CGAL users discussion list

[Olivier Devillers <>]

> 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.

You do not necessarily need exact construction. Exact computation has 
two effects: ensuring robustness of the algorithms
and a guarantee of the exactness of the result. If you allow 
approximation during dualization, you still
have robustness during the convex hull using epick.

if you have no vertical faces in your polyhedron, you can use dualization by
plane z=ax+by+c <---->   point (a,b,c)
since you do not make computation during dualization and thus do not 
need exact construction here.

The remaining point is the computation of the representation of input 
polyhedra has intersection of half spaces
(it uses computations if the real input is the vertices of the polyhedra).