Geodesic polyhedra and nets

Abstract

Geodesics have a fundamental role in geometry of curved surfaces and manifolds, as well as in discrete geometry. We are going to expand some known facts about geodesics in regular differential geometry to the discrete geometry. We present a discrete analogy of the smooth surfaces parameterized by geodesics. The goal of our consideration is the definition of discrete surfaces generated by geodesics, studying of their properties and finding the algorithm for the generation of these surfaces.