CGAL 4.12.1 - 2D Straight Skeleton and Polygon Offsetting
StraightSkeletonVertex_2 Concept Reference

## Definition

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.

Refines:
HalfedgeDSVertex
Has Models:
CGAL::Straight_skeleton_vertex_base_2
StraightSkeleton_2
StraightSkeletonHalfedge_2
CGAL::Straight_skeleton_vertex_base_2<Refs,Point,FT>
CGAL::Straight_skeleton_halfedge_base_2<Refs>

## 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 (an 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, Point_2 const &p)
Constructs a contour vertex with ID number id, at the point p

StraightSkeletonVertex_2 (int id, Point_2 const &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.

Point_2 const & 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). More...

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). More...

## 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.

## ◆ 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).