摘要
V系统是L2[0,1]上一类新的完备正交函数系,它由分段多项式组成,具有多分辨分析特性和全局/局部性,在几何模型的正交表达方面具有明显的优势,但其快速算法难以得到。利用Haar函数和Legendre多项式构造了一类由分段次多项式组成的函数系(文中称为W系),在该函数系上作函数逼近的效果等同于在V系统上的效果,并进一步讨论了一次离散W变换的快速算法,从而部分克服了直接对V系统设计快速算法的困难。
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.
出处
《计算机工程与应用》
CSCD
北大核心
2008年第8期40-44,共5页
Computer Engineering and Applications
基金
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)
