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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 197383, 14 pages
http://dx.doi.org/10.5402/2012/197383
Research Article

A Family of Even-Point Ternary Approximating Schemes

Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Received 27 July 2012; Accepted 8 September 2012

Academic Editors: L. Ju, F. Lamnabhi-Lagarrigue, G. Psihoyios, H. C. So, and X. Yang

Copyright © 2012 Abdul Ghaffar and Ghulam Mustafa. 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.

Abstract

We presented a general formula to generate the family of even-point ternary approximating subdivision schemes with a shape parameter for describing curves. Some sufficient conditions for to continuity and approximation order for certain ranges of parameter are discussed. The proposed even-point ternary schemes compare remarkably with existing even-point ternary schemes because they are able to generate limit functions with higher smoothness and approximation order. In addition, we measured curvature and torsion that assist the quality of subdivided curves.