Implicitization of 3D rational surfaces using iterated univariate resultants and avoiding extraneous factors

Abstract This paper presents an interpretation for the extraneous factors appearing in the computation of iterated resultants with respect to a variable for three multivariate polynomials defined from the rational parametrization of a surface. We introduce a method for deriving the implicit equation of a surface using only two univariate resultants, whose polynomials match the degree of the parametrization. Our results provide a new approach to extracting the implicit representation of rational surfaces.