Efficient digitizing of sculptured surfaces

In modern manufacturing industry, many tasks cannot be performed without CAD models. However, many prototypes come without prior CAD data for various reasons. Therefore, CAD information of these prototypes is obtained by means of reverse engineering. The discrete depths of the model surface are measured by digitizing machines. These depths form a dense mesh which can be used as the CAD model for further processing.; A cost-efficient digitizing approach of reverse engineering cannot only reduce the measuring time, but also maintain accuracy. The fundamental question of point-by-point digitizing is where the digitizing points should be such that the surface can be accurately portrayed and the number of digitizing points is small. In this dissertation, three new techniques of non-uniform digitizing of sculptured surfaces are presented.; The first approach uses short time Fourier transform (STFT) to divide the entire surface into small blocks. The digitizing interval for each block is determined according to the local Nyquist frequency. The associated advantages are the significant reduction of digitizing points and the modest accuracy.; An extended short time Fourier transform (ESTFT) is followed to improve the frequency resolution of STFT. The windowed signal is extended to its surrounding with sinusoidal signals which maximize the smoothness of the boundaries. The behavior of the extra signals in the spectrum is predictable because the attributes of the sinusoidal signals are obtained while smoothing the boundaries. Because of the increased length of the total signal, the frequency resolution is increased.; The wavelet transform is introduced as the third method in the dissertation. The wavelet transform uses non-periodic and compactly-supported basis functions to describe a signal. For most of the sculptured surfaces which contain irregular profiles, the wavelet transform can achieve faster convergence by retaining fewer basis functions. In addition, each wavelet has its own corresponding spatial position due to its unique localization property. The digitizing locations can therefore be positioned more precisely.; Finally a guideline is provided for readers to choose the usage of the three digitizing approaches for different applications and requirements.