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中文摘要：
在对B样条曲线进行绘制和分析时,一个常用的方法是通过细分控制多边形近似B样条曲线,其中对控制多边形到曲线的距离的上界进行估计是影响细分深度的关键因素.为了获得更紧致的距离上界,从而减小折线近似的数据量,利用控制多边形的二阶差分的模以及前两阶差分之间的夹角,并通过在每一步细分过程中可能发生的最大变化的累加和来估计局部距离的上界,使得在前两阶差分之间的夹角较小时可以得到较为紧致的上界.实验结果表明,针对平滑的曲线,采用文中方法有效地降低了估计上界.
英文摘要：
In order to be rendered or analyzed,a B-spline curve is often approximated by its control polygon after subdivision.In this approximating process,the distance between the curve and its control polygon is critical to determine the depth of subdivision.In order to achieve lower bound of the distance and reduce the segment needed for approximation,this paper proposes an upper bound only related to the norm of second order forward difference of the control polygon and the angle between the first and second order forward differences,by bounding the accumulating position changes of the control polygon through the subdivision process.Thus more compact bound can be achieved when this angle is small.Experimental results shows when the curve is smooth,this estimation could yield better result compared to previous methods.
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