#include <CGAL/General_polygon_set_2.h>

Definition

An object of the General_polygon_set_2 class-template represents a point set in the plane bounded by \( x\) monotone curves.

Points in the set lie on the boundary or on the positive side of the curves. This class template provides methods to apply regularized Boolean set-operations and few other utility methods. An Arrangement_2 data structure is internally used to represent the point set. The arrangement is represented as a doubly-connected edge-list (DCEL).

The Traits template-parameter should be instantiated with a model of the concept GeneralPolygonSetTraits_2. The traits class defines the types of points, \( x\)-monotone curves, general polygons, and general polygons with holes, that is Traits::Point_2, Traits::X_monotone_curve_2, Traits::Polygon_2, and Traits::Polygon_with_holes_2, respectively. Traits::Point_2 must be the type of the endpoints of Traits::X_monotone_curve_2, and Traits::X_monotone_curve_2 must be the type of the curves that comprise the boundaries of the general polygons. The traits class supports geometric operations on the types above. We sometimes use the term polygon instead of general polygon for simplicity hereafter.

The template parameter Dcel should be instantiated with a model of the concept GeneralPolygonSetDcel. It is instantiated by default with the type Gps_default_dcel<Traits>. You can override this default, with a different DCEL class, typically an extension of the Gps_default_dcel class template. Overriding the default is necessary only if you intend to obtain the underlying internal arrangement and process it further.

The input and output of the Boolean set-operations methods consist of one or more general polygons, some of which may have holes. In particular, these methods operate on pairs of objects of type General_polygon_set_2, or directly on objects of type Traits::Polygon_2 or Traits::Polygon_with_holes_2. An object of type Traits::Polygon_2 is a valid operand, only if it is simple and its boundary is oriented counterclockwise. An object of type Traits::Polygon_with_holes_2 is valid, only if its outer boundary bounds a relatively simple general polygon oriented counterclockwise, and each one of its holes is a simple polygon oriented clockwise. The holes are pairwise disjoint, except perhaps at the vertices, and are contained in the polygon bounded by the outer boundary. The outer boundary and the holes are also pairwise disjoint, except perhaps at the vertices.

See also: Arrangement_2; ArrangementXMonotoneTraits_2; Nef_polyhedron_2

Examples:: Boolean_set_operations_2/bezier_traits_adapter2.cpp, Boolean_set_operations_2/circle_segment.cpp, and Boolean_set_operations_2/dxf_union.cpp.

Types
typedef unspecified_type	Traits_2
	the traits class in use.

typedef unspecified_type	Polygon_2
	the general polygon type. More...

typedef unspecified_type	Polygon_with_holes_2
	the general polygon with holes type. More...

typedef unspecified_type	Size
	number of polygons with holes size type.

typedef unspecified_type	Arrangement_2
	the arrangement type used internally.

Creation
	General_polygon_set_2 ()
	default constructor; constructs an empty set of polygons `gps` represented by an empty arrangement.

	General_polygon_set_2 (const Self &other)
	copy constructor.

	General_polygon_set_2 (const Traits &traits)
	constructs an empty set of polygons that uses the given `traits` object for performing the geometric operations.

	General_polygon_set_2 (const Polygon_2 &pgn)
	constructs a set of polygons that consists of the single polygon `pgn`.

	General_polygon_set_2 (const Polygon_with_holes_2 &pgn_with_holes)
	constructs a set of polygons that consists of the single polygon with holes `pgn_with_holes`.

	General_polygon_set_2 (const Polygon_2 &pgn, const Traits &traits)
	constructs a set of polygons that uses the given traits object and consists of the single polygon `pgn`.

	General_polygon_set_2 (const Polygon_with_holes_2 &pgn_with_holes, const Traits &traits)
	constructs a set of polygons that uses the given traits object and consists of the single polygon with holes `pgn_with_holes`.

Access Functions
template<class OutputIterator >
OutputIterator	polygons_with_holes (OutputIterator out)
	obtains the polygons with holes represented by `gps`.

Size	number_of_polygons_with_holes () const
	returns the total number of general polygons represented by `gps`.

bool	is_empty () const
	returns `true` if `gps` represents an empty set.

bool	is_plane () const
	returns `true` if `gps` represents the entire plane.

Traits &	traits () const
	obtains an instance of the traits. More...

const Arrangement_2 &	arrangement () const
	obtains the arrangement data structure that internally represents the general-polygon set.

Modifiers
void	clear ()
	clears `gps`.

void	insert (Polygon_2 &pgn)
	inserts `pgn` into `gps`. More...

void	insert (Polygon_with_holes_2 &pgn_with_holes)
	inserts `pgn_with_holes` into `gps`. More...

template<class InputIterator >
void	insert (InputIterator begin, InputIterator end)
	inserts the range of polygons (or polygons with holes) into `gps`. More...

template<class InputIterator1 , class InputIterator2 >
void	insert (InputIterator1 pgn_begin, InputIterator1 pgn_end, InputIterator2 pgn_with_holes_begin, InputIterator2 pgn_with_holes_end)
	inserts the two ranges of polygons and polygons with holes into `gps`. More...

void	complement ()
	computes the complement of `gps`.

void	complement (const Polygon_set_2 &other)
	computes the complement of `other`. More...

Univariate Operations
In the following univariate and bivariate methods the result is placed in `gps` after it is cleared.
void	intersection (const General_polygon_set_2 &other)
	computes the intersection of `gps` and `other`.

void	intersection (const Polygon_2 &pgn)
	computes the intersection of `gps` and `pgn`.

void	intersection (const Polygon_with_holes_2 &pgn)
	computes the intersection of `gps` and `pgn`.

template<class InputIterator >
void	intersection (InputIterator begin, InputIterator end)
	computes the intersection of a collection of point sets. More...

template<class InputIterator1 , class InputIterator2 >
void	intersection (InputIterator1 pgn_begin, InputIterator1 pgn_end, InputIterator2 pgn_with_holes_begin, InputIterator2 pgn_with_holes_end)
	computes the intersection of a collection of point sets. More...

void	join (const General_polygon_set_2 &other)
	computes the union of `gps` and `other`.

void	join (const Polygon_2 &pgn)
	computes the union of `gps` and `pgn`.

void	join (const Polygon_with_holes_2 &pgn)
	computes the union of `gps` and `pgn`.

template<class InputIterator >
void	join (InputIterator begin, InputIterator end)
	computes the union of the polygons (or polygons with holes) in the given range and the point set represented by `gps`. More...

template<class InputIterator1 , class InputIterator2 >
void	join (InputIterator1 pgn_begin, InputIterator1 pgn_end, InputIterator2 pgn_with_holes_begin, InputIterator2 pgn_with_holes_end)
	computes the union of the polygons and polygons with holes in the given two ranges and the point set represented by `gps`.

void	difference (const General_polygon_set_2 &other)
	computes the difference between `gps` and `other`.

void	difference (const Polygon_2 &pgn)
	computes the difference between `gps` and `pgn`.

void	difference (const Polygon_with_holes_2 &pgn)
	computes the difference between `gps` and `pgn`.

void	symmetric_difference (const General_polygon_set_2 &other)
	computes the symmetric difference between `gps` and `other`.

void	symmetric_difference (const Polygon_2 &pgn)
	computes the symmetric difference between `gps` and `pgn`.

void	symmetric_difference (const Polygon_with_holes_2 &pgn)
	computes the symmetric difference between `gps` and `pgn`.

template<class InputIterator >
void	symmetric_difference (InputIterator begin, InputIterator end)
	computes the symmetric difference (xor) of a collection of point sets. More...

template<class InputIterator1 , class InputIterator2 >
void	symmetric_difference (InputIterator1 pgn_begin, InputIterator1 pgn_end, InputIterator2 pgn_with_holes_begin, InputIterator2 pgn_with_holes_end)
	computes the symmetric difference (xor) of a collection of point sets. More...

Bivariate Operations
The following bivariate function replace `gps` with the result.
void	intersection (const General_polygon_set_2 &gps1, const General_polygon_set_2 &gps2)
	computes the intersection of `gps1` and `gps2`.

void	join (const General_polygon_set_2 &gps1, const General_polygon_set_2 &gps2)
	computes the union of `gps1` and `gps2`.

void	difference (const General_polygon_set_2 &gps1, const General_polygon_set_2 &gps2)
	computes the difference between `gps1` and `gps2`.

void	symmetric_difference (const General_polygon_set_2 &gps1, const General_polygon_set_2 &gps2)
	computes the symmetric difference between `gps1` and `gps2`.

Query Functions
bool	do_intersect (const General_polygon_set_2 &other)
	returns `true` if `gps` and `other` intersect in their interior, and `false` otherwise.

bool	do_intersect (const Polygon_2 &pgn)
	returns `true` if `gps` and `pgn` intersect in their interior, and `false` otherwise.

bool	do_intersect (const Polygon_with_holes_2 &pgn)
	returns `true` if `gps` and `pgn` intersect in their interior, and `false` otherwise.

template<class InputIterator >
void	do_intersect (InputIterator begin, InputIterator end)
	returns `true` if the interior of the point sets in a collection intersect, and `false` otherwise. More...

template<class InputIterator1 , class InputIterator2 >
void	do_intersect (InputIterator1 pgn_begin, InputIterator1 pgn_end, InputIterator2 pgn_with_holes_begin, InputIterator2 pgn_with_holes_end)
	returns `true` if the interior of the point sets in a collection intersect, and `false` otherwise. More...

bool	locate (const Point_2 &p, Polygon_with_holes_2 &pgn)
	obtains a polygon with holes that contains the query point `p`, if exists, through `pgn`, and returns `true`. More...

Oriented_side	oriented_side (const Point_2 &q)
	returns either the constant `ON_ORIENTED_BOUNDARY`, `ON_POSITIVE_SIDE`, or `ON_NEGATIVE_SIDE`, iff `p` lies on the boundary, properly on the positive side, or properly on the negative side of `gps` respectively.

Oriented_side	oriented_side (const General_polygon_set_2 &other)
	returns either the constant `ON_NEGATIVE_SIDE`, `ON_ORIENTED_BOUNDARY`, or `ON_POSITIVE_SIDE`, iff `other` and `gps` are completely disjoint, in contact, or intersect in their interior, respectively.

Oriented_side	oriented_side (const Polygon_2 &pgn)
	returns either the constant `ON_NEGATIVE_SIDE`, `ON_ORIENTED_BOUNDARY`, or `ON_POSITIVE_SIDE`, iff `pgn` and `gps` are completely disjoint, in contact, or intersect in their interior, respectively.

Oriented_side	oriented_side (const Polygon_with_holes_2 &pgn)
	returns either the constant `ON_NEGATIVE_SIDE`, `ON_ORIENTED_BOUNDARY`, or `ON_POSITIVE_SIDE`, iff `pgn` and `gps` are completely disjoint, in contact, or intersect in their interior, respectively.

Miscellaneous
bool	is_valid () const
	returns `true` if `gps` represents a valid point set.

Member Typedef Documentation

◆ Polygon_2

template<typename Traits, typename Dcel>

typedef unspecified_type CGAL::General_polygon_set_2< Traits, Dcel >::Polygon_2

the general polygon type.

Must model the GpsTraitsGeneralPolygon_2 concept.

◆ Polygon_with_holes_2

template<typename Traits, typename Dcel>

typedef unspecified_type CGAL::General_polygon_set_2< Traits, Dcel >::Polygon_with_holes_2

the general polygon with holes type.

Must model the GpsTraitsGeneralPolygonWithHoles_2 concept.

Member Function Documentation

◆ complement()

template<typename Traits, typename Dcel>

void CGAL::General_polygon_set_2< Traits, Dcel >::complement ( const Polygon_set_2 & other )

computes the complement of other.

gps is overridden by the result.

◆ do_intersect() [1/2]

template<typename Traits, typename Dcel>

template<class InputIterator >

void CGAL::General_polygon_set_2< Traits, Dcel >::do_intersect	(	InputIterator	begin,
		InputIterator	end
	)

returns true if the interior of the point sets in a collection intersect, and false otherwise.

The collection consists of the polygons (or polygons with holes) in the given range and the point set represented by gps. (The value type of the input iterator is used to distinguish between the two options.)

◆ do_intersect() [2/2]

template<typename Traits, typename Dcel>

template<class InputIterator1 , class InputIterator2 >

void CGAL::General_polygon_set_2< Traits, Dcel >::do_intersect	(	InputIterator1	pgn_begin,
		InputIterator1	pgn_end,
		InputIterator2	pgn_with_holes_begin,
		InputIterator2	pgn_with_holes_end
	)

returns true if the interior of the point sets in a collection intersect, and false otherwise.

The collection consists of the polygons and polygons with holes in the given two ranges and the point set represented by gps.

◆ insert() [1/4]

template<typename Traits, typename Dcel>

void CGAL::General_polygon_set_2< Traits, Dcel >::insert ( Polygon_2 & pgn )

inserts pgn into gps.

Precondition: pgn and the point set represented by gps are disjoint. This precondition enables the use of very efficient insertion methods. Use the respective overloaded method that inserts a polygon of type Polygon_with_holes_2, if only a relaxed precondition can be guaranteed. If even the relaxed precondition cannot be guaranteed, use the join method.

◆ insert() [2/4]

template<typename Traits, typename Dcel>

void CGAL::General_polygon_set_2< Traits, Dcel >::insert ( Polygon_with_holes_2 & pgn_with_holes )

inserts pgn_with_holes into gps.

Precondition: pgn_with_holes does not intersect with the point set represented by gps, except maybe at the vertices. If this relaxed precondition cannot be guaranteed, use the join method.

◆ insert() [3/4]

template<typename Traits, typename Dcel>

template<class InputIterator >

void CGAL::General_polygon_set_2< Traits, Dcel >::insert	(	InputIterator	begin,
		InputIterator	end
	)

inserts the range of polygons (or polygons with holes) into gps.

(The value type of the input iterator is used to distinguish between the two.)

Precondition: If the given range contains objects of type Polygon_with_holes_2, then these polygons and the point set represented by gps are pairwise disjoint, except maybe at the vertices. If the given range contains objects of type Polygon_2, then these polygons and the point set represented by gps are pairwise disjoint without any exceptions.

◆ insert() [4/4]

template<typename Traits, typename Dcel>

template<class InputIterator1 , class InputIterator2 >

void CGAL::General_polygon_set_2< Traits, Dcel >::insert	(	InputIterator1	pgn_begin,
		InputIterator1	pgn_end,
		InputIterator2	pgn_with_holes_begin,
		InputIterator2	pgn_with_holes_end
	)

inserts the two ranges of polygons and polygons with holes into gps.

Precondition: All polygons in the first range, all polygon with holes in the second range, and the point set represented by gps are pairwise disjoint, except maybe at the vertices

◆ intersection() [1/2]

template<typename Traits, typename Dcel>

template<class InputIterator >

void CGAL::General_polygon_set_2< Traits, Dcel >::intersection	(	InputIterator	begin,
		InputIterator	end
	)

computes the intersection of a collection of point sets.

The collection consists of the polygons (or polygons with holes) in the given range and the point set represented by gps. (The value type of the input iterator is used to distinguish between the two options.)

◆ intersection() [2/2]

template<typename Traits, typename Dcel>

template<class InputIterator1 , class InputIterator2 >

void CGAL::General_polygon_set_2< Traits, Dcel >::intersection	(	InputIterator1	pgn_begin,
		InputIterator1	pgn_end,
		InputIterator2	pgn_with_holes_begin,
		InputIterator2	pgn_with_holes_end
	)

computes the intersection of a collection of point sets.

The collection consists of the polygons and polygons with holes in the given two ranges and the point set represented by gps.

◆ join()

template<typename Traits, typename Dcel>

template<class InputIterator >

void CGAL::General_polygon_set_2< Traits, Dcel >::join	(	InputIterator	begin,
		InputIterator	end
	)

computes the union of the polygons (or polygons with holes) in the given range and the point set represented by gps.

(The value type of the input iterator is used to distinguish between the two options.)

◆ locate()

template<typename Traits, typename Dcel>

bool CGAL::General_polygon_set_2< Traits, Dcel >::locate	(	const Point_2 &	p,
		Polygon_with_holes_2 &	pgn
	)

obtains a polygon with holes that contains the query point p, if exists, through pgn, and returns true.

Otherwise, returns false.

◆ symmetric_difference() [1/2]

template<typename Traits, typename Dcel>

template<class InputIterator >

void CGAL::General_polygon_set_2< Traits, Dcel >::symmetric_difference	(	InputIterator	begin,
		InputIterator	end
	)

computes the symmetric difference (xor) of a collection of point sets.

The collection consists of the polygons (or polygons with holes) in the given range and the point set represented by gps. (The value type of the input iterator is used to distinguish between the two options.)

◆ symmetric_difference() [2/2]

template<typename Traits, typename Dcel>

template<class InputIterator1 , class InputIterator2 >

void CGAL::General_polygon_set_2< Traits, Dcel >::symmetric_difference	(	InputIterator1	pgn_begin,
		InputIterator1	pgn_end,
		InputIterator2	pgn_with_holes_begin,
		InputIterator2	pgn_with_holes_end
	)

computes the symmetric difference (xor) of a collection of point sets.

The collection consists of the polygons and polygons with holes in the given two ranges and the point set represented by gps.

◆ traits()

template<typename Traits, typename Dcel>

Traits& CGAL::General_polygon_set_2< Traits, Dcel >::traits ( ) const

obtains an instance of the traits.

If the traits was passed as a parameter to the constructor of gps, it is returned. Otherwise, a newly created instance is returned.

Definition

Types

Creation

Access Functions

Modifiers

Univariate Operations

Bivariate Operations

Query Functions

Miscellaneous

Member Typedef Documentation

◆ Polygon_2

◆ Polygon_with_holes_2

Member Function Documentation

◆ complement()

◆ do_intersect() [1/2]

◆ do_intersect() [2/2]

◆ insert() [1/4]

◆ insert() [2/4]

◆ insert() [3/4]

◆ insert() [4/4]

◆ intersection() [1/2]

◆ intersection() [2/2]

◆ join()

◆ locate()

◆ symmetric_difference() [1/2]

◆ symmetric_difference() [2/2]

◆ traits()