Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2011, Article ID 832630, 12 pages doi:10.1155/2011/832630 Research Article 2n - 1-Point Ternary Approximating and Interpolating Subdivision Schemes Muhammad Aslam, 1 Ghulam Mustafa, 2 and Abdul Ghaffar 2 1 Department of Mathematics, Lock Haven University, Lock Haven, PA 17745, USA 2 The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan Correspondence should be addressed to Ghulam Mustafa, mustafa rakib@yahoo.com Received 25 July 2011; Accepted 19 September 2011 Academic Editor: Hui-Shen Shen Copyright q 2011 Muhammad Aslam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present an explicit formula which unifies the mask of 2n - 1-point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian 2009, Siddiqi and Rehan 2010, 2009 and Hassan and Dodgson 2003 are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. 2009 can easily be generated by our proposed masks. It is also proved from comparison that 2n - 1-point schemes are better than 2n-scheme in the sense of computational cost, support and error bounds. 1. Introduction Subdivision is an algorithmic technique to generate smooth curves and surfaces as a sequence of successively refined control polygons. The schemes involving convex combination of more or less than six points at coarse refinement level to insert a new point at next refinement level is introduced by 1–8. They introduced odd and even points ternary schemes. Zheng et al. 9 constructed 2n - 1-point ternary interpolatory subdivision schemes by using variation of constants. They also introduced ternary even symmetric 2n-point subdivision schemes 10. Mustafa and Khan 11 presented a new 4-point C 3 quaternary approximating subdivision scheme. Lian 12 generalized 3-point and 5-point interpolatory schemes into an a-ary subdivision scheme for curve design. Later on, he further generalized his work into 2m-point and 2m 1-point interpolating a-ary schemes for curve design 13. Mustafa and Najma 14 generalized and unified even-point n-ary interpolating and approximating subdivision schemes for any n 2. In this paper, we introduce an explicit formula which generalizes and unifies existing odd-point ternary interpolating and approximating