带参数的C^3连续分段七次Hermite插值样条  

The C^3 Piecewise Seventh-degree Hermite Interpolating Splines with Parameters

作　　者：李军成 刘成志 易叶青 Li Juncheng;Liu Chengzhi;Yi Yeqing(College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000;College of Information, Hunan University of Humanities, Science and Technology, Loudi 417000)

机构地区：[1]湖南人文科技学院数学与金融学院,娄底417000 [2]湖南人文科技学院信息学院,娄底417000

出　　处：《计算机辅助设计与图形学学报》2017年第12期2204-2215,共12页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61472135);湖南省自然科学基金(2017JJ3124)

摘　　要：针对分段三次Hermite插值样条在形状调控与连续性方面的不足,提出带2个参数的C^3连续分段七次Hermite插值样条.首先构造一组带2个参数的七次Hermite基函数;然后基于该组基函数定义分段七次Hermite参数样条曲线,并讨论样条曲线所带参数的选取方案;最后研究对应的分段七次Hermite样条插值函数,并给出其插值余项及最佳插值函数的确定方法.实例结果表明,当插值条件保持不变时,分段七次Hermite参数样条曲线不仅达到C^3连续,而且还可利用所带的参数实现对曲线形状的调控;通过确定所带参数的最佳取值,可使得分段七次Hermite样条插值函数获得较好的插值效果.In view of the deficiency of the piecewise cubic Hermite interpolating splines in shape adjustment and continuity,the C3piecewise seventh-degree Hermite interpolating splines with two parameters are presented in this paper.First,a class of seventh-degree Hermite basis functions with two parameters is constructed.Then,the piecewise seventh-degree Hermite parametric spline curves are defined on base of the proposed basis functions,and the parameter selection of the spline curves is discussed.Finally,the piecewise seventh-degree Hermite spline interpolation function is studied,and the interpolation error and the method for determining the optimal interpolation function are given.Example results show that,when the interpolation conditions remain unchanged,piecewise seventh-degree Hermite parametric spline curves not only achieve C3continuity,but also can realize shape control through the two parameters.By determining the optimal values of the two parameters,the piecewise seventh-degree Hermite spline interpolation function can obtain better interpolation results.

关 键 词：Hermite样条 插值样条 形状调控 C3连续 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]