Rendering Non-Euclidean Space in Virtual Reality Using Portals

Abstract

Simulating non-Euclidean geometry in virtual reality is of interest to a wide variety of fields of research. However it is still quite a challenge. Various methods are already known, but they vary greatly in performance and applicability. This paper compares some methods of rendering a non-Euclidean space. We focus on the order-5 square tiling that can be found in the hyperbolic plane, but the methods used are also relevant to other non-Euclidean spaces. We render this space using portals with two different implementations: one using render textures, an one using stencil polygons. Through an experiment where we measured and compared the frame rate of each method, we have found that, even with a small number of portals, the stencil polygon approach is more than two times as efficient. However, this method is limited in the number of portals, whereas render textures can be used for any number of portals.