학술논문
NURBS 插补快速求值算法 / An Efficient Evaluation Algorithm for NURBS Interpolation
Document Type
Academic Journal
Author
Source
华南理工大学学报（自然科学版）. 44(1):85-92
Subject
Language
Chinese
ISSN
1000-565X
Abstract
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.
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.