带形状因子的C^2连续五次Cardinal样条与Catmull-Rom样条  

C^2 Continuous Quintic Cardinal Spline and Catmull-Rom Spline with Shape Factors

作　　者：李军成[1] 刘成志[1] 易叶青[2] 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》2016年第11期1821-1831,共11页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61472135);湖南省教育厅资助科研项目(14B099)

摘　　要：针对三次Cardinal样条与Catmull-Rom样条的不足,提出带形状因子的C^2连续五次Cardinal样条与Catmull-Rom样条.首先构造一组带2个形状因子的五次Cardinal样条基函数;然后基于该组基函数定义带形状因子的五次Cardinal样条曲线与曲面,并讨论五次Cardinal样条函数的保单调插值;最后研究对应的一元与二元五次Catmull-Rom样条插值函数,并给出最优一元与二元五次Catmull-Rom样条插值函数的确定方法.实例结果表明,五次Cardinal样条与Catmull-Rom样条无需任何条件即可达到C^2连续,且其形状还可通过自带的形状因子进行灵活地调整,利用最优五次Catmull-Rom样条插值函数可获得满意的插值效果.In view of the deficiency of the cubic Cardinal spline and Catmull-Rom spline, the C2 continuousquintic Cardinal spline and Catmull-Rom spline with shape factors are presented in this paper. First, a classof quitic Cardinal spline basis functions with two shape factors is constructed. Then, the quintic Cardinalspline curves and surfaces with shape factors are defined on base of the proposed basis functions, and themonotonicity-preserving interpolation with the quintic Cardinal spline function is discussed. Finally, thecorresponding one dimensional and two dimensional quintic Catmull-Rom spline interpolation functions arestudied, and the method of determining the optimal one dimensional and two dimensional quintic Catmull-Rom spline interpolation functions are given. Example results show that, the quintic Cardinal splineand Catmull-Rom spline can not only be C2 continuous without any conditions, but also can be flexibly adjustedby the shape factors. Satisfactory interpolation results can be obtained by using the optimal quinticCatmull-Rom spline interpolation functions.

关 键 词：Cardinal样条 CATMULL-ROM样条 插值样条 形状因子 C2连续 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]