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《Computer Engineering and Applications》 2008-08
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Discrete representation and fast algorithm of new class of orthogonal system

WANG Xiao-chun1,SONG Rui-xia2 1.College of Sciences,Beijing Forestry University,Beijing 100083,China2.College of Sciences,North China University of Technology,Beijing 100041,China  
V system is a new class of complete orthogonal system,which consists of piecewise polynomials in L2[0,1].The V system has multiresolution property and global/local property.It also has great advantages in representing geometric models.However,the fast algorithm of V transform is difficult to design.Using Haar functions and Legendre polynomials a new class of function system,W system,is constructed in this paper,which consists of piecewise polynomials.The approximating effect by W series is the same as that by V series.In this paper,the fast algorithm of discrete W transform of degree 1 is proposed,which partially solves the difficulties in directly designing the fast algorithm of V system.
【Fund】: 国家重点基础研究发展规划( 973)( the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000);; 国家自然科学基金( the National Natural Science Foundation of China under Grant No.60133020 No.10671002 No.10771002);; 浙江大学CAD&CG国家重点实验室开放课题( No.A0503);; 澳门科技发展基金( No.045/2006/A)
【CateGory Index】: TP301
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