A sufficient condition for uniform convergence of stationary p-subdivision scheme

Abstract

Subdivision is a convenient tool to construct objective curves and surfaces directly from given scattered points. Stationary p-subdivision schemes are highly efficient in the acquisitions of curve/surface points in shape modeling. The features of supported set of nonnegative mask of uniform convergent stationary subdivision schemes are important to their theoretic researches and applications. According to the properties of supported set of the nonnegative mask, a sufficient condition for uniform convergence of stationary p-subdivision scheme is presented. This condition is proved with two propositions and spline function. The contribution of this work is that the convergence of a stationary p-subdivision scheme can be judged directly. This direct judge is in favor of applications of this scheme. © 2008 Springer-Verlag Berlin Heidelberg.