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Hyperbolica is mostly about the opposite, a hyperbolic universe, but there may be some section to the game that will be in a spherical universe. There's definitely some devlog video set in a spherical universe: https://www.youtube.com/watch?v=yY9GAyJtuJ0 The end of the video suggests this will be in the final game, at least as the time that video's creation.

In the meantime, the video I link is basically a video exploration of spherical geometry. One of the better ones, in my opinion, because it has "normal" objects in it, rather than floating heads or a ton of Earths or something.

(Another amusing sidebar: As you can see in the video above, an inhabitant of that space would be naturally inclined to say the space curves in above them. It would take an Einstein to assert that it's actually flat, and Spherical Einstein would have a very hard time describing "flat" to anyone. You can only make things "flat" contingent on the observer being in a very particular place. If you look at the next devlog: https://www.youtube.com/watch?v=pXWRYpdYc7Q back in Hyperbolic space, you can also see that a resident of that space would naturally believe the space they are in is a sphere (albeit one of variable radius, which is weird, but still, you can look out in the world and see the curvature, obviously it's round), and it would again take an Einstein to say that it is flat. It's flat if you are exactly on the ground, but hyperbolic space exaggerates any degree to which you are above the ground to make the horizon look round.)

Specifically, the video about spherical geometry: https://www.youtube.com/watch?v=yY9GAyJtuJ0

There’s another game being developed in a semi-3D hyperbolic geometry called Hyperbolica. The dev makes some fantastic videos [1].

[1] https://youtu.be/yY9GAyJtuJ0

⬐ jlos

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.

⬐ roywiggins

As much as I enjoy excursions in hyperbolic spaces, I also find it causes awful motion sickness. Even in 2D, it can be a bit much.

⬐ zenorogue

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.

⬐ roywiggins

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.

⬐ PostThisTooFast

"Disorientated?"

⬐ zenorogue

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.

⬐ OscarCunningham

Also see here https://www.youtube.com/channel/UCMgVKCsG_7z1jpdHDR_TwUw for development of HyperBlock, a hyperbolic Minecraft.

⬐ jedimastert

I was just about to link to code parade! He's done suck amazing things with real time rendering and perspective, it's great

⬐ zenorogue

HyperRogue has 3D modes with real-time rendering and perspective too. (And playable, not just videos ;)

⬐ ArtWomb

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!

⬐ smusamashah

The effect looks like lensing

⬐ enriquto

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).

Code Parade on Youtube has some nice tech demo for non-euclidean 3D game engine.

"Non-Euclidean Worlds Engine" - https://www.youtube.com/watch?v=kEB11PQ9Eo8

"Spherical Geometry Is Stranger Than Hyperbolic" - https://www.youtube.com/watch?v=yY9GAyJtuJ0

⬐ zenorogue

The first one of these videos is not about non-Euclidean geometry, though.

There are many cool 2D and 3D non-Euclidean games already existing and several cool new projects in development, see: https://medium.com/@ZenoRogue/non-euclidean-geometry-and-gam...

⬐ nayuki

He has a cool video on how hyperbolic geometry is really big: https://www.youtube.com/watch?v=zQo_S3yNa2w

⬐ ruytlm

At 5:45[0] in that video, he makes a reference to one of the greatest weird explanations of video game things ever: the explanation[1] of how to beat the Watch for Rolling Rocks level in Super Mario 64 with only half an A-press, which is highly worth a watch if you like this stuff about geometry.

And if that was interesting, I also recommend the history of any percent speed runs for Super Mario Sunshine.[2]

[0]: https://www.youtube.com/watch?v=zQo_S3yNa2w&t=345 [1]: https://www.youtube.com/watch?v=kpk2tdsPh0A [2]: https://www.youtube.com/watch?v=oudZMniib08

⬐ mkaic

This channel is one of my favorites!

⬐ adenadel

Here's the game that the video creator has made based on these ideas

https://store.steampowered.com/app/1256230/Hyperbolica/

⬐ centimeter

I'm hoping for VR support!

⬐ stared

Speaking about games - I love HyperRogue: https://www.roguetemple.com/z/hyper/.

⬐ nimih

HyperRogue is a lot of fun and does a great job of making the non-standard geometry central & integral to the gameplay. The levels with "gravity" are particularly interesting to navigate and reason about, IMO.