一类混合型三重细分法  

A Blending Ternary Subdivision Scheme

作　　者：黄丙耀 檀结庆[1] HUANG Bing-yao;TAN Jie-qing(School of Mathematics,Hefei University of Technology,Hefei,Anhui 230601,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601

出　　处：《电子学报》2021年第1期90-98,共9页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61472466)。

摘　　要：文章从几何的视角出发,以四点二重插值细分格式的几何解释为基础,对四点三重插值细分格式的几何意义进行分析,改造格式使其融合逼近细分,进而得到一类带参数的混合型三重细分格式.诸多已有的插值型细分和逼近型细分都是该格式的特例,采用生成多项式方法分析了其Ck连续性.得到了一种新的C4连续五点三重曲线细分格式.数值实例表明,利用提出的混合型细分法通过参数的适当选取可以实现对极限曲线的形状控制.From the perspective of geometry,based on the geometric interpretation of the four-point binary interpolating subdivision scheme,this paper analyzes the geometric meaning of the four-point ternary interpolating subdivision scheme,and modify the scheme to combine approximating subdivision;then a blending ternary subdivision scheme with parameters is obtained.Many existing interpolating subdivision schemes and approximating subdivision schemes can be seen as special cases of this scheme.We also use generating polynomial method to analyze the C k continuity of limit curve produced by the blending subdivision.A new C 4 continuous five-point ternary curve subdivision scheme is obtained.Numerical examples show that the proposed blending subdivision scheme can be used to control the shape of limit curves by selecting appropriate parameters.

关 键 词：三重细分法 混合型 插值细分 逼近细分 Ck连续性 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]