一种二元有理插值曲面的两个性质和点控制问题  

Two Properties and Point Control of Bivariate Rational Interpolating Surface

作　　者：陆海波[1] 邓四清[2] 方逵[3] 谢进[4] 

机构地区：[1]湘南学院数学系,湖南郴州423000 [2]韶关学院数学与信息科学学院,广东韶关512005 [3]湖南农业大学信息科学技术学院,湖南长沙410128 [4]合肥学院数理系,安徽合肥230601

出　　处：《工程图学学报》2011年第3期28-34,共7页Journal of Engineering Graphics

基　　金：国家自然科学基金资助项目(60773110);湘南学院科研资助项目(2010Y060);湖南省科技计划资助项目(2008FJ3046);韶关学院校级重点扶持学科建设项目;湖南省高校科技创新团队计划支持项目;安徽省教育厅自然科研资助项目(KJ2008B250)

摘　　要：文献[22]中已经构造了一种基于函数值的带参数的二元有理插值样条,它是分子为双四次、分母为双二次的有理样条。论文研究了该种二元有理插值样条的有界性,给出了插值的逼近表达式,讨论了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的需要通过对参数的选取修改,从而达到插值曲面局部修改的目的。A bivariate rational interpolation spline with parameters was created in an earlier work which was based on function values only,and this spline is a rational one with biquartic numerator and biquadratic denominator.This paper discusses the spline’s boundary property,the approximation expression of the interpolation and the point control method of the interpolating surface.It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be,which is called the boundary property of the interpolation.Also,the approximation expression of the interpolation are derived,which does not depend on the parameters.More important is that the values of the interpolating function at any 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.

关 键 词：二元插值 二元有理样条 参数 计算机辅助几何设计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O241.3[自动化与计算机技术—计算机科学与技术]