CGAL 5.5 - 2D Arrangements
ArrangementDcelVertex Concept Reference

## Definition

A vertex record in a DCEL data structure. A vertex is always associated with a point. However, the vertex record only stores a pointer to the associated point, and the actual Point object is stored elsewhere.

A vertex usually has several halfedges incident to it, such that it is possible to access one of these halfedges directly and to traverse all incident halfedges around the vertex. However, the DCEL may also contain isolated vertices that have no incident halfedges. In this case, the vertex stores an isolated vertex-information record, indicating the face that contains this vertex in its interior.

ArrangementDcel
ArrangementDcelHalfedge
ArrangementDcelIsolatedVertex

## Types

typedef unspecified_type Halfedge
the corresponding DCEL halfedge type.

typedef unspecified_type Isolated_vertex
the corresponding DCEL isolated vertex-information type.

typedef unspecified_type Point
the point type associated with the vertex.

## Creation

Arr_dcel_vertex ()
default constructor.

void assign (const Self &other)
assigns v with the contents of the other vertex.

## Access Functions

All functions below also have const counterparts, returning non-mutable pointers or references:

bool is_isolated () const
returns whether the vertex is isolated (has no incident halfedges).

Halfedgehalfedge ()
returns an incident halfedge that has v as its target. More...

Isolated_vertexisolated_vertex ()
returns the isolated vertex-information record. More...

bool has_null_point () const
returns whether the vertex is not associated with a valid point (i.e. it lies at infinity).

Pointpoint ()
returns the associated point. 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.

## Modifiers

void set_halfedge (Halfedge *e)
sets the incident halfedge, marking v as a regular vertex.

void set_isolated_vertex (Isolated_vertex *iv)
sets the isolated vertex-information record, marking v as an isolated vertex.

void set_point (Point *p)
sets the associated point.

void set_boundary (Arr_parameter_space inf_x, Arr_parameter_space inf_y)
sets v as a vertex on a boundary side. More...

## ◆ halfedge()

 Halfedge* ArrangementDcelVertex::halfedge ( )

returns an incident halfedge that has v as its target.

Precondition
v is not an isolated vertex.

## ◆ isolated_vertex()

 Isolated_vertex* ArrangementDcelVertex::isolated_vertex ( )

returns the isolated vertex-information record.

Precondition
v is an isolated vertex.

## ◆ point()

 Point& ArrangementDcelVertex::point ( )

returns the associated point.

Precondition
v() is associated with a valid point.

## ◆ set_boundary()

 void ArrangementDcelVertex::set_boundary ( Arr_parameter_space inf_x, Arr_parameter_space inf_y )

sets v as a vertex on a boundary side.

Precondition
Either inf_x or inf_y is not ARR_INTERIOR.