NURBS插补快速求值算法  

An Efficient Evaluation Algorithm for NURBS Interpolation

作　　者：孔祥洪[1] 李迪[1] 焦青松[1] 

机构地区：[1]华南理工大学机械与汽车工程学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2016年第1期85-92,共8页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家"863"计划项目(2012AA040909)~~

摘　　要：当对非均匀有理B样条(NURBS)曲线进行高密度插值时,运用分段幂函数方法对基函数进行求值的效率远高于传统的de-Boor算法.为此,文中从NURBS插补计算的特点出发,结合de-Boor递推计算规律,设计了NURBS插补快速求值算法.首先采用该算法计算NURBS在各节点区间的基函数显式方程,再运用显式方程进行NURBS插补点求值,并设计相应的NURBS曲线插补器.复杂NURBS曲线的铣削加工实验结果表明,该算法能够有效地缩减NURBS曲线插补求值的计算耗时,提高插补计算的实时性.In the high-density interpolation of non-uniform rational B-spline ( NURBS) curves, using the piecewise power function method to evaluate the B-spline basis function consumes much less computing time than the tradi-tional de-Boor algorithm.Therefore, on the basis of the characteristic of the NURBS interpolation, an efficient eva-luation algorithm for the NURBS interpolation is proposed by drawing on the recursive calculation laws of the de-Boor algorithm.First, the proposed algorithm is used to deduce the explicit equations of the B-spline basis function in each spline parameter knot interval.Then, NURBS interpolation points are evaluated by using explicit equa-tions, and a corresponding NURBS curve interpolator is designed.The results of the milling experiment with com-plex NURBS curves show that the proposed algorithm can effectively reduce the computing time of the NURBS curve interpolation and can improve the real-time performance of NURBS interpolators.

关 键 词：NURBS 基函数 快速算法 参数插补 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]