Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (26): 172-175.DOI: 10.3778/j.issn.1002-8331.2009.26.051

• 图形、图像、模式识别 • Previous Articles     Next Articles

Shape control of weighted rational cubic spline

DENG Si-qing1,FANG Kui2,3,XIE Jin4   

  1. 1.Department of Mathematics,Xiangnan University,Chenzhou,Hunan 423000,China
    2.School of Information Science and Technology,Hunan Agricultural University,Changsha 410128,China
    3.School of Mathematics and Computer,Hunan Normal University,Changsha 410081,China
    4.Department of Mathematics and Physics,Hefei University,Hefei 230601,China
  • Received:2008-10-28 Revised:2008-12-29 Online:2009-09-11 Published:2009-09-11
  • Contact: DENG Si-qing

加权有理三次样条的形状控制

邓四清1,方 逵2,3,谢 进4   

  1. 1.湘南学院 数学系,湖南 郴州 423000
    2.湖南农业大学 信息科学技术学院,长沙 410128
    3.湖南师范大学 数学与计算机科学学院,长沙 410081
    4.合肥学院 数理系,合肥 230601
  • 通讯作者: 邓四清

Abstract: In this paper,a kind of weighted rational cubic spline interpolation is constructed using the rational cubic spine with cubic polynomial denominators and the rational cubic spline based on function values.The shape control of the weighted rational cubic spline is studied,the sufficient conditions for the interpolating curves to be constrained in the given region are derived.An example is given in the end of this paper.

Key words: computer applications, curve design, rational spline, weighted interpolation, constrained interpolation

摘要: 利用带导数和不带导数的分母为三次的有理三次插值样条构造了一类加权有理三次插值样条函数,由于这种有理三次插值样条中含有参数、调节参数和权系数,因而给约束控制带来了方便。同时只要合适地选择调节参数,就可以使之变成分母为线性的和分母为二次的有理三次插值样条函数。对该样条曲线的区域控制问题进行了研究,给出了将其约束于给定的折线、二次曲线之上、之下或之间的充分条件。最后给出了数值例子。

关键词: 计算机应用, 曲线设计, 有理样条, 加权插值, 约束插值

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