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ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 174048, 14 pages
http://dx.doi.org/10.5402/2012/174048
Research Article

Local Convexity Shape-Preserving Data Visualization by Spline Function

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
3School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 16 November 2011; Accepted 21 December 2011

Academic Editor: R. Barrio

Copyright © 2012 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.

Abstract

The main purpose of this paper is the visualization of convex data that results in a smooth, pleasant, and interactive convexity-preserving curve. The rational cubic function with three free parameters is constructed to preserve the shape of convex data. The free parameters are arranged in a way that two of them are left free for user choice to refine the convex curve as desired, and the remaining one free parameter is constrained to preserve the convexity everywhere. Simple data-dependent constraints are derived on one free parameter, which guarantee to preserve the convexity of curve. Moreover, the scheme under discussion is, 𝐶1 flexible, simple, local, and economical as compared to existing schemes. The error bound for the rational cubic function is 𝑂(3).