Offsets from the perspective of computational algebraic geometry

The offset hypersurface Od(V), at distance d, to an irreducible hypersurface V is essentially the envelope of the system of spheres centered at the points of V with fixed radius d (for a formal definition, and for basic properties of offsets, see [2] and [9]). This type of geometric objects have been studied extensively by many authors in the frame of CAGD applications (see [4]). As a consequence of this research, many interesting theoretical and algorithmic questions related to algebraic and differential geometric properties of offsets have been addressed. In this context, one usually analyzes whether a certain property of the original variety V is translated to Od(V) when offsetting.In this poster we present several efficient algorithms (and examples thereof) developed in our research group for the computation of algebraic and geometric properties of offset hypersurfaces.