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Shape analysis and fairness metric of generalized fractional Bézier curve

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Abstract

In the areas of engineering and architecture, smooth curves and surfaces are crucial to produce sleek products and to prevent the structures from breaking, especially when dealing with various shapes and lengths. The designing task of smooth curves can be carried out by following certain standards of fairness. Curvatures and internal energy are two of the metrics that are commonly used to define the fairness of shapes. In this study, the generalized fractional Bézier basis functions is used to construct a fair and smooth curve using different types of continuity. The generalized fractional Bézier curve possesses shape parameters that are used to control the flexibility of the curve. It also has a notable parameter called fractional parameter that enables designers to control the length of constructed curves. The variation of the fractional parameter is directly contributed to the stretch energy. A new type of continuity called the fractional continuity that connects curve segments at different lengths of the first curve will be very conducive in satisfying the geometric conditions as well as fairness conditions. Lastly, the influence of various fractional and shape parameters of generalized fractional Bézier curve to the internal energy is demonstrated. Fractional parameter and continuity will expedite designing tasks when dealing with conflicting requirements.

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Acknowledgements

This research is supported by Universiti Sains Malaysia under Short Term Grant (Khas) (304/PMATHS/6315587) and School of Mathematical Sciences, Universiti Sains Malaysia. The authors are very grateful to the anonymous referees for their valuable suggestion.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Gelugor, Pulau Pinang, Malaysia

    Syed Ahmad Aidil Adha Said Mad Zain & Md Yushalify Misro

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  1. Syed Ahmad Aidil Adha Said Mad Zain
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  2. Md Yushalify Misro
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Correspondence to Md Yushalify Misro.

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Said Mad Zain, S.A.A.A., Misro, M.Y. Shape analysis and fairness metric of generalized fractional Bézier curve. Comp. Appl. Math. 41, 276 (2022). https://doi.org/10.1007/s40314-022-01983-3

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  • DOI: https://doi.org/10.1007/s40314-022-01983-3

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