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Journal of Applied Mathematics
Volume 2014, Article ID 872637, 12 pages
http://dx.doi.org/10.1155/2014/872637
Research Article

Local Control of the Curves Using Rational Cubic Spline

1Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan, Malaysia
2School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Minden, Penang, Malaysia

Received 22 October 2013; Accepted 7 January 2014; Published 2 March 2014

Academic Editor: Jingxin Zhang

Copyright © 2014 Samsul Ariffin Abdul Karim and Kong Voon Pang. 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

This paper discussed the local control of interpolating function by using rational cubic spline (cubic/quadratic) with three parameters originally proposed by the authors. The rational spline has continuity. The bounded properties of the rational cubic interpolants and shape controls of the rational interpolants are discussed in detail. The value control, inflection point control, and convexity control at a point by using the proposed rational cubic spline are constructed. Several numerical results are presented to show the capability of the method. Numerical comparisons with the existing scheme are also further elaborated. From the results, it was indicated that the scheme works well and it is comparable with the established existing scheme.