The 3-D digital geometric model processing, especially 3-D data acquisition, feature extraction, spectrum analysis, model classification and retrieval technology have been attracted much attention in recent years. A complete and optimal generating algorithm for a class of orthogonal function system, called V₂-System, is proposed in this paper. It has some advantages to analyze spectrum using V₂-System, such as save storage space and raise algorithm efficiency, etc. Firstly, exact expression and generating process of V₂-System is given. Secondly, a method of constructing quadratic surface model is proposed. This method construct quadratic surfaces with different accuracy and numbers freely on basis of triangular faces, consequently, it provides many conveniences for tests. Thirdly, it is given that a Bézier surface can be expressed with finite terms exactly in V₂-System. It suggests a technology on data compression. Finally, according to frequency spectrums of surface model, V₂-Descriptors and V₂-Distances are calculated. Based on V₂-Distances, different quadratic surface models are classified. It lays the foundation of model retrieval.