V-系统与几何群组信息的频域表达

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.

V-System and Expression of Geometric Group Information in Frequency Domain

The V-system is a new class of complete orthogonal functions system in L20,1], 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.