dust3d/thirdparty/cgal/CGAL-5.1/include/CGAL/Triangulation_3.h

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// Copyright (c) 1999-2003 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Triangulation_3/include/CGAL/Triangulation_3.h $
// $Id: Triangulation_3.h 022b1a7 2020-07-21T15:27:49+02:00 Laurent Rineau
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion
// Clement Jamin
#ifndef CGAL_TRIANGULATION_3_H
#define CGAL_TRIANGULATION_3_H
#include <CGAL/license/Triangulation_3.h>
#include <CGAL/disable_warnings.h>
#include <CGAL/basic.h>
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
# define CGAL_PROFILE
# include <CGAL/Profile_counter.h>
#endif
#include <iostream>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <utility>
#include <stack>
#include <CGAL/Unique_hash_map.h>
#include <CGAL/triangulation_assertions.h>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/Triangulation_data_structure_3.h>
#include <CGAL/Triangulation_cell_base_3.h>
#include <CGAL/Triangulation_vertex_base_3.h>
#include <CGAL/spatial_sort.h>
#include <CGAL/Spatial_sort_traits_adapter_3.h>
#include <CGAL/iterator.h>
#include <CGAL/function_objects.h>
#include <CGAL/Iterator_project.h>
#include <CGAL/Default.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/Spatial_lock_grid_3.h>
#include <boost/bind.hpp>
#include <boost/random/linear_congruential.hpp>
#include <boost/random/uniform_smallint.hpp>
#include <boost/random/variate_generator.hpp>
#include <boost/mpl/if.hpp>
#include <boost/property_map/function_property_map.hpp>
#include <boost/unordered_map.hpp>
#include <boost/utility/result_of.hpp>
#include <boost/container/small_vector.hpp>
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
#include <CGAL/internal/info_check.h>
#include <boost/iterator/zip_iterator.hpp>
#endif
#ifndef CGAL_NO_STRUCTURAL_FILTERING
#include <CGAL/internal/Static_filters/tools.h>
#include <CGAL/Triangulation_structural_filtering_traits.h>
#include <CGAL/determinant.h>
#endif // no CGAL_NO_STRUCTURAL_FILTERING
#ifdef CGAL_LINKED_WITH_TBB
# include <tbb/scalable_allocator.h>
#endif
#define CGAL_TRIANGULATION_3_USE_THE_4_POINTS_CONSTRUCTOR
namespace CGAL {
template < class GT, class Tds = Default,
class Lock_data_structure = Default >
class Triangulation_3;
template < class GT, class Tds, class Lds > std::istream& operator>>
(std::istream& is, Triangulation_3<GT,Tds,Lds>& tr);
#ifndef CGAL_NO_STRUCTURAL_FILTERING
namespace internal {
// structural filtering is performed only for EPIC
struct Structural_filtering_3_tag {};
struct No_structural_filtering_3_tag {};
template <bool filter>
struct Structural_filtering_selector_3
{
#ifdef FORCE_STRUCTURAL_FILTERING
typedef Structural_filtering_3_tag Tag;
#else
typedef No_structural_filtering_3_tag Tag;
#endif
};
template <>
struct Structural_filtering_selector_3<true>
{
typedef Structural_filtering_3_tag Tag;
};
} // namespace internal
#endif // no CGAL_NO_STRUCTURAL_FILTERING
/************************************************
// Class Triangulation_3_base
// Two versions: Sequential (no locking) / Parallel (with locking)
************************************************/
// Sequential (without locking)
template <typename Concurrency_tag, typename Lock_data_structure_>
class Triangulation_3_base
{
public:
// If Lock_data_structure_ = Default => void
typedef typename Default::Get<
Lock_data_structure_, void>::type Lock_data_structure;
protected:
Triangulation_3_base() {}
Triangulation_3_base(Lock_data_structure *) {}
void swap(Triangulation_3_base<Concurrency_tag, Lock_data_structure_>&) {}
template <typename Vertex_triple, typename Facet>
struct Vertex_triple_Facet_map_generator
{
typedef boost::unordered_map<Vertex_triple, Facet> type;
};
template <typename Vertex_handle>
struct Vertex_handle_unique_hash_map_generator
{
typedef Unique_hash_map<Vertex_handle,
Vertex_handle,
Handle_hash_function> type;
};
public:
bool is_parallel() const
{
return false;
}
// LOCKS (no-op functions)
template <typename Point_3>
bool try_lock_point(const Point_3&, int = 0) const
{ return true; }
template <typename Vertex_handle>
bool try_lock_vertex(const Vertex_handle&, int = 0) const
{ return true; }
template <typename Cell_handle>
bool try_lock_cell(const Cell_handle&, int = 0) const
{ return true; }
template <typename Facet>
bool try_lock_facet(const Facet&, int = 0) const
{ return true; }
template <typename P3>
bool is_point_locked_by_this_thread(const P3&) const
{ return false; }
template <typename Cell_handle>
bool is_cell_locked_by_this_thread(const Cell_handle&) const
{ return false; }
void *get_lock_data_structure() const
{
return nullptr;
}
void set_lock_data_structure(void *) const {}
void unlock_all_elements() const {}
template <typename P3> void unlock_all_elements_but_one_point(const P3&) const {}
const Bbox_3 *get_bbox() const
{
return nullptr;
}
};
#ifdef CGAL_LINKED_WITH_TBB
// Parallel (with locking)
template <typename Lock_data_structure_>
class Triangulation_3_base<Parallel_tag, Lock_data_structure_>
{
public:
// If Lock_data_structure_ = Default => use Spatial_lock_grid_3
typedef typename Default::Get<
Lock_data_structure_,
Spatial_lock_grid_3<Tag_priority_blocking> >::type Lock_data_structure;
protected:
Triangulation_3_base()
: m_lock_ds(0)
{
}
Triangulation_3_base(Lock_data_structure *lock_ds)
: m_lock_ds(lock_ds)
{
}
void swap(Triangulation_3_base<Parallel_tag, Lock_data_structure_>& tr)
{
std::swap(tr.m_lock_ds, m_lock_ds);
}
template <typename Vertex_triple, typename Facet>
struct Vertex_triple_Facet_map_generator
{
typedef boost::unordered_map
<
Vertex_triple,
Facet,
boost::hash<Vertex_triple>,
std::equal_to<Vertex_triple>,
tbb::scalable_allocator<std::pair<const Vertex_triple, Facet> >
> type;
};
template <typename Vertex_handle>
struct Vertex_handle_unique_hash_map_generator
{
typedef Unique_hash_map<Vertex_handle,
Vertex_handle,
Handle_hash_function,
tbb::scalable_allocator<Vertex_handle> > type;
};
public:
bool is_parallel() const
{
return m_lock_ds != nullptr;
}
// LOCKS
template <typename Point_3>
bool try_lock_point(const Point_3& p, int lock_radius = 0) const
{
bool locked = true;
if(m_lock_ds)
{
locked = m_lock_ds->try_lock(p, lock_radius);
}
return locked;
}
template <typename Vertex_handle>
bool try_lock_vertex(const Vertex_handle& vh, int lock_radius = 0) const
{
bool locked = true;
if(m_lock_ds)
{
locked = m_lock_ds->try_lock(vh->point(), lock_radius);
}
return locked;
}
template <typename Cell_handle>
bool try_lock_cell(const Cell_handle& cell_handle, int lock_radius = 0) const
{
bool success = true;
// Lock the element area on the grid
for(int iVertex = 0 ; success && iVertex < 4 ; ++iVertex)
{
success = try_lock_vertex(cell_handle->vertex(iVertex), lock_radius);
}
return success;
}
template <typename Facet>
bool try_lock_facet(const Facet& facet, int lock_radius = 0) const
{
bool success = true;
// Lock the element area on the grid
for(int iVertex = (facet.second+1)&3 ;
success && iVertex != facet.second ; iVertex = (iVertex+1)&3)
{
success = try_lock_vertex(facet.first->vertex(iVertex), lock_radius);
}
return success;
}
template <typename P3>
bool is_point_locked_by_this_thread(const P3& p) const
{
bool locked = true;
if(m_lock_ds)
{
locked = m_lock_ds->is_locked_by_this_thread(p);
}
return locked;
}
template <typename Cell_handle>
bool is_cell_locked_by_this_thread(const Cell_handle& cell_handle) const
{
bool locked = true;
if(m_lock_ds)
{
for(int iVertex = 0 ; locked && iVertex < 4 ; ++iVertex)
{
locked = m_lock_ds->is_locked_by_this_thread(
cell_handle->vertex(iVertex)->point());
}
}
return locked;
}
Lock_data_structure *get_lock_data_structure() const
{
return m_lock_ds;
}
void set_lock_data_structure(Lock_data_structure *lock_ds) const
{
m_lock_ds = lock_ds;
}
void unlock_all_elements() const
{
if(m_lock_ds)
m_lock_ds->unlock_all_points_locked_by_this_thread();
}
template <typename P3>
void unlock_all_elements_but_one_point(const P3& point) const
{
if(m_lock_ds)
m_lock_ds->unlock_all_tls_locked_locations_but_one_point(point);
}
const Bbox_3 *get_bbox() const
{
return &m_lock_ds->get_bbox();
}
protected:
mutable Lock_data_structure *m_lock_ds;
};
#endif // CGAL_LINKED_WITH_TBB
/************************************************
*
* Triangulation_3 class
*
************************************************/
template < class GT, class Tds_, class Lock_data_structure_ >
class Triangulation_3
: public Triangulation_3_base<
// Get Concurrency_tag from TDS
typename Default::Get<Tds_,
Triangulation_data_structure_3<
Triangulation_vertex_base_3<GT>,
Triangulation_cell_base_3<GT> >
>::type::Concurrency_tag,
Lock_data_structure_>,
public Triangulation_utils_3
{
friend std::istream& operator>> <>
(std::istream& is, Triangulation_3<GT,Tds_,Lock_data_structure_>& tr);
typedef typename Default::Get<Tds_,
Triangulation_data_structure_3 <
Triangulation_vertex_base_3<GT>,
Triangulation_cell_base_3<GT> > >::type Tds;
typedef Triangulation_3<GT, Tds_, Lock_data_structure_> Self;
typedef Triangulation_3_base<typename Tds::Concurrency_tag,
Lock_data_structure_> Base;
public:
typedef typename Base::Lock_data_structure Lock_data_structure;
typedef Tds Triangulation_data_structure;
typedef GT Geom_traits;
typedef typename GT::Segment_3 Segment;
typedef typename GT::Triangle_3 Triangle;
typedef typename GT::Tetrahedron_3 Tetrahedron;
// point types
typedef typename GT::Point_3 Point_3;
typedef typename Tds::Vertex::Point Point;
typedef typename Tds::Concurrency_tag Concurrency_tag;
typedef typename Tds::Vertex Vertex;
typedef typename Tds::Cell Cell;
typedef typename Tds::Facet Facet;
typedef typename Tds::Edge Edge;
typedef typename Tds::size_type size_type;
typedef typename Tds::difference_type difference_type;
typedef typename Tds::Vertex_handle Vertex_handle;
typedef typename Tds::Cell_handle Cell_handle;
typedef typename Tds::Cell_circulator Cell_circulator;
typedef typename Tds::Facet_circulator Facet_circulator;
// Not documented, see TDS.
typedef typename Tds::Face_circulator Face_circulator;
typedef typename Tds::Cell_iterator Cell_iterator;
typedef typename Tds::Facet_iterator Facet_iterator;
typedef typename Tds::Edge_iterator Edge_iterator;
typedef typename Tds::Vertex_iterator Vertex_iterator;
typedef Cell_iterator All_cells_iterator;
typedef Facet_iterator All_facets_iterator;
typedef Edge_iterator All_edges_iterator;
typedef Vertex_iterator All_vertices_iterator;
typedef typename Tds::Cell_handles All_cell_handles;
typedef typename Tds::Vertex_handles All_vertex_handles;
typedef typename Tds::Facets All_facets;
typedef typename Tds::Edges All_edges;
typedef typename Tds::Simplex Simplex;
typedef typename GT::Construct_point_3 Construct_point_3;
private:
// This class is used to generate the Finite_*_iterators.
class Infinite_tester
{
const Self *t;
public:
Infinite_tester() {}
Infinite_tester(const Self *tr)
: t(tr) {}
bool operator()(const Vertex_iterator& v) const
{
return t->is_infinite(v);
}
bool operator()(typename std::vector<Vertex_handle>::const_iterator v) const
{
return t->is_infinite(*v);
}
bool operator()(const Cell_iterator& c) const
{
return t->is_infinite(c);
}
bool operator()(const Edge_iterator& e) const
{
return t->is_infinite(*e);
}
bool operator()(const Facet_iterator& f) const
{
return t->is_infinite(*f);
}
};
public:
// We derive in order to add a conversion to handle.
class Finite_cells_iterator
: public Filter_iterator<Cell_iterator, Infinite_tester>
{
typedef Filter_iterator<Cell_iterator, Infinite_tester> Base;
typedef Finite_cells_iterator Self;
public:
Finite_cells_iterator() : Base() {}
Finite_cells_iterator(const Base& b) : Base(b) {}
Self& operator++() { Base::operator++(); return *this; }
Self& operator--() { Base::operator--(); return *this; }
Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
operator Cell_handle() const { return Base::base(); }
};
// We derive in order to add a conversion to handle.
class Finite_vertices_iterator
: public Filter_iterator<Vertex_iterator, Infinite_tester>
{
typedef Filter_iterator<Vertex_iterator, Infinite_tester> Base;
typedef Finite_vertices_iterator Self;
public:
Finite_vertices_iterator() : Base() {}
Finite_vertices_iterator(const Base& b) : Base(b) {}
Self& operator++() { Base::operator++(); return *this; }
Self& operator--() { Base::operator--(); return *this; }
Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
operator Vertex_handle() const { return Base::base(); }
};
typedef Iterator_range<Prevent_deref<Finite_cells_iterator> > Finite_cell_handles;
typedef Iterator_range<Prevent_deref<Finite_vertices_iterator> > Finite_vertex_handles;
typedef Filter_iterator<Edge_iterator, Infinite_tester> Finite_edges_iterator;
typedef Filter_iterator<Facet_iterator, Infinite_tester> Finite_facets_iterator;
typedef Iterator_range<Finite_edges_iterator> Finite_edges;
typedef Iterator_range<Finite_facets_iterator> Finite_facets;
private:
// Auxiliary iterators for convenience
// do not use default template argument to please VC++
typedef Project_point<Vertex> Proj_point;
public:
typedef Iterator_project<Finite_vertices_iterator,
Proj_point,
const Point&,
const Point*,
std::ptrdiff_t,
std::bidirectional_iterator_tag> Point_iterator;
typedef Iterator_range<Point_iterator> Points;
// To have a back_inserter
typedef Point value_type;
typedef const value_type& const_reference;
// Tag to distinguish triangulations with weighted_points
typedef Tag_false Weighted_tag;
// Tag to distinguish periodic triangulations from others
typedef Tag_false Periodic_tag;
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
public:
template<typename P> // Point or Point_3
typename boost::result_of<Construct_point_3(P)>::type
construct_point(const P& p) const
{
return geom_traits().construct_point_3_object()(p);
}
template<typename P> // Point or Point_3
Comparison_result compare_xyz(const P& p, const P& q) const
{
return geom_traits().compare_xyz_3_object()(construct_point(p),
construct_point(q));
}
bool equal(const Point& p, const Point& q) const
{
return compare_xyz(p, q) == EQUAL;
}
template<typename P> // Point or Point_3
Orientation orientation(const P& p, const P& q, const P& r, const P& s) const
{
return geom_traits().orientation_3_object()(construct_point(p),
construct_point(q),
construct_point(r),
construct_point(s));
}
bool coplanar(const Point& p, const Point& q, const Point& r, const Point& s) const
{
return orientation(p, q, r, s) == COPLANAR;
}
template<typename P> // Point or Point_3
Orientation coplanar_orientation(const P& p, const P& q, const P& r) const
{
return geom_traits().coplanar_orientation_3_object()(construct_point(p),
construct_point(q),
construct_point(r));
}
bool collinear(const Point& p, const Point& q, const Point& r) const
{
return coplanar_orientation(p, q, r) == COLLINEAR;
}
template<typename P> // Point or Point_3
Segment construct_segment(const P& p, const P& q) const
{
return geom_traits().construct_segment_3_object()(construct_point(p),
construct_point(q));
}
template<typename P> // Point or Point_3
Triangle construct_triangle(const P& p, const P& q, const P& r) const
{
return geom_traits().construct_triangle_3_object()(construct_point(p),
construct_point(q),
construct_point(r));
}
template<typename P> // Point or Point_3
Tetrahedron construct_tetrahedron(const P& p, const P& q, const P& r, const P& s) const
{
return geom_traits().construct_tetrahedron_3_object()(construct_point(p),
construct_point(q),
construct_point(r),
construct_point(s));
}
enum COLLINEAR_POSITION
{
BEFORE,
SOURCE,
MIDDLE,
TARGET,
AFTER
};
COLLINEAR_POSITION collinear_position(const Point& s, const Point& p, const Point& t) const
{
// (s,t) defines a line, p is on that line.
// Depending on the position of p wrt s and t, returns :
// --------------- s ---------------- t --------------
// BEFORE SOURCE MIDDLE TARGET AFTER
CGAL_triangulation_precondition(!equal(s, t));
CGAL_triangulation_precondition(collinear(s, p, t));
Comparison_result ps = compare_xyz(p, s);
if(ps == EQUAL)
return SOURCE;
Comparison_result st = compare_xyz(s, t);
if(ps == st)
return BEFORE;
Comparison_result pt = compare_xyz(p, t);
if(pt == EQUAL)
return TARGET;
if(pt == st)
return MIDDLE;
return AFTER;
}
// used as functor in std::sort in Delaunay and regular triangulations
struct Perturbation_order
{
bool operator()(const Point* p, const Point* q) const {
return t->compare_xyz(*p, *q) == SMALLER;
}
Perturbation_order(const Self *tr)
: t(tr) {}
const Self *t;
};
void init_tds()
{
infinite = _tds.insert_increase_dimension();
}
void init_tds(const Point& p0, const Point& p1, const Point& p2, const Point& p3)
{
Vertex_handle v0, v1, v2, v3;
infinite = _tds.insert_first_finite_cell(v0, v1, v2, v3, infinite);
v0->set_point(p0);
v1->set_point(p1);
v2->set_point(p2);
v3->set_point(p3);
}
void init_tds(const Point& p0, const Point& p1,
const Point& p2, const Point& p3,
Vertex_handle& vh0, Vertex_handle& vh1,
Vertex_handle& vh2, Vertex_handle& vh3)
{
infinite = _tds.insert_first_finite_cell(vh0, vh1, vh2, vh3, infinite);
vh0->set_point(p0);
vh1->set_point(p1);
vh2->set_point(p2);
vh3->set_point(p3);
}
public:
// CONSTRUCTORS
Triangulation_3(const GT& gt = GT(), Lock_data_structure *lock_ds = nullptr)
: Base(lock_ds), _tds(), _gt(gt)
{
init_tds();
}
Triangulation_3(Lock_data_structure *lock_ds, const GT& gt = GT())
: Base(lock_ds), _tds(), _gt(gt)
{
init_tds();
}
// copy constructor duplicates vertices and cells
Triangulation_3(const Triangulation_3& tr)
: Base(tr.get_lock_data_structure()), _gt(tr._gt)
{
infinite = _tds.copy_tds(tr._tds, tr.infinite);
CGAL_triangulation_expensive_postcondition(*this == tr);
}
Triangulation_3(Triangulation_3&& tr) = default;
~Triangulation_3() = default;
template < typename InputIterator >
Triangulation_3(InputIterator first, InputIterator last,
const GT& gt = GT(), Lock_data_structure *lock_ds = nullptr)
: Base(lock_ds), _gt(gt)
{
init_tds();
insert(first, last);
}
// Create the 3D triangulation of p0, p1, p3 and p4
// Precondition: p0, p1, p3 and p4 MUST BE positively oriented
Triangulation_3(const Point& p0, const Point& p1,
const Point& p3, const Point& p4,
const GT& gt = GT(), Lock_data_structure *lock_ds = nullptr)
: Base(lock_ds), _gt(gt)
{
CGAL_triangulation_precondition(orientation(p0, p1, p3, p4) == POSITIVE);
init_tds(p0, p1, p3, p4);
}
void clear()
{
_tds.clear();
init_tds();
}
Triangulation_3& operator=(const Triangulation_3& tr)
{
Triangulation_3 copy(tr);
swap(copy);
return *this;
}
Triangulation_3& operator=(Triangulation_3&& tr) = default;
// HELPING FUNCTIONS
void swap(Triangulation_3& tr) noexcept
{
using std::swap;
swap(tr._gt, _gt);
swap(tr.infinite, infinite);
_tds.swap(tr._tds);
Base::swap(tr);
}
//ACCESS FUNCTIONS
const GT& geom_traits() const { return _gt; }
const Tds& tds() const { return _tds; }
Tds& tds() { return _tds; }
int dimension() const { return _tds.dimension(); }
size_type number_of_finite_cells() const;
size_type number_of_cells() const;
size_type number_of_finite_facets() const;
size_type number_of_facets() const;
size_type number_of_finite_edges() const;
size_type number_of_edges() const;
size_type number_of_vertices() const // number of finite vertices
{ return _tds.number_of_vertices()-1; }
Vertex_handle infinite_vertex() const { return infinite; }
void set_infinite_vertex(Vertex_handle v) { infinite = v; }
Cell_handle infinite_cell() const
{
CGAL_triangulation_assertion(infinite_vertex()->cell()->has_vertex(infinite_vertex()));
return infinite_vertex()->cell();
}
// 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());
}
template<typename P> // can be 'Point' or 'Point_3'
Tetrahedron tetrahedron(const Facet& f, const P& p) const
{
const Cell_handle c = f.first;
const int index = f.second;
const P& fp1 = point(c, (index + 1)&3);
const P& fp2 = point(c, (index + 2)&3);
const P& fp3 = point(c, (index + 3)&3);
return construct_tetrahedron(construct_point(p),
construct_point(fp1),
construct_point(fp2),
construct_point(fp3));
}
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);
}
void set_point(Cell_handle c, int i, const Point& p)
{
CGAL_triangulation_precondition(dimension() >= 0);
CGAL_triangulation_precondition(i >= 0 && i <= dimension());
CGAL_triangulation_precondition(! is_infinite(c->vertex(i)));
c->vertex(i)->point() = p;
}
const Point& point(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension() >= 0);
CGAL_triangulation_precondition(i >= 0 && i <= dimension());
CGAL_triangulation_precondition(! is_infinite(c->vertex(i)));
return c->vertex(i)->point();
}
void set_point(Vertex_handle v, const Point& p)
{
CGAL_triangulation_precondition(dimension() >= 0);
CGAL_triangulation_precondition(! is_infinite(v));
v->point() = p;
}
const Point& point(Vertex_handle v) const
{
CGAL_triangulation_precondition(number_of_vertices() > 0);
CGAL_triangulation_precondition(! is_infinite(v));
return v->point();
}
// 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;
#ifdef CGAL_NO_STRUCTURAL_FILTERING
Cell_handle
locate(const Point& p,
Locate_type& lt, int& li, int& lj,
Cell_handle start = Cell_handle(),
bool *could_lock_zone = nullptr) const;
#else // no CGAL_NO_STRUCTURAL_FILTERING
# ifndef CGAL_T3_STRUCTURAL_FILTERING_MAX_VISITED_CELLS
# define CGAL_T3_STRUCTURAL_FILTERING_MAX_VISITED_CELLS 2500
# endif // no CGAL_T3_STRUCTURAL_FILTERING_MAX_VISITED_CELLS
public:
Cell_handle inexact_locate(const Point& p,
Cell_handle start = Cell_handle(),
int max_num_cells = CGAL_T3_STRUCTURAL_FILTERING_MAX_VISITED_CELLS,
bool *could_lock_zone = nullptr) const;
protected:
Cell_handle exact_locate(const Point& p,
Locate_type& lt,
int& li, int& lj,
Cell_handle start,
bool *could_lock_zone = nullptr) const;
Cell_handle generic_locate(const Point& p,
Locate_type& lt,
int& li, int& lj,
Cell_handle start,
internal::Structural_filtering_3_tag,
bool *could_lock_zone = nullptr) const
{
Cell_handle ch = inexact_locate(
p, start, CGAL_T3_STRUCTURAL_FILTERING_MAX_VISITED_CELLS, could_lock_zone);
if(could_lock_zone && *could_lock_zone == false)
return ch; // = Cell_handle() here
else
return exact_locate(p, lt, li, lj, ch, could_lock_zone);
}
Cell_handle generic_locate(const Point& p,
Locate_type& lt,
int& li, int& lj,
Cell_handle start,
internal::No_structural_filtering_3_tag,
bool *could_lock_zone = nullptr) const
{
return exact_locate(p, lt, li, lj, start, could_lock_zone);
}
public:
Orientation
inexact_orientation(const Point& p, const Point& q,
const Point& r, const Point& s) const
{
// So that this code works well with Lazy_kernel
internal::Static_filters_predicates::Get_approx<Point> get_approx;
const double px = to_double(get_approx(p).x());
const double py = to_double(get_approx(p).y());
const double pz = to_double(get_approx(p).z());
const double qx = to_double(get_approx(q).x());
const double qy = to_double(get_approx(q).y());
const double qz = to_double(get_approx(q).z());
const double rx = to_double(get_approx(r).x());
const double ry = to_double(get_approx(r).y());
const double rz = to_double(get_approx(r).z());
const double sx = to_double(get_approx(s).x());
const double sy = to_double(get_approx(s).y());
const double sz = to_double(get_approx(s).z());
const double pqx = qx - px;
const double pqy = qy - py;
const double pqz = qz - pz;
const double prx = rx - px;
const double pry = ry - py;
const double prz = rz - pz;
const double psx = sx - px;
const double psy = sy - py;
const double psz = sz - pz;
const double det = determinant(pqx, pqy, pqz,
prx, pry, prz,
psx, psy, psz);
if(det > 0)
return POSITIVE;
if(det < 0)
return NEGATIVE;
return ZERO;
}
public:
Cell_handle locate(const Point& p,
Locate_type& lt, int& li, int& lj,
Cell_handle start = Cell_handle(),
bool *could_lock_zone = nullptr) const
{
typedef Triangulation_structural_filtering_traits<Geom_traits> TSFT;
typedef typename internal::Structural_filtering_selector_3<
TSFT::Use_structural_filtering_tag::value >::Tag Should_filter_tag;
return generic_locate(p, lt, li, lj, start, Should_filter_tag(), could_lock_zone);
}
#endif // no CGAL_NO_STRUCTURAL_FILTERING
Cell_handle locate(const Point& p,
Cell_handle start = Cell_handle(),
bool *could_lock_zone = nullptr) const
{
Locate_type lt;
int li, lj;
return locate(p, lt, li, lj, start, could_lock_zone);
}
Cell_handle locate(const Point& p,
Locate_type& lt, int& li, int& lj, Vertex_handle hint,
bool *could_lock_zone = nullptr) const
{
return locate(p, lt, li, lj,
hint == Vertex_handle() ? infinite_cell() : hint->cell(),
could_lock_zone);
}
Cell_handle locate(const Point& p, Vertex_handle hint, bool *could_lock_zone = nullptr) const
{
return locate(p, hint == Vertex_handle() ? infinite_cell() : hint->cell(),
could_lock_zone);
}
// 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);
}
// Functions forwarded from TDS.
int mirror_index(Cell_handle c, int i) const { return _tds.mirror_index(c, i); }
Vertex_handle mirror_vertex(Cell_handle c, int i) const { return _tds.mirror_vertex(c, i); }
Facet mirror_facet(Facet f) const { return _tds.mirror_facet(f);}
// MODIFIERS
bool flip(const 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);
}
bool flip(Cell_handle c, int i);
void flip_flippable(const Facet& f) { flip_flippable(f.first, f.second); }
void flip_flippable(Cell_handle c, int i);
bool flip(const 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);
}
bool flip(Cell_handle c, int i, int j);
void flip_flippable(const Edge& e) { flip_flippable(e.first, e.second, e.third); }
void flip_flippable(Cell_handle c, int i, int j);
//INSERTION
Vertex_handle insert(const Point& p, Vertex_handle hint) {
return insert(p, hint == Vertex_handle() ? infinite_cell() : hint->cell());
}
Vertex_handle insert(const Point& p, Cell_handle start = Cell_handle());
Vertex_handle insert(const Point& p, Locate_type lt, Cell_handle c,
int li, int lj);
//protected: // internal methods
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Cell_handle start = Cell_handle());
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Vertex_handle hint);
template <class OutputItCells>
Vertex_handle insert_and_give_new_cells(const Point& p,
Locate_type lt,
Cell_handle c, int li, int lj,
OutputItCells fit);
template < class Conflict_tester, class Hidden_points_visitor >
inline Vertex_handle insert_in_conflict(const Point& p,
Locate_type lt,
Cell_handle c, int li, int lj,
const Conflict_tester& tester,
Hidden_points_visitor& hider,
bool *could_lock_zone = nullptr);
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
template < class InputIterator >
std::ptrdiff_t insert(InputIterator first, InputIterator last,
typename boost::enable_if<
boost::is_convertible<
typename std::iterator_traits<InputIterator>::value_type,
Point
>
>::type* = nullptr)
#else
template < class InputIterator >
std::ptrdiff_t insert(InputIterator first, InputIterator last)
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
{
size_type n = number_of_vertices();
Vertex_handle hint;
for(; first != last; ++first)
hint = insert(*first, hint);
return number_of_vertices() - n;
}
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
protected:
//top stands for tuple-or-pair
template <class Info>
const Point& top_get_first(const std::pair<Point,Info>& pair) const { return pair.first; }
template <class Info>
const Info& top_get_second(const std::pair<Point,Info>& pair) const { return pair.second; }
template <class Info>
const Point& top_get_first(const boost::tuple<Point,Info>& tuple) const { return boost::get<0>(tuple); }
template <class Info>
const Info& top_get_second(const boost::tuple<Point,Info>& tuple) const { return boost::get<1>(tuple); }
template <class Tuple_or_pair,class InputIterator>
std::ptrdiff_t insert_with_info(InputIterator first, InputIterator last)
{
size_type n = number_of_vertices();
std::vector<std::size_t> indices;
std::vector<Point> points;
std::vector<typename Triangulation_data_structure::Vertex::Info> infos;
for(InputIterator it=first;it!=last;++it)
{
Tuple_or_pair value=*it;
points.push_back(top_get_first(value));
infos.push_back(top_get_second(value));
}
Vertex_handle hint;
for(std::size_t i=0; i < points.size(); ++i)
{
hint = insert(points[i], hint);
if(hint != Vertex_handle())
hint->info() = infos[i];
}
return number_of_vertices() - n;
}
public:
template < class InputIterator >
std::ptrdiff_t insert(InputIterator first, InputIterator last,
typename boost::enable_if<
boost::is_convertible<
typename std::iterator_traits<InputIterator>::value_type,
std::pair<Point, typename internal::Info_check<
typename Triangulation_data_structure::Vertex>::type>
> >::type* =NULL)
{
return insert_with_info< std::pair<Point,typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type> >(first,last);
}
template <class InputIterator_1,class InputIterator_2>
std::ptrdiff_t
insert(boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > first,
boost::zip_iterator< boost::tuple<InputIterator_1,InputIterator_2> > last,
typename boost::enable_if<
boost::mpl::and_<
boost::is_convertible< typename std::iterator_traits<InputIterator_1>::value_type, Point >,
boost::is_convertible< typename std::iterator_traits<InputIterator_2>::value_type, typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type >
>
>::type* =NULL)
{
return insert_with_info< boost::tuple<Point, typename internal::Info_check<
typename Triangulation_data_structure::Vertex>::type> >(first,last);
}
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
Vertex_handle insert_in_cell(const Point& p, Cell_handle c);
Vertex_handle insert_in_facet(const Point& p, Cell_handle c, int i);
Vertex_handle insert_in_facet(const Point& p, const Facet& f) {
return insert_in_facet(p, f.first, f.second);
}
Vertex_handle insert_in_edge(const Point& p, Cell_handle c, int i, int j);
Vertex_handle insert_in_edge(const Point& p, const Edge& e) {
return insert_in_edge(p, e.first, e.second, e.third);
}
Vertex_handle insert_outside_convex_hull(const Point& p, Cell_handle c);
Vertex_handle insert_outside_affine_hull(const Point& p);
template <class CellIt>
Vertex_handle insert_in_hole(const Point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i)
{
// Some geometric preconditions should be tested...
Vertex_handle v = _tds.insert_in_hole(cell_begin, cell_end, begin, i);
v->set_point(p);
return v;
}
template <class CellIt>
Vertex_handle insert_in_hole(const Point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i, Vertex_handle newv)
{
// Some geometric preconditions should be tested...
newv->set_point(p);
return _tds.insert_in_hole(cell_begin, cell_end, begin, i, newv);
}
// Internal function, cells should already be marked.
template <class CellIt>
Vertex_handle _insert_in_hole(const Point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i)
{
// Some geometric preconditions should be tested...
Vertex_handle v = _tds._insert_in_hole(cell_begin, cell_end, begin, i);
v->set_point(p);
return v;
}
// Internal function, cells should already be marked.
template <class Cells, class Facets>
Vertex_handle _insert_in_small_hole(const Point& p,
const Cells& cells,
const Facets& facets )
{
Vertex_handle v = _tds._insert_in_small_hole(cells, facets);
v->set_point(p);
return v;
}
// Internal function, cells should already be marked.
template <class CellIt>
Vertex_handle _insert_in_hole(const Point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i, Vertex_handle newv)
{
// Some geometric preconditions should be tested...
newv->set_point(p);
return _tds._insert_in_hole(cell_begin, cell_end, begin, i, newv);
}
protected:
template < class InputIterator >
bool does_repeat_in_range(InputIterator first, InputIterator beyond) const;
template < class InputIterator >
bool infinite_vertex_in_range(InputIterator first, InputIterator beyond) const;
// - c is the current cell, which must be in conflict.
// - tester is the function object that tests if a cell is in conflict.
template <class Conflict_test,
class OutputIteratorBoundaryFacets,
class OutputIteratorCells,
class OutputIteratorInternalFacets>
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets>
find_conflicts(Cell_handle d,
const Conflict_test& tester,
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets> it,
bool *could_lock_zone = nullptr,
const Facet *this_facet_must_be_in_the_cz = nullptr,
bool *the_facet_is_in_its_cz = nullptr) const
{
CGAL_triangulation_precondition(dimension()>=2);
if(the_facet_is_in_its_cz)
*the_facet_is_in_its_cz = false;
if(could_lock_zone)
{
*could_lock_zone = true;
if(!this->try_lock_cell(d))
{
*could_lock_zone = false;
return it;
}
}
CGAL_triangulation_precondition(tester(d));
// To store the boundary cells, in case we need to rollback
typedef boost::container::small_vector<Cell_handle,64> SV;
SV sv;
std::stack<Cell_handle, SV > cell_stack(sv);
cell_stack.push(d);
d->tds_data().mark_in_conflict();
*it.second++ = d;
do
{
Cell_handle c = cell_stack.top();
cell_stack.pop();
// For each neighbor cell
for(int i=0; i<dimension()+1; ++i)
{
Cell_handle test = c->neighbor(i);
// "test" is either in the conflict zone,
// either facet-adjacent to the CZ
if(test->tds_data().is_in_conflict())
{
Facet f(c, i); // Internal facet.
// Is it the facet where're looking for?
if(this_facet_must_be_in_the_cz && the_facet_is_in_its_cz &&
f == *this_facet_must_be_in_the_cz)
{
*the_facet_is_in_its_cz = true;
}
if(c < test)
{
*it.third++ = f;
}
continue; // test was already in conflict.
}
if(test->tds_data().is_clear())
{
if(tester(test))
{
// "test" is in the conflict zone
if(could_lock_zone)
{
if(!this->try_lock_cell(test))
{
*could_lock_zone = false;
// Unlock
return it;
}
}
Facet f(c, i); // Internal facet.
// Is it the facet where're looking for?
if(this_facet_must_be_in_the_cz && the_facet_is_in_its_cz &&
f == *this_facet_must_be_in_the_cz)
{
*the_facet_is_in_its_cz = true;
}
if(c < test)
{
*it.third++ = f;
}
cell_stack.push(test);
test->tds_data().mark_in_conflict();
*it.second++ = test;
continue;
}
test->tds_data().mark_on_boundary();
}
Facet f(c, i); // Boundary facet.
// Is it the facet where're looking for?
if(this_facet_must_be_in_the_cz && the_facet_is_in_its_cz &&
(mirror_facet(f) == *this_facet_must_be_in_the_cz ||
f == *this_facet_must_be_in_the_cz))
{
*the_facet_is_in_its_cz = true;
}
*it.first++ = f;
}
}
while(!cell_stack.empty());
return it;
}
// This one takes a function object to recursively determine the cells in
// conflict, then calls _tds._insert_in_hole().
template < class Conflict_test >
Vertex_handle insert_conflict(Cell_handle c, const Conflict_test& tester)
{
CGAL_triangulation_precondition(dimension() >= 2);
CGAL_triangulation_precondition(c != Cell_handle());
CGAL_triangulation_precondition(tester(c));
std::vector<Cell_handle> cells;
cells.reserve(32);
Facet facet;
// Find the cells in conflict
switch(dimension())
{
case 3:
find_conflicts(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
break;
case 2:
find_conflicts(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
}
// Create the new cells and delete the old.
return _tds._insert_in_hole(cells.begin(), cells.end(),
facet.first, facet.second);
}
private:
// Here are the conflit tester function objects passed to
// insert_conflict_[23]() by insert_outside_convex_hull().
class Conflict_tester_outside_convex_hull_3
{
const Point& p;
const Self *t;
public:
Conflict_tester_outside_convex_hull_3(const Point& pt, const Self *tr)
: p(pt), t(tr)
{}
bool operator()(const Cell_handle c) const
{
Locate_type loc;
int i, j;
return t->side_of_cell(p, c, loc, i, j) == ON_BOUNDED_SIDE;
}
};
class Conflict_tester_outside_convex_hull_2
{
const Point& p;
const Self *t;
public:
Conflict_tester_outside_convex_hull_2(const Point& pt, const Self *tr)
: p(pt), t(tr)
{}
bool operator()(const Cell_handle c) const
{
Locate_type loc;
int i, j;
return t->side_of_facet(p, c, loc, i, j) == ON_BOUNDED_SIDE;
}
};
protected:
// no point being private, we might need to test whether a displacement
// decreases the dimension on others inherited triangulations
bool test_dim_down(Vertex_handle v) const;
bool test_dim_down_using_incident_cells_3(Vertex_handle v,
std::vector<Cell_handle>& incident_cells,
std::vector<Vertex_handle>& adj_vertices,
bool *could_lock_zone = nullptr) const;
// REMOVAL
template < class VertexRemover >
void remove(Vertex_handle v, VertexRemover& remover);
// Concurrency-safe version
// Pre-condition: dimension = 3
// The return value is only meaningful if *could_lock_zone = true:
// * returns true if the vertex was removed
// * returns false if the vertex wasn't removed since it would decrease
// the dimension => needs to be done sequentially
template < class VertexRemover >
bool remove(Vertex_handle v, VertexRemover& remover, bool *could_lock_zone);
template < class VertexRemover, class OutputItCells >
void remove_and_give_new_cells(Vertex_handle v, VertexRemover& remover,
OutputItCells fit);
// This function removes a batch of points at once.
// If points are grouped in cluster, the performance is increased
// compared to removing one by one.
// For now, this function is only guaranteed for Delaunay triangulations (or Regular as Delaunay).
// By doing these kind of remove followed by inserting the cluster,
// we achieve fast relocations for a batch of points (in a Delaunay triangulation).
template < class InputIterator, class VertexRemover >
size_type remove(InputIterator first, InputIterator beyond,
VertexRemover& remover);
enum REMOVE_VERTEX_STATE {CLEAR, TO_REMOVE, PROCESSED, EXTREMITY};
// MOVE
template < class VertexRemover, class VertexInserter >
Vertex_handle move_if_no_collision(Vertex_handle v, const Point& p,
VertexRemover& remover,
VertexInserter& inserter);
template < class VertexRemover, class VertexInserter >
Vertex_handle move(Vertex_handle v, const Point& p,
VertexRemover& remover, VertexInserter& inserter);
// move and give new cells
template < class VertexRemover, class VertexInserter, class OutputItCells >
Vertex_handle move_if_no_collision_and_give_new_cells(Vertex_handle v,
const Point& p,
VertexRemover& remover,
VertexInserter& inserter,
OutputItCells fit);
// This is a function better suited for tds
// but because it is not required in the model of tds
// at this time, it should be implemented here.
void flip_2D(Cell_handle f, int i)
{
CGAL_triangulation_precondition(dimension()==2);
Cell_handle n = f->neighbor(i);
int ni = this->_tds.mirror_index(f,i); // ni = n->index(f);
int cwi = (i+2)%3;
int ccwi = (i+1)%3;
int cwni = (ni+2)%3;
int ccwni = (ni+1)%3;
Vertex_handle v_cw = f->vertex(cwi);
Vertex_handle v_ccw = f->vertex(ccwi);
// bl == bottom left, tr == top right
Cell_handle tr = f->neighbor(ccwi);
int tri = this->_tds.mirror_index(f,ccwi);
Cell_handle bl = n->neighbor(ccwni);
int bli = this->_tds.mirror_index(n,ccwni);
f->set_vertex(cwi, n->vertex(ni));
n->set_vertex(cwni, f->vertex(i));
// update the neighborhood relations
this->_tds.set_adjacency(f, i, bl, bli);
this->_tds.set_adjacency(f, ccwi, n, ccwni);
this->_tds.set_adjacency(n, ni, tr, tri);
if(v_cw->cell() == f)
{
v_cw->set_cell(n);
}
if(v_ccw->cell() == n)
{
v_ccw->set_cell(f);
}
}
template < class VertexRemover, class VertexInserter >
void restore_edges_after_decrease_dimension(Vertex_handle v,
VertexRemover& remover,
VertexInserter& inserter)
{
Cell_handle fkstart = v->cell();
Cell_handle start = fkstart->neighbor(fkstart->index(v));
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover);
fill_hole_2D(hole, remover);
// make hole here will work if the link of v is a valid triangulation
// the aim here is Delaunay triangulations
// to make it more general one could have an internal function here
// to remove v without touching its handle
// This insert must be from Delaunay (or the particular trian.)
// not the basic Triangulation_3.
// Here we correct the recent triangulation (with decreased dimension) formed
// in particular here a 2D (from 3D to 2D displacement)
Vertex_handle inserted = inserter.insert(v->point(), start);
// fixing pointer
Cell_handle fc = inserted->cell(), done(fc);
std::vector<Cell_handle> faces_pt;
faces_pt.reserve(16);
do
{
faces_pt.push_back(fc);
fc = fc->neighbor((fc->index(inserted) + 1)%3);
}
while(fc != done);
std::size_t ss = faces_pt.size();
for(std::size_t k=0; k<ss; k++)
{
Cell_handle f = faces_pt[k];
int i = f->index(inserted);
f->set_vertex(i, v);
}
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
}
private:
typedef Facet Edge_2D;
typedef Triple<Vertex_handle,Vertex_handle,Vertex_handle> Vertex_triple;
typedef typename Base::template Vertex_triple_Facet_map_generator<
Vertex_triple, Facet>::type Vertex_triple_Facet_map;
typedef typename Base::template Vertex_handle_unique_hash_map_generator<
Vertex_handle>::type Vertex_handle_unique_hash_map;
Vertex_triple make_vertex_triple(const Facet& f) const;
void make_canonical_oriented_triple(Vertex_triple& t) const;
template < class VertexRemover >
VertexRemover& make_hole_2D(Vertex_handle v, std::list<Edge_2D>& hole,
VertexRemover& remover);
template < class VertexRemover >
VertexRemover& make_hole_2D(Vertex_handle v, std::list<Edge_2D>& hole,
VertexRemover& remover,
std::set<Cell_handle>& cells_set);
template < class VertexRemover >
void fill_hole_2D(std::list<Edge_2D>& hole, VertexRemover& remover);
void make_hole_3D(Vertex_handle v,
Vertex_triple_Facet_map& outer_map,
std::vector<Cell_handle>& hole);
// When the incident cells are already known
void make_hole_3D(Vertex_handle v,
const std::vector<Cell_handle>& incident_cells,
Vertex_triple_Facet_map& outer_map);
template < class VertexRemover >
VertexRemover& remove_dim_down(Vertex_handle v, VertexRemover& remover);
template < class VertexRemover >
VertexRemover& remove_1D(Vertex_handle v, VertexRemover& remover);
template < class VertexRemover >
VertexRemover& remove_2D(Vertex_handle v, VertexRemover& remover);
template < class VertexRemover >
VertexRemover& remove_3D(Vertex_handle v, VertexRemover& remover);
// Version of remove_3D if the incident cells and the adjacent vertices
// are already known
template < class VertexRemover >
VertexRemover& remove_3D(Vertex_handle v, VertexRemover& remover,
const std::vector<Cell_handle>& inc_cells,
std::vector<Vertex_handle>& adj_vertices);
template < class VertexRemover, class OutputItCells >
VertexRemover& remove_dim_down(Vertex_handle v, VertexRemover& remover,
OutputItCells fit);
template < class VertexRemover, class OutputItCells >
VertexRemover& remove_1D(Vertex_handle v, VertexRemover& remover,
OutputItCells fit);
template < class VertexRemover, class OutputItCells >
VertexRemover& remove_2D(Vertex_handle v, VertexRemover& remover,
OutputItCells fit);
template < class VertexRemover, class OutputItCells >
VertexRemover& remove_3D(Vertex_handle v, VertexRemover& remover,
OutputItCells fit);
template < class VertexRemover, class OutputItCells >
void fill_hole_2D(std::list<Edge_2D>& hole, VertexRemover& remover,
OutputItCells fit);
// They access "Self", so need to be friend.
friend class Conflict_tester_outside_convex_hull_3;
friend class Conflict_tester_outside_convex_hull_2;
friend class Infinite_tester;
friend class Finite_vertices_iterator;
friend class Finite_cells_iterator;
// remove cluster
template < class InputIterator >
void _mark_vertices_to_remove(InputIterator first, InputIterator beyond,
std::map<Vertex_handle,
REMOVE_VERTEX_STATE>& vstates) const
{
while(first != beyond) vstates[*first++] = TO_REMOVE;
}
bool _test_dim_down_cluster(std::map<Vertex_handle,
REMOVE_VERTEX_STATE>& vstates) const
{
// tests whether removing the cluster of vertices
// marked as "to remove", decreases the dimension of the triangulation
CGAL_triangulation_precondition(dimension() == 3);
int k=0;
Vertex_handle v[4];
for(Finite_vertices_iterator fit = finite_vertices_begin();
fit != finite_vertices_end(); ++fit)
{
if(vstates[fit] == TO_REMOVE)
continue;
v[k++] = fit;
if(k == 4)
{
if(!coplanar(v[0]->point(), v[1]->point(), v[2]->point(), v[3]->point()))
return false;
k--;
}
}
return k < 4;
}
template < class InputIterator, class VertexRemover >
bool _remove_cluster_3D(InputIterator first, InputIterator beyond,
VertexRemover& remover,
std::map<Vertex_handle, REMOVE_VERTEX_STATE>& vstates);
void _make_big_hole_3D(Vertex_handle v,
std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle>& hole,
std::vector<Vertex_handle>& vertices,
std::map<Vertex_handle, REMOVE_VERTEX_STATE>& vstates);
public:
//TRAVERSING : ITERATORS AND CIRCULATORS
Finite_cells_iterator finite_cells_begin() const
{
if(dimension() < 3)
return finite_cells_end();
return CGAL::filter_iterator(cells_end(), Infinite_tester(this), cells_begin());
}
Finite_cells_iterator finite_cells_end() const
{
return CGAL::filter_iterator(cells_end(), Infinite_tester(this));
}
Finite_cell_handles finite_cell_handles() const
{
return make_prevent_deref_range(finite_cells_begin(), finite_cells_end());
}
Cell_iterator cells_begin() const { return _tds.cells_begin(); }
Cell_iterator cells_end() const { return _tds.cells_end(); }
All_cells_iterator all_cells_begin() const { return _tds.cells_begin(); }
All_cells_iterator all_cells_end() const { return _tds.cells_end(); }
All_cell_handles all_cell_handles() const
{
return _tds.cell_handles();
}
Finite_vertices_iterator finite_vertices_begin() const
{
if(number_of_vertices() <= 0)
return finite_vertices_end();
return CGAL::filter_iterator(vertices_end(), Infinite_tester(this),
vertices_begin());
}
Finite_vertices_iterator finite_vertices_end() const
{
return CGAL::filter_iterator(vertices_end(), Infinite_tester(this));
}
Finite_vertex_handles finite_vertex_handles() const
{
return make_prevent_deref_range(finite_vertices_begin(), finite_vertices_end());
}
Vertex_iterator vertices_begin() const { return _tds.vertices_begin(); }
Vertex_iterator vertices_end() const { return _tds.vertices_end(); }
All_vertices_iterator all_vertices_begin() const { return _tds.vertices_begin(); }
All_vertices_iterator all_vertices_end() const { return _tds.vertices_end(); }
All_vertex_handles all_vertex_handles() const
{
return _tds.vertex_handles();
}
Finite_edges_iterator finite_edges_begin() const
{
if(dimension() < 1)
return finite_edges_end();
return CGAL::filter_iterator(edges_end(), Infinite_tester(this), edges_begin());
}
Finite_edges_iterator finite_edges_end() const
{
return CGAL::filter_iterator(edges_end(), Infinite_tester(this));
}
Finite_edges finite_edges() const
{
return Finite_edges(finite_edges_begin(),finite_edges_end());
}
Edge_iterator edges_begin() const { return _tds.edges_begin(); }
Edge_iterator edges_end() const { return _tds.edges_end(); }
All_edges_iterator all_edges_begin() const { return _tds.edges_begin(); }
All_edges_iterator all_edges_end() const { return _tds.edges_end(); }
All_edges all_edges() const
{
return _tds.edges();
}
Finite_facets_iterator finite_facets_begin() const
{
if(dimension() < 2)
return finite_facets_end();
return CGAL::filter_iterator(facets_end(), Infinite_tester(this), facets_begin());
}
Finite_facets_iterator finite_facets_end() const
{
return CGAL::filter_iterator(facets_end(), Infinite_tester(this));
}
Finite_facets finite_facets() const
{
return Finite_facets(finite_facets_begin(),finite_facets_end());
}
Facet_iterator facets_begin() const { return _tds.facets_begin(); }
Facet_iterator facets_end() const { return _tds.facets_end(); }
All_facets_iterator all_facets_begin() const { return _tds.facets_begin(); }
All_facets_iterator all_facets_end() const { return _tds.facets_end(); }
All_facets all_facets() const
{
return _tds.facets();
}
Point_iterator points_begin() const
{
return Point_iterator(finite_vertices_begin());
}
Point_iterator points_end() const
{
return Point_iterator(finite_vertices_end());
}
Points points() const
{
return Points(points_begin(),points_end());
}
// cells around an edge
Cell_circulator incident_cells(const Edge& e) const
{
return _tds.incident_cells(e);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j) const
{
return _tds.incident_cells(c, i, j);
}
Cell_circulator incident_cells(const Edge& e, Cell_handle start) const
{
return _tds.incident_cells(e, start);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j, Cell_handle start) const
{
return _tds.incident_cells(c, i, j, start);
}
// facets around an edge
Facet_circulator incident_facets(const Edge& e) const
{
return _tds.incident_facets(e);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j) const
{
return _tds.incident_facets(c, i, j);
}
Facet_circulator incident_facets(const Edge& e, const Facet& start) const
{
return _tds.incident_facets(e, start);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j, const Facet& start) const
{
return _tds.incident_facets(c, i, j, start);
}
Facet_circulator incident_facets(const Edge& e, Cell_handle start, int f) const
{
return _tds.incident_facets(e, start, f);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j, Cell_handle start, int f) const
{
return _tds.incident_facets(c, i, j, start, f);
}
// around a vertex
class Finite_filter
{
const Self* t;
public:
Finite_filter(const Self* _t): t(_t) {}
template<class T>
bool operator() (const T& e) const { return t->is_infinite(e); }
};
class Finite_filter_2D
{
const Self* t;
public:
Finite_filter_2D(const Self* _t): t(_t) {}
template<class T>
bool operator() (const T& e) const { return t->is_infinite(e); }
bool operator() (const Cell_handle c) { return t->is_infinite(c, 3); }
};
template <typename OutputIterator>
OutputIterator incident_cells(Vertex_handle v, OutputIterator cells) const
{
return _tds.incident_cells(v, cells);
}
template <typename OutputIterator>
void incident_cells_threadsafe(Vertex_handle v, OutputIterator cells) const
{
_tds.incident_cells_threadsafe(v, cells);
}
template <typename Filter, typename OutputIterator>
void incident_cells_threadsafe(Vertex_handle v,
OutputIterator cells,
const Filter& filter) const
{
_tds.incident_cells_threadsafe(v, cells, filter);
}
bool try_lock_and_get_incident_cells(Vertex_handle v, std::vector<Cell_handle>& cells) const
{
// We need to lock v individually first, to be sure v->cell() is valid
if(!this->try_lock_vertex(v))
return false;
Cell_handle d = v->cell();
if(!this->try_lock_cell(d)) // LOCK
return false;
cells.push_back(d);
d->tds_data().mark_in_conflict();
int head=0;
int tail=1;
do
{
Cell_handle c = cells[head];
for(int i=0; i<4; ++i)
{
if(c->vertex(i) == v)
continue;
Cell_handle next = c->neighbor(i);
if(!this->try_lock_cell(next)) // LOCK
{
for(Cell_handle ch : cells)
{
ch->tds_data().clear();
}
cells.clear();
return false;
}
if(! next->tds_data().is_clear())
continue;
cells.push_back(next);
++tail;
next->tds_data().mark_in_conflict();
}
++head;
}
while(head != tail);
for(Cell_handle ch : cells)
{
ch->tds_data().clear();
}
return true;
}
template <class OutputIterator>
bool try_lock_and_get_adjacent_vertices_and_cells_3(Vertex_handle v,
OutputIterator vertices,
std::vector<Cell_handle>& cells) const
{
// We need to lock v individually first, to be sure v->cell() is valid
if(!this->try_lock_vertex(v))
return false;
Cell_handle d = v->cell();
if(!this->try_lock_cell(d)) // LOCK
return false;
cells.push_back(d);
d->tds_data().mark_in_conflict();
int head=0;
int tail=1;
do
{
Cell_handle c = cells[head];
for(int i=0; i<4; ++i)
{
if(c->vertex(i) == v)
continue;
Cell_handle next = c->neighbor(i);
if(!this->try_lock_cell(next)) // LOCK
{
for(Cell_handle ch : cells)
{
ch->tds_data().clear();
}
cells.clear();
return false;
}
if(! next->tds_data().is_clear())
continue;
cells.push_back(next);
++tail;
next->tds_data().mark_in_conflict();
}
++head;
}
while(head != tail);
std::set<Vertex_handle> tmp_vertices;
for(Cell_handle ch : cells)
{
ch->tds_data().clear();
for(int i = 0; i < 4; ++i)
{
Vertex_handle w = ch->vertex(i);
if(w != v && tmp_vertices.insert(w).second)
{
*vertices = w;
}
}
}
return true;
}
template <class OutputIterator>
OutputIterator finite_incident_cells(Vertex_handle v, OutputIterator cells) const
{
if(dimension() == 2)
return _tds.incident_cells(v, cells, Finite_filter_2D(this));
return _tds.incident_cells(v, cells, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator incident_facets(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets(v, facets);
}
template <class OutputIterator>
OutputIterator finite_incident_facets(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets(v, facets, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator incident_facets_threadsafe(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets_threadsafe(v, facets);
}
template <class OutputIterator>
OutputIterator finite_incident_facets_threadsafe(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets_threadsafe(v, facets, Finite_filter(this));
}
// old name (up to CGAL 3.4)
// kept for backwards compatibility but not documented
template <class OutputIterator>
OutputIterator incident_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices);
}
// correct name
template <class OutputIterator>
OutputIterator adjacent_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices);
}
template <class OutputIterator>
OutputIterator adjacent_vertices_threadsafe(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices_threadsafe(v, vertices);
}
template <class OutputIterator>
OutputIterator adjacent_vertices_and_cells_3(Vertex_handle v, OutputIterator vertices,
std::vector<Cell_handle>& cells) const
{
return _tds.adjacent_vertices_and_cells_3(v, vertices, cells);
}
// old name (up to CGAL 3.4)
// kept for backwards compatibility but not documented
template <class OutputIterator>
OutputIterator finite_incident_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices, Finite_filter(this));
}
// correct name
template <class OutputIterator>
OutputIterator finite_adjacent_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator incident_edges(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges(v, edges);
}
template <class OutputIterator>
OutputIterator finite_incident_edges(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges(v, edges, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator incident_edges_threadsafe(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges_threadsafe(v, edges);
}
template <class OutputIterator>
OutputIterator finite_incident_edges_threadsafe(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges_threadsafe(v, edges, Finite_filter(this));
}
size_type degree(Vertex_handle v) const
{
return _tds.degree(v);
}
// 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;
//IO
template <typename Tr_src,
typename ConvertVertex,
typename ConvertCell>
std::istream& file_input(std::istream& is,
ConvertVertex convert_vertex = ConvertVertex(),
ConvertCell convert_cell = ConvertCell())
{
// 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
// If this is used for a TDS, the vertices are processed from 0 to n.
// Else, we make V[0] the infinite vertex and work from 1 to n+1.
typedef Self Triangulation;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Cell_handle Cell_handle;
typedef typename Tr_src::Vertex Vertex1;
typedef typename Tr_src::Cell Cell1;
clear();
tds().cells().clear();
std::size_t n;
int d;
if(is_ascii(is))
is >> d >> n;
else {
read(is, d);
read(is, n);
}
if(!is) return is;
tds().set_dimension(d);
std::size_t V_size = n+1;
std::vector< Vertex_handle > V(V_size);
// the infinite vertex is numbered 0
V[0] = infinite_vertex();
for (std::size_t i = 1; i < V_size; ++i) {
Vertex1 v;
if(!(is >> v)) return is;
Vertex_handle vh=tds().create_vertex( convert_vertex(v) );
V[i] = vh;
convert_vertex(v, *V[i]);
}
std::vector< Cell_handle > C;
std::size_t m;
tds().read_cells(is, V, m, C);
for (std::size_t j=0 ; j < m; j++) {
Cell1 c;
if(!(is >> c)) return is;
convert_cell(c, *C[j]);
}
CGAL_triangulation_assertion( is_valid(false) );
return is;
}
};
template < class GT, class Tds, class Lds >
std::istream& operator>> (std::istream& is, Triangulation_3<GT, Tds, Lds>& 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;
tr._tds.clear(); // infinite vertex deleted
tr.infinite = tr._tds.create_vertex();
std::size_t n;
int d;
if(is_ascii(is))
{
is >> d >> n;
}
else
{
read(is, d);
read(is, n);
}
if(!is)
return is;
tr._tds.set_dimension(d);
std::vector< Vertex_handle > V(n+1);
V[0] = tr.infinite_vertex(); // the infinite vertex is numbered 0
for(std::size_t i=1; i <= n; i++)
{
V[i] = tr._tds.create_vertex();
if(!(is >> *V[i]))
return is;
}
std::vector< Cell_handle > C;
std::size_t m;
tr._tds.read_cells(is, V, m, C);
for(std::size_t j=0 ; j < m; j++)
if(!(is >> *(C[j])))
return is;
CGAL_triangulation_assertion(tr.is_valid(false));
return is;
}
template < class GT, class Tds, class Lds >
std::ostream& operator<< (std::ostream& os, const Triangulation_3<GT, Tds, Lds>& 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::size_type size_type;
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
size_type n = tr.number_of_vertices();
if(is_ascii(os))
{
os << tr.dimension() << std::endl << n << std::endl;
}
else
{
write(os, tr.dimension());
write(os, n);
}
if(n == 0)
return os;
std::vector<Vertex_handle> TV(n+1);
size_type i = 0;
// write the vertices
for(Vertex_iterator it = tr.vertices_begin(), end = tr.vertices_end(); it != end; ++it)
TV[i++] = it;
CGAL_triangulation_assertion(i == n+1);
CGAL_triangulation_assertion(tr.is_infinite(TV[0]));
Unique_hash_map<Vertex_handle, std::size_t > 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;
}
// Asks the tds for the combinatorial information
tr.tds().print_cells(os, V);
// 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.cells_begin(), end = tr.cells_end(); it != end; ++it)
{
os << *it; // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
case 2:
{
for(Facet_iterator it = tr.facets_begin(), end = tr.facets_end(); it != end; ++it)
{
os << *((*it).first); // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
case 1:
{
for(Edge_iterator it = tr.edges_begin(), end = tr.edges_end(); it != end; ++it)
{
os << *((*it).first); // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
}
return os ;
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_finite_cells() const
{
if(dimension() < 3)
return 0;
return std::distance(finite_cells_begin(), finite_cells_end());
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_cells() const
{
return _tds.number_of_cells();
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_finite_facets() const
{
if(dimension() < 2)
return 0;
return std::distance(finite_facets_begin(), finite_facets_end());
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_facets() const
{
return _tds.number_of_facets();
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_finite_edges() const
{
if(dimension() < 1)
return 0;
return std::distance(finite_edges_begin(), finite_edges_end());
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::size_type
Triangulation_3<GT,Tds,Lds>::
number_of_edges() const
{
return _tds.number_of_edges();
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Triangle
Triangulation_3<GT,Tds,Lds>::
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(Facet(c, i)));
if((i&1)==0)
return construct_triangle(c->vertex((i+2)&3)->point(),
c->vertex((i+1)&3)->point(),
c->vertex((i+3)&3)->point());
return construct_triangle(c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point());
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Segment
Triangulation_3<GT,Tds,Lds>::
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(Edge(c, i, j)));
return construct_segment(c->vertex(i)->point(), c->vertex(j)->point());
}
template < class GT, class Tds, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
is_vertex(Vertex_handle v) const
{
return _tds.is_vertex(v);
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
is_edge(Vertex_handle u, Vertex_handle v,
Cell_handle& c, int& i, int& j) const
{
return _tds.is_edge(u, v, c, i, j);
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle& c, int& i, int& j, int& k) const
{
return _tds.is_facet(u, v, w, c, i, j, k);
}
template < class GT, class Tds, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
is_cell(Cell_handle c) const
{
return _tds.is_cell(c);
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
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
{
return _tds.is_cell(u, v, w, t, c, i, j, k, l);
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle& c) const
{
int i,j,k,l;
return _tds.is_cell(u, v, w, t, c, i, j, k, l);
}
template < class GT, class Tds, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
has_vertex(const Facet& f, Vertex_handle v) const
{
return _tds.has_vertex(f.first, f.second, v);
}
template < class GT, class Tds, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
has_vertex(Cell_handle c, int i, Vertex_handle v) const
{
return _tds.has_vertex(c, i, v);
}
template < class GT, class Tds, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
inline
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Cell_handle
Triangulation_3<GT,Tds,Lds>::
#ifdef CGAL_NO_STRUCTURAL_FILTERING
locate(const Point& p, Locate_type& lt, int& li, int& lj,
Cell_handle start, bool *could_lock_zone) const
#else
exact_locate(const Point& p, Locate_type& lt, int& li, int& lj,
Cell_handle start, bool *could_lock_zone) const
#endif
{
// Returns the (finite or infinite) cell p lies in.
// Starts at cell "start".
// 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 gives the edge of c separating p
// from the rest of the triangulation
// lt = OUTSIDE_AFFINE_HULL if p is not coplanar with the triangulation
CGAL_triangulation_expensive_assertion(start == Cell_handle() || tds().is_simplex(start));
if(could_lock_zone)
*could_lock_zone = true;
if(dimension() >= 1)
{
// Make sure we continue from here with a finite cell.
if(start == Cell_handle())
start = infinite_cell();
int ind_inf;
if(start->has_vertex(infinite, ind_inf))
start = start->neighbor(ind_inf);
}
boost::rand48 rng;
switch(dimension())
{
case 3:
{
CGAL_triangulation_precondition(start != Cell_handle());
CGAL_triangulation_precondition(! start->has_vertex(infinite));
// We implement the remembering visibility/stochastic walk.
// Remembers the previous cell to avoid useless orientation tests.
Cell_handle previous = Cell_handle();
Cell_handle c = start;
if(could_lock_zone)
{
if(!this->try_lock_cell(c))
{
*could_lock_zone = false;
return Cell_handle();
}
}
// Stores the results of the 4 orientation tests. It will be used
// at the end to decide if p lies on a face/edge/vertex/interior.
Orientation o[4];
boost::uniform_smallint<> four(0, 3);
boost::variate_generator<boost::rand48&, boost::uniform_smallint<> > die4(rng, four);
// Now treat the cell c.
bool try_next_cell = true;
while(try_next_cell)
{
try_next_cell = false;
// We know that the 4 vertices of c are positively oriented.
// So, in order to test if p is seen outside from one of c's facets,
// we just replace the corresponding point by p in the orientation
// test. We do this using the array below.
const Point* pts[4] = { &(c->vertex(0)->point()),
&(c->vertex(1)->point()),
&(c->vertex(2)->point()),
&(c->vertex(3)->point()) };
// For the remembering stochastic walk,
// we need to start trying with a random index :
int i = die4();
// For the remembering visibility walk (Delaunay and Regular only), we don't :
// int i = 0;
// for each vertex
for(int j=0; !try_next_cell && j != 4; ++j, i = (i+1)&3)
{
Cell_handle next = c->neighbor(i);
if(previous == next)
{
o[i] = POSITIVE;
}
else
{
// We temporarily put p at i's place in pts.
const Point* backup = pts[i];
pts[i] = &p;
o[i] = orientation(*pts[0], *pts[1], *pts[2], *pts[3]);
if(o[i] != NEGATIVE)
{
pts[i] = backup;
}
else
{
if(next->has_vertex(infinite, li))
{
// We are outside the convex hull.
lt = OUTSIDE_CONVEX_HULL;
return next;
}
previous = c;
c = next;
if(could_lock_zone)
{
//previous->unlock(); // DON'T do that, "c" may be in
// the same locking cell as "previous"
if(!this->try_lock_cell(c))
{
*could_lock_zone = false;
return Cell_handle();
}
}
try_next_cell = true;
}
}
} // next vertex
} // next cell
// 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) ? 0 :
(o[1] == COPLANAR) ? 1 :
(o[2] == COPLANAR) ? 2 : 3;
break;
}
case 2:
{
lt = EDGE;
li = (o[0] != COPLANAR) ? 0 :
(o[1] != COPLANAR) ? 1 : 2;
lj = (o[li+1] != COPLANAR) ? li+1 :
(o[li+2] != COPLANAR) ? li+2 : li+3;
CGAL_triangulation_assertion(collinear(p,
c->vertex(li)->point(),
c->vertex(lj)->point()));
break;
}
case 3:
{
lt = VERTEX;
li = (o[0] != COPLANAR) ? 0 :
(o[1] != COPLANAR) ? 1 :
(o[2] != COPLANAR) ? 2 : 3;
break;
}
}
return c;
}
case 2:
{
CGAL_triangulation_precondition(start != Cell_handle());
CGAL_triangulation_precondition(! start->has_vertex(infinite));
Cell_handle c = start;
boost::uniform_smallint<> three(0, 2);
boost::variate_generator<boost::rand48&, boost::uniform_smallint<> > die3(rng, three);
//first tests whether p is coplanar with the current triangulation
if(orientation(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
p) != DEGENERATE)
{
lt = OUTSIDE_AFFINE_HULL;
li = 3; // only one facet in dimension 2
return c;
}
// if p is coplanar, location in the triangulation
// only the facet numbered 3 exists in each cell
while(1)
{
int inf;
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
int i = die3();
const Point& p0 = c->vertex(i)->point();
const Point& p1 = c->vertex(ccw(i))->point();
const Point& p2 = c->vertex(cw(i))->point();
Orientation o[3];
CGAL_triangulation_assertion(coplanar_orientation(p0,p1,p2) == POSITIVE);
o[0] = coplanar_orientation(p0,p1,p);
if(o[0] == NEGATIVE)
{
c = c->neighbor(cw(i));
continue;
}
o[1] = coplanar_orientation(p1,p2,p);
if(o[1] == NEGATIVE)
{
c = c->neighbor(i);
continue;
}
o[2] = coplanar_orientation(p2,p0,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());
CGAL_triangulation_precondition(! start->has_vertex(infinite));
Cell_handle c = start;
//first tests whether p is collinear with the current triangulation
if(! collinear(p, c->vertex(0)->point(), c->vertex(1)->point()))
{
lt = OUTSIDE_AFFINE_HULL;
return c;
}
// if p is collinear, location :
while(1)
{
if(c->has_vertex(infinite))
{
// 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
switch(collinear_position(c->vertex(0)->point(), p, c->vertex(1)->point()))
{
case AFTER:
c = c->neighbor(0);
continue;
case BEFORE:
c = c->neighbor(1);
continue;
case MIDDLE:
lt = EDGE;
li = 0;
lj = 1;
return c;
case SOURCE:
lt = VERTEX;
li = 0;
return c;
case TARGET:
lt = VERTEX;
li = 1;
return c;
}
}
}
case 0:
{
Finite_vertices_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 Cell_handle();
}
default:
{
CGAL_triangulation_assertion(false);
return Cell_handle();
}
}
}
#ifndef CGAL_NO_STRUCTURAL_FILTERING
template < class Gt, class Tds, class Lds >
inline
typename Triangulation_3<Gt, Tds, Lds>::Cell_handle
Triangulation_3<Gt, Tds, Lds>::
inexact_locate(const Point& t, Cell_handle start, int n_of_turns,
bool *could_lock_zone) const
{
CGAL_triangulation_expensive_assertion(start == Cell_handle() ||
tds().is_simplex(start));
if(could_lock_zone)
*could_lock_zone = true;
if(dimension() < 3)
return start;
// Make sure we continue from here with a finite cell.
if(start == Cell_handle())
start = infinite_cell();
// CJTODO: useless?
if(could_lock_zone)
{
if(!this->try_lock_cell(start))
{
*could_lock_zone = false;
return Cell_handle();
}
}
int ind_inf;
if(start->has_vertex(infinite, ind_inf))
start = start->neighbor(ind_inf);
CGAL_triangulation_precondition(start != Cell_handle());
CGAL_triangulation_precondition(! start->has_vertex(infinite));
// We implement the remembering visibility walk.
// In this phase, no need to be stochastic
// Remembers the previous cell to avoid useless orientation tests.
Cell_handle previous = Cell_handle();
Cell_handle c = start;
if(could_lock_zone)
{
if(!this->try_lock_cell(c))
{
*could_lock_zone = false;
return Cell_handle();
}
}
// Now treat the cell c.
try_next_cell:
n_of_turns--;
// We know that the 4 vertices of c are positively oriented.
// So, in order to test if p is seen outside from one of c's facets,
// we just replace the corresponding point by p in the orientation
// test. We do this using the array below.
const Point* pts[4] = { &(c->vertex(0)->point()),
&(c->vertex(1)->point()),
&(c->vertex(2)->point()),
&(c->vertex(3)->point()) };
// (non-stochastic) visibility walk
for(int i=0; i != 4; ++i)
{
Cell_handle next = c->neighbor(i);
if(previous == next) continue;
// We temporarily put p at i's place in pts.
const Point* backup = pts[i];
pts[i] = &t;
if(inexact_orientation(*pts[0], *pts[1], *pts[2], *pts[3]) != NEGATIVE)
{
pts[i] = backup;
continue;
}
if(next->has_vertex(infinite))
{
// We are outside the convex hull.
return next;
}
previous = c;
c = next;
if(could_lock_zone)
{
//previous->unlock(); // DON'T do that, "c" may be in
// the same locking cell as "previous"
if(!this->try_lock_cell(c))
{
*could_lock_zone = false;
return Cell_handle();
}
}
if(n_of_turns) goto try_next_cell;
}
return c;
}
#endif // no CGAL_NO_STRUCTURAL_FILTERING
template < class GT, class Tds, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
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 only has meaning 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, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
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(coplanar(p,p0,p1,p2));
Orientation o012 = coplanar_orientation(p0,p1,p2);
CGAL_triangulation_precondition(o012 != COLLINEAR);
Orientation o0; // edge p0 p1
Orientation o1; // edge p1 p2
Orientation o2; // edge p2 p0
if((o0 = coplanar_orientation(p0,p1,p)) == opposite(o012) ||
(o1 = coplanar_orientation(p1,p2,p)) == opposite(o012) ||
(o2 = coplanar_orientation(p2,p0,p)) == opposite(o012))
{
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 == o012) ? 2 :
(o1 == o012) ? 0 :
1;
return ON_BOUNDARY;
}
default:
{
// cannot happen
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
}
}
template < class GT, class Tds, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
side_of_facet(const Point& p,
Cell_handle c,
Locate_type& lt, int& li, int& lj) const
{
// Assumes 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 only has meaning 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).
CGAL_triangulation_precondition(dimension() == 2);
if(! is_infinite(c,3))
{
// The following precondition is useless because it is written
// in side_of_facet
// CGAL_triangulation_precondition(coplanar (p,
// c->vertex(0)->point,
// c->vertex(1)->point,
// c->vertex(2)->point));
int i_t, j_t;
Bounded_side side = side_of_triangle(p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
lt, i_t, j_t);
// We protect the following code by this test to avoid valgrind messages.
if(side == ON_BOUNDARY)
{
// 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(coplanar (p,
// c->neighbor(inf)->vertex(0)->point(),
// c->neighbor(inf)->vertex(1)->point(),
// c->neighbor(inf)->vertex(2)->point()));
int i2 = next_around_edge(inf,3);
int i1 = 3 - inf - i2;
Vertex_handle v1 = c->vertex(i1),
v2 = c->vertex(i2);
CGAL_triangulation_assertion(coplanar_orientation(v1->point(), v2->point(),
mirror_vertex(c, inf)->point()) == POSITIVE);
switch(coplanar_orientation(v1->point(), v2->point(), p))
{
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;
default: // case ZERO:
// p collinear with v1v2
int i_e;
switch(side_of_segment(p, v1->point(), v2->point(), lt, i_e))
{
// computation of the indices in the 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;
default: // case ON_UNBOUNDED_SIDE:
// p lies on the line defined by the finite edge
return ON_UNBOUNDED_SIDE;
}
}
}
template < class GT, class Tds, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
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));
switch(collinear_position(p0, p, p1))
{
case MIDDLE:
lt = EDGE;
return ON_BOUNDED_SIDE;
case SOURCE:
lt = VERTEX;
i = 0;
return ON_BOUNDARY;
case TARGET:
lt = VERTEX;
i = 1;
return ON_BOUNDARY;
default: // case BEFORE: case AFTER:
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
}
template < class GT, class Tds, class Lds >
Bounded_side
Triangulation_3<GT,Tds,Lds>::
side_of_edge(const Point& p,
Cell_handle c,
Locate_type& lt, int& li) const
{
// Assumes 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 only has meaning when ON_BOUNDED_SIDE and ON_BOUNDARY
// li refer to indices in the cell c
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);
switch(collinear_position(c->vertex(1-inf)->point(), p,
mirror_vertex(c, inf)->point()))
{
case SOURCE:
lt = VERTEX;
li = 1-inf;
return ON_BOUNDARY;
case BEFORE:
lt = EDGE;
return ON_BOUNDED_SIDE;
default: // case MIDDLE: case AFTER: case TARGET:
return ON_UNBOUNDED_SIDE;
}
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
void
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
flip(Cell_handle c, int i, int j)
{
// Flips the 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, class Lds >
void
Triangulation_3<GT,Tds,Lds>::
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, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert(const Point& p, Cell_handle start)
{
Locate_type lt;
int li, lj;
Cell_handle c = locate(p, lt, li, lj, start);
return insert(p, lt, c, li, lj);
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert(const Point& p, Locate_type lt, Cell_handle c, int li, int lj)
{
switch(lt)
{
case VERTEX:
return c->vertex(li);
case EDGE:
return insert_in_edge(p, c, li, lj);
case FACET:
return insert_in_facet(p, c, li);
case CELL:
return insert_in_cell(p, c);
case OUTSIDE_CONVEX_HULL:
return insert_outside_convex_hull(p, c);
case OUTSIDE_AFFINE_HULL:
default:
return insert_outside_affine_hull(p);
}
}
template < class GT, class Tds, class Lds >
template < class Conflict_tester, class Hidden_points_visitor >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_in_conflict(const Point& p,
Locate_type lt, Cell_handle c, int li, int /*lj*/,
const Conflict_tester& tester,
Hidden_points_visitor& hider,
bool *could_lock_zone)
{
if(could_lock_zone)
*could_lock_zone = true;
switch(dimension())
{
case 3:
{
if((lt == VERTEX) && (tester.compare_weight(c->vertex(li)->point(), p)==0))
{
return c->vertex(li);
}
// If the new point is not in conflict with its cell, it is hidden.
if(!tester.test_initial_cell(c))
{
hider.hide_point(c,p);
return Vertex_handle();
}
// Ok, we really insert the point now.
// First, find the conflict region.
boost::container::small_vector<Cell_handle,32> cells;
Facet facet;
boost::container::small_vector<Facet,32> facets;
// Parallel
if(could_lock_zone)
{
find_conflicts(c,
tester,
make_triple(std::back_inserter(facets),
std::back_inserter(cells),
Emptyset_iterator()),
could_lock_zone);
if(*could_lock_zone == false)
{
for(Cell_handle ch : cells)
{
ch->tds_data().clear();
}
for(Facet& f : facets)
{
f.first->neighbor(f.second)->tds_data().clear();
}
return Vertex_handle();
}
}
// Sequential
else
{
find_conflicts(c,
tester,
make_triple(
std::back_inserter(facets),
std::back_inserter(cells),
Emptyset_iterator()));
}
facet = facets.back();
// Remember the points that are hidden by the conflicting cells,
// as they will be deleted during the insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
Vertex_handle v =
tds().is_small_hole(facets.size()) ?
_insert_in_small_hole(p, cells, facets) :
_insert_in_hole(p,
cells.begin(), cells.end(),
facet.first, facet.second);
// Store the hidden points in their new cells.
hider.reinsert_vertices(v);
return v;
}
case 2:
{
// This check is added compared to the 3D case
if(lt == OUTSIDE_AFFINE_HULL)
return insert_outside_affine_hull (p);
if((lt == VERTEX) && (tester.compare_weight(c->vertex(li)->point(), p)==0))
{
return c->vertex(li);
}
// If the new point is not in conflict with its cell, it is hidden.
if(!tester.test_initial_cell(c))
{
hider.hide_point(c,p);
return Vertex_handle();
}
// Ok, we really insert the point now.
// First, find the conflict region.
std::vector<Cell_handle> cells;
cells.reserve(32);
Facet facet;
find_conflicts(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
// Remember the points that are hidden by the conflicting cells,
// as they will be deleted during the insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
Vertex_handle v = _insert_in_hole(p, cells.begin(), cells.end(),
facet.first, facet.second);
// Store the hidden points in their new cells.
hider.reinsert_vertices(v);
return v;
}
default:
{
// dimension() <= 1
if(lt == OUTSIDE_AFFINE_HULL)
return insert_outside_affine_hull (p);
if(lt == VERTEX && tester.compare_weight(c->vertex(li)->point(), p) == 0)
return c->vertex(li);
// If the new point is not in conflict with its cell, it is hidden.
if(! tester.test_initial_cell(c))
{
hider.hide_point(c,p);
return Vertex_handle();
}
if(dimension() == 0)
return hider.replace_vertex(c, li, p);
// dimension() == 1;
// Ok, we really insert the point now.
// First, find the conflict region.
std::vector<Cell_handle> cells;
Facet facet;
Cell_handle bound[2];
// corresponding index: bound[j]->neighbor(1-j) is in conflict.
// We get all cells in conflict,
// and remember the 2 external boundaries.
cells.push_back(c);
for(int j = 0; j<2; ++j)
{
Cell_handle n = c->neighbor(j);
while(tester(n))
{
cells.push_back(n);
n = n->neighbor(j);
}
bound[j] = n;
}
// Insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
tds().delete_cells(cells.begin(), cells.end());
// We preserve the order (like the orientation in 2D-3D).
Vertex_handle v = tds().create_vertex();
Cell_handle c0 = tds().create_face(v, bound[0]->vertex(0), Vertex_handle());
Cell_handle c1 = tds().create_face(bound[1]->vertex(1), v, Vertex_handle());
tds().set_adjacency(c0, 1, c1, 0);
tds().set_adjacency(bound[0], 1, c0, 0);
tds().set_adjacency(c1, 1, bound[1], 0);
bound[0]->vertex(0)->set_cell(bound[0]);
bound[1]->vertex(1)->set_cell(bound[1]);
v->set_cell(c0);
v->set_point (p);
hider.reinsert_vertices(v);
return v;
}
}
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_in_cell(const Point& p, Cell_handle c)
{
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);
Vertex_handle v = _tds.insert_in_cell(c);
v->set_point(p);
return v;
}
template < class GT, class Tds, class Lds >
inline
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_in_facet(const Point& p, Cell_handle c, int i)
{
CGAL_triangulation_precondition(dimension() == 2 || dimension() == 3);
CGAL_triangulation_precondition((dimension() == 2 && i == 3) ||
(dimension() == 3 && i >= 0 && i <= 3));
CGAL_triangulation_exactness_precondition_code(
Locate_type lt;
int li; int lj;
);
CGAL_triangulation_exactness_precondition(coplanar(p, c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point()) &&
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);
Vertex_handle v = _tds.insert_in_facet(c, i);
v->set_point(p);
return v;
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_in_edge(const Point& p, Cell_handle c, int i, int j)
{
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_exactness_precondition_code(
Locate_type lt;
int li;
);
switch(dimension())
{
case 3:
case 2:
{
CGAL_triangulation_precondition(! is_infinite(c, i, j));
CGAL_triangulation_exactness_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_exactness_precondition(side_of_edge(p, c, lt, li) == ON_BOUNDED_SIDE);
break;
}
}
Vertex_handle v = _tds.insert_in_edge(c, i, j);
v->set_point(p);
return v;
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_outside_convex_hull(const Point& p, Cell_handle c)
{
// 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);
}
case 2:
{
Conflict_tester_outside_convex_hull_2 tester(p, this);
Vertex_handle v = insert_conflict(c, tester);
v->set_point(p);
return v;
}
default: // case 3:
{
Conflict_tester_outside_convex_hull_3 tester(p, this);
Vertex_handle v = insert_conflict(c, tester);
v->set_point(p);
return v;
}
}
}
template < class GT, class Tds, class Lds >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::
insert_outside_affine_hull(const Point& p)
{
CGAL_triangulation_precondition(dimension() < 3);
bool reorient;
switch(dimension())
{
case 1:
{
Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex()));
Orientation o = coplanar_orientation(n->vertex(0)->point(),
n->vertex(1)->point(), p);
CGAL_triangulation_precondition(o != COLLINEAR);
reorient = o == NEGATIVE;
break;
}
case 2:
{
Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex()));
Orientation o = orientation(n->vertex(0)->point(),
n->vertex(1)->point(),
n->vertex(2)->point(), p);
CGAL_triangulation_precondition(o != COPLANAR);
reorient = o == NEGATIVE;
break;
}
default:
reorient = false;
}
Vertex_handle v = _tds.insert_increase_dimension(infinite_vertex());
v->set_point(p);
if(reorient)
_tds.reorient();
return v;
}
template < class GT, class Tds, class Lds >
template < class OutputItCells >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Cell_handle start)
{
Vertex_handle v = insert(p, start);
int dimension = this->dimension();
if(dimension == 3) this->incident_cells(v, fit);
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do
{
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
}
while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else *fit++ = v->cell(); // dimension = 0
return v;
}
template < class GT, class Tds, class Lds >
template < class OutputItCells >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::insert_and_give_new_cells(const Point& p,
OutputItCells fit,
Vertex_handle hint)
{
Vertex_handle v = insert(p, hint);
int dimension = this->dimension();
if(dimension == 3)
{
this->incident_cells(v, fit);
}
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do
{
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
}
while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else // dimension = 0
{
*fit++ = v->cell();
}
return v;
}
template < class GT, class Tds, class Lds >
template < class OutputItCells >
typename Triangulation_3<GT,Tds,Lds>::Vertex_handle
Triangulation_3<GT,Tds,Lds>::insert_and_give_new_cells(const Point& p,
Locate_type lt,
Cell_handle c, int li, int lj,
OutputItCells fit)
{
Vertex_handle v = insert(p, lt, c, li, lj);
int dimension = this->dimension();
if(dimension == 3) this->incident_cells(v, fit);
else if(dimension == 2)
{
Cell_handle c = v->cell(), end = c;
do {
*fit++ = c;
int i = c->index(v);
c = c->neighbor((i+1)%3);
}
while(c != end);
}
else if(dimension == 1)
{
Cell_handle c = v->cell();
*fit++ = c;
*fit++ = c->neighbor((~(c->index(v)))&1);
}
else *fit++ = v->cell(); // dimension = 0
return v;
}
template < class Gt, class Tds, class Lds >
typename Triangulation_3<Gt,Tds,Lds>::Vertex_triple
Triangulation_3<Gt,Tds,Lds>::
make_vertex_triple(const Facet& f) const
{
Cell_handle ch = f.first;
int i = f.second;
return Vertex_triple(ch->vertex(vertex_triple_index(i,0)),
ch->vertex(vertex_triple_index(i,1)),
ch->vertex(vertex_triple_index(i,2)));
}
template < class Gt, class Tds, class Lds >
void
Triangulation_3<Gt,Tds,Lds>::
make_canonical_oriented_triple(Vertex_triple& t) const
{
int i = (t.first < t.second) ? 0 : 1;
if(i==0)
{
i = (t.first < t.third) ? 0 : 2;
} else
{
i = (t.second < t.third) ? 1 : 2;
}
Vertex_handle tmp;
switch(i)
{
case 0: return;
case 1:
tmp = t.first;
t.first = t.second;
t.second = t.third;
t.third = tmp;
return;
default:
tmp = t.first;
t.first = t.third;
t.third = t.second;
t.second = tmp;
}
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
test_dim_down(Vertex_handle v) const
{
// Tests whether removing v decreases the dimension of the triangulation.
// Returns true iff v is incident to all finite cells/facets
// and all the other vertices are coplanar/collinear in dim3/2.
CGAL_triangulation_precondition(dimension() >= 0);
CGAL_triangulation_precondition(! is_infinite(v));
if(dimension() == 3)
{
Finite_cells_iterator cit = finite_cells_begin();
int iv;
if(! cit->has_vertex(v,iv))
return false;
const Point& p1=cit->vertex((iv+1)&3)->point();
const Point& p2=cit->vertex((iv+2)&3)->point();
const Point& p3=cit->vertex((iv+3)&3)->point();
++cit;
for(; cit != finite_cells_end(); ++cit)
{
if(! cit->has_vertex(v,iv))
return false;
for(int i=1; i<4; i++)
if(!coplanar(p1,p2,p3,cit->vertex((iv+i)&3)->point()))
return false;
}
}
else if(dimension() == 2)
{
Finite_facets_iterator cit = finite_facets_begin();
int iv;
if(! cit->first->has_vertex(v,iv))
return false;
const Point& p1 = cit->first->vertex(cw(iv))->point();
const Point& p2 = cit->first->vertex(ccw(iv))->point();
++cit;
for(; cit != finite_facets_end(); ++cit)
{
if(! cit->first->has_vertex(v,iv))
return false;
if(!collinear(p1, p2, cit->first->vertex(cw(iv))->point()) ||
!collinear(p1, p2, cit->first->vertex(ccw(iv))->point()))
return false;
}
}
else // dimension() == 1 or 0
{
return number_of_vertices() == (size_type) dimension() + 1;
}
return true;
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
test_dim_down_using_incident_cells_3(Vertex_handle v,
std::vector<Cell_handle>& incident_cells,
std::vector<Vertex_handle>& adj_vertices,
bool *could_lock_zone) const
{
CGAL_triangulation_precondition(dimension() == 3);
CGAL_triangulation_precondition(! is_infinite(v));
// Collect all vertices on the boundary
// and all incident cells
if(could_lock_zone)
{
*could_lock_zone = try_lock_and_get_adjacent_vertices_and_cells_3(
v, std::back_inserter(adj_vertices), incident_cells);
if(*could_lock_zone == false)
return false;
}
else
{
adjacent_vertices_and_cells_3(v, std::back_inserter(adj_vertices),
incident_cells);
}
typedef Filter_iterator< typename std::vector<Vertex_handle>::const_iterator,
Infinite_tester> Finite_vertex_iterator;
Finite_vertex_iterator vit(adj_vertices.end(),
Infinite_tester(this),
adj_vertices.begin());
Finite_vertex_iterator vit_end(adj_vertices.end(),
Infinite_tester(this));
const Point& p1 = (*vit++)->point();
const Point& p2 = (*vit++)->point();
const Point& p3 = (*vit++)->point();
for(; vit != vit_end ; ++vit)
{
if(!coplanar(p1, p2, p3, (*vit)->point()))
return false;
}
for(typename std::vector<Cell_handle>::const_iterator it_inc_cell
= incident_cells.begin() ;
it_inc_cell != incident_cells.end() ;
++it_inc_cell)
{
if(!is_infinite(*it_inc_cell))
return is_infinite(mirror_vertex(*it_inc_cell, (*it_inc_cell)->index(v)));
}
return true;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
make_hole_2D(Vertex_handle v, std::list<Edge_2D>& hole, VertexRemover& remover)
{
std::vector<Cell_handle> to_delete;
to_delete.reserve(32);
Face_circulator fc = tds().incident_faces(v);
Face_circulator done(fc);
// We prepare for deleting all interior cells.
// We ->set_cell() pointers to cells outside the hole.
// We push the Edges_2D of the boundary (seen from outside) in "hole".
do
{
Cell_handle f = fc;
int i = f->index(v);
Cell_handle fn = f->neighbor(i);
int in = fn->index(f);
f->vertex(cw(i))->set_cell(fn);
fn->set_neighbor(in, Cell_handle());
hole.push_back(Edge_2D(fn, in));
remover.add_hidden_points(f);
to_delete.push_back(f);
++fc;
}
while(fc != done);
tds().delete_cells(to_delete.begin(), to_delete.end());
return remover;
}
// This method also erases a set of cells, which is useful to the move method
// that outputs newly created cells
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
make_hole_2D(Vertex_handle v, std::list<Edge_2D>& hole, VertexRemover& remover,
std::set<Cell_handle>& cells_set)
{
std::vector<Cell_handle> to_delete;
to_delete.reserve(32);
Face_circulator fc = tds().incident_faces(v);
Face_circulator done(fc);
// We prepare for deleting all interior cells.
// We ->set_cell() pointers to cells outside the hole.
// We push the Edges_2D of the boundary (seen from outside) in "hole".
do
{
Cell_handle f = fc;
int i = f->index(v);
Cell_handle fn = f->neighbor(i);
int in = fn->index(f);
f->vertex(cw(i))->set_cell(fn);
fn->set_neighbor(in, Cell_handle());
hole.push_back(Edge_2D(fn, in));
remover.add_hidden_points(f);
to_delete.push_back(f);
++fc;
}
while(fc != done);
for(typename std::vector<Cell_handle>::const_iterator ib = to_delete.begin(),
iend = to_delete.end();
ib != iend; ib++)
{
cells_set.erase(*ib);
}
tds().delete_cells(to_delete.begin(), to_delete.end());
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
void
Triangulation_3<Gt, Tds, Lds>::
fill_hole_2D(std::list<Edge_2D>& first_hole, VertexRemover& remover)
{
typedef std::list<Edge_2D> Hole;
std::vector<Hole> hole_list;
Cell_handle f, ff, fn;
int i, ii, in;
hole_list.push_back(first_hole);
while(! hole_list.empty())
{
Hole hole = hole_list.back();
hole_list.pop_back();
// If the hole has only three edges, create the triangle
if(hole.size() == 3)
{
typename Hole::iterator hit = hole.begin();
f = (*hit).first; i = (*hit).second;
ff = (* ++hit).first; ii = (*hit).second;
fn = (* ++hit).first; in = (*hit).second;
tds().create_face(f, i, ff, ii, fn, in);
continue;
}
// Else find an edge with two finite vertices on the hole boundary
// and the new triangle adjacent to that edge
// cut the hole and push it back
// First, ensure that a neighboring face
// whose vertices on the hole boundary are finite
// is the first of the hole
while(1)
{
ff = (hole.front()).first;
ii = (hole.front()).second;
if(is_infinite(ff->vertex(cw(ii))) || is_infinite(ff->vertex(ccw(ii))))
{
hole.push_back(hole.front());
hole.pop_front();
}
else
{
break;
}
}
// Take the first neighboring face and pop it;
ff = (hole.front()).first;
ii = (hole.front()).second;
hole.pop_front();
Vertex_handle v0 = ff->vertex(cw(ii));
Vertex_handle v1 = ff->vertex(ccw(ii));
Vertex_handle v2 = infinite_vertex();
const Point& p0 = v0->point();
const Point& p1 = v1->point();
const Point *p2 = nullptr; // Initialize to nullptr to avoid warning.
typename Hole::iterator hdone = hole.end();
typename Hole::iterator hit = hole.begin();
typename Hole::iterator cut_after(hit);
// If tested vertex is c with respect to the vertex opposite to nullptr neighbor,
// stop at the before last face;
hdone--;
for(; hit != hdone; ++hit)
{
fn = hit->first;
in = hit->second;
Vertex_handle vv = fn->vertex(ccw(in));
if(is_infinite(vv))
{
if(is_infinite(v2))
cut_after = hit;
}
else // vv is a finite vertex
{
const Point& p = vv->point();
if(coplanar_orientation(p0, p1, p) == COUNTERCLOCKWISE)
{
if(is_infinite(v2) ||
remover.side_of_bounded_circle(p0, p1, *p2, p, true) == ON_BOUNDED_SIDE)
{
v2 = vv;
p2 = &p;
cut_after = hit;
}
}
}
}
// Create new triangle and update adjacency relations
Cell_handle newf;
// Update the hole and push back in the Hole_List stack.
// If v2 belongs to the neighbor following or preceding *f
// the hole remains a single hole; otherwise it is split in two holes.
fn = (hole.front()).first;
in = (hole.front()).second;
if(fn->has_vertex(v2, i) && i == ccw(in))
{
newf = tds().create_face(ff, ii, fn, in);
hole.pop_front();
hole.push_front(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else
{
fn = (hole.back()).first;
in = (hole.back()).second;
if(fn->has_vertex(v2, i) && i == cw(in))
{
newf = tds().create_face(fn, in, ff, ii);
hole.pop_back();
hole.push_back(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else
{
// split the hole in two holes
newf = tds().create_face(ff, ii, v2);
Hole new_hole;
++cut_after;
while(hole.begin() != cut_after)
{
new_hole.push_back(hole.front());
hole.pop_front();
}
hole.push_front(Edge_2D(newf, 1));
new_hole.push_front(Edge_2D(newf, 0));
hole_list.push_back(hole);
hole_list.push_back(new_hole);
}
}
}
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
void
Triangulation_3<Gt, Tds, Lds>::
fill_hole_2D(std::list<Edge_2D>& first_hole, VertexRemover& remover, OutputItCells fit)
{
typedef std::list<Edge_2D> Hole;
std::vector<Hole> hole_list;
Cell_handle f, ff, fn;
int i, ii, in;
hole_list.push_back(first_hole);
while(! hole_list.empty())
{
Hole hole = hole_list.back();
hole_list.pop_back();
// If the hole has only three edges, create the triangle
if(hole.size() == 3)
{
typename Hole::iterator hit = hole.begin();
f = (*hit).first;
i = (*hit).second;
ff = (* ++hit).first;
ii = (*hit).second;
fn = (* ++hit).first;
in = (*hit).second;
*fit++ = tds().create_face(f, i, ff, ii, fn, in);
continue;
}
// Else find an edge with two finite vertices on the hole boundary
// and the new triangle adjacent to that edge
// cut the hole and push it back
// First, ensure that a neighboring face
// whose vertices on the hole boundary are finite
// is the first of the hole
while(1)
{
ff = (hole.front()).first;
ii = (hole.front()).second;
if(is_infinite(ff->vertex(cw(ii))) || is_infinite(ff->vertex(ccw(ii))))
{
hole.push_back(hole.front());
hole.pop_front();
}
else
{
break;
}
}
// take the first neighboring face and pop it;
ff = (hole.front()).first;
ii = (hole.front()).second;
hole.pop_front();
Vertex_handle v0 = ff->vertex(cw(ii));
Vertex_handle v1 = ff->vertex(ccw(ii));
Vertex_handle v2 = infinite_vertex();
const Point& p0 = v0->point();
const Point& p1 = v1->point();
const Point *p2 = nullptr; // Initialize to nullptr to avoid warning.
typename Hole::iterator hdone = hole.end();
typename Hole::iterator hit = hole.begin();
typename Hole::iterator cut_after(hit);
// if tested vertex is c with respect to the vertex opposite
// to nullptr neighbor,
// stop at the before last face;
hdone--;
for(; hit != hdone; ++hit)
{
fn = hit->first;
in = hit->second;
Vertex_handle vv = fn->vertex(ccw(in));
if(is_infinite(vv))
{
if(is_infinite(v2))
cut_after = hit;
}
else // vv is a finite vertex
{
const Point& p = vv->point();
if(coplanar_orientation(p0, p1, p) == COUNTERCLOCKWISE)
{
if(is_infinite(v2) ||
remover.side_of_bounded_circle(p0, p1, *p2, p, true) == ON_BOUNDED_SIDE)
{
v2 = vv;
p2 = &p;
cut_after = hit;
}
}
}
}
// create new triangle and update adjacency relations
Cell_handle newf;
//update the hole and push back in the Hole_List stack
// if v2 belongs to the neighbor following or preceding *f
// the hole remain a single hole
// otherwise it is split in two holes
fn = (hole.front()).first;
in = (hole.front()).second;
if(fn->has_vertex(v2, i) && i == ccw(in))
{
newf = tds().create_face(ff, ii, fn, in);
hole.pop_front();
hole.push_front(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else
{
fn = (hole.back()).first;
in = (hole.back()).second;
if(fn->has_vertex(v2, i) && i == cw(in))
{
newf = tds().create_face(fn, in, ff, ii);
hole.pop_back();
hole.push_back(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else
{
// split the hole in two holes
newf = tds().create_face(ff, ii, v2);
Hole new_hole;
++cut_after;
while(hole.begin() != cut_after)
{
new_hole.push_back(hole.front());
hole.pop_front();
}
hole.push_front(Edge_2D(newf, 1));
new_hole.push_front(Edge_2D(newf, 0));
hole_list.push_back(hole);
hole_list.push_back(new_hole);
}
}
*fit++ = newf;
}
}
template < class Gt, class Tds, class Lds >
void
Triangulation_3<Gt,Tds,Lds>::
make_hole_3D(Vertex_handle v,
Vertex_triple_Facet_map& outer_map,
std::vector<Cell_handle>& hole)
{
CGAL_triangulation_expensive_precondition(! test_dim_down(v));
incident_cells(v, std::back_inserter(hole));
for(typename std::vector<Cell_handle>::iterator cit = hole.begin(),
end = hole.end();
cit != end; ++cit)
{
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor(indv);
Facet f(opp_cit, opp_cit->index(*cit));
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
outer_map[vt] = f;
for(int i=0; i<4; i++)
{
if(i != indv)
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
}
// When the incident cells are already known
template < class Gt, class Tds, class Lds >
void
Triangulation_3<Gt,Tds,Lds>::
make_hole_3D(Vertex_handle v,
const std::vector<Cell_handle>& incident_cells,
Vertex_triple_Facet_map& outer_map)
{
CGAL_triangulation_expensive_precondition(! test_dim_down(v));
for(typename std::vector<Cell_handle>::const_iterator cit = incident_cells.begin(),
end = incident_cells.end(); cit != end; ++cit)
{
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor(indv);
Facet f(opp_cit, opp_cit->index(*cit));
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
outer_map[vt] = f;
for(int i=0; i<4; i++)
{
if(i != indv)
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds,Lds>::
remove_dim_down(Vertex_handle v, VertexRemover& remover)
{
CGAL_triangulation_precondition (dimension() >= 0);
// Collect all the hidden points.
for(All_cells_iterator ci = tds().raw_cells_begin(),
end = tds().raw_cells_end(); ci != end; ++ci)
remover.add_hidden_points(ci);
tds().remove_decrease_dimension(v, infinite_vertex());
// Now try to see if we need to re-orient.
if(dimension() == 2)
{
Facet f = *finite_facets_begin();
if(coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
{
tds().reorient();
}
}
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds,Lds>::
remove_1D(Vertex_handle v, VertexRemover& remover)
{
CGAL_triangulation_precondition (dimension() == 1);
Cell_handle c1 = v->cell();
Cell_handle c2 = c1->neighbor(c1->index(v) == 0 ? 1 : 0);
remover.add_hidden_points(c1);
remover.add_hidden_points(c2);
tds().remove_from_maximal_dimension_simplex (v);
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds,Lds>::
remove_2D(Vertex_handle v, VertexRemover& remover)
{
CGAL_triangulation_precondition(dimension() == 2);
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover);
fill_hole_2D(hole, remover);
tds().delete_vertex(v);
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds,Lds>::
remove_3D(Vertex_handle v, VertexRemover& remover)
{
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, outer_map, hole);
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
// Output the hidden points.
for(typename std::vector<Cell_handle>::iterator hi = hole.begin(),
hend = hole.end();
hi != hend; ++hi)
{
remover.add_hidden_points(*hi);
}
bool inf = false;
// collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
adjacent_vertices(v, std::back_inserter(vertices));
// create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
unsigned int i = 0;
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
#ifdef CGAL_TRIANGULATION_3_USE_THE_4_POINTS_CONSTRUCTOR
size_t num_vertices = vertices.size();
if(num_vertices >= 5)
{
for(int j = 0 ; j < 4 ; ++j)
{
if(is_infinite(vertices[j]))
{
std::swap(vertices[j], vertices[4]);
break;
}
}
Orientation o = orientation(vertices[0]->point(),
vertices[1]->point(),
vertices[2]->point(),
vertices[3]->point());
if(o == NEGATIVE)
std::swap(vertices[0], vertices[1]);
if(o != ZERO)
{
Vertex_handle vh1, vh2, vh3, vh4;
remover.tmp.init_tds(vertices[0]->point(), vertices[1]->point(),
vertices[2]->point(), vertices[3]->point(),
vh1, vh2, vh3, vh4);
ch = vh1->cell();
vmap[vh1] = vertices[0];
vmap[vh2] = vertices[1];
vmap[vh3] = vertices[2];
vmap[vh4] = vertices[3];
i = 4;
}
}
#endif
for(; i < vertices.size(); i++)
{
if(! is_infinite(vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}
else
{
inf = true;
}
}
if(remover.tmp.dimension() == 2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third))
{
++oit;
// Otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit = inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// Create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// For the other faces check, if they can also be glued
for(i = 0; i < 4; i++)
{
if(i != i_i)
{
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second,vt.third);
outer_map[vt]= f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds,Lds>::
remove_3D(Vertex_handle v, VertexRemover& remover,
const std::vector<Cell_handle>& inc_cells,
std::vector<Vertex_handle>& adj_vertices)
{
// Construct the set of vertex triples on the boundary with the facet just behind
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, inc_cells, outer_map);
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
// Output the hidden points.
for(typename std::vector<Cell_handle>::const_iterator hi = inc_cells.begin(),
hend = inc_cells.end();
hi != hend; ++hi)
{
remover.add_hidden_points(*hi);
}
bool inf = false;
// Create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
unsigned int i = 0;
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
#ifdef CGAL_TRIANGULATION_3_USE_THE_4_POINTS_CONSTRUCTOR
size_t num_vertices = adj_vertices.size();
if(num_vertices >= 5)
{
for(int j = 0 ; j < 4 ; ++j)
{
if(is_infinite(adj_vertices[j]))
{
std::swap(adj_vertices[j], adj_vertices[4]);
break;
}
}
Orientation o = orientation(adj_vertices[0]->point(),
adj_vertices[1]->point(),
adj_vertices[2]->point(),
adj_vertices[3]->point());
if(o == NEGATIVE)
std::swap(adj_vertices[0], adj_vertices[1]);
if(o != ZERO)
{
Vertex_handle vh1, vh2, vh3, vh4;
remover.tmp.init_tds(adj_vertices[0]->point(), adj_vertices[1]->point(),
adj_vertices[2]->point(), adj_vertices[3]->point(),
vh1, vh2, vh3, vh4);
ch = vh1->cell();
vmap[vh1] = adj_vertices[0];
vmap[vh2] = adj_vertices[1];
vmap[vh3] = adj_vertices[2];
vmap[vh4] = adj_vertices[3];
i = 4;
}
}
#endif
for(; i < adj_vertices.size(); i++)
{
if(! is_infinite(adj_vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(adj_vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = adj_vertices[i];
}
else
{
inf = true;
}
}
if(remover.tmp.dimension()==2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third))
{
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++)
{
if(i != i_i)
{
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second,vt.third);
outer_map[vt]= f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
tds().delete_vertex(v);
tds().delete_cells(inc_cells.begin(), inc_cells.end());
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
void
Triangulation_3<Gt, Tds, Lds>::
remove(Vertex_handle v, VertexRemover& remover)
{
CGAL_triangulation_precondition(v != Vertex_handle());
CGAL_triangulation_precondition(!is_infinite(v));
CGAL_triangulation_expensive_precondition(tds().is_vertex(v));
if(test_dim_down (v))
{
remove_dim_down (v, remover);
}
else
{
switch(dimension())
{
case 1: remove_1D (v, remover);
break;
case 2: remove_2D (v, remover);
break;
case 3: remove_3D (v, remover);
break;
default:
CGAL_triangulation_assertion (false);
}
}
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover >
bool
Triangulation_3<Gt, Tds, Lds>::
remove(Vertex_handle v, VertexRemover& remover, bool *could_lock_zone)
{
// N.B.: dimension doesn't need to be atomic since the parallel removal
// will never decrease the dimension (the last few removes are done
// sequentially)
CGAL_triangulation_precondition(v != Vertex_handle());
CGAL_triangulation_precondition(!is_infinite(v));
CGAL_triangulation_precondition(dimension() == 3);
CGAL_triangulation_expensive_precondition(tds().is_vertex(v));
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
static Profile_branch_counter_3 bcounter(
"early withdrawals / late withdrawals / successes [Delaunay_tri_3::remove]");
#endif
bool removed = true;
// Locking vertex v is a good start
if(!this->try_lock_vertex(v))
{
*could_lock_zone = false;
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
bcounter.increment_branch_2(); // THIS is an early withdrawal!
#endif
}
else
{
std::vector<Cell_handle> incident_cells;
incident_cells.reserve(64);
std::vector<Vertex_handle> adj_vertices;
adj_vertices.reserve(64);
bool dim_down = test_dim_down_using_incident_cells_3(
v, incident_cells, adj_vertices, could_lock_zone);
if(*could_lock_zone)
{
if(dim_down)
removed = false;
else
remove_3D (v, remover, incident_cells, adj_vertices);
}
}
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
if(could_lock_zone)
{
if(*could_lock_zone)
++bcounter;
else
bcounter.increment_branch_1(); // THIS is a late withdrawal!
}
#endif
return removed;
}
// The remove here uses the remover, but
// no function envolving hidden points
// will be used in this internal version
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
remove_dim_down(Vertex_handle v, VertexRemover& remover, OutputItCells fit)
{
remove_dim_down(v, remover);
for(All_cells_iterator afi = tds().raw_cells_begin();
afi != tds().raw_cells_end(); afi++)
{
*fit++ = afi;
}
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
remove_1D(Vertex_handle v, VertexRemover& remover, OutputItCells fit)
{
Point p = v->point();
remove_1D(v, remover);
*fit++ = locate(p);
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
remove_2D(Vertex_handle v, VertexRemover& remover, OutputItCells fit)
{
CGAL_triangulation_precondition(dimension() == 2);
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover);
fill_hole_2D(hole, remover, fit);
tds().delete_vertex(v);
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
VertexRemover&
Triangulation_3<Gt, Tds, Lds>::
remove_3D(Vertex_handle v, VertexRemover& remover, OutputItCells fit)
{
CGAL_triangulation_precondition(dimension() == 3);
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, outer_map, hole);
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
// Output the hidden points.
for(typename std::vector<Cell_handle>::iterator hi = hole.begin(),
hend = hole.end();
hi != hend; ++hi)
{
remover.add_hidden_points(*hi);
}
bool inf = false;
unsigned int i;
// collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
adjacent_vertices(v, std::back_inserter(vertices));
// create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
for(i=0; i<vertices.size(); i++)
{
if(! is_infinite(vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}
else
{
inf = true;
}
}
if(remover.tmp.dimension()==2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt] = f;
}
}
} else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt] = f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third))
{
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
*fit++ = new_ch;
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++)
{
if(i != i_i)
{
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
std::swap(vt.second, vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second, vt.third);
outer_map[vt]= f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2, new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
return remover;
}
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class OutputItCells >
void
Triangulation_3<Gt, Tds, Lds>::
remove_and_give_new_cells(Vertex_handle v, VertexRemover& remover,
OutputItCells fit)
{
CGAL_triangulation_precondition(v != Vertex_handle());
CGAL_triangulation_precondition(!is_infinite(v));
CGAL_triangulation_expensive_precondition(tds().is_vertex(v));
if(test_dim_down (v))
{
remove_dim_down (v, remover, fit);
}
else
{
switch(dimension())
{
case 1: remove_1D (v, remover, fit);
break;
case 2: remove_2D (v, remover, fit);
break;
case 3: remove_3D (v, remover, fit);
break;
default:
CGAL_triangulation_assertion (false);
}
}
}
// The VertexInserter is needed so as to
// allow us the usage of the insertion method
// from the particular triangulation
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class VertexInserter >
typename Triangulation_3<Gt,Tds,Lds>::Vertex_handle
Triangulation_3<Gt,Tds,Lds>::
move_if_no_collision(Vertex_handle v, const Point& p,
VertexRemover& remover, VertexInserter& inserter)
{
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
CGAL_triangulation_precondition(!is_infinite(v));
if(v->point() == p)
return v;
const int dim = dimension();
// If displacements are known to be small, we might want to optimize by checking
// whether there is a topological change or not before.
// In this version, this will not be put inside this method because
// it is for general purposes, and remaining Delaunay after motion
// is a bit too restrictive.
//
// In the filtered version optimized for displacements, it will be used
// as an a priori. However, a non-fully optimized but good version of
// is_delaunay_after_displacement is provided as an internal method of
// Delaunay_triangulation_3 (see the class for more details).
Locate_type lt;
int li, lj;
Cell_handle loc = locate(p, lt, li, lj, v->cell());
if(lt == VERTEX)
return loc->vertex(li);
if(dim == 0)
{
v->set_point(p);
return v;
}
size_type n_vertices = tds().number_of_vertices();
if((lt == OUTSIDE_AFFINE_HULL) && (dim == 1) && (n_vertices == 3))
{
v->set_point(p);
return v;
}
if((lt == OUTSIDE_AFFINE_HULL) && (dim == 2) && (n_vertices == 4))
{
v->set_point(p);
return v;
}
if((lt != OUTSIDE_AFFINE_HULL) && (dim == 1))
{
if(loc->has_vertex(v))
{
v->set_point(p);
}
else
{
Vertex_handle inserted = insert(p, lt, loc, li, lj);
Cell_handle f = v->cell();
int i = f->index(v);
if(i == 0)
f = f->neighbor(1);
CGAL_triangulation_assertion(f->index(v) == 1);
Cell_handle g= f->neighbor(0);
f->set_vertex(1, g->vertex(1));
f->set_neighbor(0,g->neighbor(0));
g->neighbor(0)->set_neighbor(1,f);
g->vertex(1)->set_cell(f);
tds().delete_cell(g);
Cell_handle f_ins = inserted->cell();
i = f_ins->index(inserted);
if(i == 0)
f_ins = f_ins->neighbor(1);
CGAL_triangulation_assertion(f_ins->index(inserted) == 1);
Cell_handle g_ins = f_ins->neighbor(0);
f_ins->set_vertex(1, v);
g_ins->set_vertex(0, v);
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
}
return v;
}
bool dim_down = test_dim_down(v);
if((lt != OUTSIDE_AFFINE_HULL) && dim_down && (dim == 2))
{
// verify if p and two static vertices are collinear in this case
int iinf;
Cell_handle finf = infinite_vertex()->cell(), fdone;
fdone = finf;
do
{
iinf = finf->index(infinite_vertex());
if(!finf->has_vertex(v))
break;
finf = finf->neighbor((iinf+1)%3);
}
while(finf != fdone);
iinf = ~iinf;
if(this->collinear(finf->vertex(iinf&1)->point(),
finf->vertex(iinf&2)->point(),
p))
{
v->set_point(p);
_tds.decrease_dimension(loc, loc->index(v));
return v;
}
}
if(((dim == 2) && (lt != OUTSIDE_AFFINE_HULL)) ||
((lt == OUTSIDE_AFFINE_HULL) && (dim == 1)))
{
// This is insert must be from Delaunay (or the particular trian.)
// not Triangulation_3 !
Vertex_handle inserted = inserter.insert(p, lt, loc, li, lj);
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover);
fill_hole_2D(hole, remover);
// fixing pointer
Cell_handle fc = inserted->cell(), done(fc);
std::vector<Cell_handle> faces_pt;
faces_pt.reserve(16);
do
{
faces_pt.push_back(fc);
fc = fc->neighbor((fc->index(inserted) + 1)%3);
}
while(fc != done);
std::size_t ss = faces_pt.size();
for(std::size_t k=0; k<ss; k++)
{
Cell_handle f = faces_pt[k];
int i = f->index(inserted);
f->set_vertex(i, v);
}
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
return v;
}
if((lt != OUTSIDE_AFFINE_HULL) && dim_down && (dim == 3))
{
// verify if p and two static vertices are collinear in this case
std::vector<Cell_handle> ics;
incident_cells(infinite_vertex(), std::back_inserter(ics));
std::size_t size = ics.size();
Cell_handle finf;
for(std::size_t i=0; i<size; i++)
{
finf = ics[i];
if(!finf->has_vertex(v))
break;
}
int iinf = finf->index(infinite_vertex());
if(remover.tmp.coplanar(finf->vertex((iinf+1)&3)->point(),
finf->vertex((iinf+2)&3)->point(),
finf->vertex((iinf+3)&3)->point(),
p))
{
v->set_point(p);
_tds.decrease_dimension(loc, loc->index(v));
Facet f = *finite_facets_begin();
if(coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
{
tds().reorient();
}
restore_edges_after_decrease_dimension(v, remover,inserter);
return v;
}
}
// This is insert must be from Delaunay (or the particular trian.)
// not Triangulation_3 !
Vertex_handle inserted = inserter.insert(p, lt, loc, li, lj);
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, outer_map, hole);
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
// Output the hidden points.
for(typename std::vector<Cell_handle>::iterator hi = hole.begin(),
hend = hole.end(); hi != hend; ++hi)
{
remover.add_hidden_points(*hi);
}
bool inf = false;
unsigned int i;
// collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
adjacent_vertices(v, std::back_inserter(vertices));
// create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
for(i=0; i < vertices.size(); i++)
{
if(! is_infinite(vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}
else
{
inf = true;
}
}
if(remover.tmp.dimension() == 2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third))
{
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++)
{
if(i != i_i)
{
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second,vt.third);
outer_map[vt]= f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
// fixing pointer
std::vector<Cell_handle> cells_pt;
cells_pt.reserve(64);
incident_cells(inserted, std::back_inserter(cells_pt));
std::size_t size = cells_pt.size();
for(std::size_t i=0; i<size; i++)
{
Cell_handle c = cells_pt[i];
c->set_vertex(c->index(inserted), v);
}
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
tds().delete_cells(hole.begin(), hole.end());
return v;
} // end of Vertex_handle
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class VertexInserter >
typename Triangulation_3<Gt,Tds,Lds>::Vertex_handle
Triangulation_3<Gt,Tds,Lds>::
move(Vertex_handle v, const Point& p,
VertexRemover& remover, VertexInserter& inserter)
{
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
CGAL_triangulation_precondition(!is_infinite(v));
if(v->point() == p)
return v;
Vertex_handle w = move_if_no_collision(v,p,remover,inserter);
if(w != v)
{
remove(v, remover);
return w;
}
return v;
}
// The VertexInserter is needed so as to allow us the usage of the insertion method
// from the particular triangulation
template < class Gt, class Tds, class Lds >
template < class VertexRemover, class VertexInserter, class OutputItCells >
typename Triangulation_3<Gt,Tds,Lds>::Vertex_handle
Triangulation_3<Gt,Tds,Lds>::
move_if_no_collision_and_give_new_cells(Vertex_handle v, const Point& p,
VertexRemover& remover, VertexInserter& inserter,
OutputItCells fit)
{
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
CGAL_triangulation_precondition(!is_infinite(v));
if(v->point() == p)
return v;
const int dim = dimension();
// If displacements are known to be small, we might want to optimize by checking
// whether there is a topological change or not before.
//
// In this version this will not be put inside this method because it is
// for general purposes, and remaining Delaunay after motion is a bit
// too restrictive.
//
// In the filtered version optimized for displacements, it will be used
// as an a priori. However, a non-fully optimized but good version of
// is_delaunay_after_displacement is provided as an internal method of
// Delaunay_triangulation_3 (see the class for more details).
Locate_type lt;
int li, lj;
Cell_handle loc = locate(p, lt, li, lj, v->cell());
if(lt == VERTEX) return loc->vertex(li);
if(dim == 0)
{
v->set_point(p);
return v;
}
int n_vertices = tds().number_of_vertices();
if((lt == OUTSIDE_AFFINE_HULL) && (dim == 1) && (n_vertices == 3))
{
v->set_point(p);
for(All_cells_iterator afi = tds().raw_cells_begin();
afi != tds().raw_cells_end(); afi++)
{
*fit++ = afi;
}
return v;
}
if((lt == OUTSIDE_AFFINE_HULL) && (dim == 2) && (n_vertices == 4))
{
v->set_point(p);
for(All_cells_iterator afi = tds().raw_cells_begin();
afi != tds().raw_cells_end(); afi++)
{
*fit++ = afi;
}
return v;
}
if((lt != OUTSIDE_AFFINE_HULL) && (dim == 1))
{
if(loc->has_vertex(v))
{
v->set_point(p);
}
else
{
Vertex_handle inserted = insert(p, lt, loc, li, lj);
Cell_handle f = v->cell();
int i = f->index(v);
if(i==0)
f = f->neighbor(1);
CGAL_triangulation_assertion(f->index(v) == 1);
Cell_handle g = f->neighbor(0);
f->set_vertex(1, g->vertex(1));
f->set_neighbor(0,g->neighbor(0));
g->neighbor(0)->set_neighbor(1,f);
g->vertex(1)->set_cell(f);
tds().delete_cell(g);
*fit++ = f;
Cell_handle f_ins = inserted->cell();
i = f_ins->index(inserted);
if(i==0)
f_ins = f_ins->neighbor(1);
CGAL_triangulation_assertion(f_ins->index(inserted) == 1);
Cell_handle g_ins = f_ins->neighbor(0);
f_ins->set_vertex(1, v);
g_ins->set_vertex(0, v);
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
}
*fit++ = v->cell();
if(v->cell()->neighbor(0)->has_vertex(v))
*fit++ = v->cell()->neighbor(0);
if(v->cell()->neighbor(1)->has_vertex(v))
*fit++ = v->cell()->neighbor(1);
return v;
}
bool dim_down = test_dim_down(v);
if((lt != OUTSIDE_AFFINE_HULL) && dim_down && (dim == 2))
{
// Verify if p and two static vertices are collinear in this case
int iinf;
Cell_handle finf = infinite_vertex()->cell(), fdone;
fdone = finf;
do
{
iinf = finf->index(infinite_vertex());
if(!finf->has_vertex(v)) break;
finf = finf->neighbor((iinf+1)%3);
}
while(finf != fdone);
iinf = ~iinf;
if(this->collinear(finf->vertex(iinf&1)->point(),
finf->vertex(iinf&2)->point(),
p))
{
v->set_point(p);
_tds.decrease_dimension(loc, loc->index(v));
for(All_cells_iterator afi = tds().raw_cells_begin();
afi != tds().raw_cells_end(); afi++)
{
*fit++ = afi;
}
return v;
}
}
if(((dim == 2) && (lt != OUTSIDE_AFFINE_HULL)) ||
((lt == OUTSIDE_AFFINE_HULL) && (dim == 1)))
{
std::set<Cell_handle> cells_set;
// This is insert must be from Delaunay (or the particular trian.)
// not Triangulation_3 !
Vertex_handle inserted = inserter.insert(p, lt, loc, li, lj);
Cell_handle c = inserted->cell(), end = c;
do
{
cells_set.insert(c);
int i = c->index(inserted);
c = c->neighbor((i+1)%3);
}
while(c != end);
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover, cells_set);
fill_hole_2D(hole, remover, fit);
// fixing pointer
Cell_handle fc = inserted->cell(), done(fc);
std::vector<Cell_handle> faces_pt;
faces_pt.reserve(16);
do
{
faces_pt.push_back(fc);
fc = fc->neighbor((fc->index(inserted) + 1)%3);
}
while(fc != done);
int ss = faces_pt.size();
for(int k=0; k<ss; k++)
{
Cell_handle f = faces_pt[k];
int i = f->index(inserted);
f->set_vertex(i, v);
}
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
for(typename std::set<Cell_handle>::const_iterator ib = cells_set.begin(),
iend = cells_set.end();
ib != iend; ib++)
{
*fit++ = *ib;
}
return v;
}
if((lt != OUTSIDE_AFFINE_HULL) && dim_down && (dim == 3))
{
// verify if p and two static vertices are collinear in this case
std::vector<Cell_handle> ics;
incident_cells(infinite_vertex(), std::back_inserter(ics));
int size = ics.size();
Cell_handle finf;
for(int i=0; i<size; i++)
{
finf = ics[i];
if(!finf->has_vertex(v)) break;
}
int iinf = finf->index(infinite_vertex());
if(remover.tmp.coplanar(finf->vertex((iinf+1)&3)->point(),
finf->vertex((iinf+2)&3)->point(),
finf->vertex((iinf+3)&3)->point(),
p))
{
v->set_point(p);
_tds.decrease_dimension(loc, loc->index(v));
Facet f = *finite_facets_begin();
if(coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
{
tds().reorient();
}
restore_edges_after_decrease_dimension(v, remover,inserter);
for(All_cells_iterator afi = tds().raw_cells_begin();
afi != tds().raw_cells_end(); afi++)
{
*fit++ = afi;
}
return v;
}
}
std::set<Cell_handle> cells_set;
// This is insert must be from Delaunay (or the particular trian.)
// not Triangulation_3 !
Vertex_handle inserted = inserter.insert(p, lt, loc, li, lj);
std::vector<Cell_handle> cells_tmp;
cells_tmp.reserve(64);
incident_cells(inserted, std::back_inserter(cells_tmp));
int size = cells_tmp.size();
for(int i=0; i<size; i++)
{
cells_set.insert(cells_tmp[i]);
}
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, outer_map, hole);
for(typename std::vector<Cell_handle>::const_iterator ib = hole.begin(),
iend = hole.end();
ib != iend; ib++)
{
cells_set.erase(*ib);
}
CGAL_assertion(remover.hidden_points_begin() == remover.hidden_points_end());
// Output the hidden points.
for(typename std::vector<Cell_handle>::iterator hi = hole.begin(),
hend = hole.end();
hi != hend; ++hi)
{
remover.add_hidden_points(*hi);
}
bool inf = false;
unsigned int i;
// Collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
adjacent_vertices(v, std::back_inserter(vertices));
// Create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
for(i=0; i < vertices.size(); i++)
{
if(! is_infinite(vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}else {
inf = true;
}
}
if(remover.tmp.dimension()==2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(i=0; i < 4; i++)
{
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third))
{
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
*fit++ = new_ch;
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++)
{
if(i != i_i)
{
Facet f = std::pair<Cell_handle, int>(new_ch, i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second,vt.third);
outer_map[vt] = f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
// fixing pointer
std::vector<Cell_handle> cells_pt;
cells_pt.reserve(64);
incident_cells(inserted, std::back_inserter(cells_pt));
size = cells_pt.size();
for(int i=0; i<size; i++)
{
Cell_handle c = cells_pt[i];
c->set_vertex(c->index(inserted), v);
}
v->set_point(p);
v->set_cell(inserted->cell());
tds().delete_vertex(inserted);
tds().delete_cells(hole.begin(), hole.end());
for(typename std::set<Cell_handle>::const_iterator ib = cells_set.begin(),
iend = cells_set.end();
ib != iend; ib++)
{
*fit++ = *ib;
}
return v;
}
template < class Gt, class Tds, class Lds >
void
Triangulation_3<Gt,Tds,Lds>::
_make_big_hole_3D(Vertex_handle v,
std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle>& hole,
std::vector<Vertex_handle>& vertices,
std::map<Vertex_handle, REMOVE_VERTEX_STATE>& vstates)
{
Cell_handle start = v->cell();
start->tds_data().mark_processed();
hole.push_back(start);
std::size_t i=0, n=1;
while(i < n)
{
Cell_handle c = hole[i++];
for(int k=0; k<4; k++)
{
Vertex_handle v0 = c->vertex(k);
const REMOVE_VERTEX_STATE vst = vstates[v0];
if(vst == CLEAR)
{
vstates[v0] = EXTREMITY;
vertices.push_back(v0);
}
else if(vst == TO_REMOVE)
{
// we mark the vertices, so all the vertices
// from the same cluster will be skipped
// in the remove_cluster_3D function
vstates[v0] = PROCESSED;
}
int i1 = vertex_triple_index(k, 0);
int i2 = vertex_triple_index(k, 1);
int i3 = vertex_triple_index(k, 2);
Vertex_handle v1 = c->vertex(i1);
Vertex_handle v2 = c->vertex(i2);
Vertex_handle v3 = c->vertex(i3);
Cell_handle opp_cit = c->neighbor(k);
int opp_i = tds().mirror_index(c, k);
Vertex_handle vm = opp_cit->vertex(opp_i);
bool pb1 = false, pb2 = false, pb3 = false, pbm = false;
const REMOVE_VERTEX_STATE vst1 = vstates[v1];
pb1 = vst1 == TO_REMOVE || vst1 == PROCESSED;
if(!pb1)
{
const REMOVE_VERTEX_STATE vst2 = vstates[v2];
pb2 = vst2 == TO_REMOVE || vst2 == PROCESSED;
if(!pb2)
{
const REMOVE_VERTEX_STATE vst3 = vstates[v3];
pb3 = vst3 == TO_REMOVE || vst3 == PROCESSED;
if(!pb3)
{
const REMOVE_VERTEX_STATE vstm = vstates[vm];
pbm = vstm == TO_REMOVE || vstm == PROCESSED;
}
}
}
bool bad_opposite_cell = pb1 || pb2 || pb3 || pbm;
// update the hole if needed
// when the vertex is not to be removed
if(bad_opposite_cell)
{
if(opp_cit->tds_data().is_clear())
{
hole.push_back(opp_cit);
opp_cit->tds_data().mark_processed();
n++;
}
continue;
}
Facet f(opp_cit, opp_i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical_oriented_triple(vt);
outer_map[vt] = f;
v1->set_cell(opp_cit);
v2->set_cell(opp_cit);
v3->set_cell(opp_cit);
vm->set_cell(opp_cit);
}
}
std::size_t vsize = vertices.size();
for(std::size_t i=0; i<vsize; i++)
vstates[vertices[i]] = CLEAR;
}
template < class Gt, class Tds, class Lds >
template < class InputIterator, class VertexRemover >
bool
Triangulation_3<Gt, Tds, Lds>::
_remove_cluster_3D(InputIterator first, InputIterator beyond, VertexRemover& remover,
std::map<Vertex_handle, REMOVE_VERTEX_STATE>& vstates)
{
InputIterator init = first;
while(first != beyond)
{
Vertex_handle v = *first++;
if(vstates[v] == PROCESSED)
continue;
// _make_big_hole_3D and we fill the hole for each cluster
vstates[v] = PROCESSED;
// here, we make the hole for the cluster with v inside
typedef std::map<Vertex_triple,Facet> Vertex_triple_Facet_map;
std::vector<Cell_handle> hole;
std::vector<Vertex_handle> vertices;
hole.reserve(64);
vertices.reserve(32);
Vertex_triple_Facet_map outer_map;
_make_big_hole_3D(v, outer_map, hole, vertices, vstates);
// the connectivity is totally lost, we need to rebuild
if(!outer_map.size())
{
std::size_t nh = hole.size();
for(std::size_t i=0; i<nh; i++) hole[i]->tds_data().clear();
return false;
}
std::size_t vsi = vertices.size();
bool inf = false;
std::size_t i;
Vertex_handle_unique_hash_map vmap;
Cell_handle ch = Cell_handle();
if(vsi > 100)
{
// spatial sort if too many points
std::vector<Point> vps;
std::map<Point, Vertex_handle> mp_vps;
for(i=0; i<vsi;i++)
{
Vertex_handle vv = vertices[i];
if(! this->is_infinite(vv))
{
vps.push_back(vv->point());
mp_vps[vv->point()] = vv;
}
else
{
inf = true;
}
}
// Spatial sorting can only be applied to bare points, so we need an adaptor
typedef typename Geom_traits::Construct_point_3 Construct_point_3;
typedef typename boost::result_of<const Construct_point_3(const Point&)>::type Ret;
typedef boost::function_property_map<Construct_point_3, Point, Ret> fpmap;
typedef CGAL::Spatial_sort_traits_adapter_3<Geom_traits, fpmap> Search_traits_3;
spatial_sort(vps.begin(), vps.end(),
Search_traits_3(
boost::make_function_property_map<Point, Ret, Construct_point_3>(
geom_traits().construct_point_3_object()), geom_traits()));
std::size_t svps = vps.size();
for(i=0; i < svps; i++)
{
Vertex_handle vv = mp_vps[vps[i]];
Vertex_handle vh = remover.tmp.insert(vv->point(), ch);
ch = vh->cell();
vmap[vh] = vv;
}
if(remover.tmp.dimension()==2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = this->infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = this->infinite_vertex();
}
}
else
{
for(i=0; i < vsi; i++)
{
if(!this->is_infinite(vertices[i]))
{
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}
else
{
inf = true;
}
}
if(remover.tmp.dimension()==2)
{
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = this->infinite_vertex();
}
else
{
vmap[remover.tmp.infinite_vertex()] = this->infinite_vertex();
}
}
Vertex_triple_Facet_map inner_map;
if(inf)
{
for(All_cells_iterator it = remover.tmp.all_cells_begin(),
end = remover.tmp.all_cells_end(); it != end; ++it)
{
for(unsigned int index=0; index < 4; index++)
{
Facet f = std::pair<Cell_handle,int>(it,index);
Vertex_triple vt_aux = this->make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
this->make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
else
{
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin(),
end = remover.tmp.finite_cells_end(); it != end; ++it)
{
for(unsigned int index=0; index < 4; index++)
{
Facet f = std::pair<Cell_handle,int>(it,index);
Vertex_triple vt_aux = this->make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first], vmap[vt_aux.third], vmap[vt_aux.second]);
this->make_canonical_oriented_triple(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty())
{
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(this->is_infinite(oit->first.first) ||
this->is_infinite(oit->first.second) ||
this->is_infinite(oit->first.third))
{
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
for(int j=0; j<4; j++)
new_ch->vertex(j)->set_cell(new_ch);
// for the other faces check, if they can also be glued
for(unsigned int index = 0; index < 4; index++)
{
if(index != i_i)
{
Facet f = std::pair<Cell_handle,int>(new_ch,index);
Vertex_triple vt = this->make_vertex_triple(f);
this->make_canonical_oriented_triple(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end())
{
std::swap(vt.second,vt.third);
outer_map[vt]= f;
}
else
{
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(index, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
this->tds().delete_cells(hole.begin(), hole.end());
remover.tmp.clear();
}
this->tds().delete_vertices(init, beyond);
return true;
}
template < class Gt, class Tds, class Lds >
template < class InputIterator >
bool
Triangulation_3<Gt, Tds, Lds>::
does_repeat_in_range(InputIterator first, InputIterator beyond) const
{
std::set<Vertex_handle> s;
while(first != beyond)
if(! s.insert(*first++).second)
return true;
return false;
}
template < class Gt, class Tds, class Lds >
template < class InputIterator >
bool
Triangulation_3<Gt, Tds, Lds>::
infinite_vertex_in_range(InputIterator first, InputIterator beyond) const
{
while(first != beyond)
if(is_infinite(*first++))
return true;
return false;
}
template < class Gt, class Tds, class Lds >
template < class InputIterator, class VertexRemover >
typename Triangulation_3<Gt, Tds, Lds>::size_type
Triangulation_3<Gt, Tds, Lds>::
remove(InputIterator first, InputIterator beyond, VertexRemover& remover)
{
CGAL_triangulation_precondition(!does_repeat_in_range(first, beyond));
CGAL_triangulation_precondition(!infinite_vertex_in_range(first, beyond));
size_type n = number_of_vertices();
InputIterator init = first, init2 = first;
if(dimension() == 3 && n > 4)
{
// If we could add states on a vertex base as it is done
// for cells, it would improve the performance.
std::map<Vertex_handle, REMOVE_VERTEX_STATE> vstates;
_mark_vertices_to_remove(first, beyond, vstates);
if(!_test_dim_down_cluster(vstates))
{
if(_remove_cluster_3D(init, beyond, remover, vstates))
return n - number_of_vertices();
}
}
// dimension() < 3 or no connectivity of the remaining vertices
// we remove one by one
while(init2 != beyond)
{
Vertex_handle v = *init2++;
remover.tmp.clear();
remove(v, remover);
}
return n - number_of_vertices();
}
template < class GT, class Tds, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
is_valid(bool verbose, int level) const
{
if(! _tds.is_valid(verbose,level))
{
if(verbose)
std::cerr << "invalid data structure" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
if(infinite_vertex() == Vertex_handle())
{
if(verbose)
std::cerr << "no infinite vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
switch(dimension())
{
case 3:
{
for(Finite_cells_iterator it = finite_cells_begin(),
end = finite_cells_end(); it != end; ++it)
is_valid_finite(it, verbose, level);
break;
}
case 2:
{
for(Finite_facets_iterator it = finite_facets_begin(),
end = finite_facets_end(); it != end; ++it)
is_valid_finite(it->first,verbose,level);
break;
}
case 1:
{
for(Finite_edges_iterator it = finite_edges_begin(),
end = finite_edges_end(); it != 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, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
is_valid(Cell_handle c, bool verbose, int level) const
{
if(! _tds.is_valid(c,verbose,level))
{
if(verbose)
{
std::cerr << "combinatorially 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, class Lds >
bool
Triangulation_3<GT,Tds,Lds>::
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:
{
if(coplanar_orientation(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point()) != POSITIVE)
{
if(verbose)
{
std::cerr << "badly oriented face "
<< c->vertex(0)->point() << ", "
<< c->vertex(1)->point() << ", "
<< c->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();
Vertex_handle v = c->neighbor(0)->vertex(c->neighbor(0)->index(c));
if(! is_infinite(v))
{
if(collinear_position(p0, p1, v->point()) != MIDDLE)
{
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()
<< ", " << v->point() << std::endl;
}
CGAL_triangulation_assertion(false);
return false;
}
}
v = c->neighbor(1)->vertex(c->neighbor(1)->index(c));
if(! is_infinite(v))
{
if(collinear_position(p1, p0, v->point()) != MIDDLE)
{
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()
<< ", " << v->point() << std::endl;
}
CGAL_triangulation_assertion(false);
return false;
}
}
break;
}
}
return true;
}
namespace internal {
// Internal function used by operator==.
template < class GT, class Tds1, class Tds2, class Lds >
bool
test_next(const Triangulation_3<GT, Tds1, Lds>& t1,
const Triangulation_3<GT, Tds2, Lds>& t2,
typename Triangulation_3<GT, Tds1, Lds>::Cell_handle c1,
typename Triangulation_3<GT, Tds2, Lds>::Cell_handle c2,
std::map<typename Triangulation_3<GT, Tds1, Lds>::Cell_handle,
typename Triangulation_3<GT, Tds2, Lds>::Cell_handle>& Cmap,
std::map<typename Triangulation_3<GT, Tds1, Lds>::Vertex_handle,
typename Triangulation_3<GT, Tds2, Lds>::Vertex_handle>& Vmap)
{
// This function tests and registers the 4 neighbors of c1/c2,
// and recursively calls itself over them.
// We don't use the call stack as it may overflow
// Returns false if an inequality has been found.
// Precondition: c1, c2 have been registered as well as their 4 vertices.
CGAL_triangulation_precondition(t1.dimension() >= 2);
CGAL_triangulation_precondition(Cmap[c1] == c2);
CGAL_triangulation_precondition(Vmap.find(c1->vertex(0)) != Vmap.end());
CGAL_triangulation_precondition(Vmap.find(c1->vertex(1)) != Vmap.end());
CGAL_triangulation_precondition(Vmap.find(c1->vertex(2)) != Vmap.end());
CGAL_triangulation_precondition(t1.dimension() == 2 ||
Vmap.find(c1->vertex(3)) != Vmap.end());
typedef Triangulation_3<GT, Tds1, Lds> Tr1;
typedef Triangulation_3<GT, Tds2, Lds> Tr2;
typedef typename Tr1::Vertex_handle Vertex_handle1;
typedef typename Tr1::Cell_handle Cell_handle1;
typedef typename Tr2::Vertex_handle Vertex_handle2;
typedef typename Tr2::Cell_handle Cell_handle2;
typedef typename std::map<Vertex_handle1, Vertex_handle2>::const_iterator Vit;
typedef typename std::map<Cell_handle1, Cell_handle2>::const_iterator Cit;
typedef typename Tr1::Geom_traits::Construct_point_3 Construct_point_3;
typedef typename Tr1::Geom_traits::Compare_xyz_3 Compare_xyz_3;
Compare_xyz_3 cmp1 = t1.geom_traits().compare_xyz_3_object();
Construct_point_3 cp = t1.geom_traits().construct_point_3_object();
std::vector<std::pair<Cell_handle1, Cell_handle2> > cell_stack;
cell_stack.push_back(std::make_pair(c1, c2));
while(! cell_stack.empty())
{
Cell_handle1 c1 = cell_stack.back().first;
Cell_handle2 c2 = cell_stack.back().second;
cell_stack.pop_back();
for(int i=0; i <= t1.dimension(); ++i)
{
Cell_handle1 n1 = c1->neighbor(i);
Cit cit = Cmap.find(n1);
Vertex_handle1 v1 = c1->vertex(i);
Vertex_handle2 v2 = Vmap[v1];
Cell_handle2 n2 = c2->neighbor(c2->index(v2));
if(cit != Cmap.end())
{
// n1 was already registered.
if(cit->second != n2)
return false;
continue;
}
// n1 has not yet been registered.
// We check that the new vertices match geometrically.
// And we register them.
Vertex_handle1 vn1 = n1->vertex(n1->index(c1));
Vertex_handle2 vn2 = n2->vertex(n2->index(c2));
Vit vit = Vmap.find(vn1);
if(vit != Vmap.end())
{
// vn1 already registered
if(vit->second != vn2)
return false;
}
else
{
if(t2.is_infinite(vn2))
return false; // vn1 can't be infinite,
// since it would have been registered.
if(cmp1(cp(vn1->point()), cp(vn2->point())) != 0)
return false;
// We register vn1/vn2.
Vmap.insert(std::make_pair(vn1, vn2));
}
// We register n1/n2.
Cmap.insert(std::make_pair(n1, n2));
cell_stack.push_back(std::make_pair(n1, n2));
}
}
return true;
}
} // namespace internal
template < class GT, class Tds1, class Tds2, class Lds >
bool
operator==(const Triangulation_3<GT, Tds1, Lds>& t1,
const Triangulation_3<GT, Tds2, Lds>& t2)
{
typedef typename Triangulation_3<GT, Tds1>::Vertex_handle Vertex_handle1;
typedef typename Triangulation_3<GT, Tds1>::Cell_handle Cell_handle1;
typedef typename Triangulation_3<GT, Tds2>::Vertex_handle Vertex_handle2;
typedef typename Triangulation_3<GT, Tds2>::Cell_handle Cell_handle2;
typedef typename Triangulation_3<GT, Tds1>::Point Point;
typedef typename Triangulation_3<GT, Tds1>::Geom_traits::Equal_3 Equal_3;
typedef typename Triangulation_3<GT, Tds1>::Geom_traits::Compare_xyz_3 Compare_xyz_3;
typedef typename Triangulation_3<GT, Tds1>::Geom_traits::Construct_point_3 Construct_point_3;
Equal_3 equal = t1.geom_traits().equal_3_object();
Compare_xyz_3 cmp1 = t1.geom_traits().compare_xyz_3_object();
Compare_xyz_3 cmp2 = t2.geom_traits().compare_xyz_3_object();
Construct_point_3 cp = t1.geom_traits().construct_point_3_object();
// Some quick checks.
if(t1.dimension() != t2.dimension() ||
t1.number_of_vertices() != t2.number_of_vertices() ||
t1.number_of_cells() != t2.number_of_cells())
return false;
int dim = t1.dimension();
// Special case for dimension < 1.
// The triangulation is uniquely defined in these cases.
if(dim < 1)
return true;
// Special case for dimension == 1.
if(dim == 1)
{
// It's enough to test that the points are the same,
// since the triangulation is uniquely defined in this case.
std::vector<Point> V1 (t1.points_begin(), t1.points_end());
std::vector<Point> V2 (t2.points_begin(), t2.points_end());
std::sort(V1.begin(), V1.end(),
boost::bind<Comparison_result>(
cmp1,
boost::bind<
typename boost::result_of<const Construct_point_3(const Point&)>::type>(cp, _1),
boost::bind<
typename boost::result_of<const Construct_point_3(const Point&)>::type>(cp, _2))
== SMALLER);
std::sort(V2.begin(), V2.end(),
boost::bind<Comparison_result>(
cmp2,
boost::bind<
typename boost::result_of<const Construct_point_3(const Point&)>::type>(cp, _1),
boost::bind<
typename boost::result_of<const Construct_point_3(const Point&)>::type>(cp, _2))
== SMALLER);
return V1 == V2;
}
// We will store the mapping between the 2 triangulations vertices and
// cells in 2 maps.
std::map<Vertex_handle1, Vertex_handle2> Vmap;
std::map<Cell_handle1, Cell_handle2> Cmap;
// Handle the infinite vertex.
Vertex_handle1 v1 = t1.infinite_vertex();
Vertex_handle2 iv2 = t2.infinite_vertex();
Vmap.insert(std::make_pair(v1, iv2));
// We pick one infinite cell of t1, and try to match it against the
// infinite cells of t2.
Cell_handle1 c = v1->cell();
Vertex_handle1 v2 = c->vertex((c->index(v1)+1)%(dim+1));
Vertex_handle1 v3 = c->vertex((c->index(v1)+2)%(dim+1));
Vertex_handle1 v4 = c->vertex((c->index(v1)+3)%(dim+1));
const Point& p2 = v2->point();
const Point& p3 = v3->point();
const Point& p4 = v4->point();
std::vector<Cell_handle2> ics;
t2.incident_cells(iv2, std::back_inserter(ics));
for(typename std::vector<Cell_handle2>::const_iterator cit = ics.begin();
cit != ics.end(); ++cit)
{
int inf = (*cit)->index(iv2);
if(equal(cp(p2), cp((*cit)->vertex((inf+1)%(dim+1))->point())))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+1)%(dim+1))));
else if(equal(cp(p2), cp((*cit)->vertex((inf+2)%(dim+1))->point())))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+2)%(dim+1))));
else if(dim == 3 && equal(cp(p2), cp((*cit)->vertex((inf+3)%(dim+1))->point())))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v2.
if(equal(cp(p3), cp((*cit)->vertex((inf+1)%(dim+1))->point())))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+1)%(dim+1))));
else if(equal(cp(p3), cp((*cit)->vertex((inf+2)%(dim+1))->point())))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+2)%(dim+1))));
else if(dim == 3 && equal(cp(p3), cp((*cit)->vertex((inf+3)%(dim+1))->point())))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v3.
if(dim == 3)
{
if(equal(cp(p4), cp((*cit)->vertex((inf+1)%(dim+1))->point())))
Vmap.insert(std::make_pair(v4, (*cit)->vertex((inf+1)%(dim+1))));
else if(equal(cp(p4), cp((*cit)->vertex((inf+2)%(dim+1))->point())))
Vmap.insert(std::make_pair(v4, (*cit)->vertex((inf+2)%(dim+1))));
else if(equal(cp(p4), cp((*cit)->vertex((inf+3)%(dim+1))->point())))
Vmap.insert(std::make_pair(v4, (*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v4.
}
// Found it !
Cmap.insert(std::make_pair(c, *cit));
break;
}
if(Cmap.size() == 0)
return false;
// We now have one cell, we need to propagate recursively.
return internal::test_next(t1, t2,
Cmap.begin()->first, Cmap.begin()->second, Cmap, Vmap);
}
template < class GT, class Tds1, class Tds2 >
inline
bool
operator!=(const Triangulation_3<GT, Tds1>& t1,
const Triangulation_3<GT, Tds2>& t2)
{
return ! (t1 == t2);
}
} //namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_TRIANGULATION_3_H