Application of cubic trigonometric Hermite interpolation curve with shape parameters in 2 dimensional objects / Nursyazni Mohamad Sukri ... [et al.]

Achieving accurate mathematical representations of an object's geometry for computer-aided design and manufacturing is a complex challenge. Designing such objects requires a method that offers the necessary flexibility and smoothness in curves, which traditional approaches often lack.. The primary aim of this study is to explore and implement cubic trigonometric Hermite interpolation as a method for constructing two-dimensional objects. Additionally, this study seeks to examine the properties of this interpolation method and determine the best value of the shape parameter that produces the smoothest curves. Cubic trigonometric Hermite interpolation is used for constructing two-dimensional objects, with the process carried out using Mathematica. Different values of the shape parameter are employed to achieve the desired curve characteristics in the geometric models. The correct images of the two-dimensional objects are also located, and the suitable shape parameters can be obtained after studying the behavior of the curve using free parameters. Two dimensional objects can be formed using cubic trigonometric Hermite interpolation without making any easy blunders or errors. This project has significant potential to enhance geometric modeling by determining the optimal shape parameters that improve the precision and efficiency of creating two-dimensional geometric models. The results can greatly benefit technical drawing, computer-aided design, and manufacturing by providing a more flexible and accurate method for representing the geometry of objects.