An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.