CGAL 6.1.1 - 2D Arrangements

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CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face Class Reference
Reference Manual » DCEL

`#include <CGAL/Arrangement_on_surface_2.h>`

## Inherits from

typename Dcel::Face.

## Definition

template<typename GeometryTraits, typename TopologyTraits>
class CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face

An object of the class `Face` represents an arrangement face, namely, a \(2\)-dimensional arrangement cell.

An arrangement that supports only bounded curves contains exactly one unbounded face, and a number of bounded faces. An arrangement that supports also unbounded curves has one or more unbounded faces. Such an arrangement has also exactly one fictitious face, which does not correspond to a real two-dimensional cell of the arrangement (and thus it is ignored in counting the number of faces of the arrangement.) Each bounded face has an outer boundary comprising a halfedge chain winding in counterclockwise orientation around it. Each unbounded face of an arrangement that has a fictitious face also has a boundary comprising a counterclockwise halfedge-chain. The edges on the boundary of a face incident to the fictitious face are fictitious, as they do not correspond to real curves. A face may also contain holes, which are defined by clockwise-oriented halfedge chains, and isolated vertices.

## Types inherited from the base Dcel::Face
typedef Base::Inner_ccb_iterator | Inner_ccb_iterator
| a bidirectional iterator over the inner CCBs of the face.
typedef Base::Outer_ccb_iterator | Outer_ccb_iterator
| a bidirectional iterator over the outer CCBs of the face.
typedef Base::Hole_iterator | Hole_iterator
| a bidirectional iterator over the holes (i.e., inner CCBs) contained inside the face.
typedef Base::Isolated_vertex_iterator | Isolated_vertex_iterator
| a bidirectional iterator over the isolated vertices contained inside the face.

## Creation
| Face ()
| default constructor.

## Access Functions
All non-const methods listed below also have `const` counterparts that return constant handles, iterators or circulators:
bool | is_fictitious () const
| obtains a Boolean indicating whether this is the fictitious face, which contain the entire arrangement (and does not have an outer CCB).
bool | is_unbounded () const
| obtains a Boolean indicating whether the face is unbounded.
Size | number_of_outer_ccbs () const
| obtains the number of outer CCBs of the face.
Outer_ccb_iterator | outer_ccbs_begin ()
| obtains a begin iterator for the outer CCBs of the face.
Outer_ccb_iterator | outer_ccbs_end ()
| obtains a past-the-end iterator for the outer CCBs.
Size | number_of_inner_ccbs () const
| obtains the number of inner CCBs of the face.
Inner_ccb_iterator | inner_ccbs_begin ()
| obtains a begin iterator for the inner CCBs of the face.
Inner_ccb_iterator | inner_ccbs_end ()
| obtains a past-the-end iterator for the inner CCBs.
bool | has_outer_ccb () const
| indicates whether the face has an outer CCB.
Ccb_halfedge_circulator | outer_ccb ()
| obtains a circulator that enables traversing the outer boundary of `f`.
Size | number_of_holes () const
| obtains the number of holes (inner CCBs) inside the face.
Hole_iterator | holes_begin ()
| obtains an iterator for traversing all the holes (inner CCBs) of `f`.
Hole_iterator | holes_end ()
| obtains a past-the-end iterator for the holes of `f`.
Isolated_vertex_iterator | isolated_vertices_begin ()
| obtains an iterator for traversing all the isolated vertices contained in the interior of `f`.
Isolated_vertex_iterator | isolated_vertices_end ()
| obtains a past-the-end iterator for the isolated vertices contained inside `f`.

## Member Typedef Documentation

## ◆ Hole_iterator

template<typename GeometryTraits , typename TopologyTraits >

typedef Base::Hole_iterator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::Hole_iterator

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

Its value type is `Ccb_halfedge_circulator`.

## ◆ Inner_ccb_iterator

template<typename GeometryTraits , typename TopologyTraits >

typedef Base::Inner_ccb_iterator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::Inner_ccb_iterator

a bidirectional iterator over the inner CCBs of the face.

Its value type is `Ccb_halfedge_circulator`.

## ◆ Isolated_vertex_iterator

template<typename GeometryTraits , typename TopologyTraits >

typedef Base::Isolated_vertex_iterator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::Isolated_vertex_iterator

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

Its value type is `Vertex`.

## ◆ Outer_ccb_iterator

template<typename GeometryTraits , typename TopologyTraits >

typedef Base::Outer_ccb_iterator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::Outer_ccb_iterator

a bidirectional iterator over the outer CCBs of the face.

Its value type is `Ccb_halfedge_circulator`.

## Member Function Documentation

## ◆ has_outer_ccb()

template<typename GeometryTraits , typename TopologyTraits >

bool CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::has_outer_ccb | ( |  | ) | const

indicates whether the face has an outer CCB.

(The fictitious face and the unbounded face of an arrangement that does not have a fictitious face do not have outer CCBs.)

## ◆ is_fictitious()

template<typename GeometryTraits , typename TopologyTraits >

bool CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::is_fictitious | ( |  | ) | const

obtains a Boolean indicating whether this is the fictitious face, which contain the entire arrangement (and does not have an outer CCB).

An arrangement that supports only bounded curves does not have a fictitious face at all.

## ◆ outer_ccb()

template<typename GeometryTraits , typename TopologyTraits >

Ccb_halfedge_circulator CGAL::Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face::outer_ccb | ( |  | ) |

obtains a circulator that enables traversing the outer boundary of `f`.

The edges along the CCB are traversed in a counterclockwise direction.

Precondition
  The face `f` has an outer CCB.