双调节因子的渐进插值Loop细分方法  

Progressive Interpolation Loop Subdivision Method with Dual Adjustable Factors

作　　者：时明珠 刘华勇 SHI Mingzhu;LIU Huayong(School of Mathematics and Physics,Anhui Jianzhu University,Hefei 230601,China)

机构地区：[1]安徽建筑大学数理学院,安徽合肥230601

出　　处：《安徽工程大学学报》2023年第6期77-83,91,共8页Journal of Anhui Polytechnic University

基　　金：安徽省高等学校自然科学基金重点项目(KJ2021A0630,KJ2021A0633,KJ2021A0634);安徽省级质量工程项目(2020kfkc163,2021jxtd070);安徽建筑大学校级质量工程项目(2020kj15,2020jy22)。

摘　　要：针对逼近型Loop细分方法产生的极限曲面易凹陷收缩等问题,本文提出了双调节因子的渐进插值Loop细分方法。该方法分别在两步Loop细分方法、渐进迭代过程中引入不同的调节因子,使生成的极限曲面插值于初始控制网格的全部顶点,同时又具有收敛性、局部性和全局性,不仅可以灵活地对极限曲面的形状进行控制,而且一定程度上扩大了形状的可控范围。从数值实验可以看出,该方法通过改变双调节因子的值,可以较好地保留初始三角网格的特征,且生成的极限曲面收缩程度较小,是可行有效的。Aiming at the problem that the limit surface produced by the approximate Loop subdivision method tends to sag and shrink,a progressive interpolation Loop subdivision method with dual adjustable factors is proposed.This method introduces different adjustable factors in the two-phase Loop subdivision method and the progressive iteration process,so that the generated limit surface is interpolated to all the vertices of the initial control mesh.Meanwhile,it has astringency,locality and globality.It can not only flexibly control the shape of limit surface,but also expand the controllable range of shape to a certain extent.From the numerical experiments,it can be seen that the method can retain the characteristics of the initial triangular mesh better by changing the value of dual adjustable factors,and the generated limit surface has a small degree of shrinkage,which proves the method to be feasible and effective.

关 键 词：LOOP细分 渐进插值 双调节因子 收敛性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O241.5[自动化与计算机技术—计算机科学与技术]