Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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G3 HEXIC Bézier CURVES APPROXIMATING CONIC SECTIONS

  • Received : 2024.03.11
  • Accepted : 2024.03.25
  • Published : 2024.03.25
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Abstract

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G3 Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

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Acknowledgement

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

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