任意次有理Bzier曲线/面对其控制多边形/网格的整体或局部逼近

THE GLOBAL OR LOCAL APPROXIMATION OF RATIONAL BEZIER CURVE/SURFACE OF ARBITRARY DEGREE TO ITS CONTROL POLYGON/NET

本文给出一种利用权因子构造整体或局部逼近控制多边形／网格的有理Ｂｅｚｉｅｒ曲线／面的方法．该法适用于任意次数的有理Ｂｅｚｉｅｒ曲线／面、任意的控制多边形／网格，权因子的选择和逼近度的估计都只依赖于一个参数ω．当ω→＋∞时，相应的曲线／面可按预定要求整体或局部地逼近其控制多边形／网格，逼近阶为Ｏ（１／ω）

An approach is developed to construct the rational Bezier curves/ surfaces of arbitrary degree that approximate to given control polygon/net globally or locally by select- ing their weights properly. With this approach, the selection of weights and the estimation of approximation order simply depend on a parameter w. When ω →+∞,the rational B6zier curves/surfaces approximate to the given control polygon/net globally or locally, and the approximation order is O (ω/1).