基于广义逆的张量积Said-Ball曲面降多阶逼近

Method of approximating tensor product Said-Ball surfaces through multi-degree reduction

文章给出张量积 Said-Ball曲面降多阶逼近的一种方法 ,即将曲面的降多阶过程视为升阶的逆过程 ,利用广义逆矩阵的理论得到降阶曲面控制顶点的显式表示式 ,从而得到了用矩阵表示的降多阶张量积 Said-Ball曲面的控制顶点的显式表示式。在降多阶过程中 ,分别考虑了带角点高阶插值条件和不带角点插值条件的情形 。

This paper deals with a new method of approximating tensor product Said-Ball surfaces through multi-degree reduction. The process of degree reduction is regarded as the opposite process of elevation,then the theory of generalized inverse matrix is used to get the explicit representation of control points of the reduced multi-degree tensor product Said-Ball surface. During the multi-degree reduction process,two cases are considered— one is with the constraint of high-order interpolations over corners and the other is without any constraint. Numerical examples are also given.