Approximation of conic section by quartic Bezier curve with endpoints continuity condition
Approximation of conic section by quartic Bezier curve with endpoints continuity condition
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端点连续条件下四次贝塞尔曲线逼近圆锥曲线
DOI：
10.1007/s11766-017-3434-3
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发表时间：
2017-03-01
影响因子：
1
通讯作者：
Xu, Chen-dong
中科院分区：
文献类型：
--
作者：
Liu, Yu;Xu, Chen-dong
基于圆弧的四次Bezier逼近，提出了一种用四次Bezier曲线逼近圆锥曲线的新方法。本文给出了二次曲线到逼近曲线的Hausdorff距离的上界，并证明了误差界的逼近阶为8。此外，我们的方法产生四次G（2）连续样条逼近的圆锥曲线时，使用细分格式，并通过一些数值例子证明了这种方法的有效性。
A new method for approximation of conic section by quartic Bezier curve is presented, based on the quartic Bezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G(2) continuous spline approximation of conic section when using the subdivision scheme, and the effectiveness of this method is demonstrated by some numerical examples.