Abstract
In order to explore the properties of frequency spectrum for geometric modeling, a complete orthogonal piecewise k -degree polynomials in L 2[0,1], so-called U-system, is introduced. The expansion in U-series has advantageous properties for approximations in both quadratic norm and uniform. Using U-system with finite items, it can be realized to exactly represent geometric modeling. This paper analyzes the properties of frequency spectrum for geometric modeling in theory and gives some interesting results in geometric transform. By comparing U-system with Fourier system, experiments indicate that U-system is more suitable for analyzing frequency spectrum for geometric modeling than Fourier system is.
This project is supported by “Mathematics mechanization method and its application on Information Technology” (the National Grand Fundamental Research 973 Program of China under Grant No.2004CB3180000), the National Natural Science Foundation of China (No. 60133020), Guangdong Provincial Science and Technology Foundation (No. 2004A10302005, No. 051Z205005) and The China Scholarship Council.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Cai, Z., Ma, H., Sun, W., Qi, D. (2006). Analysis of Frequency Spectrum for Geometric Modeling in Digital Geometry. In: Qian, T., Vai, M.I., Xu, Y. (eds) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7778-6_39
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DOI: https://doi.org/10.1007/978-3-7643-7778-6_39
Publisher Name: Birkhäuser Basel
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