Journal for Geometry and Graphics 27 (2023), No. 2, 227--236
Copyright by the authors licensed under CC BY SA 4.0
Non-Euclidean Descriptive Geometry in Engineering and Applied Visual Arts
Danail Brezov
University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria
danail.brezov@gmail.com
Yana Kancheva
University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria
kancheva fgs@uacg.bg
Tania Nikova
(1) University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria
(2) Bulgarian Academy of Sciences, Sofia, Bulgaria
tnikova@iomt.bas.bg
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.
Keywords: Descriptive geometry, curvature, perspective, virtual reality.
MSC: 51N05; 51M04, 51N15.
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