CGAL users discussion list

[Efi Fogel <>]

Michael George wrote:
> Hi,
>
> I'm using the Arrangements with history, and I can't find any 
> documentation on what order the halfedges associated with a given 
> curve are iterated.  If my original curves have an associated 
> orientation is there an easy way to traverse only the induced edges 
> that are co-aligned and ordered from source to target?
>
> Thanks,
>
> Mike
The order of the edges is arbitrary. It is a non-trivial deficiency, 
which we may fix in the future. You will need to sort them out yourself, 
or develop your own Arrangement_with_history_2.

An input geometric curve could be split several times, either in order 
to split it into x-monotone curves, or at intersection points. The edges 
induced by an x-monotone curve, which is split at intersection points, 
can be given a strict order, say left to right. However, the items 
induced by a (general) curve, cannot be given an order. As a matter of 
fact, these items could be either edges or (isolated) vertices, as in 
the case of the following curve (x+y)(x^2 + y^2 - r^2) = 0.

--
  ____  _        ____             _
 /_____/_) o    /__________  __  //
(____ (   (    (    (_/ (_/-(-'_(/
                        _/