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cgal/Triangulation/include/CGAL/Delaunay_triangulation.h

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// Copyright (c) 2009 INRIA Sophia-Antipolis (France),
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s) : Samuel Hornus
#ifndef CGAL_DELAUNAY_COMPLEX_H
#define CGAL_DELAUNAY_COMPLEX_H
#include <CGAL/Triangulation.h>
#include <CGAL/Dimension.h>
#include <CGAL/Default.h>
#include <algorithm>
namespace CGAL {
template< typename DCTraits, typename _TDS = Default >
class Delaunay_triangulation
: public Triangulation<DCTraits,
typename Default::Get<_TDS, Triangulation_data_structure<
typename DCTraits::Dimension,
Triangulation_vertex<DCTraits>,
Triangulation_full_cell<DCTraits> >
>::type >
{
typedef typename DCTraits::Dimension Maximal_dimension_;
typedef typename Default::Get<_TDS, Triangulation_data_structure<
Maximal_dimension_,
Triangulation_vertex<DCTraits>,
Triangulation_full_cell<DCTraits> >
>::type TDS;
typedef Triangulation<DCTraits, TDS> Base;
typedef Delaunay_triangulation<DCTraits, _TDS> Self;
typedef typename DCTraits::Side_of_oriented_sphere_d
Side_of_oriented_sphere_d;
typedef typename DCTraits::Orientation_d Orientation_d;
//*** Side_of_oriented_subsphere_d ***
using Base::Flat_orientation_d;
using Base::Construct_flat_orientation_d;
typedef typename DCTraits::In_flat_side_of_oriented_sphere_d In_flat_side_of_oriented_sphere_d;
// Wrapper
struct Side_of_oriented_subsphere_d
{
boost::optional<Flat_orientation_d>* fop;
Construct_flat_orientation_d cfo;
In_flat_side_of_oriented_sphere_d ifsoos;
Side_of_oriented_subsphere_d(
boost::optional<Flat_orientation_d>& x,
Construct_flat_orientation_d const&y,
In_flat_side_of_oriented_sphere_d const&z)
: fop(&x), cfo(y), ifsoos(z) {}
template<class Iter>
CGAL::Orientation operator()(Iter a, Iter b, const Point & p)const
{
if(!*fop)
*fop=cfo(a,b);
return ifsoos(fop->get(),a,b,p);
}
};
public: // PUBLIC NESTED TYPES
typedef DCTraits Geom_traits;
typedef typename Base::Triangulation_ds Triangulation_ds;
typedef typename Base::Vertex Vertex;
typedef typename Base::Full_cell Full_cell;
typedef typename Base::Facet Facet;
typedef typename Base::Face Face;
typedef typename Base::Maximal_dimension Maximal_dimension;
typedef typename DCTraits::Point_d Point;
typedef typename DCTraits::Point_d Point_d;
typedef typename Base::Vertex_handle Vertex_handle;
typedef typename Base::Vertex_iterator Vertex_iterator;
typedef typename Base::Vertex_const_handle Vertex_const_handle;
typedef typename Base::Vertex_const_iterator Vertex_const_iterator;
typedef typename Base::Full_cell_handle Full_cell_handle;
typedef typename Base::Full_cell_iterator Full_cell_iterator;
typedef typename Base::Full_cell_const_handle Full_cell_const_handle;
typedef typename Base::Full_cell_const_iterator Full_cell_const_iterator;
typedef typename Base::size_type size_type;
typedef typename Base::difference_type difference_type;
typedef typename Base::Locate_type Locate_type;
protected: // DATA MEMBERS
public:
using Base::maximal_dimension;
using Base::are_incident_full_cells_valid;
using Base::coaffine_orientation_predicate;
using Base::reset_flat_orientation;
using Base::current_dimension;
//using Base::star;
//using Base::incident_full_cells;
using Base::geom_traits;
using Base::index_of_covertex;
using Base::infinite_vertex;
using Base::insert_in_hole;
using Base::insert_outside_convex_hull_1;
using Base::is_infinite;
using Base::is_valid;
using Base::locate;
using Base::points_begin;
using Base::set_neighbors;
using Base::new_full_cell;
using Base::number_of_vertices;
using Base::orientation;
using Base::tds;
using Base::reorient_full_cells;
using Base::full_cell;
using Base::full_cells_begin;
using Base::full_cells_end;
using Base::vertices_begin;
using Base::vertices_end;
// using Base::
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - UTILITIES
// A co-dimension 2 sub-simplex. called a Rotor because we can rotate
// the two "covertices" around the sub-simplex. Useful for traversing the
// boundary of a hole. NOT DOCUMENTED
typedef cpp11::tuple<Full_cell_handle, int, int> Rotor;
Full_cell_handle full_cell(const Rotor & r) const // NOT DOCUMENTED
{
return cpp11::get<0>(r);
}
int index_of_covertex(const Rotor & r) const // NOT DOCUMENTED
{
return cpp11::get<1>(r);
}
int index_of_second_covertex(const Rotor & r) const // NOT DOCUMENTED
{
return cpp11::get<2>(r);
}
Rotor rotate_rotor(Rotor & r) // NOT DOCUMENTED...
{
int opposite = full_cell(r)->mirror_index(index_of_covertex(r));
Full_cell_handle s = full_cell(r)->neighbor(index_of_covertex(r));
int new_second = s->index(full_cell(r)->vertex(index_of_second_covertex(r)));
return Rotor(s, new_second, opposite);
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - CREATION
Delaunay_triangulation(const int dim, const Geom_traits k = Geom_traits())
: Base(dim, k)
{
}
~Delaunay_triangulation() {}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ACCESS
// Not Documented
Side_of_oriented_subsphere_d side_of_oriented_subsphere_predicate() const
{
return Side_of_oriented_subsphere_d (
flat_orientation_,
geom_traits().construct_flat_orientation_d_object(),
geom_traits().in_flat_side_of_oriented_sphere_d_object()
);
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS
Full_cell_handle remove(Vertex_handle);
Full_cell_handle remove(const Point & p, Full_cell_handle hint = Full_cell_handle())
{
Locate_type lt;
Face f(maximal_dimension());
Facet ft;
Full_cell_handle s = locate(p, lt, f, ft, hint);
if( Base::ON_VERTEX == lt )
{
return remove(s->vertex(f.index(0)));
}
return Full_cell_handle();
}
template< typename ForwardIterator >
void remove(ForwardIterator start, ForwardIterator end)
{
while( start != end )
remove(*start++);
}
// Not documented
void remove_decrease_dimension(Vertex_handle);
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - INSERTIONS
template< typename ForwardIterator >
size_type insert(ForwardIterator start, ForwardIterator end)
{
size_type n = number_of_vertices();
std::vector<Point> points(start, end);
spatial_sort(points.begin(), points.end(), geom_traits());
Full_cell_handle hint;
for( typename std::vector<Point>::const_iterator p = points.begin(); p != points.end(); ++p )
{
hint = insert(*p, hint)->full_cell();
}
return number_of_vertices() - n;
}
Vertex_handle insert(const Point &, const Locate_type, const Face &, const Facet &, const Full_cell_handle);
Vertex_handle insert(const Point & p, const Full_cell_handle start = Full_cell_handle())
{
Locate_type lt;
Face f(maximal_dimension());
Facet ft;
Full_cell_handle s = locate(p, lt, f, ft, start);
return insert(p, lt, f, ft, s);
}
Vertex_handle insert(const Point & p, const Vertex_handle hint)
{
CGAL_assertion( Vertex_handle() != hint );
return insert(p, hint->full_cell());
}
Vertex_handle insert_outside_affine_hull(const Point &);
Vertex_handle insert_in_conflicting_cell(const Point &, const Full_cell_handle);
// - - - - - - - - - - - - - - - - - - - - - - - - - GATHERING CONFLICTING SIMPLICES
bool is_in_conflict(const Point &, Full_cell_const_handle) const;
template< class OrientationPredicate >
Oriented_side perturbed_side_of_positive_sphere(const Point &,
Full_cell_const_handle, const OrientationPredicate &) const;
template< typename OutputIterator >
Facet compute_conflict_zone(const Point &, const Full_cell_handle, OutputIterator) const;
template < typename OrientationPredicate, typename SideOfOrientedSpherePredicate >
class Conflict_predicate
{
const Self & dc_;
const Point & p_;
const OrientationPredicate & ori_;
const SideOfOrientedSpherePredicate & side_of_s_;
int cur_dim_;
public:
Conflict_predicate(
const Self & dc,
const Point & p,
const OrientationPredicate & ori,
const SideOfOrientedSpherePredicate & side)
: dc_(dc), p_(p), ori_(ori), side_of_s_(side), cur_dim_(dc.current_dimension()) {}
inline
bool operator()(Full_cell_const_handle s) const
{
bool ok;
if( ! dc_.is_infinite(s) )
{
Oriented_side side = side_of_s_(dc_.points_begin(s), dc_.points_begin(s) + cur_dim_ + 1, p_);
if( ON_POSITIVE_SIDE == side )
ok = true;
else if( ON_NEGATIVE_SIDE == side )
ok = false;
else
ok = ON_POSITIVE_SIDE == dc_.perturbed_side_of_positive_sphere<OrientationPredicate>(p_, s, ori_);
}
else
{
/*int i=s->index( dc_.infinite_vertex() );
Point p_inf= s->vertex(i)->point();
s->vertex(i)->set_point(p_); // set temporarily position of infinity to p_
Orientation o = ori_(dc_.points_begin(s), dc_.points_begin(s) + cur_dim_ + 1);
s->vertex(i)->set_point(p_inf); // restore position of infinity */
typedef typename Base::Point_const_iterator Point_const_iterator;
typedef typename Base::Point_equality_predicate Point_equality_predicate;
Point_equality_predicate pred( dc_.infinite_vertex()->point() );
Substitute_iterator< Point_const_iterator, Point_equality_predicate >
begin( dc_.points_begin(s), pred, p_),
end ( dc_.points_begin(s)+ (cur_dim_+1), pred, p_);
Orientation o = ori_( begin, end);
if( POSITIVE == o )
ok = true;
else if( o == NEGATIVE )
ok = false;
else
ok = (*this)(s->neighbor( s->index( dc_.infinite_vertex() ) ));
}
return ok;
}
};
template < typename ConflictPredicate >
class Conflict_traversal_predicate
{
const Self & dc_;
const ConflictPredicate & pred_;
public:
Conflict_traversal_predicate(const Self & dc, const ConflictPredicate & pred)
: dc_(dc), pred_(pred)
{}
inline
bool operator()(const Facet & f) const
{
return pred_(dc_.full_cell(f)->neighbor(dc_.index_of_covertex(f)));
}
};
private:
// Some internal types to shorten notation
using Base::Coaffine_orientation_d;
using Base::flat_orientation_;
typedef Conflict_predicate<Coaffine_orientation_d, Side_of_oriented_subsphere_d>
Conflict_pred_in_subspace;
typedef Conflict_predicate<Orientation_d, Side_of_oriented_sphere_d>
Conflict_pred_in_fullspace;
typedef Conflict_traversal_predicate<Conflict_pred_in_subspace>
Conflict_traversal_pred_in_subspace;
typedef Conflict_traversal_predicate<Conflict_pred_in_fullspace>
Conflict_traversal_pred_in_fullspace;
// This is used in the |remove(v)| member function to manage sets of Full_cell_handles
template< typename FCH >
struct Full_cell_set : public std::vector<FCH>
{
typedef std::vector<FCH> Base_set;
using Base_set::begin;
using Base_set::end;
void make_searchable()
{ // sort the full cell handles
std::sort(begin(), end());
}
bool contains(const FCH & fch) const
{
return std::binary_search(begin(), end(), fch);
}
bool contains_1st_and_not_2nd(const FCH & fst, const FCH & snd) const
{
return ( ! contains(snd) ) && ( contains(fst) );
}
};
};
// = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
// FUNCTIONS THAT ARE MEMBER METHODS:
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - REMOVALS
template< typename DCTraits, typename TDS >
typename Delaunay_triangulation<DCTraits, TDS>::Full_cell_handle
Delaunay_triangulation<DCTraits, TDS>
::remove( Vertex_handle v )
{
CGAL_precondition( ! is_infinite(v) );
CGAL_expensive_precondition( is_vertex(v) );
// THE CASE cur_dim == 0
if( 0 == current_dimension() )
{
remove_decrease_dimension(v);
return Full_cell_handle();
}
else if( 1 == current_dimension() )
{ // THE CASE cur_dim == 1
if( 2 == number_of_vertices() )
{
remove_decrease_dimension(v);
return Full_cell_handle();
}
Full_cell_handle left = v->full_cell();
if( is_infinite(left) && left->neighbor(0)->index(left) == 0 ) // we are on the infinite right.
left = left->neighbor(0);
if( 0 == left->index(v) )
left = left->neighbor(1);
CGAL_assertion( 1 == left->index(v) );
Full_cell_handle right = left->neighbor(0);
if( ! is_infinite(right) )
{
tds().associate_vertex_with_full_cell(left, 1, right->vertex(1));
set_neighbors(left, 0, right->neighbor(0), right->mirror_index(0));
}
else
{
tds().associate_vertex_with_full_cell(left, 1, left->vertex(0));
tds().associate_vertex_with_full_cell(left, 0, infinite_vertex());
set_neighbors(left, 0, left->neighbor(1), left->mirror_index(1));
set_neighbors(left, 1, right->neighbor(1), right->mirror_index(1));
}
tds().delete_vertex(v);
tds().delete_full_cell(right);
return left;
}
// THE CASE cur_dim >= 2
// Gather the finite vertices sharing an edge with |v|
typedef Full_cell_set<Full_cell_handle> Simplices;
Simplices simps;
std::back_insert_iterator<Simplices> out(simps);
tds().incident_full_cells(v, out);
typedef std::set<Vertex_handle> Vertex_set;
Vertex_set verts;
Vertex_handle vh;
for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
for( int i = 0; i <= current_dimension(); ++i )
{
vh = (*it)->vertex(i);
if( is_infinite(vh) )
continue;
if( vh == v )
continue;
verts.insert(vh);
}
// After gathering finite neighboring vertices, create their Dark Delaunay triangulation
typedef Triangulation_vertex<Geom_traits, Vertex_handle> Dark_vertex_base;
typedef Triangulation_full_cell<Geom_traits,
internal::Triangulation::Dark_full_cell_data<Self> > Dark_full_cell_base;
typedef Triangulation_data_structure<Maximal_dimension, Dark_vertex_base, Dark_full_cell_base> Dark_tds;
typedef Delaunay_triangulation<DCTraits, Dark_tds> Dark_triangulation;
typedef typename Dark_triangulation::Face Dark_face;
typedef typename Dark_triangulation::Facet Dark_facet;
typedef typename Dark_triangulation::Vertex_handle Dark_v_handle;
typedef typename Dark_triangulation::Full_cell_handle Dark_s_handle;
Dark_triangulation dark_side(maximal_dimension());
Dark_s_handle dark_s;
Dark_v_handle dark_v;
typedef std::map<Vertex_handle, Dark_v_handle> Vertex_map;
Vertex_map light_to_dark;
typename Vertex_set::iterator vit = verts.begin();
while( vit != verts.end() )
{
dark_v = dark_side.insert((*vit)->point(), dark_s);
dark_s = dark_v->full_cell();
dark_v->data() = *vit;
light_to_dark[*vit] = dark_v;
++vit;
}
if( dark_side.current_dimension() != current_dimension() )
{
CGAL_assertion( dark_side.current_dimension() + 1 == current_dimension() );
// Here, the finite neighbors of |v| span a affine subspace of
// dimension one less than the current dimension. Two cases are possible:
if( (size_type)(verts.size() + 1) == number_of_vertices() )
{
remove_decrease_dimension(v);
return Full_cell_handle();
}
else
{ // |v| is strictly outside the convex hull of the rest of the points. This is an
// easy case: first, modify the finite full_cells, then, delete the infinite ones.
// We don't even need the Dark triangulation.
Simplices infinite_simps;
{
Simplices finite_simps;
for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
if( is_infinite(*it) )
infinite_simps.push_back(*it);
else
finite_simps.push_back(*it);
simps.swap(finite_simps);
} // now, simps only contains finite simplices
// First, modify the finite full_cells:
for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
{
int v_idx = (*it)->index(v);
tds().associate_vertex_with_full_cell(*it, v_idx, infinite_vertex());
if( v_idx != 0 )
{
// we must put the infinite vertex at index 0.
// OK, now with the new convention that the infinite vertex
// does not have to be at index 0, this is not necessary,
// but still, I prefer to keep this piece of code here. [-- Samuel Hornus]
(*it)->swap_vertices(0, v_idx);
// Now, we preserve the positive orientation of the full_cell
(*it)->swap_vertices(current_dimension() - 1, current_dimension());
}
}
// Make the handles to infinite full cells searchable
infinite_simps.make_searchable();
// Then, modify the neighboring relation
for( typename Simplices::iterator it = simps.begin(); it != simps.end(); ++it )
{
for( int i = 1; i <= current_dimension(); ++i )
{
(*it)->vertex(i)->set_full_cell(*it);
Full_cell_handle n = (*it)->neighbor(i);
// Was |n| a finite full cell prior to removing |v| ?
if( ! infinite_simps.contains(n) )
continue;
int n_idx = n->index(v);
set_neighbors(*it, i, n->neighbor(n_idx), n->neighbor(n_idx)->index(n));
}
}
Full_cell_handle ret_s;
// Then, we delete the infinite full_cells
for( typename Simplices::iterator it = infinite_simps.begin(); it != infinite_simps.end(); ++it )
tds().delete_full_cell(*it);
tds().delete_vertex(v);
return simps.front();
}
}
else // From here on, dark_side.current_dimension() == current_dimension()
{
dark_side.infinite_vertex()->data() = infinite_vertex();
light_to_dark[infinite_vertex()] = dark_side.infinite_vertex();
}
// Now, compute the conflict zone of v->point() in
// the dark side. This is precisely the set of full_cells
// that we have to glue back into the light side.
Dark_face dark_f(dark_side.maximal_dimension());
Dark_facet dark_ft;
typename Dark_triangulation::Locate_type lt;
dark_s = dark_side.locate(v->point(), lt, dark_f, dark_ft);
CGAL_assertion( lt != Dark_triangulation::ON_VERTEX
&& lt != Dark_triangulation::OUTSIDE_AFFINE_HULL );
// |ret_s| is the full_cell that we return
Dark_s_handle dark_ret_s = dark_s;
Full_cell_handle ret_s;
typedef Full_cell_set<Dark_s_handle> Dark_full_cells;
Dark_full_cells conflict_zone;
std::back_insert_iterator<Dark_full_cells> dark_out(conflict_zone);
dark_ft = dark_side.compute_conflict_zone(v->point(), dark_s, dark_out);
// Make the dark simplices in the conflict zone searchable
conflict_zone.make_searchable();
// THE FOLLOWING SHOULD MAYBE GO IN TDS.
// Here is the plan:
// 1. Pick any Facet from boundary of the light zone
// 2. Find corresponding Facet on boundary of dark zone
// 3. stitch.
// 1. Build a facet on the boudary of the light zone:
Full_cell_handle light_s = *simps.begin();
Facet light_ft(light_s, light_s->index(v));
// 2. Find corresponding Dark_facet on boundary of the dark zone
Dark_full_cells dark_incident_s;
for( int i = 0; i <= current_dimension(); ++i )
{
if( index_of_covertex(light_ft) == i )
continue;
Dark_v_handle dark_v = light_to_dark[full_cell(light_ft)->vertex(i)];
dark_incident_s.clear();
dark_out = std::back_inserter(dark_incident_s);
dark_side.tds().incident_full_cells(dark_v, dark_out);
for( typename Dark_full_cells::iterator it = dark_incident_s.begin(); it != dark_incident_s.end(); ++it )
{
(*it)->data().count_ += 1;
}
}
for( typename Dark_full_cells::iterator it = dark_incident_s.begin(); it != dark_incident_s.end(); ++it )
{
if( current_dimension() != (*it)->data().count_ )
continue;
if( ! conflict_zone.contains(*it) )
continue;
// We found a full_cell incident to the dark facet corresponding to the light facet |light_ft|
int ft_idx = 0;
while( light_s->has_vertex( (*it)->vertex(ft_idx)->data() ) )
++ft_idx;
dark_ft = Dark_facet(*it, ft_idx);
break;
}
// Pre-3. Now, we are ready to traverse both boundary and do the stiching.
// But first, we create the new full_cells in the light triangulation,
// with as much adjacency information as possible.
// Create new full_cells with vertices
for( typename Dark_full_cells::iterator it = conflict_zone.begin(); it != conflict_zone.end(); ++it )
{
Full_cell_handle new_s = new_full_cell();
(*it)->data().light_copy_ = new_s;
for( int i = 0; i <= current_dimension(); ++i )
tds().associate_vertex_with_full_cell(new_s, i, (*it)->vertex(i)->data());
if( dark_ret_s == *it )
ret_s = new_s;
}
// Setup adjacencies inside the hole
for( typename Dark_full_cells::iterator it = conflict_zone.begin(); it != conflict_zone.end(); ++it )
{
Full_cell_handle new_s = (*it)->data().light_copy_;
for( int i = 0; i <= current_dimension(); ++i )
if( conflict_zone.contains((*it)->neighbor(i)) )
tds().set_neighbors(new_s, i, (*it)->neighbor(i)->data().light_copy_, (*it)->mirror_index(i));
}
// 3. Stitch
simps.make_searchable();
typedef std::queue<std::pair<Facet, Dark_facet> > Queue;
Queue q;
q.push(std::make_pair(light_ft, dark_ft));
dark_s = dark_side.full_cell(dark_ft);
int dark_i = dark_side.index_of_covertex(dark_ft);
// mark dark_ft as visited:
// TODO try by marking with Dark_v_handle (vertex)
dark_s->neighbor(dark_i)->set_neighbor(dark_s->mirror_index(dark_i), Dark_s_handle());
while( ! q.empty() )
{
std::pair<Facet, Dark_facet> p = q.front();
q.pop();
light_ft = p.first;
dark_ft = p.second;
light_s = full_cell(light_ft);
int light_i = index_of_covertex(light_ft);
dark_s = dark_side.full_cell(dark_ft);
int dark_i = dark_side.index_of_covertex(dark_ft);
Full_cell_handle light_n = light_s->neighbor(light_i);
set_neighbors(dark_s->data().light_copy_, dark_i, light_n, light_s->mirror_index(light_i));
for( int di = 0; di <= current_dimension(); ++di )
{
if( di == dark_i )
continue;
int li = light_s->index(dark_s->vertex(di)->data());
Rotor light_r(light_s, li, light_i);
typename Dark_triangulation::Rotor dark_r(dark_s, di, dark_i);
while( simps.contains(full_cell(light_r)->neighbor(index_of_covertex(light_r))) )
light_r = rotate_rotor(light_r);
while( conflict_zone.contains(dark_side.full_cell(dark_r)->neighbor(dark_side.index_of_covertex(dark_r))) )
dark_r = dark_side.rotate_rotor(dark_r);
Dark_s_handle dark_ns = dark_side.full_cell(dark_r);
int dark_ni = dark_side.index_of_covertex(dark_r);
Full_cell_handle light_ns = full_cell(light_r);
int light_ni = index_of_covertex(light_r);
// mark dark_r as visited:
// TODO try by marking with Dark_v_handle (vertex)
Dark_s_handle outside = dark_ns->neighbor(dark_ni);
Dark_v_handle mirror = dark_ns->mirror_vertex(dark_ni, current_dimension());
int dn = outside->index(mirror);
if( Dark_s_handle() == outside->neighbor(dn) )
continue;
outside->set_neighbor(dn, Dark_s_handle());
q.push(std::make_pair(Facet(light_ns, light_ni), Dark_facet(dark_ns, dark_ni)));
}
}
tds().delete_full_cells(simps.begin(), simps.end());
tds().delete_vertex(v);
return ret_s;
}
template< typename DCTraits, typename TDS >
void
Delaunay_triangulation<DCTraits, TDS>
::remove_decrease_dimension(Vertex_handle v)
{
CGAL_precondition( current_dimension() >= 0 );
tds().remove_decrease_dimension(v, infinite_vertex());
// reset the predicates:
reset_flat_orientation();
if( 1 <= current_dimension() )
{
// FIXME: infinite vertex is NOT at index 0 a priori.
Full_cell_handle s = infinite_vertex()->full_cell()->neighbor(0);
Orientation o = orientation(s);
CGAL_assertion( ZERO != o );
if( NEGATIVE == o )
reorient_full_cells();
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - INSERTIONS
template< typename DCTraits, typename TDS >
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
Delaunay_triangulation<DCTraits, TDS>
::insert(const Point & p, const Locate_type lt, const Face & f, const Facet & ft, const Full_cell_handle s)
{
switch( lt )
{
case Base::OUTSIDE_AFFINE_HULL:
return insert_outside_affine_hull(p);
break;
case Base::ON_VERTEX:
{
Vertex_handle v = s->vertex(f.index(0));
v->set_point(p);
return v;
break;
}
default:
if( 1 == current_dimension() )
{
if( Base::OUTSIDE_CONVEX_HULL == lt )
{
return insert_outside_convex_hull_1(p, s);
}
Vertex_handle v = tds().insert_in_full_cell(s);
v->set_point(p);
return v;
}
else
return insert_in_conflicting_cell(p, s);
break;
}
}
template< typename DCTraits, typename TDS >
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
Delaunay_triangulation<DCTraits, TDS>
::insert_outside_affine_hull(const Point & p)
{
// we don't use Base::insert_outside_affine_hull(...) because here, we
// also need to reset the side_of_oriented_subsphere functor.
CGAL_precondition( current_dimension() < maximal_dimension() );
Vertex_handle v = tds().insert_increase_dimension(infinite_vertex());
// reset the predicates:
reset_flat_orientation();
v->set_point(p);
if( current_dimension() >= 1 )
{
// FIXME: infinite vertex is NOT at index 0 a priori.
Full_cell_handle s = infinite_vertex()->full_cell()->neighbor(0);
Orientation o = orientation(s);
CGAL_assertion( ZERO != o );
if( NEGATIVE == o )
reorient_full_cells();
}
return v;
}
template< typename DCTraits, typename TDS >
typename Delaunay_triangulation<DCTraits, TDS>::Vertex_handle
Delaunay_triangulation<DCTraits, TDS>
::insert_in_conflicting_cell(const Point & p, const Full_cell_handle s)
{
typedef std::vector<Full_cell_handle> Full_cell_h_vector;
typedef typename Full_cell_h_vector::iterator SHV_iterator;
static Full_cell_h_vector cs; // for storing conflicting full_cells.
cs.clear();
// cs.reserve(64);
std::back_insert_iterator<Full_cell_h_vector> out(cs);
Facet ft = compute_conflict_zone(p, s, out);
return insert_in_hole(p, cs.begin(), cs.end(), ft);
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - GATHERING CONFLICTING SIMPLICES
// NOT DOCUMENTED
template< typename DCTraits, typename TDS >
template< typename OrientationPred >
Oriented_side
Delaunay_triangulation<DCTraits, TDS>
::perturbed_side_of_positive_sphere(const Point & p, Full_cell_const_handle s,
const OrientationPred & ori) const
{
CGAL_precondition_msg( ! is_infinite(s), "full cell must be finite");
CGAL_expensive_precondition( POSITIVE == orientation(s) );
typedef std::vector<const Point *> Points;
Points points(current_dimension() + 2);
int i(0);
for( ; i <= current_dimension(); ++i )
points[i] = &(s->vertex(i)->point());
points[i] = &p;
std::sort(points.begin(), points.end(),
internal::Triangulation::Compare_points_for_perturbation<Self>(*this));
typename Points::const_reverse_iterator cut_pt = points.rbegin();
Points test_points;
while( cut_pt != points.rend() )
{
if( &p == *cut_pt )
// because the full_cell "s" is assumed to be positively oriented
return ON_NEGATIVE_SIDE; // we consider |p| to lie outside the sphere
test_points.clear();
typename Base::Point_const_iterator spit = points_begin(s);
int adjust_sign = -1;
for( i = 0; i < current_dimension(); ++i )
{
if( &(*spit) == *cut_pt )
{
++spit;
adjust_sign = (((current_dimension() + i) % 2) == 0) ? -1 : +1;
}
test_points.push_back(&(*spit));
++spit;
}
test_points.push_back(&p);
typedef typename CGAL::Iterator_project<typename Points::iterator,
internal::Triangulation::Point_from_pointer<Self>,
const Point &, const Point *> Point_pointer_iterator;
Orientation ori_value = ori(
Point_pointer_iterator(test_points.begin()),
Point_pointer_iterator(test_points.end()));
if( ZERO != ori_value )
return Oriented_side( - adjust_sign * ori_value );
++cut_pt;
}
CGAL_assertion(false); // we should never reach here
return ON_NEGATIVE_SIDE;
}
template< typename DCTraits, typename TDS >
bool
Delaunay_triangulation<DCTraits, TDS>
::is_in_conflict(const Point & p, Full_cell_const_handle s) const
{
CGAL_precondition( 2 <= current_dimension() );
if( current_dimension() < maximal_dimension() )
{
Conflict_pred_in_subspace c(*this, p, coaffine_orientation_predicate(), side_of_oriented_subsphere_predicate());
return c(s);
}
else
{
Orientation_d ori = geom_traits().orientation_d_object();
Side_of_oriented_sphere_d side = geom_traits().side_of_oriented_sphere_d_object();
Conflict_pred_in_fullspace c(*this, p, ori, side);
return c(s);
}
}
template< typename DCTraits, typename TDS >
template< typename OutputIterator >
typename Delaunay_triangulation<DCTraits, TDS>::Facet
Delaunay_triangulation<DCTraits, TDS>
::compute_conflict_zone(const Point & p, const Full_cell_handle s, OutputIterator out) const
{
CGAL_precondition( 2 <= current_dimension() );
if( current_dimension() < maximal_dimension() )
{
Conflict_pred_in_subspace c(*this, p, coaffine_orientation_predicate(), side_of_oriented_subsphere_predicate());
Conflict_traversal_pred_in_subspace tp(*this, c);
return tds().gather_full_cells(s, tp, out);
}
else
{
Orientation_d ori = geom_traits().orientation_d_object();
Side_of_oriented_sphere_d side = geom_traits().side_of_oriented_sphere_d_object();
Conflict_pred_in_fullspace c(*this, p, ori, side);
Conflict_traversal_pred_in_fullspace tp(*this, c);
return tds().gather_full_cells(s, tp, out);
}
}
} //namespace CGAL
#endif // CGAL_DELAUNAY_COMPLEX_H
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