| B样条快速求值算法及其在曲线拟合中的应用 |
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| 引用本文： | 孙海洋,;范大鹏.B样条快速求值算法及其在曲线拟合中的应用[J].飞行器测控学报,2008(3):50-55. |
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| 作者姓名： | 孙海洋 ;范大鹏 |
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| 作者单位： | [1]国防科学技术大学,湖南长沙410073; [2]中国卫星海上测控部,江苏江阴214431 |
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| 摘 要： | B样条方法是数据插值、拟合与平滑的重要方法。通过对de Boor-Cox算法计算路径的分析，给出了一种基于向量扩展的B样条基函数求值运算方法。分析表明，该方法具有并行计算结构和递推计算结构，利于计算机实现。同de Boor-Cox递推运算方法比，它能够同步计算出k次B样条的所有k＋1个非零函数值，运算效率提高了2k＋1倍。在最小二乘法B样条曲线拟合算法中的应用验证了本文算法的有效性。
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| 关 键 词： | B样条 De Boor-Cox 向量扩展 算法 数据逼近 |
A Fast Algorithm to Compute B-spline Functions and its Application in Curve Fitting |
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| Institution: | SUN Hai-yang, FAN Da-peng (1. National University of Defense Technology, Changsha, Hunan Province 410073; 2. China Satellite Maritime Tracking and Control Department, Jiangyin, Jiangsu Province 214431) |
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| Abstract: | The B-spline method plays an important role in data interpolating, fitting and smoothing. Through analyzing the computed path of the de Boor-Cox algorithm, a new method for the B-spline function calculating is proposed based on vectors extending. The proposed method is suitable to be realized by computers with the features of parallel computing architecture and recurrence formulae. Compared to the de Boor-Cox algorithm, the proposed method can improve computing efficiency by 2k＋ 1 times for calculating all nonzero values of B spine functions about degree k. The application shows it can reduce the computing efforts obviously in the least-squares B-spline curve approximation. |
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| Keywords: | B-spline Functions de Boor-Cox Vector Extending Algorithm Data Approach |
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