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DOI:
Journal of Software:2000.11(9):1202-1206

带端点插值条件的Bézier曲线降多阶逼近
陈国栋,王国瑾
(浙江大学CAD&CG国家重点实验室,杭州,310027;浙江大学数学系,杭州,310027)
Multidegree Reduction of Bézier Curves with Conditions of Endpoint Interpolations
CHEN Guo-dong,WANG Guo-jin
()
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Received:February 28, 2000    Revised:April 13, 2000
> 中文摘要: 研究了两端点具有任意阶插值条件的Bézier曲线降多阶逼近的问题.对于给定的首末端点的各阶插值条件,给出了一种新的一次降多阶逼近算法,应用Chebyshev多项式逼近理论达到了满足端点插值条件下的近似最佳一致逼近.此算法易于实现,误差计算简单,且所得降阶曲线具有很好的逼近效果,结合分割算法,可获得相当高的误差收敛速度.
Abstract:In this paper, the authors study the multidegree reduction of Bézier curves with arbitrary degree interpolation conditions of two endpoint. For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained. This algorithm is easy to implement and simple for error estimation. The approximation effects of the degree reduction curves are very good. Combined with subdivision algorithm, it can reach a higher rate of error convergence.
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基金项目:本文研究得到国家自然科学基金(No.69973041)、浙江省自然科学基金(No.698025)和国家973高科技项目基金(No.G1998030600)资助. 本文研究得到国家自然科学基金(No.69973041)、浙江省自然科学基金(No.698025)和国家973高科技项目基金(No.G1998030600)资助.
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陈国栋,王国瑾.带端点插值条件的Bézier曲线降多阶逼近.软件学报,2000,11(9):1202-1206

CHEN Guo-dong,WANG Guo-jin.Multidegree Reduction of Bézier Curves with Conditions of Endpoint Interpolations.Journal of Software,2000,11(9):1202-1206