The Odd-Point Ternary Approximating Schemes

Ghulam Mustafa, Abdul Ghaffar, Faheem Khan

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Department of Mathematics, The Islamia University of Bahawalpur Pakistan.

DOI: 10.4236/ajcm.2011.12011                

Abstract

We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C⁰ to C⁵ of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.

Keywords

Approximating Subdivision Scheme, Derivative Continuity, Smoothness Convergence, Shape Parameters and Laurent Polynomial

Conflicts of Interest

The authors declare no conflicts of interest.

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