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// ============================================================================
//
// Copyright (c) 1999,2000,2001 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_data_structure_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>)
//
// ============================================================================
//
// combinatorial triangulation of the boundary of a polytope
// of dimension d in dimension d+1
// for -1 <= d <= 3
//
// ============================================================================
#ifndef CGAL_TRIANGULATION_DATA_STRUCTURE_3_H
#define CGAL_TRIANGULATION_DATA_STRUCTURE_3_H
#include <CGAL/basic.h>
#include <utility>
#include <map>
#include <set>
#include <vector>
#include <CGAL/triple.h>
#include <CGAL/Triangulation_short_names_3.h>
#include <CGAL/triangulation_assertions.h>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/Pointer.h>
#include <CGAL/Triangulation_ds_cell_3.h>
#include <CGAL/Triangulation_ds_vertex_3.h>
#include <CGAL/Triangulation_ds_iterators_3.h>
#include <CGAL/Triangulation_ds_circulators_3.h>
#include <CGAL/DS_Container.h>
CGAL_BEGIN_NAMESPACE
template <class Vb, class Cb>
class Triangulation_data_structure_3
: public Triangulation_utils_3
{
public:
typedef Triangulation_data_structure_3<Vb,Cb> Tds;
typedef Vb Vertex_base;
typedef Cb Cell_base;
typedef Triangulation_ds_vertex_3<Tds> Vertex;
typedef Triangulation_ds_cell_3<Tds> Cell;
typedef Pointer<Cell> Cell_handle;
typedef Pointer<Vertex> Vertex_handle;
// typedef Cell * Cell_handle;
// typedef Vertex * Vertex_handle;
typedef std::pair<Cell_handle, int> Facet;
typedef triple<Cell_handle, int, int> Edge;
friend class Triangulation_ds_facet_iterator_3<Tds>;
friend class Triangulation_ds_edge_iterator_3<Tds>;
friend class Triangulation_ds_cell_circulator_3<Tds>;
friend class Triangulation_ds_facet_circulator_3<Tds>;
typedef DS_Container<Cell> Cell_container;
typedef DS_Container<Vertex> Vertex_container;
typedef typename Cell_container::iterator Cell_iterator;
typedef typename Vertex_container::iterator Vertex_iterator;
typedef Triangulation_ds_facet_iterator_3<Tds> Facet_iterator;
typedef Triangulation_ds_edge_iterator_3<Tds> Edge_iterator;
typedef Triangulation_ds_cell_circulator_3<Tds> Cell_circulator;
typedef Triangulation_ds_facet_circulator_3<Tds> Facet_circulator;
Triangulation_data_structure_3()
: _dimension(-2), _number_of_vertices(0)
{}
Triangulation_data_structure_3(const Tds & tds)
: _number_of_vertices(0)
// _number_of_vertices is set to 0 so that clear() in copy_tds() works
{
copy_tds(tds);
}
~Triangulation_data_structure_3()
{
clear();
}
Tds & operator= (const Tds & tds)
{
copy_tds(tds);
return *this;
}
int number_of_vertices() const {return _number_of_vertices;}
int dimension() const {return _dimension;}
int number_of_cells() const
{
if ( dimension() < 3 ) return 0;
return cell_container().size();
}
int number_of_facets() const
{
if ( dimension() < 2 ) return 0;
return std::distance(facets_begin(), facets_end());
}
int number_of_edges() const
{
if ( dimension() < 1 ) return 0;
return std::distance(edges_begin(), edges_end());
}
// USEFUL CONSTANT TIME FUNCTIONS
// SETTING
// to be protected ?
void set_number_of_vertices(int n) { _number_of_vertices = n; }
void set_dimension(int n) { _dimension = n; }
Vertex_handle create_vertex()
{
return vertex_container().get_new_element();
}
Cell_handle create_cell()
{
return get_new_cell();
}
Cell_handle create_cell(Cell_handle c)
{
Cell_handle cnew = get_new_cell();
*cnew = *c;
cnew->init();
return cnew;
}
Cell_handle create_cell(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3)
{
Cell_handle c = get_new_cell();
c->set_vertices(v0,v1,v2,v3);
return c;
}
Cell_handle create_cell(Vertex_handle v0, Vertex_handle v1,
Vertex_handle v2, Vertex_handle v3,
Cell_handle n0, Cell_handle n1,
Cell_handle n2, Cell_handle n3)
{
Cell_handle c = get_new_cell();
c->set_vertices(v0,v1,v2,v3);
c->set_neighbors(n0,n1,n2,n3);
return c;
}
private:
Cell_handle get_new_cell()
{
Cell_handle r = cell_container().get_new_element();
r->init();
return r;
}
public:
// not documented
void read_cells(std::istream& is, std::map< int, Vertex_handle > &V,
int & m, std::map< int, Cell_handle > &C );
// not documented
void print_cells(std::ostream& os, std::map<Vertex_handle, int> &V ) const;
// ACCESS FUNCTIONS
void delete_vertex( Vertex_handle v )
{
CGAL_triangulation_expensive_precondition( is_vertex(v) );
vertex_container().release_element(&*v);
}
void delete_cell( Cell_handle c )
{
CGAL_triangulation_expensive_precondition( dimension() != 3 ||
is_cell(c) );
CGAL_triangulation_expensive_precondition( dimension() != 2 ||
is_facet(c,3) );
CGAL_triangulation_expensive_precondition( dimension() != 1 ||
is_edge(c,0,1) );
CGAL_triangulation_expensive_precondition( dimension() != 0 ||
is_vertex(c->vertex(0)) );
cell_container().release_element(&*c);
}
template <class It>
void delete_cells(It begin, It end)
{
for(; begin != end; ++begin)
delete_cell((*begin)->handle());
}
// QUERIES
bool is_vertex(Vertex_handle v) const;
bool is_edge(Cell_handle c, int i, int j) const;
bool is_edge(Vertex_handle u, Vertex_handle v, Cell_handle & c,
int & i, int & j) const;
bool is_facet(Cell_handle c, int i) 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) 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;
// MODIFY
bool flip(Cell_handle c, int i);
bool flip(const Facet &f)
{ return flip( f.first, f.second); }
void flip_flippable(Cell_handle c, int i);
void flip_flippable(const Facet &f)
{ return flip_flippable( f.first, f.second ); }
bool flip(Cell_handle c, int i, int j);
bool flip(const Edge &e)
{ return flip( e.first, e.second, e.third ); }
void flip_flippable(Cell_handle c, int i, int j);
void flip_flippable(const Edge &e)
{ return flip_flippable( e.first, e.second, e.third ); }
private:
// common to flip and flip_flippable
void flip_really(Cell_handle c, int i, Cell_handle n, int in);
void flip_really(Cell_handle c, int i, int j,
Cell_handle c1, Vertex_handle v1, int i1, int j1, int next1,
Cell_handle c2, Vertex_handle v2, int i2, int j2, int next2,
Vertex_handle v3);
public:
//INSERTION
Vertex_handle insert_in_cell(Vertex_handle v, Cell_handle c);
Vertex_handle insert_in_facet(Vertex_handle v, const Facet & f)
{ return insert_in_facet(w,f.first,f.second); }
Vertex_handle insert_in_facet(Vertex_handle v, Cell_handle c, int i);
Vertex_handle insert_in_edge(Vertex_handle v, const Edge & e)
{ return insert_in_edge(w, e.first, e.second, e.third); }
Vertex_handle insert_in_edge(Vertex_handle v, Cell_handle c, int i, int j);
Vertex_handle insert_increase_dimension(Vertex_handle v, // new vertex
Vertex_handle star = NULL,
bool reorient = false);
// I think the find_conflicts_[23] should be in the TDS, as they do not
// depend on geometry, although they may, depending on the actual
// Conflict_test. But e.g. for incident_cells(), the tester is not
// geometric, so it makes sense to have it in the TDS.
template <class FacetIt, class CellIt>
void star_hole_3(Vertex_handle newv, FacetIt facet_begin, FacetIt facet_end,
CellIt cell_begin, CellIt cell_end)
{
star_hole_3(newv, facet_begin, facet_end);
delete_cells(cell_begin, cell_end);
}
template <class FacetIt, class CellIt>
void star_hole_2(Vertex_handle newv, FacetIt facet_begin, FacetIt facet_end,
CellIt cell_begin, CellIt cell_end)
{
star_hole_2(newv, facet_begin, facet_end);
delete_cells(cell_begin, cell_end);
}
// Facets->first is in conflict, and we walk inside the hole.
//
// Note #1 : If we can merge the FacetIt loops, then maybe we can get rid
// of the corresponding container by just walking over the boundary ?
// Thinking a bit more about that : I think it's either we have a container
// of facets, or we have a recursive function over the boundary... (?)
template <class FacetIt>
void star_hole_3(Vertex_handle newv, FacetIt facet_begin, FacetIt facet_end)
{
CGAL_triangulation_precondition(dimension()==3);
// Would be nice if there were already room reserved in the facet
// vector.
std::vector<Cell_handle > V;
V.reserve(std::distance(facet_begin, facet_end));
// For each facet on the boundary :
// - create a new cell, link its vertices and one cell pointer.
for (FacetIt fit = facet_begin; fit != facet_end; ++fit) {
Cell_handle old = fit->first;
Cell_handle bound = old->neighbor(fit->second);
// Note that the initial orientation of the new cells is positive,
// as we copy it from an existing one.
Cell_handle newc = create_cell(old->vertex(0),
old->vertex(1),
old->vertex(2),
old->vertex(3));
newc->set_vertex(fit->second, newv);
set_adjacency(newc, bound, fit->second, bound->index(old));
newc->vertex(0)->set_cell(newc);
newc->vertex(1)->set_cell(newc);
newc->vertex(2)->set_cell(newc);
newc->vertex(3)->set_cell(newc);
V.push_back(newc);
}
// For each facet on the boundary, for each of the 3 edges :
// - we must find the neighbor facet
// - link the 2 corresponding new cells.
int zz = -1;
for (FacetIt fit2 = facet_begin; fit2 != facet_end; ++fit2) {
++zz;
Cell_handle old = fit2->first;
Cell_handle newc = V[zz];
for (int i=0; i<=3; ++i) {
// We must avoid i == fit->second, but the following
// test will avoid it too.
if (newc->neighbor(i) != NULL)
continue;
// Now we turn around the edge inside the hole.
// To recognize when we hit the boundary, we look at the
// neighbor, and see if it doesn't point back to us, in which
// case it's the boundary cell we are looking for.
Cell_handle t = old;
Vertex_handle k = t->vertex(fit2->second);
int j = i;
Cell_handle newt = t->neighbor(j);
int z;
while (newt->has_neighbor(t, z)) {
j = newt->index(k);
k = newt->vertex(z);
t = newt;
newt = t->neighbor(j);
};
// Compute the address of the corresponding new cell.
Cell_handle back;
for (int l=0;; ++l) {
back = newt->neighbor(l);
if (l==3)
break;
// The vertices are those of t except vertex(j) = newv.
if (back->vertex(j) == newv &&
back->vertex(j^1) == t->vertex(j^1) &&
back->vertex(j^2) == t->vertex(j^2) &&
back->vertex(j^3) == t->vertex(j^3))
break;
}
set_adjacency(newc, back, i, back->index(k));
}
}
}
// Note : the code is almost entirely duplicated, just to have dimension() a
// constant for performance. That's not perfect...
template <class FacetIt>
void star_hole_2(Vertex_handle newv, FacetIt facet_begin, FacetIt facet_end)
{
CGAL_triangulation_precondition(dimension()==2);
// Would be nice if there were already room reserved in the facet
// vector.
std::vector<Cell_handle > V;
V.reserve(std::distance(facet_begin, facet_end));
// For each facet on the boundary :
// - create a new cell, link its vertices and one cell pointer.
for (FacetIt fit = facet_begin; fit != facet_end; ++fit) {
Cell_handle old = fit->first;
Cell_handle bound = old->neighbor(fit->second);
// Note that the initial orientation of the new cells is positive,
// as we copy it from an existing one.
Cell_handle newc = create_cell(old->vertex(0),
old->vertex(1),
old->vertex(2),
NULL);
newc->set_vertex(fit->second, newv);
set_adjacency(newc, bound, fit->second, bound->index(old));
newc->vertex(0)->set_cell(newc);
newc->vertex(1)->set_cell(newc);
newc->vertex(2)->set_cell(newc);
V.push_back(newc);
}
// For each facet on the boundary, for each of the 3 edges :
// - we must find the neighbor facet
// - link the 2 corresponding new cells.
int zz = -1;
for (FacetIt fit2 = facet_begin; fit2 != facet_end; ++fit2) {
++zz;
Cell_handle old = fit2->first;
Cell_handle newc = V[zz];
for (int i=0; i<=2; ++i) {
// We must avoid i == fit->second, but the following
// test will avoid it too.
if (newc->neighbor(i) != NULL)
continue;
// Now we turn around the edge inside the hole.
// To recognize when we hit the boundary, we look at the
// neighbor, and see if it doesn't point back to us, in which
// case it's the boundary cell we are looking for.
Cell_handle t = old;
Vertex_handle k = t->vertex(fit2->second);
int j = i;
Cell_handle newt = t->neighbor(j);
int z;
while (newt->has_neighbor(t, z)) {
j = newt->index(k);
k = newt->vertex(z);
t = newt;
newt = t->neighbor(j);
};
// Compute the address of the corresponding new cell.
Cell_handle back;
for (int l=0;; ++l) {
back = newt->neighbor(l);
if (l==2)
break;
// The vertices are those of t except vertex(j) = newv.
if (back->vertex(j) == newv &&
back->vertex(cw(j)) == t->vertex(cw(j)) &&
back->vertex(ccw(j)) == t->vertex(ccw(j)))
break;
}
set_adjacency(newc, back, i, back->index(k));
}
}
}
// ITERATOR METHODS
Cell_iterator cells_begin() const
{
if ( dimension() < 3 )
return cells_end();
return cell_container().begin();
}
Cell_iterator cells_end() const
{
return cell_container().end();
}
Facet_iterator facets_begin() const
{
if ( dimension() < 2 )
return facets_end();
return Facet_iterator(this);
}
Facet_iterator facets_end() const
{
return Facet_iterator(this, 1);
}
Edge_iterator edges_begin() const
{
if ( dimension() < 1 )
return edges_end();
return Edge_iterator(this);
}
Edge_iterator edges_end() const
{
return Edge_iterator(this,1);
}
Vertex_iterator vertices_begin() const
{
return vertex_container().begin();
}
Vertex_iterator vertices_end() const
{
return vertex_container().end();
}
// CIRCULATOR METHODS
// cells around an edge
Cell_circulator incident_cells(const Edge & e) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(e);
}
Cell_circulator incident_cells(Cell_handle ce, int i, int j) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(ce, i, j);
}
Cell_circulator incident_cells(const Edge & e, Cell_handle start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(e, start);
}
Cell_circulator incident_cells(Cell_handle ce, int i, int j,
Cell_handle start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Cell_circulator(ce, i, j, start);
}
//facets around an edge
Facet_circulator incident_facets(const Edge & e) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(e);
}
Facet_circulator incident_facets(Cell_handle ce, int i, int j) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(ce, i, j);
}
Facet_circulator incident_facets(const Edge & e, const Facet & start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(e, start);
}
Facet_circulator incident_facets(Cell_handle ce, int i, int j,
const Facet & start) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(ce, i, j, start);
}
Facet_circulator incident_facets(const Edge & e,
Cell_handle start, int f) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(e, start, f);
}
Facet_circulator incident_facets(Cell_handle ce, int i, int j,
Cell_handle start, int f) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return Facet_circulator(ce, i, j, start, f);
}
// around a vertex
private:
class Incident_tester {
Vertex_handle _v;
public :
Incident_tester(Vertex_handle v) : _v(v) {}
bool operator()(Cell_handle c) const
{ return c->has_vertex(v); }
};
private:
// TODO : This should be reimplemented. Using find_conflict is overkill...
template <class OutIt>
void
incident_cells(Vertex_handle v, OutIt outcells) const
{
if ( dimension() < 3 )
return;
std::vector<Facet> facets;
std::vector<Cell_handle > cells;
facets.reserve(64);
cells.reserve(64);
find_conflicts_3(v->cell(), Incident_tester(v), facets, cells);
for(typename std::vector<Facet>::iterator fit = facets.begin();
fit != facets.end(); ++fit)
fit->first->set_in_conflict_flag(0);
for(typename std::vector<Cell_handle >::iterator cit = cells.begin();
cit != cells.end(); ++cit) {
*cit->set_in_conflict_flag(0);
*outcells++ = *cit;
}
}
public:
void
incident_cells(Vertex_handle v, std::set<Cell_handle> & cells,
Cell_handle c = NULL ) const;
void
incident_vertices(Vertex_handle v, std::set<Vertex_handle> & vertices,
Cell_handle c = NULL ) const;
// CHECKING
bool is_valid(bool verbose = false, int level = 0) const;
// Helping functions
Vertex_handle copy_tds(const Tds & tds, Vertex_handle vert = NULL);
// returns the new vertex corresponding to vert in the new tds
void swap(Tds & tds);
void clear();
void clear_cells_only();
void set_adjacency(Cell_handle c0, Cell_handle c1, int i0, int i1) const
{
CGAL_triangulation_assertion(i0 >= 0 && i0 <= dimension());
CGAL_triangulation_assertion(i1 >= 0 && i1 <= dimension());
CGAL_triangulation_assertion(c0 != c1);
c0->set_neighbor(i0,c1);
c1->set_neighbor(i1,c0);
}
// Change the orientation of the cell by swapping indices 0 and 1.
void change_orientation(Cell_handle c) const
{
Vertex_handle tmp_v = c->vertex(0);
c->set_vertex(0, c->vertex(1));
c->set_vertex(1, tmp_v);
Cell_handle tmp_c = c->neighbor(0);
c->set_neighbor(0, c->neighbor(1));
c->set_neighbor(1, tmp_c);
}
private:
Cell_container & cell_container() { return _cell_container; }
const Cell_container & cell_container() const { return _cell_container; }
Vertex_container & vertex_container() {return _vertex_container;}
const Vertex_container & vertex_container() const {return _vertex_container;}
// in dimension i, number of vertices >= i+2
// ( the boundary of a simplex in dimension i+1 has i+2 vertices )
int _dimension;
int _number_of_vertices;
Cell_container _cell_container;
Vertex_container _vertex_container;
// used by is-valid :
bool count_vertices(int & i, bool verbose = false, int level = 0) const;
// counts AND checks the validity
bool count_facets(int & i, bool verbose = false, int level = 0) const;
// counts but does not check
bool count_edges(int & i, bool verbose = false, int level = 0) const;
// counts but does not check
bool count_cells(int & i, bool verbose = false, int level = 0) const;
// counts AND checks the validity
};
template < class Vb, class Cb>
std::istream&
operator>>(std::istream& is, Triangulation_data_structure_3<Vb,Cb>& tds)
// reads :
// the dimension
// the number of vertices
// the number of cells
// the cells by the indices of their vertices
// 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_data_structure_3<Vb,Cb> Tds;
typedef typename Tds::Vertex_handle Vertex_handle;
typedef typename Tds::Cell_handle Cell_handle;
tds.clear();
int n, d;
is >> d >> n;
tds.set_dimension(d);
tds.set_number_of_vertices(n);
if(n == 0)
return is;
std::map< int, Vertex_handle > V;
// creation of the vertices
for (int i=0; i < n; i++) {
// is >> p;
// V[i] = tds.create_vertex();
// V[i]->set_point(p);
V[i] = tds.create_vertex();
}
std::map< int, Cell_handle > C;
int m;
tds.read_cells(is, V, m, C);
CGAL_triangulation_assertion( tds.is_valid() );
return is;
}
template < class Vb, class Cb>
std::ostream&
operator<<(std::ostream& os, const Triangulation_data_structure_3<Vb,Cb> &tds)
// writes :
// the dimension
// the number of vertices
// the number of cells
// the cells by the indices of their vertices
// 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_data_structure_3<Vb,Cb> Tds;
typedef typename Tds::Vertex_handle Vertex_handle;
typedef typename Tds::Vertex_iterator Vertex_iterator;
std::map<Vertex_handle, int> V;
// outputs dimension and number of vertices
int n = tds.number_of_vertices();
if (is_ascii(os))
os << tds.dimension() << std::endl << n << std::endl;
else
os << tds.dimension() << n;
if (n == 0)
return os;
// index the vertices
int i = 0;
for (Vertex_iterator it=tds.vertices_begin(); it != tds.vertices_end(); ++it)
V[&(*it)] = i++;
CGAL_triangulation_assertion( i == n );
tds.print_cells(os, V);
return os;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_vertex(Vertex_handle v) const
{
return vertex_container().is_element(&*v);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_edge(Vertex_handle u, Vertex_handle v, Cell_handle &c, int &i, int &j) const
// returns false when dimension <1 or when indices wrong
{
if (u==v)
return false;
for(Cell_iterator cit = cell_container().begin(); cit != cells_end(); ++cit)
if (cit->has_vertex(u,i) && cit->has_vertex(v,j)) {
c = cit->handle();
return true;
}
return false;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_edge(Cell_handle c, int i, int j) const
// returns false when dimension <1
{
if ( i==j ) return false;
if ( (i<0) || (j<0) ) return false;
if ( (dimension() == 1) && ((i>1) || (j>1)) ) return false;
if ( (dimension() == 2) && ((i>2) || (j>2)) ) return false;
if ((i>3) || (j>3)) return false;
for(Cell_iterator cit = cell_container().begin(); cit != cells_end(); ++cit)
if (cit->handle() == c)
return true;
return false;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle & c, int & i, int & j, int & k) const
// returns false when dimension <2 or when indices wrong
{
if ( (u==v) || (u==w) || (v==w) ) return false;
Facet_iterator it = facets_begin();
while ( it != facets_end() ) {
if ( ( ((*it).first)->has_vertex(u,i) )
&& ( ((*it).first)->has_vertex(v,j) )
&& ( ((*it).first)->has_vertex(w,k) ) ) {
c = (*it).first;
return true;
}
++it;
}
return false;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_facet(Cell_handle c, int i) const
// returns false when dimension <2
{
CGAL_triangulation_precondition(i>=0 && i<4);
if ( (dimension() == 2) && (i!=3) )
return false;
return cell_container().is_element(&*c);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_cell( Cell_handle c ) const
// returns false when dimension <3
{
if (dimension() < 3)
return false;
return cell_container().is_element(&*c);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
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
// returns false when dimension <3
{
if ( (u==v) || (u==w) || (u==t) || (v==w) || (v==t) || (w==t) )
return false;
for(Cell_iterator it = cells_begin(); it != cells_end(); ++it) {
if ( ( it->has_vertex(u,i) )
&& ( it->has_vertex(v,j) )
&& ( it->has_vertex(w,k) )
&& ( it->has_vertex(t,l) ) ) {
c = it->handle();
return true;
}
}
return false;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
is_cell(Vertex_handle u, Vertex_handle v, Vertex_handle w, Vertex_handle t)
const
// returns false when dimension <3
{
if ( (u==v) || (u==w) || (u==t) || (v==w) || (v==t) || (w==t) )
return false;
for(Cell_iterator it = cells_begin(); it != cells_end(); ++it) {
if ( it->has_vertex(u) &&
it->has_vertex(v) &&
it->has_vertex(w) &&
it->has_vertex(t) ) {
return true;
}
}
return false;
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
has_vertex(Cell_handle c, int i, Vertex_handle v, int & j) const
// computes the index j of the vertex in the cell c giving the query
// facet (c,i)
// j has no meaning if false is returned
{
CGAL_triangulation_precondition( dimension() == 3 );
return ( c->has_vertex(v,j) && (j != i) );
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
has_vertex(Cell_handle c, int i, Vertex_handle v) const
// checks whether the query facet (c,i) has vertex v
{
CGAL_triangulation_precondition( dimension() == 3 );
int j;
return ( c->has_vertex(v,j) && (j != i) );
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
has_vertex(const Facet & f, Vertex_handle v, int & j) const
{
return has_vertex(f.first, f.second, v, j);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
has_vertex(const Facet & f, Vertex_handle v) const
{
return has_vertex(f.first, f.second, v);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
are_equal(Cell_handle c, int i, Cell_handle n, int j) const
// tests whether facets c,i and n,j, have the same 3 vertices
// the triangulation is supposed to be valid, the orientation of the
// facets is not checked here
// the neighbor relations between c and n are not tested either,
// which allows to use this method before setting these relations
// (see remove in Delaunay_3)
// if ( c->neighbor(i) != n ) return false;
// if ( n->neighbor(j) != c ) return false;
{
CGAL_triangulation_precondition( dimension() == 3 );
if ( (c==n) && (i==j) ) return true;
int j1,j2,j3;
return( n->has_vertex( c->vertex((i+1)&3), j1 ) &&
n->has_vertex( c->vertex((i+2)&3), j2 ) &&
n->has_vertex( c->vertex((i+3)&3), j3 ) &&
( j1+j2+j3+j == 6 ) );
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
are_equal(const Facet & f, const Facet & g) const
{
return are_equal(f.first, f.second, g.first, g.second);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
are_equal(const Facet & f, Cell_handle n, int j) const
{
return are_equal(f.first, f.second, n, j);
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
flip( Cell_handle c, int i )
// 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
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() > 6) );
CGAL_triangulation_expensive_precondition( is_cell(c) );
Cell_handle n = c->neighbor(i);
int in = n->index(c);
// checks that the facet is flippable,
// ie the future edge does not already exist
std::set<Vertex_handle> setc;
incident_vertices( c->vertex(i), setc );
if ( setc.find( n->vertex(in) ) != setc.end() ) return false;
flip_really(c,i,n,in);
return true;
}
template < class Vb, class Cb>
void
Triangulation_data_structure_3<Vb,Cb>::
flip_flippable( Cell_handle c, int i )
// flips facet i of cell c
// c will be replaced by one of the new cells
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() > 6) );
CGAL_triangulation_expensive_precondition( is_cell(c) );
Cell_handle n = c->neighbor(i);
int in = n->index(c);
// checks that the facet is flippable,
// ie the future edge does not already exist
typedef std::set<Vertex_handle> set_of_vertices;
CGAL_triangulation_expensive_precondition_code( set_of_vertices setc; );
CGAL_triangulation_expensive_precondition_code
( incident_vertices( c->vertex(i), setc ); );
CGAL_triangulation_expensive_precondition
( ( setc.find( n->vertex(in) ) == setc.end() ) );
flip_really(c,i,n,in);
}
template < class Vb, class Cb>
inline
void
Triangulation_data_structure_3<Vb,Cb>::
flip_really( Cell_handle c, int i, Cell_handle n, int in )
// private - used by flip and flip_flippable
{
int i1 = (i+1)&3;
int i2 = (i+2)&3;
int i3 = (i+3)&3;
int in1 = n->index(c->vertex(i1));
int in2 = n->index(c->vertex(i2));
int in3 = n->index(c->vertex(i3));
set_adjacency(c, n->neighbor(in3), i, n->neighbor(in3)->index(n));
c->set_vertex( i3, n->vertex(in) );
set_adjacency(n, c->neighbor(i1), in, c->neighbor(i1)->index(c));
n->set_vertex( in1, c->vertex(i) );
Cell_handle cnew = create_cell(c->vertex(i), c->vertex(i1),
n->vertex(in), n->vertex(in3));
set_adjacency(cnew, n->neighbor(in2), 0, n->neighbor(in2)->index(n));
set_adjacency(cnew, n, 1, in2);
set_adjacency(cnew, c->neighbor(i2), 2, c->neighbor(i2)->index(c));
set_adjacency(cnew, c, 3, i2);
set_adjacency(c, n, i1, in3);
if (i&1 != 0)
change_orientation(cnew);
c->vertex(i1)->set_cell(cnew);
c->vertex(i2)->set_cell(c);
n->vertex(in3)->set_cell(n);
// to be implemented : 2d case
// CGAL_triangulation_precondition( (0<=i) && (i<3) );
}
template < class Vb, class Cb>
bool
Triangulation_data_structure_3<Vb,Cb>::
flip( Cell_handle c, int i, int j )
// returns false if the edge is not flippable
// true otherwise and
// flips edge i,j of cell c
// c will be deleted
{
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() > 6) );
CGAL_triangulation_expensive_precondition( is_cell(c) );
// checks that the edge is flippable ie degree 3
int degree = 0;
Cell_circulator ccir = incident_cells(c,i,j);
Cell_circulator cdone = ccir;
do {
++degree;
++ccir;
} while ( ccir != cdone );
if ( degree != 3 ) return false;
int next = next_around_edge(i,j);
Cell_handle c1 = c->neighbor( next );
Vertex_handle v1 = c->vertex( next ); // will become vertex of c1
int i1 = c1->index( c->vertex(i) );
int j1 = c1->index( c->vertex(j) );
int next1 = next_around_edge(i1,j1);
Cell_handle c2 = c1->neighbor( next1 );
Vertex_handle v2 = c1->vertex( next1 ); // will become vertex of c2
int i2 = c2->index( c->vertex(i) );
int j2 = c2->index( c->vertex(j) );
int next2 = next_around_edge(i2,j2);
Vertex_handle v3 = c2->vertex( next2 );
// checks that the edge is flippable,
// is the future cells do not already exist
if ( is_cell(v1,v2,v3,c->vertex(i)) ) return false;
if ( is_cell(v1,v2,v3,c->vertex(j)) ) return false;
flip_really(c,i,j,c1,v1,i1,j1,next1,c2,v2,i2,j2,next2,v3);
return true;
}
template < class Vb, class Cb>
void
Triangulation_data_structure_3<Vb,Cb>::
flip_flippable( Cell_handle c, int i, int j )
// flips edge i,j of cell c
// c will be deleted
{
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() > 6) );
CGAL_triangulation_expensive_precondition( is_cell(c) );
// checks that the edge is flippable ie degree 3
CGAL_triangulation_precondition_code( int degree = 0; );
CGAL_triangulation_precondition_code
( Cell_circulator ccir = incident_cells(c,i,j); );
CGAL_triangulation_precondition_code( Cell_circulator cdone = ccir; );
CGAL_triangulation_precondition_code( do {
++degree;
++ccir;
} while ( ccir != cdone ); );
CGAL_triangulation_precondition( degree == 3 );
int next = next_around_edge(i,j);
Cell_handle c1 = c->neighbor( next );
Vertex_handle v1 = c->vertex( next ); // will become vertex of c1
int i1 = c1->index( c->vertex(i) );
int j1 = c1->index( c->vertex(j) );
int next1 = next_around_edge(i1,j1);
Cell_handle c2 = c1->neighbor( next1 );
Vertex_handle v2 = c1->vertex( next1 ); // will become vertex of c2
int i2 = c2->index( c->vertex(i) );
int j2 = c2->index( c->vertex(j) );
int next2 = next_around_edge(i2,j2);
Vertex_handle v3 = c2->vertex( next2 );
// checks that the edge is flippable,
// is the future cells do not already exist
CGAL_triangulation_expensive_precondition( !is_cell(v1,v2,v3,c->vertex(i)) );
CGAL_triangulation_expensive_precondition( !is_cell(v1,v2,v3,c->vertex(j)) );
flip_really(c,i,j,c1,v1,i1,j1,next1,c2,v2,i2,j2,next2,v3);
}
template < class Vb, class Cb>
inline
void
Triangulation_data_structure_3<Vb,Cb>::
flip_really( Cell_handle c, int i, int j,
Cell_handle c1, Vertex_handle v1, int i1, int j1, int next1,
Cell_handle c2, Vertex_handle v2, int i2, int j2, int next2,
Vertex_handle v3 )
{
c->vertex(i)->set_cell(c1);
c->vertex(j)->set_cell(c2);
c1->set_vertex( j1, v1 );
v1->set_cell(c1);
c2->set_vertex( i2, v2 );
v2->set_cell(c2);
set_adjacency(c1,c2->neighbor(j2), next1, c2->neighbor(j2)->index(c2));
set_adjacency(c2,c1->neighbor(i1),c2->index(v1),c1->neighbor(i1)->index(c1));
set_adjacency(c1, c2, i1, j2);
set_adjacency(c1, c->neighbor(j), 6-i1-j1-next1, c->neighbor(j)->index(c));
set_adjacency(c2, c->neighbor(i), next2, c->neighbor(i)->index(c));
v3->set_cell( c2 );
delete_cell( c );
}
template < class Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
read_cells(std::istream& is, std::map< int, Vertex_handle > &V,
int & m, std::map< int, Cell_handle > &C)
{
// creation of the cells and neighbors
switch (dimension()) {
case 3:
case 2:
case 1:
{
is >> m;
for(int i = 0; i < m; i++) {
Cell_handle c = create_cell();
for (int k=0; k<=dimension(); ++k) {
int ik;
is >> ik;
c->set_vertex(k, V[ik]);
V[ik]->set_cell(c);
}
C[i] = c;
}
for(int j = 0; j < m; j++) {
Cell_handle c = C[j];
for (int k=0; k<=dimension(); ++k) {
int ik;
is >> ik;
c->set_neighbor(k, C[ik]);
}
}
break;
}
case 0:
{
m = 2;
// CGAL_triangulation_assertion( n == 2 );
for (int i=0; i < 2; i++) {
Cell_handle c = create_cell(V[i], NULL, NULL, NULL);
C[i] = c;
V[i]->set_cell(c);
}
for (int j=0; j < 2; j++) {
Cell_handle c = C[j];
c->set_neighbor(0, C[1-j]);
}
break;
}
case -1:
{
m = 1;
// CGAL_triangulation_assertion( n == 1 );
Cell_handle c = create_cell(V[0], NULL, NULL, NULL);
C[0] = c;
V[0]->set_cell(c);
break;
}
}
}
template < class Vb, class Cb>
void
Triangulation_data_structure_3<Vb,Cb>::
print_cells(std::ostream& os, std::map<Vertex_handle, int> &V ) const
{
std::map<Cell_handle, int > C;
int i = 0;
int j;
int m;
switch ( dimension() ) {
case 3:
{
m = number_of_cells();
os << m;
if(is_ascii(os))
os << std::endl;
// write the cells
Cell_iterator it;
for(it = cells_begin(); it != cells_end(); ++it) {
C[&(*it)] = i++;
for(j = 0; j < 4; j++){
os << V[it->vertex(j)];
if(is_ascii(os)) {
if ( j==3 )
os << std::endl;
else
os << ' ';
}
}
}
CGAL_triangulation_assertion( i == m );
// write the neighbors
for(it = cells_begin(); it != cells_end(); ++it) {
for (j = 0; j < 4; j++) {
os << C[it->neighbor(j)];
if(is_ascii(os)){
if(j==3)
os << std::endl;
else
os << ' ';
}
}
}
break;
}
case 2:
{
m = number_of_facets();
os << m;
if(is_ascii(os))
os << std::endl;
// write the facets
Facet_iterator it;
for(it = facets_begin(); it != facets_end(); ++it) {
C[(*it).first] = i++;
for(j = 0; j < 3; j++){
os << V[(*it).first->vertex(j)];
if(is_ascii(os)) {
if ( j==2 )
os << std::endl;
else
os << ' ';
}
}
}
CGAL_triangulation_assertion( i == m );
// write the neighbors
for(it = facets_begin(); it != facets_end(); ++it) {
for (j = 0; j < 3; j++) {
os << C[(*it).first->neighbor(j)];
if(is_ascii(os)){
if(j==2)
os << std::endl;
else
os << ' ';
}
}
}
break;
}
case 1:
{
m = number_of_edges();
os << m;
if(is_ascii(os))
os << std::endl;
// write the edges
Edge_iterator it;
for(it = edges_begin(); it != edges_end(); ++it) {
C[(*it).first] = i++;
for(j = 0; j < 2; j++){
os << V[(*it).first->vertex(j)];
if(is_ascii(os)) {
if ( j==1 )
os << std::endl;
else
os << ' ';
}
}
}
CGAL_triangulation_assertion( i == m );
// write the neighbors
for(it = edges_begin(); it != edges_end(); ++it) {
for (j = 0; j < 2; j++) {
os << C[(*it).first->neighbor(j)];
if(is_ascii(os)){
if(j==1)
os << std::endl;
else
os << ' ';
}
}
}
break;
}
}
}
template <class Vb, class Cb >
typename Triangulation_data_structure_3<Vb,Cb>::Vertex_handle
Triangulation_data_structure_3<Vb,Cb>::
insert_in_cell( Vertex_handle v, Cell_handle c )
{
CGAL_triangulation_precondition( dimension() == 3 );
CGAL_triangulation_precondition( (c != NULL) );
CGAL_triangulation_expensive_precondition( is_cell(c) );
if ( v == NULL )
v = create_vertex();
Vertex_handle v0 = c->vertex(0);
Vertex_handle v1 = c->vertex(1);
Vertex_handle v2 = c->vertex(2);
Vertex_handle v3 = c->vertex(3);
Cell_handle n1 = c->neighbor(1);
Cell_handle n2 = c->neighbor(2);
Cell_handle n3 = c->neighbor(3);
// c will be modified to have v,v1,v2,v3 as vertices
Cell_handle c3 = create_cell(v0,v1,v2,v);
Cell_handle c2 = create_cell(v0,v1,v,v3);
Cell_handle c1 = create_cell(v0,v,v2,v3);
set_adjacency(c3, c, 0, 3);
set_adjacency(c2, c, 0, 2);
set_adjacency(c1, c, 0, 1);
set_adjacency(c2, c3, 3, 2);
set_adjacency(c1, c3, 3, 1);
set_adjacency(c1, c2, 2, 1);
set_adjacency(n1, c1, n1->index(c), 1);
set_adjacency(n2, c2, n2->index(c), 2);
set_adjacency(n3, c3, n3->index(c), 3);
c->set_vertex(0,v);
v0->set_cell(c1);
v->set_cell(c);
set_number_of_vertices(number_of_vertices() +1);
return v;
}
template <class Vb, class Cb >
typename Triangulation_data_structure_3<Vb,Cb>::Vertex_handle
Triangulation_data_structure_3<Vb,Cb>::
insert_in_facet(Vertex_handle v, Cell_handle c, int i)
{ // inserts v in the facet opposite to vertex i of cell c
CGAL_triangulation_precondition( (c != NULL));
CGAL_triangulation_precondition( dimension() >= 2 );
if ( v == NULL )
v = create_vertex();
switch ( dimension() ) {
case 3:
{
CGAL_triangulation_expensive_precondition( is_cell(c) );
CGAL_triangulation_precondition( i == 0 || i == 1 ||
i == 2 || i == 3 );
// c will be modified to have v replacing vertex(i+3)
int i1,i2,i3;
if ( (i&1) == 0 ) {
i1=(i+1)&3; i2=(i+2)&3; i3=6-i-i1-i2;
}
else {
i1=(i+1)&3; i2=(i+3)&3; i3=6-i-i1-i2;
}
// i,i1,i2,i3 is well oriented
// so v will "replace" the vertices in this order
// when creating the new cells one after another from c
Vertex_handle vi=c->vertex(i);
Vertex_handle v1=c->vertex(i1);
Vertex_handle v2=c->vertex(i2);
Vertex_handle v3=c->vertex(i3);
// new cell with v in place of i1
Cell_handle nc = c->neighbor(i1);
Cell_handle cnew1 = create_cell(vi,v,v2,v3);
set_adjacency(cnew1, nc, 1, nc->index(c));
set_adjacency(cnew1, c, 3, i1);
v3->set_cell(cnew1);
// new cell with v in place of i2
nc = c->neighbor(i2);
Cell_handle cnew2 = create_cell(vi,v1,v,v3);
set_adjacency(cnew2, nc, 2, nc->index(c));
set_adjacency(cnew2, c, 3, i2);
set_adjacency(cnew1, cnew2, 2, 1);
// v replaces i3 in c
c->set_vertex(i3,v);
// other side of facet containing v
Cell_handle d = c->neighbor(i);
int j = d->index(c);
int j1=d->index(v1);// triangulation supposed to be valid
int j2=d->index(v2);
int j3=6-j-j1-j2;
// then the orientation of j,j1,j2,j3 depends on the parity
// of i-j
// new cell with v in place of j1
Cell_handle nd = d->neighbor(j1);
Cell_handle dnew1 = create_cell(d->vertex(j),v,v3,v2);
set_adjacency(dnew1, nd, 1, nd->index(d));
set_adjacency(dnew1, d, 2, j1);
set_adjacency(dnew1, cnew1, 0, 0);
// new cell with v in place of j2
nd = d->neighbor(j2);
Cell_handle dnew2 = create_cell(d->vertex(j),v1,v3,v);
set_adjacency(dnew2, nd, 3, nd->index(d));
set_adjacency(dnew2, d, 2, j2);
set_adjacency(dnew2, cnew2, 0, 0);
set_adjacency(dnew1, dnew2, 3, 1);
// v replaces i3 in d
d->set_vertex(j3,v);
v->set_cell(d);
break;
}
case 2:
{
CGAL_triangulation_expensive_precondition( is_facet(c,i) );
Cell_handle n = c->neighbor(2);
Cell_handle cnew = create_cell(c->vertex(0),c->vertex(1),v,NULL);
set_adjacency(cnew, n, 2, n->index(c));
set_adjacency(cnew, c, 0, 2);
c->vertex(0)->set_cell(cnew);
n = c->neighbor(1);
Cell_handle dnew = create_cell(c->vertex(0),v,c->vertex(2),NULL);
set_adjacency(dnew, n, 1, n->index(c));
set_adjacency(dnew, c, 0, 1);
set_adjacency(dnew, cnew, 2, 1);
c->set_vertex(0,v);
v->set_cell(c);
break;
}
}
set_number_of_vertices(number_of_vertices() +1);
return v;
}
// end insert_in_facet
template <class Vb, class Cb >
typename Triangulation_data_structure_3<Vb,Cb>::Vertex_handle
Triangulation_data_structure_3<Vb,Cb>::
insert_in_edge(Vertex_handle v, Cell_handle c, int i, int j)
// inserts v in the edge of cell c with vertices i and j
{
CGAL_triangulation_precondition( c != NULL );
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 );
if ( v == NULL )
v = create_vertex();
switch ( dimension() ) {
case 3:
{
CGAL_triangulation_expensive_precondition( is_cell(c) );
CGAL_triangulation_precondition( i>=0 && i<=3 && j>=0 && j<=3 );
std::vector<Cell_handle > cells;
std::vector<Facet> facets;
cells.reserve(32);
facets.reserve(64);
const Vertex_handle vi=c->vertex(i);
const Vertex_handle vj=c->vertex(j);
Cell_circulator ccir = incident_cells(c, i, j);
do {
Cell_handle cc = ccir->handle();
cells.push_back(cc);
facets.push_back(Facet(cc, cc->index(vi)));
facets.push_back(Facet(cc, cc->index(vj)));
++ccir;
} while (ccir->handle() != c);
star_hole_3(v, facets.begin(), facets.end(), cells.begin(), cells.end());
break;
}
case 2:
{
CGAL_triangulation_expensive_precondition( is_edge(c,i,j) );
int k=3-i-j; // index of the third vertex of the facet
Cell_handle d = c->neighbor(k);
int kd = d->index(c);
int id = d->index(c->vertex(i));
int jd = d->index(c->vertex(j));
Cell_handle cnew = create_cell();
cnew->set_vertex(i,c->vertex(i));
c->vertex(i)->set_cell(cnew);
cnew->set_vertex(j,v);
cnew->set_vertex(k,c->vertex(k));
c->set_vertex(i,v);
Cell_handle dnew = create_cell();
dnew->set_vertex(id,d->vertex(id));
// d->vertex(id)->cell() is cnew OK
dnew->set_vertex(jd,v);
dnew->set_vertex(kd,d->vertex(kd));
d->set_vertex(id,v);
Cell_handle nj = c->neighbor(j);
set_adjacency(cnew, c, i, j);
set_adjacency(cnew, nj, j, nj->index(c));
nj = d->neighbor(jd);
set_adjacency(dnew, d, id, jd);
set_adjacency(dnew, nj, jd, nj->index(d));
set_adjacency(cnew, dnew, k, kd);
v->set_cell(cnew);
break;
}
case 1:
{
CGAL_triangulation_expensive_precondition( is_edge(c,i,j) );
Cell_handle cnew = create_cell(v,c->vertex(1),NULL,NULL);
c->vertex(1)->set_cell(cnew);
c->set_vertex(1,v);
set_adjacency(cnew, c->neighbor(0), 0, 1);
set_adjacency(cnew, c, 1, 0);
v->set_cell(cnew);
break;
}
}
set_number_of_vertices(number_of_vertices() +1);
return v;
}// end insert_in_edge
template <class Vb, class Cb >
typename Triangulation_data_structure_3<Vb,Cb>::Vertex_handle
Triangulation_data_structure_3<Vb,Cb>::
insert_increase_dimension(Vertex_handle v, // new vertex
Vertex_handle star,
bool reorient)
// star = vertex from which we triangulate the facet of the
// incremented dimension
// ( geometrically : star = infinite vertex )
// = Null only used to insert the 1st vertex (dimension -2 to dimension -1)
// changes the dimension
// if (reorient) the orientation of the cells is modified
{
CGAL_triangulation_precondition( dimension() < 3);
if ( v == NULL )
v = create_vertex();
int dim = dimension();
if (dim != -2) {
CGAL_triangulation_precondition( star != NULL );
// In this case, this precondition is not relatively expensive.
CGAL_triangulation_precondition( is_vertex(star) );
}
// this is set now, so that it becomes allowed to reorient
// new facets or cells by iterating on them (otherwise the
// dimension is too small)
set_number_of_vertices( number_of_vertices()+1 );
set_dimension( dimension()+1 );
switch ( dim ) {
case -2:
// insertion of the first vertex
// ( geometrically : infinite vertex )
{
Cell_handle c = create_cell( v, NULL, NULL, NULL);
v->set_cell(c);
break;
}
case -1:
// insertion of the second vertex
// ( geometrically : first finite vertex )
{
Cell_handle d = create_cell( v, NULL, NULL, NULL);
v->set_cell(d);
set_adjacency(d, star->cell(), 0, 0);
break;
}
case 0:
// insertion of the third vertex
// ( geometrically : second finite vertex )
{
Cell_handle c = star->cell();
Cell_handle d = c->neighbor(0);
if (reorient) {
c->set_vertex(0,d->vertex(0));
c->set_vertex(1,star);
d->set_vertex(1,d->vertex(0));
d->set_vertex(0,v);
set_adjacency(c, d, 1, 0);
Cell_handle e = create_cell( star, v, NULL, NULL);
set_adjacency(e, d, 0, 1);
set_adjacency(e, c, 1, 0);
}
else {
c->set_vertex(1,d->vertex(0));
d->set_vertex(1,v);
d->set_neighbor(1,c);
Cell_handle e = create_cell( v, star, NULL, NULL);
set_adjacency(e, c, 0, 1);
set_adjacency(e, d, 1, 0);
}
v->set_cell(d);
break;
}
case 1:
// general case : 4th vertex ( geometrically : 3rd finite vertex )
// degenerate cases geometrically : 1st non collinear vertex
{
Cell_handle c = star->cell();
int i = c->index(star); // i== 0 or 1
int j = (1-i);
Cell_handle d = c->neighbor(j);
c->set_vertex(2,v);
Cell_handle e = c->neighbor(i);
Cell_handle cnew = c;
Cell_handle enew=NULL;
while( e != d ){
enew = create_cell( );
enew->set_vertex(i,e->vertex(j));
enew->set_vertex(j,e->vertex(i));
enew->set_vertex(2,star);
set_adjacency(enew, cnew, i, j);
// false at the first iteration of the loop where it should
// be neighbor 2
// it is corrected after the loop
set_adjacency(enew, e, 2, 2);
// neighbor j will be set during next iteration of the loop
e->set_vertex(2,v);
e = e->neighbor(i);
cnew = enew;
}
d->set_vertex(2,v);
set_adjacency(enew, d, j, 2);
// corrections for star->cell() :
c = star->cell();
c->set_neighbor(2,c->neighbor(i)->neighbor(2));
c->set_neighbor(j,d);
v->set_cell(d);
if (reorient) {
// reorientation of all the cells
for (Facet_iterator fit = facets_begin(); fit != facets_end(); ++fit)
change_orientation((*fit).first);
}
break;
}
case 2:
// general case : 5th vertex ( geometrically : 4th finite vertex )
// degenerate cases : geometrically 1st non coplanar vertex
{
// used to store the new cells, in order to be able to traverse only
// them to find the missing neighbors.
std::vector<Cell_handle > new_cells;
new_cells.reserve(16);
Cell_iterator it = cells_begin();
// allowed since the dimension has already been set to 3
v->set_cell(&(*it)); // ok since there is at least one ``cell''
for(; it != cells_end(); ++it) {
// Here we must be careful since we create_cells in a loop controlled
// by an iterator. So we first take care of the cells newly created
// by the following test :
if (it->neighbor(0) == NULL)
continue;
it->set_vertex(3,v);
if ( ! it->has_vertex(star) ) {
Cell_handle cnew = create_cell( it->vertex(0), it->vertex(2),
it->vertex(1), star);
set_adjacency(cnew, it->handle(), 3, 3);
new_cells.push_back(cnew);
}
}
// traversal of the new cells only, to add missing neighbors
for(typename std::vector<Cell_handle>::iterator ncit = new_cells.begin();
ncit != new_cells.end(); ++ncit) {
Cell_handle n = (*ncit)->neighbor(3); // opposite to star
for ( int i=0; i<3; i++ ) {
int j;
if ( i==0 ) j=0;
else j=3-i; // vertex 1 and vertex 2 are always switched when
// creating a new cell (see above)
Cell_handle c = n->neighbor(i)->neighbor(3);
if ( c != NULL ) {
// i.e. star is not a vertex of n->neighbor(i)
(*ncit)->set_neighbor(j, c);
// opposite relation will be set when ncit arrives on c
// this avoids to look for the correct index
// and to test whether *ncit already has neighbor i
}
else {
// star is a vertex of n->neighbor(i)
set_adjacency(*ncit, n->neighbor(i), j, 3);//neighbor opposite to v
}
}
}
// reorientation of all the cells
if (reorient)
for(it = cells_begin(); it != cells_end(); ++it)
change_orientation(it->handle());
}
}// end switch
return v;
}
template <class Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
incident_cells(Vertex_handle v, std::set<Cell_handle> & cells,
Cell_handle c) const
{
CGAL_triangulation_precondition( v != NULL );
CGAL_triangulation_expensive_precondition( 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 Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
incident_vertices(Vertex_handle v, std::set<Vertex_handle> & vertices,
Cell_handle c) const
{
CGAL_triangulation_precondition( v != NULL );
CGAL_triangulation_expensive_precondition( is_vertex(v) );
if ( number_of_vertices() < 2 )
return;
if ( c == NULL )
c = v->cell();
else
CGAL_triangulation_precondition( c->has_vertex(v) );
int d = dimension();
int j;
int found = 0;
for ( j=0; j <= d; j++ ) {
if ( j != c->index(v) ) {
if ( vertices.find( c->vertex(j) ) == vertices.end() )
vertices.insert( c->vertex(j) );
else
found++; // c->vertex(j) was already found
}
}
if ( found == 3 )
return; // c was already visited
for ( j=0; j <= d; j++ )
if ( j != c->index(v) )
incident_vertices( v, vertices, c->neighbor(j) );
}
template <class Vb, class Cb >
bool
Triangulation_data_structure_3<Vb,Cb>::
is_valid(bool verbose, int level ) const
{
switch ( dimension() ) {
case 3:
{
int vertex_count;
if ( ! count_vertices(vertex_count,verbose,level) )
return false;
if ( number_of_vertices() != vertex_count ) {
if (verbose)
std::cerr << "wrong number of vertices" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
int cell_count;
if ( ! count_cells(cell_count,verbose,level) )
return false;
int edge_count;
if ( ! count_edges(edge_count,verbose,level) )
return false;
int facet_count;
if ( ! count_facets(facet_count,verbose,level) )
return false;
// Euler relation
if ( cell_count - facet_count + edge_count - vertex_count != 0 ) {
if (verbose)
std::cerr << "Euler relation unsatisfied" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 2:
{
int vertex_count;
if ( ! count_vertices(vertex_count,verbose,level) )
return false;
if ( number_of_vertices() != vertex_count ) {
if (verbose)
std::cerr << "false number of vertices" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
int edge_count;
if ( ! count_edges(edge_count,verbose,level) )
return false;
// Euler for edges
if ( edge_count != 3 * vertex_count - 6 ) {
if (verbose)
std::cerr << "Euler relation unsatisfied - edges/vertices"
<< std::endl;
CGAL_triangulation_assertion(false);
return false;
}
int facet_count;
if ( ! count_facets(facet_count,verbose,level) )
return false;
// Euler for facets
if ( facet_count != 2 * vertex_count - 4 ) {
if (verbose)
std::cerr << "Euler relation unsatisfied - facets/vertices"
<< std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 1:
{
int vertex_count;
if ( ! count_vertices(vertex_count,verbose,level) )
return false;
if ( number_of_vertices() != vertex_count ) {
if (verbose)
std::cerr << "false number of vertices" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
int edge_count;
if ( ! count_edges(edge_count,verbose,level) )
return false;
// Euler for edges
if ( edge_count != vertex_count ) {
if (verbose)
std::cerr << "false number of edges" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 0:
{
if ( number_of_vertices() < 2 ) {
if (verbose)
std::cerr << "less than 2 vertices but dimension 0" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
// no break; continue
}
case -1:
{
if ( number_of_vertices() < 1 ) {
if (verbose)
std::cerr << "no vertex but dimension -1" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
// vertex count
int vertex_count;
if ( ! count_vertices(vertex_count,verbose,level) )
return false;
if ( number_of_vertices() != vertex_count ) {
if (verbose)
std::cerr << "false number of vertices" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
} // end switch
if (verbose)
std::cerr << "valid data structure" << std::endl;
return true;
}
template <class Vb, class Cb >
typename Triangulation_data_structure_3<Vb,Cb>::Vertex_handle
Triangulation_data_structure_3<Vb,Cb>::
copy_tds(const Tds & tds, Vertex_handle vert )
// returns the new vertex corresponding to vert in the new tds
{
CGAL_triangulation_expensive_precondition( vert == NULL
|| tds.is_vertex(vert) );
clear();
int n = tds.number_of_vertices();
set_number_of_vertices(n);
set_dimension(tds.dimension());
if (n == 0)
return vert;
// Create 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
std::vector<Vertex_handle> TV(n);
int i = 0;
for (Vertex_iterator vit = tds.vertices_begin();
vit != tds.vertices_end(); ++vit)
TV[i++] = vit->handle();
CGAL_triangulation_assertion( i == n );
std::sort(TV.begin(), TV.end(),
Vertex_tds_compare_order_of_creation<Vertex_handle>());
std::map< Vertex_handle, Vertex_handle > V;
std::map< Cell_handle, Cell_handle > F;
for (i=0; i <= n-1; i++) {
V[ TV[i] ] = create_vertex();
*V[ TV[i] ] = *TV[i];
}
// Create the cells.
for (Cell_iterator cit = tds.cell_container().begin();
cit != tds.cells_end(); ++cit) {
F[cit->handle()] = create_cell(cit->handle());
F[cit->handle()]->set_vertices(V[cit->vertex(0)],
V[cit->vertex(1)],
V[cit->vertex(2)],
V[cit->vertex(3)]);
}
// Link the vertices to a cell.
for (Vertex_iterator vit2 = tds.vertices_begin();
vit2 != tds.vertices_end(); ++vit2)
V[&(*vit2)]->set_cell( F[vit2->cell()] );
// Hook neighbor pointers of the cells.
for (Cell_iterator cit2 = tds.cell_container().begin();
cit2 != tds.cells_end(); ++cit2) {
for (int j = 0; j < 4; j++)
F[&(*cit2)]->set_neighbor(j, F[cit2->neighbor(j)] );
}
CGAL_triangulation_postcondition( is_valid() );
return (vert != NULL) ? V[vert] : (Vertex_handle) NULL;
}
template <class Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
swap(Tds & tds)
{
// tds and *this are supposed to be valid
std::swap(_dimension, tds._dimension);
std::swap(_number_of_vertices, tds._number_of_vertices);
cell_container().swap(tds.cell_container());
vertex_container().swap(tds.vertex_container());
}
template <class Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
clear()
{
cell_container().clear();
vertex_container().clear();
set_number_of_vertices(0);
set_dimension(-2);
}
template <class Vb, class Cb >
void
Triangulation_data_structure_3<Vb,Cb>::
clear_cells_only()
{
cell_container().clear();
}
template <class Vb, class Cb >
bool
Triangulation_data_structure_3<Vb,Cb>::
count_vertices(int & i, bool verbose, int level) const
// counts AND checks the validity
{
i = 0;
for (Vertex_iterator it = vertices_begin(); it != vertices_end(); ++it) {
if ( ! it->is_valid(verbose,level) ) {
if (verbose)
std::cerr << "invalid vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
++i;
}
return true;
}
template <class Vb, class Cb >
bool
Triangulation_data_structure_3<Vb,Cb>::
count_facets(int & i, bool verbose, int level) const
// counts but does not check
{
i = 0;
for (Facet_iterator it = facets_begin(); it != facets_end(); ++it) {
if ( ! (*it).first->is_valid(dimension(),verbose, level) ) {
if (verbose)
std::cerr << "invalid facet" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
++i;
}
return true;
}
template <class Vb, class Cb >
bool
Triangulation_data_structure_3<Vb,Cb>::
count_edges(int & i, bool verbose, int level) const
// counts but does not check
{
i = 0;
for (Edge_iterator it = edges_begin(); it != edges_end(); ++it) {
if ( ! (*it).first->is_valid(dimension(),verbose, level) ) {
if (verbose)
std::cerr << "invalid edge" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
++i;
}
return true;
}
template <class Vb, class Cb >
bool
Triangulation_data_structure_3<Vb,Cb>::
count_cells(int & i, bool verbose, int level) const
// counts AND checks the validity
{
i = 0;
for (Cell_iterator it = cells_begin(); it != cells_end(); ++it) {
if ( ! it->is_valid(dimension(),verbose, level) ) {
if (verbose)
std::cerr << "invalid cell" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
++i;
}
return true;
}
CGAL_END_NAMESPACE
#endif // CGAL_TRIANGULATION_DATA_STRUCTURE_3_H
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