Geodesic
Non-Euclidean Descriptive Geometry in Engineering and Applied Visual Arts
Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 227-236 Cet article a éte moissonné depuis la source Heldermann Verlag

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We consider the non-Euclidean descriptive geometry of thee-dimensional homogeneous spaces and its possible applications to virtual reality, architecture and design. As a preparation for this mathematical adventure, we first study curved screens in Euclidean space, which are later used in the more general case. Two-dimensional models are used as an illustration of certain features. The geometries of the sphere S3 and hyperbolic space H3 are introduced projectively in analogy with the Euclidean case, but with some new peculiar features. Potential applications can be found in optics, relativity and quantum mechanics, visual arts, as well as educational and gaming virtual/augmented reality devices.
Classification : 51N05, 51M04, 51N15
Mots-clés : Descriptive geometry, curvature, perspective, virtual reality 
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D. Brezov; Y. Kancheva; T. Nikova . Non-Euclidean Descriptive Geometry in Engineering and Applied Visual Arts. Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 227-236. http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a9/