There are several overloaded function templates called complement() that compute the complement of a given polygon pgn. Depending on the type of the polygon pgn the complement is either a single (general) polygon with holes, or several (general) poylgons with holes. In the latter case the complement() function template inserts the resulting poylgons with holes into a container via an output iterator.

A function template in this group has one of the following signatures:

1.1.	void complement(const Type1& pgn, Type2& res, UsePolylines = Tag_true());
1.2.	void complement(const Type1& pgn, Type2& res);
2.	void complement(const Type1& pgn, Type2& res, const GpsTraits& traits);

Template Parameters

UsePolylines determines whether the boundary of the input polygon is treated as a cyclic sequence of single ( \(x\)-monotone) segments or as a cyclic sequence of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, the input polygon is converted to a general polygon bounded by polylines before the operation is actually performed. Then, the resulting general polygon with holes is converted back to a standard polygon. If substituted with CGAL::Tag_false, the input polygon is used as is. Refer to Traits Selection for more information.

The types Type and Type2 of the parameters must be convertible to the types specified in a row in the table below, respectively.
The types that apply to signature (1.1.) above are restricted to those listed in rows 1 and 2 in the table below.
The types that apply to signature (1.2.) above are restricted to those listed in rows 3 and 4 in the table below.

	Type1	Type2
1	Polygon_2	Polygon_with_holes_2
2	Polygon_with_holes_2	Polygon_with_holes_2
3	General_polygon_2	General_polygon_with_holes_2
4	General_polygon_with_holes_2	General_polygon_with_holes_2

Parameters

pgn	the input polygon.
res	the resulting polygon.
traits	an optional traits object.

See also: CGAL::do_intersect(); CGAL::intersection(); CGAL::join(); CGAL::difference(); CGAL::symmetric_difference()

Functions
template<typename Kernel, typename Container>
void	CGAL::complement (const Polygon_2< Kernel, Container > &pgn, Polygon_with_holes_2< Kernel, Container > &res)
	computes the complement of a polygon.
template<typename Kernel, typename Container, typename UsePolylines>
void	CGAL::complement (const Polygon_2< Kernel, Container > &pgn, Polygon_with_holes_2< Kernel, Container > &res, UsePolylines=Tag_true())
	computes the complement of a polygon.
template<typename ArrTraits>
void	CGAL::complement (const General_polygon_2< ArrTraits > &pgn, General_polygon_with_holes_2< General_polygon_2< Arr_traits > > &res)
	computes the complement of a general polygon.
template<typename Kernel, typename Container, typename OutputIterator>
OutputIterator	CGAL::complement (const Polygon_with_holes_2< Kernel, Container > &pgn, OutputIterator oi)
	computes the complement of a polygon with holes.
template<typename Traits, typename OutputIterator, typename UsePolylines>
OutputIterator	CGAL::complement (const Polygon_with_holes_2< Kernel, Container > &pgn, OutputIterator oi, UsePolylines=Tag_true())
	computes the complement of a polygon with holes.
template<typename ArrTraits, typename OutputIterator>
OutputIterator	CGAL::complement (const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &pgn, OutputIterator oi)
	computes the complement of a general polygon with holes.
template<typename Kernel, typename Container, typename GpsTraits>
void	CGAL::complement (const Polygon_2< Kernel, Container > &pgn, Polygon_with_holes_2< Kernel, Container > &res, const GpsTraits &traits)
	computes the complement of a polygon.
template<typename ArrTraits, typename GpsTraits>
void	CGAL::complement (const General_polygon_2< ArrTraits > &pgn, General_polygon_with_holes_2< General_polygon_2< Arr_traits > > &res, const GpsTraits &traits)
	computes the complement of a general polygon.
template<typename Kernel, typename Container, typename OutputIterator, typename GpsTraits>
OutputIterator	CGAL::complement (const Polygon_with_holes_2< Kernel, Container > &pgn, OutputIterator oi, const GpsTraits &traits)
	computes the complement of a polygon with holes.
template<typename Polygon, typename OutputIterato, typename GpsTraitsr>
OutputIterator	CGAL::complement (const General_polygon_with_holes_2< Polygon > &pgn, OutputIterator oi, const GpsTraits &traits)
	computes the complement of the general polygon with holes.

Function Documentation

◆ complement() [1/10]

template<typename ArrTraits>

void CGAL::complement	(	const General_polygon_2< ArrTraits > &	pgn,
		General_polygon_with_holes_2< General_polygon_2< Arr_traits > > &	res )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a general polygon.

Parameters

pgn	the input polygon.
res	the complement of `pgn`.

Precondition: ArrTraits must be a model of the concept AosDirectionalXMonotoneTraits_2.

◆ complement() [2/10]

template<typename ArrTraits, typename GpsTraits>

void CGAL::complement	(	const General_polygon_2< ArrTraits > &	pgn,
		General_polygon_with_holes_2< General_polygon_2< Arr_traits > > &	res,
		const GpsTraits &	traits )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a general polygon.

Parameters

pgn	the input polygon.
res	the resulting complement of `pgn`
traits	a traits object.

Precondition: ArrTraits must be a model of the concept AosDirectionalXMonotoneTraits_2.; GpsTraits must be a model of the concept GeneralPolygonSetTraits_2.

◆ complement() [3/10]

template<typename ArrTraits, typename OutputIterator>

OutputIterator CGAL::complement	(	const General_polygon_with_holes_2< General_polygon_2< ArrTraits > > &	pgn,
		OutputIterator	oi )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a general polygon with holes.

Parameters

pgn	the input polygon.
oi	the 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 AosDirectionalXMonotoneTraits_2.

◆ complement() [4/10]

template<typename Polygon, typename OutputIterato, typename GpsTraitsr>

OutputIterator CGAL::complement	(	const General_polygon_with_holes_2< Polygon > &	pgn,
		OutputIterator	oi,
		const GpsTraits &	traits )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of the general polygon with holes.

Parameters

pgn	the input polygon.
oi	the output iterator for the result. Its dereference type must be convertible to General_polygon_with_holes_2<<General_polygon_2<ArrTraits>>.
traits	a traits object.

Returns: the past-the-end iterator of the output container.

Precondition: ArrTraits must be a model of the concept AosDirectionalXMonotoneTraits_2.; GpsTraits must be a model of the concept GeneralPolygonSetTraits_2.

◆ complement() [5/10]

template<typename Kernel, typename Container>

void CGAL::complement	(	const Polygon_2< Kernel, Container > &	pgn,
		Polygon_with_holes_2< Kernel, Container > &	res )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon.

Parameters

pgn	the input polygon.
res	the resulting complement of `pgn`.

◆ complement() [6/10]

template<typename Kernel, typename Container, typename GpsTraits>

void CGAL::complement	(	const Polygon_2< Kernel, Container > &	pgn,
		Polygon_with_holes_2< Kernel, Container > &	res,
		const GpsTraits &	traits )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon.

Parameters

pgn	the input polygon.
res	the resulting complement of `pgn`
traits	a traits object.

Precondition: GpsTraits must be a model of the concept GeneralPolygonSetTraits_2.

◆ complement() [7/10]

template<typename Kernel, typename Container, typename UsePolylines>

void CGAL::complement	(	const Polygon_2< Kernel, Container > &	pgn,
		Polygon_with_holes_2< Kernel, Container > &	res,
		UsePolylines	= Tag_true() )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon.

Template Parameters

UsePolylines determines whether the boundary of pgn is treated as a cyclic sequence of single ( \(x\)-monotone) segments or as a cyclic sequence of ( \(x\)-monotone) polylines. If substituted with CGAL::Tag_true, which is the default, pgn is converted to a general polygon bounded by polylines before the operation is actually performed. Then, the resulting general polygon with holes is converted back to a standard polygon. If substituted with CGAL::Tag_false, pgn is used as is. Refer to Traits Selection for more information.

Parameters

pgn	the input polygon.
res	the resulting complement of `pgn`.

◆ complement() [8/10]

template<typename Kernel, typename Container, typename OutputIterator>

OutputIterator CGAL::complement	(	const Polygon_with_holes_2< Kernel, Container > &	pgn,
		OutputIterator	oi )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon with holes.

Parameters

pgn	the input polygon.
oi	the 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.

◆ complement() [9/10]

template<typename Kernel, typename Container, typename OutputIterator, typename GpsTraits>

OutputIterator CGAL::complement	(	const Polygon_with_holes_2< Kernel, Container > &	pgn,
		OutputIterator	oi,
		const GpsTraits &	traits )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon with holes.

Parameters

pgn	the input polygon.
oi	the output iterator for the result. Its dereference type must be convertible to Polygon_with_holes_2<Kernel, Container>.
traits	a traits object.

Returns: the past-the-end iterator of the output container.

Precondition: GpsTraits must be a model of the concept GeneralPolygonSetTraits_2.

◆ complement() [10/10]

template<typename Traits, typename OutputIterator, typename UsePolylines>

OutputIterator CGAL::complement	(	const Polygon_with_holes_2< Kernel, Container > &	pgn,
		OutputIterator	oi,
		UsePolylines	= Tag_true() )

#include <CGAL/Boolean_set_operations_2.h>

computes the complement of a polygon with holes.

Template Parameters

UsePolylines determines whether the boundaries of pgn is 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, pgn is converted to a general polygon with holes bounded by polylines before the operation is actually performed. Then, the resulting general polygons with holes are converted back to a standard polygon with holes. If substituted with CGAL::Tag_false, pgn is used as is. Refer to Traits Selection for more information.

Parameters

pgn	the input polygon.
oi	the 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.

Functions

Function Documentation

◆ complement() [1/10]

◆ complement() [2/10]

◆ complement() [3/10]

◆ complement() [4/10]

◆ complement() [5/10]

◆ complement() [6/10]

◆ complement() [7/10]

◆ complement() [8/10]

◆ complement() [9/10]

◆ complement() [10/10]