Surface Model Analysis Based on Quadratic V-System in Triangular Domain

DOI：

 作者 单位 E-mail 马辉 清华大学 信息技术研究院,北京 100084 neo_young@126.com 林艾静 北京交通大学 理学院,北京 100044 宋瑞霞 北方工业大学 理学院,北京 100041 路海明 清华大学 信息技术研究院,北京 100084

三维数字几何信息的处理,尤其是三维模型数据的获取技术、特征提取、频谱分析及模型分类或检索等技术,备受人们关注.本文给出一套完整的、优化的三角域上一类正交函数系(称为三角域上二次V-系统,V2-系统)的生成算法.基于此算法生成的V2-系统,将给曲面模型的频谱分析带来极大地便利,既能节省存储空间,也能提高模型分解、重构等算法的执行效率.首先给出V2-系统的精确数学表达及高效的构造过程.其次,提出一种二次曲面模型的构造方法,称为自由选取法.该方法以三角面片模型为基础,依据具体需求精度,自由地构造不同面片数的二次曲面模型,为后续实验带来了极大地便利.再次,给出V2-系统中分片二次Bézier 曲面模型的正交表达式,即二次曲面模型可以由V2-系统中有限个基函数精确表达,从而实现了对曲面几何模型的正交分解与重构,并提供了一种三维数据的压缩方法.与此同时,依据几何模型的频谱信息,计算不同曲面模型间的相似度(V2-描述子的“距离”),则可实现不同模型间的初步分类,进而为三维模型检索奠定了基础.

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.
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