三角域上球形控制点的Bézier曲面的降阶逼近

Degree reduction of ball-control-point Bézier surfaces over triangular domain

讨论了三角域上球形控制点的Bézier曲面的降阶逼近问题,给出了次数从n到n-m(1≤m≤n-1)的降阶逼近的方法.在逼近过程中,要求低阶球形控制点的Bézier曲面包含原来的实体,同时两者的差别在某种意义下尽可能地小.还给出了一些例子来说明该方法.

The problem of degree reduction of ball-control-point Bezier surfaces over triangular domain was discussed. A method to reduce degree from n to n-m （1≤m≤n-1） was proposed. In the method, the lower-degree ball-control-point Bezier surface was required to enclose the given original surface and the difference between the two surfaces was as small as possible. Some examples were provided to illustrate the method.