 CGAL 4.7 - 2D Arrangements
CGAL::Arrangement_2< Traits, Dcel >::Vertex Class Reference

#include <CGAL/Arrangement_2.h>

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.