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Abstract: Algebraic surfaces–which are frequently used in geometric modelling–are represented either in implicit or parametric form. Several techniques for parametrizing a rational algebraic surface as a whole exist. However, in many applications, it suffices to parametrize a small portion of the surface. This motivates the analysis of local parametrizations, i.e., parametrizations of a small neighborhood of a given point of the surface . In this paper we introduce several techniques for generating such parametrizations for nonsingular cubic surfaces. For this class of surfaces, it is shown that the local parametrization problem can be solved for all points, and any such surface can be covered completely. [Copyright &y& Elsevier]

In this paper, we propose a semi-numerical algorithm for computing absolute factorization of multivariate polynomials. It is based on some properties appearing after a generic change of coordinate. Using numerical computation, Galois group action and rational approximation, this method provides an efficient probabilistic algorithm for medium degrees. Two implementations are presented and compared to other algorithms. [Copyright &y& Elsevier]