计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (24): 46-49.DOI: 10.3778/j.issn.1002-8331.2009.24.015

• 研究、探讨 • 上一篇    下一篇

二元有理双四次插值曲面的点控制问题

陆海波1,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
  • 收稿日期:2008-10-14 修回日期:2008-12-29 出版日期:2009-08-21 发布日期:2009-08-21
  • 通讯作者: 陆海波

Point control of bivariate rational biquartic interpolating surface

LU Hai-bo1,DENG Si-qing1,FANG Kui 2,3,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:2008-10-14 Revised:2008-12-29 Online:2009-08-21 Published:2009-08-21
  • Contact: LU Hai-bo

摘要: 构造了一种含有两个参数的仅基于函数值的二元有理双四次插值样条函数,插值函数具有简洁的显示表示,既便于应用,又便于理论研究。给出了插值曲面在插值区域上C1光滑的一个充分条件,讨论了插值基函数的性质和插值曲面形状的点控制问题.在插值条件不变的情况下,插值区域内任一点插值函数的值可以根据设计需要通过对参数的选取进行插值曲面的局部修改。

关键词: 计算机应用, 二元插值, 二元有理样条, 参数, 计算机辅助几何设计

Abstract: A bivariate rational biquartic interpolating spline based on function values with two parameters is constructed,and this spline is with biquartic numerator and bilinear denominator.The interpolating function has a simple and explicit mathematical representation,which is convenient both in practical application and in theoretical study.The interpolating surface is C1 in the interpolating region when one of the parameters satisfies a simple condition.It is more important that the values of the interpolating function at point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters,so the interpolation surface can be modified for the given interpolation data when needed in practical design.
Key words: computer application;bivariate

Key words: computer application, bivariate interpolation, bivariate rational spline, parameter, computer aided geometric design

中图分类号: