대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권4호
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  • Pages.741-754
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  • 2002
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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AN ERROR BOUND ANALYSIS FOR CUBIC SPLINE APPROXIMATION OF CONIC SECTION

  • 발행 : 2002.10.01
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초록

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

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참고문헌

  1. Ad-vances in Computational Mathematics v.5 An analysis of cubic approximation schemes for conic sections M. Floater https://doi.org/10.1007/BF02124751
  2. Computer Aided Geometric Design v.6 Approximate conversion of rational B-spline patched L. Bardis;M. Patrikalakis https://doi.org/10.1016/0167-8396(89)90023-X
  3. Computer Aided Geometric v.4 Approximate conversion of spline curves J. Hoschek https://doi.org/10.1016/0167-8396(87)90024-0
  4. Computer Aided Design v.22 Spline conversion for trimmed rational Bezier-and B-spline surfaces J. Hoschek;F. Schneider https://doi.org/10.1016/0010-4485(90)90043-C
  5. Computer Aided Geomatric Design v.6 Approximate conversion of rational splines M. Patrikalakis https://doi.org/10.1016/0167-8396(89)90018-6
  6. NURBS for Curves and Surfaces Design Approximating rational curves using polyno-mial curves T. Sederberg;M. Kakimotor
  7. J. Computational Applied Mathematics v.81 no.1 Approximations of circular arcs by Bezier curves Y.J. Ahn;H.O. Kim https://doi.org/10.1016/S0377-0427(97)00037-X
  8. Computer Aided Geometric Design v.7 Good approximation of circles by curvature-continuous Bezier curves T. Dokken;M. Daehlen;T. Lyche;K. Morken https://doi.org/10.1016/0167-8396(90)90019-N
  9. Computer Aided Geometric Design v.15 Circular arc approximation by quintic polynomial curves L. Fang https://doi.org/10.1016/S0167-8396(98)00019-3
  10. Computer Aided Geometric Design v.8 Approximation of circular arcs by cubic polynomials M. Goldapp https://doi.org/10.1016/0167-8396(91)90007-X
  11. Curves and Surfaces Best approximation of circle segments by quadratic Bezier curves K. Morken;P.J. Laurent(ed.);A. Le Mehaute(ed.);L.L. Schumaker(ed.)
  12. Computer Aided Geometric Design v.12 High order approximation of conic sections by quadratic splines M. Floater https://doi.org/10.1016/0167-8396(94)00037-S
  13. Computer Aided Geometric Design v.14 An (h²n) Hermite approximation for conic sections https://doi.org/10.1016/S0167-8396(96)00025-8
  14. Curves and Surfaces for Comuter Aided Geometric Design G. Farin
  15. Computers and Mathematics with Applications v.36 no.9 Curvatures of the quadratic rational Bezier curves Y.J. Ahn;H.O. Kim https://doi.org/10.1016/S0898-1221(98)00193-X
  16. Computer-Aided Design v.31 G¹ arc spline approximations of quadratic Bezier curves Y.J. Ahn;H.O. Kim;K.Y. Lee
  17. In geometric modeling:Algorithms and new trends The rational Bezier representation for conics E.T. Lee
  18. Computer Aided Geometric Design v.4 High accuracy geometric Hermite interpo-lation C. de Boor;K. Holling;M. Sabin

피인용 문헌

  1. Helix approximations with conic and quadratic Bézier curves vol.22, pp.6, 2005, https://doi.org/10.1016/j.cagd.2005.02.003