CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex Class Reference

#include <CGAL/Arrangement_on_surface_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 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...

Constructor & Destructor Documentation

Vertex()

template<typename GeometryTraits, typename TopologyTraits>

CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex::Vertex

(

)

default constructor.

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.