基于广义逆矩阵的Ball曲线的降多阶逼近

A Method for Multi-degree Reduction of Ball Curves

给出了Ball曲线的一种降多阶逼近方法.将曲线的降多阶过程视为升阶的逆过程,利用广义逆矩阵的理论从而得到降阶曲线控制顶点的显式表示式.这种方法还考虑了原曲线与降阶曲线在两端点处分别达到(r,s)阶连续的情形(r≥0,s≥0).其次,给出了降阶误差界的估计.最后,给出数值例子.

We give one method for multi-degree reduction of Ball curves. We firstly regard the process of degree reduction as the opposite process of elevation, then we use the theory of generalized inverse matrix theory and get the explicit representation of control points of the degree reduction curves; In this method, we also consider the case of the original curve and the degree reduction curve are continuous on (r,s) degree respectively on two endpoints (r≥0, (s≥0)). Besides, it also gets the estimation of the degree reduction error bound. Finally, it also gives some examples.