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

CGAL 4.8 - 2D Arrangements

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
CGAL::Arrangement_2< Traits, Dcel >::Vertex Class Reference
DCEL

`#include <CGAL/Arrangement_2.h>`

## Inherits from

Vertex.

## Definition

An object \( v\) of the class `Vertex` represents an arrangement vertex, that is - a \( 0\)-dimensional cell, associated with a point on the plane.

## Creation
| Vertex ()
| default constructor.

## Access Functions
All non-const methods listed below also have `const` counterparts that return constant handles, iterators or circulators:
bool | is_at_open_boundary () const
| checks whether the vertex lies at infinity and not associated with a point with bounded coordinates.
bool | is_isolated () const
| checks whether the vertex is isolated (i.e., has no incident edges).
Size | degree () const
| returns the number of edges incident to `v`.
Halfedge_around_vertex_circulator | incident_halfedges ()
| returns a circulator circulator that allows going over the halfedges incident to `v` (that have `v` as their target). More...
Face_handle | face ()
| returns a handle to the face that contains `v` in its interior. More...
const Traits::Point_2 & | point () const
| returns the point associated with the vertex. More...
Arr_parameter_space | parameter_space_in_x () const
| returns the placement of the \( x\)-coordinate in the parameter space, that is, either the left boundary-side, the interior, or the right boundary-side.
Arr_parameter_space | parameter_space_in_y () const
| returns the placement of the \( y\)-coordinate in the parameter space, that is, either the bottom boundary-side, the interior, or the top boundary-side.

## Member Function Documentation

template<typename Traits , typename Dcel >

Face_handle CGAL::Arrangement_2< Traits, Dcel >::Vertex::face | ( | ) |  |

returns a handle to the face that contains `v` in its interior.

Precondition
  `v` is an isolated vertex.

template<typename Traits , typename Dcel >

Halfedge_around_vertex_circulator CGAL::Arrangement_2< Traits, Dcel >::Vertex::incident_halfedges | ( | ) |  |

returns a circulator circulator that allows going over the halfedges incident to `v` (that have `v` as their target).

The edges are traversed in a clockwise direction around `v`.

Precondition
  `v` is not an isolated vertex.

template<typename Traits , typename Dcel >

const Traits::Point_2& CGAL::Arrangement_2< Traits, Dcel >::Vertex::point | ( | ) |  | const

returns the point associated with the vertex.

Precondition
  `v` is not a vertex at infinity.