一种新的带参数双三次有理插值样条的有界性与点控制  

BOUNDED PROPERTY AND POINT CONTROL OF A NEW BIVARIATE RATIONAL BICUBIC INTERPOLATING SPLINE WITH PARAMETERS

作　　者：邓四清[1] 方逵[2] 谢进[3] 陈福来[4] 陆海波[4] 

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

出　　处：《计算数学》2010年第4期337-348,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目(60773110);湖南省教育厅科研资助项目(06C791;09B096);湖南省科技计划项目(2008FJ3046);安徽省教育厅自然科研项目(KJ2008B250);韶关学院校级重点扶持学科建设项目;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

摘　　要：文[19]中,作者构造了一种基于函数值的带参数的分子为双三次、分母为双二次的二元有理插值样条.本文进一步研究该种二元有理插值样条的有界性,给出插值的逼近表达式,讨论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 method with parameters was created in an earlier work which was based on function values only, and this spline is with bicubic numerator and biquadratic denominators. This paper will deal with the bounded property, approximation property 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. Also, the approximation expression of the interpolation are derived. More important is 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.

关 键 词：插值 有理样条 有界性 点控制 计算机辅助几何设计 

分 类 号：O241.3[理学—计算数学]