Orthogonal trajectories to isoptics of ovals

Abstract

For a given plane curve, consider a one-parameter family of curves consisting of those points at which two support lines to the initial curve intersect at a constant angle. Such curves are well known in differential and convex geometry and called isoptics. In this paper, we describe parametrizations of orthogonal trajectories to isoptics of ovals. We show that such parametrizations can be obtained using solutions to a specific Cauchy problem constructed from the parametrizations of the oval and its isoptics. Moreover, we provide analytical and numerical examples of orthogonal trajectories to isoptics of some ovals.