CGAL users discussion list

[Mariette Yvinec <>]

Then it is easy to query the alpha shape data structure
for tetrahedra that are in the alpha complex for one of the alpha
valu and not for the other :
iterate on the Delaunay or regular tetrahedra
and for each of them  call the classify() function
with the alpha_values of interest.

Philipp Richter CGAL wrote:

> Dear Mariette,
> I think I confused a word. I do not want to intersect them (this 
> really would be a bad idea), but to find the difference of them. If A 
> and B are polyhedra (triangulations in this case), then I want the 
> difference polyhedra C = A - B.
> Sorry for confusion.
> Philipp
> Mariette Yvinec writes:
>
> > 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 .
> > --
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