Application Of Cubic Trigonometric Hermite Interpolation curve With Shape Parameters In 2 Dimensional Objects

Abstract

Problem:  Achieving accurate mathematical representations of an object's geometry for computer-aided design and manufacturing is complex. Designing both objects demands a method that provides the necessary flexibility and smoothness in curves, which traditional methods lack of flexibility and smoothness in curves needed for precise and efficient design.

Aims/Objectives: The main objective is to explore and implement cubic trigonometric Hermite interpolation as a method for constructing two-dimensional objects. Next, to discussed the properties of this interpolation method and to determine the best value of the shape parameter that produces smooth curves

Methodology/approach:  Cubic trigonometric Hermite interpolation is used for constructing two-dimensional objects. This process is conducted using Mathematica. The different values of the shape parameter are used to achieve the desired curve characteristics in the geometric models.

Results/finding:  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 object can be formed using cubic trigonometric Hermite interpolation without making any easy blunders or errors.

Implication/impact:  The impact of this project lies in its potential to improve geometric modelling by providing the best value of shape parameter that enhances the precision and efficiency of creating two-dimensional geometric models. This can significantly benefit technical drawing, computer-aided design, and manufacturing by offering a more flexible and accurate way to represent objects' geometry.