2473 lines
84 KiB
C++
2473 lines
84 KiB
C++
// 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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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Triangulation_2/include/CGAL/Delaunay_triangulation_2.h $
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// $Id: Delaunay_triangulation_2.h d1a323c 2020-03-26T19:24:14+01:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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// Author(s) : Mariette Yvinec
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// : Olivier Devillers (remove)
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// : Pedro de Castro (displacement)
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#ifndef CGAL_DELAUNAY_TRIANGULATION_2_H
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#define CGAL_DELAUNAY_TRIANGULATION_2_H
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#include <CGAL/license/Triangulation_2.h>
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#include <CGAL/Triangulation_2.h>
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#include <CGAL/iterator.h>
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#include <CGAL/Object.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/tss.h>
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#include <boost/mpl/and.hpp>
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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 = Triangulation_data_structure_2 <
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Triangulation_vertex_base_2<Gt>,
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Triangulation_face_base_2<Gt> > >
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class Delaunay_triangulation_2
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: public Triangulation_2<Gt,Tds>
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{
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public:
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typedef Gt Geom_traits;
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typedef typename Geom_traits::Point_2 Point;
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typedef typename Geom_traits::Segment_2 Segment;
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typedef typename Geom_traits::Triangle_2 Triangle;
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typedef typename Geom_traits::Orientation_2 Orientation_2;
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typedef typename Geom_traits::Compare_x_2 Compare_x;
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typedef typename Geom_traits::Compare_y_2 Compare_y;
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typedef typename Geom_traits::Side_of_oriented_circle_2
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Side_of_oriented_circle;
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typedef Triangulation_2<Gt,Tds> Triangulation;
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typedef typename Triangulation::size_type size_type;
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typedef typename Triangulation::Locate_type Locate_type;
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typedef typename Triangulation::Face_handle Face_handle;
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typedef typename Triangulation::Vertex_handle Vertex_handle;
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typedef typename Triangulation::Edge Edge;
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typedef typename Triangulation::Edge_circulator Edge_circulator;
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typedef typename Triangulation::Face_circulator Face_circulator;
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typedef typename Triangulation::Vertex_circulator Vertex_circulator;
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typedef typename Triangulation::Finite_edges_iterator Finite_edges_iterator;
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typedef typename Triangulation::Finite_faces_iterator Finite_faces_iterator;
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typedef typename Triangulation::Finite_vertices_iterator
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Finite_vertices_iterator;
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typedef typename Triangulation::All_faces_iterator All_faces_iterator;
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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 Triangulation::side_of_oriented_circle;
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using Triangulation::circumcenter;
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using Triangulation::collinear_between;
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using Triangulation::test_dim_down;
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using Triangulation::make_hole;
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using Triangulation::fill_hole_delaunay;
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using Triangulation::delete_vertex;
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#endif
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Delaunay_triangulation_2(const Gt& gt = Gt())
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: Triangulation_2<Gt,Tds>(gt) {}
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Delaunay_triangulation_2(
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const Delaunay_triangulation_2<Gt,Tds> &tr)
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: Triangulation_2<Gt,Tds>(tr)
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{ CGAL_triangulation_postcondition(is_valid()); }
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Delaunay_triangulation_2(Delaunay_triangulation_2&&) = default;
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Delaunay_triangulation_2& operator=(const Delaunay_triangulation_2&) = default;
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Delaunay_triangulation_2& operator=(Delaunay_triangulation_2&&) = default;
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~Delaunay_triangulation_2() = default;
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template <class InputIterator>
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Delaunay_triangulation_2(InputIterator first, InputIterator last,
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const Gt& gt = Gt())
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: Triangulation_2<Gt,Tds>(gt)
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{
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insert(first,last);
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}
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// CHECK -QUERY
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bool is_valid(bool verbose = false, int level = 0) const;
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Vertex_handle
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nearest_vertex(const Point& p, Face_handle f= Face_handle()) const;
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bool does_conflict(const Point &p, Face_handle fh) const;// deprecated
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bool test_conflict(const Point &p, Face_handle fh) const;
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bool find_conflicts(const Point &p, //deprecated
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std::list<Face_handle>& conflicts,
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Face_handle start= 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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// DUAL
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Point dual (Face_handle f) const;
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Object dual(const Edge &e) const;
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Object dual(const Edge_circulator& ec) const;
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Object dual(const Finite_edges_iterator& ei) const;
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//INSERTION-REMOVAL
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Vertex_handle insert(const Point &p,
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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 &p);
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void remove(Vertex_handle v);
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// DISPLACEMENT
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void restore_Delaunay(Vertex_handle v);
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Vertex_handle move_if_no_collision(Vertex_handle v, const Point &p);
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Vertex_handle move(Vertex_handle v, const Point &p);
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protected: // some internal stuffs
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template <class OutputItFaces>
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Vertex_handle insert_and_give_new_faces(const Point &p,
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OutputItFaces fit,
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Face_handle start = Face_handle());
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template <class OutputItFaces>
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Vertex_handle insert_and_give_new_faces(const Point& p,
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Locate_type lt,
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Face_handle loc, int li,
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OutputItFaces fit);
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template <class OutputItFaces>
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Vertex_handle move_if_no_collision_and_give_new_faces(Vertex_handle v,
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const Point &p,
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OutputItFaces fit);
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template <class OutputItFaces>
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void remove_and_give_new_faces(Vertex_handle v,
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OutputItFaces fit);
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public:
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bool is_delaunay_after_displacement(Vertex_handle v,
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const Point &p) const;
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#ifndef CGAL_CFG_USING_BASE_MEMBER_BUG_2
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using Triangulation::cw;
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using Triangulation::ccw;
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using Triangulation::geom_traits;
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#endif
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private:
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#ifndef CGAL_DT2_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(const Face_handle& f, int i, int depth=0);
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#else
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void propagating_flip(const Face_handle& f,int i);
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#endif
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// auxilliary functions for remove
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void remove_degree_init(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i,int&d,int&maxd);
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void remove_degree_triangulate(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i,int d);
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void remove_degree_d(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i,int d);
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void remove_degree3(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree4(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree5(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree5_star(Vertex_handle &v,
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Face_handle &,Face_handle &,Face_handle &,
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Face_handle &,Face_handle &,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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Vertex_handle&,Vertex_handle&,
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int,int,int,
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int,int);
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void remove_degree6(Vertex_handle v, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree6_star (Vertex_handle &v,
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Face_handle &,Face_handle &,Face_handle &,
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Face_handle &,Face_handle &,Face_handle &,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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int,int,int,
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int,int,int);
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void remove_degree6_N (Vertex_handle &v,
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Face_handle &,Face_handle &,Face_handle &,
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Face_handle &,Face_handle &,Face_handle &,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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int,int,int,
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int,int,int);
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void remove_degree6_antiN (Vertex_handle &v,
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Face_handle &,Face_handle &,Face_handle &,
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Face_handle &,Face_handle &,Face_handle &,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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int,int,int,
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int,int,int);
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void remove_degree6_diamond(Vertex_handle &v,
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Face_handle &,Face_handle &,Face_handle &,
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Face_handle &,Face_handle &,Face_handle &,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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Vertex_handle&,Vertex_handle&,Vertex_handle&,
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int,int,int,
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int,int,int);
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void remove_degree7(Vertex_handle v,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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bool incircle(int x, int j, int, int l, std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i)
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{
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// k is supposed to be j+1 modulo degree, x is supposed to be finite
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//test if w[x] inside circle w[j]w[k]w[l] (f[j] has vertices w[j]w[k])
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// THE FOLLOWING LINE IS TO BE REMOVED. JUST THERE FOR STUPID PRECONDITION
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//if(geom_traits().orientation_2_object()(w[j]->point(),w[k]->point(),w[l]->point())!=POSITIVE) return true;
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f[j]->set_vertex(i[j], w[l]); // change vertex v for another one
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return (test_conflict(w[x]->point(), f[j]));
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}
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void rotate7(int j, std::vector<Vertex_handle> &w,
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std::vector<Face_handle> &f, std::vector<int> &i);
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void remove_degree7_star (Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree7_zigzag (Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree7_leftdelta (Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree7_rightdelta(Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree7_leftfan (Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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void remove_degree7_rightfan (Vertex_handle&,int,std::vector<Face_handle> &f,
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std::vector<Vertex_handle> &w, std::vector<int> &i);
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// end of auxilliary functions for remove
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Vertex_handle nearest_vertex_2D(const Point& p, Face_handle f) const;
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Vertex_handle nearest_vertex_1D(const Point& p) const;
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void look_nearest_neighbor(const Point& p,
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Face_handle f,
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int i,
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Vertex_handle& nn) const;
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public:
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template < class Stream>
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Stream& draw_dual(Stream & ps)
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{
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Finite_edges_iterator eit= this->finite_edges_begin();
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for (; eit != this->finite_edges_end(); ++eit) {
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Object o = dual(eit);
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typename Geom_traits::Line_2 l;
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typename Geom_traits::Ray_2 r;
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Segment s;
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if(CGAL::assign(s,o)) ps << s;
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if(CGAL::assign(r,o)) ps << r;
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if(CGAL::assign(l,o)) ps << l;
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}
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return ps;
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}
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#ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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template < class InputIterator >
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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 std::iterator_traits<InputIterator>::value_type,
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Point
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>
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>::type* = nullptr)
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#else
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template < class InputIterator >
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std::ptrdiff_t
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insert(InputIterator first, InputIterator last)
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#endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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{
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size_type n = this->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 this->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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using Triangulation::top_get_first;
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using Triangulation::top_get_second;
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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(), 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 std::iterator_traits<InputIterator>::value_type,
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std::pair<Point,typename internal::Info_check<typename Tds::Vertex>::type>
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> >::type* = nullptr)
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{
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return insert_with_info< std::pair<Point,typename internal::Info_check<typename Tds::Vertex>::type> >(first,last);
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}
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template <class InputIterator_1,class InputIterator_2>
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std::ptrdiff_t
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insert(boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > first,
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boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > last,
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typename boost::enable_if<
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boost::mpl::and_<
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boost::is_convertible< typename std::iterator_traits<InputIterator_1>::value_type, Point >,
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boost::is_convertible< typename std::iterator_traits<InputIterator_2>::value_type, typename internal::Info_check<typename Tds::Vertex>::type >
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>
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>::type* = nullptr)
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{
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return insert_with_info< boost::tuple<Point,typename internal::Info_check<typename Tds::Vertex>::type> >(first,last);
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}
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#endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
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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 = Face_handle()) const
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{
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CGAL_triangulation_precondition(this->dimension() == 2);
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int li;
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Locate_type lt;
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Face_handle fh = this->locate(p,lt,li, start);
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switch(lt) {
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case Triangulation::OUTSIDE_AFFINE_HULL:
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case Triangulation::VERTEX:
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return std::make_pair(fit,eit);
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case Triangulation::FACE:
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case Triangulation::EDGE:
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case Triangulation::OUTSIDE_CONVEX_HULL:
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*fit++ = fh; //put fh in OutputItFaces
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std::pair<OutputItFaces,OutputItBoundaryEdges> pit = std::make_pair(fit,eit);
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pit = propagate_conflicts(p,fh,0,pit);
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pit = propagate_conflicts(p,fh,1,pit);
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pit = propagate_conflicts(p,fh,2,pit);
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return pit;
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}
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CGAL_triangulation_assertion(false);
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return std::make_pair(fit,eit);
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}
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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= Face_handle()) const
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{
|
|
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;
|
|
}
|
|
|
|
private:
|
|
#ifdef CGAL_DT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
|
propagate_conflicts (const Point &p,
|
|
const Face_handle fh,
|
|
const int i,
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges> pit) const
|
|
{
|
|
Face_handle fn = fh->neighbor(i);
|
|
if(! 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_DT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
|
template <class OutputItFaces, class OutputItBoundaryEdges>
|
|
std::pair<OutputItFaces,OutputItBoundaryEdges>
|
|
non_recursive_propagate_conflicts(const Point &p,
|
|
const Face_handle fh,
|
|
const 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();
|
|
Face_handle fn = fh->neighbor(i);
|
|
if(! test_conflict(p,fn))
|
|
{
|
|
*(pit.second)++ = Edge(fn, fn->index(fh));
|
|
} else {
|
|
*(pit.first)++ = fn;
|
|
int j = fn->index(fh);
|
|
|
|
// In the non-recursive version, we walk via 'ccw(j)' first. Here, we are filling the stack
|
|
// and the order is thus the opposite (we want the top element of the stack to be 'ccw(j)')
|
|
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,
|
|
const Face_handle fh,
|
|
const 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(! 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_DT2_USE_RECURSIVE_PROPAGATE_CONFLICTS
|
|
|
|
protected:
|
|
void restore_edges(Vertex_handle v)
|
|
{
|
|
std::list<Edge> edges;
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
|
int degree = 0;
|
|
|
|
do {
|
|
if((++degree) > 3) break;
|
|
} while(++fc != done);
|
|
|
|
fc = this->incident_faces(v);
|
|
done = fc;
|
|
|
|
if(degree == 3) {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
} while(++fc != done);
|
|
} else {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
edges.push_back(Edge(fc, this->cw(i)));
|
|
} while(++fc != done);
|
|
}
|
|
|
|
while(!edges.empty()) {
|
|
const Edge &e = edges.front();
|
|
Face_handle f = e.first;
|
|
int i = e.second;
|
|
edges.pop_front();
|
|
if(this->is_infinite(f->vertex(i))) continue;
|
|
Face_handle fi = f->neighbor(i);
|
|
int mi = this->_tds.mirror_index(f, i);
|
|
Vertex_handle vm = this->_tds.mirror_vertex(f, i);
|
|
if(this->is_infinite(vm)) continue;
|
|
if(this->side_of_oriented_circle(f, vm->point(),true) == ON_POSITIVE_SIDE) {
|
|
this->_tds.flip(f, i);
|
|
edges.push_back(Edge(f, i));
|
|
edges.push_back(Edge(f, this->cw(i)));
|
|
edges.push_back(Edge(fi, this->cw(mi)));
|
|
edges.push_back(Edge(fi, mi));
|
|
}
|
|
}
|
|
}
|
|
|
|
void restore_edges(Vertex_handle v, std::set<Face_handle> &faces)
|
|
{
|
|
typedef std::list<Edge> Edges_list;
|
|
Edges_list edges;
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
|
int degree = 0;
|
|
|
|
do {
|
|
if((++degree) > 3) break;
|
|
} while(++fc != done);
|
|
|
|
fc = this->incident_faces(v);
|
|
done = fc;
|
|
|
|
if(degree == 3) {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
} while(++fc != done);
|
|
} else {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
edges.push_back(Edge(fc, this->cw(i)));
|
|
} while(++fc != done);
|
|
}
|
|
|
|
while(!edges.empty()) {
|
|
const Edge &e = edges.front();
|
|
Face_handle f = e.first;
|
|
int i = e.second;
|
|
edges.pop_front();
|
|
faces.insert(f);
|
|
if(this->is_infinite(f->vertex(i))) continue;
|
|
Face_handle fi = f->neighbor(i);
|
|
int mi = this->_tds.mirror_index(f, i);
|
|
Vertex_handle vm = this->_tds.mirror_vertex(f, i);
|
|
if(this->is_infinite(vm)) continue;
|
|
if(this->side_of_oriented_circle(f, vm->point()) == ON_POSITIVE_SIDE) {
|
|
this->_tds.flip(f, i);
|
|
edges.push_back(Edge(f, i));
|
|
edges.push_back(Edge(f, this->cw(i)));
|
|
edges.push_back(Edge(fi, this->cw(mi)));
|
|
edges.push_back(Edge(fi, mi));
|
|
}
|
|
}
|
|
}
|
|
};
|
|
|
|
template < class Gt, class Tds >
|
|
inline bool
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
test_conflict(const Point &p, Face_handle fh) const
|
|
{
|
|
// return true if P is inside the circumcircle of fh
|
|
// if fh is infinite, return true when p is in the positive
|
|
// halfspace or on the boundary and in the finite edge of fh
|
|
Oriented_side os = side_of_oriented_circle(fh,p,true);
|
|
if(os == ON_POSITIVE_SIDE)
|
|
return true;
|
|
|
|
if(os == ON_ORIENTED_BOUNDARY && this->is_infinite(fh)) {
|
|
int i = fh->index(this->infinite_vertex());
|
|
return collinear_between(fh->vertex(cw(i))->point(), p,
|
|
fh->vertex(ccw(i))->point());
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline bool
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
does_conflict(const Point &p, Face_handle fh) const
|
|
{
|
|
return test_conflict(p,fh);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline bool
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
find_conflicts(const Point &p,
|
|
std::list<Face_handle>& conflicts,
|
|
Face_handle start) const
|
|
{
|
|
get_conflicts(p, std::back_inserter(conflicts), start);
|
|
return (! conflicts.empty());
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
bool
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
is_valid(bool verbose, int level) const
|
|
{
|
|
bool result = Triangulation_2<Gt,Tds>::is_valid(verbose, level);
|
|
|
|
for(Finite_faces_iterator it = this->finite_faces_begin();
|
|
it != this->finite_faces_end(); it++) {
|
|
for(int i=0; i<3; i++) {
|
|
if(! this->is_infinite(this->mirror_vertex(it,i))) {
|
|
result = result && ON_POSITIVE_SIDE !=
|
|
side_of_oriented_circle(it, this->mirror_vertex(it,i)->point(), false);
|
|
}
|
|
CGAL_triangulation_assertion(result);
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
nearest_vertex(const Point &p, Face_handle f) const
|
|
{
|
|
switch (this->dimension()) {
|
|
case 0:
|
|
if(this->number_of_vertices() == 0) return Vertex_handle();
|
|
return this->finite_vertex();
|
|
//break;
|
|
case 1:
|
|
return nearest_vertex_1D(p);
|
|
//break;
|
|
case 2:
|
|
return nearest_vertex_2D(p,f);
|
|
//break;
|
|
}
|
|
return Vertex_handle();
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
nearest_vertex_2D(const Point& p, Face_handle f) const
|
|
{
|
|
CGAL_triangulation_precondition(this->dimension() == 2);
|
|
f = this->locate(p,f);
|
|
|
|
typename Geom_traits::Compare_distance_2
|
|
compare_distance = this->geom_traits().compare_distance_2_object();
|
|
Vertex_handle nn = !this->is_infinite(f->vertex(0)) ? f->vertex(0):f->vertex(1);
|
|
if(!this->is_infinite(f->vertex(1)) && compare_distance(p,
|
|
f->vertex(1)->point(),
|
|
nn->point()) == SMALLER)
|
|
nn = f->vertex(1);
|
|
if(!this->is_infinite(f->vertex(2)) && compare_distance(p,
|
|
f->vertex(2)->point(),
|
|
nn->point()) == SMALLER)
|
|
nn = f->vertex(2);
|
|
|
|
look_nearest_neighbor(p,f,0,nn);
|
|
look_nearest_neighbor(p,f,1,nn);
|
|
look_nearest_neighbor(p,f,2,nn);
|
|
return nn;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
nearest_vertex_1D(const Point& p) const
|
|
{
|
|
typename Geom_traits::Compare_distance_2
|
|
compare_distance = this->geom_traits().compare_distance_2_object();
|
|
Vertex_handle nn;
|
|
|
|
Finite_vertices_iterator vit=this->finite_vertices_begin();
|
|
nn = vit;
|
|
for (; vit != this->finite_vertices_end(); ++vit) {
|
|
if(compare_distance(p, vit->point(), nn->point()) == SMALLER)
|
|
nn = vit;
|
|
}
|
|
return nn;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
look_nearest_neighbor(const Point& p,
|
|
Face_handle f,
|
|
int i,
|
|
Vertex_handle& nn) const
|
|
{
|
|
Face_handle ni=f->neighbor(i);
|
|
if(ON_POSITIVE_SIDE != side_of_oriented_circle(ni,p,true))
|
|
return;
|
|
|
|
typename Geom_traits::Compare_distance_2
|
|
compare_distance = this->geom_traits().compare_distance_2_object();
|
|
i = ni->index(f);
|
|
if(!this->is_infinite(ni->vertex(i)) &&
|
|
compare_distance(p, ni->vertex(i)->point(), nn->point()) == SMALLER)
|
|
nn = ni->vertex(i);
|
|
|
|
// recursive exploration of triangles whose circumcircle contains p
|
|
look_nearest_neighbor(p, ni, ccw(i), nn);
|
|
look_nearest_neighbor(p, ni, cw(i), nn);
|
|
}
|
|
|
|
//DUALITY
|
|
template<class Gt, class Tds>
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Point
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
dual(Face_handle f) const
|
|
{
|
|
CGAL_triangulation_precondition(this->_tds.is_face(f));
|
|
CGAL_triangulation_precondition(this->dimension()==2);
|
|
return circumcenter(f);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
Object
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
dual(const Edge &e) const
|
|
{
|
|
CGAL_triangulation_precondition(this->_tds.is_edge(e.first,e.second));
|
|
|
|
typedef typename Geom_traits::Line_2 Line;
|
|
typedef typename Geom_traits::Ray_2 Ray;
|
|
|
|
CGAL_triangulation_precondition (!this->is_infinite(e));
|
|
if(this->dimension()== 1) {
|
|
const Point& p = (e.first)->vertex(cw(e.second))->point();
|
|
const Point& q = (e.first)->vertex(ccw(e.second))->point();
|
|
Line l = this->geom_traits().construct_bisector_2_object()(p,q);
|
|
return make_object(l);
|
|
}
|
|
|
|
// dimension==2
|
|
if((!this->is_infinite(e.first)) &&
|
|
(!this->is_infinite(e.first->neighbor(e.second)))) {
|
|
Segment s = this->geom_traits().construct_segment_2_object()
|
|
(dual(e.first),dual(e.first->neighbor(e.second)));
|
|
return make_object(s);
|
|
}
|
|
|
|
// one of the adjacent faces is infinite
|
|
Face_handle f; int i;
|
|
if(this->is_infinite(e.first)) {
|
|
f = e.first->neighbor(e.second); i=f->index(e.first);
|
|
}
|
|
else {
|
|
f = e.first; i=e.second;
|
|
}
|
|
|
|
const Point& p = f->vertex(cw(i))->point();
|
|
const Point& q = f->vertex(ccw(i))->point();
|
|
Line l = this->geom_traits().construct_bisector_2_object()(p,q);
|
|
Ray r = this->geom_traits().construct_ray_2_object()(dual(f), l);
|
|
return make_object(r);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline Object
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
dual(const Edge_circulator& ec) const
|
|
{
|
|
return dual(*ec);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline Object
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
dual(const Finite_edges_iterator& ei) const
|
|
{
|
|
return dual(*ei);
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////
|
|
// INSERT
|
|
|
|
template < class Gt, class Tds >
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
insert(const Point &p, Face_handle start)
|
|
{
|
|
Locate_type lt;
|
|
int li;
|
|
Face_handle loc = this->locate(p, lt, li, start);
|
|
return insert(p, lt, loc, li);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
push_back(const Point &p)
|
|
{
|
|
return insert(p);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
insert(const Point &p, Locate_type lt, Face_handle loc, int li)
|
|
{
|
|
Vertex_handle v = Triangulation_2<Gt,Tds>::insert(p,lt,loc,li);
|
|
restore_Delaunay(v);
|
|
return(v);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
template < class OutputItFaces >
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
insert_and_give_new_faces(const Point &p,
|
|
OutputItFaces oif,
|
|
Face_handle start)
|
|
{
|
|
Vertex_handle v = insert(p, start);
|
|
int dimension = this->dimension();
|
|
if(dimension == 2)
|
|
{
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
|
do {
|
|
*oif++ = fc;
|
|
} while(++fc != done);
|
|
}
|
|
else if(dimension == 1)
|
|
{
|
|
Face_handle c = v->face();
|
|
*oif++ = c;
|
|
*oif++ = c->neighbor((~(c->index(v)))&1);
|
|
}
|
|
else *oif++ = v->face(); // dimension == 0
|
|
return v;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
template < class OutputItFaces >
|
|
inline
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
insert_and_give_new_faces(const Point &p,
|
|
Locate_type lt,
|
|
Face_handle loc, int li,
|
|
OutputItFaces oif)
|
|
{
|
|
Vertex_handle v = insert(p, lt, loc, li);
|
|
int dimension = this->dimension();
|
|
if(dimension == 2)
|
|
{
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
|
do {
|
|
*oif++ = fc;
|
|
} while(++fc != done);
|
|
}
|
|
else if(dimension == 1)
|
|
{
|
|
Face_handle c = v->face();
|
|
*oif++ = c;
|
|
*oif++ = c->neighbor((~(c->index(v)))&1);
|
|
}
|
|
else *oif++ = v->face(); // dimension == 0
|
|
return v;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
restore_Delaunay(Vertex_handle v)
|
|
{
|
|
if(this->dimension() <= 1) return;
|
|
|
|
Face_handle f=v->face();
|
|
Face_handle next;
|
|
int i;
|
|
Face_handle start(f);
|
|
do {
|
|
i = f->index(v);
|
|
next = f->neighbor(ccw(i)); // turn ccw around v
|
|
propagating_flip(f,i);
|
|
f = next;
|
|
} while(next != start);
|
|
return;
|
|
}
|
|
|
|
#ifndef CGAL_DT2_USE_RECURSIVE_PROPAGATING_FLIP
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
non_recursive_propagating_flip(Face_handle f, int i)
|
|
{
|
|
std::stack<Edge> edges;
|
|
const Vertex_handle& vp = f->vertex(i);
|
|
const Point& p = vp->point();
|
|
edges.push(Edge(f,i));
|
|
|
|
while(! edges.empty()) {
|
|
const Edge& e = edges.top();
|
|
f = e.first;
|
|
i = e.second;
|
|
const Face_handle& n = f->neighbor(i);
|
|
|
|
if(ON_POSITIVE_SIDE != side_of_oriented_circle(n, p, true)) {
|
|
edges.pop();
|
|
continue;
|
|
}
|
|
|
|
this->flip(f, i);
|
|
// As we haven't popped it, we don't have to push it
|
|
edges.push(Edge(n,n->index(vp)));
|
|
}
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
propagating_flip(const Face_handle& f,int i, int depth)
|
|
{
|
|
#ifdef CGAL_DT2_IMMEDIATELY_NON_RECURSIVE_PROPAGATING_FLIP
|
|
non_recursive_propagating_flip(f,i);
|
|
#else
|
|
int max_depth = 100;
|
|
if(depth==max_depth) {
|
|
non_recursive_propagating_flip(f,i);
|
|
return;
|
|
}
|
|
Face_handle n = f->neighbor(i);
|
|
|
|
if(ON_POSITIVE_SIDE !=
|
|
side_of_oriented_circle(n, f->vertex(i)->point(), true)) {
|
|
return;
|
|
}
|
|
|
|
this->flip(f, i);
|
|
propagating_flip(f,i,depth+1);
|
|
i = n->index(f->vertex(i));
|
|
propagating_flip(n,i,depth+1);
|
|
#endif
|
|
}
|
|
#else
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
propagating_flip(const Face_handle& f,int i)
|
|
{
|
|
Face_handle n = f->neighbor(i);
|
|
|
|
if(ON_POSITIVE_SIDE != side_of_oriented_circle(n, f->vertex(i)->point(), true))
|
|
return;
|
|
|
|
this->flip(f, i);
|
|
propagating_flip(f,i);
|
|
i = n->index(f->vertex(i));
|
|
propagating_flip(n,i);
|
|
}
|
|
#endif
|
|
|
|
///////////////////////////////////////////////////////////////
|
|
// REMOVE see INRIA RResearch Report 7104
|
|
|
|
template < class Gt, class Tds >
|
|
template <class OutputItFaces>
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_and_give_new_faces(Vertex_handle v, OutputItFaces fit)
|
|
{
|
|
CGAL_triangulation_precondition(v != Vertex_handle());
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
|
|
if(this->number_of_vertices() == 1) this->remove_first(v);
|
|
else if(this->number_of_vertices() == 2) this->remove_second(v);
|
|
else if(this->dimension() == 1)
|
|
{
|
|
Point p = v->point();
|
|
Triangulation::remove(v);
|
|
*fit++ = this->locate(p);
|
|
}
|
|
else if(this->test_dim_down(v)) {
|
|
this->_tds.remove_dim_down(v);
|
|
for(All_faces_iterator afi = this-> all_faces_begin();
|
|
afi != this->all_faces_end();
|
|
afi++) *fit++ = afi;
|
|
}
|
|
else {
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, maxd,30);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Face_handle>, f, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<int>, i, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Vertex_handle>, w, maxd);
|
|
|
|
int d;
|
|
remove_degree_init(v,f,w,i,d,maxd);
|
|
remove_degree_triangulate(v,f,w,i,d);
|
|
this->delete_vertex(v);
|
|
Face_circulator fc(v[0]),done;
|
|
do *fit++ = fc++; while (fc!=done);
|
|
}
|
|
return;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove(Vertex_handle v)
|
|
{
|
|
int d;
|
|
|
|
CGAL_triangulation_precondition(v != Vertex_handle());
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
|
|
if(this->dimension() <= 1) { Triangulation::remove(v); return; }
|
|
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, maxd,30);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Face_handle>, f, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<int>, i, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Vertex_handle>, w, maxd);
|
|
|
|
remove_degree_init(v,f,w,i,d,maxd);
|
|
if(d == 0) return; // dim is going down
|
|
remove_degree_triangulate(v,f,w,i,d);
|
|
this->delete_vertex(v);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree_init(Vertex_handle v, std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w, std::vector<int> &i,
|
|
int &d, int &maxd)
|
|
{
|
|
f[0] = v->face();d=0;
|
|
do{
|
|
i[d] = f[d]->index(v);
|
|
w[d] = f[d]->vertex(ccw(i[d]));
|
|
if(this->is_infinite(w[d])) {
|
|
f[0] = f[d]; i[0]=i[d]; w[0]=w[d];
|
|
w[0]->set_face(f[0]->neighbor(i[0]));
|
|
f[1] = f[0]->neighbor(ccw(i[0]));
|
|
i[1] = f[1]->index(v);
|
|
w[1] = f[1]->vertex(ccw(i[1]));
|
|
if(this->is_infinite(f[1]->neighbor(i[1]))) {//otherwise dim remains 2
|
|
if(this->test_dim_down(v)) {
|
|
d=0;
|
|
this->tds().remove_dim_down(v);
|
|
return;
|
|
}
|
|
}
|
|
d=1;
|
|
}
|
|
w[d]->set_face(f[d]->neighbor(i[d]));//do no longer bother about set_face
|
|
++d;
|
|
if(d==maxd) { maxd *=2; f.resize(maxd); w.resize(maxd); i.resize(maxd);}
|
|
f[d] = f[d-1]->neighbor(ccw(i[d-1]));
|
|
} while(f[d]!=f[0]);
|
|
// all vertices finite but possibly w[0]
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree_triangulate(Vertex_handle v,
|
|
std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w,
|
|
std::vector<int> &i,int d)
|
|
{
|
|
switch (d) {
|
|
case 3:
|
|
remove_degree3(v,f,w,i); break;
|
|
case 4:
|
|
remove_degree4(v,f,w,i); break;
|
|
case 5:
|
|
remove_degree5(v,f,w,i); break;
|
|
case 6:
|
|
remove_degree6(v,f,w,i); break;
|
|
case 7:
|
|
remove_degree7(v,f,w,i); break;
|
|
default:
|
|
remove_degree_d(v,f,w,i,d); break;
|
|
}
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree_d(Vertex_handle v, std::vector<Face_handle> &,
|
|
std::vector<Vertex_handle> &,
|
|
std::vector<int> &,int)
|
|
{
|
|
// removing a degree d vertex, (dim is not going down)
|
|
// this is the old removal procedure that is used now only if d > 7
|
|
|
|
std::list<Edge> hole;
|
|
make_hole(v, hole);
|
|
fill_hole_delaunay(hole);
|
|
return;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree3(Vertex_handle, std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &, std::vector<int> &i)
|
|
{
|
|
// removing a degree 3 vertex
|
|
// only w[0] can be infinite
|
|
|
|
// modify the triangulation
|
|
Face_handle nn = f[1]->neighbor(i[1]);
|
|
this->tds().set_adjacency(f[0], ccw(i[0]), nn, nn->index(f[1]));
|
|
nn = f[2]->neighbor(i[2]);
|
|
this->tds().set_adjacency(f[0], cw(i[0]), nn, nn->index(f[2]));
|
|
f[0]->set_vertex(i[0], f[1]->vertex(cw(i[1])));
|
|
|
|
// clean container
|
|
this->tds().delete_face(f[1]);
|
|
this->tds().delete_face(f[2]);
|
|
|
|
return;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree4(Vertex_handle, std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{
|
|
// removing a degree 4 vertex
|
|
// only w[0] can be infinite
|
|
|
|
Face_handle nn;
|
|
// modify f[0] f[1] for incircle test
|
|
f[0]->set_vertex(i[0], w[3]); //w0 w1 w3
|
|
|
|
if(!test_conflict(w[2]->point(), f[0])) {
|
|
// diagonal 1 3
|
|
f[1]->set_vertex(i[1], w[3]); //w1 w2 w3
|
|
nn = f[3]->neighbor(i[3]);
|
|
this->tds().set_adjacency(f[0], cw(i[0]), nn, nn->index(f[3]));
|
|
nn = f[2]->neighbor(i[2]);
|
|
this->tds().set_adjacency(f[1], ccw(i[1]), nn, nn->index(f[2]));
|
|
// clean container
|
|
this->tds().delete_face(f[2]);
|
|
this->tds().delete_face(f[3]);
|
|
} else {
|
|
// diagonal 0 2
|
|
f[0]->set_vertex(i[0], w[2]); //w0 w1 w2
|
|
f[3]->set_vertex(i[3], w[2]); //w3 w0 w2
|
|
nn = f[1]->neighbor(i[1]);
|
|
this->tds().set_adjacency(f[0], ccw(i[0]), nn, nn->index(f[1]));
|
|
nn = f[2]->neighbor(i[2]);
|
|
this->tds().set_adjacency(f[3], cw(i[3]), nn, nn->index(f[2]));
|
|
// clean container
|
|
this->tds().delete_face(f[1]);
|
|
this->tds().delete_face(f[2]);
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree5(Vertex_handle v, std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{
|
|
// removing a degree 5 vertex
|
|
// only w[0] can be infinite
|
|
|
|
if(incircle(3,0,1,2,f,w,i)) {
|
|
if(incircle(4,0,1,3,f,w,i)) {
|
|
if(incircle(4,1,2,3,f,w,i)) {
|
|
// star from 4
|
|
remove_degree5_star(v,f[4],f[0],f[1],f[2],f[3],
|
|
w[4],w[0],w[1],w[2],w[3],
|
|
i[4],i[0],i[1],i[2],i[3]);
|
|
} else {
|
|
//star from 1
|
|
remove_degree5_star(v,f[1],f[2],f[3],f[4],f[0],
|
|
w[1],w[2],w[3],w[4],w[0],
|
|
i[1],i[2],i[3],i[4],i[0]);
|
|
}
|
|
} else {
|
|
// star from 3
|
|
remove_degree5_star(v,f[3],f[4],f[0],f[1],f[2],
|
|
w[3],w[4],w[0],w[1],w[2],
|
|
i[3],i[4],i[0],i[1],i[2]);
|
|
}
|
|
} else {
|
|
if(incircle(4,2,3,0,f,w,i)) {
|
|
if(incircle(4,0,1,2,f,w,i)) {
|
|
// star from 4
|
|
remove_degree5_star(v,f[4],f[0],f[1],f[2],f[3],
|
|
w[4],w[0],w[1],w[2],w[3],
|
|
i[4],i[0],i[1],i[2],i[3]);
|
|
} else {
|
|
//star from 2
|
|
remove_degree5_star(v,f[2],f[3],f[4],f[0],f[1],
|
|
w[2],w[3],w[4],w[0],w[1],
|
|
i[2],i[3],i[4],i[0],i[1]);
|
|
}
|
|
} else {
|
|
// star from 0
|
|
remove_degree5_star(v,f[0],f[1],f[2],f[3],f[4],
|
|
w[0],w[1],w[2],w[3],w[4],
|
|
i[0],i[1],i[2],i[3],i[4]);
|
|
}
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::remove_degree5_star
|
|
(
|
|
Vertex_handle &,
|
|
Face_handle & f0, Face_handle & f1, Face_handle & f2,
|
|
Face_handle & f3, Face_handle & f4,
|
|
Vertex_handle &v0, Vertex_handle &, Vertex_handle &,
|
|
Vertex_handle &, Vertex_handle &,
|
|
int i0, int i1, int i2, int i3, int i4)
|
|
{ // removing a degree 5 vertex, staring from v0
|
|
Face_handle nn;
|
|
f1->set_vertex(i1, v0); // f1 = v1v2v0
|
|
f2->set_vertex(i2, v0); // f2 = v2v3v0
|
|
f3->set_vertex(i3, v0); // f3 = v3v4v0
|
|
nn = f0->neighbor(i0);
|
|
this->tds().set_adjacency(f1, cw(i1), nn, nn->index(f0));
|
|
nn = f4->neighbor(i4);
|
|
this->tds().set_adjacency(f3, ccw(i3), nn, nn->index(f4));
|
|
this->tds().delete_face(f0);
|
|
this->tds().delete_face(f4);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree6(Vertex_handle v, std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{
|
|
// removing a degree 6 vertex
|
|
// only w[0] can be infinite
|
|
|
|
if(incircle(1,2,3,0,f,w,i)) {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
if(incircle(1,2,3,4,f,w,i)) {
|
|
if(incircle(4,0,1,3,f,w,i)) {
|
|
if(incircle(5,0,1,4,f,w,i)) {
|
|
remove_degree6_star(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
} else {
|
|
remove_degree6_N(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
}} else {
|
|
remove_degree6_antiN(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
}} else {
|
|
if(incircle(5,1,2,4,f,w,i)) {
|
|
remove_degree6_N(v,f[2],f[3],f[4],f[5],f[0],f[1],
|
|
w[2],w[3],w[4],w[5],w[0],w[1],
|
|
i[2],i[3],i[4],i[5],i[0],i[1]);
|
|
} else {
|
|
if(incircle(5,0,1,4,f,w,i)) {
|
|
remove_degree6_antiN(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
} else {
|
|
remove_degree6_star(v,f[4],f[5],f[0],f[1],f[2],f[3],
|
|
w[4],w[5],w[0],w[1],w[2],w[3],
|
|
i[4],i[5],i[0],i[1],i[2],i[3]);
|
|
}}}} else {
|
|
if(incircle(1,2,3,5,f,w,i)) {
|
|
if(incircle(1,3,4,5,f,w,i)) {
|
|
if(incircle(4,0,1,3,f,w,i)) {
|
|
if(incircle(5,0,1,4,f,w,i)) {
|
|
remove_degree6_star(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
} else {
|
|
remove_degree6_N(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
}} else {
|
|
remove_degree6_antiN(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
}} else {
|
|
if(incircle(5,0,1,3,f,w,i)) {
|
|
remove_degree6_diamond(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
} else {
|
|
if(incircle(4,5,0,3,f,w,i)) {
|
|
remove_degree6_antiN(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
} else {
|
|
remove_degree6_star(v,f[3],f[4],f[5],f[0],f[1],f[2],
|
|
w[3],w[4],w[5],w[0],w[1],w[2],
|
|
i[3],i[4],i[5],i[0],i[1],i[2]);
|
|
}}}} else {
|
|
remove_degree6_star(v,f[5],f[0],f[1],f[2],f[3],f[4],
|
|
w[5],w[0],w[1],w[2],w[3],w[4],
|
|
i[5],i[0],i[1],i[2],i[3],i[4]);
|
|
}}} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
if(incircle(4,2,3,0,f,w,i)) {
|
|
if(incircle(4,0,1,2,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
if(incircle(4,0,1,5,f,w,i)) {
|
|
remove_degree6_star(v,f[4],f[5],f[0],f[1],f[2],f[3],
|
|
w[4],w[5],w[0],w[1],w[2],w[3],
|
|
i[4],i[5],i[0],i[1],i[2],i[3]);
|
|
} else {
|
|
remove_degree6_antiN(v,f[1],f[2],f[3],f[4],f[5],f[0],
|
|
w[1],w[2],w[3],w[4],w[5],w[0],
|
|
i[1],i[2],i[3],i[4],i[5],i[0]);
|
|
}} else {
|
|
remove_degree6_N(v,f[2],f[3],f[4],f[5],f[0],f[1],
|
|
w[2],w[3],w[4],w[5],w[0],w[1],
|
|
i[2],i[3],i[4],i[5],i[0],i[1]);
|
|
}} else {
|
|
if(incircle(4,5,0,2,f,w,i)) {
|
|
remove_degree6_diamond(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
} else {
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
remove_degree6_N(v,f[2],f[3],f[4],f[5],f[0],f[1],
|
|
w[2],w[3],w[4],w[5],w[0],w[1],
|
|
i[2],i[3],i[4],i[5],i[0],i[1]);
|
|
} else {
|
|
remove_degree6_star(v,f[2],f[3],f[4],f[5],f[0],f[1],
|
|
w[2],w[3],w[4],w[5],w[0],w[1],
|
|
i[2],i[3],i[4],i[5],i[0],i[1]);
|
|
}}}} else {
|
|
remove_degree6_star(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
}} else {
|
|
if(incircle(5,2,3,0,f,w,i)) {
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
remove_degree6_star(v,f[5],f[0],f[1],f[2],f[3],f[4],
|
|
w[5],w[0],w[1],w[2],w[3],w[4],
|
|
i[5],i[0],i[1],i[2],i[3],i[4]);
|
|
} else {
|
|
remove_degree6_antiN(v,f[2],f[3],f[4],f[5],f[0],f[1],
|
|
w[2],w[3],w[4],w[5],w[0],w[1],
|
|
i[2],i[3],i[4],i[5],i[0],i[1]);
|
|
}} else {
|
|
if(incircle(4,5,0,3,f,w,i)) {
|
|
remove_degree6_star(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
} else {
|
|
remove_degree6_N(v,f[0],f[1],f[2],f[3],f[4],f[5],
|
|
w[0],w[1],w[2],w[3],w[4],w[5],
|
|
i[0],i[1],i[2],i[3],i[4],i[5]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::remove_degree6_star(
|
|
Vertex_handle &,
|
|
Face_handle & f0, Face_handle & f1, Face_handle & f2,
|
|
Face_handle & f3, Face_handle & f4, Face_handle & f5,
|
|
Vertex_handle &v0, Vertex_handle &, Vertex_handle &,
|
|
Vertex_handle &, Vertex_handle &, Vertex_handle &,
|
|
int i0, int i1, int i2, int i3, int i4, int i5)
|
|
{ // removing a degree 6 vertex, staring from v0
|
|
Face_handle nn;
|
|
f1->set_vertex(i1, v0); // f1 = v1v2v0
|
|
f2->set_vertex(i2, v0); // f2 = v2v3v0
|
|
f3->set_vertex(i3, v0); // f3 = v3v4v0
|
|
f4->set_vertex(i4, v0); // f4 = v4v5v0
|
|
nn = f0->neighbor(i0);
|
|
this->tds().set_adjacency(f1, cw(i1), nn, nn->index(f0));
|
|
nn = f5->neighbor(i5);
|
|
this->tds().set_adjacency(f4, ccw(i4), nn, nn->index(f5));
|
|
this->tds().delete_face(f0);
|
|
this->tds().delete_face(f5);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::remove_degree6_N(
|
|
Vertex_handle &,
|
|
Face_handle & f0, Face_handle & f1, Face_handle & f2,
|
|
Face_handle & f3, Face_handle & f4, Face_handle & f5,
|
|
Vertex_handle &v0, Vertex_handle &, Vertex_handle &,
|
|
Vertex_handle &v3, Vertex_handle &, Vertex_handle &,
|
|
int i0, int i1, int i2, int i3, int i4, int i5)
|
|
{ // removing a degree 6 vertex, N configuration with diagonal v0v3
|
|
Face_handle nn;
|
|
f1->set_vertex(i1, v0); // f1 = v1v2v0
|
|
f2->set_vertex(i2, v0); // f2 = v2v3v0
|
|
f4->set_vertex(i4, v3); // f4 = v4v5v3
|
|
f5->set_vertex(i5, v3); // f5 = v5v0v3
|
|
nn = f0->neighbor(i0);
|
|
this->tds().set_adjacency(f1, cw(i1), nn, nn->index(f0));
|
|
nn = f3->neighbor(i3);
|
|
this->tds().set_adjacency(f4, cw(i4), nn, nn->index(f3));
|
|
this->tds().set_adjacency(f2, ccw(i2), f5, ccw(i5));
|
|
this->tds().delete_face(f0);
|
|
this->tds().delete_face(f3);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::remove_degree6_antiN(
|
|
Vertex_handle &,
|
|
Face_handle & f0, Face_handle & f1, Face_handle & f2,
|
|
Face_handle & f3, Face_handle & f4, Face_handle & f5,
|
|
Vertex_handle &v0, Vertex_handle &, Vertex_handle &,
|
|
Vertex_handle &v3, Vertex_handle &, Vertex_handle &,
|
|
int i0, int i1, int i2, int i3, int i4, int i5)
|
|
{ // removing a degree 6 vertex, antiN configuration with diagonal v0v3
|
|
Face_handle nn;
|
|
f0->set_vertex(i0, v3); // f0 = v0v1v3
|
|
f1->set_vertex(i1, v3); // f1 = v1v2v3
|
|
f3->set_vertex(i3, v0); // f3 = v3v4v0
|
|
f4->set_vertex(i4, v0); // f4 = v4v5v0
|
|
nn = f2->neighbor(i2);
|
|
this->tds().set_adjacency(f1, ccw(i1), nn, nn->index(f2));
|
|
nn = f5->neighbor(i5);
|
|
this->tds().set_adjacency(f4, ccw(i4), nn, nn->index(f5));
|
|
this->tds().set_adjacency(f0, cw(i0), f3, cw(i3));
|
|
this->tds().delete_face(f2);
|
|
this->tds().delete_face(f5);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::remove_degree6_diamond(
|
|
Vertex_handle &,
|
|
Face_handle & f0, Face_handle & f1, Face_handle & f2,
|
|
Face_handle & f3, Face_handle & f4, Face_handle & f5,
|
|
Vertex_handle &v0, Vertex_handle &, Vertex_handle &v2,
|
|
Vertex_handle &, Vertex_handle &v4, Vertex_handle &,
|
|
int i0, int i1, int i2, int i3, int i4, int i5)
|
|
{ // removing a degree 6 vertex, with chords v0v2 v2v4 v4v0
|
|
Face_handle nn;
|
|
f0->set_vertex(i0, v2); // f0 = v0v1v2
|
|
f2->set_vertex(i2, v4); // f2 = v2v3v4
|
|
f4->set_vertex(i4, v0); // f4 = v4v5v0
|
|
f1->set_vertex(i1, v4);
|
|
f1->set_vertex(ccw(i1), v0); // f1 = v0v2v4
|
|
nn = f1->neighbor(i1);
|
|
this->tds().set_adjacency(f0, ccw(i0), nn, nn->index(f1));
|
|
nn = f3->neighbor(i3);
|
|
this->tds().set_adjacency(f2, ccw(i2), nn, nn->index(f3));
|
|
nn = f5->neighbor(i5);
|
|
this->tds().set_adjacency(f4, ccw(i4), nn, nn->index(f5));
|
|
this->tds().set_adjacency(f0, cw(i0), f1, i1);
|
|
this->tds().set_adjacency(f4, cw(i4), f1, cw(i1));
|
|
|
|
this->tds().delete_face(f3);
|
|
this->tds().delete_face(f5);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7(Vertex_handle v,std::vector<Face_handle> &f,
|
|
std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{
|
|
// removing a degree 7 vertex
|
|
// only w[0] can be infinite
|
|
|
|
if(incircle(2,0,1,3,f,w,i)) { // sweeping from above
|
|
if(incircle(2,3,4,0,f,w,i)) {
|
|
if(incircle(5,3,4,6,f,w,i)) {
|
|
if(incircle(5,3,4,2,f,w,i)) {
|
|
if(incircle(6,2,3,5,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,6,f,w,i);
|
|
}} else {
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(2,5,6,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightdelta(v,5,f,w,i);
|
|
}}}} else {
|
|
if(incircle(4,0,1,2,f,w,i)) {
|
|
if(incircle(5,1,2,4,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(5,0,1,4,f,w,i)) {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
}}} else {
|
|
if(incircle(2,4,5,0,f,w,i)) {
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(2,5,6,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftdelta(v,2,f,w,i);
|
|
}}} else {
|
|
remove_degree7_rightdelta(v,0,f,w,i);
|
|
}}}} else {
|
|
if(incircle(6,3,4,2,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_star(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,6,f,w,i);
|
|
}} else {
|
|
if(incircle(4,0,1,2,f,w,i)) {
|
|
if(incircle(2,4,5,6,f,w,i)) {
|
|
if(incircle(5,1,2,4,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(5,0,1,4,f,w,i)) {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
}} else{
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
}}} else {
|
|
if(incircle(6,1,2,4,f,w,i)) {
|
|
remove_degree7_leftdelta(v,6,f,w,i);
|
|
} else {
|
|
if(incircle(1,4,5,6,f,w,i)) {
|
|
if(incircle(1,4,5,0,f,w,i)) {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
}} else {
|
|
if(incircle(6,0,1,4,f,w,i)) {
|
|
remove_degree7_rightdelta(v,4,f,w,i);
|
|
} else {
|
|
if(incircle(6,4,5,0,f,w,i)) {
|
|
remove_degree7_star(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
}}}}}} else {
|
|
if(incircle(2,4,5,6,f,w,i)) {
|
|
if(incircle(2,4,5,0,f,w,i)) {
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(2,5,6,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftdelta(v,2,f,w,i);
|
|
}}} else {
|
|
remove_degree7_rightdelta(v,0,f,w,i);
|
|
}} else {
|
|
if(incircle(2,6,0,4,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftdelta(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_rightdelta(v,2,f,w,i);
|
|
}} else {
|
|
if(incircle(6,4,5,0,f,w,i)) {
|
|
remove_degree7_leftdelta(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_rightdelta(v,0,f,w,i);
|
|
}}}}}}} else{
|
|
if(incircle(5,3,4,6,f,w,i)) {
|
|
if(incircle(5,3,4,0,f,w,i)) {
|
|
if(incircle(5,2,3,0,f,w,i)) {
|
|
if(incircle(6,2,3,5,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,6,f,w,i);
|
|
}}else
|
|
if(incircle(5,0,1,2,f,w,i)) {
|
|
if(incircle(6,1,2,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
} else {
|
|
if(incircle(6,0,1,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(2,5,6,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightdelta(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(3,5,6,0,f,w,i)) {
|
|
if(incircle(6,2,3,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,6,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftfan(v,3,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftdelta(v,0,f,w,i);
|
|
}}} else {
|
|
remove_degree7_star(v,0,f,w,i);
|
|
}} else {
|
|
if(incircle(6,3,4,0,f,w,i)) {
|
|
if(incircle(6,2,3,0,f,w,i)) {
|
|
if(incircle(6,0,1,2,f,w,i)) {
|
|
remove_degree7_star(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,6,f,w,i);
|
|
}} else {
|
|
remove_degree7_zigzag(v,3,f,w,i);
|
|
}} else {
|
|
if(incircle(6,4,5,0,f,w,i)) {
|
|
remove_degree7_leftfan(v,0,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,0,f,w,i);
|
|
}}}}} else { //sweeping from below
|
|
if(incircle(1,6,0,3,f,w,i)) {
|
|
if(incircle(5,6,0,4,f,w,i)) {
|
|
if(incircle(5,6,0,1,f,w,i)) {
|
|
if(incircle(4,0,1,5,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,4,f,w,i);
|
|
}} else {
|
|
if(incircle(5,2,3,1,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(1,4,5,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftdelta(v,5,f,w,i);
|
|
}}}} else {
|
|
if(incircle(6,2,3,1,f,w,i)) {
|
|
if(incircle(5,1,2,6,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(5,2,3,6,f,w,i)) {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
}}} else {
|
|
if(incircle(1,5,6,3,f,w,i)) {
|
|
if(incircle(5,2,3,1,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(1,4,5,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightdelta(v,1,f,w,i);
|
|
}}} else {
|
|
remove_degree7_leftdelta(v,3,f,w,i);
|
|
}}}} else {
|
|
if(incircle(4,6,0,1,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_star(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,4,f,w,i);
|
|
}} else {
|
|
if(incircle(6,2,3,1,f,w,i)) {
|
|
if(incircle(1,5,6,4,f,w,i)) {
|
|
if(incircle(5,1,2,6,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(5,2,3,6,f,w,i)) {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
}} else{
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
}}} else {
|
|
if(incircle(4,1,2,6,f,w,i)) {
|
|
remove_degree7_rightdelta(v,4,f,w,i);
|
|
} else {
|
|
if(incircle(2,5,6,4,f,w,i)) {
|
|
if(incircle(2,5,6,3,f,w,i)) {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,2,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,2,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
}} else {
|
|
if(incircle(4,2,3,6,f,w,i)) {
|
|
remove_degree7_leftdelta(v,6,f,w,i);
|
|
} else {
|
|
if(incircle(4,5,6,3,f,w,i)) {
|
|
remove_degree7_star(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,6,f,w,i);
|
|
}}}}}} else {
|
|
if(incircle(1,5,6,4,f,w,i)) {
|
|
if(incircle(1,5,6,3,f,w,i)) {
|
|
if(incircle(5,2,3,1,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_rightfan(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(1,4,5,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightfan(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightdelta(v,1,f,w,i);
|
|
}}} else {
|
|
remove_degree7_leftdelta(v,3,f,w,i);
|
|
}} else {
|
|
if(incircle(1,3,4,6,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightdelta(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_leftdelta(v,1,f,w,i);
|
|
}} else {
|
|
if(incircle(4,5,6,3,f,w,i)) {
|
|
remove_degree7_rightdelta(v,6,f,w,i);
|
|
} else {
|
|
remove_degree7_leftdelta(v,3,f,w,i);
|
|
}}}}}}} else{
|
|
if(incircle(5,6,0,4,f,w,i)) {
|
|
if(incircle(5,6,0,3,f,w,i)) {
|
|
if(incircle(5,0,1,3,f,w,i)) {
|
|
if(incircle(4,0,1,5,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,4,f,w,i);
|
|
}}else
|
|
if(incircle(5,2,3,1,f,w,i)) {
|
|
if(incircle(4,1,2,5,f,w,i)) {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
} else {
|
|
if(incircle(4,2,3,5,f,w,i)) {
|
|
remove_degree7_leftfan(v,5,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,5,f,w,i);
|
|
}}} else {
|
|
if(incircle(1,4,5,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_zigzag(v,1,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,1,f,w,i);
|
|
}} else {
|
|
remove_degree7_leftdelta(v,5,f,w,i);
|
|
}}} else {
|
|
if(! incircle(3,4,5,0,f,w,i)) {
|
|
if(incircle(4,0,1,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_rightfan(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_zigzag(v,4,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightfan(v,0,f,w,i);
|
|
}} else {
|
|
remove_degree7_rightdelta(v,3,f,w,i);
|
|
}}} else {
|
|
remove_degree7_star(v,3,f,w,i);
|
|
}} else {
|
|
if(incircle(4,6,0,3,f,w,i)) {
|
|
if(incircle(4,0,1,3,f,w,i)) {
|
|
if(incircle(4,2,3,1,f,w,i)) {
|
|
remove_degree7_star(v,4,f,w,i);
|
|
} else {
|
|
remove_degree7_leftfan(v,4,f,w,i);
|
|
}} else {
|
|
remove_degree7_zigzag(v,0,f,w,i);
|
|
}} else {
|
|
if(incircle(4,5,6,3,f,w,i)) {
|
|
remove_degree7_rightfan(v,3,f,w,i);
|
|
} else {
|
|
remove_degree7_star(v,3,f,w,i);
|
|
}}}}}
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
rotate7(int j, std::vector<Vertex_handle> &w,
|
|
std::vector<Face_handle> &f, std::vector<int> &i)
|
|
{
|
|
if(j==0) return;
|
|
Face_handle ff=f[0];
|
|
int ii=i[0],k=0,kk=(6*j)%7;
|
|
Vertex_handle ww=w[0];
|
|
for (int jj=0; k!=kk; jj=k) { // 7 is prime
|
|
k=(jj+j)%7;
|
|
w[jj]=w[k]; f[jj]=f[k]; i[jj]=i[k];
|
|
}
|
|
w[kk]=ww;f[kk]=ff;i[kk]=ii;
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_star (Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f, std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, staring from w[j]
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[1]->set_vertex(i[1], w[0]); // f1 = w1w2w0
|
|
f[2]->set_vertex(i[2], w[0]); // f2 = w2w3w0
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w3w4w0
|
|
f[4]->set_vertex(i[4], w[0]); // f4 = w4w5w0
|
|
f[5]->set_vertex(i[5], w[0]); // f5 = w5w6w0
|
|
|
|
nn = f[0]->neighbor(i[0]);
|
|
this->tds().set_adjacency(f[1], cw(i[1]), nn, nn->index(f[0]));
|
|
nn = f[6]->neighbor(i[6]);
|
|
this->tds().set_adjacency(f[5], ccw(i[5]), nn, nn->index(f[6]));
|
|
this->tds().delete_face(f[0]);
|
|
this->tds().delete_face(f[6]);
|
|
}
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_zigzag (Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f,std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, zigzag, w[j] = middle point
|
|
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[1]->set_vertex(i[1], w[3]); // f1 = w1w2w3
|
|
f[2]->set_vertex(ccw(i[2]), w[1]);
|
|
f[2]->set_vertex(i[2], w[0]); // f2 = w1w3w0
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w3w4w0
|
|
f[4]->set_vertex(cw(i[4]), w[6]);
|
|
f[4]->set_vertex(i[4], w[0]); // f4 = w4w6w0
|
|
f[5]->set_vertex(i[5], w[4]); // f5 = w5w6w4
|
|
|
|
nn = f[2]->neighbor(i[2]);
|
|
this->tds().set_adjacency(f[1], ccw(i[1]), nn, nn->index(f[2]));
|
|
nn = f[0]->neighbor(i[0]);
|
|
this->tds().set_adjacency(f[2], cw(i[2]), nn, nn->index(f[0]));
|
|
nn = f[6]->neighbor(i[6]);
|
|
this->tds().set_adjacency(f[4], ccw(i[4]), nn, nn->index(f[6]));
|
|
nn = f[4]->neighbor(i[4]);
|
|
this->tds().set_adjacency(f[5], cw(i[5]), nn, nn->index(f[4]));
|
|
this->tds().set_adjacency(f[1], cw(i[1]), f[2], i[2]);
|
|
this->tds().set_adjacency(f[4], i[4], f[5], ccw(i[5]));
|
|
|
|
this->tds().delete_face(f[0]);
|
|
this->tds().delete_face(f[6]);
|
|
}
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_leftdelta(Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f,std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, left delta from w[j]
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[1]->set_vertex(i[1], w[0]); // f1 = w1w2w0
|
|
f[2]->set_vertex(i[2], w[0]); // f2 = w2w3w0
|
|
f[3]->set_vertex(cw(i[3]), w[5]);
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w3w5w0
|
|
f[4]->set_vertex(i[4], w[3]); // f4 = w4w5w3
|
|
f[5]->set_vertex(i[5], w[0]); // f5 = w5w6w0
|
|
|
|
nn = f[0]->neighbor(i[0]);
|
|
this->tds().set_adjacency(f[1], cw(i[1]), nn, nn->index(f[0]));
|
|
nn = f[3]->neighbor(i[3]);
|
|
this->tds().set_adjacency(f[4], cw(i[4]), nn, nn->index(f[3]));
|
|
nn = f[6]->neighbor(i[6]);
|
|
this->tds().set_adjacency(f[5], ccw(i[5]), nn, nn->index(f[6]));
|
|
this->tds().set_adjacency(f[3], i[3], f[4], ccw(i[4]));
|
|
this->tds().set_adjacency(f[3], ccw(i[3]), f[5], cw(i[5]));
|
|
|
|
this->tds().delete_face(f[0]);
|
|
this->tds().delete_face(f[6]);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_rightdelta(Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f,std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, right delta from w[j]
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[1]->set_vertex(i[1], w[0]); // f1 = w1w2w0
|
|
f[2]->set_vertex(i[2], w[4]); // f2 = w2w3w4
|
|
f[3]->set_vertex(ccw(i[3]), w[2]);
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w2w4w0
|
|
f[4]->set_vertex(i[4], w[0]); // f4 = w4w5w0
|
|
f[5]->set_vertex(i[5], w[0]); // f5 = w5w6w0
|
|
|
|
nn = f[0]->neighbor(i[0]);
|
|
this->tds().set_adjacency(f[1], cw(i[1]), nn, nn->index(f[0]));
|
|
nn = f[3]->neighbor(i[3]);
|
|
this->tds().set_adjacency(f[2], ccw(i[2]), nn, nn->index(f[3]));
|
|
nn = f[6]->neighbor(i[6]);
|
|
this->tds().set_adjacency(f[5], ccw(i[5]), nn, nn->index(f[6]));
|
|
this->tds().set_adjacency(f[1], ccw(i[1]), f[3], cw(i[3]));
|
|
this->tds().set_adjacency(f[3], i[3], f[2], cw(i[2]));
|
|
|
|
this->tds().delete_face(f[0]);
|
|
this->tds().delete_face(f[6]);
|
|
}
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_leftfan(Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f,std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, left fan from w[j]
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[1]->set_vertex(i[1], w[0]); // f1 = w1w2w0
|
|
f[2]->set_vertex(i[2], w[0]); // f2 = w2w3w0
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w3w4w0
|
|
f[4]->set_vertex(i[4], w[6]); // f4 = w4w5w6
|
|
f[6]->set_vertex(i[6], w[4]); // f6 = w6w0w4
|
|
|
|
nn = f[0]->neighbor(i[0]);
|
|
this->tds().set_adjacency(f[1], cw(i[1]), nn, nn->index(f[0]));
|
|
nn = f[5]->neighbor(i[5]);
|
|
this->tds().set_adjacency(f[4], ccw(i[4]), nn, nn->index(f[5]));
|
|
this->tds().set_adjacency(f[3], ccw(i[3]), f[6], ccw(i[6]));
|
|
this->tds().set_adjacency(f[6], cw(i[6]), f[4], cw(i[4]));
|
|
|
|
this->tds().delete_face(f[0]);
|
|
this->tds().delete_face(f[5]);
|
|
}
|
|
|
|
template < class Gt, class Tds >
|
|
inline void
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
remove_degree7_rightfan(Vertex_handle &, int j,
|
|
std::vector<Face_handle> &f,std::vector<Vertex_handle> &w, std::vector<int> &i)
|
|
{ // removing a degree 7 vertex, right fan from w[j]
|
|
rotate7(j,w,f,i);
|
|
|
|
Face_handle nn;
|
|
f[0]->set_vertex(i[0], w[3]); // f0 = w0w1w3
|
|
f[2]->set_vertex(i[2], w[1]); // f2 = w2w3w1
|
|
f[3]->set_vertex(i[3], w[0]); // f3 = w3w4w0
|
|
f[4]->set_vertex(i[4], w[0]); // f4 = w4w5w0
|
|
f[5]->set_vertex(i[5], w[0]); // f5 = w5w6w0
|
|
|
|
nn = f[1]->neighbor(i[1]);
|
|
this->tds().set_adjacency(f[2], cw(i[2]), nn, nn->index(f[1]));
|
|
nn = f[6]->neighbor(i[6]);
|
|
this->tds().set_adjacency(f[5], ccw(i[5]), nn, nn->index(f[6]));
|
|
this->tds().set_adjacency(f[2], ccw(i[2]), f[0], ccw(i[0]));
|
|
this->tds().set_adjacency(f[0], cw(i[0]), f[3], cw(i[3]));
|
|
|
|
this->tds().delete_face(f[1]);
|
|
this->tds().delete_face(f[6]);
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////
|
|
// DISPLACEMENT
|
|
|
|
template <class Gt, class Tds >
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
move_if_no_collision(Vertex_handle v, const Point &p)
|
|
{
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
if(v->point() == p) return v;
|
|
const int dim = this->dimension();
|
|
|
|
if(dim == 2) {
|
|
Point ant = v->point();
|
|
v->set_point(p);
|
|
// This option optimizes only when most of the
|
|
// displacements would not break the orientation
|
|
// of the faces.. we will consider this as an a priori,
|
|
// because otherwise it is pointless to just do
|
|
// not rebuild from scratch.
|
|
if(this->well_oriented(v)) {
|
|
restore_edges(v);
|
|
return v;
|
|
}
|
|
v->set_point(ant);
|
|
}
|
|
|
|
Locate_type lt;
|
|
int li;
|
|
Vertex_handle inserted;
|
|
Face_handle loc = this->locate(p, lt, li, v->face());
|
|
|
|
if(lt == Triangulation_2<Gt,Tds>::VERTEX)
|
|
return loc->vertex(li);
|
|
|
|
if(dim == 0) {
|
|
v->point() = p;
|
|
return v;
|
|
}
|
|
|
|
size_type n_vertices = this->tds().number_of_vertices();
|
|
|
|
if((lt == Triangulation::OUTSIDE_AFFINE_HULL) &&
|
|
(dim == 1) && (n_vertices == 3)) {
|
|
v->point() = p;
|
|
return v;
|
|
}
|
|
|
|
if((lt != Triangulation::OUTSIDE_AFFINE_HULL) && (dim == 1)) {
|
|
if(loc->has_vertex(v)) {
|
|
v->point() = p;
|
|
} else {
|
|
inserted = insert(p, lt, loc, li);
|
|
Face_handle f = v->face();
|
|
int i = f->index(v);
|
|
if(i==0) {f = f->neighbor(1);}
|
|
CGAL_triangulation_assertion(f->index(v) == 1);
|
|
Face_handle g= f->neighbor(0);
|
|
f->set_vertex(1, g->vertex(1));
|
|
f->set_neighbor(0,g->neighbor(0));
|
|
g->neighbor(0)->set_neighbor(1,f);
|
|
g->vertex(1)->set_face(f);
|
|
this->delete_face(g);
|
|
Face_handle f_ins = inserted->face();
|
|
i = f_ins->index(inserted);
|
|
if(i==0) {f_ins = f_ins->neighbor(1);}
|
|
CGAL_triangulation_assertion(f_ins->index(inserted) == 1);
|
|
Face_handle g_ins = f_ins->neighbor(0);
|
|
f_ins->set_vertex(1, v);
|
|
g_ins->set_vertex(0, v);
|
|
v->set_point(p);
|
|
v->set_face(inserted->face());
|
|
this->delete_vertex(inserted);
|
|
}
|
|
return v;
|
|
}
|
|
|
|
if((lt != Triangulation::OUTSIDE_AFFINE_HULL) && this->test_dim_down(v)) {
|
|
// verify if p and two static vertices are collinear in this case
|
|
int iinf = 0;
|
|
Face_circulator finf = this->incident_faces(this->infinite_vertex()),
|
|
fdone(finf);
|
|
do {
|
|
if(!finf->has_vertex(v))
|
|
{
|
|
iinf = ~(finf->index(this->infinite_vertex()));
|
|
break;
|
|
}
|
|
} while(++finf != fdone);
|
|
if(this->orientation(finf->vertex(iinf&1)->point(),
|
|
finf->vertex(iinf&2)->point(),
|
|
p) == COLLINEAR)
|
|
{
|
|
v->point() = p;
|
|
this->tds().dim_down(loc, loc->index(v));
|
|
return v;
|
|
}
|
|
}
|
|
|
|
inserted = insert(p, lt, loc, li);
|
|
|
|
{
|
|
int d;
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, maxd,30);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Face_handle>, f, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<int>, i, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Vertex_handle>, w, maxd);
|
|
|
|
remove_degree_init(v,f,w,i,d,maxd);
|
|
remove_degree_triangulate(v,f,w,i,d);
|
|
}
|
|
|
|
// fixing pointer
|
|
Face_circulator fc = this->incident_faces(inserted), done(fc);
|
|
std::vector<Face_handle> faces_pt;
|
|
faces_pt.reserve(16);
|
|
do { faces_pt.push_back(fc); } while(++fc != done);
|
|
std::size_t ss = faces_pt.size();
|
|
for(std::size_t k=0; k<ss; k++)
|
|
{
|
|
Face_handle f = faces_pt[k];
|
|
int i = f->index(inserted);
|
|
f->set_vertex(i, v);
|
|
}
|
|
|
|
v->set_point(p);
|
|
v->set_face(inserted->face());
|
|
|
|
this->delete_vertex(inserted);
|
|
|
|
return v;
|
|
}
|
|
|
|
template <class Gt, class Tds >
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
move(Vertex_handle v, const Point &p)
|
|
{
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
if(v->point() == p) return v;
|
|
Vertex_handle w = move_if_no_collision(v,p);
|
|
if(w != v) {
|
|
remove(v);
|
|
return w;
|
|
}
|
|
return v;
|
|
}
|
|
|
|
template <class Gt, class Tds >
|
|
bool
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
is_delaunay_after_displacement(Vertex_handle v, const Point &p) const
|
|
{
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
CGAL_triangulation_precondition(this->dimension() == 2);
|
|
CGAL_triangulation_precondition(!this->test_dim_down(v));
|
|
if(v->point() == p) return true;
|
|
Point ant = v->point();
|
|
v->set_point(p);
|
|
if(!this->well_oriented(v))
|
|
{
|
|
v->set_point(ant);
|
|
return false;
|
|
}
|
|
std::list<Edge> edges;
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
|
int degree = 0;
|
|
do {
|
|
if((++degree) > 3) break;
|
|
} while(++fc != done);
|
|
fc = this->incident_faces(v);
|
|
done = fc;
|
|
if(degree == 3) {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
} while(++fc != done);
|
|
} else {
|
|
do {
|
|
int i = fc->index(v);
|
|
edges.push_back(Edge(fc, i));
|
|
edges.push_back(Edge(fc, this->cw(i)));
|
|
} while(++fc != done);
|
|
}
|
|
while(!edges.empty()) {
|
|
const Edge &e = edges.front();
|
|
Face_handle f = e.first;
|
|
int i = e.second;
|
|
edges.pop_front();
|
|
if(this->is_infinite(f->vertex(i))) continue;
|
|
Vertex_handle vm = this->_tds.mirror_vertex(f, i);
|
|
if(this->is_infinite(vm)) continue;
|
|
if(this->side_of_oriented_circle(f, vm->point()) == ON_POSITIVE_SIDE) {
|
|
v->set_point(ant);
|
|
return false;
|
|
}
|
|
}
|
|
v->set_point(ant);
|
|
return true;
|
|
}
|
|
|
|
template <class Gt, class Tds >
|
|
template <class OutputItFaces>
|
|
typename Delaunay_triangulation_2<Gt,Tds>::Vertex_handle
|
|
Delaunay_triangulation_2<Gt,Tds>::
|
|
move_if_no_collision_and_give_new_faces(Vertex_handle v,
|
|
const Point &p,
|
|
OutputItFaces oif)
|
|
{
|
|
CGAL_triangulation_precondition(!this->is_infinite(v));
|
|
if(v->point() == p) return v;
|
|
|
|
const int dim = this->dimension();
|
|
|
|
if(dim == 2) {
|
|
Point ant = v->point();
|
|
v->set_point(p);
|
|
// This option optimizes only when most of the
|
|
// displacements would not break the orientation
|
|
// of the faces.. we will consider this as an a priori,
|
|
// because otherwise it is pointless to just do
|
|
// not rebuild from scratch.
|
|
if(well_oriented(v)) {
|
|
std::set<Face_handle> faces_set;
|
|
restore_edges(v, faces_set);
|
|
for(typename std::set<Face_handle>::iterator ib = faces_set.begin(),
|
|
iend = faces_set.end(); ib != iend; ib++) *oif++ = *ib;
|
|
return v;
|
|
}
|
|
v->set_point(ant);
|
|
}
|
|
|
|
Locate_type lt;
|
|
int li;
|
|
Vertex_handle inserted;
|
|
Face_handle loc = this->locate(p, lt, li, v->face());
|
|
|
|
if(lt == Triangulation::VERTEX) return loc->vertex(li);
|
|
|
|
if(dim == 0) {
|
|
v->point() = p;
|
|
return v;
|
|
}
|
|
|
|
size_type n_vertices = this->tds().number_of_vertices();
|
|
|
|
if((lt == Triangulation::OUTSIDE_AFFINE_HULL) &&
|
|
(dim == 1) && (n_vertices == 3)) {
|
|
v->point() = p;
|
|
for(All_faces_iterator afi = this-> all_faces_begin();
|
|
afi != this->all_faces_end();
|
|
afi++) *oif++ = afi;
|
|
return v;
|
|
}
|
|
|
|
if((lt != Triangulation::OUTSIDE_AFFINE_HULL) && (dim == 1)) {
|
|
if(loc->has_vertex(v)) {
|
|
v->point() = p;
|
|
} else {
|
|
inserted = insert(p, lt, loc, li);
|
|
Face_handle f = v->face();
|
|
int i = f->index(v);
|
|
if(i==0) {f = f->neighbor(1);}
|
|
CGAL_triangulation_assertion(f->index(v) == 1);
|
|
Face_handle g= f->neighbor(0);
|
|
f->set_vertex(1, g->vertex(1));
|
|
f->set_neighbor(0,g->neighbor(0));
|
|
g->neighbor(0)->set_neighbor(1,f);
|
|
g->vertex(1)->set_face(f);
|
|
this->delete_face(g);
|
|
*oif++ = f;
|
|
Face_handle f_ins = inserted->face();
|
|
i = f_ins->index(inserted);
|
|
if(i==0) {f_ins = f_ins->neighbor(1);}
|
|
CGAL_triangulation_assertion(f_ins->index(inserted) == 1);
|
|
Face_handle g_ins = f_ins->neighbor(0);
|
|
f_ins->set_vertex(1, v);
|
|
g_ins->set_vertex(0, v);
|
|
v->set_face(inserted->face());
|
|
v->set_point(p);
|
|
this->delete_vertex(inserted);
|
|
}
|
|
*oif++ = v->face();
|
|
if(v->face()->neighbor(0)->has_vertex(v))
|
|
*oif++ = v->face()->neighbor(0);
|
|
if(v->face()->neighbor(1)->has_vertex(v))
|
|
*oif++ = v->face()->neighbor(1);
|
|
return v;
|
|
}
|
|
|
|
if((lt != Triangulation::OUTSIDE_AFFINE_HULL) && this->test_dim_down(v)) {
|
|
// verify if p and two static vertices are collinear in this case
|
|
int iinf;
|
|
Face_circulator finf = incident_faces(this->infinite_vertex()),
|
|
fdone(finf);
|
|
do {
|
|
if(!finf->has_vertex(v))
|
|
{
|
|
iinf = ~(finf->index(this->infinite_vertex()));
|
|
break;
|
|
}
|
|
} while(++finf != fdone);
|
|
if(this->orientation(finf->vertex(iinf&1)->point(),
|
|
finf->vertex(iinf&2)->point(),
|
|
p) == COLLINEAR)
|
|
{
|
|
v->point() = p;
|
|
this->tds().dim_down(loc, loc->index(v));
|
|
for(All_faces_iterator afi = this-> all_faces_begin();
|
|
afi != this->all_faces_end();
|
|
afi++) *oif++ = afi;
|
|
return v;
|
|
}
|
|
}
|
|
|
|
std::set<Face_handle> faces_set;
|
|
inserted = Delaunay_triangulation_2<Gt,Tds>::insert(p, lt, loc, li);
|
|
Face_circulator fc = this->incident_faces(inserted), done(fc);
|
|
do { faces_set.insert(fc); } while(++fc != done);
|
|
|
|
{
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, maxd,30);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Face_handle>, f, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<int>, i, maxd);
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(std::vector<Vertex_handle>, w, maxd);
|
|
|
|
int d;
|
|
remove_degree_init(v,f,w,i,d,maxd);
|
|
remove_degree_triangulate(v,f,w,i,d);
|
|
this->delete_vertex(v);
|
|
Face_circulator fc(v[0]),done;
|
|
do *oif++ = fc++; while (fc!=done);
|
|
}
|
|
|
|
fc = this->incident_faces(inserted), done(fc);
|
|
std::vector<Face_handle> faces_pt;
|
|
faces_pt.reserve(16);
|
|
do { faces_pt.push_back(fc); } while(++fc != done);
|
|
int ss = faces_pt.size();
|
|
for(int k=0; k<ss; k++)
|
|
{
|
|
Face_handle f = faces_pt[k];
|
|
int i = f->index(inserted);
|
|
f->set_vertex(i, v);
|
|
}
|
|
v->set_point(p);
|
|
v->set_face(inserted->face());
|
|
this->delete_vertex(inserted);
|
|
|
|
for(typename std::set<Face_handle>::const_iterator ib = faces_set.begin(),
|
|
iend = faces_set.end(); ib != iend; ib++)
|
|
*oif++ = *ib;
|
|
|
|
return v;
|
|
}
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_DELAUNAY_TRIANGULATION_2_H
|