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Volume 39 Number 1 Volume 39 Number 2 Volume 39S Number 1

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Research articles

ScienceAsia 39(2013): 208-213 |doi: 10.2306/scienceasia1513-1874.2013.39.208


Positivity-preserving C2 rational cubic spline interpolation


Muhammad Abbasa,*, Ahmad Abd Majida, Mohd Nain Hj Awangb, Jamaludin Md Alia

 
ABSTRACT:     This work addresses the shape preserving interpolation problem for visualization of positive data. A piecewise rational function in cubic/quadratic form involving three shape parameters is presented. Simple data dependent conditions for a single shape parameter are derived to preserve the inherited shape feature (positivity) of data. The remaining two shape parameters are left free for the designer to modify the shape of positive curves as per industrial needs. The interpolant is not only C2, local, computationally economical, but it is also a visually pleasant and smooth in comparison with existing schemes. Several numerical examples are supplied to illustrate the proposed interpolant.

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a School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang Malaysia
b School of Distance Education, Universiti Sains Malaysia, 11800 Penang Malaysia

* Corresponding author, E-mail: m.abbas@uos.edu.pk

Received 5 Jun 2012, Accepted 20 Mar 2013