Non-Euclidean Third Dimension in Games

Hello! In this video we take you on a journey through a small game world and showcase the non-Euclidean transformations of its third dimension.

We stretch the space to get: Euclidean cylinder, hyperbolic geometry, anisotropic version of hyperbolic geometry, Solv geometry, spherical geometry, (teaser) Nil geometry.

Narrated by    / @tehorarogue  

Play HyperRogue to have more fun with non-Euclidean geometry! Embeddings can be obtained using settings → 3d configuration → 3d style. (For most embeddings shown in this video, you also need to change the 2D geometry to Euclidean.) To learn more about non-Euclidean geometry, play HyperRogue or visit our discord:   / discord  

This world (with less 3D models) can be played in RogueViz (https://zenorogue.itch.io/rogueviz version 12.1p), RogueViz demos ⟶ non-Euclidean third dimension. Note: some of the scenes in this video are very complex and the engine is not optimized, so the framerate might be very low. Yes, it works with VR, but the framerate might be a problem.

Should we do a video on more embeddings (only visuals, no voice) in the same world, or somewhere different? Please tell us in a comment!

Made with RogueViz, our non-Euclidean geometry engine. Assets used:

Online games:
Pac-Man live: https://pacman.live
BeatRocks: https://js13kgames.com/entries/beat-r...

Sounds:
Excavator 1: https://freesound.org/people/eZZin/so... (CC-0)
Excavator 2: https://freesound.org/people/eZZin/so... (CC-0)
Cat purr: Dodek (recorded)

3D models:

Polyfjord 2D/3D chess:   / 59047159   (GPL 3.0) by @polyfjord (from this video:    • Modeling a Chess Set That Works in 2D and 3D  )
Maxwell Cat: https://sketchfab.com/3d-models/dingu... (CC-BY 4.0)
Spinning Rat: https://sketchfab.com/3d-models/horiz... (CC-BY 4.0)
Stanford Bunny: http://graphics.stanford.edu/data/3Ds... by Stanford Computer Graphics Laboratory

Royalty-free from CG Trader:
Tulip: https://www.cgtrader.com/free-3d-mode...
Coffee: https://www.cgtrader.com/free-3d-mode...
Duck: https://www.cgtrader.com/free-3d-mode...
Lily: https://www.cgtrader.com/free-3d-mode...
Table: https://www.cgtrader.com/free-3d-mode...
Cheese: https://www.cgtrader.com/free-3d-mode...
Excavator: https://www.cgtrader.com/free-3d-mode...