计算机应用 ›› 2012, Vol. 32 ›› Issue (07): 1868-1870.DOI: 10.3724/SP.J.1087.2012.01868

• 图形图像技术 • 上一篇    下一篇

带参数的四次Hermite插值样条

李军成,刘纯英,杨炼   

  1. 湖南人文科技学院 数学与应用数学系,湖南 娄底417000
  • 收稿日期:2011-12-07 修回日期:2012-02-03 发布日期:2012-07-05 出版日期:2012-07-01
  • 通讯作者: 李军成
  • 作者简介:李军成(1982-),男,湖北汉川人,讲师,博士研究生,CCF会员,主要研究方向:计算机辅助几何设计、图像处理;刘纯英(1979-),女,湖南衡阳人,助教,硕士,主要研究方向:计算机辅助几何设计;杨炼(1980-),男,湖南隆回人,讲师,硕士,主要研究方向:计算机辅助几何设计。
  • 基金资助:

    湖南省教育厅资助科研项目(10C1263)

Quartic Hermite interpolating splines with parameters

LI Jun-cheng,LIU Chun-ying,YANG Lian   

  1. Department of Mathematics and Applied Mathematics, Hunan Institute of Humanities, Science and Technology, Loudi Hunan 417000, China
  • Received:2011-12-07 Revised:2012-02-03 Online:2012-07-05 Published:2012-07-01
  • Contact: LI Jun-cheng

摘要: 为了克服标准三次Hermite插值样条的不足,给出了一种带参数的四次Hermite插值样条,具有标准三次Hermite插值样条完全相同的性质。在插值条件给定时,四次Hermite插值样条的形状可通过改变参数的取值进行调控。通过选择合适的参数,四次Hermite曲线能达到C2连续,而且其整体逼近效果要好于标准三次Hermite插值样条。所提出的新样条进一步丰富了Hermite插值样条理论,也为工程中插值曲线曲面的构造提供了一种新方法。

关键词: 三次Hermite样条, 四次Hermite样条, 形状参数, 逼近

Abstract: To overcome the defects of the standard cubic Hermite interpolating splines, a class of quartic Hermite interpolating splines with parameters was presented in this paper, which inherited the same properties of the standard cubic Hermite interpolating splines. Given the set interpolating conditions, the shape of the proposed splines could be adjusted by changing the values of the parameters. If the parameters were chosen properly, the quartic Hermite interpolating splines could achieve C2 continuity and approximate to the interpolated functions better than the standard cubic Hermite interpolating splines. The proposed new splines further enriched the theories of Hermite interpolating splines, and provided a new method for constructing interpolation curves and surfaces.

Key words: cubic Hermite spline, quartic Hermite spline, shape parameter, approximation

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