CGAL 4.7  CGAL and the Boost Graph Library

The concept HalfedgeGraph
is a refinement of the Bgl concept Graph
and adds the notion of a halfedge: Each edge is associated with two opposite halfedges with source and target vertices swapped. Furthermore, halfedges have a successor and predecessor, and form cycles we call faces. However, this concept does not introduce a face type. A HalfedgeGraph
is undirected and does not allow parallel edges.
Using the composition of the successor and opposite functions results in another cycle, namely the cycle of halfedges which are incident to the same vertex. We refer to Iterators and Circulators for a description of iterators and circulators for these halfedge cycles.
A model of HalfedgeGraph
must have the interior property vertex_point
attached to its vertices.
Notations
G
HalfedgeGraph
. g
G
. u
, v
e
h
Associated Types
Type  Description 

boost::graph_traits<G>::halfedge_descriptor  A halfedge_descriptor corresponds to a halfedge in a graph. Must be DefaultConstructible , Assignable , EqualityComparable and LessThanComparable . 
Valid Expressions
Expression  Returns  Description 

edge(h, g)  edge_descriptor  The edge corresponding to h and opposite(h) . 
halfedge(e, g)  halfedge_descriptor  One of the halfedges corresponding to e . 
halfedge(v, g)  halfedge_descriptor  A halfedge with target v . 
halfedge(u, v, g)  std::pair<halfedge_descriptor,bool>  The halfedge with source u and target v . The Boolean is true , iff this halfedge exists. 
opposite(h, g)  halfedge_descriptor  The halfedge with source and target swapped. 
source(h,g)  vertex_descriptor  The source vertex of h . 
target(h,g)  vertex_descriptor  The target vertex of h . 
next(h, g)  halfedge_descriptor  The next halfedge around its face. 
prev(h, g)  halfedge_descriptor  The previous halfedge around its face. 
boost::graph_traits<G>::null_halfedge()  halfedge_descriptor  Returns a special halfedge that is not equal to any other halfedge. 