Offsets and front tire tracks to projective hedgehogs

Abstract

There are some known properties on curves of constant width and Zindler curves and their relationship with offsets and front tire-track curves in convex geometry. In this work, a generalization of all these concepts and results to hedgehogs is presented. Discontinuity issues coming from the common parametric definition of offsets and front track curves are solved with parameterizations by a support function. Finally, it is seen that there is a one-to-one correspondence between constant width hedgehogs of constant width and generalized Zindler curves.