Developability comparison of enveloping developable quintic trigonometric Bézier surface

In Computer-Aided Geometric Design (CAGD), developable surfaces have been the main topic of interest among researchers due to their practicality and cost-effectiveness. This intriguing surface is essential for creating various inventive and aesthetic surface designs in the engineering and architecture sectors. In this paper, the enveloping developable surfaces constructed using quintic trigonometric Bézier basis functions with shape parameters will enhance the adjustability of the surfaces without modifying their initial control points. The developability of generated enveloping developable surfaces will be evaluated and compared using various approaches which are differential geometry and algebraic invariants. Moreover, the Root Mean Square Error (RMSE) is computed and graphical plots are also presented to support the findings. In conclusion, the shape parameters provide adjustability in constructing enveloping developable surfaces. The result of this research also revealed that enveloping developable quintic trigonometric Bézier surface with shape parameters has higher developability. Besides that, the differential geometry approach outperforms the algebraic invariants method. Therefore, the main significance of this study is to boost a higher surface developability of enveloping developable surfaces which can be obtained using quintic trigonometric Bézier basis functions with the aid of shape parameters.