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等距曲线有理逼近的一种方法 被引量：5

A Method for Rational Approximation of Offset Curves
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摘要 利用多项式逼近平面Bézier多项式曲线的参数速度模长,得到Bézier多项式曲线的等距曲线的有理逼近曲线,所得有理逼近曲线与等距曲线在端点处能够达到高阶插值.该方法与离散算法相结合,可得到等距曲线的高阶连续的有理样条逼近曲线,最后,通过数值实例与已有方法作了比较. The rational approximation of offset curve of Bézier curve is obtained when a polynomial is used to approximate the norm of parametric speed of Bézier curve. The obtained rational curve and the offset curve of Bézier curve have the same higher derivates at the endpoints. If the method is combined with the subdivision method of curve, the rational spline curve with higher-order continuity is presented which is the approximation of offset curve. Numerical examples are given to show effectiveness of the method. The results are compared with other methods, and conclusions are made based on the numerical examples.
作者 郭清伟
机构地区 复旦大学数学所
出处 《应用科学学报》 CAS CSCD 北大核心 2006年第3期278-282,共5页 Journal of Applied Sciences
基金 国家自然科学基金资助项目(60473114)
关键词 BÉZIER曲线 等距曲线 有理逼近 离散 Bézier curves offset curves rational approximation subdivision
分类号 TP391 [自动化与计算机技术—计算机应用技术]
  • 相关文献

参考文献14

  • 1Maekawa T.An overview of offset curves and surfaces[J].Computer Aided Dseign,1999,31(3):165-173.
  • 2Farouki R T,Sakkalis T.Pythagorean hodographs[J].IBM Journal of Research and Development,1990,34 (5):736 -752.
  • 3Lu Wei.Offsets-rational parametric plane curves[J].Computer Aided Geometric Design,1995,12(6):601-616.
  • 4Coquillart S.Computing offsets of B-spline curves[J].Computer Aided Design,1987,19(6):305-309.
  • 5Elber G,Cohen E.Error bounded variable distance offset operator for freeform curves and surfaces[J].International Journal of Computational Geometry and Application,1991,1(1):67-78.
  • 6Lee I K,Kim M S,Elber G.Planar curve offset based on circle approximation[J].Computer Aided Design,1996,28(8):617-630.
  • 7Klass R.An offset spline approximation for plane cubic splines[J].Computer Aided Design,1983,15(4):297-299.
  • 8Hoscheck J.Spline approximation of offset curves[J].Computer Aided Design,1988,20 (1):33-40.
  • 9Hoscheck J,Wisse l N.Optimal approximate conversion of spline curves and spline approximation of offset curves[J].Computer Aided Design,1988,20(8):475-483.
  • 10Pham B.Offset approximation of uniform B-splines[J].Computer Aided Design,1988,20(8):471-474.

二级参考文献27

  • 1[11]Tiller W, Hanson E G. Offsets of two-dimensional profiles. IEEE Computer Graphics and Application, 1984, 4(9): 36-46
  • 2[12]Coquillart S. Computing offsets of B-spline curves. Computer Aided Design, 1987, 19(6):305-309
  • 3[13]Elber G, Cohen E. Error bounded variable distance offset operator for free form curves and surfaces. International Journal of Computational Geometry and Application, 1991, 1(1): 67-78
  • 4[14]Elber G, Cohen E. Offset approximation improvement by control points perturbation. In: Lyche T, Schumaker L L eds. Mathematical Methods in Computer Aided Geometric Design II, New York: Academic Press, 1992. 229-237
  • 5[15]Lee I K, Kim M S, Elber G. Planar cuve offset based on circle approximation. Computer Aided Design, 1996, 28(8): 617-630
  • 6[16]Klass R. An offset spline approximation for plane cubic splines. Computer Aided Design, 1983, 15(4): 297-299
  • 7[17]Hoscheck J. Spline approximation of offset curves. Computer Aided Design, 1988, 20(1): 33-40
  • 8[18]Hoscheck J, Wissel N. Optimal approximate conversion of spline curves and spline approximation of offset curves. Computer Aided Design, 1988, 20(8): 475-483
  • 9[19]Pham, B. Offset approximation of uniform B-splines. Computer Aided Design, 1988, 20(8): 471-474
  • 10[20]Sederberg T W, Buehler D B. Offsets of polynomial Bézier curves: Hermite approximation with error bounds. In: Lyche T, Schumaker L L, eds. Mathematical Methods in Computer Aided Geometric Design II, New York: Academic Press, 1992. 549-558

共引文献11

同被引文献43

引证文献5

二级引证文献7

应用科学学报
2006年 第3期

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