CGAL users discussion list

[Peter Hachenberger <>]

Hi Markus,

On Mon, 2007-04-16 at 15:29 +0200, Markus Maier wrote:
> Dear all,
> 
> I use Nef_polyhedron_3 in CGAL in order to compute the intersection of a 
> (large) number of half spaces in 3D. Using and extended cartesian kernel 
> with number type Gmpq, everything works fine. However, the time and 
> space requirements are very high.
> Is there a possibility to use floating-point arithmetic for 
> Nef_polyhedron_3? 


Yes, I basically optimized Nef_3 for normal kernels. The use of the
extended is still very slow. This includes floating point support, which
I recently implemented, but only for normal kernels. Sorry.

> Or do you know other ways of computing the 
> intersection of half spaces using floating-point arithmetic?

If you are only doing intersections of halfplanes, there must be faster
means than Nef polyhedra. Is your result always a bounded polyhedron?
What about computing all intersection points of three planes and compute
the convex_hull? Just an idea.

If you really don't find another solution, I will have a look how I can
help you with floating-point support for unbounded Nef_3. But as I said,
there should be faster solutions.

Best, Peter