbose, int level) const
|
||
|
|
{
|
||
|
|
bool result = Ctr::is_valid(verbose, level);
|
||
|
|
CGAL_triangulation_assertion( result );
|
||
|
|
|
||
|
|
Finite_faces_iterator fit= finite_faces_begin();
|
||
|
|
for (; fit != finite_faces_end(); fit++) {
|
||
|
|
for(int i=0;i<3;i++) {
|
||
|
|
result = result && !is_flipable(fit,i, false);
|
||
|
|
CGAL_triangulation_assertion( result );
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
#endif // CGAL_CONSTRAINED_DELAUNAY_TRIANGULATION_2_H
|