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cgal/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h

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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 may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// 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 <Sylvain.Pion@sophia.inria.fr>
// 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_short_names_3.h>
#include <CGAL/Triangulation_3.h>
#include <CGAL/Delaunay_remove_tds_3.h>
#include <CGAL/Unique_hash_map.h>
#include <CGAL/iterator.h>
CGAL_BEGIN_NAMESPACE
template < class Tr > class Natural_neighbors_3;
template < class Gt,
class Tds = Triangulation_data_structure_3 <
Triangulation_vertex_base_3<Gt>,
Triangulation_cell_base_3<Gt> > >
class Delaunay_triangulation_3 : public Triangulation_3<Gt,Tds>
{
typedef Delaunay_triangulation_3<Gt, Tds> Self;
typedef Triangulation_3<Gt,Tds> Tr_Base;
friend class Natural_neighbors_3<Self>;
public:
typedef Tds Triangulation_data_structure;
typedef Gt Geom_traits;
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::Locate_type Locate_type;
typedef Triple<Vertex_handle,Vertex_handle,Vertex_handle> Vertex_triple;
#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;
#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);
}
template < class InputIterator >
int
insert(InputIterator first, InputIterator last)
{
int n = number_of_vertices();
std::vector<Point> points (first, last);
std::random_shuffle (points.begin(), points.end());
spatial_sort (points.begin(), points.end(), geom_traits());
Cell_handle hint;
for (typename std::vector<Point>::const_iterator p = points.begin(), end = points.end();
p != end; ++p)
hint = insert (*p, hint)->cell();
return number_of_vertices() - n;
}
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);
Vertex_handle move_point(Vertex_handle v, const Point & p);
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)->set_in_conflict_flag(0);
*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)->set_in_conflict_flag(0);
*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);
}
// 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
{
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);
}
// We return bool only for backward compatibility (it's always true).
// The documentation mentions void.
bool remove(Vertex_handle v);
template < typename InputIterator >
int remove(InputIterator first, InputIterator beyond)
{
int n = number_of_vertices();
while (first != beyond) {
remove(*first);
++first;
}
return n - number_of_vertices();
}
private:
typedef Facet Edge_2D;
void remove_2D(Vertex_handle v);
void make_hole_2D(Vertex_handle v, std::list<Edge_2D> & hole);
void fill_hole_delaunay_2D(std::list<Edge_2D> & hole);
void make_canonical(Vertex_triple& t) const;
Vertex_triple
make_vertex_triple(const Facet& f) const;
void remove_3D(Vertex_handle v);
void remove_3D_new(Vertex_handle v);
Bounded_side
side_of_sphere(const Vertex_handle& v0, const Vertex_handle& v1,
const Vertex_handle& v2, const Vertex_handle& v3,
const Point &p, bool perturb) const;
public:
// Queries
Bounded_side
side_of_sphere(const 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( const Cell_handle& c, int i, const Point & p,
bool perturb = false) const;
Vertex_handle
nearest_vertex_in_cell(const Point& p, const 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;
// 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 Point *p = object_cast<Point>(&o)) os << *p;
if (const Segment *s = object_cast<Segment>(&o)) os << *s;
if (const Ray *r = object_cast<Ray>(&o)) os << *r;
}
return os;
}
private:
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;
}
#ifndef CGAL_CFG_NET2003_MATCHING_BUG
void make_hole_3D_ear( Vertex_handle v,
std::vector<Facet> & boundhole,
std::vector<Cell_handle> & hole);
#else
void make_hole_3D_ear( Vertex_handle v,
std::vector<Facet> & boundhole,
std::vector<Cell_handle> & hole)
{
CGAL_triangulation_expensive_precondition( ! test_dim_down(v) );
incident_cells(v, std::back_inserter(hole));
for (typename std::vector<Cell_handle>::iterator cit = hole.begin();
cit != hole.end(); ++cit) {
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor( indv );
boundhole.push_back(Facet( opp_cit, opp_cit->index(*cit)) );
for (int i=0; i<4; i++)
if ( i != indv )
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
#endif
void fill_hole_3D_ear(const std::vector<Facet> & boundhole);
void make_hole_3D_new( Vertex_handle v,
std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle> & hole);
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;
}
};
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 >
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());
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
remove_2D(Vertex_handle v)
{
CGAL_triangulation_precondition(dimension() == 2);
std::list<Edge_2D> hole;
make_hole_2D(v, hole);
fill_hole_delaunay_2D(hole);
tds().delete_vertex(v);
}
template <class Gt, class Tds >
void
Delaunay_triangulation_3<Gt, Tds>::
fill_hole_delaunay_2D(std::list<Edge_2D> & first_hole)
{
typedef std::list<Edge_2D> Hole;
std::vector<Hole> hole_list;
Cell_handle f, ff, fn;
int i, ii, in;
hole_list.push_back(first_hole);
while( ! hole_list.empty())
{
Hole hole = hole_list.back();
hole_list.pop_back();
// if the hole has only three edges, create the triangle
if (hole.size() == 3) {
typename Hole::iterator hit = hole.begin();
f = (*hit).first; i = (*hit).second;
ff = (* ++hit).first; ii = (*hit).second;
fn = (* ++hit).first; in = (*hit).second;
tds().create_face(f, i, ff, ii, fn, in);
continue;
}
// else find an edge with two finite vertices
// on the hole boundary
// and the new triangle adjacent to that edge
// cut the hole and push it back
// first, ensure that a neighboring face
// whose vertices on the hole boundary are finite
// is the first of the hole
while (1) {
ff = (hole.front()).first;
ii = (hole.front()).second;
if ( is_infinite(ff->vertex(cw(ii))) ||
is_infinite(ff->vertex(ccw(ii)))) {
hole.push_back(hole.front());
hole.pop_front();
}
else
break;
}
// take the first neighboring face and pop it;
ff = (hole.front()).first;
ii = (hole.front()).second;
hole.pop_front();
Vertex_handle v0 = ff->vertex(cw(ii));
Vertex_handle v1 = ff->vertex(ccw(ii));
Vertex_handle v2 = infinite_vertex();
const Point &p0 = v0->point();
const Point &p1 = v1->point();
const Point *p2 = NULL; // Initialize to NULL to avoid warning.
typename Hole::iterator hdone = hole.end();
typename Hole::iterator hit = hole.begin();
typename Hole::iterator cut_after(hit);
// if tested vertex is c with respect to the vertex opposite
// to NULL neighbor,
// stop at the before last face;
hdone--;
for (; hit != hdone; ++hit) {
fn = hit->first;
in = hit->second;
Vertex_handle vv = fn->vertex(ccw(in));
if (is_infinite(vv)) {
if (is_infinite(v2))
cut_after = hit;
}
else { // vv is a finite vertex
const Point &p = vv->point();
if (coplanar_orientation(p0, p1, p) == COUNTERCLOCKWISE) {
if (is_infinite(v2) ||
coplanar_side_of_bounded_circle(p0, p1, *p2, p, true)
== ON_BOUNDED_SIDE) {
v2 = vv;
p2 = &p;
cut_after = hit;
}
}
}
}
// create new triangle and update adjacency relations
Cell_handle newf;
//update the hole and push back in the Hole_List stack
// if v2 belongs to the neighbor following or preceding *f
// the hole remain a single hole
// otherwise it is split in two holes
fn = (hole.front()).first;
in = (hole.front()).second;
if (fn->has_vertex(v2, i) && i == ccw(in)) {
newf = tds().create_face(ff, ii, fn, in);
hole.pop_front();
hole.push_front(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
fn = (hole.back()).first;
in = (hole.back()).second;
if (fn->has_vertex(v2, i) && i == cw(in)) {
newf = tds().create_face(fn, in, ff, ii);
hole.pop_back();
hole.push_back(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
// split the hole in two holes
newf = tds().create_face(ff, ii, v2);
Hole new_hole;
++cut_after;
while( hole.begin() != cut_after )
{
new_hole.push_back(hole.front());
hole.pop_front();
}
hole.push_front(Edge_2D(newf, 1));
new_hole.push_front(Edge_2D(newf, 0));
hole_list.push_back(hole);
hole_list.push_back(new_hole);
}
}
}
}
template <class Gt, class Tds >
void
Delaunay_triangulation_3<Gt, Tds>::
make_hole_2D(Vertex_handle v, std::list<Edge_2D> & hole)
{
std::vector<Cell_handle> to_delete;
typename Tds::Face_circulator fc = tds().incident_faces(v);
typename Tds::Face_circulator done(fc);
// We prepare for deleting all interior cells.
// We ->set_cell() pointers to cells outside the hole.
// We push the Edges_2D of the boundary (seen from outside) in "hole".
do {
Cell_handle f = fc;
int i = f->index(v);
Cell_handle fn = f->neighbor(i);
int in = fn->index(f);
f->vertex(cw(i))->set_cell(fn);
fn->set_neighbor(in, Cell_handle());
hole.push_back(Edge_2D(fn, in));
to_delete.push_back(f);
++fc;
} while (fc != done);
tds().delete_cells(to_delete.begin(), to_delete.end());
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
make_canonical(Vertex_triple& t) const
{
int i = (&*(t.first) < &*(t.second))? 0 : 1;
if(i==0) {
i = (&*(t.first) < &*(t.third))? 0 : 2;
} else {
i = (&*(t.second) < &*(t.third))? 1 : 2;
}
Vertex_handle tmp;
switch(i){
case 0: return;
case 1:
tmp = t.first;
t.first = t.second;
t.second = t.third;
t.third = tmp;
return;
default:
tmp = t.first;
t.first = t.third;
t.third = t.second;
t.second = tmp;
}
}
template < class Gt, class Tds >
typename Delaunay_triangulation_3<Gt,Tds>::Vertex_triple
Delaunay_triangulation_3<Gt,Tds>::
make_vertex_triple(const Facet& f) const
{
// static const int vertex_triple_index[4][3] = { {1, 3, 2}, {0, 2, 3},
// {0, 3, 1}, {0, 1, 2} };
Cell_handle ch = f.first;
int i = f.second;
return Vertex_triple(ch->vertex(vertex_triple_index(i,0)),
ch->vertex(vertex_triple_index(i,1)),
ch->vertex(vertex_triple_index(i,2)));
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
remove_3D(Vertex_handle v)
{
std::vector<Facet> boundhole; // facets on the boundary of the hole
boundhole.reserve(64); // 27 on average.
std::vector<Cell_handle> hole;
hole.reserve(64);
make_hole_3D_ear(v, boundhole, hole);
fill_hole_3D_ear(boundhole);
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
remove_3D_new(Vertex_handle v)
{
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
typedef std::map<Vertex_triple,Facet> Vertex_triple_Facet_map;
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D_new(v, outer_map, hole);
bool inf = false;
unsigned int i;
// collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
incident_vertices(v, std::back_inserter(vertices));
// create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in aux towards the vertices in *this
Self aux;
Unique_hash_map<Vertex_handle,Vertex_handle> vmap;
Cell_handle ch = Cell_handle();
for(i=0; i < vertices.size(); i++){
if(! is_infinite(vertices[i])){
Vertex_handle vh = aux.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}else {
inf = true;
}
}
if(aux.dimension()==2){
Vertex_handle fake_inf = aux.insert(v->point());
vmap[fake_inf] = infinite_vertex();
} else {
vmap[aux.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(aux.dimension() == 3);
// Construct the set of vertex triples of aux
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of aux
if(inf){
for(All_cells_iterator it = aux.all_cells_begin();
it != aux.all_cells_end();
++it){
for(i=0; i < 4; i++){
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical(vt);
inner_map[vt]= f;
}
}
} else {
for(Finite_cells_iterator it = aux.finite_cells_begin();
it != aux.finite_cells_end();
++it){
for(i=0; i < 4; i++){
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty()){
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third)){
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++){
if(i != i_i){
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end()){
std::swap(vt.second,vt.third);
outer_map[vt]= f;
} else {
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
}
template < class Gt, class Tds >
bool
Delaunay_triangulation_3<Gt,Tds>::
remove(Vertex_handle v)
{
CGAL_triangulation_precondition( v != Vertex_handle());
CGAL_triangulation_precondition( !is_infinite(v));
CGAL_triangulation_expensive_precondition(is_vertex(v));
if (dimension() >= 0 && test_dim_down(v)) {
tds().remove_decrease_dimension(v);
// Now try to see if we need to re-orient.
if (dimension() == 2) {
Facet f = *finite_facets_begin();
if (coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
tds().reorient();
}
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
if (dimension() == 1) {
tds().remove_from_maximal_dimension_simplex(v);
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
if (dimension() == 2) {
remove_2D(v);
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
CGAL_triangulation_assertion( dimension() == 3 );
#ifdef CGAL_DELAUNAY_3_OLD_REMOVE
remove_3D(v);
#else
remove_3D_new(v);
#endif
CGAL_triangulation_expensive_postcondition(is_valid());
return true;
}
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(const Vertex_handle& v0, const Vertex_handle& v1,
const Vertex_handle& v2, const Vertex_handle& v3,
const Point &p, bool perturb) const
{
CGAL_triangulation_precondition( dimension() == 3 );
// TODO :
// - avoid accessing points of infinite vertex
// - share the 4 codes below (see old version)
const Point &p0 = v0->point();
const Point &p1 = v1->point();
const Point &p2 = v2->point();
const Point &p3 = v3->point();
if (is_infinite(v0)) {
Orientation o = orientation(p2, p1, p3, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p2, p1, p3, p, perturb);
}
if (is_infinite(v1)) {
Orientation o = orientation(p2, p3, p0, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p2, p3, p0, p, perturb);
}
if (is_infinite(v2)) {
Orientation o = orientation(p1, p0, p3, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p1, p0, p3, p, perturb);
}
if (is_infinite(v3)) {
Orientation o = orientation(p0, p1, p2, p);
if (o != COPLANAR)
return Bounded_side(o);
return coplanar_side_of_bounded_circle(p0, p1, p2, p, perturb);
}
return (Bounded_side) side_of_oriented_sphere(p0, p1, p2, p3, p, perturb);
}
template < class Gt, class Tds >
Bounded_side
Delaunay_triangulation_3<Gt,Tds>::
side_of_circle(const 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, const Cell_handle& c) const
// Returns the finite vertex of the cell c which is the closest to p.
{
CGAL_triangulation_precondition(dimension() >= 1);
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;
for (++vit; vit != finite_vertices_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;
incident_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;
}
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)
unsigned char ind[3] = {(in+1)&3,(in+2)&3,(in+3)&3};
if ( (in&1) == 1 )
std::swap(ind[0], ind[1]);
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:
{
Finite_cells_iterator it;
for ( it = finite_cells_begin(); it != finite_cells_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:
{
Finite_facets_iterator it;
for ( it = finite_facets_begin(); it != finite_facets_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:
{
Finite_edges_iterator it;
for ( it = finite_edges_begin(); it != finite_edges_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;
}
#ifndef CGAL_CFG_NET2003_MATCHING_BUG
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
make_hole_3D_ear( Vertex_handle v,
std::vector<Facet> & boundhole,
std::vector<Cell_handle> & hole)
{
CGAL_triangulation_expensive_precondition( ! test_dim_down(v) );
incident_cells(v, std::back_inserter(hole));
for (typename std::vector<Cell_handle>::iterator cit = hole.begin();
cit != hole.end(); ++cit) {
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor( indv );
boundhole.push_back(Facet( opp_cit, opp_cit->index(*cit)) );
for (int i=0; i<4; i++)
if ( i != indv )
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
#endif
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
make_hole_3D_new( Vertex_handle v,
std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle> & hole)
{
CGAL_triangulation_expensive_precondition( ! test_dim_down(v) );
incident_cells(v, std::back_inserter(hole));
for (typename std::vector<Cell_handle>::iterator cit = hole.begin();
cit != hole.end(); ++cit) {
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor( indv );
Facet f(opp_cit, opp_cit->index(*cit));
Vertex_triple vt = make_vertex_triple(f);
make_canonical(vt);
outer_map[vt] = f;
for (int i=0; i<4; i++)
if ( i != indv )
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
template < class Gt, class Tds >
void
Delaunay_triangulation_3<Gt,Tds>::
fill_hole_3D_ear(const std::vector<Facet> & boundhole)
{
typedef Delaunay_remove_tds_3_2<Delaunay_triangulation_3> Surface;
typedef typename Surface::Face_3_2 Face_3_2;
typedef typename Surface::Face_handle_3_2 Face_handle_3_2;
typedef typename Surface::Vertex_handle_3_2 Vertex_handle_3_2;
Surface surface(boundhole);
Face_handle_3_2 f = surface.faces_begin();
Face_handle_3_2 last_op = f; // This is where the last ear was inserted
int k = -1;
// This is a loop over the halfedges of the surface of the hole
// As edges are not explicitely there, we loop over the faces instead,
// and an index.
// The current face is f, the current index is k = -1, 0, 1, 2
for(;;) {
next_edge: ;
k++;
if(k == 3) {
// The faces form a circular list. With f->n() we go to the next face.
f = f->n();
CGAL_assertion_msg(f != last_op, "Unable to find an ear");
k = 0;
}
// The edges are marked, if they are a candidate for an ear.
// This saves time, for example an edge gets not considered
// from both adjacent faces.
if (!f->is_halfedge_marked(k))
continue;
Vertex_handle_3_2 w0, w1, w2, w3;
Vertex_handle v0, v1, v2, v3;
int i = ccw(k);
int j = cw(k);
Face_handle_3_2 n = f->neighbor(k);
int fi = n->index(f);
w1 = f->vertex(i);
w2 = f->vertex(j);
v1 = w1->info();
v2 = w2->info();
if( is_infinite(v1) || is_infinite(v2) ){
// there will be another ear, so let's ignore this one,
// because it is complicated to treat
continue;
}
w0 = f->vertex(k);
w3 = n->vertex(fi);
v0 = w0->info();
v3 = w3->info();
if( !is_infinite(v0) && !is_infinite(v3) &&
orientation(v0->point(), v1->point(),
v2->point(), v3->point()) != POSITIVE)
continue;
// the two faces form a concavity, in which we might plug a cell
// we now look at all vertices that are on the boundary of the hole
for(typename Surface::Vertex_iterator vit = surface.vertices_begin();
vit != surface.vertices_end(); ++vit) {
Vertex_handle v = vit->info();
if (is_infinite(v) || v == v0 || v == v1 || v == v2 || v == v3)
continue;
if (side_of_sphere(v0,v1,v2,v3, v->point(), true) == ON_BOUNDED_SIDE)
goto next_edge;
}
// we looked at all vertices
Face_handle_3_2 m_i = f->neighbor(i);
Face_handle_3_2 m_j = f->neighbor(j);
bool neighbor_i = m_i == n->neighbor(cw(fi));
bool neighbor_j = m_j == n->neighbor(ccw(fi));
// Test if the edge that would get introduced is on the surface
if ( !neighbor_i && !neighbor_j &&
surface.is_edge(f->vertex(k), n->vertex(fi)))
continue;
// none of the vertices violates the Delaunay property
// We are ready to plug a new cell
Cell_handle ch = tds().create_cell(v0, v1, v2, v3);
// The new cell touches the faces that form the ear
Facet fac = n->info();
tds().set_adjacency(ch, 0, fac.first, fac.second);
fac = f->info();
tds().set_adjacency(ch, 3, fac.first, fac.second);
// It may touch another face,
// or even two other faces if it is the last cell
if(neighbor_i) {
fac = m_i->info();
tds().set_adjacency(ch, 1, fac.first, fac.second);
}
if(neighbor_j) {
fac = m_j->info();
tds().set_adjacency(ch, 2, fac.first, fac.second);
}
if( !neighbor_i && !neighbor_j) {
surface.flip(f,k);
int fi = n->index(f);
int ni = f->index(n);
// The flipped edge is not a concavity
f->unmark_edge(ni);
// The adjacent edges may be a concavity
// that is they are candidates for an ear
// In the list of faces they get moved behind f
f->mark_edge(cw(ni), f);
f->mark_edge(ccw(ni), f);
n->mark_edge(cw(fi), f);
n->mark_edge(ccw(fi), f);
f->set_info(Facet(ch,2));
n->set_info(Facet(ch,1));
} else if (neighbor_i && (! neighbor_j)) {
surface.remove_degree_3(f->vertex(j), f);
// all three edges adjacent to f are
// candidate for an ear
f->mark_adjacent_edges();
f->set_info(Facet(ch,2));
} else if ((! neighbor_i) && neighbor_j) {
surface.remove_degree_3(f->vertex(i), f);
f->mark_adjacent_edges();
f->set_info(Facet(ch,1));
} else {
CGAL_assertion(surface.number_of_vertices() == 4);
// when we leave the function the vertices and faces of the surface
// are deleted by the destructor
return;
}
// we successfully inserted a cell
last_op = f;
// we have to reconsider all edges incident to f
k = -1;
} // for(;;)
}
CGAL_END_NAMESPACE
#endif // CGAL_DELAUNAY_TRIANGULATION_3_H
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