Residue and implicitization problem for rational surfaces (Q1879277)

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.