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The Odd-Point Ternary Approximating Schemes

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DOI: 10.4236/ajcm.2011.12011    4,625 Downloads   9,511 Views   Citations


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.

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The authors declare no conflicts of interest.

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G. Mustafa, A. Ghaffar and F. Khan, "The Odd-Point Ternary Approximating Schemes," American Journal of Computational Mathematics, Vol. 1 No. 2, 2011, pp. 111-118. doi: 10.4236/ajcm.2011.12011.


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