932 lines
35 KiB
C++
932 lines
35 KiB
C++
// Copyright (c) 2009-2014 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/include/CGAL/Delaunay_triangulation.h $
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// $Id: Delaunay_triangulation.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) : Samuel Hornus
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#ifndef CGAL_DELAUNAY_COMPLEX_H
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#define CGAL_DELAUNAY_COMPLEX_H
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#include <CGAL/license/Triangulation.h>
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#include <CGAL/disable_warnings.h>
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#include <CGAL/tss.h>
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#include <CGAL/Triangulation.h>
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#include <CGAL/Dimension.h>
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#include <CGAL/Default.h>
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#include <CGAL/boost/iterator/transform_iterator.hpp>
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#include <algorithm>
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namespace CGAL {
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template< typename DCTraits, typename _TDS = Default >
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class Delaunay_triangulation
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: public Triangulation<DCTraits,
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typename Default::Get<_TDS, Triangulation_data_structure<
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typename DCTraits::Dimension,
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Triangulation_vertex<DCTraits>,
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Triangulation_full_cell<DCTraits> >
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>::type >
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{
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typedef typename DCTraits::Dimension Maximal_dimension_;
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typedef typename Default::Get<_TDS, Triangulation_data_structure<
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Maximal_dimension_,
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Triangulation_vertex<DCTraits>,
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Triangulation_full_cell<DCTraits> >
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>::type TDS;
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typedef Triangulation<DCTraits, TDS> Base;
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typedef Delaunay_triangulation<DCTraits, _TDS> Self;
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typedef typename DCTraits::Side_of_oriented_sphere_d
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Side_of_oriented_sphere_d;
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typedef typename DCTraits::Orientation_d Orientation_d;
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public: // PUBLIC NESTED TYPES
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typedef DCTraits Geom_traits;
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typedef typename Base::Triangulation_ds Triangulation_ds;
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typedef typename Base::Vertex Vertex;
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typedef typename Base::Full_cell Full_cell;
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typedef typename Base::Facet Facet;
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typedef typename Base::Face Face;
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typedef typename Base::Maximal_dimension Maximal_dimension;
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typedef typename DCTraits::Point_d Point;
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typedef typename DCTraits::Point_d Point_d;
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typedef typename Base::Vertex_handle Vertex_handle;
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typedef typename Base::Vertex_iterator Vertex_iterator;
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typedef typename Base::Vertex_const_handle Vertex_const_handle;
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typedef typename Base::Vertex_const_iterator Vertex_const_iterator;
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typedef typename Base::Full_cell_handle Full_cell_handle;
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typedef typename Base::Full_cell_iterator Full_cell_iterator;
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typedef typename Base::Full_cell_const_handle Full_cell_const_handle;
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typedef typename Base::Full_cell_const_iterator Full_cell_const_iterator;
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typedef typename Base::Finite_full_cell_const_iterator
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Finite_full_cell_const_iterator;
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typedef typename Base::size_type size_type;
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typedef typename Base::difference_type difference_type;
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typedef typename Base::Locate_type Locate_type;
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//Tag to distinguish triangulations with weighted_points
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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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public:
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typedef typename Base::Rotor Rotor;
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using Base::maximal_dimension;
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using Base::are_incident_full_cells_valid;
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using Base::coaffine_orientation_predicate;
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using Base::reset_flat_orientation;
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using Base::current_dimension;
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//using Base::star;
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//using Base::incident_full_cells;
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using Base::geom_traits;
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using Base::index_of_covertex;
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//using Base::index_of_second_covertex;
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using Base::infinite_vertex;
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using Base::rotate_rotor;
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using Base::insert_in_hole;
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using Base::insert_outside_convex_hull_1;
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using Base::is_infinite;
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using Base::locate;
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using Base::points_begin;
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using Base::points_end;
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using Base::set_neighbors;
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using Base::new_full_cell;
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using Base::number_of_vertices;
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using Base::orientation;
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using Base::tds;
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using Base::reorient_full_cells;
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using Base::full_cell;
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using Base::full_cells_begin;
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using Base::full_cells_end;
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using Base::finite_full_cells_begin;
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using Base::finite_full_cells_end;
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using Base::vertices_begin;
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using Base::vertices_end;
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// using Base::
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private:
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//*** Side_of_oriented_subsphere_d ***
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typedef typename Base::Flat_orientation_d Flat_orientation_d;
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typedef typename Base::Construct_flat_orientation_d Construct_flat_orientation_d;
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typedef typename DCTraits::In_flat_side_of_oriented_sphere_d In_flat_side_of_oriented_sphere_d;
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// Wrapper
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struct Side_of_oriented_subsphere_d
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{
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boost::optional<Flat_orientation_d>* fop;
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Construct_flat_orientation_d cfo;
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In_flat_side_of_oriented_sphere_d ifsoos;
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Side_of_oriented_subsphere_d(
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boost::optional<Flat_orientation_d>& x,
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Construct_flat_orientation_d const&y,
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In_flat_side_of_oriented_sphere_d const&z)
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: fop(&x), cfo(y), ifsoos(z) {}
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template<class Iter>
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CGAL::Orientation operator()(Iter a, Iter b, const Point & p)const
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{
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if(!*fop)
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*fop=cfo(a,b);
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return ifsoos(fop->get(),a,b,p);
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}
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};
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public:
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// - - - - - - - - - - - - - - - - - - - - - - - - - - CREATION / CONSTRUCTORS
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Delaunay_triangulation(int dim, const Geom_traits &k = Geom_traits())
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: Base(dim, k)
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{
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}
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// With this constructor,
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// the user can specify a Flat_orientation_d object to be used for
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// orienting simplices of a specific dimension
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// (= preset_flat_orientation_.first)
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// It it used by the dark triangulations created by DT::remove
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Delaunay_triangulation(
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int dim,
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const std::pair<int, const Flat_orientation_d *> &preset_flat_orientation,
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const Geom_traits &k = Geom_traits())
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: Base(dim, preset_flat_orientation, k)
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{
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}
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~Delaunay_triangulation() {}
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// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ACCESS
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// Not Documented
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Side_of_oriented_subsphere_d side_of_oriented_subsphere_predicate() const
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{
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return Side_of_oriented_subsphere_d (
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flat_orientation_,
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geom_traits().construct_flat_orientation_d_object(),
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geom_traits().in_flat_side_of_oriented_sphere_d_object()
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);
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}
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// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS
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Full_cell_handle remove(Vertex_handle);
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Full_cell_handle remove(const Point & p, Full_cell_handle hint = Full_cell_handle())
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{
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Locate_type lt;
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Face f(maximal_dimension());
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Facet ft;
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Full_cell_handle s = locate(p, lt, f, ft, hint);
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if( Base::ON_VERTEX == lt )
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{
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return remove(s->vertex(f.index(0)));
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}
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return Full_cell_handle();
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}
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template< typename ForwardIterator >
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void remove(ForwardIterator start, ForwardIterator end)
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{
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while( start != end )
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remove(*start++);
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}
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// Not documented
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void remove_decrease_dimension(Vertex_handle);
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// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - INSERTIONS
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template< typename ForwardIterator >
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size_type insert(ForwardIterator start, ForwardIterator end)
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{
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size_type n = number_of_vertices();
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std::vector<Point> points(start, end);
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spatial_sort(points.begin(), points.end(), geom_traits());
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Full_cell_handle hint;
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for( typename std::vector<Point>::const_iterator p = points.begin(); p != points.end(); ++p )
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{
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hint = insert(*p, hint)->full_cell();
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}
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return number_of_vertices() - n;
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}
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Vertex_handle insert(const Point &, Locate_type, const Face &, const Facet &, Full_cell_handle);
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Vertex_handle insert(const Point & p, Full_cell_handle start = Full_cell_handle())
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{
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Locate_type lt;
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Face f(maximal_dimension());
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Facet ft;
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Full_cell_handle s = locate(p, lt, f, ft, start);
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return insert(p, lt, f, ft, s);
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}
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Vertex_handle insert(const Point & p, Vertex_handle hint)
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{
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CGAL_assertion( Vertex_handle() != hint );
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return insert(p, hint->full_cell());
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}
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Vertex_handle insert_outside_affine_hull(const Point &);
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Vertex_handle insert_in_conflicting_cell(const Point &, Full_cell_handle);
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// - - - - - - - - - - - - - - - - - - - - - - - - - GATHERING CONFLICTING SIMPLICES
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bool is_in_conflict(const Point &, Full_cell_const_handle) const;
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template< class OrientationPredicate >
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Oriented_side perturbed_side_of_positive_sphere(const Point &,
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Full_cell_const_handle, const OrientationPredicate &) const;
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template< typename OutputIterator >
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Facet compute_conflict_zone(const Point &, Full_cell_handle, OutputIterator) const;
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template < typename OrientationPredicate, typename SideOfOrientedSpherePredicate >
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class Conflict_predicate
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{
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const Self & dc_;
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const Point & p_;
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OrientationPredicate ori_;
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SideOfOrientedSpherePredicate side_of_s_;
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int cur_dim_;
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public:
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Conflict_predicate(
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const Self & dc,
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const Point & p,
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const OrientationPredicate & ori,
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const SideOfOrientedSpherePredicate & side)
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: dc_(dc), p_(p), ori_(ori), side_of_s_(side), cur_dim_(dc.current_dimension()) {}
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inline
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bool operator()(Full_cell_const_handle s) const
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{
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bool ok;
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if( ! dc_.is_infinite(s) )
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{
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Oriented_side side = side_of_s_(dc_.points_begin(s), dc_.points_begin(s) + cur_dim_ + 1, p_);
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if( ON_POSITIVE_SIDE == side )
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ok = true;
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else if( ON_NEGATIVE_SIDE == side )
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ok = false;
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else
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ok = ON_POSITIVE_SIDE == dc_.perturbed_side_of_positive_sphere<OrientationPredicate>(p_, s, ori_);
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}
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else
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{
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typedef typename Full_cell::Vertex_handle_const_iterator VHCI;
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typedef Substitute_point_in_vertex_iterator<VHCI> F;
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F spivi(dc_.infinite_vertex(), &p_);
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Orientation o = ori_(
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boost::make_transform_iterator(s->vertices_begin(), spivi),
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boost::make_transform_iterator(s->vertices_begin() + cur_dim_ + 1,
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spivi));
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if( POSITIVE == o )
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ok = true;
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else if( o == NEGATIVE )
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ok = false;
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else
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ok = (*this)(s->neighbor( s->index( dc_.infinite_vertex() ) ));
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}
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return ok;
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}
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};
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template < typename ConflictPredicate >
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class Conflict_traversal_predicate
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{
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const Self & dc_;
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const ConflictPredicate & pred_;
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public:
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Conflict_traversal_predicate(const Self & dc, const ConflictPredicate & pred)
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: dc_(dc), pred_(pred)
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{}
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inline
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bool operator()(const Facet & f) const
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{
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return pred_(dc_.full_cell(f)->neighbor(dc_.index_of_covertex(f)));
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}
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};
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// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - VALIDITY
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bool is_valid(bool verbose = false, int level = 0) const;
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private:
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// Some internal types to shorten notation
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typedef typename Base::Coaffine_orientation_d Coaffine_orientation_d;
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using Base::flat_orientation_;
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typedef Conflict_predicate<Coaffine_orientation_d, Side_of_oriented_subsphere_d>
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Conflict_pred_in_subspace;
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typedef Conflict_predicate<Orientation_d, Side_of_oriented_sphere_d>
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Conflict_pred_in_fullspace;
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typedef Conflict_traversal_predicate<Conflict_pred_in_subspace>
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Conflict_traversal_pred_in_subspace;
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typedef Conflict_traversal_predicate<Conflict_pred_in_fullspace>
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Conflict_traversal_pred_in_fullspace;
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};
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// = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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// FUNCTIONS THAT ARE MEMBER METHODS:
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// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS
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template< typename DCTraits, typename TDS >
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typename Delaunay_triangulation<DCTraits, TDS>::Full_cell_handle
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Delaunay_triangulation<DCTraits, TDS>
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::remove( Vertex_handle v )
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{
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CGAL_precondition( ! is_infinite(v) );
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CGAL_expensive_precondition( is_vertex(v) );
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// THE CASE cur_dim == 0
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if( 0 == current_dimension() )
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{
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remove_decrease_dimension(v);
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return Full_cell_handle();
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}
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else if( 1 == current_dimension() )
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{ // THE CASE cur_dim == 1
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if( 2 == number_of_vertices() )
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{
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remove_decrease_dimension(v);
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return Full_cell_handle();
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}
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Full_cell_handle left = v->full_cell();
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if( 0 == left->index(v) )
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left = left->neighbor(1);
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CGAL_assertion( 1 == left->index(v) );
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Full_cell_handle right = left->neighbor(0);
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tds().associate_vertex_with_full_cell(left, 1, right->vertex(1));
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set_neighbors(left, 0, right->neighbor(0), right->mirror_index(0));
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tds().delete_vertex(v);
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tds().delete_full_cell(right);
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return left;
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}
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// THE CASE cur_dim >= 2
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// Gather the finite vertices sharing an edge with |v|
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typedef typename Base::template Full_cell_set<Full_cell_handle> Simplices;
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Simplices simps;
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std::back_insert_iterator<Simplices> out(simps);
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tds().incident_full_cells(v, out);
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typedef std::set<Vertex_handle> Vertex_set;
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Vertex_set verts;
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Vertex_handle vh;
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for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
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for( int i = 0; i <= current_dimension(); ++i )
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{
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vh = (*it)->vertex(i);
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if( is_infinite(vh) )
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continue;
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if( vh == v )
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continue;
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verts.insert(vh);
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}
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// After gathering finite neighboring vertices, create their Dark Delaunay triangulation
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typedef Triangulation_vertex<Geom_traits, Vertex_handle> Dark_vertex_base;
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typedef Triangulation_full_cell<Geom_traits,
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internal::Triangulation::Dark_full_cell_data<Self> > Dark_full_cell_base;
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typedef Triangulation_data_structure<Maximal_dimension, Dark_vertex_base, Dark_full_cell_base> Dark_tds;
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typedef Delaunay_triangulation<DCTraits, Dark_tds> Dark_triangulation;
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typedef typename Dark_triangulation::Face Dark_face;
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typedef typename Dark_triangulation::Facet Dark_facet;
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typedef typename Dark_triangulation::Vertex_handle Dark_v_handle;
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typedef typename Dark_triangulation::Full_cell_handle Dark_s_handle;
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// If flat_orientation_ is defined, we give it the Dark triangulation
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// so that the orientation it uses for "current_dimension()"-simplices is
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// coherent with the global triangulation
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Dark_triangulation dark_side(
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maximal_dimension(),
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flat_orientation_ ?
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std::pair<int, const Flat_orientation_d *>(current_dimension(), flat_orientation_.get_ptr())
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: std::pair<int, const Flat_orientation_d *>((std::numeric_limits<int>::max)(), (Flat_orientation_d*) nullptr) );
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Dark_s_handle dark_s;
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Dark_v_handle dark_v;
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typedef std::map<Vertex_handle, Dark_v_handle> Vertex_map;
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Vertex_map light_to_dark;
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typename Vertex_set::iterator vit = verts.begin();
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while( vit != verts.end() )
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{
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dark_v = dark_side.insert((*vit)->point(), dark_s);
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dark_s = dark_v->full_cell();
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dark_v->data() = *vit;
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light_to_dark[*vit] = dark_v;
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++vit;
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}
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if( dark_side.current_dimension() != current_dimension() )
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{
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CGAL_assertion( dark_side.current_dimension() + 1 == current_dimension() );
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// Here, the finite neighbors of |v| span a affine subspace of
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// dimension one less than the current dimension. Two cases are possible:
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if( (size_type)(verts.size() + 1) == number_of_vertices() )
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{
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remove_decrease_dimension(v);
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return Full_cell_handle();
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}
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else
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{ // |v| is strictly outside the convex hull of the rest of the points. This is an
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// easy case: first, modify the finite full_cells, then, delete the infinite ones.
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// We don't even need the Dark triangulation.
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Simplices infinite_simps;
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{
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Simplices finite_simps;
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for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
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if( is_infinite(*it) )
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infinite_simps.push_back(*it);
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else
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finite_simps.push_back(*it);
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simps.swap(finite_simps);
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} // now, simps only contains finite simplices
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// First, modify the finite full_cells:
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for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
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{
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int v_idx = (*it)->index(v);
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tds().associate_vertex_with_full_cell(*it, v_idx, infinite_vertex());
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}
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// Make the handles to infinite full cells searchable
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infinite_simps.make_searchable();
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// Then, modify the neighboring relation
|
|
for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
|
|
{
|
|
for( int i = 0; i <= current_dimension(); ++i )
|
|
{
|
|
if (is_infinite((*it)->vertex(i)))
|
|
continue;
|
|
(*it)->vertex(i)->set_full_cell(*it);
|
|
Full_cell_handle n = (*it)->neighbor(i);
|
|
// Was |n| a finite full cell prior to removing |v| ?
|
|
if( ! infinite_simps.contains(n) )
|
|
continue;
|
|
int n_idx = n->index(v);
|
|
set_neighbors(*it, i, n->neighbor(n_idx), n->neighbor(n_idx)->index(n));
|
|
}
|
|
}
|
|
Full_cell_handle ret_s;
|
|
// Then, we delete the infinite full_cells
|
|
for( typename Simplices::iterator it = infinite_simps.begin(); it != infinite_simps.end(); ++it )
|
|
tds().delete_full_cell(*it);
|
|
tds().delete_vertex(v);
|
|
return simps.front();
|
|
}
|
|
}
|
|
else // From here on, dark_side.current_dimension() == current_dimension()
|
|
{
|
|
dark_side.infinite_vertex()->data() = infinite_vertex();
|
|
light_to_dark[infinite_vertex()] = dark_side.infinite_vertex();
|
|
}
|
|
|
|
// Now, compute the conflict zone of v->point() in
|
|
// the dark side. This is precisely the set of full_cells
|
|
// that we have to glue back into the light side.
|
|
Dark_face dark_f(dark_side.maximal_dimension());
|
|
Dark_facet dark_ft;
|
|
typename Dark_triangulation::Locate_type lt;
|
|
dark_s = dark_side.locate(v->point(), lt, dark_f, dark_ft);
|
|
CGAL_assertion( lt != Dark_triangulation::ON_VERTEX
|
|
&& lt != Dark_triangulation::OUTSIDE_AFFINE_HULL );
|
|
|
|
// |ret_s| is the full_cell that we return
|
|
Dark_s_handle dark_ret_s = dark_s;
|
|
Full_cell_handle ret_s;
|
|
|
|
typedef typename Base::template Full_cell_set<Dark_s_handle> Dark_full_cells;
|
|
Dark_full_cells conflict_zone;
|
|
std::back_insert_iterator<Dark_full_cells> dark_out(conflict_zone);
|
|
|
|
dark_ft = dark_side.compute_conflict_zone(v->point(), dark_s, dark_out);
|
|
// Make the dark simplices in the conflict zone searchable
|
|
conflict_zone.make_searchable();
|
|
|
|
// THE FOLLOWING SHOULD MAYBE GO IN TDS.
|
|
// Here is the plan:
|
|
// 1. Pick any Facet from boundary of the light zone
|
|
// 2. Find corresponding Facet on boundary of dark zone
|
|
// 3. stitch.
|
|
|
|
// 1. Build a facet on the boudary of the light zone:
|
|
Full_cell_handle light_s = *simps.begin();
|
|
Facet light_ft(light_s, light_s->index(v));
|
|
|
|
// 2. Find corresponding Dark_facet on boundary of the dark zone
|
|
Dark_full_cells dark_incident_s;
|
|
for( int i = 0; i <= current_dimension(); ++i )
|
|
{
|
|
if( index_of_covertex(light_ft) == i )
|
|
continue;
|
|
Dark_v_handle dark_v = light_to_dark[full_cell(light_ft)->vertex(i)];
|
|
dark_incident_s.clear();
|
|
dark_out = std::back_inserter(dark_incident_s);
|
|
dark_side.tds().incident_full_cells(dark_v, dark_out);
|
|
for( typename Dark_full_cells::iterator it = dark_incident_s.begin(); it != dark_incident_s.end(); ++it )
|
|
{
|
|
(*it)->data().count_ += 1;
|
|
}
|
|
}
|
|
|
|
for( typename Dark_full_cells::iterator it = dark_incident_s.begin(); it != dark_incident_s.end(); ++it )
|
|
{
|
|
if( current_dimension() != (*it)->data().count_ )
|
|
continue;
|
|
if( ! conflict_zone.contains(*it) )
|
|
continue;
|
|
// We found a full_cell incident to the dark facet corresponding to the light facet |light_ft|
|
|
int ft_idx = 0;
|
|
while( light_s->has_vertex( (*it)->vertex(ft_idx)->data() ) )
|
|
++ft_idx;
|
|
dark_ft = Dark_facet(*it, ft_idx);
|
|
break;
|
|
}
|
|
// Pre-3. Now, we are ready to traverse both boundary and do the stiching.
|
|
|
|
// But first, we create the new full_cells in the light triangulation,
|
|
// with as much adjacency information as possible.
|
|
|
|
// Create new full_cells with vertices
|
|
for( typename Dark_full_cells::iterator it = conflict_zone.begin(); it != conflict_zone.end(); ++it )
|
|
{
|
|
Full_cell_handle new_s = new_full_cell();
|
|
(*it)->data().light_copy_ = new_s;
|
|
for( int i = 0; i <= current_dimension(); ++i )
|
|
tds().associate_vertex_with_full_cell(new_s, i, (*it)->vertex(i)->data());
|
|
if( dark_ret_s == *it )
|
|
ret_s = new_s;
|
|
}
|
|
|
|
// Setup adjacencies inside the hole
|
|
for( typename Dark_full_cells::iterator it = conflict_zone.begin(); it != conflict_zone.end(); ++it )
|
|
{
|
|
Full_cell_handle new_s = (*it)->data().light_copy_;
|
|
for( int i = 0; i <= current_dimension(); ++i )
|
|
if( conflict_zone.contains((*it)->neighbor(i)) )
|
|
tds().set_neighbors(new_s, i, (*it)->neighbor(i)->data().light_copy_, (*it)->mirror_index(i));
|
|
}
|
|
|
|
// 3. Stitch
|
|
simps.make_searchable();
|
|
typedef std::queue<std::pair<Facet, Dark_facet> > Queue;
|
|
Queue q;
|
|
q.push(std::make_pair(light_ft, dark_ft));
|
|
dark_s = dark_side.full_cell(dark_ft);
|
|
int dark_i = dark_side.index_of_covertex(dark_ft);
|
|
// mark dark_ft as visited:
|
|
// TODO try by marking with Dark_v_handle (vertex)
|
|
dark_s->neighbor(dark_i)->set_neighbor(dark_s->mirror_index(dark_i), Dark_s_handle());
|
|
while( ! q.empty() )
|
|
{
|
|
std::pair<Facet, Dark_facet> p = q.front();
|
|
q.pop();
|
|
light_ft = p.first;
|
|
dark_ft = p.second;
|
|
light_s = full_cell(light_ft);
|
|
int light_i = index_of_covertex(light_ft);
|
|
dark_s = dark_side.full_cell(dark_ft);
|
|
int dark_i = dark_side.index_of_covertex(dark_ft);
|
|
Full_cell_handle light_n = light_s->neighbor(light_i);
|
|
set_neighbors(dark_s->data().light_copy_, dark_i, light_n, light_s->mirror_index(light_i));
|
|
for( int di = 0; di <= current_dimension(); ++di )
|
|
{
|
|
if( di == dark_i )
|
|
continue;
|
|
int li = light_s->index(dark_s->vertex(di)->data());
|
|
Rotor light_r(light_s, li, light_i);
|
|
typename Dark_triangulation::Rotor dark_r(dark_s, di, dark_i);
|
|
|
|
while (simps.contains(std::get<0>(light_r)->neighbor(std::get<1>(light_r))))
|
|
light_r = rotate_rotor(light_r);
|
|
|
|
while (conflict_zone.contains(std::get<0>(dark_r)->neighbor(std::get<1>(dark_r))))
|
|
dark_r = dark_side.rotate_rotor(dark_r);
|
|
|
|
Dark_s_handle dark_ns = std::get<0>(dark_r);
|
|
int dark_ni = std::get<1>(dark_r);
|
|
Full_cell_handle light_ns = std::get<0>(light_r);
|
|
int light_ni = std::get<1>(light_r);
|
|
// mark dark_r as visited:
|
|
// TODO try by marking with Dark_v_handle (vertex)
|
|
Dark_s_handle outside = dark_ns->neighbor(dark_ni);
|
|
Dark_v_handle mirror = dark_ns->mirror_vertex(dark_ni, current_dimension());
|
|
int dn = outside->index(mirror);
|
|
if( Dark_s_handle() == outside->neighbor(dn) )
|
|
continue;
|
|
outside->set_neighbor(dn, Dark_s_handle());
|
|
q.push(std::make_pair(Facet(light_ns, light_ni), Dark_facet(dark_ns, dark_ni)));
|
|
}
|
|
}
|
|
tds().delete_full_cells(simps.begin(), simps.end());
|
|
tds().delete_vertex(v);
|
|
return ret_s;
|
|
}
|
|
|
|
template< typename DCTraits, typename TDS >
|
|
void
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::remove_decrease_dimension(Vertex_handle v)
|
|
{
|
|
CGAL_precondition( current_dimension() >= 0 );
|
|
tds().remove_decrease_dimension(v, infinite_vertex());
|
|
// reset the predicates:
|
|
reset_flat_orientation();
|
|
if( 1 <= current_dimension() )
|
|
{
|
|
Full_cell_handle inf_v_cell = infinite_vertex()->full_cell();
|
|
int inf_v_index = inf_v_cell->index(infinite_vertex());
|
|
Full_cell_handle s = inf_v_cell->neighbor(inf_v_index);
|
|
Orientation o = orientation(s);
|
|
CGAL_assertion( ZERO != o );
|
|
if( NEGATIVE == o )
|
|
reorient_full_cells();
|
|
}
|
|
}
|
|
|
|
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - INSERTIONS
|
|
|
|
template< typename DCTraits, typename TDS >
|
|
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::insert(const Point & p, Locate_type lt, const Face & f, const Facet &, Full_cell_handle s)
|
|
{
|
|
switch( lt )
|
|
{
|
|
case Base::OUTSIDE_AFFINE_HULL:
|
|
return insert_outside_affine_hull(p);
|
|
break;
|
|
case Base::ON_VERTEX:
|
|
{
|
|
Vertex_handle v = s->vertex(f.index(0));
|
|
v->set_point(p);
|
|
return v;
|
|
break;
|
|
}
|
|
default:
|
|
if( 1 == current_dimension() )
|
|
{
|
|
if( Base::OUTSIDE_CONVEX_HULL == lt )
|
|
{
|
|
return insert_outside_convex_hull_1(p, s);
|
|
}
|
|
Vertex_handle v = tds().insert_in_full_cell(s);
|
|
v->set_point(p);
|
|
return v;
|
|
}
|
|
else
|
|
return insert_in_conflicting_cell(p, s);
|
|
break;
|
|
}
|
|
}
|
|
|
|
/*
|
|
[Undocumented function]
|
|
|
|
Inserts the point `p` in the Delaunay triangulation. Returns a handle to the
|
|
(possibly newly created) vertex at that position.
|
|
\pre The point `p`
|
|
must lie outside the affine hull of the Delaunay triangulation. This implies that
|
|
`dt`.`current_dimension()` must be less than `dt`.`maximal_dimension()`.
|
|
*/
|
|
template< typename DCTraits, typename TDS >
|
|
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::insert_outside_affine_hull(const Point & p)
|
|
{
|
|
// we don't use Base::insert_outside_affine_hull(...) because here, we
|
|
// also need to reset the side_of_oriented_subsphere functor.
|
|
CGAL_precondition( current_dimension() < maximal_dimension() );
|
|
Vertex_handle v = tds().insert_increase_dimension(infinite_vertex());
|
|
// reset the predicates:
|
|
reset_flat_orientation();
|
|
v->set_point(p);
|
|
if( current_dimension() >= 1 )
|
|
{
|
|
Full_cell_handle inf_v_cell = infinite_vertex()->full_cell();
|
|
int inf_v_index = inf_v_cell->index(infinite_vertex());
|
|
Full_cell_handle s = inf_v_cell->neighbor(inf_v_index);
|
|
Orientation o = orientation(s);
|
|
CGAL_assertion( ZERO != o );
|
|
if( NEGATIVE == o )
|
|
reorient_full_cells();
|
|
|
|
// We just inserted the second finite point and the right infinite
|
|
// cell is like : (inf_v, v), but we want it to be (v, inf_v) to be
|
|
// consistent with the rest of the cells
|
|
if (current_dimension() == 1)
|
|
{
|
|
// Is "inf_v_cell" the right infinite cell?
|
|
// Then inf_v_index should be 1
|
|
if (inf_v_cell->neighbor(inf_v_index)->index(inf_v_cell) == 0
|
|
&& inf_v_index == 0)
|
|
{
|
|
inf_v_cell->swap_vertices(
|
|
current_dimension() - 1, current_dimension());
|
|
}
|
|
// Otherwise, let's find the right infinite cell
|
|
else
|
|
{
|
|
inf_v_cell = inf_v_cell->neighbor((inf_v_index + 1) % 2);
|
|
inf_v_index = inf_v_cell->index(infinite_vertex());
|
|
// Is "inf_v_cell" the right infinite cell?
|
|
// Then inf_v_index should be 1
|
|
if (inf_v_cell->neighbor(inf_v_index)->index(inf_v_cell) == 0
|
|
&& inf_v_index == 0)
|
|
{
|
|
inf_v_cell->swap_vertices(
|
|
current_dimension() - 1, current_dimension());
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return v;
|
|
}
|
|
|
|
/*!
|
|
[Undocumented function]
|
|
|
|
Inserts the point `p` in the Delaunay triangulation. Returns a handle to the
|
|
(possibly newly created) vertex at that position.
|
|
\pre The point `p` must be in conflict with the full cell `c`.
|
|
*/
|
|
template< typename DCTraits, typename TDS >
|
|
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::insert_in_conflicting_cell(const Point & p, Full_cell_handle s)
|
|
{
|
|
CGAL_precondition(is_in_conflict(p, s));
|
|
|
|
// for storing conflicting full_cells.
|
|
typedef std::vector<Full_cell_handle> Full_cell_h_vector;
|
|
CGAL_STATIC_THREAD_LOCAL_VARIABLE(Full_cell_h_vector,cs,0);
|
|
cs.clear();
|
|
|
|
std::back_insert_iterator<Full_cell_h_vector> out(cs);
|
|
Facet ft = compute_conflict_zone(p, s, out);
|
|
return insert_in_hole(p, cs.begin(), cs.end(), ft);
|
|
}
|
|
|
|
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - GATHERING CONFLICTING SIMPLICES
|
|
|
|
// NOT DOCUMENTED
|
|
template< typename DCTraits, typename TDS >
|
|
template< typename OrientationPred >
|
|
Oriented_side
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::perturbed_side_of_positive_sphere(const Point & p, Full_cell_const_handle s,
|
|
const OrientationPred & ori) const
|
|
{
|
|
CGAL_precondition_msg( ! is_infinite(s), "full cell must be finite");
|
|
CGAL_expensive_precondition( POSITIVE == orientation(s) );
|
|
typedef std::vector<const Point *> Points;
|
|
Points points(current_dimension() + 2);
|
|
int i(0);
|
|
for( ; i <= current_dimension(); ++i )
|
|
points[i] = &(s->vertex(i)->point());
|
|
points[i] = &p;
|
|
std::sort(points.begin(), points.end(),
|
|
internal::Triangulation::Compare_points_for_perturbation<Self>(*this));
|
|
typename Points::const_reverse_iterator cut_pt = points.rbegin();
|
|
Points test_points;
|
|
while( cut_pt != points.rend() )
|
|
{
|
|
if( &p == *cut_pt )
|
|
// because the full_cell "s" is assumed to be positively oriented
|
|
return ON_NEGATIVE_SIDE; // we consider |p| to lie outside the sphere
|
|
test_points.clear();
|
|
typename Base::Point_const_iterator spit = points_begin(s);
|
|
int adjust_sign = -1;
|
|
for( i = 0; i < current_dimension(); ++i )
|
|
{
|
|
if( &(*spit) == *cut_pt )
|
|
{
|
|
++spit;
|
|
adjust_sign = (((current_dimension() + i) % 2) == 0) ? -1 : +1;
|
|
}
|
|
test_points.push_back(&(*spit));
|
|
++spit;
|
|
}
|
|
test_points.push_back(&p);
|
|
|
|
typedef typename CGAL::Iterator_project<typename Points::iterator,
|
|
internal::Triangulation::Point_from_pointer<Self>,
|
|
const Point &, const Point *> Point_pointer_iterator;
|
|
|
|
Orientation ori_value = ori(
|
|
Point_pointer_iterator(test_points.begin()),
|
|
Point_pointer_iterator(test_points.end()));
|
|
|
|
if( ZERO != ori_value )
|
|
return Oriented_side( - adjust_sign * ori_value );
|
|
|
|
++cut_pt;
|
|
}
|
|
CGAL_assertion(false); // we should never reach here
|
|
return ON_NEGATIVE_SIDE;
|
|
}
|
|
|
|
template< typename DCTraits, typename TDS >
|
|
bool
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::is_in_conflict(const Point & p, Full_cell_const_handle s) const
|
|
{
|
|
CGAL_precondition( 2 <= current_dimension() );
|
|
if( current_dimension() < maximal_dimension() )
|
|
{
|
|
Conflict_pred_in_subspace c(*this, p, coaffine_orientation_predicate(), side_of_oriented_subsphere_predicate());
|
|
return c(s);
|
|
}
|
|
else
|
|
{
|
|
Orientation_d ori = geom_traits().orientation_d_object();
|
|
Side_of_oriented_sphere_d side = geom_traits().side_of_oriented_sphere_d_object();
|
|
Conflict_pred_in_fullspace c(*this, p, ori, side);
|
|
return c(s);
|
|
}
|
|
}
|
|
|
|
template< typename DCTraits, typename TDS >
|
|
template< typename OutputIterator >
|
|
typename Delaunay_triangulation<DCTraits, TDS>::Facet
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::compute_conflict_zone(const Point & p, Full_cell_handle s, OutputIterator out) const
|
|
{
|
|
CGAL_precondition( 2 <= current_dimension() );
|
|
if( current_dimension() < maximal_dimension() )
|
|
{
|
|
Conflict_pred_in_subspace c(*this, p, coaffine_orientation_predicate(), side_of_oriented_subsphere_predicate());
|
|
Conflict_traversal_pred_in_subspace tp(*this, c);
|
|
return tds().gather_full_cells(s, tp, out);
|
|
}
|
|
else
|
|
{
|
|
Orientation_d ori = geom_traits().orientation_d_object();
|
|
Side_of_oriented_sphere_d side = geom_traits().side_of_oriented_sphere_d_object();
|
|
Conflict_pred_in_fullspace c(*this, p, ori, side);
|
|
Conflict_traversal_pred_in_fullspace tp(*this, c);
|
|
return tds().gather_full_cells(s, tp, out);
|
|
}
|
|
}
|
|
|
|
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - VALIDITY
|
|
|
|
template< typename DCTraits, typename TDS >
|
|
bool
|
|
Delaunay_triangulation<DCTraits, TDS>
|
|
::is_valid(bool verbose, int level) const
|
|
{
|
|
if (!Base::is_valid(verbose, level))
|
|
return false;
|
|
|
|
int dim = current_dimension();
|
|
if (dim == maximal_dimension())
|
|
{
|
|
for (Finite_full_cell_const_iterator cit = this->finite_full_cells_begin() ;
|
|
cit != this->finite_full_cells_end() ; ++cit )
|
|
{
|
|
Full_cell_const_handle ch = cit.base();
|
|
for(int i = 0; i < dim+1 ; ++i )
|
|
{
|
|
// If the i-th neighbor is not an infinite cell
|
|
Vertex_handle opposite_vh =
|
|
ch->neighbor(i)->vertex(ch->neighbor(i)->index(ch));
|
|
if (!is_infinite(opposite_vh))
|
|
{
|
|
Side_of_oriented_sphere_d side =
|
|
geom_traits().side_of_oriented_sphere_d_object();
|
|
if (side(points_begin(ch),
|
|
points_end(ch),
|
|
opposite_vh->point()) == ON_POSITIVE_SIDE)
|
|
{
|
|
if (verbose)
|
|
CGAL_warning_msg(false, "Non-empty sphere");
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
} //namespace CGAL
|
|
|
|
#include <CGAL/enable_warnings.h>
|
|
|
|
#endif // CGAL_DELAUNAY_COMPLEX_H
|