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cgal/Packages/Triangulation_3/include/CGAL/Triangulation_3.h

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// ============================================================================
//
// Copyright (c) 1999 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------------
//
// release :
// release_date :
//
// file : include/CGAL/Triangulation_3.h
// revision : $Revision$
//
// author(s) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
//
// coordinator : INRIA Sophia Antipolis (<Mariette.Yvinec@sophia.inria.fr>)
//
// ============================================================================
#ifndef CGAL_TRIANGULATION_3_H
#define CGAL_TRIANGULATION_3_H
#include <CGAL/basic.h>
#include <iostream>
#include <list>
#include <map>
#include <utility>
#include <CGAL/Triangulation_short_names_3.h>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/triple.h>
#include <CGAL/Pointer.h>
#include <CGAL/circulator.h>
#include <CGAL/triangulation_assertions.h>
#include <CGAL/Triangulation_data_structure_3.h>
#include <CGAL/Triangulation_cell_base_3.h>
#include <CGAL/Triangulation_vertex_base_3.h>
#include <CGAL/Triangulation_cell_3.h>
#include <CGAL/Triangulation_vertex_3.h>
#include <CGAL/Triangulation_handles_3.h>
#include <CGAL/Triangulation_iterators_3.h>
#include <CGAL/Triangulation_circulators_3.h>
CGAL_BEGIN_NAMESPACE
template < class GT, class Tds > std::istream& operator>>
(std::istream& is, Triangulation_3<GT,Tds> &tr);
template < class GT,
class Tds = Triangulation_data_structure_3 <
Triangulation_vertex_base_3<GT>,
Triangulation_cell_base_3<void> > >
class Triangulation_3
:public Triangulation_utils_3
{
friend std::istream& operator>> CGAL_NULL_TMPL_ARGS
(std::istream& is, Triangulation_3<GT,Tds> &tr);
friend class Triangulation_cell_3<GT,Tds>;
friend class Triangulation_vertex_3<GT,Tds>;
friend class Triangulation_cell_iterator_3<GT,Tds>;
friend class Triangulation_facet_iterator_3<GT,Tds>;
friend class Triangulation_edge_iterator_3<GT,Tds>;
friend class Triangulation_vertex_iterator_3<GT,Tds>;
friend class Triangulation_cell_circulator_3<GT,Tds>;
friend class Triangulation_facet_circulator_3<GT,Tds>;
public:
typedef Tds Triangulation_data_structure;
typedef GT Geom_traits;
typedef Triangulation_3<GT, Tds> Self;
typedef typename GT::Point_3 Point;
typedef typename GT::Segment_3 Segment;
typedef typename GT::Triangle_3 Triangle;
typedef typename GT::Tetrahedron_3 Tetrahedron;
typedef typename GT::Compare_x_3 Compare_x_3;
typedef typename GT::Compare_y_3 Compare_y_3;
typedef typename GT::Compare_z_3 Compare_z_3;
typedef typename GT::Equal_3 Equal_3;
typedef typename GT::Collinear_3 Collinear_3;
typedef typename GT::Orientation_3 Orientation_3;
typedef typename GT::Coplanar_orientation_3 Coplanar_orientation_3;
typedef typename GT::Construct_segment_3 Construct_segment_3;
typedef typename GT::Construct_triangle_3 Construct_triangle_3;
typedef typename GT::Construct_tetrahedron_3 Construct_tetrahedron_3;
typedef Triangulation_cell_handle_3<GT,Tds> Cell_handle;
typedef Triangulation_vertex_handle_3<GT,Tds> Vertex_handle;
typedef Triangulation_cell_3<GT,Tds> Cell;
typedef Triangulation_vertex_3<GT,Tds> Vertex;
typedef std::pair<Cell_handle, int> Facet;
typedef triple<Cell_handle, int, int> Edge;
typedef Triangulation_cell_circulator_3<GT,Tds> Cell_circulator;
typedef Triangulation_facet_circulator_3<GT,Tds> Facet_circulator;
typedef Triangulation_cell_iterator_3<GT,Tds> Cell_iterator;
typedef Triangulation_facet_iterator_3<GT,Tds> Facet_iterator;
typedef Triangulation_edge_iterator_3<GT,Tds> Edge_iterator;
typedef Triangulation_vertex_iterator_3<GT,Tds> Vertex_iterator;
typedef Point value_type; // to have a back_inserter
typedef const value_type& const_reference;
enum Locate_type {
VERTEX=0,
EDGE, //1
FACET, //2
CELL, //3
OUTSIDE_CONVEX_HULL, //4
OUTSIDE_AFFINE_HULL };//5
protected:
Tds _tds;
GT _gt;
Vertex_handle infinite; //infinite vertex
Compare_x_3 compare_x;
Compare_y_3 compare_y;
Compare_z_3 compare_z;
Equal_3 equal;
Collinear_3 collinear;
Orientation_3 orientation;
Coplanar_orientation_3 coplanar_orientation;
Construct_segment_3 construct_segment;
Construct_triangle_3 construct_triangle;
Construct_tetrahedron_3 construct_tetrahedron;
void init_tds()
{
infinite = (Vertex*) _tds.insert_increase_dimension(NULL);
// Forces the compiler to instantiate handle2pointer.
handle2pointer( Vertex_handle() );
handle2pointer( Cell_handle() );
}
void init_function_objects()
{
compare_x = geom_traits().compare_x_3_object();
compare_y = geom_traits().compare_y_3_object();
compare_z = geom_traits().compare_z_3_object();
equal = geom_traits().equal_3_object();
collinear = geom_traits().collinear_3_object();
orientation = geom_traits().orientation_3_object();
coplanar_orientation = geom_traits().coplanar_orientation_3_object();
construct_segment = geom_traits().construct_segment_3_object();
construct_triangle = geom_traits().construct_triangle_3_object();
construct_tetrahedron = geom_traits().construct_tetrahedron_3_object();
}
bool test_dim_down(Vertex_handle v);
public:
// CONSTRUCTORS
Triangulation_3()
: _tds(), _gt()
{
init_tds();
init_function_objects();
}
Triangulation_3(const GT & gt)
: _tds(), _gt(gt)
{
init_tds();
init_function_objects();
}
// copy constructor duplicates vertices and cells
Triangulation_3(const Triangulation_3<GT,Tds> & tr)
: _gt(tr._gt)
{
infinite = (Vertex *) _tds.copy_tds(tr._tds, &(*(tr.infinite)) );
init_function_objects();
}
void clear()
{
_tds.clear();
init_tds();
}
Triangulation_3 & operator=(const Triangulation_3 & tr)
{
// clear(); BUG !!
// infinite.Delete();
infinite = (Vertex *) _tds.copy_tds( tr._tds, &*tr.infinite );
_gt = tr._gt;
return *this;
}
// HELPING FUNCTIONS
void copy_triangulation(const Triangulation_3<GT,Tds> & tr)
{
// clear(); BUG !!
// infinite.Delete();
_gt = tr._gt;
infinite = (Vertex *) _tds.copy_tds( tr._tds, &*tr.infinite );
}
void swap(Triangulation_3 &tr)
{
GT t(geom_traits());
_gt = tr.geom_traits();
tr._gt = t;
Vertex_handle inf = infinite_vertex();
infinite = tr.infinite_vertex();
tr.infinite = inf;
_tds.swap(tr._tds);
}
//ACCESS FUNCTIONS
const GT & geom_traits() const
{ return _gt;}
const Tds & tds() const
{ return _tds;}
int dimension() const
{ return _tds.dimension();}
int number_of_finite_cells() const;
int number_of_cells() const;
int number_of_finite_facets() const;
int number_of_facets() const;
int number_of_finite_edges() const;
int number_of_edges() const;
int number_of_vertices() const // number of finite vertices
{return _tds.number_of_vertices()-1;}
Vertex_handle infinite_vertex() const
{ return infinite; }
Cell_handle infinite_cell() const
{
// CGAL_triangulation_precondition(infinite_vertex()->cell()->
// has_vertex(infinite_vertex()));
return infinite_vertex()->cell();
}
// ASSIGNMENT
void set_number_of_vertices(int n)
{ _tds.set_number_of_vertices(n+1); }
// GEOMETRIC ACCESS FUNCTIONS
Tetrahedron tetrahedron(const Cell_handle c) const
{
CGAL_triangulation_precondition( dimension() == 3 );
CGAL_triangulation_precondition( ! is_infinite(c) );
return construct_tetrahedron(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point());
}
Triangle triangle(const Cell_handle c, int i) const;
Triangle triangle(const Facet & f) const
{ return triangle(f.first, f.second); }
Segment segment(const Cell_handle c, int i, int j) const;
Segment segment(const Edge & e) const
{ return segment(e.first,e.second,e.third); }
// TEST IF INFINITE FEATURES
bool is_infinite(const Vertex_handle v) const
{ return v == infinite_vertex(); }
bool is_infinite(const Cell_handle c) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return c->has_vertex(infinite_vertex());
}
bool is_infinite(const Cell_handle c, int i) const;
bool is_infinite(const Facet & f) const
{ return is_infinite(f.first,f.second); }
bool is_infinite(const Cell_handle c, int i, int j) const;
bool is_infinite(const Edge & e) const
{ return is_infinite(e.first,e.second,e.third); }
//QUERIES
bool is_vertex(const Point & p, Vertex_handle & v) const;
bool is_vertex(Vertex_handle v) const;
bool is_edge(Vertex_handle u, Vertex_handle v,
Cell_handle & c, int & i, int & j) const;
bool is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle & c, int & i, int & j, int & k) const;
bool is_cell(Cell_handle c) const;
bool is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c, int & i, int & j, int & k, int & l) const;
bool is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c) const;
bool has_vertex(const Facet & f, Vertex_handle v, int & j) const;
bool has_vertex(Cell_handle c, int i, Vertex_handle v, int & j) const;
bool has_vertex(const Facet & f, Vertex_handle v) const;
bool has_vertex(Cell_handle c, int i, Vertex_handle v) const;
bool are_equal(Cell_handle c, int i, Cell_handle n, int j) const;
bool are_equal(const Facet & f, const Facet & g) const;
bool are_equal(const Facet & f, Cell_handle n, int j) const;
Cell_handle
locate(const Point & p,
Locate_type & lt, int & li, int & lj,
Cell_handle start = Cell_handle()) const;
Cell_handle
locate(const Point & p, Cell_handle start = Cell_handle()) const
{
Locate_type lt;
int li, lj;
return locate( p, lt, li, lj, start);
}
// This one is for backward compatibility with CGAL 2.2.
Cell_handle
locate(const Point & p, Cell_handle start,
Locate_type & lt, int & li, int & lj) const
{
bool WARNING_YOU_ARE_USING_THE_DEPRECATED_VERSION_OF_LOCATE;
return locate(p, lt, li, lj, start);
}
// PREDICATES ON POINTS ``TEMPLATED'' by the geom traits
Bounded_side
side_of_tetrahedron(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
const Point & p3,
Locate_type & lt, int & i, int & j ) const;
Bounded_side
side_of_cell(const Point & p,
Cell_handle c,
Locate_type & lt, int & i, int & j) const;
Bounded_side
side_of_triangle(const Point & p,
const Point & p0, const Point & p1, const Point & p2,
Locate_type & lt, int & i, int & j ) const;
Bounded_side
side_of_facet(const Point & p,
Cell_handle c,
Locate_type & lt, int & li, int & lj) const;
Bounded_side
side_of_facet(const Point & p,
const Facet & f,
Locate_type & lt, int & li, int & lj) const
{
CGAL_triangulation_precondition( f.second == 3 );
return side_of_facet(p, f.first, lt, li, lj);
}
Bounded_side
side_of_segment(const Point & p,
const Point & p0, const Point & p1,
Locate_type & lt, int & i ) const;
Bounded_side
side_of_edge(const Point & p,
Cell_handle c,
Locate_type & lt, int & li) const;
Bounded_side
side_of_edge(const Point & p,
const Edge & e,
Locate_type & lt, int & li) const
{
CGAL_triangulation_precondition( e.second == 0 );
CGAL_triangulation_precondition( e.third == 1 );
return side_of_edge(p, e.first, lt, li);
}
// MODIFIERS
bool flip(Facet f);
bool flip(Cell_handle c, int i);
void flip_flippable(Facet f);
void flip_flippable(Cell_handle c, int i);
bool flip(Edge e);
bool flip(Cell_handle c, int i, int j);
void flip_flippable(Edge e);
void flip_flippable(Cell_handle c, int i, int j);
//INSERTION
Vertex_handle insert(const Point & p,
Cell_handle start = Cell_handle(),
Vertex_handle v = NULL);
Vertex_handle push_back(const Point & p)
{
return insert(p);
}
template < class InputIterator >
int insert(InputIterator first, InputIterator last)
{
int n = number_of_vertices();
while(first != last){
insert(*first);
++first;
}
return number_of_vertices() - n;
}
Vertex_handle
insert_in_cell(const Point & p, Cell_handle c, Vertex_handle v = NULL);
Vertex_handle
insert_in_facet(const Point & p, Cell_handle c, int i,
Vertex_handle v = NULL);
Vertex_handle
insert_in_facet(const Point & p, const Facet & f,
Vertex_handle v = NULL)
{
return insert_in_facet(p, f.first,f.second, v);
}
Vertex_handle
insert_in_edge(const Point & p, Cell_handle c, int i, int j,
Vertex_handle v = NULL);
Vertex_handle
insert_in_edge(const Point & p, const Edge & e,
Vertex_handle v = NULL)
{
return insert_in_edge(p, e.first,e.second,e.third, v);
}
Vertex_handle
insert_outside_convex_hull(const Point & p, Cell_handle c,
Vertex_handle v = NULL);
Vertex_handle
insert_outside_affine_hull(const Point & p, Vertex_handle v = NULL );
private:
// Here are the conflit tester function object passed to
// _tds.insert_conflict() by insert_outside_convex_hull().
class Conflict_tester_outside_convex_hull_3
{
const Point &p;
Self *t;
public:
Conflict_tester_outside_convex_hull_3(const Point &pt, Self *tr)
: p(pt), t(tr) {}
bool operator()(const typename Tds::Cell *c) const
{
Locate_type loc;
int i, j;
return t->side_of_cell( p, (Cell_handle)(Cell*) c, loc, i, j )
== ON_BOUNDED_SIDE;
}
};
class Conflict_tester_outside_convex_hull_2
{
const Point &p;
Self *t;
public:
Conflict_tester_outside_convex_hull_2(const Point &pt, Self *tr)
: p(pt), t(tr) {}
bool operator()(const typename Tds::Cell *c) const
{
Locate_type loc;
int i, j;
return t->side_of_facet( p, (Cell_handle)(Cell*) c, loc, i, j )
== ON_BOUNDED_SIDE;
}
};
public:
//TRAVERSING : ITERATORS AND CIRCULATORS
Cell_iterator finite_cells_begin() const
{
if ( dimension() < 3 )
return cells_end();
return Cell_iterator(this, false); // false means without infinite cells.
}
Cell_iterator all_cells_begin() const
{
if ( dimension() < 3 )
return cells_end();
return Cell_iterator(this, true); // true means with infinite cells.
}
Cell_iterator cells_end() const
{
return Cell_iterator(this); // no second argument -> past-end
}
Vertex_iterator finite_vertices_begin() const
{
if ( number_of_vertices() <= 0 )
return vertices_end();
return Vertex_iterator(this, false);
}
Vertex_iterator all_vertices_begin() const
{
if ( number_of_vertices() <= 0 )
return vertices_end();
return Vertex_iterator(this, true);
}
Vertex_iterator vertices_end() const
{
return Vertex_iterator(this);
}
Edge_iterator finite_edges_begin() const
{
if ( dimension() < 1 )
return edges_end();
return Edge_iterator(this, false);
}
Edge_iterator all_edges_begin() const
{
if ( dimension() < 1 )
return edges_end();
return Edge_iterator(this, true);
}
Edge_iterator edges_end() const
{
return Edge_iterator(this);
}
Facet_iterator finite_facets_begin() const
{
if ( dimension() < 2 )
return facets_end();
return Facet_iterator(this, false);
}
Facet_iterator all_facets_begin() const
{
if ( dimension() < 2 )
return facets_end();
return Facet_iterator(this, true);
}
Facet_iterator facets_end() const
{
return Facet_iterator(this);
}
// cells around an edge
Cell_circulator incident_cells(const Edge & e) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(this, e);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(this,c,i,j);
}
Cell_circulator incident_cells(const Edge & e, Cell_handle start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(this, e, start);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j,
Cell_handle start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(this, c, i, j, start);
}
// facets around an edge
Facet_circulator incident_facets(const Edge & e) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, e);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, c, i, j);
}
Facet_circulator incident_facets(const Edge & e,
const Facet & start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, e, start);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j,
const Facet & start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, c, i, j, start);
}
Facet_circulator incident_facets(const Edge & e,
Cell_handle start, int f) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, e, start, f);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j,
Cell_handle start, int f) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(this, c, i, j, start, f);
}
// around a vertex
void
incident_cells(Vertex_handle v,
std::set<Cell_handle> & cells,
Cell_handle c = Cell_handle() ) const;
void
incident_vertices(Vertex_handle v,
std::set<Vertex_handle> & vertices,
Cell_handle c = Cell_handle() ) const;
// old methods, kept for compatibility with previous versions
void
incident_cells(Vertex_handle v,
std::set<Cell*> & cells,
Cell_handle c = Cell_handle(),
int dummy_for_windows = 0) const;
void
incident_vertices(Vertex_handle v,
std::set<Vertex*> & vertices,
Cell_handle c = Cell_handle(),
int dummy_for_windows = 0) const;
private:
void
util_incident_vertices(Vertex_handle v,
std::set<Vertex_handle> & vertices,
std::set<Cell_handle> & cells,
Cell_handle c ) const;
void
util_incident_vertices(Vertex_handle v,
std::set<Vertex*> & vertices,
std::set<Cell*> & cells,
Cell_handle c,
int dummy_for_windows = 0) const;
public:
// CHECKING
bool is_valid(bool verbose = false, int level = 0) const;
bool is_valid(Cell_handle c, bool verbose = false, int level = 0) const;
bool is_valid_finite(Cell_handle c,
bool verbose = false, int level = 0) const;
};
template < class GT, class Tds >
std::istream &
operator>> (std::istream& is, Triangulation_3<GT, Tds> &tr)
// reads
// the dimension
// the number of finite vertices
// the non combinatorial information on vertices (point, etc)
// the number of cells
// the cells by the indices of their vertices in the preceding list
// of vertices, plus the non combinatorial information on each cell
// the neighbors of each cell by their index in the preceding list of cells
// when dimension < 3 : the same with faces of maximal dimension
{
typedef Triangulation_3<GT, Tds> Triangulation;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Cell_handle Cell_handle;
typedef typename Triangulation::Vertex Vertex;
typedef typename Tds::Vertex TdsVertex;
typedef typename Tds::Cell TdsCell;
tr._tds.clear(); // infinite vertex deleted
tr.infinite = (Vertex *) tr._tds.create_vertex();
int n, d;
is >> d >> n;
tr._tds.set_dimension(d);
tr.set_number_of_vertices(n);
std::map< int, TdsVertex* > V;
V[0] = &*(tr.infinite_vertex());
// the infinite vertex is numbered 0
for (int i=1; i <= n; i++) {
V[i] = tr._tds.create_vertex();
is >> *V[i];
}
std::map< int, TdsCell* > C;
int m;
tr._tds.read_cells(is, V, m, C);
for (int j=0 ; j < m; j++)
is >> *(C[j]);
CGAL_triangulation_assertion( tr.is_valid(false) );
return is;
}
template < class VH>
class Vertex_handle_compare_order_of_creation {
public:
bool operator()(VH u, VH v){
return ( (&(*u))->get_order_of_creation()
< (&(*v))->get_order_of_creation() );
}
};
template < class GT, class Tds >
std::ostream &
operator<< (std::ostream& os, const Triangulation_3<GT, Tds> &tr)
// writes :
// the dimension
// the number of finite vertices
// the non combinatorial information on vertices (point, etc)
// the number of cells
// the cells by the indices of their vertices in the preceding list
// of vertices, plus the non combinatorial information on each cell
// the neighbors of each cell by their index in the preceding list of cells
// when dimension < 3 : the same with faces of maximal dimension
{
typedef Triangulation_3<GT, Tds> Triangulation;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Vertex_iterator Vertex_iterator;
typedef typename Triangulation::Cell_iterator Cell_iterator;
typedef typename Triangulation::Edge_iterator Edge_iterator;
typedef typename Triangulation::Facet_iterator Facet_iterator;
// outputs dimension and number of vertices
int n = tr.number_of_vertices();
if (is_ascii(os))
os << tr.dimension() << std::endl << n << std::endl;
else
os << tr.dimension() << n;
if (n == 0)
return os;
std::vector<Vertex_handle> TV(n+1);
int i = 0;
// write the vertices
// the vertices must be indexed by their order of creation so
// that when reread from file, the orders of vertices are the
// same - important for remove
for (Vertex_iterator it=tr.all_vertices_begin(); it!=tr.vertices_end(); ++it)
TV[i++] = &(*it);
CGAL_triangulation_assertion( i == n+1 );
std::sort(TV.begin(), TV.end(),
Vertex_handle_compare_order_of_creation<Vertex_handle>());
CGAL_triangulation_assertion( tr.is_infinite(TV[0]) );
std::map< void*, int > V;
V[&(*tr.infinite_vertex())] = 0;
for (i=1; i <= n; i++) {
os << *TV[i];
V[&(*TV[i])] = i;
if (is_ascii(os))
os << std::endl;
}
// write the non combinatorial information on the cells
// using the << operator of Cell
// works because the iterator of the tds traverses the cells in the
// same order as the iterator of the triangulation
switch ( tr.dimension() ) {
case 3:
{
for(Cell_iterator it=tr.all_cells_begin(); it != tr.cells_end(); ++it)
os << *it; // other information
break;
}
case 2:
{
for(Facet_iterator it=tr.all_facets_begin(); it != tr.facets_end(); ++it)
os << *((*it).first); // other information
break;
}
case 1:
{
for(Edge_iterator it=tr.all_edges_begin(); it != tr.edges_end(); ++it)
os << *((*it).first); // other information
break;
}
}
// asks the tds for the combinatorial information
tr.tds().print_cells(os, V);
return os ;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
test_dim_down(Vertex_handle v)
// tests whether removing v decreases the dimension of the triangulation
// true iff
// v is incident to all finite cells
// and all the other vertices are coplanar
{
CGAL_triangulation_precondition(dimension() == 3);
CGAL_triangulation_precondition(! is_infinite(v) );
Cell_iterator cit = finite_cells_begin();
Cell_iterator cdone = cells_end();
int i, iv;
if ( ! cit->has_vertex(v,iv) ) return false;
Point p1=cit->vertex((iv+1)&3)->point();
Point p2=cit->vertex((iv+2)&3)->point();
Point p3=cit->vertex((iv+3)&3)->point();
++cit;
while ( cit != cdone ) {
if ( ! cit->has_vertex(v,iv) )
return false;
for ( i=1; i<4; i++ ) {
if ( orientation
(p1,p2,p3,cit->vertex((iv+i)&3)->point()) != COPLANAR )
return false;
}
++cit;
}
return true;
}// test_dim_down
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_finite_cells() const
{
if ( dimension() < 3 ) return 0;
return std::distance(finite_cells_begin(), cells_end());
}
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_cells() const
{
if ( dimension() < 3 ) return 0;
return std::distance(all_cells_begin(), cells_end());
}
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_finite_facets() const
{
if ( dimension() < 2 ) return 0;
return std::distance(finite_facets_begin(), facets_end());
}
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_facets() const
{
if ( dimension() < 2 ) return 0;
return std::distance(all_facets_begin(), facets_end());
}
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_finite_edges() const
{
if ( dimension() < 1 ) return 0;
return std::distance(finite_edges_begin(), edges_end());
}
template < class GT, class Tds >
int
Triangulation_3<GT,Tds>::
number_of_edges() const
{
if ( dimension() < 1 ) return 0;
return std::distance(all_edges_begin(), edges_end());
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Triangle
Triangulation_3<GT,Tds>::
triangle(const Cell_handle c, int i) const
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3 );
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
CGAL_triangulation_precondition( ! is_infinite(std::make_pair(c, i)) );
return construct_triangle(c->vertex(i<=0 ? 1 : 0)->point(),
c->vertex(i<=1 ? 2 : 1)->point(),
c->vertex(i<=2 ? 3 : 2)->point());
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Segment
Triangulation_3<GT,Tds>::
segment(const Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition( i >= 0 && i <= dimension()
&& j >= 0 && j <= dimension() );
CGAL_triangulation_precondition( ! is_infinite(make_triple(c, i, j)) );
return construct_segment( c->vertex(i)->point(), c->vertex(j)->point() );
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_infinite(const Cell_handle c, int i) const
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3 );
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
return is_infinite(c->vertex(i<=0 ? 1 : 0)) ||
is_infinite(c->vertex(i<=1 ? 2 : 1)) ||
is_infinite(c->vertex(i<=2 ? 3 : 2));
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_infinite(const Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition(
i >= 0 && i <= dimension() && j >= 0 && j <= dimension() );
return is_infinite( c->vertex(i) ) || is_infinite( c->vertex(j) );
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_vertex(const Point & p, Vertex_handle & v) const
{
Locate_type lt;
int li, lj;
Cell_handle c = locate( p, lt, li, lj );
if ( lt != VERTEX )
return false;
v = c->vertex(li);
return true;
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_vertex(Vertex_handle v) const
{
return _tds.is_vertex(&(*v));
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_edge(Vertex_handle u, Vertex_handle v,
Cell_handle & c, int & i, int & j) const
{
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*u)) &&
_tds.is_vertex(&(*v)) );
typename Tds::Cell* cstar;
bool b = _tds.is_edge(&(*u), &(*v), cstar, i, j);
if (b)
c = ((Cell*) cstar)->handle();
return b;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle & c, int & i, int & j, int & k) const
{
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*u)) &&
_tds.is_vertex(&(*v)) &&
_tds.is_vertex(&(*w)) );
typename Tds::Cell* cstar;
bool b = _tds.is_facet(&(*u), &(*v), &(*w), cstar, i, j, k);
if (b)
c = ((Cell*) cstar)->handle();
return b;
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_cell(Cell_handle c) const
{
return _tds.is_cell(&(*c));
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c, int & i, int & j, int & k, int & l) const
{
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*u)) &&
_tds.is_vertex(&(*v)) &&
_tds.is_vertex(&(*w)) &&
_tds.is_vertex(&(*t)) );
typename Tds::Cell* cstar;
bool b = _tds.is_cell(&(*u), &(*v), &(*w), &(*t), cstar, i, j, k, l);
if (b)
c = ((Cell*) cstar)->handle();
return b;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c) const
{
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*u)) &&
_tds.is_vertex(&(*v)) &&
_tds.is_vertex(&(*w)) &&
_tds.is_vertex(&(*t)) );
int i,j,k,l;
typename Tds::Cell* cstar;
bool b = _tds.is_cell(&(*u), &(*v), &(*w), &(*t), cstar, i, j, k, l);
if (b)
c = ((Cell*) cstar)->handle();
return b;
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(const Facet & f, Vertex_handle v, int & j) const
{
return _tds.has_vertex(&*(f.first), f.second, &*v, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(Cell_handle c, int i, Vertex_handle v, int & j) const
{
return _tds.has_vertex(&*c, i, &*v, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(const Facet & f, Vertex_handle v) const
{
return _tds.has_vertex(&*(f.first), f.second, &*v);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(Cell_handle c, int i, Vertex_handle v) const
{
return _tds.has_vertex(&*c, i, &*v);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(Cell_handle c, int i, Cell_handle n, int j) const
{
return _tds.are_equal(&*c, i, &*n, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(const Facet & f, const Facet & g) const
{
return _tds.are_equal(&*(f.first), f.second, &*(g.first), g.second);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(const Facet & f, Cell_handle n, int j) const
{
return _tds.are_equal(&*(f.first), f.second, &*n, j);
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Cell_handle
Triangulation_3<GT,Tds>::
locate(const Point & p, Locate_type & lt, int & li, int & lj,
Cell_handle start ) const
// returns the (finite or infinite) cell p lies in
// starts at cell "start"
// start must be finite
// if lt == OUTSIDE_CONVEX_HULL, li is the
// index of a facet separating p from the rest of the triangulation
// in dimension 2 :
// returns a facet (Cell_handle,li) if lt == FACET
// returns an edge (Cell_handle,li,lj) if lt == EDGE
// returns a vertex (Cell_handle,li) if lt == VERTEX
// if lt == OUTSIDE_CONVEX_HULL, li, lj give the edge of c
// separating p from the rest of the triangulation
// lt = OUTSIDE_AFFINE_HULL if p is not coplanar with the triangulation
{
int i, inf;
if ( dimension() >= 1 && start == Cell_handle() )
// there is at least one finite "cell" (or facet or edge)
start = infinite_vertex()->cell()->neighbor
( infinite_vertex()->cell()->index( infinite_vertex()) );
switch (dimension()) {
case 3:
{
CGAL_triangulation_precondition( start != Cell_handle() );
Cell_handle c, previous;
int ind_inf;
if ( start->has_vertex(infinite, ind_inf) )
c = start->neighbor(ind_inf);
else
c = start;
Orientation o[4];
// We implement the remembering visibility/stochastic walk.
// Main locate loop
while(1) {
if ( c->has_vertex(infinite,li) ) {
// c must contain p in its interior
lt = OUTSIDE_CONVEX_HULL;
return c;
}
// FIXME: do more benchmarks.
i = rand_4(); // For the (remembering) stochastic walk
// i = 0; // For the (remembering) visibility walk. Ok for Delaunay only
Orientation test_or = (i&1)==0 ? NEGATIVE : POSITIVE;
const Point & p0 = c->vertex( i )->point();
const Point & p1 = c->vertex( (i+1)&3 )->point();
const Point & p2 = c->vertex( (i+2)&3 )->point();
const Point & p3 = c->vertex( (i+3)&3 )->point();
// Note : among the four Points, 3 are common with the previous cell...
// Something can probably be done to take advantage of this, like
// storing the four in an array and changing only one ?
// We could make a loop of these 4 blocks, for clarity, but not speed.
Cell_handle next = c->neighbor(i);
if (previous != next) {
o[0] = orientation(p, p1, p2, p3);
if ( o[0] == test_or) {
previous = c;
c = next;
continue;
}
} else
o[0] = (Orientation) - test_or;
next = c->neighbor((i+1)&3);
if (previous != next) {
o[1] = orientation(p0, p, p2, p3);
if ( o[1] == test_or) {
previous = c;
c = next;
continue;
}
} else
o[1] = (Orientation) - test_or;
next = c->neighbor((i+2)&3);
if (previous != next) {
o[2] = orientation(p0, p1, p, p3);
if ( o[2] == test_or) {
previous = c;
c = next;
continue;
}
} else
o[2] = (Orientation) - test_or;
next = c->neighbor((i+3)&3);
if (previous != next) {
o[3] = orientation(p0, p1, p2, p);
if ( o[3] == test_or) {
// previous = c; // not necessary because it's the last one.
c = next;
continue;
}
} else
o[3] = (Orientation) - test_or;
break;
}
// now p is in c or on its boundary
int sum = ( o[0] == COPLANAR )
+ ( o[1] == COPLANAR )
+ ( o[2] == COPLANAR )
+ ( o[3] == COPLANAR );
switch (sum) {
case 0:
{
lt = CELL;
break;
}
case 1:
{
lt = FACET;
li = ( o[0] == COPLANAR ) ? i :
( o[1] == COPLANAR ) ? (i+1)&3 :
( o[2] == COPLANAR ) ? (i+2)&3 :
(i+3)&3;
break;
}
case 2:
{
lt = EDGE;
li = ( o[0] != COPLANAR ) ? i :
( o[1] != COPLANAR ) ? ((i+1)&3) :
((i+2)&3);
lj = ( o[ (li+1-i)&3 ] != COPLANAR ) ? ((li+1)&3) :
( o[ (li+2-i)&3 ] != COPLANAR ) ? ((li+2)&3) :
((li+3)&3);
CGAL_triangulation_assertion(collinear( p,
c->vertex( li )->point(),
c->vertex( lj )->point() ));
break;
}
case 3:
{
lt = VERTEX;
li = ( o[0] != COPLANAR ) ? i :
( o[1] != COPLANAR ) ? (i+1)&3 :
( o[2] != COPLANAR ) ? (i+2)&3 :
(i+3)&3;
break;
}
}
return c;
}
case 2:
{
CGAL_triangulation_precondition( start != Cell_handle() );
Cell_handle c;
int ind_inf;
if ( start->has_vertex(infinite, ind_inf) )
c = start->neighbor(ind_inf);
else
c = start;
//first tests whether p is coplanar with the current triangulation
Facet_iterator finite_fit = finite_facets_begin();
if ( orientation( p,
(*finite_fit).first->vertex(0)->point(),
(*finite_fit).first->vertex(1)->point(),
(*finite_fit).first->vertex(2)->point() )
!= DEGENERATE ) {
lt = OUTSIDE_AFFINE_HULL;
li = 3; // only one facet in dimension 2
return (*finite_fit).first;
}
// if p is coplanar, location in the triangulation
// only the facet numbered 3 exists in each cell
Orientation o[3];
while (1) {
if ( c->has_vertex(infinite,inf) ) {
// c must contain p in its interior
lt = OUTSIDE_CONVEX_HULL;
li = cw(inf);
lj = ccw(inf);
return c;
}
// else c is finite
// we test its edges in a random order until we find a
// neighbor to go further
i = rand_3();
const Point & p0 = c->vertex( i )->point();
const Point & p1 = c->vertex( ccw(i) )->point();
const Point & p2 = c->vertex( cw(i) )->point();
o[0] = coplanar_orientation(p0,p1,p2,p);
if ( o[0] == NEGATIVE ) {
c = c->neighbor( cw(i) );
continue;
}
o[1] = coplanar_orientation(p1,p2,p0,p);
if ( o[1] == NEGATIVE ) {
c = c->neighbor( i );
continue;
}
o[2] = coplanar_orientation(p2,p0,p1,p);
if ( o[2] == NEGATIVE ) {
c = c->neighbor( ccw(i) );
continue;
}
// now p is in c or on its boundary
int sum = ( o[0] == COLLINEAR )
+ ( o[1] == COLLINEAR )
+ ( o[2] == COLLINEAR );
switch (sum) {
case 0:
{
lt = FACET;
li = 3; // useless ?
break;
}
case 1:
{
lt = EDGE;
li = ( o[0] == COLLINEAR ) ? i :
( o[1] == COLLINEAR ) ? ccw(i) :
cw(i);
lj = ccw(li);
break;
}
case 2:
{
lt = VERTEX;
li = ( o[0] != COLLINEAR ) ? cw(i) :
( o[1] != COLLINEAR ) ? i :
ccw(i);
break;
}
}
return c;
}
}
case 1:
{
CGAL_triangulation_precondition( start != Cell_handle() );
Cell_handle c;
int ind_inf;
if ( start->has_vertex(infinite, ind_inf) )
c = start->neighbor(ind_inf);
else
c = start;
//first tests whether p is collinear with the current triangulation
Edge_iterator finite_eit = finite_edges_begin();
if ( ! collinear( p,
(*finite_eit).first->vertex(0)->point(),
(*finite_eit).first->vertex(1)->point()) ) {
lt = OUTSIDE_AFFINE_HULL;
return (*finite_eit).first;
}
// if p is collinear, location :
Comparison_result o, o0, o1;
int xyz;
Point p0 = c->vertex(0)->point();
Point p1 = c->vertex(1)->point();
CGAL_triangulation_assertion( ( compare_x(p0,p1) != EQUAL ) ||
( compare_y(p0,p1) != EQUAL ) ||
( compare_z(p0,p1) != EQUAL ) );
o = compare_x(p0,p1);
if ( o == EQUAL ) {
o = compare_y(p0,p1);
if ( o == EQUAL ) {
o = compare_z(p0,p1);
xyz = 3;
}
else
xyz = 2;
}
else
xyz = 1;
// bool notfound = true;
while (1) {
if ( c->has_vertex(infinite,inf) ) {
// c must contain p in its interior
lt = OUTSIDE_CONVEX_HULL;
return c;
}
// else c is finite
// we test on which direction to continue the traversal
p0 = c->vertex(0)->point();
p1 = c->vertex(1)->point();
switch ( xyz ) {
case 1:
{
o = compare_x(p0,p1);
o0 = compare_x(p0,p);
o1 = compare_x(p,p1);
break;
}
case 2:
{
o = compare_y(p0,p1);
o0 = compare_y(p0,p);
o1 = compare_y(p,p1);
break;
}
default: // case 3
{
o = compare_z(p0,p1);
o0 = compare_z(p0,p);
o1 = compare_z(p,p1);
}
}
if (o0 == EQUAL) {
lt = VERTEX;
li = 0;
return c;
}
if (o1 == EQUAL) {
lt = VERTEX;
li = 1;
return c;
}
if ( o0 == o1 ) {
lt = EDGE;
li = 0;
lj = 1;
return c;
}
if ( o0 == o ) {
c = c->neighbor(0);
continue;
}
if ( o1 == o ) {
c = c->neighbor(1);
continue;
}
}
}
case 0:
{
Vertex_iterator vit = finite_vertices_begin();
if ( ! equal( p, vit->point() ) ) {
lt = OUTSIDE_AFFINE_HULL;
}
else {
lt = VERTEX;
li = 0;
}
return vit->cell();
}
case -1:
{
lt = OUTSIDE_AFFINE_HULL;
return NULL;
}
default:
{
CGAL_triangulation_assertion(false);
return NULL;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_tetrahedron(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
const Point & p3,
Locate_type & lt, int & i, int & j ) const
// p0,p1,p2,p3 supposed to be non coplanar
// tetrahedron p0,p1,p2,p3 is supposed to be well oriented
// returns :
// ON_BOUNDED_SIDE if p lies strictly inside the tetrahedron
// ON_BOUNDARY if p lies on one of the facets
// ON_UNBOUNDED_SIDE if p lies strictly outside the tetrahedron
{
CGAL_triangulation_precondition
( orientation(p0,p1,p2,p3) == POSITIVE );
Orientation o0,o1,o2,o3;
if ( ((o0 = orientation(p,p1,p2,p3)) == NEGATIVE) ||
((o1 = orientation(p0,p,p2,p3)) == NEGATIVE) ||
((o2 = orientation(p0,p1,p,p3)) == NEGATIVE) ||
((o3 = orientation(p0,p1,p2,p)) == NEGATIVE) ) {
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
// now all the oi's are >=0
// sum gives the number of facets p lies on
int sum = ( (o0 == ZERO) ? 1 : 0 )
+ ( (o1 == ZERO) ? 1 : 0 )
+ ( (o2 == ZERO) ? 1 : 0 )
+ ( (o3 == ZERO) ? 1 : 0 );
switch (sum) {
case 0:
{
lt = CELL;
return ON_BOUNDED_SIDE;
}
case 1:
{
lt = FACET;
// i = index such that p lies on facet(i)
i = ( o0 == ZERO ) ? 0 :
( o1 == ZERO ) ? 1 :
( o2 == ZERO ) ? 2 :
3;
return ON_BOUNDARY;
}
case 2:
{
lt = EDGE;
// i = smallest index such that p does not lie on facet(i)
// i must be < 3 since p lies on 2 facets
i = ( o0 == POSITIVE ) ? 0 :
( o1 == POSITIVE ) ? 1 :
2;
// j = larger index such that p not on facet(j)
// j must be > 0 since p lies on 2 facets
j = ( o3 == POSITIVE ) ? 3 :
( o2 == POSITIVE ) ? 2 :
1;
return ON_BOUNDARY;
}
case 3:
{
lt = VERTEX;
// i = index such that p does not lie on facet(i)
i = ( o0 == POSITIVE ) ? 0 :
( o1 == POSITIVE ) ? 1 :
( o2 == POSITIVE ) ? 2 :
3;
return ON_BOUNDARY;
}
default:
{
// impossible : cannot be on 4 facets for a real tetrahedron
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_cell(const Point & p,
Cell_handle c,
Locate_type & lt, int & i, int & j) const
// returns
// ON_BOUNDED_SIDE if p inside the cell
// (for an infinite cell this means that p lies strictly in the half space
// limited by its finite facet)
// ON_BOUNDARY if p on the boundary of the cell
// (for an infinite cell this means that p lies on the *finite* facet)
// ON_UNBOUNDED_SIDE if p lies outside the cell
// (for an infinite cell this means that p is not in the preceding
// two cases)
// lt has a meaning only when ON_BOUNDED_SIDE or ON_BOUNDARY
{
CGAL_triangulation_precondition( dimension() == 3 );
if ( ! is_infinite(c) ) {
return side_of_tetrahedron(p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point(),
lt, i, j);
}
else {
int inf = c->index(infinite);
Orientation o;
Vertex_handle
v1=c->vertex((inf+1)&3),
v2=c->vertex((inf+2)&3),
v3=c->vertex((inf+3)&3);
if ( (inf&1) == 0 )
o = orientation(p, v1->point(), v2->point(), v3->point());
else
o = orientation(v3->point(), p, v1->point(), v2->point());
switch (o) {
case POSITIVE:
{
lt = CELL;
return ON_BOUNDED_SIDE;
}
case NEGATIVE:
return ON_UNBOUNDED_SIDE;
case ZERO:
{
// location in the finite facet
int i_f, j_f;
Bounded_side side =
side_of_triangle(p, v1->point(), v2->point(), v3->point(),
lt, i_f, j_f);
// lt need not be modified in most cases :
switch (side) {
case ON_BOUNDED_SIDE:
{
// lt == FACET ok
i = inf;
return ON_BOUNDARY;
}
case ON_BOUNDARY:
{
// lt == VERTEX OR EDGE ok
i = ( i_f == 0 ) ? ((inf+1)&3) :
( i_f == 1 ) ? ((inf+2)&3) :
((inf+3)&3);
if ( lt == EDGE ) {
j = (j_f == 0 ) ? ((inf+1)&3) :
( j_f == 1 ) ? ((inf+2)&3) :
((inf+3)&3);
}
return ON_BOUNDARY;
}
case ON_UNBOUNDED_SIDE:
{
// p lies on the plane defined by the finite facet
// lt must be initialized
return ON_UNBOUNDED_SIDE;
}
default:
{
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
} // switch side
}// case ZERO
default:
{
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
} // switch o
} // else infinite cell
} // side_of_cell
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_triangle(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
Locate_type & lt, int & i, int & j ) const
// p0,p1,p2 supposed to define a plane
// p supposed to lie on plane p0,p1,p2
// triangle p0,p1,p2 defines the orientation of the plane
// returns
// ON_BOUNDED_SIDE if p lies strictly inside the triangle
// ON_BOUNDARY if p lies on one of the edges
// ON_UNBOUNDED_SIDE if p lies strictly outside the triangle
{
CGAL_triangulation_precondition( ! collinear(p0,p1,p2) );
CGAL_triangulation_precondition( orientation(p,p0,p1,p2) == COPLANAR );
// edge p0 p1 :
Orientation o0 = coplanar_orientation(p0,p1,p2,p);
// edge p1 p2 :
Orientation o1 = coplanar_orientation(p1,p2,p0,p);
// edge p2 p0 :
Orientation o2 = coplanar_orientation(p2,p0,p1,p);
if ( (o0 == NEGATIVE) ||
(o1 == NEGATIVE) ||
(o2 == NEGATIVE) ) {
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
// now all the oi's are >=0
// sum gives the number of edges p lies on
int sum = ( (o0 == ZERO) ? 1 : 0 )
+ ( (o1 == ZERO) ? 1 : 0 )
+ ( (o2 == ZERO) ? 1 : 0 );
switch (sum) {
case 0:
{
lt = FACET;
return ON_BOUNDED_SIDE;
}
case 1:
{
lt = EDGE;
i = ( o0 == ZERO ) ? 0 :
( o1 == ZERO ) ? 1 :
2;
if ( i == 2 )
j=0;
else
j = i+1;
return ON_BOUNDARY;
}
case 2:
{
lt = VERTEX;
i = ( o0 == POSITIVE ) ? 2 :
( o1 == POSITIVE ) ? 0 :
1;
return ON_BOUNDARY;
}
default:
{
// cannot happen
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_facet(const Point & p,
Cell_handle c,
Locate_type & lt, int & li, int & lj) const
// supposes dimension 2 otherwise does not work for infinite facets
// returns :
// ON_BOUNDED_SIDE if p inside the facet
// (for an infinite facet this means that p lies strictly in the half plane
// limited by its finite edge)
// ON_BOUNDARY if p on the boundary of the facet
// (for an infinite facet this means that p lies on the *finite* edge)
// ON_UNBOUNDED_SIDE if p lies outside the facet
// (for an infinite facet this means that p is not in the
// preceding two cases)
// lt has a meaning only when ON_BOUNDED_SIDE or ON_BOUNDARY
// when they mean anything, li and lj refer to indices in the cell c
// giving the facet (c,i)
{//side_of_facet
CGAL_triangulation_precondition( dimension() == 2 );
// CGAL_triangulation_precondition( i == 3 );
// if ( ! is_infinite(c,i) ) {
if ( ! is_infinite(c,3) ) {
// The following precondition is useless because it is written
// in side_of_facet
// CGAL_triangulation_precondition( orientation
// (p,
// c->vertex(0)->point,
// c->vertex(1)->point,
// c->vertex(2)->point)
// == COPLANAR );
// int i0, i1, i2; // indices in the considered facet
Bounded_side side;
int i_t, j_t;
side = side_of_triangle(p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
lt, i_t, j_t);
// indices in the original cell :
li = ( i_t == 0 ) ? 0 :
( i_t == 1 ) ? 1 :
2;
lj = ( j_t == 0 ) ? 0 :
( j_t == 1 ) ? 1 :
2;
return side;
}
// else infinite facet
int inf = c->index(infinite);
// The following precondition is useless because it is written
// in side_of_facet
// CGAL_triangulation_precondition( orientation
// (p,
// c->neighbor(inf)->vertex(0)->point(),
// c->neighbor(inf)->vertex(1)->point(),
// c->neighbor(inf)->vertex(2)->point())
// == COPLANAR );
int i1,i2;
i2 = next_around_edge(inf,3);
i1 = 3-inf-i2;
Vertex_handle
v1 = c->vertex(i1),
v2 = c->vertex(i2);
// does not work in dimension 3
Cell_handle n = c->neighbor(inf);
// n must be a finite cell
Orientation o =
coplanar_orientation( v1->point(), v2->point(),
n->vertex(n->index(c))->point(), p );
switch (o) {
case POSITIVE:
// p lies on the same side of v1v2 as vn, so not in f
{
return ON_UNBOUNDED_SIDE;
}
case NEGATIVE:
// p lies in f
{
lt = FACET;
li = 3;
return ON_BOUNDED_SIDE;
}
case ZERO:
// p collinear with v1v2
{
int i_e;
Bounded_side side =
side_of_segment( p, v1->point(), v2->point(), lt, i_e );
switch (side) {
// computation of the indices inthe original cell
case ON_BOUNDED_SIDE:
{
// lt == EDGE ok
li = i1;
lj = i2;
return ON_BOUNDARY;
}
case ON_BOUNDARY:
{
// lt == VERTEX ok
li = ( i_e == 0 ) ? i1 : i2;
return ON_BOUNDARY;
}
case ON_UNBOUNDED_SIDE:
{
// p lies on the line defined by the finite edge
return ON_UNBOUNDED_SIDE;
}
default:
{
// cannot happen. only to avoid warning with eg++
return ON_UNBOUNDED_SIDE;
}
}
}// case ZERO
}// switch o
// end infinite facet
// cannot happen. only to avoid warning with eg++
CGAL_triangulation_assertion(false);
return ON_UNBOUNDED_SIDE;
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_segment(const Point & p,
const Point & p0,
const Point & p1,
Locate_type & lt, int & i ) const
// p0, p1 supposed to be different
// p supposed to be collinear to p0, p1
// returns :
// ON_BOUNDED_SIDE if p lies strictly inside the edge
// ON_BOUNDARY if p equals p0 or p1
// ON_UNBOUNDED_SIDE if p lies strictly outside the edge
{
CGAL_triangulation_precondition( ! equal(p0, p1) );
CGAL_triangulation_precondition( collinear(p, p0, p1) );
Comparison_result c = compare_x(p0,p1);
Comparison_result c0;
Comparison_result c1;
if ( c == EQUAL ) {
c = compare_y(p0,p1);
if ( c == EQUAL ) {
c0 = compare_z(p0,p);
c1 = compare_z(p,p1);
}
else {
c0 = compare_y(p0,p);
c1 = compare_y(p,p1);
}
}
else {
c0 = compare_x(p0,p);
c1 = compare_x(p,p1);
}
// if ( (c0 == SMALLER) && (c1 == SMALLER) ) {
if ( c0 == c1 ) {
lt = EDGE;
return ON_BOUNDED_SIDE;
}
if (c0 == EQUAL) {
lt = VERTEX;
i = 0;
return ON_BOUNDARY;
}
if (c1 == EQUAL) {
lt = VERTEX;
i = 1;
return ON_BOUNDARY;
}
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_edge(const Point & p,
Cell_handle c,
Locate_type & lt, int & li) const
// supposes dimension 1 otherwise does not work for infinite edges
// returns :
// ON_BOUNDED_SIDE if p inside the edge
// (for an infinite edge this means that p lies in the half line
// defined by the vertex)
// ON_BOUNDARY if p equals one of the vertices
// ON_UNBOUNDED_SIDE if p lies outside the edge
// (for an infinite edge this means that p lies on the other half line)
// lt has a meaning when ON_BOUNDED_SIDE and ON_BOUNDARY
// li refer to indices in the cell c
{//side_of_edge
CGAL_triangulation_precondition( dimension() == 1 );
if ( ! is_infinite(c,0,1) )
return side_of_segment(p, c->vertex(0)->point(), c->vertex(1)->point(),
lt, li);
// else infinite edge
int inf = c->index(infinite);
if ( equal( p, c->vertex(1-inf)->point() ) ) {
lt = VERTEX;
li = 1-inf;
return ON_BOUNDARY;
}
// does not work in dimension > 2
Cell_handle n = c->neighbor(inf);
int i_e = n->index(c);
// we know that n is finite
Vertex_handle
v0 = n->vertex(0),
v1 = n->vertex(1);
Comparison_result c01 = compare_x(v0->point(), v1->point());
Comparison_result cp;
if ( c01 == EQUAL ) {
c01 = compare_y(v0->point(),v1->point());
if ( i_e == 0 ) {
cp = compare_y( v1->point(), p );
}
else {
cp = compare_y( p, v0->point() );
}
}
else {
if ( i_e == 0 )
cp = compare_x( v1->point(), p );
else
cp = compare_x( p, v0->point() );
}
if ( c01 == cp ) {
// p lies on the same side of n as infinite
lt = EDGE;
return ON_BOUNDED_SIDE;
}
return ON_UNBOUNDED_SIDE;
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
flip( Facet f )
// returns false if the facet is not flippable
// true other wise and
// flips facet i of cell c
// c will be replaced by one of the new cells
{
return flip( f.first, f.second);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
flip( Cell_handle c, int i )
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() > 5) );
Cell_handle n = c->neighbor(i);
int in = n->index(c);
if ( is_infinite( c ) || is_infinite( n ) ) return false;
if ( i%2 == 1 ) {
if ( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
}
else {
if ( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
}
_tds.flip_flippable( &(*c), i);
return true;
}
template < class GT, class Tds >
inline
void
Triangulation_3<GT,Tds>::
flip_flippable( Facet f )
{
return flip_flippable( f.first, f.second);
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
flip_flippable( Cell_handle c, int i )
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() > 5) );
CGAL_triangulation_precondition_code( Cell_handle n = c->neighbor(i); );
CGAL_triangulation_precondition_code( int in = n->index(c); );
CGAL_triangulation_precondition( ( ! is_infinite( c ) ) &&
( ! is_infinite( n ) ) );
if ( i%2 == 1 ) {
CGAL_triangulation_precondition( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
}
else {
CGAL_triangulation_precondition( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
}
_tds.flip_flippable( &(*c), i);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
flip( Edge e )
// returns false if the edge is not flippable
// true otherwise and
// flips edge i,j of cell c
// c will be deleted
{
return flip( e.first, e.second, e.third );
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
flip( Cell_handle c, int i, int j )
// flips edge i,j of cell c
{
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() > 5) );
// checks that degree 3 and not on the convex hull
int degree = 0;
Cell_circulator ccir = incident_cells(c,i,j);
Cell_circulator cdone = ccir;
do {
if ( is_infinite(&(*ccir)) ) return false;
++degree;
++ccir;
} while ( ccir != cdone );
if ( degree != 3 ) return false;
// checks that future tetrahedra are well oriented
Cell_handle n = c->neighbor( next_around_edge(i,j) );
int in = n->index( c->vertex(i) );
int jn = n->index( c->vertex(j) );
if ( orientation( c->vertex(next_around_edge(i,j))->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(j)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex(i)->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(next_around_edge(i,j))->point() )
!= POSITIVE ) return false;
_tds.flip_flippable( &(*c), i, j );
return true;
}
template < class GT, class Tds >
inline
void
Triangulation_3<GT,Tds>::
flip_flippable( Edge e )
{
return flip_flippable( e.first, e.second, e.third );
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
flip_flippable( Cell_handle c, int i, int j )
// flips edge i,j of cell c
{
#if !defined CGAL_TRIANGULATION_NO_PRECONDITIONS && \
!defined CGAL_NO_PRECONDITIONS && !defined NDEBUG
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() > 5) );
int degree = 0;
Cell_circulator ccir = incident_cells(c,i,j);
Cell_circulator cdone = ccir;
do {
CGAL_triangulation_precondition( ! is_infinite(&(*ccir)) );
++degree;
++ccir;
} while ( ccir != cdone );
CGAL_triangulation_precondition( degree == 3 );
Cell_handle n = c->neighbor( next_around_edge(i, j) );
int in = n->index( c->vertex(i) );
int jn = n->index( c->vertex(j) );
CGAL_triangulation_precondition
( orientation( c->vertex(next_around_edge(i,j))->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(j)->point() ) == POSITIVE );
CGAL_triangulation_precondition
( orientation( c->vertex(i)->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(next_around_edge(i,j))->point() ) == POSITIVE );
#endif
_tds.flip_flippable( &(*c), i, j );
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert(const Point & p, Cell_handle start, Vertex_handle v)
{
Locate_type lt;
int li, lj;
Cell_handle c = locate( p, lt, li, lj, start);
switch (lt) {
case VERTEX:
return c->vertex(li);
case EDGE:
return insert_in_edge(p, c, li, lj, v);
case FACET:
return insert_in_facet(p, c, li, v);
case CELL:
return insert_in_cell(p, c, v);
case OUTSIDE_CONVEX_HULL:
return insert_outside_convex_hull(p, c, v);
case OUTSIDE_AFFINE_HULL:
default:
return insert_outside_affine_hull(p, v);
}
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_cell(const Point & p, Cell_handle c, Vertex_handle v)
{
CGAL_triangulation_precondition( dimension() == 3 );
CGAL_triangulation_precondition_code
( Locate_type lt;
int i; int j; );
CGAL_triangulation_precondition
( side_of_tetrahedron( p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point(),
lt,i,j ) == ON_BOUNDED_SIDE );
v = (Vertex*)_tds.insert_in_cell( &(*v), &(*c) );
v->set_point(p);
return v;
}
template < class GT, class Tds >
inline
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_facet(const Point & p, Cell_handle c, int i, Vertex_handle v)
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3);
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
CGAL_triangulation_precondition_code
( Locate_type lt;
int li; int lj; );
CGAL_triangulation_precondition
( orientation( p,
c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point() ) == COPLANAR
&&
side_of_triangle( p,
c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
lt, li, lj) == ON_BOUNDED_SIDE );
v = (Vertex*) _tds.insert_in_facet( &(*v), &(*c), i);
v->set_point(p);
return v;
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_edge(const Point & p, Cell_handle c, int i, int j, Vertex_handle v)
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition( i >= 0 && i <= dimension()
&& j >= 0 && j <= dimension() );
CGAL_triangulation_precondition_code( Locate_type lt; int li; );
switch ( dimension() ) {
case 3:
case 2:
{
CGAL_triangulation_precondition( ! is_infinite(c, i, j) );
CGAL_triangulation_precondition( collinear( c->vertex(i)->point(),
p,
c->vertex(j)->point() )
&&
side_of_segment( p,
c->vertex(i)->point(),
c->vertex(j)->point(),
lt, li )
== ON_BOUNDED_SIDE );
break;
}
case 1:
{
CGAL_triangulation_precondition( side_of_edge(p, c, lt, li)
== ON_BOUNDED_SIDE );
break;
}
}
v = (Vertex*) _tds.insert_in_edge( &(*v), &(*c), i, j);
v->set_point(p);
return v;
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_outside_convex_hull(const Point & p, Cell_handle c, Vertex_handle v)
// c is an infinite cell containing p
// p is strictly outside the convex hull
// dimension 0 not allowed, use outside-affine-hull
{
CGAL_triangulation_precondition( dimension() > 0 );
CGAL_triangulation_precondition( c->has_vertex(infinite) );
// the precondition that p is in c is tested in each of the
// insertion methods called from this method
switch ( dimension() ) {
case 1:
{
// // p lies in the infinite edge neighboring c
// // on the other side of li
// return insert_in_edge(p,c->neighbor(1-li),0,1);
return insert_in_edge(p,c,0,1,v);
}
case 2:
{
set_number_of_vertices(number_of_vertices()+1);
Conflict_tester_outside_convex_hull_2 tester(p, this);
Vertex_handle v = (Vertex *) _tds.insert_conflict(NULL, &(*c), tester);
v->set_point(p);
return v;
}
case 3:
default:
{
set_number_of_vertices(number_of_vertices()+1);
Conflict_tester_outside_convex_hull_3 tester(p, this);
Vertex_handle v = (Vertex *) _tds.insert_conflict(NULL, &(*c), tester);
v->set_point(p);
return v;
}
}
}
template < class GT, class Tds >
Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_outside_affine_hull(const Point & p, Vertex_handle v)
{
CGAL_triangulation_precondition( dimension() < 3 );
bool reorient;
switch ( dimension() ) {
case 1:
{
CGAL_triangulation_precondition_code
( Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex())); )
CGAL_triangulation_precondition( !collinear(p,
n->vertex(0)->point(),
n->vertex(1)->point()) );
// no reorientation : the first non-collinear point determines
// the orientation of the plane
reorient = false;
break;
}
case 2:
{
Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex()));
Orientation oo = orientation( n->vertex(0)->point(),
n->vertex(1)->point(),
n->vertex(2)->point(), p );
CGAL_triangulation_precondition ( oo != COPLANAR );
reorient = oo == NEGATIVE;
break;
}
default:
reorient = false;
}
v = (Vertex*) _tds.insert_increase_dimension( &(*v),
&(*infinite_vertex()),
reorient);
v->set_point(p);
return v;
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
incident_cells(Vertex_handle v,
std::set<Cell*> & cells,
Cell_handle c,
int dummy_for_windows) const
{
bool WARNING_THIS_FUNCTION_IS_DEPRECATED;
CGAL_triangulation_precondition( &(*v) != NULL );
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*v)) );
if ( dimension() < 3 )
return;
if ( &(*c) == NULL )
c = v->cell();
else {
CGAL_triangulation_precondition( c->has_vertex(v) );
}
if ( cells.find( &(*c) ) != cells.end() )
return; // c was already found
cells.insert( &(*c) );
for ( int j=0; j<4; j++ )
if ( j != c->index(v) )
incident_cells( v, cells, c->neighbor(j), dummy_for_windows);
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
incident_cells(Vertex_handle v,
std::set<Cell_handle> & cells,
Cell_handle c ) const
{
CGAL_triangulation_precondition( &(*v) != NULL );
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*v)) );
if ( dimension() < 3 )
return;
if ( &(*c) == NULL )
c = v->cell();
else
CGAL_triangulation_precondition( c->has_vertex(v) );
if ( cells.find( c ) != cells.end() )
return; // c was already found
cells.insert( c );
for ( int j=0; j<4; j++ )
if ( j != c->index(v) )
incident_cells( v, cells, c->neighbor(j) );
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
incident_vertices(Vertex_handle v,
std::set<Vertex*> & vertices,
Cell_handle c,
int dummy_for_windows) const
{
bool WARNING_THIS_FUNCTION_IS_DEPRECATED;
CGAL_triangulation_precondition( &(*v) != NULL );
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*v)) );
if ( number_of_vertices() < 2 )
return;
if ( &(*c) == NULL )
c = v->cell();
else
CGAL_triangulation_precondition( c->has_vertex(v) );
std::set<Cell*> cells;
util_incident_vertices(v, vertices, cells, c, dummy_for_windows);
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
incident_vertices(Vertex_handle v,
std::set<Vertex_handle> & vertices,
Cell_handle c ) const
{
CGAL_triangulation_precondition( &(*v) != NULL );
CGAL_triangulation_expensive_precondition( _tds.is_vertex(&(*v)) );
if ( number_of_vertices() < 2 )
return;
if ( &(*c) == NULL )
c = v->cell();
else
CGAL_triangulation_precondition( c->has_vertex(v) );
std::set<Cell_handle> cells;
util_incident_vertices(v, vertices, cells, c);
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
util_incident_vertices(Vertex_handle v,
std::set<Vertex*> & vertices,
std::set<Cell*> & cells,
Cell_handle c,
int dummy_for_windows) const
{
bool WARNING_THIS_FUNCTION_IS_DEPRECATED;
if ( cells.find( &(*c) ) != cells.end() )
return; // c was already visited
cells.insert( &(*c) );
int d = dimension();
for (int j=0; j <= d; j++ )
if ( j != c->index(v) ) {
if ( vertices.find( &(*(c->vertex(j))) ) == vertices.end() )
vertices.insert( &(*(c->vertex(j))) );
util_incident_vertices( v, vertices, cells, c->neighbor(j),
dummy_for_windows);
}
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
util_incident_vertices(Vertex_handle v,
std::set<Vertex_handle> & vertices,
std::set<Cell_handle> & cells,
Cell_handle c ) const
{
if ( cells.find( c ) != cells.end() )
return; // c was already visited
cells.insert( c );
int d = dimension();
for (int j=0; j <= d; j++ )
if ( j != c->index(v) ) {
if ( vertices.find( c->vertex(j) ) == vertices.end() )
vertices.insert( c->vertex(j) );
util_incident_vertices( v, vertices, cells, c->neighbor(j) );
}
}
template < class GT, class Tds >
bool
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()) == NULL ) {
if (verbose)
std::cerr << "no infinite vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
Cell_iterator it;
for ( it = finite_cells_begin(); it != cells_end(); ++it )
is_valid_finite((*it).handle(),verbose,level);
break;
}
case 2:
{
Facet_iterator it;
for ( it = finite_facets_begin(); it != facets_end(); ++it )
is_valid_finite((*it).first,verbose,level);
break;
}
case 1:
{
Edge_iterator it;
for ( it = finite_edges_begin(); it != edges_end(); ++it )
is_valid_finite((*it).first,verbose,level);
break;
}
}
if (verbose)
std::cerr << "valid triangulation" << std::endl;
return true;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_valid(Cell_handle c, bool verbose, int level) const
{
if ( ! (&(*c))->is_valid(dimension(),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;
}
if ( ! is_infinite(c) )
is_valid_finite(c, verbose, level);
if (verbose)
std::cerr << "geometrically valid cell" << std::endl;
return true;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_valid_finite(Cell_handle c, bool verbose, int) const
{
switch ( dimension() ) {
case 3:
{
if ( orientation(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point()) != POSITIVE ) {
if (verbose)
std::cerr << "badly oriented cell "
<< c->vertex(0)->point() << ", "
<< c->vertex(1)->point() << ", "
<< c->vertex(2)->point() << ", "
<< c->vertex(3)->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 2:
{
for ( int i=0; i<3; i++ ) {
if ( ! is_infinite ( c->neighbor(i)->vertex(c->neighbor(i)->index(c)) )
&& coplanar_orientation
( c->vertex(cw(i))->point(),
c->vertex(ccw(i))->point(),
c->vertex(i)->point(),
c->neighbor(i)->vertex(c->neighbor(i)->index(c))->point()
) != NEGATIVE ) {
if (verbose)
std::cerr << "badly oriented face "
<< c->vertex(0)->point() << ", "
<< c->vertex(1)->point() << ", "
<< c->vertex(2)->point()
<< "with neighbor " << i
<< c->neighbor(i)->vertex(0)->point() << ", "
<< c->neighbor(i)->vertex(1)->point() << ", "
<< c->neighbor(i)->vertex(2)->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
break;
}
case 1:
{
const Point & p0 = c->vertex(0)->point();
const Point & p1 = c->vertex(1)->point();
if ( ! is_infinite ( c->neighbor(0)->vertex(c->neighbor(0)->index(c)) ) )
{
const Point & n0 =
c->neighbor(0)->vertex(c->neighbor(0)->index(c))->point();
if ( ( compare_x( p0, p1 ) != compare_x( p1, n0 ) )
|| ( compare_y( p0, p1 ) != compare_y( p1, n0 ) )
|| ( compare_z( p0, p1 ) != compare_z( p1, n0 ) ) ) {
if (verbose)
std::cerr << "badly oriented edge "
<< p0 << ", " << p1 << std::endl
<< "with neighbor 0"
<< c->neighbor(0)->vertex(1-c->neighbor(0)->index(c))
->point()
<< ", " << n0 << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
if ( ! is_infinite ( c->neighbor(1)->vertex(c->neighbor(1)->index(c)) ) )
{
const Point & n1 =
c->neighbor(1)->vertex(c->neighbor(1)->index(c))->point();
if ( ( compare_x( p1, p0 ) != compare_x( p0, n1 ) )
|| ( compare_y( p1, p0 ) != compare_y( p0, n1 ) )
|| ( compare_z( p1, p0 ) != compare_z( p0, n1 ) ) ) {
if (verbose)
std::cerr << "badly oriented edge "
<< p0 << ", " << p1 << std::endl
<< "with neighbor 1"
<< c->neighbor(1)->vertex(1-c->neighbor(1)->index(c))
->point()
<< ", " << n1 << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
break;
}
}
return true;
}
CGAL_END_NAMESPACE
#endif // CGAL_TRIANGULATION_3_H
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