The m-Point Quaternary Approximating Subdivision Schemes

Shahid S. Siddiqi, Muhammad Younis

Centre for Undergraduate Studies, University of the Punjab, Lahore, Pakistan.
Department of Mathematics, University of the Punjab, Lahore, Pakistan.

DOI: 10.4236/ajcm.2013.31A002                

Abstract

In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer m>1) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence and smoothness of the proposed schemes, the Laurent polynomial method has been used.

Keywords

Cox-De Boor Recursion Formula; Quaternary; Approximating Subdivision Schemes; Convergence and Smoothness

Conflicts of Interest

The authors declare no conflicts of interest.

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