Journal of Software:2000.11(9):1263-1267

Preserving-Convexity and Fractal Properties of a Nonlinear Subdivision Scheme
DING You dong,HUA Xuan ji
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Received:February 28, 2000    Revised:April 26, 2000
> 中文摘要: 在分析Dyn等人的经典4点线性插值离散细分格式的基础上,提出了一类函数型非线性离散细分格式,它具有保凸性质,即在满足一定条件时, 这种格式保证了对于凸数据,其每一步细分多边形都是凸的,从而极限曲线也是凸的.数值例子说明,在不光滑情况下,这种格式会产生具有分形性质的曲线.
Abstract:Based on the analysis of the classifical 4 point linear interpolatory subdivision scheme introduced by Dyn, a functional nonlinear discrete subdivision scheme is presented. This scheme has the preserving convexity property, i.e., for any given convex discrete data, when some conditions are satisfied, the subdivision polygon curve produced in any step by this scheme is convex, so the limit curve is also convex. Some numerical examples show that the limit curves are fractal like when the smooth condition is not satisfied.
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基金项目:本文研究得到国家自然科学基金(No.69603009)、上海市博士后基金(No.KL28001)和上海市高校青年基金(No.B-54)资助. 本文研究得到国家自然科学基金(No.69603009)、上海市博士后基金(No.KL28001)和上海市高校青年基金(No.B-54)资助.
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DING You dong,HUA Xuan ji.Preserving-Convexity and Fractal Properties of a Nonlinear Subdivision Scheme.Journal of Software,2000,11(9):1263-1267