中文摘要：

一维情形下的W系统是一类新的由分段多项式构成的混合正交函数系.文中对二维情形的W系统进行研究,利用Haar矩阵和一组规范正交的二元多项式,采用递归的方式,以及复制、平移、压缩的方法,构造出了三角域上的W系统,它是一类既包含连续函数又包含各个层次间断的非连续函数的规范正交函数系.三角域上W系统与V系统是等价的,然而W系统的构造过程较V系统更简捷.实验检测例子表明,利用文中给出的系统可以实现由多个分离曲面组成的曲面组的正交分解,从而实现对曲面组的精确重构.

英文摘要：

W-system on L2 is a kind of hybrid orthogonal function system constructed by untilizing Haar function and Legendre polynomials.In this paper,we extend the one-dimensional W-system to the case of two variables.The proposed 2D W-system over triangular domain is recursively constructed with Haar matrix and a group of orthonormal bivariate polynomials,using the squeezing,shifting and duplicating methods.The constructed hybrid orthogonal function system is composed of both continuous functions and functions with jumps.It turns out that the new function system is equivalent to the V-system over triangular domain,but its construction process is much simpler.Finally this paper shows that the orthogonal decomposition of a surface group can be realized by the proposed orthogonal function system,and the surface group can be perfectly reconstructed with the obtained frequency spectra.