AlphaWrapTraits_2 Concept Reference

Definition

The concept AlphaWrapTraits_2 defines the requirements for the geometric traits class of an alpha wrap oracle.

Refines

AABBRayIntersectionGeomTraits_2

DelaunayTriangulationTraits_2

PolygonTraits_2

Has models

Any CGAL kernel is a model of this traits concept

Public Types
typedef unspecified_type	FT
	The field type, must be a model of FieldNumberType and FromDoubleConstructible
typedef unspecified_type	Is_degenerate_2
	A predicate object that must provide the following function operator:
typedef unspecified_type	Angle_2
	A predicate object that must provide the following function operator:
typedef unspecified_type	Construct_bbox_2
	A construction object that must provide the following function operators:
typedef unspecified_type	Construct_scaled_vector_2
	A construction object that must provide the following function operator:
typedef unspecified_type	Construct_translated_point_2
	A construction object that must provide the following function operator:
typedef unspecified_type	Construct_vertex_2
	A construction object that must be a model of Kernel::ConstructVertex_2
typedef unspecified_type	Has_on_bounded_side_2
	A predicate object that must provide the following function operator:
typedef unspecified_type	Has_on_unbounded_side_2
	A predicate object that must provide the following function operator:
typedef unspecified_type	Side_of_bounded_circle_2
	A predicate object that must provide the following function operator:

Public Member Functions
Is_degenerate_2	is_degenerate_2_object ()
	returns the Is_degenerate_2 predicate.
Angle_2	angle_2_object ()
	returns the Angle_2 functor.
Construct_bbox_2	construct_bbox_2_object ()
	returns the Construct_bbox_2 functor.
Construct_scaled_vector_2	construct_scaled_vector_2_object ()
	returns the Construct_scaled_vector_2 functor.
Construct_translated_point_2	construct_translated_point_2_object ()
	returns the Construct_translated_point_2 functor.
Construct_vertex_2	construct_vertex_2_object ()
	returns the Construct_vertex_2 functor.
Has_on_bounded_side_2	has_on_bounded_side_2_object ()
	returns the Has_on_bounded_side_2 predicate.
Has_on_unbounded_side_2	has_on_unbounded_side_2_object ()
	returns the Has_on_unbounded_side_2 predicate.
Side_of_bounded_circle_2	side_of_bounded_circle_2_object ()
	returns the Side_of_bounded_circle_2 predicate.

Member Typedef Documentation

Angle_2

typedef unspecified_type AlphaWrapTraits_2::Angle_2

A predicate object that must provide the following function operator:

Angle operator()(Point_2 p, Point_2 q, Point_2 r),

which returns the angle at point q formed by the points p, q, and r.

Construct_bbox_2

typedef unspecified_type AlphaWrapTraits_2::Construct_bbox_2

A construction object that must provide the following function operators:

CGAL::Bbox_2 operator()(Point_2 p),

CGAL::Bbox_2 operator()(Segment_2 s),

CGAL::Bbox_2 operator()(Triangle_2 tr),

that constructs the bounding box of these 2D objects.

Construct_scaled_vector_2

typedef unspecified_type AlphaWrapTraits_2::Construct_scaled_vector_2

A construction object that must provide the following function operator:

Vector_2 operator()(Vector_2 v, FT l),

that constructs the scaled vector l * v.

Construct_translated_point_2

typedef unspecified_type AlphaWrapTraits_2::Construct_translated_point_2

A construction object that must provide the following function operator:

Point_2 operator()(Point_2 p, Vector_2 v),

that returns the point obtained by translating p by the vector v.

Has_on_bounded_side_2

typedef unspecified_type AlphaWrapTraits_2::Has_on_bounded_side_2

A predicate object that must provide the following function operator:

bool operator()(Triangle_2 tr, Point_2 p),

which returns whether p is on the bounded side of the triangle tr or not.

Has_on_unbounded_side_2

typedef unspecified_type AlphaWrapTraits_2::Has_on_unbounded_side_2

A predicate object that must provide the following function operator:

bool operator()(Circle_2 c, Point_2 p),

which returns whether p is on the unbounded side of the circle c or not.

Is_degenerate_2

typedef unspecified_type AlphaWrapTraits_2::Is_degenerate_2

A predicate object that must provide the following function operator:

bool operator()(Segment_2 s),

which returns true iff the segment is degenerate.

Side_of_bounded_circle_2

typedef unspecified_type AlphaWrapTraits_2::Side_of_bounded_circle_2

A predicate object that must provide the following function operator:

Bounded_side operator()(Point_2 p, Point_2 q, Point_2 t),

which returns the position of the point t relative to the circle that has the line segment pq as its diameter.