Shape-Preserving Positive Trigonometric Spline Curves

Abstract

This paper deliberates on the development of new smooth shape-preserving schemes. These schemes are also demonstrated with data in the form of shape-preserving trigonometric spline curves. For this persistence, a trigonometric spline function is developed, which also nourishes all the fundamental geometric properties of Bézier function as well. The developed trigonometric spline function comprises two parameters $\alpha_{i}$ and $\beta_{i}$, which ensures flexible tangents at the end points of each subinterval. Furthermore, constraints are derived on $\beta_{i}$ to generate the shape-preserving trigonometric spline curves, whereas $\alpha_{i}$ is any positive real number used for the modification of shape-preserving trigonometric spline curves. The error approximation of the developed function is $O\left( {h_{i}^{3} } \right)$.