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The Scientific World Journal
Volume 2014, Article ID 391568, 10 pages
Research Article

Local Convexity-Preserving Rational Cubic Spline for Convex Data

1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 George Town, Penang, Malaysia

Received 31 August 2013; Accepted 10 February 2014; Published 13 March 2014

Academic Editors: S. De Marchi and J. Tan

Copyright © 2014 Muhammad Abbas 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 the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.