三进制四点法的连续性与误差估计  

Continuity and Error Estimate of 4-Point Ternary Stationary Subdivision Scheme

作　　者：朱斌全[1] 曹沅[2] 

机构地区：[1]复旦大学数学研究所,上海200433 [2]复旦大学数学科学学院,上海200433

出　　处：《计算机辅助设计与图形学学报》2006年第1期128-136,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60333010)

摘　　要：2002年,Hassan提出了一类三进制四点法.对比Dyn的四点法,前者的插值极限曲线可以达到C2连续.详细研究了三进制四点细分算法生成的极限曲线的连续性,分别给出了极限曲线C0,C1,C2连续的充分条件和必要条件,并给出了极限曲线在顶点以及中点处的一阶导数与二阶导数显式公式.最后根据算法的二次多项式再生性质,得到算法最高具有三次收敛阶.In 2002, Dr. Hassan presented a novel approach named for 4-point ternary stationary subdivision scheme. Compared with Dyn＇s 4-point scheme, the limit curve generated by Hassan＇s approach reaches C2 continuity. We studied the same topic with great care and worked out the necessary conditions and sufficient conditions for the C^0, C^1,C^2 situations of limit curve. During the derivation, we obtained the explicit expression of the first and second order derivative for limit curve at vertex and mid-point. As the scheme can reproduce polynomials of degree≤2, so it has an error of order O （h^3）.

关 键 词：细分 插值 曲线 三进制 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]