1132 lines
31 KiB
C
1132 lines
31 KiB
C
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// Copyright (c) 2010-2018 INRIA Sophia Antipolis, INRIA Nancy (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/Hyperbolic_triangulation_2/include/CGAL/Hyperbolic_Delaunay_triangulation_2.h $
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// $Id: Hyperbolic_Delaunay_triangulation_2.h 0779373 2020-03-26T13:31:46+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) : Mikhail Bogdanov
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// Monique Teillaud <Monique.Teillaud@inria.fr>
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#ifndef CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_2_H
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#define CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_2_H
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#include <CGAL/license/Hyperbolic_triangulation_2.h>
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#include <CGAL/Hyperbolic_triangulation_face_base_2.h>
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#include <CGAL/Delaunay_triangulation_2.h>
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#include <stack>
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#include <set>
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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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Hyperbolic_triangulation_face_base_2<Gt> > >
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class Hyperbolic_Delaunay_triangulation_2
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: private Delaunay_triangulation_2<Gt,Tds>
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{
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public:
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typedef Hyperbolic_Delaunay_triangulation_2<Gt, Tds> Self;
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typedef Delaunay_triangulation_2<Gt,Tds> Base;
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typedef typename Tds::size_type size_type;
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typedef typename Tds::Vertex_handle Vertex_handle;
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typedef typename Tds::Face_handle Face_handle;
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typedef typename Tds::Edge Edge;
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typedef Gt Geom_traits;
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typedef typename Geom_traits::FT FT;
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typedef typename Geom_traits::Hyperbolic_point_2 Point;
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typedef typename Geom_traits::Hyperbolic_Voronoi_point_2 Hyperbolic_Voronoi_point;
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typedef typename Geom_traits::Hyperbolic_segment_2 Hyperbolic_segment;
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typedef typename Geom_traits::Hyperbolic_triangle_2 Hyperbolic_triangle;
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// Tag to distinguish regular triangulations from others
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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 Base::cw;
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using Base::ccw;
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using Base::geom_traits;
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#endif
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enum Locate_type {
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VERTEX = 0,
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EDGE,
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FACE,
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OUTSIDE_CONVEX_HULL,
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OUTSIDE_AFFINE_HULL
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};
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typedef typename Geom_traits::Side_of_oriented_hyperbolic_segment_2 Side_of_oriented_hyperbolic_segment;
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typedef typename Geom_traits::Is_Delaunay_hyperbolic Is_Delaunay_hyperbolic;
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Hyperbolic_Delaunay_triangulation_2(const Geom_traits& gt = Geom_traits())
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: Delaunay_triangulation_2<Gt,Tds>(gt), _gt(gt)
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{
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}
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Hyperbolic_Delaunay_triangulation_2(const Hyperbolic_Delaunay_triangulation_2<Gt,Tds> &tr)
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: Delaunay_triangulation_2<Gt,Tds>(tr), _gt()
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{
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CGAL_triangulation_postcondition(this->is_valid());
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}
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template<class InputIterator>
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Hyperbolic_Delaunay_triangulation_2(InputIterator first, InputIterator last,
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const Geom_traits& gt = Geom_traits())
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: Delaunay_triangulation_2<Gt,Tds>(gt), _gt(gt)
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{
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insert(first, last);
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for(All_vertices_iterator vit=all_vertices_begin(); vit!=all_vertices_end(); ++vit)
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ensure_hyperbolic_face_handle(vit);
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}
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/*************************************
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Circulators and iterators
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*************************************/
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private:
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// This class is used to generate the iterators.
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class Non_hyperbolic_tester
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{
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const Self *t;
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public:
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Non_hyperbolic_tester() {} // needs a default constructor for Filter_iterator
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Non_hyperbolic_tester(const Self *tr) : t(tr) {}
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bool operator()(const typename Base::All_vertices_iterator & vit) const { return Base::is_infinite(vit); }
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bool operator()(const typename Base::All_faces_iterator & fit) const { return !t->is_Delaunay_hyperbolic(fit); }
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bool operator()(const typename Base::All_edges_iterator & eit) const
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{
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Edge e(eit->first, eit->second);
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return !t->is_Delaunay_hyperbolic(e);
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}
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};
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Non_hyperbolic_tester non_hyperbolic_tester() const { return Non_hyperbolic_tester(this); }
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public:
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class Hyperbolic_faces_iterator
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: public Filter_iterator<typename Base::All_faces_iterator, Non_hyperbolic_tester>
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{
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typedef Filter_iterator<typename Base::All_faces_iterator, Non_hyperbolic_tester> PBase;
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typedef Hyperbolic_faces_iterator Self;
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public:
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Hyperbolic_faces_iterator() : PBase() {}
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Hyperbolic_faces_iterator(const PBase &b) : PBase(b) {}
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Self & operator++() { PBase::operator++(); return *this; }
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Self & operator--() { PBase::operator--(); return *this; }
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Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
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Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
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operator const Face_handle() const { return PBase::base(); }
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};
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Hyperbolic_faces_iterator hyperbolic_faces_begin() const
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{
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if(dimension() < 2)
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return hyperbolic_faces_end();
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return CGAL::filter_iterator(Base::all_faces_end(),
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Non_hyperbolic_tester(this),
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Base::all_faces_begin());
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}
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Hyperbolic_faces_iterator hyperbolic_faces_end() const
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{
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return CGAL::filter_iterator(Base::all_faces_end(), Non_hyperbolic_tester(this));
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}
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typedef Filter_iterator<typename Base::All_edges_iterator, Non_hyperbolic_tester> Hyperbolic_edges_iterator;
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Hyperbolic_edges_iterator hyperbolic_edges_begin() const
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{
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if(dimension() < 1)
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return hyperbolic_edges_end();
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return CGAL::filter_iterator(Base::all_edges_end(),
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Non_hyperbolic_tester(this),
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Base::all_edges_begin());
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}
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Hyperbolic_edges_iterator hyperbolic_edges_end() const
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{
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return CGAL::filter_iterator(Base::all_edges_end(), Non_hyperbolic_tester(this));
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}
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template <typename HTriangulation>
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class Hyperbolic_adjacent_vertex_circulator
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: Base::Vertex_circulator
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{
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typedef typename Base::Vertex_circulator VBase;
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typedef Hyperbolic_adjacent_vertex_circulator Self;
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typedef typename Tds::Vertex Vertex;
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Vertex_handle _v;
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Face_handle pos;
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int _ri;
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int _iv;
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public:
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Hyperbolic_adjacent_vertex_circulator(const HTriangulation& tri) : VBase(), _v(Vertex_handle()), pos(Face_handle()), _ri(0), _tri(tri) {}
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Hyperbolic_adjacent_vertex_circulator(Vertex_handle v, const HTriangulation& tri, Face_handle fh = Face_handle())
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: VBase(v, fh), _tri(tri)
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{
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_v = v;
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if (fh == Face_handle())
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pos = _v->face();
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else
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pos = fh;
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_iv = pos->index(_v);
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bool ok = false;
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do
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{
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_ri = cw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, ccw(_iv)))
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{
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_ri = ccw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, cw(_iv)))
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{
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pos = pos->neighbor(cw(_iv));
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_iv = pos->index(_v);
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}
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else
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{
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ok = true;
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}
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}
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else {
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ok = true;
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}
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} while (!ok);
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}
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Self& operator++()
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{
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pos = pos->neighbor(cw(_iv));
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_iv = pos->index(_v);
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bool ok = false;
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do
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{
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_ri = cw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, ccw(_iv)))
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{
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_ri = ccw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, cw(_iv)))
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{
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pos = pos->neighbor(cw(_iv));
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_iv = pos->index(_v);
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}
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else
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{
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ok = true;
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}
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}
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else {
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ok = true;
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}
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} while (!ok);
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return *this;
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}
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Self& operator--()
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{
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pos = pos->neighbor(ccw(_iv));
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_iv = pos->index(_v);
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bool ok = false;
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do
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{
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_ri = ccw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, cw(_iv)))
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{
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_ri = cw(_iv);
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if (_tri.is_finite_non_hyperbolic(pos, ccw(_iv)))
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{
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pos = pos->neighbor(ccw(_iv));
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_iv = pos->index(_v);
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}
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else
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{
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ok = true;
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}
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}
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else {
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ok = true;
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}
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} while (!ok);
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return *this;
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}
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bool operator==(const Self &vc) const
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{
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return (this->_v == vc->_v &&
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this->pos == vc->pos &&
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this->_ri == vc->_ri &&
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this->_iv == vc->_iv);
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}
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bool operator!=(const Self &vc) const { return !this->operator==(vc); }
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bool operator==(const Vertex_handle &vh) const { return (this->pos->vertex(_ri) == vh); }
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bool operator!=(const Vertex_handle &vh) const { return !this->operator==(vh); }
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bool is_empty() const { return (this->pos == Face_handle() && this->_v == Vertex_handle()); }
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Vertex& operator*() const
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{
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CGAL_triangulation_precondition(pos != Face_handle() && _v != Vertex_handle());
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return *(pos->vertex(_ri));
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}
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Vertex* operator->() const
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{
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CGAL_triangulation_precondition(pos != Face_handle() && _v != Vertex_handle());
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return &*(pos->vertex(_ri));
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}
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Vertex_handle base() const { return pos->vertex(_ri); }
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operator Vertex_handle() const { return pos->vertex(_ri); }
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private:
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const HTriangulation& _tri;
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};
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private:
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Geom_traits _gt;
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public:
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Tds& tds()
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{
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return Base::tds();
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}
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const Tds& tds() const
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{
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return Base::tds();
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}
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Geom_traits& geom_traits()
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{
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return _gt;
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}
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const Geom_traits& geom_traits() const
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{
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return _gt;
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}
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void swap (Self& tr)
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{
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Base::swap(tr);
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Geom_traits t = _gt;
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_gt = tr._gt;
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tr._gt = t;
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this->mark_finite_non_hyperbolic_faces();
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tr.mark_finite_non_hyperbolic_faces();
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}
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Self& operator=(const Self &tr)
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{
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Self newone = Self(tr);
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this->swap(newone);
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return *this;
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}
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bool operator==(const Self& tr )
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{
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if (tr.number_of_vertices() != this->number_of_vertices())
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return false;
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if (tr.number_of_hyperbolic_faces() != this->number_of_hyperbolic_faces())
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return false;
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if (tr.number_of_vertices() == 0)
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return true; // as in Periodic_2_triangulation_2
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return Base::operator==(tr);
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}
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typedef Hyperbolic_adjacent_vertex_circulator<Self> Vertex_circulator;
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typedef typename Tds::Edge_circulator Edge_circulator;
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typedef typename Tds::Face_circulator Face_circulator;
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typedef Hyperbolic_faces_iterator All_faces_iterator;
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All_faces_iterator all_faces_begin() const { return hyperbolic_faces_begin(); }
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All_faces_iterator all_faces_end() const { return hyperbolic_faces_end(); }
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||
|
|
|
||
|
|
typedef Hyperbolic_edges_iterator All_edges_iterator;
|
||
|
|
All_edges_iterator all_edges_begin() const { return hyperbolic_edges_begin(); }
|
||
|
|
All_edges_iterator all_edges_end() const { return hyperbolic_edges_end(); }
|
||
|
|
|
||
|
|
typedef typename Base::Finite_vertices_iterator All_vertices_iterator;
|
||
|
|
All_vertices_iterator all_vertices_begin() const { return Base::finite_vertices_begin(); }
|
||
|
|
All_vertices_iterator all_vertices_end() const { return Base::finite_vertices_end(); }
|
||
|
|
|
||
|
|
// The declarations below are required by apply_to_range: do not document!
|
||
|
|
typedef All_vertices_iterator Finite_vertices_iterator;
|
||
|
|
Finite_vertices_iterator finite_vertices_begin() const { return all_vertices_begin(); }
|
||
|
|
Finite_vertices_iterator finite_vertices_end() const { return all_vertices_end(); }
|
||
|
|
typedef All_faces_iterator Finite_faces_iterator;
|
||
|
|
Finite_faces_iterator finite_faces_begin() const { return all_faces_begin(); }
|
||
|
|
Finite_faces_iterator finite_faces_end() const { return all_faces_end(); }
|
||
|
|
|
||
|
|
// Algebraic_kernel_for_circles_2 needs this for some reason
|
||
|
|
typedef typename Base::Line_face_circulator Line_face_circulator;
|
||
|
|
|
||
|
|
void clear() { Base::clear(); }
|
||
|
|
|
||
|
|
void mark_star(Vertex_handle v) const
|
||
|
|
{
|
||
|
|
if(!is_star_bounded(v))
|
||
|
|
mark_star_faces(v);
|
||
|
|
}
|
||
|
|
|
||
|
|
template<class OutputItFaces>
|
||
|
|
OutputItFaces find_conflicts(const Point& p, OutputItFaces fit, Face_handle start = Face_handle()) const
|
||
|
|
{
|
||
|
|
return Base::get_conflicts(p, fit, start);
|
||
|
|
}
|
||
|
|
|
||
|
|
Vertex_handle insert(const Point& p,
|
||
|
|
Face_handle start = Face_handle())
|
||
|
|
{
|
||
|
|
Vertex_handle v = Base::insert(p, start);
|
||
|
|
mark_star(v);
|
||
|
|
ensure_hyperbolic_face_handle(v);
|
||
|
|
|
||
|
|
return v;
|
||
|
|
}
|
||
|
|
|
||
|
|
Vertex_handle insert(const Point& p,
|
||
|
|
typename Base::Locate_type lt,
|
||
|
|
Face_handle loc, int li)
|
||
|
|
{
|
||
|
|
Vertex_handle v = Base::insert(p, lt, loc, li);
|
||
|
|
mark_star(v);
|
||
|
|
ensure_hyperbolic_face_handle(v);
|
||
|
|
|
||
|
|
return v;
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifndef CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
|
||
|
|
template < class InputIterator >
|
||
|
|
std::ptrdiff_t insert(InputIterator first, InputIterator last,
|
||
|
|
typename boost::enable_if<
|
||
|
|
boost::is_base_of<Point, typename std::iterator_traits<InputIterator>::value_type>
|
||
|
|
>::type* = nullptr)
|
||
|
|
#else
|
||
|
|
template < class InputIterator >
|
||
|
|
std::ptrdiff_t insert(InputIterator first, InputIterator last)
|
||
|
|
#endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
|
||
|
|
{
|
||
|
|
size_type n = Base::insert(first, last);
|
||
|
|
|
||
|
|
mark_finite_non_hyperbolic_faces();
|
||
|
|
for(All_vertices_iterator vit = all_vertices_begin(); vit != all_vertices_end(); ++vit)
|
||
|
|
ensure_hyperbolic_face_handle(vit);
|
||
|
|
|
||
|
|
return n;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
void remove(Vertex_handle v)
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(tds().is_vertex(v));
|
||
|
|
std::vector<Vertex_handle> nbr;
|
||
|
|
bool dim_was_2 = false;
|
||
|
|
if (this->dimension() == 2)
|
||
|
|
{
|
||
|
|
dim_was_2 = true;
|
||
|
|
typename Base::Vertex_circulator nbv = Base::incident_vertices(v), done(nbv);
|
||
|
|
do
|
||
|
|
{
|
||
|
|
nbr.push_back(nbv);
|
||
|
|
} while (++nbv != done);
|
||
|
|
}
|
||
|
|
|
||
|
|
Base::remove(v);
|
||
|
|
|
||
|
|
if (dim_was_2)
|
||
|
|
{
|
||
|
|
for (unsigned int i = 0; i < nbr.size(); ++i)
|
||
|
|
{
|
||
|
|
mark_star_faces(nbr[i]);
|
||
|
|
ensure_hyperbolic_face_handle(nbr[i]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class VertexRemoveIterator>
|
||
|
|
void remove(VertexRemoveIterator first, VertexRemoveIterator last)
|
||
|
|
{
|
||
|
|
for (VertexRemoveIterator vit = first; vit != last; ++vit)
|
||
|
|
{
|
||
|
|
remove(*vit);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
Needed by DT_2: do not document!
|
||
|
|
*/
|
||
|
|
template <typename T>
|
||
|
|
bool is_infinite(T v) const { return Base::is_infinite(v); }
|
||
|
|
|
||
|
|
bool is_Delaunay_hyperbolic(Face_handle f) const
|
||
|
|
{
|
||
|
|
return !Base::is_infinite(f) && !is_finite_non_hyperbolic(f);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_Delaunay_hyperbolic(Face_handle f, int i) const
|
||
|
|
{
|
||
|
|
return !Base::is_infinite(f, i) && !is_finite_non_hyperbolic(f, i);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_Delaunay_hyperbolic(const Edge& e) const
|
||
|
|
{
|
||
|
|
return is_Delaunay_hyperbolic(e.first, e.second);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_Delaunay_hyperbolic(const Edge_circulator& ec) const
|
||
|
|
{
|
||
|
|
return is_Delaunay_hyperbolic(*ec);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_Delaunay_hyperbolic(const All_edges_iterator& ei) const
|
||
|
|
{
|
||
|
|
return is_Delaunay_hyperbolic(*ei);
|
||
|
|
}
|
||
|
|
|
||
|
|
private:
|
||
|
|
class Face_data
|
||
|
|
{
|
||
|
|
private:
|
||
|
|
// a finite face is non_hyperbolic if its circumscribing circle intersects the circle at infinity
|
||
|
|
bool _is_Delaunay_hyperbolic;
|
||
|
|
|
||
|
|
// defined only if the face is finite and non_hyperbolic
|
||
|
|
unsigned int _non_hyperbolic_edge;
|
||
|
|
|
||
|
|
public:
|
||
|
|
Face_data() : _is_Delaunay_hyperbolic(true), _non_hyperbolic_edge(UCHAR_MAX) {}
|
||
|
|
|
||
|
|
unsigned int get_non_hyperbolic_edge() const
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(!_is_Delaunay_hyperbolic);
|
||
|
|
CGAL_triangulation_precondition(_non_hyperbolic_edge <= 2);
|
||
|
|
|
||
|
|
return _non_hyperbolic_edge;
|
||
|
|
}
|
||
|
|
|
||
|
|
void set_non_hyperbolic_edge(unsigned int uschar)
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(!_is_Delaunay_hyperbolic);
|
||
|
|
CGAL_triangulation_precondition(uschar <= 2);
|
||
|
|
|
||
|
|
_non_hyperbolic_edge = uschar;
|
||
|
|
}
|
||
|
|
|
||
|
|
bool get_is_Delaunay_hyperbolic() const { return _is_Delaunay_hyperbolic; }
|
||
|
|
void set_is_Delaunay_hyperbolic(bool flag) { _is_Delaunay_hyperbolic = flag; }
|
||
|
|
};
|
||
|
|
|
||
|
|
/*
|
||
|
|
During the insertion of a new point in the triangulation, the added vertex points to a face.
|
||
|
|
This function ensures that the face to which the vertex points is hyperbolic.
|
||
|
|
*/
|
||
|
|
void ensure_hyperbolic_face_handle(Vertex_handle v)
|
||
|
|
{
|
||
|
|
if(dimension() > 2)
|
||
|
|
{
|
||
|
|
Face_circulator fc = this->incident_faces(v), done(fc);
|
||
|
|
if(fc != 0)
|
||
|
|
{
|
||
|
|
do
|
||
|
|
{
|
||
|
|
if(is_Delaunay_hyperbolic(fc))
|
||
|
|
{
|
||
|
|
v->set_face(fc);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
while(++fc != done);
|
||
|
|
}
|
||
|
|
CGAL_triangulation_postcondition(is_Delaunay_hyperbolic(v->face()));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side side_of_hyperbolic_triangle(const Point& p, const Point& q, const Point& r,
|
||
|
|
const Point& query, Locate_type <, int& li) const
|
||
|
|
{
|
||
|
|
// The triangle (p,q,r) must be Delaunay hyperbolic
|
||
|
|
CGAL_triangulation_precondition(geom_traits().is_Delaunay_hyperbolic_2_object()(p, q, r));
|
||
|
|
|
||
|
|
// Point p is assumed to be at index 0, q at index 1 and r at index 2 in the face.
|
||
|
|
li = -1;
|
||
|
|
|
||
|
|
if(query == p)
|
||
|
|
{
|
||
|
|
lt = VERTEX;
|
||
|
|
li = 0;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(query == q)
|
||
|
|
{
|
||
|
|
lt = VERTEX;
|
||
|
|
li = 1;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(query == r)
|
||
|
|
{
|
||
|
|
lt = VERTEX;
|
||
|
|
li = 2;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side cp1 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(p, q, query);
|
||
|
|
if(cp1 == ON_ORIENTED_BOUNDARY)
|
||
|
|
{
|
||
|
|
lt = EDGE;
|
||
|
|
li = 2;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side cp2 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(q, r, query);
|
||
|
|
if(cp2 == ON_ORIENTED_BOUNDARY)
|
||
|
|
{
|
||
|
|
lt = EDGE;
|
||
|
|
li = 0;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side cp3 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(r, p, query);
|
||
|
|
if(cp3 == ON_ORIENTED_BOUNDARY)
|
||
|
|
{
|
||
|
|
lt = EDGE;
|
||
|
|
li = 1;
|
||
|
|
return ON_ORIENTED_BOUNDARY;
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side cs1 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(p, q, r);
|
||
|
|
Oriented_side cs2 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(q, r, p);
|
||
|
|
Oriented_side cs3 = geom_traits().side_of_oriented_hyperbolic_segment_2_object()(r, p, q);
|
||
|
|
|
||
|
|
// Cannot be on the boundary here.
|
||
|
|
lt = FACE;
|
||
|
|
if(cs1 != cp1 || cs2 != cp2 || cs3 != cp3)
|
||
|
|
return ON_NEGATIVE_SIDE;
|
||
|
|
else
|
||
|
|
return ON_POSITIVE_SIDE;
|
||
|
|
}
|
||
|
|
|
||
|
|
int get_finite_non_hyperbolic_edge(Face_handle f) const
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(is_finite_non_hyperbolic(f));
|
||
|
|
Face_data fd = object_cast<Face_data>(f->tds_data());
|
||
|
|
return fd.get_non_hyperbolic_edge();
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_finite_non_hyperbolic(Face_handle f) const
|
||
|
|
{
|
||
|
|
if(const Face_data* td = object_cast<Face_data>(&f->tds_data()))
|
||
|
|
{
|
||
|
|
return !td->get_is_Delaunay_hyperbolic();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_finite_non_hyperbolic(Face_handle f, int i) const
|
||
|
|
{
|
||
|
|
if(dimension() <= 1)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
if(is_finite_non_hyperbolic(f) && get_finite_non_hyperbolic_edge(f) == i)
|
||
|
|
return true;
|
||
|
|
|
||
|
|
// another incident face and corresponding index
|
||
|
|
Face_handle f2 = f->neighbor(i);
|
||
|
|
int i2 = f2->index(f);
|
||
|
|
|
||
|
|
if(is_finite_non_hyperbolic(f2) && get_finite_non_hyperbolic_edge(f2) == i2)
|
||
|
|
return true;
|
||
|
|
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_finite_non_hyperbolic(const Edge& e) const
|
||
|
|
{
|
||
|
|
return is_finite_non_hyperbolic(e.first, e.second);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Depth-first search (dfs) and marking the finite non_hyperbolic faces.
|
||
|
|
void mark_finite_non_hyperbolic_faces() const
|
||
|
|
{
|
||
|
|
if(dimension() <= 1)
|
||
|
|
return;
|
||
|
|
|
||
|
|
std::set<Face_handle> visited_faces;
|
||
|
|
|
||
|
|
// maintain a stack to be able to backtrack
|
||
|
|
// to the most recent faces which neighbors are not visited
|
||
|
|
std::stack<Face_handle> backtrack;
|
||
|
|
|
||
|
|
// start from a face with infinite vertex
|
||
|
|
Face_handle current = Base::infinite_face();
|
||
|
|
|
||
|
|
// mark it as visited
|
||
|
|
visited_faces.insert(current);
|
||
|
|
|
||
|
|
// put the element whose neighbors we are going to explore.
|
||
|
|
backtrack.push(current);
|
||
|
|
|
||
|
|
Face_handle next;
|
||
|
|
|
||
|
|
while(!backtrack.empty())
|
||
|
|
{
|
||
|
|
// take a face
|
||
|
|
current = backtrack.top();
|
||
|
|
|
||
|
|
// start visiting the neighbors
|
||
|
|
int i = 0;
|
||
|
|
for(; i<3; ++i)
|
||
|
|
{
|
||
|
|
next = current->neighbor(i);
|
||
|
|
|
||
|
|
// if a neighbor is already visited, then stop going deeper
|
||
|
|
if(visited_faces.find(next) != visited_faces.end())
|
||
|
|
continue;
|
||
|
|
|
||
|
|
visited_faces.insert(next);
|
||
|
|
mark_face(next);
|
||
|
|
|
||
|
|
// go deeper if the neighbor is non_hyperbolic
|
||
|
|
if(!is_Delaunay_hyperbolic(next))
|
||
|
|
{
|
||
|
|
backtrack.push(next);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// if all the neighbors are already visited, then remove "current" face.
|
||
|
|
if(i == 3)
|
||
|
|
backtrack.pop();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// check if a star is bounded by finite faces
|
||
|
|
bool is_star_bounded(Vertex_handle v) const
|
||
|
|
{
|
||
|
|
if(dimension() <= 1)
|
||
|
|
return true;
|
||
|
|
|
||
|
|
Face_handle f = v->face();
|
||
|
|
Face_handle next;
|
||
|
|
int i;
|
||
|
|
Face_handle start(f);
|
||
|
|
Face_handle opposite_face;
|
||
|
|
|
||
|
|
do
|
||
|
|
{
|
||
|
|
i = f->index(v);
|
||
|
|
next = f->neighbor(ccw(i)); // turn ccw around v
|
||
|
|
|
||
|
|
opposite_face = f->neighbor(i);
|
||
|
|
if(!is_Delaunay_hyperbolic(opposite_face))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
f = next;
|
||
|
|
}
|
||
|
|
while(next != start);
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
void mark_star_faces(Vertex_handle v) const
|
||
|
|
{
|
||
|
|
if(dimension() <= 1)
|
||
|
|
return;
|
||
|
|
|
||
|
|
Face_handle f = v->face();
|
||
|
|
Face_handle start(f), next;
|
||
|
|
int i;
|
||
|
|
do
|
||
|
|
{
|
||
|
|
i = f->index(v);
|
||
|
|
next = f->neighbor(ccw(i)); // turn ccw around v
|
||
|
|
|
||
|
|
mark_face(f);
|
||
|
|
|
||
|
|
f = next;
|
||
|
|
} while(next != start);
|
||
|
|
}
|
||
|
|
|
||
|
|
void mark_face(const Face_handle f) const
|
||
|
|
{
|
||
|
|
Is_Delaunay_hyperbolic del;
|
||
|
|
int idx;
|
||
|
|
bool flag = del(point(f,0),
|
||
|
|
point(f,1),
|
||
|
|
point(f,2),
|
||
|
|
idx);
|
||
|
|
|
||
|
|
Face_data fd;
|
||
|
|
fd.set_is_Delaunay_hyperbolic(flag);
|
||
|
|
|
||
|
|
if(!flag)
|
||
|
|
fd.set_non_hyperbolic_edge(idx);
|
||
|
|
|
||
|
|
f->tds_data() = make_object(fd);
|
||
|
|
}
|
||
|
|
|
||
|
|
public:
|
||
|
|
|
||
|
|
Line_face_circulator line_walk(const Point& p, const Point& q, Face_handle f = Face_handle()) const
|
||
|
|
{
|
||
|
|
return Base::line_walk(p, q, f);
|
||
|
|
}
|
||
|
|
|
||
|
|
Hyperbolic_triangle hyperbolic_triangle(const Face_handle f) const { return Base::triangle(f); }
|
||
|
|
|
||
|
|
// needed by DT_2: do not document!
|
||
|
|
Hyperbolic_triangle triangle(const Face_handle f) const { return hyperbolic_triangle(f); }
|
||
|
|
|
||
|
|
Hyperbolic_segment hyperbolic_segment(const Face_handle f, const int i) const
|
||
|
|
{
|
||
|
|
return geom_traits().construct_hyperbolic_segment_2_object()(point(f,cw(i)),
|
||
|
|
point(f,ccw(i)));
|
||
|
|
}
|
||
|
|
|
||
|
|
Hyperbolic_segment hyperbolic_segment(const Edge& e) const
|
||
|
|
{
|
||
|
|
Face_handle f = e.first;
|
||
|
|
int i = e.second;
|
||
|
|
return hyperbolic_segment(f, i);
|
||
|
|
}
|
||
|
|
|
||
|
|
Hyperbolic_segment hyperbolic_segment(const Edge_circulator& e) const { return hyperbolic_segment(*e); }
|
||
|
|
|
||
|
|
// needed by DT_2: do not document!
|
||
|
|
Hyperbolic_segment segment(const Face_handle f, const int i) const { return hyperbolic_segment(f,i); }
|
||
|
|
Hyperbolic_segment segment(const Edge& e) const { return hyperbolic_segment(e); }
|
||
|
|
Hyperbolic_segment segment(const Edge_circulator& e) const { return hyperbolic_segment(e); }
|
||
|
|
|
||
|
|
size_type number_of_vertices() const { return Base::number_of_vertices(); }
|
||
|
|
Vertex_circulator adjacent_vertices(Vertex_handle v) const { return Vertex_circulator(v, *this); }
|
||
|
|
|
||
|
|
size_type number_of_hyperbolic_faces() const
|
||
|
|
{
|
||
|
|
return std::distance(hyperbolic_faces_begin(), hyperbolic_faces_end());
|
||
|
|
}
|
||
|
|
|
||
|
|
size_type number_of_hyperbolic_edges() const
|
||
|
|
{
|
||
|
|
return std::distance(hyperbolic_edges_begin(), hyperbolic_edges_end());
|
||
|
|
}
|
||
|
|
|
||
|
|
int dimension() const { return Base::dimension(); }
|
||
|
|
|
||
|
|
Hyperbolic_Voronoi_point dual(Face_handle f) const
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(is_Delaunay_hyperbolic(f));
|
||
|
|
return geom_traits().construct_hyperbolic_circumcenter_2_object()(point(f,0),
|
||
|
|
point(f,1),
|
||
|
|
point(f,2));
|
||
|
|
}
|
||
|
|
|
||
|
|
Hyperbolic_segment dual(const Edge& e) const { return dual(e.first, e.second); }
|
||
|
|
|
||
|
|
Hyperbolic_segment dual(Face_handle f, int i) const
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(is_Delaunay_hyperbolic(f, i));
|
||
|
|
|
||
|
|
if(dimension() == 1)
|
||
|
|
{
|
||
|
|
const Point& p = point(f,cw(i));
|
||
|
|
const Point& q = point(f,ccw(i));
|
||
|
|
|
||
|
|
// hyperbolic line
|
||
|
|
Hyperbolic_segment line = geom_traits().construct_hyperbolic_bisector_2_object()(p, q);
|
||
|
|
return line;
|
||
|
|
}
|
||
|
|
|
||
|
|
Face_handle n = f->neighbor(i);
|
||
|
|
int in = n->index(f);
|
||
|
|
|
||
|
|
bool fhyp = is_Delaunay_hyperbolic(f);
|
||
|
|
bool nhyp = is_Delaunay_hyperbolic(n);
|
||
|
|
|
||
|
|
// both faces are non_hyperbolic, but the incident edge is hyperbolic
|
||
|
|
if(!fhyp && !nhyp)
|
||
|
|
{
|
||
|
|
const Point& p = point(f,ccw(i));
|
||
|
|
const Point& q = point(f,cw(i));
|
||
|
|
|
||
|
|
// hyperbolic line
|
||
|
|
Hyperbolic_segment line = geom_traits().construct_hyperbolic_bisector_2_object()(p, q);
|
||
|
|
return line;
|
||
|
|
}
|
||
|
|
|
||
|
|
// both faces are hyperbolic
|
||
|
|
if(fhyp && nhyp)
|
||
|
|
{
|
||
|
|
const Point& p = point(f,ccw(i));
|
||
|
|
const Point& q = point(f,cw(i));
|
||
|
|
|
||
|
|
Hyperbolic_segment s = geom_traits().construct_hyperbolic_bisector_2_object()(
|
||
|
|
p, q, point(f,i), point(n,in));
|
||
|
|
return s;
|
||
|
|
}
|
||
|
|
|
||
|
|
// one of the incident faces is non_hyperbolic
|
||
|
|
Face_handle hyp_face = f;
|
||
|
|
|
||
|
|
if(!fhyp)
|
||
|
|
{
|
||
|
|
hyp_face = n;
|
||
|
|
i = in;
|
||
|
|
}
|
||
|
|
|
||
|
|
const Point& p = point(hyp_face,ccw(i));
|
||
|
|
const Point& q = point(hyp_face,cw(i));
|
||
|
|
|
||
|
|
Hyperbolic_segment ray = geom_traits().construct_hyperbolic_bisector_2_object()(
|
||
|
|
p, q, point(hyp_face,i));
|
||
|
|
return ray;
|
||
|
|
}
|
||
|
|
|
||
|
|
public:
|
||
|
|
|
||
|
|
const Point point(const Vertex_handle vh) const
|
||
|
|
{
|
||
|
|
return vh->point();
|
||
|
|
}
|
||
|
|
|
||
|
|
const Point point(const Face_handle fh, const int i) const
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(0 <= i);
|
||
|
|
CGAL_triangulation_precondition(i <= 2);
|
||
|
|
return fh->vertex(i)->point();
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
Point point(const Vertex_handle vh)
|
||
|
|
{
|
||
|
|
return vh->point();
|
||
|
|
}
|
||
|
|
|
||
|
|
Point point(const Face_handle fh, const int i)
|
||
|
|
{
|
||
|
|
CGAL_triangulation_precondition(0 <= i);
|
||
|
|
CGAL_triangulation_precondition(i <= 2);
|
||
|
|
return fh->vertex(i)->point();
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
bool is_valid()
|
||
|
|
{
|
||
|
|
if (Base::is_valid())
|
||
|
|
{
|
||
|
|
for (Hyperbolic_faces_iterator fit = hyperbolic_faces_begin(); fit != hyperbolic_faces_end(); fit++)
|
||
|
|
{
|
||
|
|
if (!is_Delaunay_hyperbolic(fit))
|
||
|
|
{
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
for (Hyperbolic_edges_iterator eit = hyperbolic_edges_begin(); eit != hyperbolic_edges_end(); eit++)
|
||
|
|
{
|
||
|
|
if (!is_Delaunay_hyperbolic(eit))
|
||
|
|
{
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
Face_handle locate(const Point& p, const Face_handle hint = Face_handle()) const
|
||
|
|
{
|
||
|
|
Locate_type lt;
|
||
|
|
int li;
|
||
|
|
return locate(p, lt, li, hint);
|
||
|
|
}
|
||
|
|
|
||
|
|
Face_handle locate(const Point& query, Locate_type& lt, int &li, Face_handle hint = Face_handle()) const
|
||
|
|
{
|
||
|
|
// Perform an Euclidean location first and get close to the hyperbolic face containing the query point
|
||
|
|
typename Base::Locate_type blt;
|
||
|
|
Face_handle fh = Base::locate(query, blt, li, hint);
|
||
|
|
|
||
|
|
if(blt == Base::VERTEX) {
|
||
|
|
lt = VERTEX;
|
||
|
|
} else {
|
||
|
|
if(blt == Base::EDGE) {
|
||
|
|
lt = EDGE;
|
||
|
|
} else {
|
||
|
|
if(blt == Base::FACE) {
|
||
|
|
lt = FACE;
|
||
|
|
} else {
|
||
|
|
if(blt == Base::OUTSIDE_CONVEX_HULL) {
|
||
|
|
lt = OUTSIDE_CONVEX_HULL;
|
||
|
|
} else {
|
||
|
|
lt = OUTSIDE_AFFINE_HULL;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if(lt == VERTEX)
|
||
|
|
return fh;
|
||
|
|
|
||
|
|
if(lt == OUTSIDE_CONVEX_HULL || lt == OUTSIDE_AFFINE_HULL)
|
||
|
|
return Face_handle();
|
||
|
|
|
||
|
|
// This case corresponds to when the point is located on an Euclidean edge.
|
||
|
|
if(lt == EDGE)
|
||
|
|
{
|
||
|
|
Point p = point(fh, 0);
|
||
|
|
Point q = point(fh, 1);
|
||
|
|
Point r = point(fh, 2);
|
||
|
|
|
||
|
|
if(geom_traits().is_Delaunay_hyperbolic_2_object()(p, q, r))
|
||
|
|
{
|
||
|
|
Oriented_side side = side_of_hyperbolic_triangle(p, q, r, query, lt, li);
|
||
|
|
if(side == ON_ORIENTED_BOUNDARY) {
|
||
|
|
lt = EDGE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
if(side == ON_POSITIVE_SIDE) {
|
||
|
|
lt = FACE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
// do nothing -- we still have to check the neighboring face
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
p = point(fh, ccw(li));
|
||
|
|
q = point(Base::mirror_vertex(fh, li));
|
||
|
|
r = point(fh, cw(li));
|
||
|
|
|
||
|
|
if(geom_traits().is_Delaunay_hyperbolic_2_object()(p, q, r))
|
||
|
|
{
|
||
|
|
Oriented_side side = side_of_hyperbolic_triangle(p, q, r, query, lt, li);
|
||
|
|
if(side == ON_ORIENTED_BOUNDARY) {
|
||
|
|
lt = EDGE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
if(side == ON_POSITIVE_SIDE) {
|
||
|
|
lt = FACE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
// There is nothing to be done now -- the point is outside the convex hull of the triangulation
|
||
|
|
lt = OUTSIDE_CONVEX_HULL;
|
||
|
|
return Face_handle();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Here, the face has been located in the Euclidean face lh
|
||
|
|
const Point& p = point(fh, 0);
|
||
|
|
const Point& q = point(fh, 1);
|
||
|
|
const Point& r = point(fh, 2);
|
||
|
|
int idx;
|
||
|
|
if(!geom_traits().is_Delaunay_hyperbolic_2_object()(p, q, r, idx))
|
||
|
|
{
|
||
|
|
// Need to check if the point lies on one of the sides of the face
|
||
|
|
// Note that at least one side is Delaunay hyperbolic!
|
||
|
|
if (geom_traits().side_of_oriented_hyperbolic_segment_2_object()(p,q,query) == ON_ORIENTED_BOUNDARY ||
|
||
|
|
geom_traits().side_of_oriented_hyperbolic_segment_2_object()(q,r,query) == ON_ORIENTED_BOUNDARY ||
|
||
|
|
geom_traits().side_of_oriented_hyperbolic_segment_2_object()(r,p,query) == ON_ORIENTED_BOUNDARY )
|
||
|
|
lt = EDGE;
|
||
|
|
else
|
||
|
|
lt = OUTSIDE_CONVEX_HULL;
|
||
|
|
return Face_handle();
|
||
|
|
}
|
||
|
|
|
||
|
|
Oriented_side side = side_of_hyperbolic_triangle(p, q, r, query, lt, li);
|
||
|
|
if(side == ON_POSITIVE_SIDE) {
|
||
|
|
lt = FACE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
if(side == ON_ORIENTED_BOUNDARY) {
|
||
|
|
lt = EDGE;
|
||
|
|
return fh;
|
||
|
|
} else {
|
||
|
|
// Here, the point lies in a face that is a neighbor to fh
|
||
|
|
for(int i = 0; i < 3; i++) {
|
||
|
|
Face_handle nfh = fh->neighbor(i);
|
||
|
|
if(geom_traits().is_Delaunay_hyperbolic_2_object()(point(nfh,0),
|
||
|
|
point(nfh,1),
|
||
|
|
point(nfh,2)))
|
||
|
|
{
|
||
|
|
Oriented_side nside = side_of_hyperbolic_triangle(point(nfh,0),
|
||
|
|
point(nfh,1),
|
||
|
|
point(nfh,2),
|
||
|
|
query, lt, li);
|
||
|
|
if(nside == ON_POSITIVE_SIDE) {
|
||
|
|
lt = FACE;
|
||
|
|
return nfh;
|
||
|
|
} else if(nside == ON_ORIENTED_BOUNDARY) {
|
||
|
|
lt = EDGE;
|
||
|
|
return nfh;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// At this point, the point lies outside of the convex hull of the triangulation,
|
||
|
|
// since it has not been found in any of the hyperbolic faces adjacent to fh.
|
||
|
|
lt = OUTSIDE_CONVEX_HULL;
|
||
|
|
return Face_handle();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// We never reach this point, but we have to make the compiler happy
|
||
|
|
lt = OUTSIDE_CONVEX_HULL;
|
||
|
|
return Face_handle();
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
} // end namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_2_H
|