计算机应用 ›› 2011, Vol. 31 ›› Issue (07): 1800-1803.DOI: 10.3724/SP.J.1087.2011.01800

• 先进计算 • 上一篇    下一篇

周期B样条基函数系数的并行算法

周凯汀1,郑力新1,林福泳2   

  1. 1. 华侨大学 信息科学与工程学院,福建 泉州 362021
    2. 华侨大学 机电及自动化学院,福建 泉州 362021
  • 收稿日期:2010-12-15 修回日期:2011-02-07 发布日期:2011-07-01 出版日期:2011-07-01
  • 通讯作者: 周凯汀
  • 作者简介:周凯汀(1968-),女,辽宁大连人,副教授,硕士,主要研究方向:数值逼近、信号处理;郑力新(1967-),男,福建永春人,教授,博士,主要研究方向:信号处理、模式识别;林福泳(1959-),男,福建福州人,教授,博士,主要研究方向:工程计算、信号处理。
  • 基金资助:

    教育部科学技术研究重点项目;福建省高等学校新世纪优秀人才支持计划

Parallel algorithm for computing coefficients of periodic B-spline basis functions

Kai-ting ZHOU1,Li-xin ZHENG1,Fu-yong LIN2   

  1. 1. College of Information Science and Engineering,Huaqiao University,Quanzhou Fujian 362021,China
    2. College of Mechanical Engineering and Automation,Huaqiao University,Quanzhou Fujian 362021,China
  • Received:2010-12-15 Revised:2011-02-07 Online:2011-07-01 Published:2011-07-01
  • Contact: Kai-ting ZHOU

摘要: 在现有周期B样条插值方法中,需要用迭代算法确定B样条基函数系数。针对现有方法的不足,建立B样条基函数系数的并行算法。首先构造周期区域的正交B样条基,得出正交B样条基函数系数的并行算法;进一步利用正交B样条基函数系数与B样条基函数系数的关系,得出B样条基函数系数的并行算法;最后推导二阶、三阶、四阶周期插值B样条基函数系数及插值点函数值的显式算式。实验证明了该方法在实现B样条基函数系数快速并行算法的同时保持了B样条基函数简单的函数关系。

关键词: 样条函数, 样条插值, 周期样条, 正交样条, 并行算法

Abstract: In the existing methods of periodic B-spline interpolation, coefficients of B-spline basis functions are determined by iterative algorithms. To overcome the weakness of the existing methods, new parallel algorithm for computing coefficients of B-spline basis functions were established. First, this paper established orthogonal B-spline basis and derived parallel algorithm for coefficients of orthogonal B-spline basis functions; and then derived parallel algorithm for coefficients of B-spline basis functions by using the relation between coefficients of orthogonal B-spline basis functions and coefficients of B-spline basis functions; at last this paper derived explicit formulas for both coefficients of B-spline basis functions and value of interpolated point with the 2nd, the 3rd and the 4th order periodic interpolating B-spline functions. The presented method retains the simplicity of B-spline basis functions while realizing fast parallel algorithm for coefficients of B-spline basis functions.

Key words: spline, spline interpolation, periodic spline, orthogonal spline, parallel algorithms