东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (7): 1021-1024.DOI: -

• 论著 • 上一篇    下一篇

NURBS直接插补技术中快速求值求导算法

王国勋;舒启林;王军;王宛山;   

  1. 东北大学机械工程与自动化学院;沈阳理工大学机械工程学院;沈阳建筑大学交通与机械工程学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家高技术研究发展计划项目(SS2012AA041303)

Algorithm of fast evaluation and derivation for the technique of NURBS direct interpolation

Wang, Guo-Xun (1); Shu, Qi-Lin (2); Wang, Jun (3); Wang, Wan-Shan (1)   

  1. (1) School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China; (2) School of Mechanical Engineering, Shenyang Ligong University, Shenyang 110159, China; (3) Traffic and Mechanical Engineering Institute, Shenyang Jianzhu University, Shenyang 110168, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Wang, G.-X.
  • About author:-
  • Supported by:
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摘要： 为了提高NURBS直接插补算法的实时性,研究了NURBS曲线和曲面的快速求值与求导计算算法.根据de Boor-Cox的非均匀B样条求导的递推公式,提出了一种快速递推算法.该算法基于NURBS曲线、曲面的矩阵表示形式,推导了非均匀B样条基函数的系数矩阵快速计算方法.与传统de Boor-Cox等算法相比,该算法推导简单,计算快速,有利于提高计算速度,缩短插补周期,提高插补的实时性.另外,该算法还可用于计算非均匀B样条曲线、曲面,并且可用于计算机辅助几何设计的相关研究.

关键词: 非均匀有理B样条, 递推矩阵, 插补, 快速算法

Abstract: In order to improve the real-time of the NURBS direct interpolation algorithm, a fast evaluation and derivation compute algorithm of the NURBS curve and surface was researched. According to the non-uniform B-spline derivation of de Boor-Cox algorithm, a fast recursive algorithm was put forward to derive the coefficient matrix of non-uniform B-spline basis function, which is based on the matrix representation of NURBS curve and surface. Compared with the traditional algorithms such as de Boor-Cox, the fast recursive algorithm has significant advantages in enhancing computation speeds, shorten interpolation cycle and improving interpolation real-time. The algorithm can be used to calculate the non-uniform B-spline curve and surface, except for the application in computer-aided geometric design.

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