CGAL users discussion list

[Monique Teillaud <>]

Laurent Rineau (GeometryFactory) wrote:
> On Thursday 18 February 2010 06:18:01 
>
>  wrote:
> > Hi,
> > I did not find any way to set a Distance Metric for my Voronoi Diagram. The
> > Euclidean metric is not what I want. Is there a way to feed or set a
> >  desired distance metric in Voronoi Diagrams?

Hi

In fact you have some (limited) freedom about this.
I guess you are plugging the CGAL::Delaunay_triangulation_2 as Delaunay 
graph.
Then you can modify the in-circle test used in the Delaunay 
triangulation though the traits class (look at the documentation of the 
2D Delaunay triangulation, in particular the concept 
DelaunayTriangulationTraits_2). This predicate can modify the shape of a 
ball, thus the metric used.
Of course you cannot put any arbitrary function there, or the algorithms 
will fail... For instance the metric must really satisfy the properties 
of a metric.

> No. Voronoi diagram package is able to compute only euclidean distance Voronoï 
> diagram.
>
> If your distance is simply additive, then that is the Apollonius diagram:
>   
> http://upcoming.cgal.org/Manual/last/doc_html/cgal_manual/Apollonius_graph_2/Chapter_main.html
>
> Otherwise, as far as I know, there is nothing in CGAL that computes Voronoi 
> diagrams of arbitrary functions.


--
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée
http://www.inria.fr/sophia/members/Monique.Teillaud/