A new class of non-stationary interpolatory subdivision schemes based on exponential polynomials

Abstract

We present a new class of non-stationary, interpolatory subdivision schemes that can exactly reconstruct parametric surfaces including exponential polynomials. The subdivision rules in our scheme are interpolatory and are obtained using the property of reproducing exponential polynomials which constitute a shift-invariant space. It enables our scheme to exactly reproduce rotational features in surfaces which have trigonometric polynomials in their parametric equations. And the mask of our scheme converges to that of the polynomial-based scheme, so that the analytical smoothness of our scheme can be inferred from the smoothness of the polynomial based scheme. © Springer-Verlag Berlin Heidelberg 2006.