A new cubic trigonometric Nu-Spline with shape control parameter and its applications

Abstract

This study introduces a novel Cubic Trigonometric Nu-Spline (CTNS) with a shape parameter tailored for curve designing, ensuring geometric continuity of order 2. The CTNS possesses fundamental geometric properties such as convex hull, partition of unity, affine invariance, and variation diminishing, which are thoroughly discussed herein. Notably, our spline technique is enriched with Nu-Spline constraints, offering compelling local and global shape control capabilities. These capabilities encompass point tension, interval, or global tensions, enhancing versatility across various shape impacts. Beyond its curve designing prowess, the proposed technique exhibits commendable precision in estimating control points. Furthermore, its utility extends to diverse fields including electronics, medical image interpolation, manipulator path planning, and discrete time signal processing. Through numerical experimentation, we demonstrate the simplicity of implementing the CTNS algorithm alongside its superior accuracy compared to existing techniques.