Hermite interpolation by hypocycloids and epicycloids with rational offsets

We show that all rational hypocycloids and epicycloids are curves with Pythagorean normals and thus have rational offsets. Then, exploiting the convolution properties and (implicit) support function representation of these curves, we design an efficient algorithm for G1 Hermite interpolation with their arcs. We show that for all regular data, there is a unique interpolating hypocycloidal or epicycloidal arc of the given canonical type.