| 总结: | 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.
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