形状可调的C2连续三次三角Hermite插值样条

doi:10.12286/jssx.2016.2.187

计算数学 ›› 2016, Vol. 38 ›› Issue (2): 187-199.DOI: 10.12286/jssx.2016.2.187

形状可调的C²连续三次三角Hermite插值样条

李军成, 刘成志

湖南人文科技学院数学系, 湖南娄底 417000

收稿日期:2015-04-23 出版日期:2016-04-15 发布日期:2016-05-13
基金资助:
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).

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李军成, 刘成志. 形状可调的C²连续三次三角Hermite插值样条[J]. 计算数学, 2016, 38(2): 187-199.

Li Juncheng, Liu Chengzhi. SHAPE-ADJUSTABLE AND C² CONTINUOUS CUBIC TRIGONOMETRIC HERMITE INTERPOLATION SPLINE[J]. Mathematica Numerica Sinica, 2016, 38(2): 187-199.

SHAPE-ADJUSTABLE AND C² CONTINUOUS CUBIC TRIGONOMETRIC HERMITE INTERPOLATION SPLINE

Li Juncheng, Liu Chengzhi

Department of Mathematics, Hunan Institute of Humanities, Science and Technology, Loudi 417000, Hunan, China

Received:2015-04-23 Online:2016-04-15 Published:2016-05-13

基于函数空间{1,sint,cost,sin²t,sin³t,cos³t}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.

关键词： Hermite插值样条, 三角Hermite插值样条, 形状可调, C²连续

This paper presents a class of shape-adjustable cubic trigonometric Hermite interpolation spline based on the space{1, sint, cost, sin²t, sin³t, cos³t}, which shares the main properties of the Hermite-type interpolation spline with parameters. The proposed spline not only automatically satisfies C² 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.

Key words: Hermite interpolation spline, trigonometric Hermite interpolation spline, shape-adjustable, C² continuous

MR(2010)主题分类:

65D05
65D17

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