三角域上一类正交函数系的构造

THE CONSTRUCTION OF A NEW CLASS OF ORTHOGONAL FUNCTIONS OVER TRIANGULAR DOMAIN

V系统是作者2005年构造的一类L_2[0,1]空间上的正交完备函数系.κ次V系统由κ次分片多项式组成,具有多分辨特性,是Haar小波函数的推广.基于V系统的正交表达,可以对CAGD中常见的几何模型用有限项V-级数做到精确重构,完全消除Gibbs现象,这是有限项Fourier级数或连续小波级数不能做到的.针对多变量情形,给出了三角域上的κ次正交V系统的构造方法.三角域上的V系统的重要应用显现在对3D复杂几何图组的整体频谱分析上.

V-system is a complete orthogonal system on L2[0, 1], which was constructed in 2005 by the author of this paper. V-system of degree k is composed of piecewise k-order polynomials, has multiresolution property, and is a generalization of Harr wavelet. Based on the V-system and by using finite terms of V-series, it can be realized to reconstruct the common geometric models exactly and without Gibbs phenomena which can not avoid in the case of Fourier or continuous wavelets in CAGD. In this paper, the V-system of degree k over triangular domain is considered. The obtained results can be used for the analysis of frequency spectrum for 3D complex group of geometric models.