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Diffstat (limited to 'include/gudhi_patches/CGAL/Delaunay_triangulation.h')
| -rw-r--r-- | include/gudhi_patches/CGAL/Delaunay_triangulation.h | 933 |
1 files changed, 0 insertions, 933 deletions
diff --git a/include/gudhi_patches/CGAL/Delaunay_triangulation.h b/include/gudhi_patches/CGAL/Delaunay_triangulation.h deleted file mode 100644 index 071cd184..00000000 --- a/include/gudhi_patches/CGAL/Delaunay_triangulation.h +++ /dev/null @@ -1,933 +0,0 @@ -// Copyright (c) 2009-2014 INRIA Sophia-Antipolis (France). -// All rights reserved. -// -// This file is part of CGAL (www.cgal.org). -// You can redistribute it and/or modify it under the terms of the GNU -// General Public License as published by the Free Software Foundation, -// either version 3 of the License, or (at your option) any later version. -// -// Licensees holding a valid commercial license may use this file in -// accordance with the commercial license agreement provided with the software. -// -// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE -// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. -// -// $URL$ -// $Id$ -// -// Author(s) : Samuel Hornus - -#ifndef CGAL_DELAUNAY_COMPLEX_H -#define CGAL_DELAUNAY_COMPLEX_H - -#include <CGAL/tss.h> -#include <CGAL/Triangulation.h> -#include <CGAL/Dimension.h> -#include <CGAL/Default.h> - -#include <boost/iterator/transform_iterator.hpp> - -#include <algorithm> - -namespace CGAL { - -template< typename DCTraits, typename _TDS = Default > -class Delaunay_triangulation -: public Triangulation<DCTraits, - typename Default::Get<_TDS, Triangulation_data_structure< - typename DCTraits::Dimension, - Triangulation_vertex<DCTraits>, - Triangulation_full_cell<DCTraits> > - >::type > -{ - typedef typename DCTraits::Dimension Maximal_dimension_; - typedef typename Default::Get<_TDS, Triangulation_data_structure< - Maximal_dimension_, - Triangulation_vertex<DCTraits>, - Triangulation_full_cell<DCTraits> > - >::type TDS; - typedef Triangulation<DCTraits, TDS> Base; - typedef Delaunay_triangulation<DCTraits, _TDS> Self; - - typedef typename DCTraits::Side_of_oriented_sphere_d - Side_of_oriented_sphere_d; - typedef typename DCTraits::Orientation_d Orientation_d; - -public: // PUBLIC NESTED TYPES - - typedef DCTraits Geom_traits; - typedef typename Base::Triangulation_ds Triangulation_ds; - - typedef typename Base::Vertex Vertex; - typedef typename Base::Full_cell Full_cell; - typedef typename Base::Facet Facet; - typedef typename Base::Face Face; - - typedef typename Base::Maximal_dimension Maximal_dimension; - typedef typename DCTraits::Point_d Point; - typedef typename DCTraits::Point_d Point_d; - - typedef typename Base::Vertex_handle Vertex_handle; - typedef typename Base::Vertex_iterator Vertex_iterator; - typedef typename Base::Vertex_const_handle Vertex_const_handle; - typedef typename Base::Vertex_const_iterator Vertex_const_iterator; - - typedef typename Base::Full_cell_handle Full_cell_handle; - typedef typename Base::Full_cell_iterator Full_cell_iterator; - typedef typename Base::Full_cell_const_handle Full_cell_const_handle; - typedef typename Base::Full_cell_const_iterator Full_cell_const_iterator; - typedef typename Base::Finite_full_cell_const_iterator - Finite_full_cell_const_iterator; - - typedef typename Base::size_type size_type; - typedef typename Base::difference_type difference_type; - - typedef typename Base::Locate_type Locate_type; - - //Tag to distinguish triangulations with weighted_points - typedef Tag_false Weighted_tag; - -protected: // DATA MEMBERS - - -public: - - using typename Base::Rotor; - using Base::maximal_dimension; - using Base::are_incident_full_cells_valid; - using Base::coaffine_orientation_predicate; - using Base::reset_flat_orientation; - using Base::current_dimension; - //using Base::star; - //using Base::incident_full_cells; - using Base::geom_traits; - using Base::index_of_covertex; - //using Base::index_of_second_covertex; - using Base::infinite_vertex; - using Base::rotate_rotor; - using Base::insert_in_hole; - using Base::insert_outside_convex_hull_1; - using Base::is_infinite; - using Base::locate; - using Base::points_begin; - using Base::set_neighbors; - using Base::new_full_cell; - using Base::number_of_vertices; - using Base::orientation; - using Base::tds; - using Base::reorient_full_cells; - using Base::full_cell; - using Base::full_cells_begin; - using Base::full_cells_end; - using Base::finite_full_cells_begin; - using Base::finite_full_cells_end; - using Base::vertices_begin; - using Base::vertices_end; - // using Base:: - -private: - //*** Side_of_oriented_subsphere_d *** - typedef typename Base::Flat_orientation_d Flat_orientation_d; - typedef typename Base::Construct_flat_orientation_d Construct_flat_orientation_d; - typedef typename DCTraits::In_flat_side_of_oriented_sphere_d In_flat_side_of_oriented_sphere_d; - // Wrapper - struct Side_of_oriented_subsphere_d - { - boost::optional<Flat_orientation_d>* fop; - Construct_flat_orientation_d cfo; - In_flat_side_of_oriented_sphere_d ifsoos; - - Side_of_oriented_subsphere_d( - boost::optional<Flat_orientation_d>& x, - Construct_flat_orientation_d const&y, - In_flat_side_of_oriented_sphere_d const&z) - : fop(&x), cfo(y), ifsoos(z) {} - - template<class Iter> - CGAL::Orientation operator()(Iter a, Iter b, const Point & p)const - { - if(!*fop) - *fop=cfo(a,b); - return ifsoos(fop->get(),a,b,p); - } - }; -public: - -// - - - - - - - - - - - - - - - - - - - - - - - - - - CREATION / CONSTRUCTORS - - Delaunay_triangulation(int dim, const Geom_traits &k = Geom_traits()) - : Base(dim, k) - { - } - - // With this constructor, - // the user can specify a Flat_orientation_d object to be used for - // orienting simplices of a specific dimension - // (= preset_flat_orientation_.first) - // It it used by the dark triangulations created by DT::remove - Delaunay_triangulation( - int dim, - const std::pair<int, const Flat_orientation_d *> &preset_flat_orientation, - const Geom_traits &k = Geom_traits()) - : Base(dim, preset_flat_orientation, k) - { - } - - ~Delaunay_triangulation() {} - -// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ACCESS - - // Not Documented - Side_of_oriented_subsphere_d side_of_oriented_subsphere_predicate() const - { - return Side_of_oriented_subsphere_d ( - flat_orientation_, - geom_traits().construct_flat_orientation_d_object(), - geom_traits().in_flat_side_of_oriented_sphere_d_object() - ); - } - - - // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS - - Full_cell_handle remove(Vertex_handle); - Full_cell_handle remove(const Point & p, Full_cell_handle hint = Full_cell_handle()) - { - Locate_type lt; - Face f(maximal_dimension()); - Facet ft; - Full_cell_handle s = locate(p, lt, f, ft, hint); - if( Base::ON_VERTEX == lt ) - { - return remove(s->vertex(f.index(0))); - } - return Full_cell_handle(); - } - - template< typename ForwardIterator > - void remove(ForwardIterator start, ForwardIterator end) - { - while( start != end ) - remove(*start++); - } - - // Not documented - void remove_decrease_dimension(Vertex_handle); - - // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - INSERTIONS - - template< typename ForwardIterator > - size_type insert(ForwardIterator start, ForwardIterator end) - { - size_type n = number_of_vertices(); - std::vector<Point> points(start, end); - spatial_sort(points.begin(), points.end(), geom_traits()); - Full_cell_handle hint; - for( typename std::vector<Point>::const_iterator p = points.begin(); p != points.end(); ++p ) - { - hint = insert(*p, hint)->full_cell(); - } - return number_of_vertices() - n; - } - Vertex_handle insert(const Point &, Locate_type, const Face &, const Facet &, Full_cell_handle); - Vertex_handle insert(const Point & p, Full_cell_handle start = Full_cell_handle()) - { - Locate_type lt; - Face f(maximal_dimension()); - Facet ft; - Full_cell_handle s = locate(p, lt, f, ft, start); - return insert(p, lt, f, ft, s); - } - Vertex_handle insert(const Point & p, Vertex_handle hint) - { - CGAL_assertion( Vertex_handle() != hint ); - return insert(p, hint->full_cell()); - } - Vertex_handle insert_outside_affine_hull(const Point &); - Vertex_handle insert_in_conflicting_cell(const Point &, Full_cell_handle); - -// - - - - - - - - - - - - - - - - - - - - - - - - - GATHERING CONFLICTING SIMPLICES - - bool is_in_conflict(const Point &, Full_cell_const_handle) const; - template< class OrientationPredicate > - Oriented_side perturbed_side_of_positive_sphere(const Point &, - Full_cell_const_handle, const OrientationPredicate &) const; - - template< typename OutputIterator > - Facet compute_conflict_zone(const Point &, Full_cell_handle, OutputIterator) const; - - template < typename OrientationPredicate, typename SideOfOrientedSpherePredicate > - class Conflict_predicate - { - const Self & dc_; - const Point & p_; - OrientationPredicate ori_; - SideOfOrientedSpherePredicate side_of_s_; - int cur_dim_; - public: - Conflict_predicate( - const Self & dc, - const Point & p, - const OrientationPredicate & ori, - const SideOfOrientedSpherePredicate & side) - : dc_(dc), p_(p), ori_(ori), side_of_s_(side), cur_dim_(dc.current_dimension()) {} - - inline - bool operator()(Full_cell_const_handle s) const - { - bool ok; - if( ! dc_.is_infinite(s) ) - { - Oriented_side side = side_of_s_(dc_.points_begin(s), dc_.points_begin(s) + cur_dim_ + 1, p_); - if( ON_POSITIVE_SIDE == side ) - ok = true; - else if( ON_NEGATIVE_SIDE == side ) - ok = false; - else - ok = ON_POSITIVE_SIDE == dc_.perturbed_side_of_positive_sphere<OrientationPredicate>(p_, s, ori_); - } - else - { - typedef typename Full_cell::Vertex_handle_const_iterator VHCI; - typedef Substitute_point_in_vertex_iterator<VHCI> F; - F spivi(dc_.infinite_vertex(), &p_); - - Orientation o = ori_( - boost::make_transform_iterator(s->vertices_begin(), spivi), - boost::make_transform_iterator(s->vertices_begin() + cur_dim_ + 1, - spivi)); - - if( POSITIVE == o ) - ok = true; - else if( o == NEGATIVE ) - ok = false; - else - ok = (*this)(s->neighbor( s->index( dc_.infinite_vertex() ) )); - } - return ok; - } - }; - - template < typename ConflictPredicate > - class Conflict_traversal_predicate - { - const Self & dc_; - const ConflictPredicate & pred_; - public: - Conflict_traversal_predicate(const Self & dc, const ConflictPredicate & pred) - : dc_(dc), pred_(pred) - {} - inline - bool operator()(const Facet & f) const - { - return pred_(dc_.full_cell(f)->neighbor(dc_.index_of_covertex(f))); - } - }; - -// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - VALIDITY - - bool is_valid(bool verbose = false, int level = 0) const; - -private: - // Some internal types to shorten notation - typedef typename Base::Coaffine_orientation_d Coaffine_orientation_d; - using Base::flat_orientation_; - typedef Conflict_predicate<Coaffine_orientation_d, Side_of_oriented_subsphere_d> - Conflict_pred_in_subspace; - typedef Conflict_predicate<Orientation_d, Side_of_oriented_sphere_d> - Conflict_pred_in_fullspace; - typedef Conflict_traversal_predicate<Conflict_pred_in_subspace> - Conflict_traversal_pred_in_subspace; - typedef Conflict_traversal_predicate<Conflict_pred_in_fullspace> - Conflict_traversal_pred_in_fullspace; -}; - -// = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = -// FUNCTIONS THAT ARE MEMBER METHODS: - -// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS - -template< typename DCTraits, typename TDS > -typename Delaunay_triangulation<DCTraits, TDS>::Full_cell_handle -Delaunay_triangulation<DCTraits, TDS> -::remove( Vertex_handle v ) -{ - CGAL_precondition( ! is_infinite(v) ); - CGAL_expensive_precondition( is_vertex(v) ); - - // THE CASE cur_dim == 0 - if( 0 == current_dimension() ) - { - remove_decrease_dimension(v); - return Full_cell_handle(); - } - else if( 1 == current_dimension() ) - { // THE CASE cur_dim == 1 - if( 2 == number_of_vertices() ) - { - remove_decrease_dimension(v); - return Full_cell_handle(); - } - Full_cell_handle left = v->full_cell(); - if( 0 == left->index(v) ) - left = left->neighbor(1); - CGAL_assertion( 1 == left->index(v) ); - Full_cell_handle right = left->neighbor(0); - - tds().associate_vertex_with_full_cell(left, 1, right->vertex(1)); - set_neighbors(left, 0, right->neighbor(0), right->mirror_index(0)); - - tds().delete_vertex(v); - tds().delete_full_cell(right); - return left; - } - - // THE CASE cur_dim >= 2 - // Gather the finite vertices sharing an edge with |v| - typedef typename Base::template Full_cell_set<Full_cell_handle> Simplices; - Simplices simps; - std::back_insert_iterator<Simplices> out(simps); - tds().incident_full_cells(v, out); - typedef std::set<Vertex_handle> Vertex_set; - Vertex_set verts; - Vertex_handle vh; - for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it ) - for( int i = 0; i <= current_dimension(); ++i ) - { - vh = (*it)->vertex(i); - if( is_infinite(vh) ) - continue; - if( vh == v ) - continue; - verts.insert(vh); - } - - // After gathering finite neighboring vertices, create their Dark Delaunay triangulation - typedef Triangulation_vertex<Geom_traits, Vertex_handle> Dark_vertex_base; - typedef Triangulation_full_cell<Geom_traits, - internal::Triangulation::Dark_full_cell_data<Self> > Dark_full_cell_base; - typedef Triangulation_data_structure<Maximal_dimension, Dark_vertex_base, Dark_full_cell_base> Dark_tds; - typedef Delaunay_triangulation<DCTraits, Dark_tds> Dark_triangulation; - typedef typename Dark_triangulation::Face Dark_face; - typedef typename Dark_triangulation::Facet Dark_facet; - typedef typename Dark_triangulation::Vertex_handle Dark_v_handle; - typedef typename Dark_triangulation::Full_cell_handle Dark_s_handle; - - // If flat_orientation_ is defined, we give it the Dark triangulation - // so that the orientation it uses for "current_dimension()"-simplices is - // coherent with the global triangulation - Dark_triangulation dark_side( - maximal_dimension(), - flat_orientation_ ? - std::pair<int, const Flat_orientation_d *>(current_dimension(), flat_orientation_.get_ptr()) - : std::pair<int, const Flat_orientation_d *>((std::numeric_limits<int>::max)(), (Flat_orientation_d*) NULL) ); - - Dark_s_handle dark_s; - Dark_v_handle dark_v; - typedef std::map<Vertex_handle, Dark_v_handle> Vertex_map; - Vertex_map light_to_dark; - typename Vertex_set::iterator vit = verts.begin(); - while( vit != verts.end() ) - { - dark_v = dark_side.insert((*vit)->point(), dark_s); - dark_s = dark_v->full_cell(); - dark_v->data() = *vit; - light_to_dark[*vit] = dark_v; - ++vit; - } - - if( dark_side.current_dimension() != current_dimension() ) - { - CGAL_assertion( dark_side.current_dimension() + 1 == current_dimension() ); - // Here, the finite neighbors of |v| span a affine subspace of - // dimension one less than the current dimension. Two cases are possible: - if( (size_type)(verts.size() + 1) == number_of_vertices() ) - { - remove_decrease_dimension(v); - return Full_cell_handle(); - } - else - { // |v| is strictly outside the convex hull of the rest of the points. This is an - // easy case: first, modify the finite full_cells, then, delete the infinite ones. - // We don't even need the Dark triangulation. - Simplices infinite_simps; - { - Simplices finite_simps; - for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it ) - if( is_infinite(*it) ) - infinite_simps.push_back(*it); - else - finite_simps.push_back(*it); - simps.swap(finite_simps); - } // now, simps only contains finite simplices - // First, modify the finite full_cells: - for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it ) - { - int v_idx = (*it)->index(v); - tds().associate_vertex_with_full_cell(*it, v_idx, infinite_vertex()); - } - // Make the handles to infinite full cells searchable - infinite_simps.make_searchable(); - // 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(cpp11::get<0>(light_r)->neighbor(cpp11::get<1>(light_r)))) - light_r = rotate_rotor(light_r); - - while (conflict_zone.contains(cpp11::get<0>(dark_r)->neighbor(cpp11::get<1>(dark_r)))) - dark_r = dark_side.rotate_rotor(dark_r); - - Dark_s_handle dark_ns = cpp11::get<0>(dark_r); - int dark_ni = cpp11::get<1>(dark_r); - Full_cell_handle light_ns = cpp11::get<0>(light_r); - int light_ni = cpp11::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(Point_const_iterator(ch->vertices_begin()), - Point_const_iterator(ch->vertices_end()), - opposite_vh->point()) == ON_BOUNDED_SIDE) - { - if (verbose) - CGAL_warning_msg(false, "Non-empty sphere"); - return false; - } - } - } - } - } - return true; -} - - -} //namespace CGAL - -#endif // CGAL_DELAUNAY_COMPLEX_H |