Computing self-intersection curves of rational ruled surfaces

An algorithm is presented to compute the self-intersection curves of a rational ruled surface based on the theory of μ-bases. The algorithm starts by constructing the principal subresultants for a μ-basis of the rational ruled surface. The principal subresultant coefficients provide information about not only the parametric loci of the self-intersection curves, but also the orders of the self-intersection curves. Based on this observation, an efficient algorithm is provided to compute the parametric loci of the self-intersection curves as well as their corresponding orders. The isolated singular points of the rational ruled surface are also computed.