CGAL 6.1.1 - 2D Arrangements

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AosDcelFace Concept Reference
Reference Manual » Concepts » DCEL Concepts

## Definition

A face record in a DCEL data structure. A face represents a region, which may have outer and inner boundaries. A boundary conists of a chain of incident halfedges, referred to as a Connected Component of the Boundary (CCB). A face may be unbounded. Otherwise, it has one or more outer CCBs. A face may also be bounded by inner CCBs, and it may contain isolated vertices in its interior. A planar face may have only one outer CCBs and its inner CCBs are referred to as holes.

See also
  `AosDcel`
  `AosDcelVertex`
  `AosDcelHalfedge`

## Types
The non-mutable iterators `Outer_ccb_const_iterator`, `Inner_ccb_const_iterator`, `Hole_const_iterator`, and `Isolated_vertex_const_iterator` are also defined.
typedef unspecified_type | Vertex
| the corresponding DCEL vertex type.
typedef unspecified_type | Halfedge
| the corresponding DCEL halfedge type.
typedef unspecified_type | Outer_ccb_iterator
| a bidirectional iterator over the outer CCBs of the face.
typedef unspecified_type | Inner_ccb_iterator
| a bidirectional iterator over the inner CCBs of the face.
typedef unspecified_type | Hole_iterator
| a bidirectional iterator over the holes (i.e., inner CCBs) of the face.
typedef unspecified_type | Isolated_vertex_iterator
| a bidirectional iterator over the isolated vertices in inside the face.

## Creation
| Arr_dcel_face ()
| default constructor.
void | assign (const Self &other)
| assigns `f` with the contents of the `other` face.

## Access Functions
All functions below also have `const` counterparts, returning non-mutable pointers or iterators:
bool | is_unbounded () const
| determines whether the face is unbounded.
Halfedge * | halfedge ()
| obtains an incident halfedge along the outer boundaries of the face.
std::size_t | number_of_outer_ccbs () const
| obtains the number of outer CCBs of `f`.
Outer_ccb_iterator | outer_ccbs_begin ()
| obtains a begin iterator for the outer CCBs of `f`.
Outer_ccb_iterator | outer_ccbs_end ()
| obtains a past-the-end iterator for the outer CCBs of `f`.
std::size_t | number_of_inner_ccbs () const
| obtains the number of inner CCBs of `f`.
Inner_ccb_iterator | inner_ccbs_begin ()
| obtains a begin iterator for the inner CCBs of `f`.
Inner_ccb_iterator | inner_ccbs_end ()
| obtains a past-the-end iterator for the inner CCBs of `f`.
std::size_t | number_of_holes () const
| obtains the number of holes (i.e., inner CCBs) inside `f`.
Hole_iterator | holes_begin ()
| obtains a begin-iterator for the holes (i.e., inner CCBs) of `f`.
Hole_iterator | holes_end ()
| obtains a past-the-end iterator for the holes (i.e., inner CCBs) of `f`.
std::size_t | number_of_isolated_vertices () const
| obtains the number of isolated vertices inside `f`.
Isolated_vertex_iterator | isolated_vertices_begin ()
| obtains a begin-iterator for the isolated vertices inside `f`.
Isolated_vertex_iterator | isolated_vertices_end ()
| obtains a past-the-end iterator for the isolated vertices inside `f`.

## Modifiers
void | set_unbounded (bool flag)
| sets the face as unbounded (if `flag` is `true`), or as a bounded face (if it is `false`).
void | set_halfedge (Halfedge *e)
| sets the incident halfedge.
void | add_outer_ccb (Halfedge *e)
| adds `e` as an outer CCB of `f`.
void | erase_outer_ccb (Outer_ccb_iterator it)
| removes the outer CCB that `it` points to from `f`.
void | add_inner_ccb (Halfedge *e)
| adds `e` as an inner CCB of `f`.
void | erase_inner_ccb (Inner_ccb_iterator it)
| removes the inner CCB that `it` points to from `f`.
void | add_hole (Halfedge *e)
| adds `e` as a hole (i.e., inner CCB) of `f`.
void | erase_hole (Hole_iterator it)
| removes the hole (i.e., inner CCB) that `it` points to from `f`.
void | add_isolated_vertex (Vertex *v)
| adds `v` as an isolated vertex inside `f`.
void | erase_isolated_vertex (Isolated_vertex_iterator it)
| removes the isolated vertex that `it` points to from inside `f`.

## Member Typedef Documentation

## ◆ Hole_iterator

typedef unspecified_type AosDcelFace::Hole_iterator

a bidirectional iterator over the holes (i.e., inner CCBs) of the face.

Its value-type is `Halfedge*`.

## ◆ Inner_ccb_iterator

typedef unspecified_type AosDcelFace::Inner_ccb_iterator

a bidirectional iterator over the inner CCBs of the face.

Its value-type is `Halfedge*`.

## ◆ Isolated_vertex_iterator

typedef unspecified_type AosDcelFace::Isolated_vertex_iterator

a bidirectional iterator over the isolated vertices in inside the face.

Its value-type is `Vertex*`.

## ◆ Outer_ccb_iterator

typedef unspecified_type AosDcelFace::Outer_ccb_iterator

a bidirectional iterator over the outer CCBs of the face.

Its value-type is `Halfedge*`.

## Member Function Documentation

## ◆ halfedge()

Halfedge * AosDcelFace::halfedge | ( |  | ) |

obtains an incident halfedge along the outer boundaries of the face.

If `f` has no outer boundary, the function returns `nullptr`.

## ◆ number_of_outer_ccbs()

std::size_t AosDcelFace::number_of_outer_ccbs | ( |  | ) | const

obtains the number of outer CCBs of `f`.

In case of planar arrangement this is either 0 or 1.