Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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APPROXIMATION OF HELIX BY G2 CUBIC POLYNOMIAL CURVES

  • YOUNG JOON AHN (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
  • Received : 2023.11.26
  • Accepted : 2024.03.24
  • Published : 2024.06.25
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Abstract

In this paper we present the approximation method of the circular helix by G2 cubic polynomial curves. The approximants are G1 Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G2 continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

Keywords

Acknowledgement

This study was supported by research funds from Chosun University, 2023. The author is very grateful to two anonymous reviewers for their valuable comments and constructive suggestions.

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