摘要
讨论了球形控制点的Bézier曲面的降阶逼近问题.为了简单起见,只考虑了从次数(m,n)到次数(m-1,n)的降阶逼近.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尽可能的小.分别针对插值边界,不插值边界情况在两种范数下给出了问题的解析解,并且给出了逼近误差的界.
The problem of degree reduction of ball control point Bézier surfaces was discussed, For simplicity, only the degree reduction from （m,n） to （m- 1,n） was considered. In the approximation process, it was required that the lower-degree ball control point Bézier surface enclosed the given surface, and at the same time, their differences were to be minimized as soon as possible. Solution to these problems were given, along with error analyses with and without interpolating endpoint conditions, respectively.
基金
国家自然科学基金(10201030)
教育部留学回国人员科研启动基金资助
