PARAMETRIC GENERALIZED OFFSETS TO HYPERSURFACES

In this paper we extend the classical notion of offset to the concept of generalized offset to hypersurfaces. In addition, we present a comp lete theoretical analysis of the rationality and unirationality of gen eralized offsets. Characterizations for deciding whether the generaliz ed offset to a hypersurface is parametric or it has two parametric com ponents are given. As an application, an algorithm to analyse the rati onality of the components of the generalized offset to a plane curve o r to a surface, and to compute rational parametrizations of its ration al components, is outlined. (C) 1997 Academic Press Limited.