【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 .更多还原

【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.更多还原