\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D Arrangements
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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.