Eur. Phys. J. Plus (2019) 134: 319
https://doi.org/10.1140/epjp/i2019-12704-1

Regular Article

Shape preserving fractional order KNR C¹ cubic spline

¹ Department of Mathematics, University of Management and Technology, Lahore, Pakistan
² Faculty of Computing, University Technology Malaysia, Skudai, Malaysia

^* e-mail: bilal.riaz@umt.edu.pk

Received: 5 March 2019
Accepted: 16 April 2019
Published online: 8 July 2019

Abstract

In the field of computer graphics, spline curves and surfaces are playing a vital role. In fact, they are known as standard tools for computer graphics. Due to this reason, much work has been done in this field and is still going on. This research adopted a novel technique, called Caputo fractional derivatives, to find all unknowns that appear in a spline cubic polynomial. This new method of finding unknowns could be an important technique in the cases where one does not need a curve to be C². The fractional derivative technique can further be applied on other kinds of spline curves. Our technique provides an alternate impressive approach to develop piecewise cubic spline polynomials for shape preservation. These polynomials are C¹ continuous in nature.