Good Local Behavior of Offsets to Implicit Algebraic Curves

Abstract.

The notion of good local behavior of an offset curve was introduced in [2,4] to denote that the behavior of an offset was locally good from a topological point of view. Also, in these papers the problem of checking whether good local behavior holds for a particular offsetting distance, and of computing intervals of distances with this nice property, was addressed for the case of rational algebraic curves. Thus, here we generalize the results and techniques of these papers to the case when the curve to work with is an implicitly given, possibly singular, non-necessarily rational algebraic curve. Furthermore, a generalization of the (already known) results relating offsets and evolutes of regularly parametrized curves, is presented for the case of possibly singular, implicit algebraic curves.