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N. Dyn, K. Hormann, M. A. Sabin and Z. Shen, “Polynomial Reproduction by Symmetric Subdivision Schemes,” Journal of Approximation Theory, Vol. 155, No. 1, 2008, pp. 28-42. doi:10.1016/j.jat.2008.04.008

has been cited by the following article:

• TITLE: The Odd-Point Ternary Approximating Schemes

  AUTHORS: Ghulam Mustafa, Abdul Ghaffar, Faheem Khan

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.2, July 1, 2011

  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.