一种基于线性无关函数组的三角域V-系统构造  

A kind of a triangular V-system construction scheme based on linear independent function groups

作　　者：王相海[1,2] 李炜 吕芳 宋传鸣[2] WANG Xianghai;LI Wei;LU Fang;SONG Chuanming(School of Mathematics,Liaoning Normal University,Dalian 116029,China;School of Computer and Information Technology,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029 [2]辽宁师范大学计算机与信息技术学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2019年第3期330-334,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(41671439);辽宁省高等学校创新团队支持计划项目(LT2017013)

摘　　要：近年来随着非连续正交函数系的发展,出现了一类L^2[0,1]上的正交完备函数系,即U-系统和V-系统,它们对连续和非连续信号具有极强的表达能力.三角面片因在复杂曲面造型中具有灵活、方便和适应性强的特性而受到重视,在三维几何建模中有着显著的优势.本文提出一种基于线性无关函数组的三角域1次V-系统构造方案.首先,在1级剖分三角域下选择一组线性无关的函数组;其次,对其进行Gram-Schmidt正交化,获得12个规范正交函数;再次,通过对其中的生成元进行旋转、压缩、平移等操作生成1次V-系统的其他函数.进一步对该V-系统的特性进行了分析,同时对三角域上V-系统在实际应用中的过程进行说明.所构造的基于线性无关函数组的1次V-系统的生成元避免了大量0的出现,在应用中可以更加有效的提取三维几何模型的频谱信息.In recent years,with the development of non-continuous orthogonal function systems,a class of orthogonal complete function systems on L^2 [0,1],U-system and V-system,have emerged,which have strong expression ability for continuous and discontinuous signals.Triangular patches are valued for their flexibility,convenience,and adaptability in complex surface modeling,and have significant advantages in 3D geometric modeling.This paper proposes a triangular domain 1st V-system construction scheme based on linear independent function groups.First,select a set of linearly independent function groups under the 1st-level triangulation domain,then perform Gram-Schmidt orthogonalization to obtain 12 canonical orthogonal functions,and then rotate,compress and translate the generators.Other operations generate other functions of the V-system in turn;At the same time,the process of the V-system on the triangular domain in practical application is explained.The generators of the 1st V-system based on the linear independent function group constructed in this paper avoid a large number of 0,and the spectrum information of the 3D geometric model can be extracted more effectively in the application.

关 键 词：V-系统 三角域 线性无关函数组 非连续正交系 生成元 剖分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]