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一种基于函数值的二元有理插值函数及其性质 被引量：6

A BIVARIATE RATIONAL INTERPOLATION BASED ON FUNCTION VALUES AND THE PROPERTIES
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摘要 利用带参数的仅以被插函数的函数值作为插值条件的一元有理插值方法,构造了一种分母为双二次的仅基于函数值的二元有理双三次插值函数,插值函数具有简洁的显示表示.插值函数中含有四个参数,当这些参数满足一定条件时,插值曲面在插值区域上C^1光滑.由于插值函数中含有参数,这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改.最后讨论了插值函数的一些性质. A bivariate rational bicubic interpolating spline based on function values with four parameters is constructed, and this spline is with bicubic numerator and biquadratic denominator. The interpolation function has a simple and explicit mathematical representation. The interpolating surface is C^1 in the interpolating region when two parameters satisfy a simple condition, and the interpolating surface can be modified by selecting suitable parameters under the condition that the interpolating data are not changed. Some properties of the interpolation are derived.
作者 邓四清 方逵 谢进 陈福来 陆海波
机构地区 湘南学院数学系 湖南农业大学信息科学技术学院 湖南师范大学数学与计算机科学学院 合肥学院数理系
出处 《计算数学》 CSCD 北大核心 2009年第1期77-86,共10页 Mathematica Numerica Sinica
基金 国家自然科学基金资助项目(60773110) 湖南省自然科学基金资助项目(06JJY4073) 湖南省教育厅科研资助项目(06C791) 湖南省科技计划项目(2008FJ3046) 安徽省教育厅自然科研项目(KJ2008B250) 湖南省重点学科建设项目资助 湖南省高校科技创新团队支持计划资助.
关键词 计算机应用 二元插值 有理样条 曲面设计 computer application bivariate interpolation rational interpolation surface design
分类号 O174.42 [理学—基础数学]
  • 相关文献

参考文献17

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  • 2Chui C K. Multivariate spline. SIAM, 1988.
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二级参考文献14

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共引文献18

同被引文献75

  • 1谢楠,张晓平.一类有理三次样条的区域控制和逼近性质[J].山东大学学报（工学版）,2004,34(6):106-111. 被引量：8
  • 2朱春钢,王仁宏.空间曲线几何Hermite插值的B样条方法(英文)[J].软件学报,2005,16(4):634-642. 被引量：6
  • 3邓四清,方逵,谢进.一类基于函数值的有理三次样条曲线的形状控制[J].工程图学学报,2007,28(2):89-94. 被引量：19
  • 4Duan Q,Djidjeli K,Price W G,et al.A rational cubic spline based on function values[J].Computer and Graphics,1998,22(4):479-486.
  • 5Duan Q,Wang L,Twizell E H.A new bivarlate rational interpolation based on function values[J].Information Sciences,2004,166:181-191.
  • 6Duan Q,Zhang H,Zhang Y,et al.Bounded property and point control of a bivariate rational interpolating surface[J].Computers and Mathematics with Applications,2006,52:975-984.
  • 7Farin G.Curves and surfaces for computer aided geometric design:A practical guide[M].Academic press,1988.
  • 8Chui C K.Multivariate spline[M].SIAM,1988.
  • 9Bezier P E.The mathematical basis of the UNISURF CAD system[M].Butterworth,London,1986.
  • 10Boor C.A practical guide to splines[M].Revised Edition,Springer-Verlag,New York,2001.

引证文献6

二级引证文献10

计算数学
2009年 第1期

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