Interpolatory Subdivision Curves with Local Shape Control

In this paper we present a novel subdivision scheme that can produce a nice-looking interpolation of the control points of the initial polyline, giving the possibility of adjusting the local shape of the limit curve by choosing a set of tension parameters associated with the polyline edges. If compared with the other existing methods, the proposed model is the only one that allows to exactly reproduce conic section arcs of arbitrary length, create a variety of shape effects like bumps and flat edges, and mix them in the same curve in an unrestricted way. While this is impossible using existing 4-point interpolatory schemes, it can be easily done here, since the proposed subdivision scheme is non-stationary and non-uniform at the same time.