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//A class that follows a straight line through a Delaunay triangulation structure.
//Copyright (C) 2012 Utrecht University
//
//This program is free software: you can redistribute it and/or modify
//it under the terms of the GNU General Public License as published by
//the Free Software Foundation, either version 3 of the License, or
//(at your option) any later version.
//
//This program is distributed in the hope that it will be useful,
//but WITHOUT ANY WARRANTY; without even the implied warranty of
//MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
//GNU General Public License for more details.
//
//You should have received a copy of the GNU General Public License
//along with this program. If not, see <http://www.gnu.org/licenses/>.
//
// Author(s): Thijs van Lankveld
#ifndef CGAL_TRIANGULATION_SEGMENT_TRAVERSER_3_H
#define CGAL_TRIANGULATION_SEGMENT_TRAVERSER_3_H
#include <CGAL/basic.h>
#include <iostream>
#include <list>
#include <set>
#include <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/tuple.h>
// If defined, type casting is done statically,
// reducing type-safety overhead.
#define CGAL_TST_ASSUME_CORRECT_TYPES
namespace CGAL {
template < class Tr, class Inc >
class Triangulation_segment_cell_iterator_3;
namespace internal {
template < class Tr >
struct Incrementer {
typedef Incrementer<Tr> Self;
typedef Triangulation_segment_cell_iterator_3<Tr,Self> SCI; // describes the type of iterator expected by the incrementer.
Incrementer() {}
void increment( SCI& sci ) { sci.walk_to_next(); }
}; // struct Incrementer
} // namespace internal
// provides an iterator over the cells intersected by a line segment.
/*
* The `Triangulation_segment_traverser_3` iterates over the cells
* of a `Triangulation_3` by following a straight line segment \f$ st \f$.
*
* This class is closely related to `Triangulation_3::locate(...)`.
* However, unlike this `locate(...)` method, all the cells traversed
* by the `Triangulation_segment_traverser_3` intersect the interior of the line
* segment \f$ st \f$.
*
* Traversal starts from a cell containing \f$ s \f$ and it ends in a cell containing
* \f$ t \f$.
* If \f$ st \f$ is coplanar with a facet or collinear with an edge, at most one of the
* incident cells is traversed.
* If \f$ st \f$ intersects an edge or vertex, at most two incident cells are traversed:
* the cells intersecting \f$ st \f$ strictly in their interior.
*
* If \f$ s \f$ lies on the convex hull, traversal starts in an incident cell inside
* the convex hull. Similarly, if \f$ t \f$ lies on the convex hull, traversal ends in
* an adjacent cell inside the convex hull.
*
* Both \f$ s \f$ and \f$ t \f$ may lie outside the convex hull of the triangulation,
* but they must lie within the affine hull of the triangulation. In either case, the
* finite facet of any infinite cells traversed must intersect \f$ st \f$.
*
* The traverser may be applied to any triangulation of dimension > 0.
* However, for triangulations of dimension 1, the functionality is somewhat trivial.
*
* The traverser becomes invalid whenever the triangulation is changed.
*
* \tparam Tr_ is the triangulation type to traverse.
*
* \cgalModels{ForwardIterator}
*
* \sa `Triangulation_3`
* \sa `Forward_circulator_base`
*/
template < class Tr_, class Inc = internal::Incrementer<Tr_> >
class Triangulation_segment_cell_iterator_3 {
typedef Tr_ Tr;
typedef typename Tr::Triangulation_data_structure Tds;
typedef typename Tr::Geom_traits Gt;
typedef Inc Incrementer;
public:
// \name Types
// \{
typedef Tr Triangulation; //< defines the triangulation type.
typedef Triangulation_segment_cell_iterator_3<Tr,Inc>
Segment_cell_iterator; //< defines the segment cell iterator type.
typedef typename Tr::Point Point; //< defines the point type.
typedef typename Tr::Segment Segment; //< defines the line segment type.
typedef typename Tr::Cell Cell; //< defines the type of a cell of the triangulation.
typedef typename Tr::Edge Edge; //< defines the type of an edge of the triangulation.
typedef typename Tr::Vertex_handle Vertex_handle; //< defines the type of a handle for a vertex in the triangulation.
typedef typename Tr::Cell_handle Cell_handle; //< defines the type of a handle for a cell in the triangulation.
typedef typename Tr::Locate_type Locate_type; //< defines the simplex type returned from location.
typedef CGAL::cpp11::tuple<Cell_handle,Locate_type,int,int>
Simplex; //< defines the simplex type.
typedef Cell value_type; //< defines the value type the iterator refers to.
typedef Cell& reference; //< defines the reference type of the iterator.
typedef Cell* pointer; //< defines the pointer type of the iterator.
typedef std::size_t size_type; //< defines the integral type that can hold the size of a sequence.
typedef std::ptrdiff_t difference_type; //< defines the signed integral type that can hold the distance between two iterators.
typedef std::forward_iterator_tag iterator_category; //< defines the iterator category.
// \}
// describes the iterator type when applied to another type of triangulation or incrementer.
template < class Tr2, class Inc2 >
struct Rebind { typedef Triangulation_segment_cell_iterator_3<Tr2,Inc2> Other; };
private:
typedef Segment_cell_iterator SCI;
friend internal::Incrementer<Tr>;
protected:
// \internal \name Protected Attributes
// \{
// \internal The triangulation to traverse.
const Tr& _tr;
// \}
// The source and target points of the traversal.
// These are also stored as vertices for cheaper equality computation.
Point _source;
Point _target;
Vertex_handle _s_vertex;
Vertex_handle _t_vertex;
// The current cell with its entry point and the previous cell with its
// exit point.
// Note that the current cell will be Cell_handle() after incrementing past
// the first cell containing the target.
Simplex _cur, _prev;
public:
// \name Constructors
// \{
// constructs an iterator.
/* \param tr the triangulation to iterate though. This triangulation must have dimension > 0.
* \param s the source vertex. This vertex must be initialized and cannot be the infinite vertex.
* \param t the target vertex. This vertex must be initialized and cannot be the infinite vertex.
* It cannot equal `s`.
*/
Triangulation_segment_cell_iterator_3( const Tr& tr, Vertex_handle s, Vertex_handle t );
// constructs an iterator.
/* \param tr the triangulation to iterate though. This triangulation must have dimension > 0.
* \param s the source vertex. This vertex must be initialized and cannot be the infinite vertex.
* \param t the target point. This point must be initialized and it cannot be be at the same location as `s`.
* If `tr` has dimension < 3, `t` must lie inside the affine hull of `tr`.
*/
Triangulation_segment_cell_iterator_3( const Tr& tr, Vertex_handle s, const Point& t );
// constructs an iterator.
/* \param tr the triangulation to iterate though. This triangulation must have dimension > 0.
* \param s the source point. This point must be initialized and it cannot be be at the same location as `t`.
* \param t the target vertex. This vertex must be initialized and cannot be the infinite vertex.
* If `tr` has dimension < 3, `s` must lie inside the affine hull of `tr`.
* \param hint the starting point to search for `s`.
*/
Triangulation_segment_cell_iterator_3( const Tr& tr, const Point& s, Vertex_handle t, Cell_handle hint = Cell_handle() );
// constructs an iterator.
/* \param tr the triangulation to iterate though. This triangulation must have dimension > 0.
* \param s the source point. This point must be initialized. If `tr` has dimension < 3, `s` must lie inside
* the affine hull of `tr`.
* \param t the target point. This point must be initialized and it cannot be be at the same location as `s`.
* If `tr` has dimension < 3, `t` must lie inside the affine hull of `tr`.
* \param hint the starting point to search for `s`.
*/
Triangulation_segment_cell_iterator_3( const Tr& tr, const Point& s, const Point& t, Cell_handle hint = Cell_handle() );
// constructs an iterator.
/* \param tr the triangulation to iterate though. This triangulation must have dimension > 0.
* \param S the segment to be traversed. If `tr` has dimension < 3, `S` must lie inside
* the affine hull of `tr`. `S` must not be degenerate, i.e. its source and target must not be equal.
* \param hint the starting point to search for `S`.
*/
Triangulation_segment_cell_iterator_3( const Tr& tr, const Segment& S, Cell_handle hint = Cell_handle() );
// \}
// The virtual destructor is mainly defined to indicate to the casting
// operators that this is a dynamic type.
virtual ~Triangulation_segment_cell_iterator_3() {}
private:
// private constructor that does not initialize the source and target.
Triangulation_segment_cell_iterator_3( const Tr& tr );
public:
// \name Accessors
// \{
// gives the source point of the segment followed.
/* \return the source point.
*/
const Point& source() const { return _source; }
// gives the target point of the segment follwoed.
/* \return the target point.
*/
const Point& target() const { return _target; }
// gives the current cell.
/* By invariance, this cell is intersected by the segment
* between `source()` and `target()`.
* \return the current cell.
* \sa `handle()`.
*/
const Cell cell() const { return *get<0>(_cur); }
// gives a handle to the current cell.
/* By invariance, this cell is intersected by the segment
* between `source()` and `target()`.
* \return a handle to the current cell.
* \sa `cell()`.
*/
Cell_handle handle() { return get<0>(_cur); }
// gives the previous cell.
/* This cell is uninitialized until the iterator leaves the initial
* cell.
* By invariance, once initialized, this cell must be intersected by the segment
* between `source()` and `target()`.
* \return the previous cell.
* \sa `handle()`.
*/
Cell_handle previous() const { return get<0>(_prev); }
// provides a dereference operator.
/* \return a pointer to the current cell.
*/
Cell* operator->() { return &*get<0>(_cur); }
// provides an indirection operator.
/* \return the current cell.
*/
Cell& operator*() { return *get<0>(_cur); }
// provides a conversion operator.
/* \return a handle to the current cell.
*/
operator const Cell_handle() const { return get<0>(_cur); }
// provides a conversion operator.
/* \return the simplex through wich the current cell was entered.
*/
operator const Simplex() const { return _cur; }
// checks whether the iterator has reached the final cell, which contains the `target()`.
/* If the `target()` lies on a facet, edge, or vertex, the final cell is the cell containing
* the interior of the segment between `source()` and `target()`.
* \return true iff the current cell contains the `target()`.
*/
bool has_next() const { return get<0>(_cur) != Cell_handle(); }
// gives the simplex through which the current cell was entered.
/* For the first cell, containing the `source()` \f$ s \f$,
* this indicates the location of \f$ s \f$ in this cell.
*/
void entry( Locate_type& lt, int& li, int& lj ) const { lt = get<1>(_cur); li = get<2>(_cur); lj = get<3>(_cur); }
// gives the simplex through which the previous cell was exited.
/* \pre the current cell is not the initial cell.
*/
void exit( Locate_type& lt, int& li, int& lj ) const { lt = get<1>(_prev); li = get<2>(_prev); lj = get<3>(_prev); }
// gives the past-the-end iterator associated with this iterator.
SCI end() const;
// \}
public:
// \name Mutators
// \{
// provides the increment postfix operator.
/* After incrementing the iterator, the current cell intersects the segment
* between `source()` and `target()` closer to the `target()` than the previous cell.
* \sa `operator++(int)`.
* \pre The current cell does not contain the `target()`.
*/
SCI& operator++();
// provides the increment prefix operator.
/* After incrementing the iterator, the current cell intersects the segment
* between `source()` and `target()` closer to the `target()` than the previous cell.
* than the previous cell.
* \sa `operator++()`.
* \pre The current cell does not contain the `target()`.
*/
SCI operator++( int );
// iterates to the final cell, which contains the `target()`.
/* \return the final cell.
*/
Cell_handle complete();
// \}
public:
// \name Comparison
// \{
// compares this iterator with `sci`.
/* \param sci the other iterator.
* \return true iff the other iterator iterates the same triangulation along the same line segment
* and has the same current cell.
* \sa `operator!=( const SCI& t )`.
*/
bool operator==( const SCI& sci ) const;
// compares this iterator with `sci`.
/* \param sci the other iterator.
* \return `false` iff the other iterator iterates the same triangulation along the same line segment
* and has the same current cell.
* \sa `operator==( const SCI& t ) const`.
*/
bool operator!=( const SCI& sci ) const;
// compares the current cell with `ch`.
/* \param ch a handle to the other cell.
* \return true iff the current cell is the same as the one pointed to by `ch`.
* \sa `operator!=( const Cell_handle& ch ) const`.
* \sa `operator==( typename TriangulationTraits_3::Cell_handle ch, Triangulation_segment_cell_iterator_3<TriangulationTraits_3> t )`.
*/
bool operator==( const Cell_handle& ch ) const { return ch == get<0>(_cur); }
// compares the current cell with `ch`.
/* \param ch a handle to the other cell.
* \return `false` iff the current cell is the same as the one pointed to by `ch`.
* \sa `operator==( const Cell_handle& ch )`.
* \sa `operator!=( typename TriangulationTraits_3::Cell_handle ch, Triangulation_segment_cell_iterator_3<TriangulationTraits_3> t )`.
*/
bool operator!=( const Cell_handle& ch ) const { return ch != get<0>(_cur); }
// \}
bool operator==( Nullptr_t CGAL_triangulation_assertion_code(n) ) const;
bool operator!=( Nullptr_t n ) const;
protected:
// \internal \name Protected Member Functions
// \{
// walks to the next cell.
/* \sa `complete()`.
*/
void walk_to_next();
// increments the iterator.
/* This method may perform more actions based on the superclass.
* \sa `complete()`.
*/
void increment() {
typedef Incrementer::SCI Expected;
#ifdef CGAL_TST_ASSUME_CORRECT_TYPES
Expected& sci = static_cast<Expected&>( *this );
#else // CGAL_TST_ASSUME_CORRECT_TYPES
Expected& sci = dynamic_cast<Expected&>( *this );
#endif // CGAL_TST_ASSUME_CORRECT_TYPES
Incrementer().increment( sci );
}
// \}
private:
// walk_to_next(), if the triangulation is 3D.
void walk_to_next_3();
void walk_to_next_3_inf( int inf );
// walk_to_next(), if the triangulation is 2D.
void walk_to_next_2();
void walk_to_next_2_inf( int inf );
private:
inline int edgeIndex( int i, int j ) const {
CGAL_triangulation_precondition( i>=0 && i<=3 );
CGAL_triangulation_precondition( j>=0 && j<=3 );
CGAL_triangulation_precondition( i != j );
return ( i==0 || j==0 ) ? i+j-1 : i+j;
}
}; // class Triangulation_segment_cell_iterator_3
// compares a handle to a cell to a traverser.
/* \param ch the handle to a cell.
* \param t the traverser.
* \return true iff the cell currently traversed by `t` is the same as the one pointed to by `ch`.
* \sa `operator!=( typename TriangulationTraits_3::Cell_handle ch, Triangulation_segment_cell_iterator_3<TriangulationTraits_3> t )`.
* \sa `Triangulation_segment_cell_iterator_3::operator==( const Cell_handle& ch )`.
*/
template < class Tr, class Inc >
inline bool operator==( typename Tr::Cell_handle ch, Triangulation_segment_cell_iterator_3<Tr,Inc> tci ) { return tci == ch; }
// compares a handle to a cell to a traverser.
/* \param ch the handle to a cell.
* \param t the traverser.
* \return `false` iff the cell currently traversed by `t` is the same as the one pointed to by `ch`.
* \sa `operator==( typename TriangulationTraits_3::Cell_handle ch, Triangulation_segment_cell_iterator_3<TriangulationTraits_3> t )`.
* \sa `Triangulation_segment_cell_iterator_3::operator!=( const Cell_handle& ch )`.
*/
template < class Tr, class Inc >
inline bool operator!=( typename Tr::Cell_handle ch, Triangulation_segment_cell_iterator_3<Tr,Inc> tci ) { return tci != ch; }
/********************************************************************/
/********************************************************************/
/********************************************************************/
template < class Tr_, class Inc = internal::Incrementer<Tr_> >
class Triangulation_segment_simplex_iterator_3
{
typedef Tr_ Tr;
typedef typename Tr::Triangulation_data_structure Tds;
typedef typename Tr::Geom_traits Gt;
typedef Inc Incrementer;
private:
typedef Triangulation_segment_simplex_iterator_3<Tr_, Inc> Simplex_iterator;
typedef Triangulation_segment_cell_iterator_3<Tr_, Inc> SCI;
private:
typedef typename SCI::Point Point;
typedef typename SCI::Segment Segment;
public:
// \{
typedef typename SCI::Vertex_handle Vertex_handle;//< defines the type of a handle for a vertex in the triangulation
typedef typename SCI::Cell_handle Cell_handle; //< defines the type of a handle for a cell in the triangulation.
typedef typename SCI::Triangulation::Edge Edge; //< defines the type of an edge in the triangulation.
typedef typename SCI::Triangulation::Facet Facet; //< defines the type of a facet in the triangulation.
typedef typename SCI::Locate_type Locate_type; //< defines the simplex type returned from location.
typedef boost::variant<Vertex_handle, Edge, Facet, Cell_handle> Simplex_type; //types sorted by dimension
typedef Simplex_type value_type; //< defines the value type the iterator refers to.
typedef Simplex_type& reference; //< defines the reference type of the iterator.
typedef Simplex_type* pointer; //< defines the pointer type of the iterator.
typedef std::size_t size_type; //< defines the integral type that can hold the size of a sequence.
typedef std::ptrdiff_t difference_type; //< defines the signed integral type that can hold the distance between two iterators.
typedef std::forward_iterator_tag iterator_category; //< defines the iterator category.
// \}
private:
SCI _cell_iterator;
Simplex_type _curr_simplex;
public:
Triangulation_segment_simplex_iterator_3(const Tr& tr
, Vertex_handle s, Vertex_handle t)
: _cell_iterator(tr, s, t)
{ set_curr_simplex(); }
Triangulation_segment_simplex_iterator_3(const Tr& tr
, Vertex_handle s, const Point& t)
: _cell_iterator(tr, s, t)
{ set_curr_simplex(); }
Triangulation_segment_simplex_iterator_3(const Tr& tr
, const Point& s, Vertex_handle t, Cell_handle hint = Cell_handle())
: _cell_iterator(tr, s, t, hint)
{ set_curr_simplex(); }
Triangulation_segment_simplex_iterator_3(const Tr& tr
, const Point& s, const Point& t, Cell_handle hint = Cell_handle())
: _cell_iterator(tr, s, t, hint)
{ set_curr_simplex(); }
Triangulation_segment_simplex_iterator_3(const Tr& tr
, const Segment& seg, Cell_handle hint = Cell_handle())
: _cell_iterator(tr, seg, hint)
{ set_curr_simplex(); }
bool operator==(const Simplex_iterator& sit) const
{
return sit._cell_iterator == _cell_iterator
&& sit._curr_simplex == _curr_simplex;
}
bool operator!=(const Simplex_iterator& sit) const
{
return sit._cell_iterator != _cell_iterator
|| sit._curr_simplex != _curr_simplex;
}
private:
Triangulation_segment_simplex_iterator_3
(const SCI& sci)
: _cell_iterator(sci)
, _curr_simplex(Cell_handle())
{}
private:
void set_curr_simplex()
{
//check what is the entry type of _cell_iterator
if (Cell_handle(_cell_iterator) == Cell_handle())
{
_curr_simplex = Cell_handle();
return;//end has been reached
}
Cell_handle cell = Cell_handle(_cell_iterator);
Locate_type lt;
int li, lj;
_cell_iterator.entry(lt, li, lj);
switch (lt)
{
case Locate_type::VERTEX:
if (is_vertex()) //previous visited simplex was also a vertex
{
lj = cell->index(get_vertex());
_curr_simplex = Edge(cell, li, lj);
}
else
_curr_simplex = cell->vertex(li);
break;
case Locate_type::EDGE:
_curr_simplex = Edge(cell, li, lj);
break;
case Locate_type::FACET: //basic case where segment enters a cell
//by crossing a facet
//the 3 cases below correspond to the case when _cell_iterator
//is in its initial position: _cur is locate(source)
case Locate_type::CELL:
case Locate_type::OUTSIDE_CONVEX_HULL:
case Locate_type::OUTSIDE_AFFINE_HULL:
_curr_simplex = cell;
break;
default:
CGAL_assertion(false);
};
}
public:
Simplex_iterator end() const
{
Simplex_iterator sit(_cell_iterator.end());
return sit;
}
// provides the increment postfix operator.
Simplex_iterator& operator++()
{
CGAL_assertion(!_curr_simplex.empty());
switch(_curr_simplex.which())
{
case 3 :/*Cell_handle*/
{
++_cell_iterator;
set_curr_simplex();
break;
}
case 2 :/*Facet*/
{
//todo
break;
}
case 1:/*Edge*/
{
//todo
break;
}
case 0 :/*Vertex_handle*/
{
Cell_handle ch = Cell_handle(_cell_iterator);
++_cell_iterator;
Cell_handle chnext = Cell_handle(_cell_iterator);
//_cell_iterator is one step forward _curr_simplex
Locate_type lt;
int li, lj;
_cell_iterator.entry(lt, li, lj);
int index_v = ch->index(get_vertex());
int index_vnext = ch->index(chnext->vertex(li));
if (lt == Locate_type::VERTEX)
{
_curr_simplex = Edge(ch, index_v, index_vnext);
}
else if (lt == Locate_type::EDGE)
{
int index_f = 6 - (index_v + index_vnext + ch->index(chnext->vertex(lj)));
_curr_simplex = Facet(ch, index_f);
}
else
_curr_simplex = Cell_handle(_cell_iterator);
break;
}
default:
CGAL_assertion(false);
};
return *this;
}
// provides the increment prefix operator.
Simplex_iterator operator++(int)
{
Simplex_iterator tmp(*this);
++(*this);
return tmp;
}
// provides a dereference operator.
/* \return a pointer to the current cell.
*/
Simplex_type* operator->() { return &*_curr_simplex; }
// provides an indirection operator.
/* \return the current cell.
*/
Simplex_type& operator*() { return _curr_simplex; }
// provides a conversion operator.
/* \return a handle to the current cell.
*/
operator const Cell_handle() const { return Cell_handle(_cell_iterator); }
bool is_vertex() const { return _curr_simplex.which() == 0; }
bool is_edge() const { return _curr_simplex.which() == 1; }
bool is_facet() const { return _curr_simplex.which() == 2; }
bool is_cell() const { return _curr_simplex.which() == 3; }
const Simplex_type& get_simplex() const { return _curr_simplex; }
Vertex_handle get_vertex() const
{
CGAL_assertion(is_vertex());
return boost::get<Vertex_handle>(_curr_simplex);
}
Vertex_handle get_edge() const
{
CGAL_assertion(is_edge());
return boost::get<Edge>(_curr_simplex);
}
Vertex_handle get_facet() const
{
CGAL_assertion(is_facet());
return boost::get<Facet>(_curr_simplex);
}
Vertex_handle get_cell() const
{
CGAL_assertion(is_cell());
return boost::get<Cell_handle>(_curr_simplex);
}
};//class Triangulation_segment_simplex_iterator_3
} // namespace CGAL
#include <CGAL/Triangulation_segment_traverser_3_impl.h>
#endif // CGAL_TRIANGULATION_SEGMENT_TRAVERSER_3_H
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