Study of geometric morphology control in generalized α, λ, s Bézier curves based on statistical analysis

The main objective of Computer Aided Geometric Design (CAGD) is the construction of a high-quality Bezier curve that satisfies design requirements and ensures high manufacturing efficiency.This research aimed to investigate the behavior of the Bezier curve with shape parameters (α, λ, s) resulting in Generalized Bezier curves.The main goal was to yield minimum surface area from the Generalized Bezier surface of revolution to enhance manufacturing efficiency, material usage, and fabrication.To study the influence of shape parameters on curve geometric morphology, it is required to generate a miscellaneous design with a range of shape parameter values and then statistically evaluate.Also, the Taguchi method was used to investigate the most significant contribution of each parameter that yields the minimum surface area.ANOVA results indicated that parameters S & λ have the most significant influence on the SA.The results clarified the non-linear behavior between shape parameters that makes the direct prediction of curve configuration intricate for variations of shape parameters, especially for S-curve shapes.