Computing the topology and geometric structure of objects defined by implicit equations is an important operation in Geometric modeling. It appears for instance in intersection, self-intersection or arrangement computation of parametric surfaces.

Two main families of methods exists to compute the topology these curves or surfaces defined implicitly. One is based on sweeping techniques which analyse the object at critical values of a given map. The other type of methods use the localisation of characteristic points to output the correct topology in each final cell of the recursive subdivision process. In this talk, we will compare the two approaches and their practical behavior.