CGAL users discussion list

["Wayne C. Gramlich" <>]

Chris Hamilton wrote:
> > > Makes sense.  However, the intersection of any two closed and bounded
> > > polyhedra should itself be a closed and bounded polyhedron, which should
> > > be representable by the .off file format.  Whatever the degeneracy
> > > implied by "intersecting constraints", it should be representable in
> > > Polyhedron_3 objects (and hence .off files) somehow, no?
> > I'm not sure what you say is true.  I can easily come up with two
> > .off files which when intersected would not be representable in
> > .off format.
>
> Yeah, a little bit of a rash statement on my part.  Definitely possible
> to come up with counter-examples.  However, the whole point of
> Nef_polyhedra is to get around these ugly cases (ie: where the
> intersection are or contain surfaces, etc).  Is it possible for two
> nef_polyhedron_3 without holes to produce an intersection with holes?

Easily.  Take a cube, hollow it out some, and cut it in half.
Nudge the two halves towards one another and intersect.  You will
get a flat square plate with a square hole in it.

I have pounded on Nef3 and basically "it just works".

[snip intersecting constraints]

> > > > There is a file format called .nef3 that can represent all
> > > > .nef3 objects.  The demo program ../dem/Nef_3/nef_3_homgeneous
> > > > can read .nef3 objects.  It used to be able to write .nef3
> > > > objects but that code was removed for some reason.  I have
> > > > a snippet of code that adds back the "savenef3" command
> > > > to the demo program if you are interested.
> > > Are these files viewable somehow, or is only the internals of CGAL that
> > > can make use of them?
> > Yes.  The unmodified nef_3_homgeneous program can read,
> > intersect, and display both .off and .nef3 files.  The only
> > thing it can not do (currently) is write .nef3 files.  For
> > example:
> >
> >   nef_3_homogeneous loadoff file1.off loadoff file2.off int reg vis
> >
> > will read in file1.off, followed by file2.off, compute the
> > intersection, regularize it, and then display the result in
> > a visualization window.
>
> Excellent.  Thanks for this.

Glad to help.

-Wayne