细分Bézier网的误差估计

An error estimate for the subdivision Bézier net

研究Bezier曲线和Bezier网的相互关系,讨论细分Bezier网的性质,分析细分Bezier网与其相应的Bezier曲线之间的误差,并给出一个相对较优的上界估计,其结果在Bezier曲线的几何计算与图形绘制中都有重要的应用。

The relationship between Bézier curves and their corresponding Bézier nets is studied, and the properties of subdivision Bézier nets are discussed. The error between a Bézier eurve and the eorresponding subdivided Bézier net is analyzed, and an optimal upper bound is given. The result ean be applied in geometrie eomputation and rendering of Bézier eurves.