Local shape of generalized offsets to algebraic curves

Offsetting is an important operation in computer aided design, with applications also in other contexts like robot path planning or tolerance analysis. In this paper we study the local behavior of an algebraic curve under a variation of the usual offsetting construction, namely the generalized offsetting process (Sendra and Sendra, 2000a). More precisely, here we discuss when and how this geometric construction may cause local changes in the shape of an algebraic curve, and we compare our results with those obtained for the case of classical offsets (Alcazar and Sendra, 2007). For these purposes, we use well-known notions of Differential Geometry, and also the notion of local shape introduced in Alcazar and Sendra (2007). Our analysis shows important differences between the topological properties of classical and generalized offsets, both at regular and singular points.