Definition

A doubly-connected edge-list (Dcel for short) data-structure. It consists of three containers of records: vertices \( V\), halfedges \( E\), and faces \( F\). It maintains the incidence relation among them. The halfedges are ordered in pairs sometimes referred to as twins, such that each halfedge pair represent an edge.

A model of the ArrangementDcel concept must provide the following types and operations. (In addition to the requirements here, the local types Vertex,Halfedge, Face Hole and Isolated_vertex must be models of the concepts ArrangementDcelVertex, ArrangementDcelHalfedge, ArrangementDcelFace, ArrangementDcelHole, and ArrangementDcelIsolatedVertex respectively.)

Has Models:

CGAL::Arr_dcel_base<V,H,F>

CGAL::Arr_default_dcel<Traits>

CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>

CGAL::Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>

See Also: ArrangementDcelVertex; ArrangementDcelHalfedge; ArrangementDcelFace; ArrangementDcelHole; ArrangementDcelIsolatedVertex

Types
typedef unspecified_type	Vertex
	the vertex type.

typedef unspecified_type	Halfedge
	the halfedge type.

typedef unspecified_type	Face
	the face type.

typedef unspecified_type	Hole
	the hole type.

typedef unspecified_type	Isolated_vertex
	the isolated vertex type.

typedef unspecified_type	Size
	used to represent size values (e.g., `size_t`).

typedef unspecified_type	Vertex_iterator
	a bidirectional iterator over the vertices. More...

typedef unspecified_type	Vertex_const_iterator
	a bidirectional iterator over the vertices. More...

typedef unspecified_type	Halfedge_iterator
	a bidirectional iterator over the halfedges. More...

typedef unspecified_type	Halfedge_const_iterator
	a bidirectional iterator over the halfedges. More...

typedef unspecified_type	Face_iterator
	a bidirectional iterator over the faces. More...

typedef unspecified_type	Face_const_iterator
	a bidirectional iterator over the faces. More...

Creation
	Arr_dcel ()
	constructs an empty Dcel with one unbounded face.

Face *	assign (const Self &other, const Face *uf)
	assigns the contents of the `other` Dcel whose unbounded face is given by `uf`, to `dcel`. More...

Access Functions
Size	size_of_vertices () const
	returns the number of vertices.

Size	size_of_halfedges () const
	returns the number of halfedges (always even).

Size	size_of_faces () const
	returns the number of faces.

Size	size_of_holes () const
	returns the number of holes (the number of connected components).

Size	size_of_isolated_vertices () const
	returns the number of isolated vertices.

Vertex_iterator	vertices_begin ()
	returns a begin-iterator of the vertices in `dcel`.

Vertex_iterator	vertices_end ()
	returns a past-the-end iterator of the vertices in `dcel`.

unspecified_type	vertex_handles ()
	returns a range over handles of the vertices in `dcel`.

Vertex_const_iterator	vertices_begin () const
	returns a begin-iterator of the vertices in `dcel`.

Vertex_const_iterator	vertices_end () const
	returns a past-the-end iterator of the vertices in `dcel`.

unspecified_type	vertex_handles () const
	returns a const range (model of `ConstRange`) over handles of the vertices in `dcel`.

Halfedge_iterator	halfedges_begin ()
	returns a begin-iterator of the halfedges in `dcel`.

Halfedge_iterator	halfedges_end ()
	returns a past-the-end iterator of the halfedges in `dcel`.

unspecified_type	halfedge_handles ()
	returns a range over handles of the halfedges in `dcel`.

Halfedge_const_iterator	halfedges_begin () const
	returns a begin-iterator of the halfedges in `dcel`.

Halfedge_const_iterator	halfedges_end () const
	returns a past-the-end iterator of the halfedges in `dcel`.

unspecified_type	halfedge_handles () const
	returns a const range (model of `ConstRange`) over handles of the halfedges in `dcel`.

Face_iterator	faces_begin ()
	returns a begin-iterator of the faces in `dcel`.

Face_iterator	faces_end ()
	returns a past-the-end iterator of the faces in `dcel`.

unspecified_type	face_handles ()
	returns a range over handles of the faces in `dcel`.

Face_const_iterator	faces_begin () const
	returns a begin-iterator of the faces in `dcel`.

Face_const_iterator	faces_end () const
	returns a past-the-end iterator of the faces in `dcel`.

unspecified_type	face_handles () const
	returns a const range (model of `ConstRange`) over handles of the faces in `dcel`.

Modifiers
The following operations allocate a new element of the respective type. Halfedges are always allocated in pairs of opposite halfedges. The halfedges and their opposite pointers are automatically set.
Vertex *	new_vertex ()
	creates a new vertex.

Halfedge *	new_edge ()
	creates a new pair of twin halfedges.

Face *	new_face ()
	creates a new face.

Hole *	new_hole ()
	creates a new hole record.

Isolated_vertex *	new_isolated_vertex ()
	creates a new isolated vertex record.

void	delete_vertex (Vertex *v)
	deletes the vertex `v`.

void	delete_edge (Halfedge *e)
	deletes the halfedge `e` as well as its twin.

void	delete_face (Face *f)
	deletes the face `f`.

void	delete_hole (Hole *ho)
	deletes the hole `ho`.

void	delete_isolated_vertex (Isolated_vertex *iv)
	deletes the isolated vertex `iv`.