形状可调的C^2连续三次三角Hermite插值样条  

SHAPE-ADJUSTABLE AND C^2 CONTINUOUS CUBIC TRIGONOMETRIC HERMITE INTERPOLATION SPLINE

作　　者：李军成[1] 刘成志[1] 

机构地区：[1]湖南人文科技学院数学系,湖南娄底417000

出　　处：《计算数学》2016年第2期187-199,共13页Mathematica Numerica Sinica

基　　金：湖南省教育厅资助科研项目(14B099);湖南省自然科学基金资助项目(13JJ6081)

摘　　要：基于函数空间{1,sint,cost,sin^2t,sin^3t,cos^3t}构造了一种形状可调的三次三角Hermite插值样条.该样条不仅具有带参数的Hermite型插值样条的主要特性,而且在插值节点为等距时可自动满足C2连续,其形状还可通过所带的参数进行调节.在适当条件下,该样条对应的Ferguson曲线可精确表示工程中一些常见的曲线.This paper presents a class of shape-adjustable cubic trigonometric Hermite interpolation spline based on the space {1, sint, cost, sin^2t, sin^3t, cos^3t}, which shares the main properties of the Hermite-type interpolation spline with parameters. The proposed spline not only automatically satisfies C^2 continuity when the interpolation nodes are equally spaced, but also can be adjusted by the parameters. Under the proper conditions, the corresponding Ferguson curve can precisely represent some general curves in engineering.

关 键 词：Hermite插值样条 三角Hermite插值样条 形状可调 C^2连续 

分 类 号：O241.3[理学—计算数学]