StraightSkeletonVertex_2 Concept Reference

Definition

Refines

HalfedgeDSVertex

The concept StraightSkeletonVertex_2 describes the requirements for the vertex type of the StraightSkeleton_2 concept. It is a refinement of the HalfedgeDSVertex concept with support for storage of the incident halfedge. The StraightSkeletonVertex_2 concept requires the geometric embedding to be a 2D point.

Has models

CGAL::Straight_skeleton_vertex_base_2

See also

StraightSkeletonHalfedge_2

StraightSkeletonFace_2

Types
typedef unspecified_type	Point_2
	The type of the 2D point being the geometric embedding of the vertex.
typedef unspecified_type	FT
	A model of the FieldWithSqrt concept representing the time of a vertex (a Euclidean distance)
typedef unspecified_type	Halfedge_around_vertex_const_circulator
typedef unspecified_type	Halfedge_around_vertex_circulator
	The circulator type used to visit all the incident halfedges around a vertex.
typedef unspecified_type	Defining_contour_halfedge_const_circulator
typedef unspecified_type	Defining_contour_halfedge_circulator
	The circulator type used to visit all the defining contour halfedges of a vertex.

Creation
	StraightSkeletonVertex_2 ()
	Default constructor
	StraightSkeletonVertex_2 (int id, const Point_2 &p)
	constructs a contour vertex with ID number id, at the point p
	StraightSkeletonVertex_2 (int id, const Point_2 &p, FT time)
	constructs a skeleton vertex with ID number id, at point p and time time.

Access Functions
int	id () const
	The ID of the vertex.
const Point_2 &	point () const
	The vertex point.
FT	time () const
	The time of the vertex: the distance from the vertex point to the lines supporting the defining contour edges.
Halfedge_handle	primary_bisector ()
Halfedge_const_handle	primary_bisector () const
	returns the skeleton halfedge incident upon the vertex (called the primary bisector).
Halfedge_around_vertex_circulator	halfedge_around_vertex_begin ()
Halfedge_around_vertex_const_circulator	halfedge_around_vertex_begin () const
	returns a bi-directional circulator pointing to one of the incident halfedges (which one is unspecified).
Defining_contour_halfedge_circulator	defining_contour_halfedges_begin ()
Defining_contour_halfedge_const_circulator	defining_contour_halfedges_begin () const
	returns a bi-directional circulator pointing to one of the defining contour halfedges of the vertex (which one is unspecified).

Queries
bool	is_contour () const
	returns true iff this is a contour vertex.
bool	is_skeleton () const
	returns true iff this is a skeleton vertex.

Member Function Documentation

defining_contour_halfedges_begin()

Defining_contour_halfedge_const_circulator StraightSkeletonVertex_2::defining_contour_halfedges_begin

(

)

const

returns a bi-directional circulator pointing to one of the defining contour halfedges of the vertex (which one is unspecified).

There will always be as many incident defining contour halfedges as the degree of the vertex.

Each halfedge pointed to by this circulator is the one having its left side facing inwards (which happens to be the contour halfedge for which is_border() is false).

halfedge_around_vertex_begin()

Halfedge_around_vertex_const_circulator StraightSkeletonVertex_2::halfedge_around_vertex_begin

(

)

const

returns a bi-directional circulator pointing to one of the incident halfedges (which one is unspecified).

There will always be as many incident halfedges as the degree of the vertex.

If this is a contour vertex, its degree is exactly 3, and from the halfedges pointed to by the circulator, 2 are contour and 1 is a bisector.

If this is an skeleton vertex, its degree is at least 3 and all of the halfedges pointed to by the circulator are bisectors.

Each halfedge pointed to by this circulator is the one which is oriented towards the vertex (according to the geometric embedding).