CGAL 5.1 - 2D Arrangements
CGAL::Arrangement_2< Traits, Dcel >::Vertex Class Reference

#include <CGAL/Arrangement_2.h>

Inherits Vertex.

Definition

template<typename Traits, typename Dcel>
class CGAL::Arrangement_2< Traits, Dcel >::Vertex

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. More...
 

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. More...
 
bool is_isolated () const
 checks whether the vertex is isolated (i.e., has no incident edges). More...
 
Size degree () const
 returns the number of edges incident to v. More...
 
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. More...
 
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. More...
 

Constructor & Destructor Documentation

◆ Vertex()

template<typename Traits , typename Dcel >
CGAL::Arrangement_2< Traits, Dcel >::Vertex::Vertex ( )

default constructor.

Member Function Documentation

◆ degree()

template<typename Traits , typename Dcel >
Size CGAL::Arrangement_2< Traits, Dcel >::Vertex::degree ( ) const

returns the number of edges incident to v.

◆ face()

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.

◆ incident_halfedges()

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.

◆ is_at_open_boundary()

template<typename Traits , typename Dcel >
bool CGAL::Arrangement_2< Traits, Dcel >::Vertex::is_at_open_boundary ( ) const

checks whether the vertex lies at infinity and not associated with a point with bounded coordinates.

◆ is_isolated()

template<typename Traits , typename Dcel >
bool CGAL::Arrangement_2< Traits, Dcel >::Vertex::is_isolated ( ) const

checks whether the vertex is isolated (i.e., has no incident edges).

◆ parameter_space_in_x()

template<typename Traits , typename Dcel >
Arr_parameter_space CGAL::Arrangement_2< Traits, Dcel >::Vertex::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.

◆ parameter_space_in_y()

template<typename Traits , typename Dcel >
Arr_parameter_space CGAL::Arrangement_2< Traits, Dcel >::Vertex::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.

◆ point()

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.