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Circular arc approximation by hexic polynomial curves

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Abstract

In this paper we consider a circular arc approximation by hexic polynomial curves having 12 contacts with the circular arc. We present two methods for obtaining \(G^k\) approximation curves, \(k=3,4,\) which interpolate at both endpoints and the midpoint of the circular arc. The approximation curves can be obtained by solving an equation of degree six. We show that the approximation orders of our methods are 12. We find the optimal approximation for each method and present numerical examples illustrating that the approximation orders are 12.

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Acknowledgements

The authors are very grateful to two anonymous reviewers for their valuable comments and constructive suggestions.

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  1. Department of Mathematics Education, Chosun University, Gwangju, 61452, South Korea

    Hyeong Moon Yoon & Young Joon Ahn

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  1. Hyeong Moon Yoon
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  2. Young Joon Ahn
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Correspondence to Young Joon Ahn.

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This study was supported by research funds from Chosun University, 2023, and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. NRF-2021R1F1A1045830).

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Yoon, H.M., Ahn, Y.J. Circular arc approximation by hexic polynomial curves. Comp. Appl. Math. 42, 265 (2023). https://doi.org/10.1007/s40314-023-02315-9

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