Malaysian Journal of Mathematical Sciences, January 2022, Vol. 16, No. 1

$C^{1}$ Cubic Trigonometric Spline with a Shape Parameter for Positive Shape Preservation

Munir, N. A. A. A., Hadi, N. A., and Nasir, M. A. S.

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Received date: 31 March 2021
Accepted date: 29 September 2021

This paper presents a new construction of $C^{1}$ cubic trigonometric spline interpolation. Instead of repositioning control points, a shape parameter is introduced in the spline to control the shape and behaviour of the curves. The built basis functions fulfil all the geometric properties of the standard cubic Bezier curve, and the proof is included in this paper. Then, the interpolation of the spline is illustrated using suitable parameter values. Every curve segment comprises four successive control points with a cubic trigonometric spline that carries out all the curve properties. The result showed effective approximation since the developed $C^{1}$ cubic trigonometric spline produced a smooth and pleasant interpolating curve while preserving the positive data features. The flexibility of the developed spline is compared with the other two existing works: b-spline and bezier-like curves. The analysis shows that the proposed spline gives greater flexibility since it has a broader parameter value range. Therefore, this helps the spline interpolation build opened and closed curves, as incorporated in the paper.

Keywords: continuity; interpolation; shape parameters; trigonometric spline



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