四点四重细分法  

FOUR-POINTT QUATERNARY SUBDIVISION SCHEM

作　　者：刘植[1] 李睿 王旭辉[2] Liu Zhi;Li Rui;Wang Xuhui(School of Mathematics,Hefei University of Technology,Hefei 230009;School of Mathematics,Hohai university,Nanjing 210098)

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]河海大学数学学院,南京210098

出　　处：《高等学校计算数学学报》2023年第4期289-302,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(62172135,61772167).

摘　　要：1引言。细分方法是一种由计算机根据给定的细分规则对初始控制顶点或初始控制多边形进行不断加细,进而生成曲线或曲面的离散造型方法,近年来已成为CAGD&CG领域的一项重要研究内容.因其具有算法简单高效、适用性强等优点,细分方法在几何造型中得到了广泛的应用.A class of four-point quaternary subdivision schemes are proposed,and the continuity,support interval and polynomial reproduction property are analyzed.By selecting appropriate parameter Qo,a non-stationary four-point qua-ternary subdivision scheme with C3 continuity and better fitting effect is obtained.The comparison with the legend shows that the proposed non-stationary four-point quaternary subdivision scheme has strong applicability,and the limit curve gen-erated by it is closer to the initial control polygon which can better represent the shape of items.

关 键 词：几何造型 控制顶点 细分法 CAGD 控制多边形 造型方法 计算机 细分方法 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]