一个反求Bezier曲面控制点的算法  

An Algorithm for the Inverse Solution of Bezier Surface Control Points

作　　者：王天军[1] 

机构地区：[1]北京航空航天大学,100083

出　　处：《计算机辅助设计与图形学学报》1992年第3期36-40,35,共6页Journal of Computer-Aided Design & Computer Graphics

摘　　要：本文将反求m×n次Bezier曲面控制点问题,转化为求解m+1个n+1阶线性方程组和n+1个m+1阶线性方程组问题。这些线性方程组的系数矩阵是著名的Vandermonde矩阵。通过求解Vandermonde矩阵的逆矩阵,使CAD/CAM曲面造型中常常遇到的反求Bezier曲面控制点问题得到有效的解决。同时本文给出了一种求解Vandermonde矩阵的逆矩阵的方法。In this paper, the inverse solving of the control points of Bezier surface of degree(m,n) is converted into a process to solve m+1 systems of n+1 linear equations in n+1 unknowns and n+1 systems of m+1 linear equations in m+1 unknowns. The coefficient matrices of these systems of linear equations are the well-known Vandermonde matrices. The inverse solving of the Bezier surface control points is often to be dealt with in CAD/ CAM surface modeling and this is effectively worked out here by solving the inverse matrices of the Vandermonde matrices. And a method is introduced for solving the inverse matrix of the Vandermonde matrix.

关 键 词：算法 控制点 BEZIER曲面 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]