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 Bezier 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 \( O\left( {h_{i}^{3} } \right) \).