Proper Reparametrization of Rational Ruled Surface

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