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// Copyright (c) 1999-2004 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) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion
// Andreas Fabri <Andreas.Fabri@sophia.inria.fr>
#ifndef CGAL_DELAUNAY_TRIANGULATION_3_H
#define CGAL_DELAUNAY_TRIANGULATION_3_H
#include <CGAL/basic.h>
#include <utility>
#include <vector>
#include <CGAL/Triangulation_3.h>
#include <CGAL/iterator.h>
#include <CGAL/Location_policy.h>
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
#include <CGAL/Spatial_sort_traits_adapter_3.h>
#include <CGAL/internal/info_check.h>
#include <boost/tuple/tuple.hpp>
#include <boost/iterator/zip_iterator.hpp>
#include <boost/mpl/and.hpp>
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
#ifdef CGAL_DELAUNAY_3_OLD_REMOVE
# error "The old remove() code has been removed. Please report any issue you may have with the current one."
#endif
namespace CGAL {
// Here is the declaration of a class template with three arguments, one
// having a default value. There is no definition of that class template.
template < class Gt,
class Tds_ = Default,
class Location_policy = Default >
class Delaunay_triangulation_3;
// There is a specialization Delaunay_triangulation_3<Gt, Tds, Fast_location>
// defined in <CGAL/internal/Delaunay_triangulation_hierarchy_3.h>.
// Here is the specialization Delaunay_triangulation_3<Gt, Tds>, with two
// arguments, that is if Location_policy being the default value 'Default'.
template < class Gt, class Tds_ >
class Delaunay_triangulation_3<Gt, Tds_>
: public Triangulation_3<Gt, Tds_>
{
typedef Delaunay_triangulation_3<Gt, Tds_> Self;
typedef Triangulation_3<Gt,Tds_> Tr_Base;
public:
typedef typename Tr_Base::Triangulation_data_structure
Triangulation_data_structure;
typedef Gt Geom_traits;
typedef Compact_location Location_policy;
typedef typename Gt::Point_3 Point;
typedef typename Gt::Segment_3 Segment;
typedef typename Gt::Triangle_3 Triangle;
typedef typename Gt::Tetrahedron_3 Tetrahedron;
// types for dual:
typedef typename Gt::Line_3 Line;
typedef typename Gt::Ray_3 Ray;
//typedef typename Gt::Plane_3 Plane;
typedef typename Gt::Object_3 Object;
typedef typename Tr_Base::Cell_handle Cell_handle;
typedef typename Tr_Base::Vertex_handle Vertex_handle;
typedef typename Tr_Base::Cell Cell;
typedef typename Tr_Base::Vertex Vertex;
typedef typename Tr_Base::Facet Facet;
typedef typename Tr_Base::Edge Edge;
typedef typename Tr_Base::Cell_circulator Cell_circulator;
typedef typename Tr_Base::Facet_circulator Facet_circulator;
typedef typename Tr_Base::Cell_iterator Cell_iterator;
typedef typename Tr_Base::Facet_iterator Facet_iterator;
typedef typename Tr_Base::Edge_iterator Edge_iterator;
typedef typename Tr_Base::Vertex_iterator Vertex_iterator;
typedef typename Tr_Base::Finite_vertices_iterator Finite_vertices_iterator;
typedef typename Tr_Base::Finite_cells_iterator Finite_cells_iterator;
typedef typename Tr_Base::Finite_facets_iterator Finite_facets_iterator;
typedef typename Tr_Base::Finite_edges_iterator Finite_edges_iterator;
typedef typename Tr_Base::All_cells_iterator All_cells_iterator;
typedef typename Tr_Base::size_type size_type;
typedef typename Tr_Base::Locate_type Locate_type;
#ifndef CGAL_CFG_USING_BASE_MEMBER_BUG_2
using Tr_Base::cw;
using Tr_Base::ccw;
using Tr_Base::geom_traits;
using Tr_Base::number_of_vertices;
using Tr_Base::dimension;
using Tr_Base::finite_facets_begin;
using Tr_Base::finite_facets_end;
using Tr_Base::finite_vertices_begin;
using Tr_Base::finite_vertices_end;
using Tr_Base::finite_cells_begin;
using Tr_Base::finite_cells_end;
using Tr_Base::finite_edges_begin;
using Tr_Base::finite_edges_end;
using Tr_Base::tds;
using Tr_Base::infinite_vertex;
using Tr_Base::next_around_edge;
using Tr_Base::vertex_triple_index;
using Tr_Base::mirror_vertex;
using Tr_Base::coplanar;
using Tr_Base::coplanar_orientation;
using Tr_Base::orientation;
using Tr_Base::adjacent_vertices;
using Tr_Base::construct_segment;
using Tr_Base::incident_facets;
using Tr_Base::insert_in_conflict;
using Tr_Base::is_infinite;
using Tr_Base::is_valid_finite;
using Tr_Base::locate;
using Tr_Base::side_of_edge;
using Tr_Base::side_of_segment;
using Tr_Base::find_conflicts;
#endif
protected:
Oriented_side
side_of_oriented_sphere(const Point &p0, const Point &p1, const Point &p2,
const Point &p3, const Point &t, bool perturb = false) const;
Bounded_side
coplanar_side_of_bounded_circle(const Point &p, const Point &q,
const Point &r, const Point &s, bool perturb = false) const;
// for dual:
Point
construct_circumcenter(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().construct_circumcenter_3_object()(p, q, r);
}
Line
construct_equidistant_line(const Point &p1, const Point &p2,
const Point &p3) const
{
return geom_traits().construct_equidistant_line_3_object()(p1, p2, p3);
}
Ray
construct_ray(const Point &p, const Line &l) const
{
return geom_traits().construct_ray_3_object()(p, l);
}
Object
construct_object(const Point &p) const
{
return geom_traits().construct_object_3_object()(p);
}
Object
construct_object(const Segment &s) const
{
return geom_traits().construct_object_3_object()(s);
}
Object
construct_object(const Ray &r) const
{
return geom_traits().construct_object_3_object()(r);
}
bool
less_distance(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().compare_distance_3_object()(p, q, r) == SMALLER;
}
public:
Delaunay_triangulation_3(const Gt& gt = Gt())
: Tr_Base(gt)
{}
// copy constructor duplicates vertices and cells
Delaunay_triangulation_3(const Delaunay_triangulation_3 & tr)
: Tr_Base(tr)
{
CGAL_triangulation_postcondition( is_valid() );
}
template < typename InputIterator >
Delaunay_triangulation_3(InputIterator first, InputIterator last,
const Gt& gt = Gt())
: Tr_Base(gt)
{
insert(first, last);
}
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
template < class InputIterator >
std::ptrdiff_t
insert( InputIterator first, InputIterator last,
typename boost::enable_if<
boost::is_convertible<
typename std::iterator_traits<InputIterator>::value_type,
Point
>
>::type* = NULL
)
#else
template < class InputIterator >
std::ptrdiff_t
insert( InputIterator first, InputIterator last)
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
{
size_type n = number_of_vertices();
std::vector<Point> points (first, last);
spatial_sort (points.begin(), points.end(), geom_traits());
Vertex_handle hint;
for (typename std::vector<Point>::const_iterator p = points.begin(), end = points.end();
p != end; ++p)
hint = insert(*p, hint);
return number_of_vertices() - n;
}
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
private:
//top stands for tuple-or-pair
template <class Info>
const Point& top_get_first(const std::pair<Point,Info>& pair) const { return pair.first; }
template <class Info>
const Info& top_get_second(const std::pair<Point,Info>& pair) const { return pair.second; }
template <class Info>
const Point& top_get_first(const boost::tuple<Point,Info>& tuple) const { return boost::get<0>(tuple); }
template <class Info>
const Info& top_get_second(const boost::tuple<Point,Info>& tuple) const { return boost::get<1>(tuple); }
template <class Tuple_or_pair,class InputIterator>
std::ptrdiff_t insert_with_info(InputIterator first,InputIterator last)
{
size_type n = number_of_vertices();
std::vector<std::ptrdiff_t> indices;
std::vector<Point> points;
std::vector<typename Triangulation_data_structure::Vertex::Info> infos;
std::ptrdiff_t index=0;
for (InputIterator it=first;it!=last;++it){
Tuple_or_pair value=*it;
points.push_back( top_get_first(value) );
infos.push_back ( top_get_second(value) );
indices.push_back(index++);
}
typedef Spatial_sort_traits_adapter_3<Geom_traits,Point*> Search_traits;
spatial_sort(indices.begin(),indices.end(),Search_traits(&(points[0]),geom_traits()));
Vertex_handle hint;
for (typename std::vector<std::ptrdiff_t>::const_iterator
it = indices.begin(), end = indices.end();
it != end; ++it){
hint = insert(points[*it], hint);
if (hint!=Vertex_handle()) hint->info()=infos[*it];
}
return number_of_vertices() - n;
}
public:
template < class InputIterator >
std::ptrdiff_t
insert( InputIterator first,
InputIterator last,
typename boost::enable_if<
boost::is_convertible<
typename std::iterator_traits<InputIterator>::value_type,
std::pair<Point,typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type>
> >::type* =NULL
)
{
return insert_with_info< std::pair<Point,typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type> >(first,last);
}
template <class InputIterator_1,class InputIterator_2>
std::ptrdiff_t
insert( boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > first,
boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > last,
typename boost::enable_if<
boost::mpl::and_<
boost::is_convertible< typename std::iterator_traits<InputIterator_1>::value_type, Point >,
boost::is_convertible< typename std::iterator_traits<InputIterator_2>::value_type, typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type >
>
>::type* =NULL
)
{
return insert_with_info< boost::tuple<Point,typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type> >(first,last);
}
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
Vertex_handle insert(const Point & p, Vertex_handle hint)
{
return insert(p, hint == Vertex_handle() ? this->infinite_cell() : hint->cell());
}
Vertex_handle insert(const Point & p, Cell_handle start = Cell_handle());
Vertex_handle insert(const Point & p, Locate_type lt,
Cell_handle c, int li, int);
public: // internal methods
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point &p,
OutputItCells fit,
Cell_handle start = Cell_handle() );
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Vertex_handle hint);
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point& p,
Locate_type lt,
Cell_handle c, int li, int lj,
OutputItCells fit);
public:
#ifndef CGAL_NO_DEPRECATED_CODE
CGAL_DEPRECATED Vertex_handle move_point(Vertex_handle v, const Point & p);
#endif
template <class OutputIteratorBoundaryFacets,
class OutputIteratorCells,
class OutputIteratorInternalFacets>
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets>
find_conflicts(const Point &p, Cell_handle c,
OutputIteratorBoundaryFacets bfit,
OutputIteratorCells cit,
OutputIteratorInternalFacets ifit) const
{
CGAL_triangulation_precondition(dimension() >= 2);
std::vector<Cell_handle> cells;
cells.reserve(32);
std::vector<Facet> facets;
facets.reserve(64);
if (dimension() == 2) {
Conflict_tester_2 tester(p, this);
ifit = Tr_Base::find_conflicts
(c, tester,
make_triple(std::back_inserter(facets),
std::back_inserter(cells),
ifit)).third;
}
else {
Conflict_tester_3 tester(p, this);
ifit = Tr_Base::find_conflicts
(c, tester,
make_triple(std::back_inserter(facets),
std::back_inserter(cells),
ifit)).third;
}
// Reset the conflict flag on the boundary.
for(typename std::vector<Facet>::iterator fit=facets.begin();
fit != facets.end(); ++fit) {
fit->first->neighbor(fit->second)->tds_data().clear();
*bfit++ = *fit;
}
// Reset the conflict flag in the conflict cells.
for(typename std::vector<Cell_handle>::iterator ccit=cells.begin();
ccit != cells.end(); ++ccit) {
(*ccit)->tds_data().clear();
*cit++ = *ccit;
}
return make_triple(bfit, cit, ifit);
}
template <class OutputIteratorBoundaryFacets, class OutputIteratorCells>
std::pair<OutputIteratorBoundaryFacets, OutputIteratorCells>
find_conflicts(const Point &p, Cell_handle c,
OutputIteratorBoundaryFacets bfit,
OutputIteratorCells cit) const
{
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
Emptyset_iterator> t = find_conflicts(p, c, bfit, cit,
Emptyset_iterator());
return std::make_pair(t.first, t.second);
}
#ifndef CGAL_NO_DEPRECATED_CODE
// Returns the vertices on the boundary of the conflict hole.
template <class OutputIterator>
OutputIterator
vertices_in_conflict(const Point&p, Cell_handle c, OutputIterator res) const
{
return vertices_on_conflict_zone_boundary(p, c, res);
}
#endif // CGAL_NO_DEPRECATED_CODE
// Returns the vertices on the boundary of the conflict hole.
template <class OutputIterator>
OutputIterator
vertices_on_conflict_zone_boundary(const Point&p, Cell_handle c,
OutputIterator res) const
{
CGAL_triangulation_precondition(dimension() >= 2);
// Get the facets on the boundary of the hole.
std::vector<Facet> facets;
find_conflicts(p, c, std::back_inserter(facets),
Emptyset_iterator(), Emptyset_iterator());
// Then extract uniquely the vertices.
std::set<Vertex_handle> vertices;
if (dimension() == 3) {
for (typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i) {
vertices.insert(i->first->vertex((i->second+1)&3));
vertices.insert(i->first->vertex((i->second+2)&3));
vertices.insert(i->first->vertex((i->second+3)&3));
}
} else {
for (typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i) {
vertices.insert(i->first->vertex(cw(i->second)));
vertices.insert(i->first->vertex(ccw(i->second)));
}
}
return std::copy(vertices.begin(), vertices.end(), res);
}
// REMOVE
void remove(Vertex_handle v);
// return new cells (internal)
template <class OutputItCells>
void remove_and_give_new_cells(Vertex_handle v,
OutputItCells fit);
template < typename InputIterator >
size_type remove(InputIterator first, InputIterator beyond)
{
CGAL_triangulation_precondition(!this->does_repeat_in_range(first, beyond));
size_type n = number_of_vertices();
while (first != beyond) {
remove(*first);
++first;
}
return n - number_of_vertices();
}
template < typename InputIterator >
size_type remove_cluster(InputIterator first, InputIterator beyond)
{
Self tmp;
Vertex_remover<Self> remover (tmp);
return Tr_Base::remove(first, beyond, remover);
}
// MOVE
Vertex_handle move_if_no_collision(Vertex_handle v, const Point &p);
Vertex_handle move(Vertex_handle v, const Point &p);
// return new cells (internal)
template <class OutputItCells>
Vertex_handle move_if_no_collision_and_give_new_cells(Vertex_handle v,
const Point &p,
OutputItCells fit);
private:
Bounded_side
side_of_sphere(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3,
const Point &p, bool perturb) const;
public:
// Queries
Bounded_side
side_of_sphere(Cell_handle c, const Point & p,
bool perturb = false) const
{
return side_of_sphere(c->vertex(0), c->vertex(1),
c->vertex(2), c->vertex(3), p, perturb);
}
Bounded_side
side_of_circle( const Facet & f, const Point & p, bool perturb = false) const
{
return side_of_circle(f.first, f.second, p, perturb);
}
Bounded_side
side_of_circle( Cell_handle c, int i, const Point & p,
bool perturb = false) const;
Vertex_handle
nearest_vertex_in_cell(const Point& p, Cell_handle c) const;
Vertex_handle
nearest_vertex(const Point& p, Cell_handle c = Cell_handle()) const;
bool is_Gabriel(Cell_handle c, int i) const;
bool is_Gabriel(Cell_handle c, int i, int j) const;
bool is_Gabriel(const Facet& f)const ;
bool is_Gabriel(const Edge& e) const;
bool is_delaunay_after_displacement(Vertex_handle v,
const Point &p) const;
// Dual functions
Point dual(Cell_handle c) const;
Object dual(const Facet & f) const
{ return dual( f.first, f.second ); }
Object dual(Cell_handle c, int i) const;
Line dual_support(Cell_handle c, int i) const;
bool is_valid(bool verbose = false, int level = 0) const;
bool is_valid(Cell_handle c, bool verbose = false, int level = 0) const;
template < class Stream>
Stream& draw_dual(Stream & os)
{
for (Finite_facets_iterator fit = finite_facets_begin(),
end = finite_facets_end();
fit != end; ++fit) {
Object o = dual(*fit);
if (const Segment *s = object_cast<Segment>(&o)) os << *s;
else if (const Ray *r = object_cast<Ray>(&o)) os << *r;
else if (const Point *p = object_cast<Point>(&o)) os << *p;
}
return os;
}
protected:
Vertex_handle
nearest_vertex(const Point &p, Vertex_handle v, Vertex_handle w) const
{
// In case of equality, v is returned.
CGAL_triangulation_precondition(v != w);
if (is_infinite(v))
return w;
if (is_infinite(w))
return v;
return less_distance(p, w->point(), v->point()) ? w : v;
}
class Conflict_tester_3
{
const Point &p;
const Self *t;
public:
Conflict_tester_3(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
return t->side_of_sphere(c, p, true) == ON_BOUNDED_SIDE;
}
Oriented_side compare_weight(const Point &, const Point &) const
{
return ZERO;
}
bool test_initial_cell(Cell_handle) const
{
return true;
}
};
class Conflict_tester_2
{
const Point &p;
const Self *t;
public:
Conflict_tester_2(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
return t->side_of_circle(c, 3, p, true) == ON_BOUNDED_SIDE;
}
Oriented_side compare_weight(const Point &, const Point &) const
{
return ZERO;
}
bool test_initial_cell(Cell_handle) const
{
return true;
}
};
class Hidden_point_visitor
{
public:
Hidden_point_visitor() {}
template <class InputIterator>
void process_cells_in_conflict(InputIterator, InputIterator) const {}
void reinsert_vertices(Vertex_handle ) {}
Vertex_handle replace_vertex(Cell_handle c, int index,
const Point &) {
return c->vertex(index);
}
void hide_point(Cell_handle, const Point &) {}
};
class Perturbation_order {
const Self *t;
public:
Perturbation_order(const Self *tr)
: t(tr) {}
bool operator()(const Point *p, const Point *q) const {
return t->compare_xyz(*p, *q) == SMALLER;
}
};
template < class DelaunayTriangulation_3 >
class Vertex_remover;
template < class DelaunayTriangulation_3 >
class Vertex_inserter;
friend class Perturbation_order;
friend class Conflict_tester_3;
friend class Conflict_tester_2;
Hidden_point_visitor hidden_point_visitor;
};
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert(const Point & p, Cell_handle start)
{
Locate_type lt;
int li, lj;
Cell_handle c = locate(p, lt, li, lj, start);
return insert(p, lt, c, li, lj);
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert(const Point & p, Locate_type lt, Cell_handle c, int li, int lj)
{
switch (dimension()) {
case 3:
{
Conflict_tester_3 tester(p, this);
Vertex_handle v = insert_in_conflict(p, lt, c, li, lj,
tester, hidden_point_visitor);
return v;
}// dim 3
case 2:
{
Conflict_tester_2 tester(p, this);
return insert_in_conflict(p, lt, c, li, lj,
tester, hidden_point_visitor);
}//dim 2
default :
// dimension <= 1
// Do not use the generic insert.
return Tr_Base::insert(p, c);
}
}
template < class Gt, class Tds >
template <class OutputItCells>
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert_and_give_new_cells(const Point &p,
OutputItCells fit,
Cell_handle start)
{
Vertex_handle v = insert(p, start);
int dimension = this->dimension();
if(dimension == 3) this->incident_cells(v, fit);
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do {
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
} while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else *fit++ = v->cell(); // dimension = 0
return v;
}
template < class Gt, class Tds >
template <class OutputItCells>
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Vertex_handle hint)
{
Vertex_handle v = insert(p, hint);
int dimension = this->dimension();
if(dimension == 3) this->incident_cells(v, fit);
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do {
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
} while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else *fit++ = v->cell(); // dimension = 0
return v;
}
template < class Gt, class Tds >
template <class OutputItCells>
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
insert_and_give_new_cells(const Point& p,
Locate_type lt,
Cell_handle c, int li, int lj,
OutputItCells fit)
{
Vertex_handle v = insert(p, lt, c, li, lj);
int dimension = this->dimension();
if(dimension == 3) this->incident_cells(v, fit);
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do {
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
} while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else *fit++ = v->cell(); // dimension = 0
return v;
}
#ifndef CGAL_NO_DEPRECATED_CODE
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
move_point(Vertex_handle v, const Point & p)
{
CGAL_triangulation_precondition(! is_infinite(v));
CGAL_triangulation_expensive_precondition(is_vertex(v));
// Dummy implementation for a start.
// Remember an incident vertex to restart
// the point location after the removal.
Cell_handle c = v->cell();
Vertex_handle old_neighbor = c->vertex(c->index(v) == 0 ? 1 : 0);
CGAL_triangulation_assertion(old_neighbor != v);
remove(v);
if (dimension() <= 0)
return insert(p);
return insert(p, old_neighbor->cell());
}
#endif
template <class Gt, class Tds >
template <class DelaunayTriangulation_3>
class Delaunay_triangulation_3<Gt, Tds>::Vertex_remover {
typedef DelaunayTriangulation_3 Delaunay;
public:
typedef Nullptr_t Hidden_points_iterator;
Vertex_remover(Delaunay &tmp_) : tmp(tmp_) {}
Delaunay &tmp;
void add_hidden_points(Cell_handle) {}
Hidden_points_iterator hidden_points_begin() { return NULL; }
Hidden_points_iterator hidden_points_end() { return NULL; }
Bounded_side side_of_bounded_circle(const Point &p, const Point &q,
const Point &r, const Point &s, bool perturb = false) const {
return tmp.coplanar_side_of_bounded_circle(p,q,r,s,perturb);
}
};
template <class Gt, class Tds >
template <class DelaunayTriangulation_3>
class Delaunay_triangulation_3<Gt, Tds>::Vertex_inserter {
typedef DelaunayTriangulation_3 Delaunay;
public:
typedef Nullptr_t Hidden_points_iterator;
Vertex_inserter(Delaunay &tmp_) : tmp(tmp_) {}
Delaunay &tmp;
void add_hidden_points(Cell_handle) {}
Hidden_points_iterator hidden_points_begin() { return NULL; }
Hidden_points_iterator hidden_points_end() { return NULL; }
Vertex_handle insert(const Point& p,
Locate_type lt, Cell_handle c, int li, int lj) {
return tmp.insert(p, lt, c, li, lj);
}
Vertex_handle insert(const Point& p, Cell_handle c) {
return tmp.insert(p, c);
}
Vertex_handle insert(const Point& p) {
return tmp.insert(p);
}
};
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
remove(Vertex_handle v)
{
Self tmp;
Vertex_remover<Self> remover (tmp);
Tr_Base::remove(v,remover);
CGAL_triangulation_expensive_postcondition(is_valid());
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
move_if_no_collision(Vertex_handle v, const Point &p)
{
Self tmp;
Vertex_remover<Self> remover (tmp);
Vertex_inserter<Self> inserter (*this);
Vertex_handle res = Tr_Base::move_if_no_collision(v,p,remover,inserter);
CGAL_triangulation_expensive_postcondition(is_valid());
return res;
}
template <class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
move(Vertex_handle v, const Point &p) {
CGAL_triangulation_precondition(!is_infinite(v));
if(v->point() == p) return v;
Self tmp;
Vertex_remover<Self> remover (tmp);
Vertex_inserter<Self> inserter (*this);
return Tr_Base::move(v,p,remover,inserter);
}
template < class Gt, class Tds >
template <class OutputItCells>
void
Delaunay_triangulation_3<Gt,Tds>::
remove_and_give_new_cells(Vertex_handle v, OutputItCells fit)
{
Self tmp;
Vertex_remover<Self> remover (tmp);
Tr_Base::remove_and_give_new_cells(v,remover,fit);
CGAL_triangulation_expensive_postcondition(is_valid());
}
template < class Gt, class Tds >
template <class OutputItCells>
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
move_if_no_collision_and_give_new_cells(Vertex_handle v, const Point &p,
OutputItCells fit)
{
Self tmp;
Vertex_remover<Self> remover (tmp);
Vertex_inserter<Self> inserter (*this);
Vertex_handle res =
Tr_Base::move_if_no_collision_and_give_new_cells(v,p,
remover,inserter,fit);
CGAL_triangulation_expensive_postcondition(is_valid());
return res;
}
template < class Gt, class Tds >
Oriented_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_oriented_sphere(const Point &p0, const Point &p1, const Point &p2,
const Point &p3, const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( orientation(p0, p1, p2, p3) == POSITIVE );
Oriented_side os =
geom_traits().side_of_oriented_sphere_3_object()(p0, p1, p2, p3, p);
if (os != ON_ORIENTED_BOUNDARY || !perturb)
return os;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
const Point * points[5] = {&p0, &p1, &p2, &p3, &p};
std::sort(points, points+5, Perturbation_order(this) );
// We successively look whether the leading monomial, then 2nd monomial
// of the determinant has non null coefficient.
// 2 iterations are enough (cf paper)
for (int i=4; i>2; --i) {
if (points[i] == &p)
return ON_NEGATIVE_SIDE; // since p0 p1 p2 p3 are non coplanar
// and positively oriented
Orientation o;
if (points[i] == &p3 && (o = orientation(p0,p1,p2,p)) != COPLANAR )
return o;
if (points[i] == &p2 && (o = orientation(p0,p1,p,p3)) != COPLANAR )
return o;
if (points[i] == &p1 && (o = orientation(p0,p,p2,p3)) != COPLANAR )
return o;
if (points[i] == &p0 && (o = orientation(p,p1,p2,p3)) != COPLANAR )
return o;
}
CGAL_triangulation_assertion(false);
return ON_NEGATIVE_SIDE;
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
coplanar_side_of_bounded_circle(const Point &p0, const Point &p1,
const Point &p2, const Point &p, bool perturb) const
{
// In dim==2, we should even be able to assert orient == POSITIVE.
CGAL_triangulation_precondition( coplanar_orientation(p0, p1, p2)
!= COLLINEAR );
Bounded_side bs =
geom_traits().coplanar_side_of_bounded_circle_3_object()(p0, p1, p2, p);
if (bs != ON_BOUNDARY || !perturb)
return bs;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
const Point * points[4] = {&p0, &p1, &p2, &p};
std::sort(points, points+4, Perturbation_order(this) );
Orientation local = coplanar_orientation(p0, p1, p2);
// we successively look whether the leading monomial, then 2nd monimial,
// then 3rd monomial, of the determinant which has non null coefficient
// [syl] : TODO : Probably it can be stopped earlier like the 3D version
for (int i=3; i>0; --i) {
if (points[i] == &p)
return Bounded_side(NEGATIVE); // since p0 p1 p2 are non collinear
// but not necessarily positively oriented
Orientation o;
if (points[i] == &p2
&& (o = coplanar_orientation(p0,p1,p)) != COLLINEAR )
// [syl] : TODO : I'm not sure of the signs here (nor the rest :)
return Bounded_side(o*local);
if (points[i] == &p1
&& (o = coplanar_orientation(p0,p,p2)) != COLLINEAR )
return Bounded_side(o*local);
if (points[i] == &p0
&& (o = coplanar_orientation(p,p1,p2)) != COLLINEAR )
return Bounded_side(o*local);
}
// case when the first non null coefficient is the coefficient of
// the 4th monomial
// moreover, the tests (points[] == &p) were false up to here, so the
// monomial corresponding to p is the only monomial with non-zero
// coefficient, it is equal to coplanar_orient(p0,p1,p2) == positive
// so, no further test is required
return Bounded_side(-local); //ON_UNBOUNDED_SIDE;
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_sphere(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3,
const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( dimension() == 3 );
if (is_infinite(v0)) {
Orientation o = orientation(v2->point(), v1->point(), v3->point(), p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(v2->point(), v1->point(), v3->point(), p, perturb);
}
if (is_infinite(v1)) {
Orientation o = orientation(v2->point(), v3->point(), v0->point(), p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(v2->point(), v3->point(), v0->point(), p, perturb);
}
if (is_infinite(v2)) {
Orientation o = orientation(v1->point(), v0->point(), v3->point(), p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(v1->point(), v0->point(), v3->point(), p, perturb);
}
if (is_infinite(v3)) {
Orientation o = orientation(v0->point(), v1->point(), v2->point(), p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(v0->point(), v1->point(), v2->point(), p, perturb);
}
return (Bounded_side) side_of_oriented_sphere(v0->point(), v1->point(), v2->point(), v3->point(), p, perturb);
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_circle(Cell_handle c, int i,
const Point & p, bool perturb) const
// precondition : dimension >=2
// in dimension 3, - for a finite facet
// returns ON_BOUNDARY if the point lies on the circle,
// ON_UNBOUNDED_SIDE when exterior, ON_BOUNDED_SIDE
// interior
// for an infinite facet, considers the plane defined by the
// adjacent finite facet of the same cell, and does the same as in
// dimension 2 in this plane
// in dimension 2, for an infinite facet
// in this case, returns ON_BOUNDARY if the point lies on the
// finite edge (endpoints included)
// ON_BOUNDED_SIDE for a point in the open half-plane
// ON_UNBOUNDED_SIDE elsewhere
{
CGAL_triangulation_precondition( dimension() >= 2 );
int i3 = 5;
if ( dimension() == 2 ) {
CGAL_triangulation_precondition( i == 3 );
// the triangulation is supposed to be valid, ie the facet
// with vertices 0 1 2 in this order is positively oriented
if ( ! c->has_vertex( infinite_vertex(), i3 ) )
return coplanar_side_of_bounded_circle( c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
p, perturb);
// else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex( ccw(i3) ),
v2 = c->vertex( cw(i3) );
CGAL_triangulation_assertion(coplanar_orientation(v1->point(), v2->point(),
mirror_vertex(c, i3)->point()) == NEGATIVE);
Orientation o = coplanar_orientation(v1->point(), v2->point(), p);
if ( o != COLLINEAR )
return Bounded_side( o );
// because p is in f iff
// it does not lie on the same side of v1v2 as vn
int i_e;
Locate_type lt;
// case when p collinear with v1v2
return side_of_segment( p,
v1->point(), v2->point(),
lt, i_e );
}
// else dimension == 3
CGAL_triangulation_precondition( i >= 0 && i < 4 );
if ( ( ! c->has_vertex(infinite_vertex(),i3) ) || ( i3 != i ) ) {
// finite facet
// initialization of i0 i1 i2, vertices of the facet positively
// oriented (if the triangulation is valid)
int i0 = (i>0) ? 0 : 1;
int i1 = (i>1) ? 1 : 2;
int i2 = (i>2) ? 2 : 3;
CGAL_triangulation_precondition( coplanar( c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p ) );
return coplanar_side_of_bounded_circle( c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p, perturb);
}
//else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex( next_around_edge(i3,i) ),
v2 = c->vertex( next_around_edge(i,i3) );
Orientation o = (Orientation)
(coplanar_orientation( v1->point(), v2->point(),
c->vertex(i)->point()) *
coplanar_orientation( v1->point(), v2->point(), p ));
// then the code is duplicated from 2d case
if ( o != COLLINEAR )
return Bounded_side( -o );
// because p is in f iff
// it is not on the same side of v1v2 as c->vertex(i)
int i_e;
Locate_type lt;
// case when p collinear with v1v2
return side_of_segment( p,
v1->point(), v2->point(),
lt, i_e );
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
nearest_vertex_in_cell(const Point& p, Cell_handle c) const
// Returns the finite vertex of the cell c which is the closest to p.
{
CGAL_triangulation_precondition(dimension() >= 0);
Vertex_handle nearest = nearest_vertex(p, c->vertex(0), c->vertex(1));
if (dimension() >= 2) {
nearest = nearest_vertex(p, nearest, c->vertex(2));
if (dimension() == 3)
nearest = nearest_vertex(p, nearest, c->vertex(3));
}
return nearest;
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
Delaunay_triangulation_3<Gt,Tds>::
nearest_vertex(const Point& p, Cell_handle start) const
{
if (number_of_vertices() == 0)
return Vertex_handle();
// Use a brute-force algorithm if dimension < 3.
if (dimension() < 3) {
Finite_vertices_iterator vit = finite_vertices_begin();
Vertex_handle res = vit;
++vit;
for (Finite_vertices_iterator end = finite_vertices_end(); vit != end; ++vit)
res = nearest_vertex(p, res, vit);
return res;
}
Locate_type lt;
int li, lj;
Cell_handle c = locate(p, lt, li, lj, start);
if (lt == Tr_Base::VERTEX)
return c->vertex(li);
// - start with the closest vertex from the located cell.
// - repeatedly take the nearest of its incident vertices if any
// - if not, we're done.
Vertex_handle nearest = nearest_vertex_in_cell(p, c);
std::vector<Vertex_handle> vs;
vs.reserve(32);
while (true) {
Vertex_handle tmp = nearest;
adjacent_vertices(nearest, std::back_inserter(vs));
for (typename std::vector<Vertex_handle>::const_iterator
vsit = vs.begin(); vsit != vs.end(); ++vsit)
tmp = nearest_vertex(p, tmp, *vsit);
if (tmp == nearest)
break;
vs.clear();
nearest = tmp;
}
return nearest;
}
// This is not a fast version.
// The optimized version needs an int for book-keeping in
// tds() so as to avoiding the need to clear
// the tds marker in each cell (which is an unsigned char)
// Also the visitor in TDS could be more clever.
// The Delaunay triangulation which filters displacements
// will do these optimizations.
template <class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_delaunay_after_displacement(Vertex_handle v, const Point &p) const
{
CGAL_triangulation_precondition(!this->is_infinite(v));
CGAL_triangulation_precondition(this->dimension() == 2);
CGAL_triangulation_precondition(!this->test_dim_down(v));
if(v->point() == p) return true;
Point ant = v->point();
v->set_point(p);
std::size_t size;
// are incident cells well-oriented
std::vector<Cell_handle> cells;
cells.reserve(64);
this->incident_cells(v, std::back_inserter(cells));
size = cells.size();
for(std::size_t i=0; i<size; i++)
{
Cell_handle c = cells[i];
if(this->is_infinite(c)) continue;
if(this->orientation(c->vertex(0)->point(), c->vertex(1)->point(),
c->vertex(2)->point(), c->vertex(3)->point())
!= POSITIVE)
{
v->set_point(ant);
return false;
}
}
// are incident bi-cells Delaunay?
std::vector<Facet> facets;
facets.reserve(128);
this->incident_facets(v, std::back_inserter(facets));
size = facets.size();
for(std::size_t i=0; i<size; i++)
{
const Facet &f = facets[i];
Cell_handle c = f.first;
int j = f.second;
Cell_handle cj = c->neighbor(j);
int mj = this->mirror_index(c, j);
Vertex_handle h1 = c->vertex(j);
if(this->is_infinite(h1)) {
if(this->side_of_sphere(c, cj->vertex(mj)->point(), true)
!= ON_UNBOUNDED_SIDE) {
v->set_point(ant);
return false;
}
} else {
if(this->side_of_sphere(cj, h1->point(), true) != ON_UNBOUNDED_SIDE) {
v->set_point(ant);
return false;
}
}
}
v->set_point(ant);
return true;
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_Gabriel(const Facet& f) const
{
return is_Gabriel(f.first, f.second);
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_Gabriel(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension() == 3 && !is_infinite(c,i));
typename Geom_traits::Side_of_bounded_sphere_3
side_of_bounded_sphere =
geom_traits().side_of_bounded_sphere_3_object();
if ((!is_infinite(c->vertex(i))) &&
side_of_bounded_sphere (
c->vertex(vertex_triple_index(i,0))->point(),
c->vertex(vertex_triple_index(i,1))->point(),
c->vertex(vertex_triple_index(i,2))->point(),
c->vertex(i)->point()) == ON_BOUNDED_SIDE ) return false;
Cell_handle neighbor = c->neighbor(i);
int in = neighbor->index(c);
if ((!is_infinite(neighbor->vertex(in))) &&
side_of_bounded_sphere(
c->vertex(vertex_triple_index(i,0))->point(),
c->vertex(vertex_triple_index(i,1))->point(),
c->vertex(vertex_triple_index(i,2))->point(),
neighbor->vertex(in)->point()) == ON_BOUNDED_SIDE ) return false;
return true;
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_Gabriel(const Edge& e) const
{
return is_Gabriel(e.first, e.second, e.third);
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_Gabriel(Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition(dimension() == 3 && !is_infinite(c,i,j));
typename Geom_traits::Side_of_bounded_sphere_3
side_of_bounded_sphere =
geom_traits().side_of_bounded_sphere_3_object();
Facet_circulator fcirc = incident_facets(c,i,j),
fdone(fcirc);
Vertex_handle v1 = c->vertex(i);
Vertex_handle v2 = c->vertex(j);
do {
// test whether the vertex of cc opposite to *fcirc
// is inside the sphere defined by the edge e = (s, i,j)
Cell_handle cc = (*fcirc).first;
int ii = (*fcirc).second;
if (!is_infinite(cc->vertex(ii)) &&
side_of_bounded_sphere( v1->point(),
v2->point(),
cc->vertex(ii)->point())
== ON_BOUNDED_SIDE ) return false;
} while(++fcirc != fdone);
return true;
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Point
Delaunay_triangulation_3<Gt,Tds>::
dual(Cell_handle c) const
{
CGAL_triangulation_precondition(dimension()==3);
CGAL_triangulation_precondition( ! is_infinite(c) );
return c->circumcenter(geom_traits());
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Object
Delaunay_triangulation_3<Gt,Tds>::
dual(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension()>=2);
CGAL_triangulation_precondition( ! is_infinite(c,i) );
if ( dimension() == 2 ) {
CGAL_triangulation_precondition( i == 3 );
return construct_object( construct_circumcenter(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point()) );
}
// dimension() == 3
Cell_handle n = c->neighbor(i);
if ( ! is_infinite(c) && ! is_infinite(n) )
return construct_object(construct_segment( dual(c), dual(n) ));
// either n or c is infinite
int in;
if ( is_infinite(c) )
in = n->index(c);
else {
n = c;
in = i;
}
// n now denotes a finite cell, either c or c->neighbor(i)
int ind[3] = {(in+1)&3,(in+2)&3,(in+3)&3};
if ( (in&1) == 1 )
std::swap(ind[0], ind[1]);
// in=0: 1 2 3
// in=1: 3 2 0
// in=2: 3 0 1
// in=3: 1 0 2
const Point& p = n->vertex(ind[0])->point();
const Point& q = n->vertex(ind[1])->point();
const Point& r = n->vertex(ind[2])->point();
Line l = construct_equidistant_line( p, q, r );
return construct_object(construct_ray( dual(n), l));
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Line
Delaunay_triangulation_3<Gt,Tds>::
dual_support(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension()>=2);
CGAL_triangulation_precondition( ! is_infinite(c,i) );
if ( dimension() == 2 ) {
CGAL_triangulation_precondition( i == 3 );
return construct_equidistant_line( c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point() );
}
return construct_equidistant_line( c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point() );
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_valid(bool verbose, int level) const
{
if ( ! tds().is_valid(verbose,level) ) {
if (verbose)
std::cerr << "invalid data structure" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
if ( infinite_vertex() == Vertex_handle() ) {
if (verbose)
std::cerr << "no infinite vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
for(Finite_cells_iterator it = finite_cells_begin(), end = finite_cells_end(); it != end; ++it) {
is_valid_finite(it);
for(int i=0; i<4; i++ ) {
if ( !is_infinite
(it->neighbor(i)->vertex(it->neighbor(i)->index(it))) ) {
if ( side_of_sphere
(it,
it->neighbor(i)->vertex(it->neighbor(i)->index(it))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty sphere " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
}
break;
}
case 2:
{
for(Finite_facets_iterator it = finite_facets_begin(), end = finite_facets_end(); it != end; ++it) {
is_valid_finite((*it).first);
for(int i=0; i<3; i++ ) {
if( !is_infinite
((*it).first->neighbor(i)->vertex( (((*it).first)->neighbor(i))
->index((*it).first))) ) {
if ( side_of_circle ( (*it).first, 3,
(*it).first->neighbor(i)->
vertex( (((*it).first)->neighbor(i))
->index((*it).first) )->point() )
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty circle " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
}
break;
}
case 1:
{
for(Finite_edges_iterator it = finite_edges_begin(), end = finite_edges_end(); it != end; ++it)
is_valid_finite((*it).first);
break;
}
}
if (verbose)
std::cerr << "Delaunay valid triangulation" << std::endl;
return true;
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
is_valid(Cell_handle c, bool verbose, int level) const
{
if ( ! Tr_Base::is_valid(c,verbose,level) ) {
if (verbose) {
std::cerr << "combinatorically invalid cell" ;
for (int i=0; i <= dimension(); i++ )
std::cerr << c->vertex(i)->point() << ", " ;
std::cerr << std::endl;
}
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
if ( ! is_infinite(c) ) {
is_valid_finite(c,verbose,level);
for (int i=0; i<4; i++ ) {
if (side_of_sphere(c, c->vertex((c->neighbor(i))->index(c))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty sphere " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
case 2:
{
if ( ! is_infinite(c,3) ) {
for (int i=0; i<2; i++ ) {
if (side_of_circle(c, 3, c->vertex(c->neighbor(i)->index(c))->point())
== ON_BOUNDED_SIDE ) {
if (verbose)
std::cerr << "non-empty circle " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
break;
}
}
if (verbose)
std::cerr << "Delaunay valid cell" << std::endl;
return true;
}
} //namespace CGAL
#include <CGAL/internal/Delaunay_triangulation_hierarchy_3.h>
#endif // CGAL_DELAUNAY_TRIANGULATION_3_H
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