\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.9 - 2D Voronoi Diagram Adaptor
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CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex Class Reference

#include <CGAL/Voronoi_diagram_2.h>

Definition

Types

typedef unspecified_type Halfedge
 A type for the halfedges of the Voronoi diagram.
 
typedef unspecified_type Face
 A type for the faces of the Voronoi diagram.
 
typedef unspecified_type Vertex_handle
 Handle for the vertices of the Voronoi diagram.
 
typedef unspecified_type Face_handle
 Handle for the faces of the Voronoi diagram.
 
typedef unspecified_type Halfedge_handle
 Handle for the halfedges of the Voronoi diagram.
 
typedef unspecified_type Point_2
 A type for the point represented by the vertex.
 
typedef unspecified_type size_type
 A type for sizes.
 
typedef unspecified_type Halfedge_around_vertex_circulator
 A type for a bidirectional circulator that allows to traverse all incident halfedges, i.e., all halfedges that have the vertex as their target. More...
 
typedef unspecified_type Delaunay_graph
 A type for the Delaunay graph. More...
 
typedef Delaunay_graph::Face_handle Delaunay_face_handle
 A type for the handle of the dual face.
 
typedef
Delaunay_graph::Vertex_handle 
Delaunay_vertex_handle
 A type for the vertex handles in the Delaunay graph.
 

Access Methods

Halfedge_handle halfedge ()
 Returns an incident halfedge that has v as its target.
 
size_type degree ()
 Returns the in-degree of the vertex, i.e. the number of halfedges that have v as their target.
 
Point_2 point ()
 Returns the point represented by the vertex.
 
Delaunay_face_handle dual ()
 Returns a handle to the corresponding dual face in the Delaunay graph.
 
Delaunay_vertex_handle site (unsigned int i)
 Returns a handle to the vertex in the Delaunay graph corresponding to the \( (i+1)\)-th generating site of the Voronoi vertex. More...
 
Halfedge_around_vertex_circulator incident_halfedges ()
 Returns a bidirectional circulator that allows the traversal of the halfedges that have v as their target. More...
 

Predicate Methods

bool is_incident_edge (Halfedge_handle e)
 Returns true if the halfedge e is incident to v.
 
bool is_incident_face (Face_handle e)
 Returns true if the face f is incident to v.
 
bool is_valid ()
 Returns true if the following conditions are met: the dual face is not an infinite face; all incident halfedges have the vertex as their target.
 

Member Typedef Documentation

template<typename DG , typename AT , typename AP >
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex::Delaunay_graph

A type for the Delaunay graph.

It is a model of the DelaunayGraph_2 concept.

template<typename DG , typename AT , typename AP >
typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex::Halfedge_around_vertex_circulator

A type for a bidirectional circulator that allows to traverse all incident halfedges, i.e., all halfedges that have the vertex as their target.

The value type of the circulator is CGAL::Voronoi_diagram_2<DG,AT,AP>::Halfedge and is convertible to Halfedge_handle.

Member Function Documentation

template<typename DG , typename AT , typename AP >
Halfedge_around_vertex_circulator CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex::incident_halfedges ( )

Returns a bidirectional circulator that allows the traversal of the halfedges that have v as their target.

Applying operator++ (resp. operator-) to this circulator returns the next incident halfedge in the counterclockwise (resp. clockwise) sense.

template<typename DG , typename AT , typename AP >
Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex::site ( unsigned int  i)

Returns a handle to the vertex in the Delaunay graph corresponding to the \( (i+1)\)-th generating site of the Voronoi vertex.

Precondition
i must be smaller or equal to 2.