CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 04/19/2012 04:24 PM, Olivier Devillers wrote:
> Le 4/19/12 3:32 PM, ochyomdu a écrit :
> > Hallo Dimitris.
> >
> > The easiest way to calculate intersection of two polyhedrons is using of
> > class Nef_Polyhedron_3.
> >
> > If You need to use some functions from Polyhedron_3 You can just convert
> > Polyhedron_3 into Nef_Polyhedron_3 (using constructor), calculate
> > intersection of polyhedrons and convert the resulting Nef_Polyhedron_3
> > into
> > Polyhedron_3 back (using function convert_to_polyhedron()).
> >
> > Intersection is calculated with operation *
> > N1*N2
> >
> > You find more information about Nef_Polyhedron_3 here:
> > http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Nef_3/Chapter_main.html
>
> yes,
> but it will be quite inneficient if the two polyhedra ere known to be
> convex.
>
> by dualization and convex hull you will do it in (N1+N2)log(N1+N2)
>
> (and nef-polyhedra deals with very special cases (degenerate) but for that
> they require exact arithmetic and it costs some time)
Olivier is right.
Note that for the dualization, you also need exact constructions as the 
dualization is a construction. Exact_predicates_exact_constructions can 
be used for that.

Sebastien.