The Construction of a New Class of Orthogonal Functions over Triangular Domain
三角域上一类正交函数系的构造

V-system is a complete orthogonal system on L_20,1], 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.