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// Copyright (c) 1999-2004 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/Regular_triangulation_3.h $
// $Id: Regular_triangulation_3.h 07eacf5 2020-06-30T16:38:05+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
// Christophe Delage <Christophe.Delage@sophia.inria.fr>
// Clement Jamin
#ifndef CGAL_REGULAR_TRIANGULATION_3_H
#define CGAL_REGULAR_TRIANGULATION_3_H
#include <CGAL/license/Triangulation_3.h>
#include <CGAL/disable_warnings.h>
#include <CGAL/basic.h>
#ifdef CGAL_LINKED_WITH_TBB
# include <CGAL/point_generators_3.h>
# include <tbb/parallel_for.h>
# include <thread>
# include <tbb/enumerable_thread_specific.h>
# include <tbb/concurrent_vector.h>
#endif
#include <CGAL/Triangulation_3.h>
#include <CGAL/Regular_triangulation_vertex_base_3.h>
#include <CGAL/Regular_triangulation_cell_base_3.h>
#include <CGAL/internal/Has_nested_type_Bare_point.h>
#include <CGAL/Cartesian_converter.h>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Kernel_traits.h>
#include <CGAL/result_of.h>
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
#include <CGAL/Spatial_sort_traits_adapter_3.h>
#include <CGAL/internal/info_check.h>
#include <boost/iterator/zip_iterator.hpp>
#include <boost/mpl/and.hpp>
#endif //CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
#ifdef CGAL_TRIANGULATION_3_PROFILING
# include <CGAL/Mesh_3/Profiling_tools.h>
#endif
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
#include <CGAL/point_generators_3.h>
#endif
#include <boost/bind.hpp>
#include <boost/mpl/if.hpp>
#include <boost/mpl/identity.hpp>
#include <boost/property_map/function_property_map.hpp>
#include <boost/utility/result_of.hpp>
#include <algorithm>
#include <iostream>
#include <iterator>
#include <set>
#include <thread>
#include <utility>
#include <vector>
namespace CGAL {
/************************************************
*
* Regular_triangulation_3 class
*
************************************************/
template < class Gt, class Tds_ = Default, class Lock_data_structure_ = Default >
class Regular_triangulation_3
: public Triangulation_3<
Gt,
typename Default::Get<Tds_, Triangulation_data_structure_3 <
Regular_triangulation_vertex_base_3<Gt>,
Regular_triangulation_cell_base_3<Gt> > >::type,
Lock_data_structure_>
{
private:
typedef typename Default::Get<Tds_, Triangulation_data_structure_3 <
Regular_triangulation_vertex_base_3<Gt>,
Regular_triangulation_cell_base_3<Gt> >
>::type Tds;
typedef Regular_triangulation_3<Gt, Tds_, Lock_data_structure_> Self;
public:
typedef Triangulation_3<Gt, Tds, Lock_data_structure_> Tr_Base;
typedef Gt Geom_traits;
typedef Tds Triangulation_data_structure;
typedef Geom_traits Traits;
typedef typename Tr_Base::Concurrency_tag Concurrency_tag;
typedef typename Tr_Base::Lock_data_structure Lock_data_structure;
typedef typename Tr_Base::Vertex_handle Vertex_handle;
typedef typename Tr_Base::Cell_handle Cell_handle;
typedef typename Tr_Base::Vertex Vertex;
typedef typename Tr_Base::Cell Cell;
typedef typename Tr_Base::Facet Facet;
typedef typename Tr_Base::Edge Edge;
typedef typename Tr_Base::size_type size_type;
typedef typename Tr_Base::Locate_type Locate_type;
typedef typename Tr_Base::Cell_iterator Cell_iterator;
typedef typename Tr_Base::Facet_iterator Facet_iterator;
typedef typename Tr_Base::Edge_iterator Edge_iterator;
typedef typename Tr_Base::Facet_circulator Facet_circulator;
typedef typename Tr_Base::Finite_vertices_iterator Finite_vertices_iterator;
typedef typename Tr_Base::Finite_cells_iterator Finite_cells_iterator;
typedef typename Tr_Base::Finite_facets_iterator Finite_facets_iterator;
typedef typename Tr_Base::Finite_edges_iterator Finite_edges_iterator;
typedef typename Tr_Base::All_cells_iterator All_cells_iterator;
// Traits are not supposed to define Bare_point, but leaving below
// for backward compatibility
typedef typename boost::mpl::eval_if_c<
internal::Has_nested_type_Bare_point<Gt>::value,
typename internal::Bare_point_type<Gt>,
boost::mpl::identity<typename Gt::Point_3>
>::type Bare_point;
typedef typename Gt::Weighted_point_3 Weighted_point;
typedef typename Gt::Segment_3 Segment;
typedef typename Gt::Triangle_3 Triangle;
typedef typename Gt::Tetrahedron_3 Tetrahedron;
// types for dual:
typedef typename Gt::Line_3 Line;
typedef typename Gt::Ray_3 Ray;
typedef typename Gt::Plane_3 Plane;
typedef typename Gt::Object_3 Object;
//Tag to distinguish Delaunay from regular triangulations
typedef Tag_true Weighted_tag;
// Tag to distinguish periodic triangulations from others
typedef Tag_false Periodic_tag;
#ifndef CGAL_CFG_USING_BASE_MEMBER_BUG_2
using Tr_Base::geom_traits;
#endif
using Tr_Base::adjacent_vertices;
using Tr_Base::adjacent_vertices_threadsafe;
using Tr_Base::cw;
using Tr_Base::ccw;
using Tr_Base::construct_point;
using Tr_Base::coplanar_orientation;
using Tr_Base::dimension;
using Tr_Base::find_conflicts;
using Tr_Base::finite_facets_begin;
using Tr_Base::finite_facets_end;
using Tr_Base::finite_vertices_begin;
using Tr_Base::finite_vertices_end;
using Tr_Base::finite_cells_begin;
using Tr_Base::finite_cells_end;
using Tr_Base::finite_edges_begin;
using Tr_Base::finite_edges_end;
using Tr_Base::incident_facets;
using Tr_Base::insert_in_conflict;
using Tr_Base::infinite_vertex;
using Tr_Base::is_infinite;
using Tr_Base::is_valid;
using Tr_Base::is_valid_finite;
using Tr_Base::locate;
using Tr_Base::mirror_vertex;
using Tr_Base::mirror_index;
using Tr_Base::next_around_edge;
using Tr_Base::number_of_vertices;
using Tr_Base::orientation;
using Tr_Base::point;
using Tr_Base::side_of_segment;
using Tr_Base::side_of_edge;
using Tr_Base::tds;
using Tr_Base::vertex_triple_index;
Regular_triangulation_3(const Gt& gt = Gt(), Lock_data_structure *lock_ds = nullptr)
: Tr_Base(gt, lock_ds), hidden_point_visitor(this)
{ }
Regular_triangulation_3(Lock_data_structure *lock_ds, const Gt& gt = Gt())
: Tr_Base(lock_ds, gt), hidden_point_visitor(this)
{ }
Regular_triangulation_3(const Regular_triangulation_3& rt)
: Tr_Base(rt), hidden_point_visitor(this)
{
CGAL_triangulation_postcondition(is_valid());
}
Regular_triangulation_3(Regular_triangulation_3&& rt)
noexcept(noexcept(Tr_Base(std::move(rt))))
: Tr_Base(std::move(rt)), hidden_point_visitor(this)
{
CGAL_triangulation_postcondition(is_valid());
}
~Regular_triangulation_3() = default;
void swap(Regular_triangulation_3& tr)
{
// The 'vertices' and 'hidden_points' members of
// 'hidden_point_visitor' should be empty as they are only filled
// (and cleared) during the insertion of a point. Hidden points
// are not stored there, but rather in cells. Thus, the only thing
// that must be set is the triangulation pointer, and it is
// already correctly set. There is nothing to do about
// 'hidden_point_visitor'.
Tr_Base::swap(tr);
}
Regular_triangulation_3& operator=(const Regular_triangulation_3& tr)
{
Regular_triangulation_3 copy(tr);
copy.swap(*this);
return *this;
}
Regular_triangulation_3& operator=(Regular_triangulation_3&& tr)
noexcept(noexcept(Regular_triangulation_3(std::move(tr))))
{
Tr_Base::operator=(std::move(tr));
return *this;
}
//insertion
template < typename InputIterator >
Regular_triangulation_3(InputIterator first, InputIterator last,
const Gt& gt = Gt(), Lock_data_structure *lock_ds = nullptr)
: Tr_Base(gt, lock_ds), hidden_point_visitor(this)
{
insert(first, last);
}
template < typename InputIterator >
Regular_triangulation_3(InputIterator first, InputIterator last,
Lock_data_structure *lock_ds, const Gt& gt = Gt())
: Tr_Base(gt, lock_ds), hidden_point_visitor(this)
{
insert(first, last);
}
private:
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
std::vector<Vertex_handle>
add_temporary_points_on_far_sphere(const size_t num_points)
{
std::vector<Vertex_handle> far_sphere_vertices;
const size_t MIN_NUM_POINTS_FOR_FAR_SPHERE_POINTS = 1000000;
if(num_points >= MIN_NUM_POINTS_FOR_FAR_SPHERE_POINTS)
{
// Add temporary vertices on a "far sphere" to reduce contention on
// the infinite vertex
// Get bbox
const Bbox_3& bbox = *this->get_bbox();
// Compute radius for far sphere
const double& xdelta = bbox.xmax() - bbox.xmin();
const double& ydelta = bbox.ymax() - bbox.ymin();
const double& zdelta = bbox.zmax() - bbox.zmin();
const double radius = 1.3 * 0.5 * std::sqrt(xdelta*xdelta +
ydelta*ydelta +
zdelta*zdelta);
// WARNING - TODO @fixme this code has to be fixed because Vector_3 is not
// required by the traits concept
const typename Gt::Vector_3 center(bbox.xmin() + 0.5*xdelta,
bbox.ymin() + 0.5*ydelta,
bbox.zmin() + 0.5*zdelta);
Random_points_on_sphere_3<Bare_point> random_point(radius);
const int NUM_PSEUDO_INFINITE_VERTICES = static_cast<int>(
std::thread::hardware_concurrency() * 3.5);
typename Gt::Construct_weighted_point_3 cwp =
geom_traits().construct_weighted_point_3_object();
std::vector<Weighted_point> points_on_far_sphere;
for(int i = 0 ; i < NUM_PSEUDO_INFINITE_VERTICES ; ++i, ++random_point)
points_on_far_sphere.push_back(cwp(*random_point + center));
// 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 Weighted_point&)>::type Ret;
typedef boost::function_property_map<Construct_point_3, Weighted_point, Ret> fpmap;
typedef CGAL::Spatial_sort_traits_adapter_3<Geom_traits, fpmap> Search_traits_3;
spatial_sort(points_on_far_sphere.begin(), points_on_far_sphere.end(),
Search_traits_3(
boost::make_function_property_map<Weighted_point, Ret, Construct_point_3>(
geom_traits().construct_point_3_object()), geom_traits()));
typename std::vector<Weighted_point>::const_iterator it_p =
points_on_far_sphere.begin();
typename std::vector<Weighted_point>::const_iterator it_p_end =
points_on_far_sphere.end();
for(; it_p != it_p_end ; ++it_p)
{
Locate_type lt;
Cell_handle c, hint;
int li, lj;
c = locate(*it_p, lt, li, lj, hint);
Vertex_handle v = insert(*it_p, lt, c, li, lj);
hint = (v == Vertex_handle() ? c : v->cell());
far_sphere_vertices.push_back(v);
}
}
return far_sphere_vertices;
}
void remove_temporary_points_on_far_sphere(
const std::vector<Vertex_handle>& far_sphere_vertices)
{
if(!far_sphere_vertices.empty())
{
// Remove the temporary vertices on far sphere
remove(far_sphere_vertices.begin(), far_sphere_vertices.end());
}
}
#endif // CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
public:
#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,
Weighted_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
{
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
static Profile_branch_counter_3 bcounter(
"early withdrawals / late withdrawals / successes [Regular_tri_3::insert]");
#endif
#ifdef CGAL_TRIANGULATION_3_PROFILING
WallClockTimer t;
#endif
size_type n = number_of_vertices();
std::vector<Weighted_point> points(first, last);
// Spatial sorting can only be applied to bare points, so we need an adaptor
// @todo Unary_function_to_property_map makes a copy (get() returns a value_type) but
// we could hope to get a const& to the bare point. Unfortunately, the lazy
// kernel creates temporaries and prevent it.
typedef typename Geom_traits::Construct_point_3 Construct_point_3;
typedef typename boost::result_of<const Construct_point_3(const Weighted_point&)>::type Ret;
typedef boost::function_property_map<Construct_point_3, Weighted_point, Ret> fpmap;
typedef CGAL::Spatial_sort_traits_adapter_3<Geom_traits, fpmap> Search_traits_3;
spatial_sort(points.begin(), points.end(),
Search_traits_3(
boost::make_function_property_map<Weighted_point, Ret, Construct_point_3>(
geom_traits().construct_point_3_object()), geom_traits()));
// Parallel
#ifdef CGAL_LINKED_WITH_TBB
if(this->is_parallel())
{
size_t num_points = points.size();
Cell_handle hint;
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
std::vector<Vertex_handle> far_sphere_vertices =
add_temporary_points_on_far_sphere(num_points);
#endif
size_t i = 0;
// Insert "num_points_seq" points sequentially
// (or more if dim < 3 after that)
size_t num_points_seq = (std::min)(num_points, (size_t)100);
while (i < num_points_seq || (dimension() < 3 && i < num_points))
{
Locate_type lt;
Cell_handle c;
int li, lj;
c = locate(points[i], lt, li, lj, hint);
Vertex_handle v = insert (points[i], lt, c, li, lj);
hint = (v == Vertex_handle() ? c : v->cell());
++i;
}
tbb::enumerable_thread_specific<Vertex_handle> tls_hint(hint->vertex(0));
tbb::parallel_for(tbb::blocked_range<size_t>(i, num_points),
Insert_point<Self>(*this, points, tls_hint));
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
remove_temporary_points_on_far_sphere(far_sphere_vertices);
#endif
}
// Sequential
else
#endif // CGAL_LINKED_WITH_TBB
{
Cell_handle hint;
for(typename std::vector<Weighted_point>::const_iterator p = points.begin(),
end = points.end(); p != end; ++p)
{
Locate_type lt;
Cell_handle c;
int li, lj;
c = locate(*p, lt, li, lj, hint);
Vertex_handle v = insert(*p, lt, c, li, lj);
hint = v == Vertex_handle() ? c : v->cell();
}
}
#ifdef CGAL_TRIANGULATION_3_PROFILING
std::cerr << "Points inserted in " << t.elapsed() << " seconds." << std::endl;
#endif
return number_of_vertices() - n;
}
#ifndef CGAL_TRIANGULATION_3_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
private:
//top stands for tuple-or-pair
template <class Info>
const Weighted_point& top_get_first(const std::pair<Weighted_point,Info>& pair) const { return pair.first; }
template <class Info>
const Info& top_get_second(const std::pair<Weighted_point,Info>& pair) const { return pair.second; }
template <class Info>
const Weighted_point& top_get_first(const boost::tuple<Weighted_point,Info>& tuple) const { return boost::get<0>(tuple); }
template <class Info>
const Info& top_get_second(const boost::tuple<Weighted_point,Info>& tuple) const { return boost::get<1>(tuple); }
// Functor to go from an index of a container of Weighted_point to
// the corresponding Bare_point
template<class Construct_bare_point, class Container>
struct Index_to_Bare_point
{
typename boost::result_of<const Construct_bare_point(const Weighted_point&)>::type
operator()(const std::size_t& i) const
{
return cp(c[i]);
}
Index_to_Bare_point(const Container& c, const Construct_bare_point& cp)
: c(c), cp(cp) { }
const Container& c;
const Construct_bare_point cp;
};
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<Weighted_point> points;
std::vector<typename Triangulation_data_structure::Vertex::Info> infos;
std::size_t index=0;
for(InputIterator it=first;it!=last;++it)
{
Tuple_or_pair pair = *it;
points.push_back(top_get_first(pair));
infos.push_back(top_get_second(pair));
indices.push_back(index++);
}
// We need to sort the points and their info at the same time through
// the `indices` vector AND spatial sort can only handle Gt::Point_3.
typedef typename Geom_traits::Construct_point_3 Construct_point_3;
typedef Index_to_Bare_point<Construct_point_3,
std::vector<Weighted_point> > Access_bare_point;
typedef typename boost::result_of<const Construct_point_3(const Weighted_point&)>::type Ret;
typedef boost::function_property_map<Access_bare_point, std::size_t, Ret> fpmap;
typedef CGAL::Spatial_sort_traits_adapter_3<Gt, fpmap> Search_traits_3;
Access_bare_point accessor(points, geom_traits().construct_point_3_object());
spatial_sort(indices.begin(), indices.end(),
Search_traits_3(
boost::make_function_property_map<
std::size_t, Ret, Access_bare_point>(accessor),
geom_traits()));
#ifdef CGAL_LINKED_WITH_TBB
if(this->is_parallel())
{
size_t num_points = points.size();
Cell_handle hint;
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
std::vector<Vertex_handle> far_sphere_vertices =
add_temporary_points_on_far_sphere(num_points);
#endif
size_t i = 0;
// Insert "num_points_seq" points sequentially
// (or more if dim < 3 after that)
size_t num_points_seq = (std::min)(num_points, (size_t)100);
while (i < num_points_seq || (dimension() < 3 && i < num_points))
{
Locate_type lt;
Cell_handle c;
int li, lj;
c = locate(points[indices[i]], lt, li, lj, hint);
Vertex_handle v = insert(points[indices[i]], lt, c, li, lj);
if(v != Vertex_handle())
{
v->info() = infos[indices[i]];
hint = v->cell();
}
else
hint = c;
++i;
}
tbb::enumerable_thread_specific<Vertex_handle> tls_hint(hint->vertex(0));
tbb::parallel_for(tbb::blocked_range<size_t>(i, num_points),
Insert_point_with_info<Self>(*this, points, infos, indices, tls_hint));
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_ADD_TEMPORARY_POINTS_ON_FAR_SPHERE
remove_temporary_points_on_far_sphere(far_sphere_vertices);
#endif
}
// Sequential
else
#endif // CGAL_LINKED_WITH_TBB
{
Cell_handle hint;
for(typename std::vector<std::size_t>::const_iterator
it = indices.begin(), end = indices.end();
it != end; ++it)
{
Locate_type lt;
Cell_handle c;
int li, lj;
c = locate(points[*it], lt, li, lj, hint);
Vertex_handle v = insert(points[*it], lt, c, li, lj);
if(v!=Vertex_handle())
{
v->info()=infos[*it];
hint=v->cell();
}
else
{
hint = c;
}
}
}
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<Weighted_point,typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type>
>
>::type* = nullptr)
{
return insert_with_info<
std::pair<Weighted_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_<
typename boost::is_convertible< typename std::iterator_traits<InputIterator_1>::value_type, Weighted_point >,
typename boost::is_convertible< typename std::iterator_traits<InputIterator_2>::value_type, typename internal::Info_check<typename Triangulation_data_structure::Vertex>::type >
> >::type* =nullptr)
{
return insert_with_info<
boost::tuple<Weighted_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(const Weighted_point& p, Vertex_handle hint,
bool *could_lock_zone = nullptr)
{
return insert(p,
hint == Vertex_handle() ? this->infinite_cell() : hint->cell(),
could_lock_zone);
}
Vertex_handle insert(const Weighted_point& p,
Cell_handle start = Cell_handle(), bool *could_lock_zone = nullptr);
Vertex_handle insert(const Weighted_point& p, Locate_type lt,
Cell_handle c, int li, int, bool *could_lock_zone = nullptr);
template <class CellIt>
Vertex_handle insert_in_hole(const Weighted_point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i);
template <class CellIt>
Vertex_handle insert_in_hole(const Weighted_point& p,
CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i, Vertex_handle newv);
template <class OutputIteratorBoundaryFacets,
class OutputIteratorCells,
class OutputIteratorInternalFacets>
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets>
find_conflicts(const Weighted_point& p, Cell_handle c,
OutputIteratorBoundaryFacets bfit,
OutputIteratorCells cit,
OutputIteratorInternalFacets ifit,
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);
std::vector<Cell_handle> cells;
cells.reserve(32);
std::vector<Facet> facets;
facets.reserve(64);
if(dimension() == 2)
{
Conflict_tester_2 tester(p, this);
if(! tester(c))
return make_triple(bfit, cit, ifit);
ifit = Tr_Base::find_conflicts(c, tester,
make_triple(std::back_inserter(facets),
std::back_inserter(cells),
ifit),
could_lock_zone,
this_facet_must_be_in_the_cz,
the_facet_is_in_its_cz).third;
}
else
{
Conflict_tester_3 tester(p, this);
if(! tester(c))
return make_triple(bfit, cit, ifit);
ifit = Tr_Base::find_conflicts(c, tester,
make_triple(std::back_inserter(facets),
std::back_inserter(cells),
ifit),
could_lock_zone,
this_facet_must_be_in_the_cz,
the_facet_is_in_its_cz).third;
}
// Reset the conflict flag on the boundary.
for(typename std::vector<Facet>::iterator fit = facets.begin();
fit != facets.end(); ++fit)
{
fit->first->neighbor(fit->second)->tds_data().clear();
*bfit++ = *fit;
}
// Reset the conflict flag in the conflict cells.
for(typename std::vector<Cell_handle>::iterator ccit = cells.begin();
ccit != cells.end(); ++ccit)
{
(*ccit)->tds_data().clear();
*cit++ = *ccit;
}
return make_triple(bfit, cit, ifit);
}
template <class OutputIteratorBoundaryFacets, class OutputIteratorCells>
std::pair<OutputIteratorBoundaryFacets, OutputIteratorCells>
find_conflicts(const Weighted_point& p, Cell_handle c,
OutputIteratorBoundaryFacets bfit,
OutputIteratorCells cit,
bool *could_lock_zone = nullptr) const
{
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
Emptyset_iterator> t = find_conflicts(p, c, bfit, cit,
Emptyset_iterator(),
could_lock_zone);
return std::make_pair(t.first, t.second);
}
// Returns the vertices on the interior of the conflict hole.
template <class OutputIterator>
OutputIterator vertices_inside_conflict_zone(const Weighted_point&p, Cell_handle c,
OutputIterator res) const
{
CGAL_triangulation_precondition(dimension() >= 2);
// Get the facets on the boundary of the hole, and the cells of the hole
std::vector<Cell_handle> cells;
std::vector<Facet> facets;
find_conflicts(p, c, std::back_inserter(facets),
std::back_inserter(cells), Emptyset_iterator());
// Put all vertices on the hole in 'vertices'
const int d = dimension();
std::set<Vertex_handle> vertices;
for(typename std::vector<Cell_handle>::const_iterator it = cells.begin(),
end = cells.end(); it != end; ++it)
{
for(int i = 0; i <= d; ++i)
vertices.insert((*it)->vertex(i));
}
// Then extract the vertices of the boundary and remove them from
// 'vertices'
if(dimension() == 3)
{
for(typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i)
{
vertices.erase(i->first->vertex((i->second+1)&3));
vertices.erase(i->first->vertex((i->second+2)&3));
vertices.erase(i->first->vertex((i->second+3)&3));
}
}
else
{
for(typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i)
{
vertices.erase(i->first->vertex(cw(i->second)));
vertices.erase(i->first->vertex(ccw(i->second)));
}
}
return std::copy(vertices.begin(), vertices.end(), res);
}
#ifndef CGAL_NO_DEPRECATED_CODE
// Returns the vertices on the boundary of the conflict hole.
template <class OutputIterator>
OutputIterator vertices_in_conflict(const Weighted_point&p, Cell_handle c,
OutputIterator res) const
{
return vertices_on_conflict_zone_boundary(p, c, res);
}
#endif // CGAL_NO_DEPRECATED_CODE
// Returns the vertices on the boundary of the conflict hole.
template <class OutputIterator>
OutputIterator vertices_on_conflict_zone_boundary(const Weighted_point&p,
Cell_handle c,
OutputIterator res) const
{
CGAL_triangulation_precondition(dimension() >= 2);
// Get the facets on the boundary of the hole.
std::vector<Facet> facets;
find_conflicts(p, c, std::back_inserter(facets),
Emptyset_iterator(), Emptyset_iterator());
// Then extract uniquely the vertices.
std::set<Vertex_handle> vertices;
if(dimension() == 3)
{
for(typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i)
{
vertices.insert(i->first->vertex((i->second+1)&3));
vertices.insert(i->first->vertex((i->second+2)&3));
vertices.insert(i->first->vertex((i->second+3)&3));
}
} else {
for(typename std::vector<Facet>::const_iterator i = facets.begin();
i != facets.end(); ++i)
{
vertices.insert(i->first->vertex(cw(i->second)));
vertices.insert(i->first->vertex(ccw(i->second)));
}
}
return std::copy(vertices.begin(), vertices.end(), res);
}
// In parallel operations, we need to be able to check the health of the 'hint' vertex handle,
// which might be invalided by other threads. One way to do that is the 'is_vertex()' function
// of the TDS, but it runs in O(sqrt(n)) complexity. When we are using our TDS, we can use
// a lower level function from the compact container, which runs in constant time.
BOOST_MPL_HAS_XXX_TRAIT_DEF(Is_CGAL_TDS_3)
template <typename TDS_,
bool has_TDS_tag = has_Is_CGAL_TDS_3<TDS_>::value>
struct Is_CGAL_TDS_3 : public CGAL::Tag_false
{ };
template <typename TDS_>
struct Is_CGAL_TDS_3<TDS_, true> : public CGAL::Boolean_tag<TDS_::Is_CGAL_TDS_3::value>
{ };
template <typename TDS_,
bool is_CGAL_TDS_3 = Is_CGAL_TDS_3<TDS_>::value>
struct Vertex_validity_checker
{
bool operator()(const typename TDS_::Vertex_handle vh_, const TDS_& tds_) {
return tds_.is_vertex(vh_);
}
};
template <typename TDS_>
struct Vertex_validity_checker<TDS_, true /* is_CGAL_TDS_3 */>
{
bool operator()(const typename TDS_::Vertex_handle vh_, const TDS_& tds_) {
return tds_.vertices().is_used(vh_);
}
};
void remove(Vertex_handle v);
// Concurrency-safe
// See Triangulation_3::remove for more information
bool remove(Vertex_handle v, bool *could_lock_zone);
template < typename InputIterator >
size_type remove(InputIterator first, InputIterator beyond)
{
CGAL_triangulation_precondition(!this->does_repeat_in_range(first, beyond));
size_type n = number_of_vertices();
#ifdef CGAL_TRIANGULATION_3_PROFILING
WallClockTimer t;
#endif
// Parallel
#ifdef CGAL_LINKED_WITH_TBB
if(this->is_parallel())
{
// TODO: avoid that by asking for ramdom-access iterators?
std::vector<Vertex_handle> vertices(first, beyond);
tbb::concurrent_vector<Vertex_handle> vertices_to_remove_sequentially;
tbb::parallel_for(tbb::blocked_range<size_t>(0, vertices.size()),
Remove_point<Self>(*this, vertices, vertices_to_remove_sequentially));
// Do the rest sequentially
for(typename tbb::concurrent_vector<Vertex_handle>::const_iterator
it = vertices_to_remove_sequentially.begin(),
it_end = vertices_to_remove_sequentially.end()
; it != it_end
; ++it)
{
remove(*it);
}
}
// Sequential
else
#endif // CGAL_LINKED_WITH_TBB
{
while(first != beyond)
{
remove(*first);
++first;
}
}
#ifdef CGAL_TRIANGULATION_3_PROFILING
std::cerr << "Points removed in " << t.elapsed() << " seconds." << std::endl;
#endif
return n - number_of_vertices();
}
template <class OutputItCells>
void remove_and_give_new_cells(Vertex_handle v, OutputItCells cit)
{
Self tmp;
Vertex_remover<Self> remover(tmp);
Tr_Base::remove_and_give_new_cells(v, remover, cit);
CGAL_triangulation_expensive_postcondition(is_valid());
}
// Displacement works only for regular triangulation
// without hidden points at any time
Vertex_handle move_if_no_collision(Vertex_handle v, const Weighted_point& p);
Vertex_handle move(Vertex_handle v, const Weighted_point& p);
// REMOVE CLUSTER - works only when Regular has no hidden point at all
// "regular as Delaunay"
template < typename InputIterator >
size_type remove_cluster(InputIterator first, InputIterator beyond)
{
Self tmp;
Vertex_remover<Self> remover(tmp);
return Tr_Base::remove(first, beyond, remover);
}
protected:
Oriented_side side_of_oriented_power_sphere(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p3,
const Weighted_point& p,
bool perturb = false) const;
Oriented_side side_of_oriented_power_circle(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p,
bool perturb = false) const;
Bounded_side side_of_bounded_power_circle(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p,
bool perturb = false) const;
Bounded_side side_of_bounded_power_segment(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p,
bool perturb = false) const;
public:
// Queries
Bounded_side side_of_power_sphere(Cell_handle c, const Weighted_point& p,
bool perturb = false) const;
Bounded_side side_of_power_circle(const Facet& f, const Weighted_point& p,
bool /* perturb */ = false) const
{
return side_of_power_circle(f.first, f.second, p);
}
Bounded_side side_of_power_circle(Cell_handle c, int i, const Weighted_point& p,
bool perturb = false) const;
Bounded_side side_of_power_segment(Cell_handle c, const Weighted_point& p,
bool perturb = false) const;
// Undocumented, needed for Mesh_3 (because of Periodic_3_mesh_3)
bool greater_or_equal_power_distance(const Bare_point& p,
const Weighted_point& q,
const Weighted_point& r) const;
Vertex_handle nearest_power_vertex_in_cell(const Bare_point& p,
Cell_handle c) const;
Vertex_handle nearest_power_vertex(const Bare_point& p, Cell_handle c = Cell_handle()) const;
bool is_Gabriel(Cell_handle c, int i) const;
bool is_Gabriel(Cell_handle c, int i, int j) const;
bool is_Gabriel(const Facet& f)const ;
bool is_Gabriel(const Edge& e) const;
bool is_Gabriel(Vertex_handle v) const;
// Dual functions
Bare_point dual(Cell_handle c) const;
Object dual(Cell_handle c, int i) const;
Object dual(const Facet& facet) const;
void dual_segment(Cell_handle c, int i, Bare_point& p, Bare_point&q) const;
void dual_segment(const Facet& facet, Bare_point& p, Bare_point&q) const;
void dual_segment_exact(const Facet& facet, Bare_point& p, Bare_point&q) const;
void dual_ray(Cell_handle c, int i, Ray& ray) const;
void dual_ray(const Facet& facet, Ray& ray) const;
void dual_ray_exact(const Facet& facet, Ray& ray) const;
template < class Stream>
Stream& draw_dual(Stream& os) const;
bool is_valid(bool verbose = false, int level = 0) const;
protected:
bool less_power_distance(const Bare_point& p,
const Weighted_point& q,
const Weighted_point& r) const
{
return geom_traits().compare_power_distance_3_object()(p, q, r) == SMALLER;
}
Bare_point construct_weighted_circumcenter(const Weighted_point& p,
const Weighted_point& q,
const Weighted_point& r,
const Weighted_point& s) const
{
return geom_traits().construct_weighted_circumcenter_3_object()(p,q,r,s);
}
Bare_point construct_weighted_circumcenter(const Weighted_point& p,
const Weighted_point& q,
const Weighted_point& r) const
{
return geom_traits().construct_weighted_circumcenter_3_object()(p,q,r);
}
Segment construct_segment(const Bare_point& p, const Bare_point& q) const
{
return geom_traits().construct_segment_3_object()(p, q);
}
Line construct_perpendicular_line(const Plane& pl, const Bare_point& p) const
{
return geom_traits().construct_perpendicular_line_3_object()(pl, p);
}
Plane construct_plane(const Bare_point& p, const Bare_point& q, const Bare_point& r) const
{
return geom_traits().construct_plane_3_object()(p, q, r);
}
Ray construct_ray(const Bare_point& p, const Line& l) const
{
return geom_traits().construct_ray_3_object()(p, l);
}
Object construct_object(const Bare_point& p) const
{
return geom_traits().construct_object_3_object()(p);
}
Object construct_object(const Segment& s) const
{
return geom_traits().construct_object_3_object()(s);
}
Object construct_object(const Ray& r) const
{
return geom_traits().construct_object_3_object()(r);
}
Vertex_handle nearest_power_vertex(const Bare_point& p,
Vertex_handle v,
Vertex_handle w) const
{
// In case of equality, v is returned.
CGAL_triangulation_precondition(v != w);
if(is_infinite(v))
return w;
if(is_infinite(w))
return v;
return less_power_distance(p, w->point(), v->point()) ? w : v;
}
Oriented_side power_test(const Weighted_point& p, const Weighted_point& q) const
{
CGAL_triangulation_precondition(this->equal(p, q));
return geom_traits().power_side_of_oriented_power_sphere_3_object()(p, q);
}
Oriented_side power_test(const Weighted_point& p, const Weighted_point& q,
const Weighted_point& r) const
{
CGAL_triangulation_precondition(this->collinear(p, q, r));
return geom_traits().power_side_of_oriented_power_sphere_3_object()(p, q, r);
}
Oriented_side power_test(const Weighted_point& p, const Weighted_point& q,
const Weighted_point& r, const Weighted_point& s) const
{
CGAL_triangulation_precondition(this->coplanar(p, q, r, s));
return geom_traits().power_side_of_oriented_power_sphere_3_object()(p, q, r, s);
}
Oriented_side power_test(const Weighted_point& p, const Weighted_point& q,
const Weighted_point& r, const Weighted_point& s,
const Weighted_point& t) const
{
return geom_traits().power_side_of_oriented_power_sphere_3_object()(p, q, r, s, t);
}
bool in_conflict_3(const Weighted_point& p, const Cell_handle c) const
{
return side_of_power_sphere(c, p, true) == ON_BOUNDED_SIDE;
}
bool in_conflict_2(const Weighted_point& p, const Cell_handle c, int i) const
{
return side_of_power_circle(c, i, p, true) == ON_BOUNDED_SIDE;
}
bool in_conflict_1(const Weighted_point& p, const Cell_handle c) const
{
return side_of_power_segment(c, p, true) == ON_BOUNDED_SIDE;
}
bool in_conflict_0(const Weighted_point& p, const Cell_handle c) const
{
return power_test(c->vertex(0)->point(), p) == ON_POSITIVE_SIDE;
}
bool in_conflict(const Weighted_point& p, const Cell_handle c) const
{
switch(dimension())
{
case 0:
return in_conflict_0(p, c);
case 1:
return in_conflict_1(p, c);
case 2:
return in_conflict_2(p, c, 3);
case 3:
return in_conflict_3(p, c);
}
return true;
}
class Conflict_tester_3
{
const Weighted_point& p;
const Self *t;
public:
Conflict_tester_3(const Weighted_point& pt, const Self *tr)
: p(pt), t(tr)
{
}
bool operator()(const Cell_handle c) const
{
return t->in_conflict_3(p, c);
}
bool test_initial_cell(const Cell_handle c) const
{
return operator()(c);
}
Oriented_side compare_weight(const Weighted_point& wp1,
const Weighted_point& wp2) const
{
return t->power_test(wp1, wp2);
}
};
class Conflict_tester_2
{
const Weighted_point& p;
const Self *t;
public:
Conflict_tester_2(const Weighted_point& pt, const Self *tr)
: p(pt), t(tr)
{
}
bool operator()(const Cell_handle c) const
{
return t->in_conflict_2(p, c, 3);
}
bool test_initial_cell(const Cell_handle c) const
{
return operator()(c);
}
Oriented_side compare_weight(const Weighted_point& wp1,
const Weighted_point& wp2) const
{
return t->power_test(wp1, wp2);
}
};
class Conflict_tester_1
{
const Weighted_point& p;
const Self *t;
public:
Conflict_tester_1(const Weighted_point& pt, const Self *tr)
: p(pt), t(tr)
{
}
bool operator()(const Cell_handle c) const
{
return t->in_conflict_1(p, c);
}
bool test_initial_cell(const Cell_handle c) const
{
return operator()(c);
}
Oriented_side compare_weight(const Weighted_point& wp1,
const Weighted_point& wp2) const
{
return t->power_test(wp1, wp2);
}
};
class Conflict_tester_0
{
const Weighted_point& p;
const Self *t;
public:
Conflict_tester_0(const Weighted_point& pt, const Self *tr)
: p(pt), t(tr)
{
}
bool operator()(const Cell_handle c) const
{
return t->in_conflict_0(p, c);
}
bool test_initial_cell(const Cell_handle c) const
{
return operator()(c);
}
int compare_weight(const Weighted_point& wp1,
const Weighted_point& wp2) const
{
return t->power_test(wp1, wp2);
}
};
// Sequential version
// "dummy" is here to allow the specialization (see below)
// See http://groups.google.com/group/comp.lang.c++.moderated/browse_thread/thread/285ab1eec49e1cb6
template<typename Concurrency_tag_, typename dummy = void>
class Hidden_point_visitor
{
Self *t;
mutable std::vector<Vertex_handle> vertices;
mutable std::vector<Weighted_point> hidden_points;
public:
Hidden_point_visitor(Self *tr) : t(tr) {}
template <class InputIterator>
void process_cells_in_conflict(InputIterator start, InputIterator end) const
{
int dim = t->dimension();
while(start != end)
{
std::copy((*start)->hidden_points_begin(),
(*start)->hidden_points_end(),
std::back_inserter(hidden_points));
for(int i=0; i<=dim; i++)
{
Vertex_handle v = (*start)->vertex(i);
if(v->cell() != Cell_handle())
{
vertices.push_back(v);
v->set_cell(Cell_handle());
}
}
start ++;
}
}
void reinsert_vertices(Vertex_handle v)
{
Cell_handle hc = v->cell();
for(typename std::vector<Vertex_handle>::iterator
vi = vertices.begin(); vi != vertices.end(); ++vi)
{
if((*vi)->cell() != Cell_handle())
continue;
hc = t->locate((*vi)->point(), hc);
hide_point(hc, (*vi)->point());
t->tds().delete_vertex(*vi);
}
vertices.clear();
for(typename std::vector<Weighted_point>::iterator
hp = hidden_points.begin(); hp != hidden_points.end(); ++hp)
{
hc = t->locate(*hp, hc);
hide_point (hc, *hp);
}
hidden_points.clear();
}
Vertex_handle replace_vertex(Cell_handle c, int index, const Weighted_point& p)
{
Vertex_handle v = c->vertex(index);
hide_point(c, v->point());
v->set_point(p);
return v;
}
void hide_point(Cell_handle c, const Weighted_point& p)
{
c->hide_point(p);
}
};
#ifdef CGAL_LINKED_WITH_TBB
// Parallel version specialization
template<typename dummy>
class Hidden_point_visitor<Parallel_tag, dummy>
{
typedef Hidden_point_visitor<Parallel_tag> HPV;
Self *t;
mutable tbb::enumerable_thread_specific<std::vector<Vertex_handle> > vertices;
mutable tbb::enumerable_thread_specific<std::vector<Weighted_point> > hidden_points;
public:
Hidden_point_visitor(Self *tr) : t(tr) {}
template <class InputIterator>
void process_cells_in_conflict(InputIterator start, InputIterator end) const
{
int dim = t->dimension();
while(start != end)
{
std::copy((*start)->hidden_points_begin(),
(*start)->hidden_points_end(),
std::back_inserter(hidden_points.local()));
for(int i=0; i<=dim; i++)
{
Vertex_handle v = (*start)->vertex(i);
if(v->cell() != Cell_handle())
{
vertices.local().push_back(v);
v->set_cell(Cell_handle());
}
}
start ++;
}
}
void reinsert_vertices(Vertex_handle v)
{
Cell_handle hc = v->cell();
for(typename std::vector<Vertex_handle>::iterator
vi = vertices.local().begin(); vi != vertices.local().end(); ++vi)
{
if((*vi)->cell() != Cell_handle())
continue;
hc = t->locate((*vi)->point(), hc);
hide_point(hc, (*vi)->point());
t->tds().delete_vertex(*vi);
}
vertices.local().clear();
for(typename std::vector<Weighted_point>::iterator
hp = hidden_points.local().begin(); hp != hidden_points.local().end(); ++hp)
{
hc = t->locate(*hp, hc);
hide_point (hc, *hp);
}
hidden_points.local().clear();
}
Vertex_handle replace_vertex(Cell_handle c, int index, const Weighted_point& p)
{
Vertex_handle v = c->vertex(index);
hide_point(c, v->point());
v->set_point(p);
return v;
}
void hide_point(Cell_handle c, const Weighted_point& p)
{
c->hide_point(p);
}
};
// Functor for parallel insert(begin, end) function
template <typename RT>
class Insert_point
{
typedef typename RT::Weighted_point Weighted_point;
typedef typename RT::Vertex_handle Vertex_handle;
RT& m_rt;
const std::vector<Weighted_point>& m_points;
tbb::enumerable_thread_specific<Vertex_handle>& m_tls_hint;
public:
// Constructor
Insert_point(RT& rt,
const std::vector<Weighted_point>& points,
tbb::enumerable_thread_specific<Vertex_handle>& tls_hint)
: m_rt(rt), m_points(points), m_tls_hint(tls_hint)
{}
// operator()
void operator()(const tbb::blocked_range<size_t>& r) const
{
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
static Profile_branch_counter_3 bcounter(
"early withdrawals / late withdrawals / successes [Delaunay_tri_3::insert]");
#endif
Vertex_handle& hint = m_tls_hint.local();
Vertex_validity_checker<typename RT::Triangulation_data_structure> vertex_validity_check;
for(size_t i_point = r.begin() ; i_point != r.end() ; ++i_point)
{
bool success = false;
const Weighted_point& p = m_points[i_point];
while(!success)
{
// The 'hint' is unsafe to use immediately because we are in a regular triangulation,
// and the insertion of a (weighted) point in another thread might have hidden (deleted)
// the hint.
if(!vertex_validity_check(hint, m_rt.tds()))
{
hint = m_rt.finite_vertices_begin();
continue;
}
// We need to make sure that while are locking the position P1 := hint->point(), 'hint'
// does not get its position changed to P2 != P1.
const Weighted_point hint_point_mem = hint->point();
if(m_rt.try_lock_point(hint_point_mem) && m_rt.try_lock_point(p))
{
// Make sure that the hint is still valid (so that we can safely take hint->cell()) and
// that its position hasn't changed to ensure that we will start the locate from where
// we have locked.
if(!vertex_validity_check(hint, m_rt.tds()) ||
hint->point() != hint_point_mem)
{
hint = m_rt.finite_vertices_begin();
m_rt.unlock_all_elements();
continue;
}
bool could_lock_zone;
Locate_type lt;
int li, lj;
Cell_handle c = m_rt.locate(p, lt, li, lj, hint->cell(), &could_lock_zone);
Vertex_handle v;
if(could_lock_zone)
v = m_rt.insert(p, lt, c, li, lj, &could_lock_zone);
if(could_lock_zone)
{
hint = (v == Vertex_handle() ? c->vertex(0) : v);
m_rt.unlock_all_elements();
success = true;
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
++bcounter;
#endif
}
else
{
m_rt.unlock_all_elements();
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
bcounter.increment_branch_1(); // THIS is a late withdrawal!
#endif
}
}
else
{
m_rt.unlock_all_elements();
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
bcounter.increment_branch_2(); // THIS is an early withdrawal!
#endif
}
}
}
}
};
// Functor for parallel insert_with_info(begin, end) function
template <typename RT>
class Insert_point_with_info
{
typedef typename RT::Weighted_point Weighted_point;
typedef typename RT::Vertex_handle Vertex_handle;
typedef typename RT::Triangulation_data_structure::Vertex::Info Info;
RT& m_rt;
const std::vector<Weighted_point>& m_points;
const std::vector<Info>& m_infos;
const std::vector<std::size_t>& m_indices;
tbb::enumerable_thread_specific<Vertex_handle>& m_tls_hint;
public:
// Constructor
Insert_point_with_info(RT& rt,
const std::vector<Weighted_point>& points,
const std::vector<Info>& infos,
const std::vector<std::size_t>& indices,
tbb::enumerable_thread_specific<Vertex_handle>& tls_hint)
: m_rt(rt), m_points(points), m_infos(infos), m_indices(indices),
m_tls_hint(tls_hint)
{}
// operator()
void operator()(const tbb::blocked_range<size_t>& r) const
{
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
static Profile_branch_counter_3 bcounter(
"early withdrawals / late withdrawals / successes [Delaunay_tri_3::insert]");
#endif
Vertex_handle& hint = m_tls_hint.local();
Vertex_validity_checker<typename RT::Triangulation_data_structure> vertex_validity_check;
for(size_t i_idx = r.begin() ; i_idx != r.end() ; ++i_idx)
{
bool success = false;
std::ptrdiff_t i_point = m_indices[i_idx];
const Weighted_point& p = m_points[i_point];
while(!success)
{
// The 'hint' is unsafe to use immediately because we are in a regular triangulation,
// and the insertion of a (weighted) point in another thread might have hidden (deleted)
// the hint.
if(!vertex_validity_check(hint, m_rt.tds()))
{
hint = m_rt.finite_vertices_begin();
continue;
}
// We need to make sure that while are locking the position P1 := hint->point(), 'hint'
// does not get its position changed to P2 != P1.
const Weighted_point hint_point_mem = hint->point();
if(m_rt.try_lock_point(hint_point_mem) && m_rt.try_lock_point(p))
{
// Make sure that the hint is still valid (so that we can safely take hint->cell()) and
// that its position hasn't changed to ensure that we will start the locate from where
// we have locked.
if(!vertex_validity_check(hint, m_rt.tds()) ||
hint->point() != hint_point_mem)
{
hint = m_rt.finite_vertices_begin();
m_rt.unlock_all_elements();
continue;
}
bool could_lock_zone;
Locate_type lt;
int li, lj;
Cell_handle c = m_rt.locate(p, lt, li, lj, hint->cell(), &could_lock_zone);
Vertex_handle v;
if(could_lock_zone)
v = m_rt.insert(p, lt, c, li, lj, &could_lock_zone);
if(could_lock_zone)
{
if(v == Vertex_handle())
{
hint = c->vertex(0);
}
else
{
v->info() = m_infos[i_point];
hint = v;
}
m_rt.unlock_all_elements();
success = true;
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
++bcounter;
#endif
}
else
{
m_rt.unlock_all_elements();
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
bcounter.increment_branch_1(); // THIS is a late withdrawal!
#endif
}
}
else
{
m_rt.unlock_all_elements();
#ifdef CGAL_CONCURRENT_TRIANGULATION_3_PROFILING
bcounter.increment_branch_2(); // THIS is an early withdrawal!
#endif
}
}
}
}
};
// Functor for parallel remove(begin, end) function
template <typename RT>
class Remove_point
{
typedef typename RT::Weighted_point Weighted_point;
typedef typename RT::Vertex_handle Vertex_handle;
RT& m_rt;
const std::vector<Vertex_handle>& m_vertices;
tbb::concurrent_vector<Vertex_handle>& m_vertices_to_remove_sequentially;
public:
// Constructor
Remove_point(RT& rt,
const std::vector<Vertex_handle>& vertices,
tbb::concurrent_vector<Vertex_handle>& vertices_to_remove_sequentially)
: m_rt(rt), m_vertices(vertices),
m_vertices_to_remove_sequentially(vertices_to_remove_sequentially)
{}
// operator()
void operator()(const tbb::blocked_range<size_t>& r) const
{
for(size_t i_vertex = r.begin() ; i_vertex != r.end() ; ++i_vertex)
{
Vertex_handle v = m_vertices[i_vertex];
bool could_lock_zone, needs_to_be_done_sequentially;
do
{
needs_to_be_done_sequentially = !m_rt.remove(v, &could_lock_zone);
m_rt.unlock_all_elements();
}
while(!could_lock_zone);
if(needs_to_be_done_sequentially)
m_vertices_to_remove_sequentially.push_back(v);
}
}
};
#endif // CGAL_LINKED_WITH_TBB
Hidden_point_visitor<Concurrency_tag>& get_hidden_point_visitor()
{
return hidden_point_visitor;
}
template < class RegularTriangulation_3 >
class Vertex_remover;
template < class RegularTriangulation_3 >
class Vertex_inserter;
Hidden_point_visitor<Concurrency_tag> hidden_point_visitor;
};
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
nearest_power_vertex_in_cell(const Bare_point& p, Cell_handle c) const
// Returns the finite vertex of the cell c with smaller
// power distance to p.
{
CGAL_triangulation_precondition(dimension() >= 1);
Vertex_handle nearest = nearest_power_vertex(p, c->vertex(0), c->vertex(1));
if(dimension() >= 2)
{
nearest = nearest_power_vertex(p, nearest, c->vertex(2));
if(dimension() == 3)
nearest = nearest_power_vertex(p, nearest, c->vertex(3));
}
return nearest;
}
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
nearest_power_vertex(const Bare_point& p, Cell_handle start) const
{
if(number_of_vertices() == 0)
return Vertex_handle();
// Use a brute-force algorithm if dimension < 3.
if(dimension() < 3)
{
Finite_vertices_iterator vit = finite_vertices_begin();
Vertex_handle res = vit;
++vit;
for(Finite_vertices_iterator end = finite_vertices_end(); vit != end; ++vit)
res = nearest_power_vertex(p, res, vit);
return res;
}
Locate_type lt;
int li, lj;
typename Gt::Construct_weighted_point_3 p2wp = geom_traits().construct_weighted_point_3_object();
Cell_handle c = locate(p2wp(p), lt, li, lj, start);
// - start with the closest vertex from the located cell.
// - repeatedly take the nearest of its incident vertices if any
// - if not, we're done.
Vertex_handle nearest = nearest_power_vertex_in_cell(p, c);
std::vector<Vertex_handle> vs;
vs.reserve(32);
while(true)
{
Vertex_handle tmp = nearest;
adjacent_vertices_threadsafe(nearest, std::back_inserter(vs));
for(typename std::vector<Vertex_handle>::const_iterator
vsit = vs.begin(); vsit != vs.end(); ++vsit)
tmp = nearest_power_vertex(p, tmp, *vsit);
if(tmp == nearest)
break;
vs.clear();
nearest = tmp;
}
return nearest;
}
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Bare_point
Regular_triangulation_3<Gt,Tds,Lds>::
dual(Cell_handle c) const
{
CGAL_triangulation_precondition(dimension()==3);
CGAL_triangulation_precondition(! is_infinite(c));
return c->weighted_circumcenter(geom_traits());
}
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_segment(Cell_handle c, int i, Bare_point& p, Bare_point&q) const
{
Cell_handle n = c->neighbor(i);
CGAL_assertion(! is_infinite(c) && ! is_infinite(n));
p = dual(c);
q = dual(n);
}
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_segment(const Facet& facet, Bare_point& p, Bare_point&q) const
{
return dual_segment(facet.first, facet.second, p, q);
}
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_ray(Cell_handle c, int i, Ray& ray) const
{
Cell_handle n = c->neighbor(i);
CGAL_triangulation_precondition((!is_infinite(c) != !is_infinite(n))); // xor
// either n or c is infinite
int in;
if(is_infinite(c))
{
in = n->index(c);
}
else
{
n = c;
in = i;
}
// n now denotes a finite cell, either c or c->neighbor(i)
int ind[3] = {(in+1)&3,(in+2)&3,(in+3)&3};
if((in&1) == 1)
std::swap(ind[0], ind[1]);
const Weighted_point& p = n->vertex(ind[0])->point();
const Weighted_point& q = n->vertex(ind[1])->point();
const Weighted_point& r = n->vertex(ind[2])->point();
const Bare_point& bp = construct_point(p);
const Bare_point& bq = construct_point(q);
const Bare_point& br = construct_point(r);
Line l = construct_perpendicular_line(construct_plane(bp, bq, br),
construct_weighted_circumcenter(p,q,r));
ray = construct_ray(dual(n), l);
}
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_ray(const Facet& facet, Ray& ray) const
{
return dual_ray(facet.first, facet.second, ray);
}
// Exact versions of dual_segment() and dual_ray() for Mesh_3.
// These functions are really dirty: they assume that the point type is nice enough
// such that EPECK can manipulate it (e.g. convert it to EPECK::Point_3) AND
// that the result of these manipulations will make sense.
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_segment_exact(const Facet& facet, Bare_point& p, Bare_point&q) const
{
typedef typename Kernel_traits<Bare_point>::Kernel K;
typedef Exact_predicates_exact_constructions_kernel EK;
typedef Cartesian_converter<K, EK> To_exact;
typedef Cartesian_converter<EK,K> Back_from_exact;
typedef EK Exact_Rt;
To_exact to_exact;
Back_from_exact back_from_exact;
Exact_Rt::Construct_weighted_circumcenter_3 exact_weighted_circumcenter =
Exact_Rt().construct_weighted_circumcenter_3_object();
Cell_handle c = facet.first;
int i = facet.second;
Cell_handle n = c->neighbor(i);
const typename Exact_Rt::Weighted_point_3& cp = to_exact(c->vertex(0)->point());
const typename Exact_Rt::Weighted_point_3& cq = to_exact(c->vertex(1)->point());
const typename Exact_Rt::Weighted_point_3& cr = to_exact(c->vertex(2)->point());
const typename Exact_Rt::Weighted_point_3& cs = to_exact(c->vertex(3)->point());
const typename Exact_Rt::Weighted_point_3& np = to_exact(n->vertex(0)->point());
const typename Exact_Rt::Weighted_point_3& nq = to_exact(n->vertex(1)->point());
const typename Exact_Rt::Weighted_point_3& nr = to_exact(n->vertex(2)->point());
const typename Exact_Rt::Weighted_point_3& ns = to_exact(n->vertex(3)->point());
p = back_from_exact(exact_weighted_circumcenter(cp, cq, cr, cs));
q = back_from_exact(exact_weighted_circumcenter(np, nq, nr, ns));
}
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
dual_ray_exact(const Facet& facet, Ray& ray) const
{
Cell_handle c = facet.first;
int i = facet.second;
Cell_handle n = c->neighbor(i);
CGAL_triangulation_precondition(!is_infinite(c) != !is_infinite(n)); // xor
// either n or c is infinite
int in;
if(is_infinite(c))
{
in = n->index(c);
}
else
{
n = c;
in = i;
}
// n now denotes a finite cell, either c or c->neighbor(i)
int ind[3] = {(in+1)&3,(in+2)&3,(in+3)&3};
if((in&1) == 1)
std::swap(ind[0], ind[1]);
// exact part
typedef typename Kernel_traits<Bare_point>::Kernel K;
typedef Exact_predicates_exact_constructions_kernel EK;
typedef Cartesian_converter<K, EK> To_exact;
typedef Cartesian_converter<EK,K> Back_from_exact;
typedef EK Exact_Rt;
To_exact to_exact;
Back_from_exact back_from_exact;
Exact_Rt::Construct_weighted_circumcenter_3 exact_weighted_circumcenter =
Exact_Rt().construct_weighted_circumcenter_3_object();
Exact_Rt::Construct_perpendicular_line_3 exact_perpendicular_line =
Exact_Rt().construct_perpendicular_line_3_object();
Exact_Rt::Construct_plane_3 exact_plane_3 = Exact_Rt().construct_plane_3_object();
Exact_Rt::Construct_ray_3 exact_ray_3 = Exact_Rt().construct_ray_3_object();
Exact_Rt::Construct_point_3 exact_point_3 = Exact_Rt().construct_point_3_object();
const typename Exact_Rt::Weighted_point_3& p = to_exact(n->vertex(ind[0])->point());
const typename Exact_Rt::Weighted_point_3& q = to_exact(n->vertex(ind[1])->point());
const typename Exact_Rt::Weighted_point_3& r = to_exact(n->vertex(ind[2])->point());
const typename Exact_Rt::Weighted_point_3& s = to_exact(n->vertex(in)->point());
const typename Exact_Rt::Point_3& bp = exact_point_3(p);
const typename Exact_Rt::Point_3& bq = exact_point_3(q);
const typename Exact_Rt::Point_3& br = exact_point_3(r);
typename Exact_Rt::Line_3 l = exact_perpendicular_line(
exact_plane_3(bp, bq, br),
exact_weighted_circumcenter(p, q, r));
ray = back_from_exact(exact_ray_3(exact_weighted_circumcenter(p, q, r, s), l));
}
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Object
Regular_triangulation_3<Gt,Tds,Lds>::
dual(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension()>=2);
CGAL_triangulation_precondition(! is_infinite(c,i));
if(dimension() == 2)
{
CGAL_triangulation_precondition(i == 3);
return construct_object(construct_weighted_circumcenter(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point()));
}
// dimension() == 3
Cell_handle n = c->neighbor(i);
if(! is_infinite(c) && ! is_infinite(n))
{
// dual is a segment
Bare_point bp = dual(c);
Bare_point np = dual(n);
return construct_object(construct_segment(bp, np));
}
// either n or c is infinite, dual is a ray
Ray r;
dual_ray(c, i, r);
return construct_object(r);
}
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Object
Regular_triangulation_3<Gt,Tds,Lds>::
dual(const Facet& facet) const
{
return dual(facet.first, facet.second);
}
template < class Gt, class Tds, class Lds >
template < class Stream>
Stream&
Regular_triangulation_3<Gt,Tds,Lds>::
draw_dual(Stream& os) const
{
for(Finite_facets_iterator fit = finite_facets_begin(), end = finite_facets_end();
fit != end; ++fit)
{
Object o = dual(*fit);
if(const Segment* s = object_cast<Segment>(&o))
os << *s;
else if(const Ray* r = object_cast<Ray>(&o))
os << *r;
else if(const Bare_point* p = object_cast<Bare_point>(&o))
os << *p;
}
return os;
}
template < class Gt, class Tds, class Lds >
Oriented_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_oriented_power_sphere(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p3,
const Weighted_point& p, bool perturb) const
{
CGAL_triangulation_precondition(orientation(p0, p1, p2, p3) == POSITIVE);
using namespace boost;
Oriented_side os = power_test(p0, p1, p2, p3, p);
if(os != ON_ORIENTED_BOUNDARY || !perturb)
return os;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
const Weighted_point * points[5] = {&p0, &p1, &p2, &p3, &p};
std::sort(points, points + 5, typename Tr_Base::Perturbation_order(this));
// We successively look whether the leading monomial, then 2nd monomial
// of the determinant has non null coefficient.
for(int i=4; i>1; --i)
{
if(points[i] == &p)
return ON_NEGATIVE_SIDE; // since p0 p1 p2 p3 are non coplanar and positively oriented
Orientation o;
if(points[i] == &p3 && (o = orientation(p0,p1,p2,p)) != COPLANAR)
return o;
if(points[i] == &p2 && (o = orientation(p0,p1,p,p3)) != COPLANAR)
return o;
if(points[i] == &p1 && (o = orientation(p0,p,p2,p3)) != COPLANAR)
return o;
if(points[i] == &p0 && (o = orientation(p,p1,p2,p3)) != COPLANAR)
return o;
}
CGAL_triangulation_assertion(false);
return ON_NEGATIVE_SIDE;
}
template < class Gt, class Tds, class Lds >
Bounded_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_power_sphere(Cell_handle c, const Weighted_point& p, bool perturb) const
{
CGAL_triangulation_precondition(dimension() == 3);
int i3;
if(! c->has_vertex(infinite_vertex(), i3))
{
return Bounded_side(side_of_oriented_power_sphere(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point(),
p, perturb));
}
// else infinite cell :
int i0,i1,i2;
if((i3%2) == 1)
{
i0 = (i3+1)&3;
i1 = (i3+2)&3;
i2 = (i3+3)&3;
}
else
{
i0 = (i3+2)&3;
i1 = (i3+1)&3;
i2 = (i3+3)&3;
}
// general case
Orientation o = orientation(c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(), p);
if(o != ZERO)
return Bounded_side(o);
// else p coplanar with i0,i1,i2
return side_of_bounded_power_circle(c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p, perturb);
}
template < class Gt, class Tds, class Lds >
Bounded_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_bounded_power_circle(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p, bool perturb) const
{
CGAL_triangulation_precondition(coplanar_orientation(p0, p1, p2) != 0);
if(coplanar_orientation(p0, p1, p2) == POSITIVE)
return Bounded_side (side_of_oriented_power_circle(p0, p1, p2, p, perturb));
// Wrong because the low level power test already does a coplanar orientation test.
// return Bounded_side (- side_of_oriented_power_circle (p0, p2, p1, p, perturb));
return Bounded_side (side_of_oriented_power_circle(p0, p2, p1, p, perturb));
}
template < class Gt, class Tds, class Lds >
Oriented_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_oriented_power_circle(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p2,
const Weighted_point& p, bool perturb) const
{
CGAL_triangulation_precondition(coplanar_orientation(p0, p1, p2) == POSITIVE);
using namespace boost;
Oriented_side os = power_test(p0, p1, p2, p);
if(os != ON_ORIENTED_BOUNDARY || !perturb)
return os;
// We are now in a degenerate case => we do a symbolic perturbation.
// We sort the points lexicographically.
const Weighted_point * points[4] = {&p0, &p1, &p2, &p};
std::sort(points, points + 4, typename Tr_Base::Perturbation_order(this));
// We successively look whether the leading monomial, then 2nd monomial
// of the determinant has non null coefficient.
// 2 iterations are enough (cf paper)
for(int i=3; i>1; --i)
{
if(points[i] == &p)
return ON_NEGATIVE_SIDE; // since p0 p1 p2 are non collinear and positively oriented
Orientation o;
if(points[i] == &p2 && (o = coplanar_orientation(p0,p1,p)) != COPLANAR)
return o;
if(points[i] == &p1 && (o = coplanar_orientation(p0,p,p2)) != COPLANAR)
return o;
if(points[i] == &p0 && (o = coplanar_orientation(p,p1,p2)) != COPLANAR)
return o;
}
CGAL_triangulation_assertion(false);
return ON_NEGATIVE_SIDE;
}
template < class Gt, class Tds, class Lds >
Bounded_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_power_circle(Cell_handle c, int i, const Weighted_point& p,
bool perturb) const
{
CGAL_triangulation_precondition(dimension() >= 2);
int i3 = 5;
if(dimension() == 2)
{
CGAL_triangulation_precondition(i == 3);
// the triangulation is supposed to be valid, ie the facet
// with vertices 0 1 2 in this order is positively oriented
if(! c->has_vertex(infinite_vertex(), i3))
return Bounded_side(side_of_oriented_power_circle(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
p, perturb));
// else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex(ccw(i3)),
v2 = c->vertex(cw(i3));
CGAL_triangulation_assertion(
coplanar_orientation(v1->point(), v2->point(), mirror_vertex(c, i3)->point()) == NEGATIVE);
Orientation o = coplanar_orientation(v1->point(), v2->point(), p);
if(o != ZERO)
return Bounded_side(o);
// case when p collinear with v1v2
return side_of_bounded_power_segment(v1->point(),
v2->point(),
p, perturb);
} // dim 2
// else dimension == 3
CGAL_triangulation_precondition((i >= 0) && (i < 4));
if((! c->has_vertex(infinite_vertex(),i3)) || (i3 != i))
{
// finite facet
// initialization of i0 i1 i2, vertices of the facet positively
// oriented (if the triangulation is valid)
int i0 = (i>0) ? 0 : 1;
int i1 = (i>1) ? 1 : 2;
int i2 = (i>2) ? 2 : 3;
CGAL_triangulation_precondition(this->coplanar(c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(), p));
return side_of_bounded_power_circle(c->vertex(i0)->point(),
c->vertex(i1)->point(),
c->vertex(i2)->point(),
p, perturb);
}
//else infinite facet
// v1, v2 finite vertices of the facet such that v1,v2,infinite
// is positively oriented
Vertex_handle v1 = c->vertex(next_around_edge(i3,i)),
v2 = c->vertex(next_around_edge(i,i3));
Orientation o = (Orientation)
(coplanar_orientation(v1->point(), v2->point(),
c->vertex(i)->point()) *
coplanar_orientation(v1->point(), v2->point(), p));
// then the code is duplicated from 2d case
if(o != ZERO)
return Bounded_side(-o);
// because p is in f iff
// it is not on the same side of v1v2 as c->vertex(i)
// case when p collinear with v1v2 :
return side_of_bounded_power_segment(v1->point(),
v2->point(),
p, perturb);
}
template < class Gt, class Tds, class Lds >
Bounded_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_bounded_power_segment(const Weighted_point& p0,
const Weighted_point& p1,
const Weighted_point& p, bool perturb) const
{
Oriented_side os = power_test(p0, p1, p);
if(os != ON_ORIENTED_BOUNDARY || !perturb)
return Bounded_side(os);
// We are now in a degenerate case => we do a symbolic perturbation.
switch (this->collinear_position(p0, p, p1))
{
case Tr_Base::BEFORE:
case Tr_Base::AFTER:
return ON_UNBOUNDED_SIDE;
case Tr_Base::MIDDLE:
return ON_BOUNDED_SIDE;
default:
;
}
CGAL_triangulation_assertion(false);
return ON_UNBOUNDED_SIDE;
}
template < class Gt, class Tds, class Lds >
Bounded_side
Regular_triangulation_3<Gt,Tds,Lds>::
side_of_power_segment(Cell_handle c, const Weighted_point& p, bool perturb) const
{
CGAL_triangulation_precondition(dimension() == 1);
if(! is_infinite(c,0,1))
return side_of_bounded_power_segment(c->vertex(0)->point(),
c->vertex(1)->point(),
p, perturb);
Locate_type lt; int i;
Bounded_side soe = side_of_edge(p, c, lt, i);
if(soe != ON_BOUNDARY)
return soe;
// Either we compare weights, or we use the finite neighboring edge
Cell_handle finite_neighbor = c->neighbor(c->index(infinite_vertex()));
CGAL_triangulation_assertion(!is_infinite(finite_neighbor,0,1));
return side_of_bounded_power_segment(finite_neighbor->vertex(0)->point(),
finite_neighbor->vertex(1)->point(),
p, perturb);
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
greater_or_equal_power_distance(const Bare_point& p,
const Weighted_point& q,
const Weighted_point& r) const
{
return ! less_power_distance(p, q, r);
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_Gabriel(const Facet& f) const
{
return is_Gabriel(f.first, f.second);
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_Gabriel(Cell_handle c, int i) const
{
CGAL_triangulation_precondition(dimension() == 3 && !is_infinite(c,i));
typename Geom_traits::Power_side_of_bounded_power_sphere_3
side_of_bounded_orthogonal_sphere =
geom_traits().power_side_of_bounded_power_sphere_3_object();
if((!is_infinite(c->vertex(i))) &&
side_of_bounded_orthogonal_sphere(c->vertex(vertex_triple_index(i,0))->point(),
c->vertex(vertex_triple_index(i,1))->point(),
c->vertex(vertex_triple_index(i,2))->point(),
c->vertex(i)->point()) == ON_BOUNDED_SIDE)
return false;
Cell_handle neighbor = c->neighbor(i);
int in = neighbor->index(c);
if((!is_infinite(neighbor->vertex(in))) &&
side_of_bounded_orthogonal_sphere(c->vertex(vertex_triple_index(i,0))->point(),
c->vertex(vertex_triple_index(i,1))->point(),
c->vertex(vertex_triple_index(i,2))->point(),
neighbor->vertex(in)->point()) == ON_BOUNDED_SIDE)
return false;
return true;
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_Gabriel(const Edge& e) const
{
return is_Gabriel(e.first, e.second, e.third);
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_Gabriel(Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition(dimension() == 3 && !is_infinite(c,i,j));
typename Geom_traits::Power_side_of_bounded_power_sphere_3
side_of_bounded_orthogonal_sphere =
geom_traits().power_side_of_bounded_power_sphere_3_object();
Facet_circulator fcirc = incident_facets(c,i,j), fdone(fcirc);
Vertex_handle v1 = c->vertex(i);
Vertex_handle v2 = c->vertex(j);
do
{
// test whether the vertex of cc opposite to *fcirc
// is inside the sphere defined by the edge e = (s, i,j)
Cell_handle cc = (*fcirc).first;
int ii = (*fcirc).second;
if(!is_infinite(cc->vertex(ii)) &&
side_of_bounded_orthogonal_sphere(v1->point(),
v2->point(),
cc->vertex(ii)->point()) == ON_BOUNDED_SIDE)
return false;
}
while(++fcirc != fdone);
return true;
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_Gabriel(Vertex_handle v) const
{
typename Geom_traits::Power_side_of_bounded_power_sphere_3
side_of_bounded_orthogonal_sphere = geom_traits().power_side_of_bounded_power_sphere_3_object();
Vertex_handle nearest_v = nearest_power_vertex(geom_traits().construct_point_3_object()(v->point()),
v->cell());
return (side_of_bounded_orthogonal_sphere(v->point(), nearest_v->point()) != CGAL::ON_BOUNDED_SIDE);
}
// Returns
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
insert(const Weighted_point& p, Cell_handle start, bool *could_lock_zone)
{
Locate_type lt;
int li, lj;
// Parallel
if(could_lock_zone)
{
Cell_handle c = locate(p, lt, li, lj, start, could_lock_zone);
if(*could_lock_zone)
return insert(p, lt, c, li, lj, could_lock_zone);
else
return Vertex_handle();
}
// Sequential
else
{
Cell_handle c = locate(p, lt, li, lj, start);
return insert(p, lt, c, li, lj);
}
}
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
insert(const Weighted_point& p, Locate_type lt, Cell_handle c,
int li, int lj, bool *could_lock_zone)
{
switch(dimension())
{
case 3:
{
Conflict_tester_3 tester(p, this);
return insert_in_conflict(p, lt,c,li,lj, tester,
get_hidden_point_visitor(),
could_lock_zone);
}
case 2:
{
Conflict_tester_2 tester(p, this);
return insert_in_conflict(p, lt,c,li,lj, tester,
get_hidden_point_visitor(),
could_lock_zone);
}
case 1:
{
Conflict_tester_1 tester(p, this);
return insert_in_conflict(p, lt,c,li,lj, tester,
get_hidden_point_visitor(),
could_lock_zone);
}
}
Conflict_tester_0 tester(p, this);
return insert_in_conflict(p, lt,c,li,lj, tester,
get_hidden_point_visitor(),
could_lock_zone);
}
template < class Gt, class Tds, class Lds >
template <class CellIt>
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
insert_in_hole(const Weighted_point& p, CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i)
{
CGAL_triangulation_precondition(cell_begin != cell_end);
get_hidden_point_visitor().process_cells_in_conflict(cell_begin,cell_end);
Vertex_handle v = Tr_Base::insert_in_hole(p, cell_begin, cell_end, begin, i);
// Store the hidden points in their new cells and hide vertices that
// have to be hidden
get_hidden_point_visitor().reinsert_vertices(v);
return v;
}
template < class Gt, class Tds, class Lds >
template <class CellIt>
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
insert_in_hole(const Weighted_point& p, CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i, Vertex_handle newv)
{
CGAL_triangulation_precondition(cell_begin != cell_end);
get_hidden_point_visitor().process_cells_in_conflict(cell_begin,cell_end);
Vertex_handle v = Tr_Base::insert_in_hole(p, cell_begin, cell_end, begin, i, newv);
// Store the hidden points in their new cells and hide vertices that
// have to be hidden
get_hidden_point_visitor().reinsert_vertices(v);
return v;
}
template <class Gt, class Tds, class Lds >
template <class RegularTriangulation_3>
class Regular_triangulation_3<Gt, Tds, Lds>::Vertex_remover
{
typedef RegularTriangulation_3 Regular;
typedef typename Regular::Weighted_point Weighted_point;
public:
typedef typename std::vector<Weighted_point>::iterator Hidden_points_iterator;
Vertex_remover(Regular &tmp_) : tmp(tmp_) {}
Regular& tmp;
void add_hidden_points(Cell_handle ch)
{
std::copy(ch->hidden_points_begin(), ch->hidden_points_end(),
std::back_inserter(hidden));
}
Hidden_points_iterator hidden_points_begin() { return hidden.begin(); }
Hidden_points_iterator hidden_points_end() { return hidden.end(); }
Bounded_side side_of_bounded_circle(const Weighted_point& p, const Weighted_point& q,
const Weighted_point& r, const Weighted_point& s, bool perturb = false) const
{
return tmp.side_of_bounded_power_circle(p,q,r,s,perturb);
}
private:
// The removal of v may un-hide some points,
// Space functions output them.
std::vector<Weighted_point> hidden;
};
// The displacement method works only
// on regular triangulation without hidden points at any time
// the vertex inserter is used only
// for the purpose of displacements
template <class Gt, class Tds, class Lds >
template <class RegularTriangulation_3>
class Regular_triangulation_3<Gt, Tds, Lds>::Vertex_inserter
{
typedef RegularTriangulation_3 Regular;
public:
typedef std::nullptr_t Hidden_points_iterator;
Vertex_inserter(Regular &tmp_) : tmp(tmp_) {}
Regular& tmp;
void add_hidden_points(Cell_handle) {}
Hidden_points_iterator hidden_points_begin() { return nullptr; }
Hidden_points_iterator hidden_points_end() { return nullptr; }
Vertex_handle insert(const Weighted_point& p,
Locate_type lt, Cell_handle c, int li, int lj)
{
return tmp.insert(p, lt, c, li, lj);
}
Vertex_handle insert(const Weighted_point& p, Cell_handle c)
{
return tmp.insert(p, c);
}
Vertex_handle insert(const Weighted_point& p)
{
return tmp.insert(p);
}
};
template < class Gt, class Tds, class Lds >
void
Regular_triangulation_3<Gt,Tds,Lds>::
remove(Vertex_handle v)
{
Cell_handle c;
if(dimension() > 0)
c = v->cell()->neighbor(v->cell()->index(v));
Self tmp;
Vertex_remover<Self> remover(tmp);
Tr_Base::remove(v,remover);
// Re-insert the points that v was hiding.
for(typename Vertex_remover<Self>::Hidden_points_iterator
hi = remover.hidden_points_begin();
hi != remover.hidden_points_end(); ++hi)
{
Vertex_handle hv = insert(*hi, c);
if(hv != Vertex_handle())
c = hv->cell();
}
CGAL_triangulation_expensive_postcondition(is_valid());
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
remove(Vertex_handle v, bool *could_lock_zone)
{
bool removed = true;
// Locking vertex v...
if(!this->try_lock_vertex(v))
{
*could_lock_zone = false;
}
else
{
Vertex_validity_checker<Tds> vertex_validity_check;
// Check that the vertex hasn't be deleted from the TDS while we were locking it
if(!vertex_validity_check(v, tds()))
return true; // vertex is already gone from the TDS, nothing to do
Vertex_handle hint = v->cell()->vertex(0) == v ? v->cell()->vertex(1) : v->cell()->vertex(0);
Self tmp;
Vertex_remover<Self> remover(tmp);
removed = Tr_Base::remove(v, remover, could_lock_zone);
if(*could_lock_zone && removed)
{
// The vertex has been removed, re-insert the points that 'v' was hiding
// Start by unlocking the area of the removed vertex to avoid deadlocks
this->unlock_all_elements();
for(typename Vertex_remover<Self>::Hidden_points_iterator
hi = remover.hidden_points_begin();
hi != remover.hidden_points_end(); ++hi)
{
const Weighted_point& wp = *hi;
// try to lock the positions of the hint and the hidden point
bool success = false;
while(!success)
{
// The 'hint' is unsafe to use immediately because we are in a regular triangulation,
// and the insertion of a (weighted) point in another thread might have hidden (deleted)
// the hint.
if(!vertex_validity_check(hint, tds()))
{
hint = finite_vertices_begin();
continue;
}
// We need to make sure that while are locking the position P1 := hint->point(), 'hint'
// does not get its position changed to P2 != P1.
const Weighted_point hint_point_mem = hint->point();
if(this->try_lock_point(hint_point_mem) && this->try_lock_point(wp))
{
// Make sure that the hint is still valid (so that we can safely take hint->cell()) and
// that its position hasn't changed to ensure that we will start the locate from where
// we have locked.
if(!vertex_validity_check(hint, tds()) ||
hint->point() != hint_point_mem)
{
hint = finite_vertices_begin();
this->unlock_all_elements();
continue;
}
Vertex_handle hv = insert(wp, hint, could_lock_zone);
if(*could_lock_zone)
{
success = true;
if(hv != Vertex_handle())
hint = hv;
}
}
// This unlocks everything in all cases: partial lock failure, failed insertion, successful insertion
this->unlock_all_elements();
}
}
CGAL_triangulation_expensive_postcondition(is_valid());
}
}
return removed;
}
// Displacement works only for regular triangulation
// without hidden points at any time
template < class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
move_if_no_collision(Vertex_handle v, const Weighted_point& p)
{
Self tmp;
Vertex_remover<Self> remover(tmp);
Vertex_inserter<Self> inserter(*this);
Vertex_handle res = Tr_Base::move_if_no_collision(v,p,remover,inserter);
CGAL_triangulation_expensive_postcondition(is_valid());
return res;
}
template <class Gt, class Tds, class Lds >
typename Regular_triangulation_3<Gt,Tds,Lds>::Vertex_handle
Regular_triangulation_3<Gt,Tds,Lds>::
move(Vertex_handle v, const Weighted_point& p)
{
CGAL_triangulation_precondition(!is_infinite(v));
if(v->point() == p)
return v;
Self tmp;
Vertex_remover<Self> remover(tmp);
Vertex_inserter<Self> inserter(*this);
return Tr_Base::move(v,p,remover,inserter);
}
template < class Gt, class Tds, class Lds >
bool
Regular_triangulation_3<Gt,Tds,Lds>::
is_valid(bool verbose, int level) const
{
if(! Tr_Base::is_valid(verbose,level))
{
if(verbose)
std::cerr << "invalid base triangulation" << 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);
for(int i=0; i<4; i++)
{
if(!is_infinite(it->neighbor(i)->vertex(it->neighbor(i)->index(it))))
{
if(side_of_power_sphere(it,
it->neighbor(i)->vertex(
it->neighbor(i)->index(it))->point()) == ON_BOUNDED_SIDE)
{
if(verbose)
std::cerr << "non-empty sphere " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
}
break;
}
case 2:
{
for(Finite_facets_iterator it = finite_facets_begin(), end = finite_facets_end(); it!= end; ++it)
{
is_valid_finite((*it).first, verbose, level);
for(int i=0; i<3; i++)
{
if(!is_infinite((*it).first->neighbor(i)->vertex(
(((*it).first)->neighbor(i))->index((*it).first))))
{
if(side_of_power_circle((*it).first, 3,
(*it).first->neighbor(i)->
vertex((((*it).first)->neighbor(i))
->index((*it).first))->point()) == ON_BOUNDED_SIDE)
{
if(verbose)
std::cerr << "non-empty circle " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
}
break;
}
case 1:
{
for(Finite_edges_iterator it = finite_edges_begin(),
end = finite_edges_end(); it != end; ++it)
{
is_valid_finite((*it).first, verbose, level);
for(int i=0; i<2; i++)
{
if(!is_infinite
((*it).first->neighbor(i)->vertex(
(((*it).first)->neighbor(i))->index((*it).first))))
{
if(side_of_power_segment((*it).first,
(*it).first->neighbor(i)->vertex(
(((*it).first)->neighbor(i))->index(
(*it).first))->point()) == ON_BOUNDED_SIDE)
{
if(verbose)
std::cerr << "non-empty edge " << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
}
}
break;
}
}
if(verbose)
std::cerr << "valid regular triangulation" << std::endl;
return true;
}
} //namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_REGULAR_TRIANGULATION_3_H
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