CGAL 5.5.1  2D Straight Skeleton and Polygon Offsetting

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.
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, 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 bidirectional 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 bidirectional 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_halfedge_const_circulator StraightSkeletonVertex_2::defining_contour_halfedges_begin  (  )  const 
returns a bidirectional 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_const_circulator StraightSkeletonVertex_2::halfedge_around_vertex_begin  (  )  const 
returns a bidirectional 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).