\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - 2D Voronoi Diagram Adaptor

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CGAL::Voronoi_diagram_2< DG, AT, AP >::Vertex Class Reference
2D Voronoi Diagram Adaptor Reference

`#include <CGAL/Voronoi_diagram_2.h>`

## Definition

The class `Vertex` is the Voronoi vertex class provided by the class `Voronoi_diagram_2<DG,AT,AP>` class.

Below we present its interface.

Is Model Of:

  `DefaultConstructible`

  `CopyConstructible`

  `Assignable`,

  `EqualityComparable`

  `LessThanComparable`

See Also
  `CGAL::Voronoi_diagram_2<DG,AT,AP>`
  `CGAL::Voronoi_diagram_2<DG,AT,AP>::Halfedge`
  `CGAL::Voronoi_diagram_2<DG,AT,AP>::Face`
  `DelaunayGraph_2`

## 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.