CGAL 5.5.1 - 2D Arrangements
CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex Class Reference

#include <CGAL/Arrangement_on_surface_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 ambient surface.

## 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.

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

Size degree () const
obtains the number of edges incident to v.

Halfedge_around_vertex_circulator incident_halfedges ()
obtains a circulator circulator that allows going over the halfedges incident to v (that have v as their target). More...

Face_handle face ()
obtains a handle to the face that contains v in its interior. More...

const Traits::Point_2 & point () const
obtains the point associated with the vertex. More...

Arr_parameter_space parameter_space_in_x () const
obtains 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
obtains 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...

## ◆ Vertex()

template<typename GeometryTraits, typename TopologyTraits>
 CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::Vertex ( )

default constructor.

## ◆ face()

template<typename GeometryTraits, typename TopologyTraits>
 Face_handle CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::face ( )

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

Precondition
v is an isolated vertex.

## ◆ incident_halfedges()

template<typename GeometryTraits, typename TopologyTraits>
 Halfedge_around_vertex_circulator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::incident_halfedges ( )

obtains 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.

## ◆ parameter_space_in_x()

template<typename GeometryTraits, typename TopologyTraits>
 Arr_parameter_space CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::parameter_space_in_x ( ) const

obtains the placement of the $$x$$-coordinate in the parameter space, that is, either the left boundary-side, the interior, or the right boundary-side.

If the vertex lies on an identified vertical side, the return value is non-deterministic.

## ◆ parameter_space_in_y()

template<typename GeometryTraits, typename TopologyTraits>
 Arr_parameter_space CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::parameter_space_in_y ( ) const

obtains the placement of the $$y$$-coordinate in the parameter space, that is, either the bottom boundary-side, the interior, or the top boundary-side.

If the vertex lies on an identified horizontal side, the return value is non-deterministic.

## ◆ point()

template<typename GeometryTraits, typename TopologyTraits>
 const Traits::Point_2& CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::point ( ) const

obtains the point associated with the vertex.

Precondition
v is not a vertex at infinity.