Journal of the Korean Society for Industrial and Applied Mathematics

  • 제17권3호
  • /
  • Pages.171-179
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  • 2013
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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CIRCLE APPROXIMATION BY QUARTIC G2 SPLINE USING ALTERNATION OF ERROR FUNCTION

  • Kim, Soo Won (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY) ;
  • Ahn, Young Joon (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
  • Received : 2013.04.03
  • Accepted : 2013.06.04
  • Published : 2013.09.25
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Abstract

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

Keywords

Acknowledgement

Supported by : Chosun University

References

  1. Y. J. Ahn. Approximation of conic sections by curvature continuous quartic Bezier curves. Comp. Math. Appl., 60:1986-1993, 2010. https://doi.org/10.1016/j.camwa.2010.07.032
  2. Y. J. Ahn and H. O. Kim. Approximation of circular arcs by Bezier curves. J. Comp. Appl. Math., 81:145-163, 1997. https://doi.org/10.1016/S0377-0427(97)00037-X
  3. T. Dokken, M. Daehlen, T. Lyche, and K. Morken. Good approximation of circles by curvature-continuous bezier curves. Comp. Aided Geom. Desi., 7:33-41, 1990. https://doi.org/10.1016/0167-8396(90)90019-N
  4. L. Fang. Circular arc approximation by quintic polynomial curves. Comp. Aided Geom. Desi., 15:843-861, 1998. https://doi.org/10.1016/S0167-8396(98)00019-3
  5. L. Fang. $G^{3}$ approximation of conic sections by quintic polynomial. Comp. Aided Geom. Desi., 16:755-766, 1999. https://doi.org/10.1016/S0167-8396(99)00017-5
  6. M. Floater. High-order approximation of conic sections by quadratic splines. Comp. Aided Geom. Desi., 12(6):617-637, 1995. https://doi.org/10.1016/0167-8396(94)00037-S
  7. M. Floater. An O($h^{2n}$) Hermite approximation for conic sectoins. Comp. Aided Geom. Desi., 14:135-151, 1997. https://doi.org/10.1016/S0167-8396(96)00025-8
  8. M. Goldapp. Approximation of circular arcs by cubic polynomials. Comp. Aided Geom. Desi., 8:227-238, 1991. https://doi.org/10.1016/0167-8396(91)90007-X
  9. S. Hur and T. Kim. The best $G^{1}$ cubic and $G^{2}$ quartic Bezier approximations of circular arcs. J. Comp. Appl. Math., 236:1183-1192, 2011. https://doi.org/10.1016/j.cam.2011.08.002
  10. S. H. Kim and Y. J. Ahn. Approximation of circular arcs by quartic bezier curves. Comp. Aided Desi., 39(6):490-493, 2007. https://doi.org/10.1016/j.cad.2007.01.004
  11. I. K. Lee, M. S. Kim, and G. Elber. Planar curve offset based on circle approximation. Comp. Aided Desi., 28:617-630, 1996. https://doi.org/10.1016/0010-4485(95)00078-X
  12. Z. Liu, J. Tan, X. Chen, and L. Zhang. An approximation method to circular arcs. Appl. Math. Comp., 15:1306-1311, 2012.
  13. K. Morken. Best approximation of circle segments by quadratic Bezier curves. In P.J. Laurent, A. Le Mehaute, and L.L. Schumaker, editors, Curves and Surfaces, pages 387-396. Academic Press, 1990.

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  2. A new method approximating offset curve by Bézier curve using parallel derivative curves vol.37, pp.2, 2013, https://doi.org/10.1007/s40314-017-0437-x