On the interpolation of concentric curvature elements

A convex G2G2 Hermite interpolation problem of concentric curvature elements is considered in this paper. It is first proved that there is no spiral arc solution with turning angle less than or equal to ππ and then, that any convex solution admits at least two vertices. The curvature and the evolute profiles of such an interpolant are analyzed. In particular, conditions for the existence of a G2G2 convex interpolant with prescribed extremal curvatures are given.

Research highlights
► Convex G2G2 Hermite interpolation problem of concentric curvature elements.
► Proof of non-existence of a spiral arc solution with turning angle lower than ππ.
► Any convex solution admits at least two vertices.
► Analysis of curvature and evolute profiles of the interpolant.
► Conditions for the existence of an interpolant with prescribed extremal curvatures.