Moving frames are local orthonormal coordinate systems that provide a reference similar to the Euclidean frame in the neighborhood of a point P. Unlike the classical Cartesian coordinate system, moving frames are constructed at every grid point. The tangent vectors of moving frames may vary in direction and magnitude. In an isotropic medium, their orientations and lengths can appear random; however, they still lie on the tangent plane or tangent volume of the domain to represent the shape of that domain. The direction and magnitude of moving frames can be organized or aligned by a signal, such as a wave or light propagation described by PDEs.