Residue and implicitization problem for rational surfaces
The implicitization problem for rational surfaces has been studied intensively in the last 10 years, because of its relevance for applications in computer-aided geometric design. The approach studied here is based on resultants: the implicit equation is obtained by computing determinants of Bezout-type matrices and analyzing their factors. Many theoretical problems in the resultant methods arise from the presence of base points. In this paper, the authors present a resultant-based implicitization method that works in the presence of arbitrary base points. The algorithm does not require factorisation of polynomials. The paper also contains a method for computing the equation of the offset of a rational surface.
scientific article; zbMATH DE number 2101930