基于正交完备U-系统的参数曲线图组表达

为了探索参数曲线图组的频谱性质,引进一类属于L20,1]的正交完备分片k次多项式系统（简称U-系统）.该系统下的U级数展开式具有良好的平方逼近及一致逼近性质,而且能用有限项U级数实现对分段k次多项式参数曲线图组的精确表达;基于U-系统理论,给出了用以计算给定几何图组U-谱的信息转换算法,该算法具有直观、简便、快速的特点.构建的数据处理平台可用于几何信息的分析与综合,并且能在信息安全（信息隐藏、数字水印）及模式识别等方面有实用价值;提供了用U-系统表达参数曲线图组的实验图例.

Representation for a Group of Parametric Curves Based on the Orthogonal Complete U-System

In order to probe into the properties of frequency spectrum for a group of parametric curves, a class of orthogonal complete piecewise k-degree polynomials in L 20,1],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 express a group of parametric curves which are piecewise k-degree polynomials in a number of finite terms of U-series. Based on U-system, the transfer process is described, by which U-spectrum is obtained for a given group of parametric curves; The algorithm is visible, simple and fast; The program for processing data can be used to analyze and synthesize geometric information, and may have applications in the field such as information security (information hiding, watermarking), and pattern recognition etc. Some graphic examples of check test for expressing a group of parametric curves in U-system are given.