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

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