Family of a-point b-ary subdivision schemes with bell-shaped mask

In this paper, we present a generalized Refine-Smooth algorithm to design a family of a-point b-ary approximating subdivision schemes with bell-shaped mask, where a 3 and b 2. We use the combination of corner cutting b-ary subdivision scheme and weighted average of (b+1)-points to construct the proposed family. We demonstrate that the proposed family has smaller complexity and support width and higher continuity than the existing Refine-Smooth subdivision schemes. We also study the shape preserving properties of the proposed family. In addition, it is observed that the proposed family is suitable for fitting the locally noisy, oscillatory, and irregular data.

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