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Quasi-quintic trigonometric Bézier curves with two shape parameters

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Abstract

In this work, we propose a family of six new quasi-quintic trigonometric blending functions with two shape parameters. Based on these blending functions, a class of quasi-quintic trigonometric Bézier curve is proposed, which has some properties analogous to the classical quintic Bézier curves. For the same control points, the resulting quasi-quintic trigonometric Bézier curves can be closer to the control polygon than the classical quintic Bézier curves. The shape of the quasi-quintic trigonometric Bézier curves can be flexibly adjusted by altering the values of the two shape parameters without changing their control points. Under the \({C^2}\) smooth connection conditions, the resulting composite quasi-quintic trigonometric Bézier curves can automatically reach \({C^2} \cap F{C^3}\) continuity.

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Acknowledgements

The research is supported by the National Natural Science Foundation of China (Grant No. 61802129), the Postdoctoral Science Foundation of China (Grant No. 2015M571931), the Fundamental Research Funds for the Central Universities (Grant No. 2017MS121) and the Natural Science Foundation Guangdong Province, China (Grant No. 2018A030310381).

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Authors and Affiliations

  1. School of Business Administration, South China University of Technology, Guangzhou, 510641, Guangdong, People’s Republic of China

    Xuewen Tan

  2. Department of Mathematics, South China University of Technology, Guangzhou, 510641, Guangdong, People’s Republic of China

    Yuanpeng Zhu

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  1. Xuewen Tan
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  2. Yuanpeng Zhu
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Correspondence to Yuanpeng Zhu.

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Communicated by Antonio José Silva Neto.

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Tan, X., Zhu, Y. Quasi-quintic trigonometric Bézier curves with two shape parameters. Comp. Appl. Math. 38, 157 (2019). https://doi.org/10.1007/s40314-019-0961-y

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  • DOI: https://doi.org/10.1007/s40314-019-0961-y

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