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Nonlinear Weighted Average and Blossoming

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Abstract

In this paper, we introduce a new averaging rule, the nonlinear weighted averaging rule. As an application, this averaging rule is used to replace the midpoint averaging in the de Casteljau evaluation algorithm and with this scheme we can also generate transcendental functions which cannot be generated by the classical de Casteljau algorithm. We also investigate the properties of the curves of the functions generated by blossoming, where the results show that these curves and the classical Bézier curves have some similar properties, including variation diminishing property and endpoint interpolation. However, the curves obtained by blossoming using nonlinear weighted averaging rules induced by certain functions violate some properties like convex hull property.

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Acknowledgements

We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful suggestions and comments. Rongin Uwitije acknowledges the support of CAS-TWAS President’s Fellowship for International Ph.D. Students.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Rongin Uwitije, Ammar Qarariyah & Jiansong Deng

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Xuhui Wang

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  1. Rongin Uwitije
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  2. Xuhui Wang
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  3. Ammar Qarariyah
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  4. Jiansong Deng
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Correspondence to Jiansong Deng.

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Uwitije, R., Wang, X., Qarariyah, A. et al. Nonlinear Weighted Average and Blossoming. Commun. Math. Stat. 8, 361–378 (2020). https://doi.org/10.1007/s40304-020-00208-5

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  • DOI: https://doi.org/10.1007/s40304-020-00208-5

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