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Class

CGAL::Arrangement_2<Traits,Dcel>::Face

Definition

An object of the class Arrangement_2<Traits,Dcel>::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.

Inherits From

typename Dcel::Face

Creation

Arrangement_2<Traits,Dcel>::Face f;
default constructor.

Access Functions

All non-const methods listed below also have const counterparts that return constant handles, iterators or circulators:

bool f.is_fictitious () const returns 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.

bool f.is_unbounded () const returns a Boolean indicating whether the face is unbounded.

bool f.has_outer_ccb () const returns a Boolean indicating 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.)

Ccb_halfedge_circulator f.outer_ccb () returns 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.

Hole_iterator f.holes_begin () returns an iterator for traversing all the holes (inner CCBs) of f.
Hole_iterator f.holes_end () returns a past-the-end iterator for the holes of f.

Isolated_vertex_iterator f.isolated_vertices_begin () returns an iterator for traversing all the isolated vertices contained in the interior of f.
Isolated_vertex_iterator f.isolated_vertices_end () returns a past-the-end iterator for the isolated vertices contained inside f.

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CGAL Open Source Project. Release 4.1. 23 October 2012.