Orthogonal Complete U-system and Its Application in CAGD

A class of orthogonal complete piecewise k-degree polynomials in L2[0,1](so-called U-system) is introduced.The expansion in U-series has advantageous properties for approximations in both quadratic norm and uniform,and it can be realized to exactly express a group of parametric curves and surfaces which are piecewise k-degree polynomials with limited number of terms of U-system.Based on U-system,the transfer process is described,by which U-spectrum is obtained for a given group of parametric curves and surfaces.The algorithm is visible,simple and fast.Frequency spectrums obtained under U-system can be used to analyze and synthesize geometric information.U-system may have wide applications in the fields,such as pattern recognition,geometric modeling,and digital image processing etc.In this paper,some graphic examples are tested for expressing a group of parametric curves and surfaces in U-system.