In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference invariants, and this approach enables one to obtain the corresponding discrete invariant curve flows simultaneously. Several examples in the cases of centro-affine plane, pseudo-Euclidean plane, and high-dimensional centro-affine space are presented.

中文翻译：

---

离散不变曲线流，正交多项式和移动框架

本文提出了一种基于正交多项式（OPs）的方法来生成离散的运动帧和不变量。结果表明，运算符可以为离散运动帧以及相关的不变量提供显式表达式，并且这种方法使人们能够同时获得相应的不变量不变曲线流。给出了中心仿射平面，拟欧几里德平面和高维中心仿射空间的几个例子。