Games in Non-Euclidean Geometries

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When applied to video games, the term ‘non-Euclidean’ is not always used strictly in its mathematical sense. It is often employed to describe virtual worlds whose properties diverge from what we would expect of the world we live in. There are, however, approaches, that successfully utilize properties of non-Euclidean geometry as a game mechanic both in two and in three dimensions. Additionally, the existing rendering pipeline of graphic cards allows for simple visualization of these geometries in 3D with only slight modifications making even virtual reality exploration of these geometries possible. To highlight the differences of these geometries, in this work we want to examine how well classic games would translate from Euclidean to non-Euclidean geometries. Properties of the game play and rules are first examined in Euclidean space for games such as football or billiards. We then describe how these properties change and what rules would need to be adapted when entering spherical or hyperbolic geometry. Furthermore, we investigate challenges in their visualization and compare our findings to the existing approaches.

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5th Croatian Conference on Geometry and Graphics

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