CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

Ben Haller wrote:
>   Hi!  I'm currently using CGAL's Delaunay_d to do d-dimensional 
> triangulations, with some success.  I realize that CGAL does not provide a 
> d-dimensional Voronoi package, but I'm hoping it is possible to extract just 
> enough information from Delaunay_d to be able to do a computation I'd like to 
> do.  Specifically, if vertices v1 and v2 are connected in the Delaunay 
> triangulation, they have a (d-1)-dimensional Voronoi facet between them, and 
> I would like to be able to find the centroid of that facet.  If I've got all 
> this stuff straight in my head, the vertices of the facet are the centers of 
> the hyperspheres bounding the simplices that contain both v1 and v2.  I can 
> get the set of simplices that contain both v1 and v2 from Delaunay_d.  There 
> seems to be no API available to get the bounding hypersphere of a simplex, 
> unfortunately; I get the impression that the Delaunay_d object has that 
> information, but it does not expose it in the API.  If I could get the 
> hypersphere centers,
then the centroid of a set of n-dimensional points is computed easily enough. 
 In a perfect world, I'd really like to get the centroids of *clipped* 
Voronoi facets, such that facets of infinite extent are clipped to the unit 
hypercube before the centroid is computed, but I haven't the slightest idea 
how I'd go about that.  That's really what I'd like, though, so that the 
infinite-extent facets don't blow up my algorithm; the centroid of the 
clipped facet is actually exactly what I want, for my application.
>   Anyhow, my grasp of both d-dimensional geometry and the CGAL APIs is not 
> really up to solving this problem, but I'm hoping somebody else on the list 
> has already tackled it, or can point me in the right direction.  Thanks!
>
> Ben Haller
> McGill University
Have a look here

http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_d_ref/Class_Sphere_d.html#Function_Sphere_d6Kernel9_operator+6const_Vector_d6Kernel9__v9_;

The constructor should do what you want.

S.