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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 andnonstationary) methods. The refinement rules are formulated via the reproducingproperty of exponential polynomials. An exponential polynomial has a shapeparameter so that it may be adapted to the characteristic of the given data. Inthis study, we propose a method of selecting the shape parameter, so that itenables the associated scheme to achieve an improved approximation order (thatis, {\em three}), while 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 classicalChaikin's corner-cutting algorithm, that is, $C^1$. Finally, some numericalexamples are presented to demonstrate the advantages of the new corner-cuttingalgorithm.

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