  In this paper we present algorithms for computing the topology of planar and
space rational curves defined by a parametrization. The algorithms given here
work directly with the parametrization of the curve, and do not require to
compute or use the implicit equation of the curve (in the case of planar
curves) or of any projection (in the case of space curves). Moreover, these
algorithms have been implemented in Maple; the examples considered and the
timings obtained show good performance skills.
