Geometrical Analysis Of Quintic Trigonometric Bézier Surface - Mohd Kamarudzaman, Anis Solehah Binti (2023)
The quintic trigonometric Bézier curve with two shape parameters has been extensively investigated due to its flexibility. Commonly, the Bézier curve has been widely used as a curve or surface designing tool in manufacturing industries. Hence, the study of surface curvature is required in design analysis. In this research, the quintic trigonometric Bézier curve has been implemented to generate various adjustable surfaces such as tensor product, swept, swung, ruled, and developable surfaces by using various value of shape parameters. The effect of the shape parameters on the surfaces has been demonstrated. Gaussian curvature, mean curvature, and Shape Index-Curvedness (SC Curvature) will be used to examine the geometric characteristics of surfaces. The Gaussian and mean curvature plots for each surface are visualised and evaluated. In addition, this study presents an alternate method for inspecting the geometrical properties of a surface using algebraic invariants. Surface curvature can be compared using differential geometry and algebraic invariants approach, leading to interesting discoveries. Additionally, the numerical data are presented to support the surface’s geometrical analysis that has been demonstrated by the 3D plot display. In conclusion, different surfaces will produce different curvature value, however, the shape parameters will alter the curvature’s intensity.