Ha! the title of that video "Spherical Geometry Is Stranger Than Hyperbolic" is very insightful. Due to the convergence of the light rays on positive curvature, objects appear larger the further they are! Hyperbolic geometry is like euclidean with a spacious horizon. But spherical geometry is a wickedly different thing. All your "sky" is covered by the single point at your antipodes (when it's not occluded by a tiny object very far away from you).
I'm at a standing desk on a balance board and I had to get off. I got disorientated and nauseous just watching that. I can't even imagine spherical geometry with VR.
Well, if we see an object with our eye, we know that it is on a particular line. When the brain sees the object with two eyes, it knows that the object is where the two lines cross.
As long as they cross in front of the eyes. If they cross in the back, the math works, but the brain is not trained for it.
In spherical geometry that happens -- you see things which are just behind you, but the brain has problems interpreting that.
Simulating binocular vision is not the only approach though -- you can use a perspective where the objects appear at the correct distances, some non-Euclidean VR games do this.
How much have you played? It seems you need to get used to it -- for me it caused motion sickness initially, but after getting used to it (which did not require much playing in my case), not anymore (except with experimenting with new graphical settings). I still get motion sickness in Euclidean 3D games. Changing the options could help too.
I expect that's true. I got very strong motion sickness with VR, but after dedicating a few hours to it I can do low-motion games fine.
Mostly I've managed to make myself slightly ill with my own experiments in rendering motion in hyperbolic space, so I haven't spent too long in HyperRogue.
Perceptually, it's interesting that in the "2D" hyperbolic plane, the game map tests the limits of the human mind. But in "3D" this becomes virtually impossible. Even with practice it becomes intractable for the typical player to imagine "spaces expanding within spaces" at 60fps!
The point about rendering hyperbolic 2D using the Poincare embedding is that you see more of the game world, but what is "closest" is larger, somewhat like POV 3D but unlike traditional roguelikes.
John Lamping invented a file browser based on hyperbolic 2D [1,2].
At the first encounter I find this game very aesthetically pleasing and groundbreaking in an original dimension. I see it's been around for a while but I missed it before. I personally am a bit saturated with the mainstream 3d game mechanics, somehow 2d games captivate me more.
Cool! That inspired me to try to generate such a rendering myself, but googling it is not as easy as it seems. Sure, there is an article on Wikipedia about "https://en.wikipedia.org/wiki/Order-6_hexagonal_tiling", about a "regular tiling of the hyperbolic plane" with hexagons, but the hexagons themselves in that tiling aren't regular...
I'm curious, how would you store data about the maps of these worlds? Is there a certain format that's needed? I imagine it couldn't just be a 2D array, or if so, it would need to be a lot larger than a normal map and you wouldn't check all cells.
I'm a roguelike enthusiast who's attempted to play HyperRogue many times but always get stuck on not understanding the geometry at all. Any tips from those who have?
There is a free software version of HyperRogue, and also a paid version e.g. from Steam. The Steam version has some minor features that the free version does not have (leaderboards, Strange Challenge, etc.).
It appears that tunneler is a pixel-based game (not sure whether there is a commonly used term for that, but I mean games like Lemmings or Scorched Earth or Liero or Noita which are grid-based at pixel precision).
It is not clear how to make a hyperbolic pixel-based game because there is no fixed relation between the map and the screen pixels. (This is also why HyperRogue cannot use pixel art.)
Of course, one could still just pick a dense grid and use it instead of the actual pixels.
There is nothing very close to Tunneler, but there is an Asteroids clone mini-game inside HyperRogue, and a "shmup mode" which is real-time and can be played in local coop.
[1] https://youtu.be/yY9GAyJtuJ0