CGAL 5.6 - 2D Regularized Boolean Set-Operations

There are several overloaded function templates called symmetric_difference() that compute the symmetric difference between two or more input polygons and insert the resulting polygons with holes into a container via an output iterator.

A function template in this group that accepts two input polygons has one of the following signatures:

1.1.OutputIterator symmetric_difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi, UsePolylines = Tag_true());
1.2.OutputIterator symmetric_difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi);
2.OutputIterator symmetric_difference(const Type1& pgn1, const Type2& pgn2, OutputIterator oi, const GpsTraits& traits);

There are also function templates that accept one or two ranges of input polygons:

3.1.OutputIterator symmetric_difference(InputIterator begin, InputIterator end, OutputIterator oi, UsePolylines = Tag_true());
3.2.OutputIterator symmetric_difference(InputIterator begin, InputIterator end, OutputIterator oi);
4.OutputIterator symmetric_difference(InputIterator begin, InputIterator end, OutputIterator oi, const GpsTraits& traits);
5.1.OutputIterator symmetric_difference(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, UsePolylines = Tag_true());
5.2.OutputIterator symmetric_difference(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi);
6.OutputIterator symmetric_difference(InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, const GpsTraits& traits);
Template Parameters
UsePolylinesdetermines whether the boundaries of the input polygons are treated as cyclic sequences of single ( \(x\)-monotone) segments or as cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, the input polygons are converted to general polygons bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, the input polygons are used as is. Refer to Traits Selection for more information.
 Type1 Type2 Dereference Type of oi
1Polygon_2 Polygon_2 Polygon_with_holes_2
2Polygon_2 Polygon_with_holes_2 Polygon_with_holes_2
3Polygon_with_holes_2 Polygon_2 Polygon_with_holes_2
4Polygon_with_holes_2 Polygon_with_holes_2 Polygon_with_holes_2
5General_polygon_2 General_polygon_2 General_polygon_with_holes_2
6General_polygon_2 General_polygon_with_holes_2General_polygon_with_holes_2
7General_polygon_with_holes_2General_polygon_2 General_polygon_with_holes_2
8General_polygon_with_holes_2General_polygon_with_holes_2General_polygon_with_holes_2
Parameters
pgn1,pgn2the input polygons.
(end,begin)a range of input polygons.
(end1,begin1)the first range of input polygons.
(end2,begin2)the second range of input polygons.
oithe output iterator for the result.
traitsan optional traits object.
See also
CGAL::complement()
CGAL::do_intersect()
CGAL::intersection()
CGAL::join()
CGAL::difference()

Functions

template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi)
 computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, UsePolylines=Tag_true())
 computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &pgn2, OutputIterator oi)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename Polygon , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (const General_polygon_with_holes_2< Polygon > &pgn1, const General_polygon_with_holes_2< Polygon > &pgn2, OutputIterator oi)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename InputIterator , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (InputIterator begin, InputIterator end, OutputIterator oi)
 Given a range of polygons (resp. More...
 
template<typename InputIterator , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (InputIterator begin, InputIterator end, OutputIterator oi, UsePolylines=Tag_true())
 Given a range of polygons (resp. More...
 
template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator >
OutputIterator CGAL::symmetric_difference (InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi)
 Given a range of polygons (resp. More...
 
template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference (InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, UsePolylines=Tag_true())
 Given a range of polygons (resp. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const Polygon_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const Polygon_with_holes_2< Kernel, Container > &pgn1, const Polygon_with_holes_2< Kernel, Container > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &pgn1, const General_polygon_2< ArrTraits > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const General_polygon_2< ArrTraits > &pgn1, const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename Polygon , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (const General_polygon_with_holes_2< Polygon > &pgn1, const General_polygon_with_holes_2< Polygon > &pgn2, OutputIterator oi, const GpsTraits &traits)
 computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator. More...
 
template<typename InputIterator , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (InputIterator begin, InputIterator end, OutputIterator oi, const GpsTraits &traits)
 Given a range of polygons (resp. More...
 
template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference (InputIterator1 begin1, InputIterator1 end1, InputIterator2 begin2, InputIterator2 end2, OutputIterator oi, const GpsTraits &traits)
 Given a range of polygons (resp. More...
 

Function Documentation

◆ symmetric_difference() [1/26]

template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.
Examples:
Boolean_set_operations_2/symmetric_difference.cpp.

◆ symmetric_difference() [2/26]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters
UsePolylinesdetermines whether the boundaries of pgn1 and pgn2 are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, pgn1 and pgn2 are converted to a general polygons bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [3/26]

template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [4/26]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters
UsePolylinesdetermines whether the boundaries of pgn1 and pgn2 are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, pgn1 and pgn2 are converted to a general polygon and a general polygon with holes, respectively, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [5/26]

template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [6/26]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters
UsePolylinesdetermines whether the boundaries of pgn1 and pgn2 are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, pgn1 and pgn2 are converted to a general polygon with holes and a general polygon, respectively, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [7/26]

template<typename Kernel , typename Container , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [8/26]

template<typename Kernel , typename Container , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator.

Template Parameters
UsePolylinesdetermines whether the boundaries of pgn1 and pgn2 are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, pgn1 and pgn2 are converted to general polygons with holes, bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [9/26]

template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const General_polygon_2< ArrTraits > &  pgn1,
const General_polygon_2< ArrTraits > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.

◆ symmetric_difference() [10/26]

template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &  pgn1,
const General_polygon_2< ArrTraits > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.

◆ symmetric_difference() [11/26]

template<typename ArrTraits , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const General_polygon_2< ArrTraits > &  pgn1,
const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.

◆ symmetric_difference() [12/26]

template<typename Polygon , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( const General_polygon_with_holes_2< Polygon > &  pgn1,
const General_polygon_with_holes_2< Polygon > &  pgn2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<Polygon>.
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [13/26]

template<typename InputIterator , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( InputIterator  begin,
InputIterator  end,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) or a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference of all polygons in the range and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Parameters
beginthe first iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
endthe past-the-end iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [14/26]

template<typename InputIterator , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( InputIterator  begin,
InputIterator  end,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) or a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference of all polygons in the range and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Template Parameters
UsePolylinesdetermines whether the boundaries of the polygons in the input range are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, the input polygons are converted to general polygon with holes , bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
beginthe first iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
endthe past-the-end iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [15/26]

template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator >
OutputIterator CGAL::symmetric_difference ( InputIterator1  begin1,
InputIterator1  end1,
InputIterator2  begin2,
InputIterator2  end2,
OutputIterator  oi 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) and a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference between all polygons in the two ranges and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Parameters
begin1the first iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
end1the past-the-end iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
begin2the first iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
end2the past-the-end iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [16/26]

template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator , typename UsePolylines >
OutputIterator CGAL::symmetric_difference ( InputIterator1  begin1,
InputIterator1  end1,
InputIterator2  begin2,
InputIterator2  end2,
OutputIterator  oi,
UsePolylines  = Tag_true() 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) and a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference between all polygons in the two ranges and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Template Parameters
UsePolylinesdetermines whether the boundaries of the polygons in the input ranges are treated as cyclic sequences of single ( \(x\)-monotone) segments or as a cyclic sequences of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, the input polygons are converted to general polygon with holes , bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to standard polygons with holes. If substituted with CGAL::Tag_false, pgn1 and pgn2 are used as is. Refer to Traits Selection for more information.
Parameters
begin1the first iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
end1the past-the-end iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
begin2the first iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
end2the past-the-end iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
Returns
the past-the-end iterator of the output container.

◆ symmetric_difference() [17/26]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [18/26]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const Polygon_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [19/26]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [20/26]

template<typename Kernel , typename Container , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const Polygon_with_holes_2< Kernel, Container > &  pgn1,
const Polygon_with_holes_2< Kernel, Container > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two polygons with holes and inserts the resulting polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [21/26]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const General_polygon_2< ArrTraits > &  pgn1,
const General_polygon_2< ArrTraits > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [22/26]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &  pgn1,
const General_polygon_2< ArrTraits > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [23/26]

template<typename ArrTraits , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const General_polygon_2< ArrTraits > &  pgn1,
const General_polygon_with_holes_2< General_polygon_2< ArrTraits >> &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<General_polygon_2<ArrTraits>>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
ArrTraits must be a model of the concept ArrangementDirectionalXMonotoneTraits_2.
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [24/26]

template<typename Polygon , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( const General_polygon_with_holes_2< Polygon > &  pgn1,
const General_polygon_with_holes_2< Polygon > &  pgn2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

computes the symmetric difference between two general polygons and inserts the resulting general polygons with holes into a container via an output iterator.

Parameters
pgn1the 1st input polygon.
pgn2the 2nd input polygon.
oithe output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<Polygon>.
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [25/26]

template<typename InputIterator , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( InputIterator  begin,
InputIterator  end,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) or a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference of all polygons in the range and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Parameters
beginthe first iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
endthe past-the-end iterator of the input range. Its value type is either Polygon_2 (resp. General_polygon_2) or Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.

◆ symmetric_difference() [26/26]

template<typename InputIterator1 , typename InputIterator2 , typename OutputIterator , typename GpsTraits >
OutputIterator CGAL::symmetric_difference ( InputIterator1  begin1,
InputIterator1  end1,
InputIterator2  begin2,
InputIterator2  end2,
OutputIterator  oi,
const GpsTraits &  traits 
)

#include <CGAL/Boolean_set_operations_2.h>

Given a range of polygons (resp.

general polygons) and a range of polygons with holes (resp. general polygons with holes) computes the symmetric difference between all polygons in the two ranges and inserts the resulting polygons with holes (resp. general polygons with holes) into a container via an output iterator. A point is contained in the symmetric difference, if and only if it is contained in an odd number of input polygons.

Parameters
begin1the first iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
end1the past-the-end iterator of the 1st input range. Its value type is Polygon_2 (resp. General_polygon_2).
begin2the first iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
end2the past-the-end iterator of the 2nd input range. Its value type is Polygon_with_holes_2 (resp. General_polygon_with_holes_2).
oithe output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2 (resp. General_polygons_with_holes_2).
traitsa traits object.
Returns
the past-the-end iterator of the output container.
Precondition
GpsTraits must be a model of GeneralPolygonSetTraits_2.