基于FFT的三维CAD模型形状描述

Shape Description of 3D CAD Models Using FFT

针对三维CAD模型,以快速傅立叶变换为基础,建立了一种CAD模型几何形状描述方法。首先,在对模型几何面进行统一表示的基础上,根据模型边界表示中的面片邻接信息,采用完全图旅行商回路算法建立模型的面片序列,并由参考模型保证面片序列的一致性;然后,根据面片序列将模型几何信息转换为5个一维离散信号,并对信号进行采样和幅度缩放,通过快速傅立叶变换(Fast Fourier Transform,FFT)将信号转换到频域,以频域振幅作为三维CAD模型几何形状的描述。如果忽略面片序列引起的偏差,该方法描述模型几何形状的能力与FFT描述离散信号的能力类似。通过实例阐述了描述方法的直观可解释性。

A Fast Fourier-Transform based shape description method for 3D CAD models was presented. First,based on uniform representation of geometric facet and according to the facet adjacency relation in the CAD model, a facet sequence was achieved with the TSP（Traveling Salesman Problem） algorithm for complete graphs, and the consistency of the facet sequence was ensured by adopting a reference CAD model. Then,according to the facet sequence, the geometric information was transformed into five 1D discrete signals. After sampling and amplification, the discrete signals were transformed into frequency domain with FFT and the description of the CAD model was composed of the magnitudes in frequency domain. If ignoring the deviation caused by facet sequence, describing geometric shapes of CAD models with the method presented in this paper is similar to describing discrete signals with FFT. Experiments were elaborated for physical interpretability too.