A System for Visualizing the Three-Dimensional Spherical and Elliptic Spaces
Denis I. Migranov · 2021 IEEE 22nd International Conference of Young Professionals in Electron Devices and Materials (EDM) · 2021
Non-Euclidean geometries and spaces find application in various fields of knowledge. The possibilities of computer graphics and visualization make it possible to present such spaces in a way that makes it easy to explore their properties even for people who are not acquainted with the mathematics of non-Euclidean geometry. Not only that, it is also possible to add some interactivity and allow users to explore such spaces freely. In this paper, we present a system for visualizing three-dimensional spherical and elliptic spaces, which are two examples of non-Euclidean spaces. First, we describe the theoretical basis and some algorithms the system is built upon: the group-theoretic way of exploring non-Euclidean spaces and defining transformations of objects lying in them, an algorithm for implementing camera controls similar to those seen in first-person video games, and an algorithm for implementing the distance fog effect in such spaces. Then, we describe the system created based on these approaches and its capabilities.