CGAL users discussion list

[Mariette Yvinec <>]

Philipp Richter CGAL wrote:

> Hi CGAL users!
> I am currently working on alpha shape triangulations of 3D point sets 
> and would like to find intersections of those alpha shapes (same point 
> set, different alpha values).
> What would be a way to do this? It seems like one can find 3D 
> intersections of  NEF Polyhedra. So converting my alpha shapes to Nef 
> Polyhedra, then find the intersection and then triangulate again (I 
> want to have a triangulation in the end) sounds like it works but also 
> sounds wasteful.
> Is there a way to intersect triangulations easily? I did not find 
> information on this in the manual or using google.
> Thank you for your help!
> Philipp Richter


Alpha_shapes for the same point sets and different alpha value
are subcomplexes of the same 3D  Delaunay triangulations.
The different alpha_shapes are thus nested,
and their boundary  facets will be either  shared,
or sharing edges or disjoint.
So it is of course possible, but may be a somewhat bad idea to intersect 
them.
If really you want to intersect them, Cgal as a package called
"Intersecting sequences of iso-oriented box" which is dedicated to this 
kind of application.
Look at the examples in the corresponding chapter of the  user manual .