In this diploma thesis we delve into ray tracing in non-Euclidean spaces. Ray tracing is a method that simulates traveling of light rays and is used in computer graphics to draw realistic images. Usually it is implemented in standard Euclidean space. We present the notion of geodesic curves, which allow us to trace rays in non-Euclidean spaces. Then, a general system of differential equations determining geodesics is derived and numerical methods for solving it are presented. We implement and apply the algorithm to the Euclidean space, a flat torus and a two-dimensional sphere, and then explain the results. Finally, we visually present the properties of these spaces, which are more difficult to understand using only the corresponding mathematical models.
|
