V-系统是一类由分片多项式构成的正交函数系,函数系中既有连续函数又有间断函数.它既能用于信号处理,也能适应几何图组整体表达,在计算机辅助几何设计(CAGD)中可以精确重构几何造型信息,做到消除Gibbs现象,从而可以进行复杂造型的整体特征分析.利用三角域上V-系统进行三维复杂几何模型的重构实验,实验结果表明,V-系统对复杂的、连续间断并存的几何信息重构特别有效,这与经典的连续正交函数系及强间断的Walsh及Haar函数系有本质的不同.

The V-system is a new class of complete orthogonal functions system in L2[0,1], which is composed of piecewise kth-order polynomials. There are continuous functions as well as discontinuous functions in V-system. It can be used for signal processing and global expression of a geometric graph group. Moreover, the information of geometric modeling in CAGD can be reconstructed precisely by finite terms of V-system without Gibbs phenomenon, so global feature analysis of the complicated modeling can be implemented. This paper shows that 3-dimension complicated geometric model can be reconstructed by the V-system over triangulated domain. The experiment results indicate that V-system is an effective tool used to reconstruct complicated geometric information with both continuous and discontinuous signals. This is the essential difference among V-system, the classical complete orthogonal system with continuous functions and Walsh and Haar system which include intense discontinuous functions.

Supported by the National Natural Science Foundation of China under Grant Nos.10631080,10771002 (国家自然科学基金); the National Basic Research Program of China under Grant No.2004CB318000 (国家重点基础研究发展计划(973)); the Science and Technology Development Fund of Macao SAR of China under Grant No.045/2006/A (澳门科学技术发展基金)