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.


the corresponding Dcel halfedge type.

the corresponding Dcel isolated vertex-information type.

the point type associated with the vertex.


ArrangementDcelVertex v;
default constructor.

void v.assign ( 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 v.is_isolated () const returns whether the vertex is isolated (has no incident halfedges).

Halfedge* v.halfedge () returns an incident halfedge that has v as its target.
Precondition: v is not an isolated vertex.

Isolated_vertex* v.isolated_vertex () returns the isolated vertex-information record.
Precondition: v is an isolated vertex.

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

Point& v.point () returns the associated point.
Precondition: v() is associated with a valid point.

Arr_parameter_space v.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 v.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.


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

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

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

void v.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.

See Also