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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The authors are very grateful to two anonymous reviewers for their valuable comments and constructive suggestions.
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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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DOI: https://doi.org/10.1007/s40314-023-02315-9
Keywords
- Circular arc approximation
- Hexic polynomial curve
- Approximation order
- Series expansion
- Hausdorff distance