一类新的(2n-1)点二重动态逼近细分  

A NEW FAMILY OF(2n-1)-POINT BINARY NON-STATIONARY APPROXIMATING SUBDIVISION SCHEMES

作　　者：张莉[1] 孙燕[1] 檀结庆[1] 时军[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《计算数学》2017年第1期59-69,共11页Mathematica Numerica Sinica

基　　金：国家自然科学基金重点项目(U1135003);国家自然科学基金(61472466;61100126);中国博士后科学基金面上资助项目(2015M571926);浙江大学CAD;CG国家重点实验室开放课题(A1607)

摘　　要：利用正弦函数构造了一类新的带有形状参数ω的(2n-1)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的C^k连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.In this paper, a new family of （2n - 1）-point binary non-stationary approximating subdivision schemes with shape parameter ω is presented with the help of the sine function. With the changing of n and w, the theoretical analysis of support length and continuities of the schemes are also given. The corresponding stationary schemes include the methods given by Chaikin, Hormann, Dyn, Daniel and Hassan. With the same control points and the same continuities for the limit curves, comparisons with other methods are given. It shows that the new family of schemes can generate limit curves with better representability than the others.

关 键 词：动态细分格式 逼近细分 正弦函数 形状参数 

分 类 号：O174.41[理学—数学]