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CGAL::General_polygon_set_2<Traits,Dcel>

Definition

An object of the General_polygon_set_2<Traits,Dcel> 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<Traits,Dcel>, 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.

Types

General_polygon_set_2<Traits,Dcel>::Traits_2
the traits class in use.

General_polygon_set_2<Traits,Dcel>::Polygon_2
the general polygon type. Must model the GpsTraitsGeneralPolygon_2 Concept.

General_polygon_set_2<Traits,Dcel>::Polygon_with_holes_2
the general polygon with holes type. Must model the GpsTraitsGeneralPolygonWithHoles_2 Concept.


General_polygon_set_2<Traits,Dcel>::Size
number of polygons with holes size type.


General_polygon_set_2<Traits,Dcel>::Arrangement_2
the arrangement type used internally.

Creation

General_polygon_set_2<Traits,Dcel> gps;
constructs an empty set of polygons represented by an empty arrangement.


General_polygon_set_2<Traits,Dcel> gps ( Self other);
copy constructor.


General_polygon_set_2<Traits,Dcel> gps ( Traits & traits);
constructs an empty set of polygons that uses the given traits instance for performing the geometric operations.


General_polygon_set_2<Traits,Dcel> gps ( Polygon_2 pgn);
constructs a set of polygons that consists of the single polygon pgn.


General_polygon_set_2<Traits,Dcel> gps ( Polygon_with_holes_2 pgn_with_holes);
constructs a set of polygons that consists of the single polygon with holes pgn_with_holes.

Access Functions

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

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

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

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

Traits & gps.traits () 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.

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

Modifiers

void gps.clear () clears gps.

void gps.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.

void gps.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.

template <class InputIterator>
void gps.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.

template <class InputIterator1, class InputIterator2>
void
gps.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

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

void gps.complement ( Polygon_set_2 other)
computes the complement of other. gps is overriden by the result.

Univariate Operations

In the following univariate and bivariate methods the result is placed in gps after it is cleared.

void gps.intersection ( General_polygon_set_2 other)
computes the intersection of gps and other.
void gps.intersection ( Polygon_2 pgn)
computes the intersection of gps and pgn.
void gps.intersection ( Polygon_with_holes_2 pgn)
computes the intersection of gps and pgn.

template <class InputIterator>
void gps.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.)
template <class InputIterator1, class InputIterator2>
void
gps.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.

void gps.join ( General_polygon_set_2 other)
computes the union of gps and other.
void gps.join ( Polygon_2 pgn) computes the union of gps and pgn.
void gps.join ( Polygon_with_holes_2 pgn)
computes the union of gps and pgn.

template <class InputIterator>
void gps.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.)
template <class InputIterator1, class InputIterator2>
void
gps.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 gps.difference ( General_polygon_set_2 other)
computes the difference between gps and other.
void gps.difference ( Polygon_2 pgn) computes the difference between gps and pgn.
void gps.difference ( Polygon_with_holes_2 pgn)
computes the difference between gps and pgn.

void gps.symmetric_difference ( General_polygon_set_2 other)
computes the symmetric difference between gps and other.
void gps.symmetric_difference ( Polygon_2 pgn)
computes the symmetric difference between gps and pgn.
void gps.symmetric_difference ( Polygon_with_holes_2 pgn)
computes the symmetric difference between gps and pgn.

template <class InputIterator>
void gps.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.)
template <class InputIterator1, class InputIterator2>
void
gps.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.

Bivariate Operations

The following bivariate function replace gps with the result.

void gps.intersection ( General_polygon_set_2 gps1, General_polygon_set_2 gps2)
computes the intersection of gps1 and gps2.

void gps.join ( General_polygon_set_2 gps1, General_polygon_set_2 gps2)
computes the union of gps1 and gps2.

void gps.difference ( General_polygon_set_2 gps1, General_polygon_set_2 gps2)
computes the difference between gps1 and gps2.

void gps.symmetric_difference ( General_polygon_set_2 gps1, General_polygon_set_2 gps2)
computes the symmetric difference between gps1 and gps2.

Query Functions

bool gps.do_intersect ( General_polygon_set_2 other)
returns true if gps and other intersect in their interior, and false otherwise.
bool gps.do_intersect ( Polygon_2 pgn)
returns true if gps and pgn intersect in their interior, and false otherwise.
bool gps.do_intersect ( Polygon_with_holes_2 pgn)
returns true if gps and pgn intersect in their interior, and false otherwise.

template <class InputIterator>
void gps.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.)
template <class InputIterator1, class InputIterator2>
void
gps.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.

bool gps.locate ( 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 flase.

Oriented_side gps.oriented_side ( 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 gps.oriented_side ( 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 gps.oriented_side ( 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 gps.oriented_side ( 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 gps.is_valid () returns true if gps represents a valid point set.

See Also

Arrangement_2
ArrangementXMonotoneTraits_2
Nef_2

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CGAL Open Source Project. Release 3.7. 14 October 2010.