A non-uniform corner-cutting subdivision scheme with an improved accuracy

The aim of this paper is to construct a new non-uniform corner-cutting (NUCC) subdivision scheme that improves the accuracy of the classical (stationary and non-stationary) methods. The refinement rules are formulated via the reproducing property of exponential polynomials. An exponential polynomial has a shape parameter so that it may be adapted to the characteristic of the given data. In this study, we propose a method of selecting the shape parameter, so that it enables the associated scheme to achieve an improved approximation order (that is, three), in case that either the initial data or its derivative is bounded away from zero. In contrast, the classical methods attain the second-order accuracy. An analysis of convergence and smoothness of the proposed scheme is conducted. The proposed scheme is shown to have the same smoothness as the classical Chaikin's corner-cutting algorithm, that is, C¹. Finally, some numerical examples are presented to demonstrate the advantages of the new corner-cutting algorithm.