Residue and Implicitization Problem for Rational Surfaces

The implicitization problem of rational surfaces is a central challenge in computational aided geometric design. We propose a new algorithm to solve it, based on the residue calculus in the general multivariate setting. The proposed approach allows us to treat surfaces with base points (without geometric hypothesis on the zero-locus of base points). The efficiency of the method is illustrated by some examples computed with maple software. We also give another application of the residue calculus to the computation of offsets of rational parametric surfaces.