We are interested in Non-Euclidean Geometries possibly with Non-Trivial Topologies.

In this context, the ambient space is defined mathematically as a Three-Dimensional Riemannian Manifold. Consequently, since the underlying geometry is not flat, rays in such spaces are “curved”.

Graph of Functions

Space geometry modeled as the three-dimensional graph of a function of three variables.

Local Diffeomorphisms

Space geometry modeled using a general deformation of the 3D space that is localized by a gaussian bump function.