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In Proceedings of International ACM Conference on 3D Web Technology

Holonomy: a virtual environment based on hyperbolic space

Martin Skrodzki, Scott Jochems, Joris Rijsdijk, Ravi Snellenberg, and Rafael Bidarra

Left: Rendering of the hyperbolic virtual environment Holonomy, including a mini-map in the HUD. Hyperbolic effects are visible in the flag and the creeks partially vanishing behind the trees. Right: A player in the physical move area, with the corresponding square tiles marked on the floor.

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Holonomy is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, Holonomy allows users to seamlessly explore an infinite hyperbolic space by physically walking. They use their body as the controller, eliminating the need for teleportation or other artificial VR locomotion methods. This paper discusses the development of Holonomy, highlighting the technical challenges faced and overcome during its creation, including rendering complex hyperbolic environments, populating the space with objects, and implementing algorithms for finding shortest paths in the underlying non-Euclidean geometry. Furthermore, we present a proof-of-concept implementation in the form of a VR navigation game and some preliminary learning outcomes from this implementation.

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Martin Skrodzki, Scott Jochems, Joris Rijsdijk, Ravi Snellenberg, and Rafael Bidarra, Holonomy: a virtual environment based on hyperbolic space, In Proceedings of International ACM Conference on 3D Web Technology, 2024.

BibTex 

@inproceedings{bib:skrodzki:2024,
    author       = { Skrodzki, Martin and Jochems, Scott and Rijsdijk, Joris and Snellenberg, Ravi and Bidarra, Rafael },    
    title        = { Holonomy: a virtual environment based on hyperbolic space },
    booktitle    = { In Proceedings of International ACM Conference on 3D Web Technology },
    year         = { 2024 },
    publisher    = { ACM Press },
    note         = { ISBN 979-8-4007-0689-9/24/09 },
    doi          = { 10.1145/3665318.3677149 },
    url          = { https://publications.graphics.tudelft.nl/papers/19 },
}