On the interpolation of concentric curvature elements
A convex G2 G 2 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 ? ? 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 G2 G 2 convex interpolant with prescribed extremal curvatures are given.
spiral arc geometric design geometric continuity