In order to explore the properties of frequency spectrum for geometric modeling, a complete orthogonal piecewise k -degree polynomials in
[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.
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