C2  Rational Cubic Ball Spline Functions

Wan Nurhadani Wan Jaafar; Muhammad Abbas  and Abd Rahni Mt Piah

doi:10.17485/ijst/2015/v8i32/92137

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i32/92137

Year: 2015, Volume: 8, Issue: 32, Pages: 1-13

Original Article

C2 Rational Cubic Ball Spline Functions

Wan Nurhadani Wan Jaafar^1*, Muhammad Abbas² and Abd Rahni Mt Piah³

¹Institute of Engineering Mathematics, Universiti Malaysia Perlis, Kampus Pauh Putra, Arau - 02600, Perlis, Malaysia; [email protected]
^1,3 School of Mathematical Sciences, Universiti Sains Malaysia, Minden - 11800, Pulau Pinang, Malaysia; [email protected]
² Department of Mathematics, University of Sargodha, Sargodha - 40100, Pakistan; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This study deals with the problems of shape preserving curves through positive curves through positive, constrained and convex data. The alternative curve interpolations are developed using a piecewise C² rational cubic Ball spline function with three shape parameters in each subinterval. Simple data dependent conditions are derived for a single shape parameters to preserve the shape of data while the remaining two shape parameters are free used to modify the positive, constrained and convex curves as desired. Graphical results through different numerical examples are presented to show the effectiveness of the proposed schemes.
Keywords: Ball Function, Constrained, Convexity, Interpolation, Positivity