CGAL 5.6 - 2D Arrangements
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CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex Class Reference

#include <CGAL/Arrangement_on_surface_2.h>

Inherits from

typename Dcel::Vertex.

Definition

template<typename GeometryTraits, typename TopologyTraits>
class CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex

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.
 

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).
 
Face_handle face ()
 obtains a handle to the face that contains v in its interior.
 
const Traits::Point_2 & point () const
 obtains the point associated with the vertex.
 
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.
 
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.
 

Member Function Documentation

◆ 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.