NURBS直接插补技术中快速求值求导算法

Algorithm of Fast Evaluation and Derivation for the Technique of NURBS Direct Interpolation

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.

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 realtime. The algorithm can be used to calculate the non-uniform B-spline curve and surface, except for the application in computer-aided geometric design.