Proper Reparametrization of Rational Ruled Surface

In this paper, we present a properreparametrization algorithm for rational ruled surfaces. That is, for animproper rational parametrization of a ruled surface, we construct aproper rational parametrization for the same surface. The algorithmconsists of three steps. We first reparametrize the improper rationalparametrization caused by improper supports. Then the improper rationalparametrization is transformed to a new one which is proper in one ofthe parameters. Finally, the problem is reduced to the properreparametrization of planar rational algebraic curves.