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Rendering Non-Euclidean Space in Real-Time Using Spherical and Hyperbolic Trigonometry

Child, C. H. T. ORCID: 0000-0001-5425-2308, Osudin, D. & He, Y-H. ORCID: 0000-0002-0787-8380 (2019). Rendering Non-Euclidean Space in Real-Time Using Spherical and Hyperbolic Trigonometry. Computational Science – ICCS 2019, 19th International Conference, Proceedings, Part V, 11540, pp. 543-550. doi: 10.1007/978-3-030-22750-0_49


We introduce a method of calculating and rendering shapes in a non-Euclidean 2D space in real-time using hyperbolic and spherical trigonometry. We record the objects’ parameters in a polar coordinate system and use azimuthal equidistant projection to render the space onto the screen. We discuss the complexity of this method, renderings produced, limitations and possible applications of the created software as well as potential future developments.

Publication Type: Article
Additional Information: The final authenticated version is available online at
Publisher Keywords: non-Euclidean geometry, spherical trigonometry, hyperbolic trigonometry, azimuthal equidistant projection, Polar coordinate system, real-time
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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