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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (2): 175-180    DOI: 10.3785/j.issn.1008-9497.2016.02.009
数学与计算机科学     
自动满足C2连续的带参数五次Hermite插值样条
李军成1, 谢炜2
1. 湖南人文科技学院数学系, 湖南娄底 417000;
2. 桂林理工大学理学院, 广西桂林 541004
The automatic C2 continuous quintic Hermite interpolating spline with parameters
LI Juncheng1, XIE Wei2
1. Department of Mathematics, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China;
2. College of Science, Guilin University of Technology, Guilin 541004, Guangxi Zhuang Autonomous Region, China
 全文: PDF(1272 KB)  
摘要： 为了克服已有的带形状参数的三次或四次Hermite型插值样条不能自动满足C2连续这一不足,提出了一类新的五次Hermite插值样条.该样条除了具有带形状参数Hermite型插值样条的特性外,在插值条件保持不变的情形下可自动满足C2连续且其形状还可通过所带的形状参数进行调控.进一步,给出了一种确定形状参数最优取值的方法,该法可使得五次Hermite插值样条曲线具有最优插值效果.
关键词： Hermite插值;  五次Hermite插值样条;  C2连续;  形状调控    
Abstract: In order to solve the problem that the cubic or quartic Hermite-type interpolating splines with shape parameters can not automatically satisfy C2 continuity, a new class of quintic Hermite interpolating spline with shape parameters is presented. The proposed spline not only has the same characteristics as the Hermite-type interpolating spline with shape parameters, but also automatically satisfies C2 continuity and can be controlled by the shape parameters when the interpolation conditions remain unchanged. Furthermore, a method for determining the optimal value of the shape parameters is given, which can make the quintic Hermite interpolating spline curve with the optimal interpolation effects.
Key words: Hermite interpolation    quintic Hermite interpolating spline    C2 continuity    shape adjustment
收稿日期: 2015-08-19 出版日期: 2016-03-12
CLC:  O241.5  
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).
作者简介: 李军成(1982-),ORCID:http:/orcid.org/0000-0002-1904-4068,男,博士,副教授,主要从事计算机辅助几何设计及其应用研究,E-mail:lijuncheng82@126.com.
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李军成, 谢炜. 自动满足C2连续的带参数五次Hermite插值样条[J]. 浙江大学学报（理学版）, 2016, 43(2): 175-180.

LI Juncheng, XIE Wei. The automatic C2 continuous quintic Hermite interpolating spline with parameters. Journal of ZheJIang University(Science Edition), 2016, 43(2): 175-180.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.02.009    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I2/175

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