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中文摘要：
为提高Bézier曲线降阶的稳定性,提出以基于L2范数的逼近误差为指导的一种迭代算法。该算法从一条初始Bézier曲线开始逐渐地对其控制顶点进行偏移,得到具有误差最小的逼近曲线；同时,应用线性搜索方法来优化控制顶点的偏移,使得在每次迭代后逼近误差可以达到局部最小。实例结果表明了该算法的快速收敛性。
英文摘要：
In order to improve the stability for degree reduction of Bézier curves, this paper presents an iterative algorithm to minimize the approximation error based on the L2-norm. Starting with an initial Bézier curve, control points are gradually displaced to obtain the approximate curve with a minimal error. The linear search algorithm is adopted to optimize the displacements of the control points, so that the error is reduced to be locally minimal after each iteration step. Finally, numerical examples demonstrate the fast convergence of the proposed algorithm.
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