PolygonTraits_2 Concept Reference

Definition

The CGAL::Polygon_2 class and the functions that implement the functionality found in that class each are parameterized by a traits class that defines the primitives used in the algorithms. The concept PolygonTraits_2 defines this common set of requirements.

The requirements of PolygonTraits_2 are a subset of the kernel requirements. We only list the types and methods which are required and refer to the description of the kernel concept for details.

Refines:

DefaultConstructible and CopyConstructable

Has Models:

The kernels supplied by CGAL are models of PolygonTraits_2.

CGAL::Projection_traits_xy_3<K>

CGAL::Projection_traits_yz_3<K>

CGAL::Projection_traits_xz_3<K>

See also

CGAL::Polygon_2<PolygonTraits_2, Container>

Types
typedef unspecified_type	FT
	number type
typedef unspecified_type	Point_2
	The point type.
typedef unspecified_type	Segment_2
	The segment type.
typedef unspecified_type	Construct_segment_2
	functor providing Segment_2 operator()(Point_2, Point_2) to construct a segment from two points.
typedef unspecified_type	Equal_2
	functor providing bool operator()(Point_2, Point_2) to test equality of two points.
typedef unspecified_type	Less_xy_2
	functor providing bool operator()(Point_2, Point_2) to compare lexicographically of two points.
typedef unspecified_type	Less_yx_2
	functor providing bool operator()(Point_2, Point_2) to compare inverse-lexicographically of two points.
typedef unspecified_type	Compare_x_2
	functor providing bool operator()(Point_2, Point_2) to compare the x-coordinate of two points.
typedef unspecified_type	Compare_y_2
	functor providing bool operator()(Point_2, Point_2) to compare the y-coordinate of two points.
typedef unspecified_type	Orientation_2
	functor providing Oriention operator()(Point_2 p, Point_2 q, Point_2 r) that returns CGAL::LEFT_TURN, if r lies to the left of the oriented line l defined by p and q, CGAL::RIGHT_TURN if r lies to the right of l, and CGAL::COLLINEAR if r lies on l.
typedef unspecified_type	Compute_area_2
	Computes the signed area of the oriented triangle defined by 3 Point_2 passed as arguments.

Operations
The following functions that create instances of the above predicate object types must exist.
Equal_2	equal_2_object ()
	returns the corresponding function object
Less_xy_2	less_xy_2_object ()
	returns the corresponding function object
Less_yx_2	less_yx_2_object ()
	returns the corresponding function object
Compare_y_2	compare_y_2_object ()
	returns the corresponding function object
Compare_x_2	compare_x_2_object ()
	returns the corresponding function object
Orientation_2	orientation_2_object ()
	returns the corresponding function object
Compute_area_2	compute_area_2_object ()
	returns the corresponding function object
Construct_segment_2	construct_segment_2_object ()
	returns the corresponding function object