Aesthetic modelling: exploring beauty in shape via Bézier curves

Computer-Aided Geometric Design (CAGD) utilizes Bézier curves and surfaces as fundamental tools for representing and manipulating shapes due to their simplicity, stability, and intuitive control. However, classical Bézier curves, while mathematically smooth, often lack the visual appeal required in design applications. This study addresses the problem of modeling aesthetically pleasing shapes by comparing classical cubic Bézier curves with aesthetic Bézier curves. The research objectives are to model shapes using cubic Bézier and evaluate it performance based on continuity and shape parameters. Using Maple software, fish and duck shapes were constructed by joining multiple cubic Bézier curve segments, leveraging properties such as endpoint interpolation, convex hull, and tangent direction. The methodology incorporated Bernstein basis functions and parametric representation to generate smooth curves. This research bridges the gap between mathematical precision and aesthetic quality, contributing valuable insights for CAD, computer graphics, and geometric modeling applications.