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.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
1992年第3期36-40,35,共6页
Journal of Computer-Aided Design & Computer Graphics
关键词
算法
控制点
BEZIER曲面
Bezier surface,control point, surface modeling, Vandennonde matrix, system of linear equations.
