A comparative study of classical and aesthetic Bézier curves in engineering surface design

Computer Aided Geometric Design (CAGD) is important in engineering and design for creating smooth and complex surfaces used in areas like automotive, aerospace, and computer graphics. Classical Bezier curves and surfaces are commonly used because they are easy to control using control points and have good geometric properties. However, one main limitation is that any change to the control points affects the entire shape, making it difficult to adjust specific parts of a surface. To solve this issue, aesthetic Bezier methods introduce shape parameters that allow better control of the curve and surface, improving smoothness and visual appearance. While many studies focus on curves, there is still limited research on how these methods perform for full surface construction. Therefore, this study compares classical Bezier and aesthetic Bezier approaches in engineering surface design by analysing their mathematical properties, flexibility, and effects on surface smoothness and visual quality using computational modelling. The results aim to help engineers and designers choose the most suitable method for producing high-quality and visually pleasing surfaces.