Sample-based polynomial approximation of rational Bézier curves
Sample-based polynomial approximation of rational Bézier curves
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DOI：
10.1016/j.cam.2010.08.008
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Lizheng Lu
中科院分区：
文献类型：
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作者：
Lizheng Lu
提出了有理bsamizier曲线多项式逼近的一种迭代方法。从初始的bsamzier曲线出发，采用加权渐进迭代逼近的方法逐步调整其控制点。利用采样点的梯形规则计算的lp误差来指导迭代逼近。我们在每次迭代中通过一个预定义的因子来减小lp误差，以获得误差最小的最佳逼近。数值算例证明了该方法的快速收敛性，并表明采用l1误差准则得到的结果优于采用l2误差和L∞误差准则得到的结果。
We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The Lp-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the Lp-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L1-error criterion are better than those obtained using the L2-error and L∞-error criteria.