中文摘要：

为了在数字几何信息处理中采用信号处理中常用的频谱分析方法,需要选择恰当的正交系.通过给出三角域上一类正交系（称为三角域上二次V-系统）的精确数学表达,作为这类新的正交系的一个具体应用,提出一种曲面模型的频谱分析方法.该方法将由分片二次曲面构成的几何模型在三角域二次V-系统下展开,得到相应的频谱,利用这些频谱对几何信息进行精确重构,实现了几何对象的正交表达.与已有方法相比,采用文中提出的用二次V-系统表达的几何模型可使数据量大大减少.最后通过实验结果表明该方法是切实可行的.

英文摘要：

To apply frequency spectrum analysis method,which is commonly used in signal processing and on digital geometry processing,it is necessary to choose a proper orthogonal function system.This paper first presents the detailed mathematic expressions of orthogonal V-system of degree 2 over triangulated domains,and then proposes a frequency spectrum analysis method to surface models,which is a direct application of the new constructed system.The method is to expand a surface model represented by piecewise polynomial of degree 2 in two variables in a V-series and then get the frequency spectrums,with which the surface model can be precisely reconstructed.Therefore orthogonal decomposition and reconstruction of a geometry object can be realized.Compared with the previous research,the expression of geometry information with the V-system of degree 2 has advantage of significant reduction in the quantity of data involved.The experimental results show that the proposed method is practical and feasible.