The Quadratic Trigonometric Bezier like Curve With two Shape Parameters

Abstract

The quadratic trigonometric Bezier model serves as a potent and valuable tool in computer-aided geometric design, boasting exceptional geometric properties. In this study, Novel functions are introduced by leveraging a trigonometric Bezier-like curve with adjustable shape parameters. Each curve segment is formed by three consecutive control points, providing precise control over shape by adjusting these parameters while keeping the control polygon unchanged. These curves exhibit superior proximity to the control polygon compared to quadratic Bezier curves across all shape parameter values, gradually approaching the control polygon as the shape parameter increases. Moreover, for practical application, the quadratic trigonometric Bezier-like curve was utilized to artfully design the Arabic word "الله" (Allah) and define flower contours, employing MATHEMATICA software. The results underscore the model's effectiveness in accurately representing intricate shapes, offering a versatile and efficient solution for diverse design challenges. Furthermore, the fusion of the quadratic trigonometric Bezier-like curve with shape parameters significantly augments design flexibility and adaptability, making it a valuable asset in computer graphics, geometric modeling, and artistic design across multiple domains.