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.
@article{arxiv.2409.05460,
title = {Holonomy: A Virtual Reality Exploration of Hyperbolic Geometry},
author = {Martin Skrodzki and Scott Jochems and Joris Rijsdijk and Ravi Snellenberg and Rafael Bidarra},
journal= {arXiv preprint arXiv:2409.05460},
year = {2024}
}
Comments
Published at the WEB 3D 2024 conference, September 25-27, 2024, Guimaraes, Portugal. in Proceedings of the 29th International ACM Conference on 3D Web Technology. 2024