Diagram reference: CGAL and BGL concepts diagram

CellIncidenceGraph Halfedge Adaptor

The purpose of the Halfedge Adaptor of a CellIncidenceGraph is for a CellIncidenceGraph to provide, through an adaptor, a partial implementation of CGAL's halfedge concept. Although the halfedge is well suited to manifold surfaces, and not general enough to handle non-manifold cases (refer to CellIncidenceGraphConceptPage), this adaptor still enables simple walks on the non-manifold which in turn permit to abstract the vizualization code.

Notations

G A type that is a model of HalfedgeGraphAdapter.
g An object of type G.
h A halfedge descriptor.

Expression	Reference	Returns	Description
HalfedgeGraph
`next(h, g)`	HalfedgeGraph (CGAL)	`halfedge_descriptor`	The next halfedge around its face.
`prev(h, g)`	HalfedgeGraph (CGAL)	`halfedge_descriptor`	The previous halfedge around its face.
`faces(h,g)`	Generalization of FaceGraph's `face(h, g,)`	`std::pair<face_iterator, face_iterator>`	Returns an iterator-range providing access to the incident faces edge `e` in graph `g`. Note: when the ordering of faces is a partial order then the ordering criteria is unspecified and can change arbitrarily.
To be discussed
`boost::graph_traits<G>::null_halfedge()`	HalfedgeGraph (CGAL)	`halfedge_descriptor`	Returns a special halfedge that is not equal to any other halfedge.

FIXME:

How does one access an halfedge out of an CellIncidenceGraph instance ? (constructor out of an edge)
Do we need source, target, ...

Design notes:

An halfedge h of a HalfedgeGraphAdapter can be implemented as a triplet of references
- a reference to a cell-vertex v of the wrapped CellIncidenceGraph
- a reference to an cell-edgea e of the wrapped CellIncidenceGraph
- a reference to an cell-face f of the wrapped CellIncidenceGraph where f is incident to e and e is incident to v.