CGAL users discussion list

[Peter Hachenberger <>]

Hi Wayne,

> I took the basic cube.off file from Nef_3/demo and
> converted it to cube.nef3.  It is attached below
> at the end of this message.
> 
> At the facet[0] (marked as A), it references volume[0]
> and shalfedge[28] (marked as B).  shalfedge[28] back
> references facet[0] (which is correct) and sface[8]
> (marked as C).  However sface[8] references volume[1]
> which does not match the volume[0] referenced in facet[0].
> I am confused.

Yes, that's actually correct and I agree that it is odd. I think there
was a reason for it, but I cannot remember. But that's the only odd
thing of the data structure. 
> 
> Along similar lines.  I am having some difficulties
> trying to figure out what all of the volumes are for.
> For a simple cube I was expecting a single volume,
> instead there are two.  Is one the inverse of the other?
> 
> I took a large cube and subtracted a smaller cube and
> wound up with a .nef3 file with 3 volumes in it.
> Volume 1 strictly contained facets from the outer
> cube.  Volume 2 contained facets from the both the
> inner and outer cubes.  Volume 3 contained facets
> from just inner cube.  Is it the case that the union
> of all three volumes would equal R^3?

The volumes, facets, edges and vertices comprise a decomposition of the
R^3. The mark decides whether a feature is part of the polyhedron or
not. This way, we can model open and closed polyhedra, and we can model
the cube and its complement.

Peter