\((\alpha,A)\)-manifolds (Q5948719)

By a differential manifold digitalization one can understand a sampling of a discrete set of points from a manifold. If the sampling set is finite, the coordinates can be stored in a computer memory, but then the differential structure of the manifold is lost. NEWLINENEWLINENEWLINEIn this paper, the author defines the notion of \((\alpha,A)\)-manifold that is a discrete sampling without a complete loss of the differential structure of a manifold. One application of an \((\alpha,A)\)-manifold is a type of manifold digitalization. The model presents a computer simulation of the differential geometric information for the digitalized curves, surfaces, and other types of manifolds.