Complex quadratic trigonometric spline with a shape parameter

Trigonometric spline is an immerging field in Computer Aided Geometric Design (CAGD). Various trigonometric splines have been developed with different basis functions, degrees, and continuity. Another essential feature of the trigonometric spline is the shape parameter, which is used to control the shape of the curve and increase flexibility. However, the range of this shape parameter is limited because it is restricted to the properties of the curve, such as convex hull and positivity. Therefore, this paper widens the shape parameter range by considering the complex number. The complex number as a shape parameter not just only has increased the flexibility of the curve, and it is also crucial in engineering and science. They have application in many areas, including control theory, signal analysis, relativity, and fluid dynamics. It is a need to interpolate these complex data using an appropriate curve for presentation and further analysis of the data. The basis functions developed by Munir, N.A.A.A et al. (2018) is modified using Euler’s formula for trigonometric functions. The proving of the new basis properties is also presented. This new function has two shape parameters, r and m, which have different curve shape control. Finally, the function has experimented on several data points, including the font of the letter ‘B’ and ‘C’. The results show that the complex basis function and the complex shape parameters have increased the flexibility of the curve and represent straight lines perfectly. Furthermore, one parameter gives a unique wiggle shape to the curve shape.