Impossible Geometry will change VR forever

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Impossible Geometry will change VR forever
---E--PHIA-Phia Master Assets Folder-Thumbnails-DIS BITCH NONEUCLIDEANNN.jpg
TVRS Episode 13's Thumbnail
Date June 15, 2020
Duration 8:58
Previous episode Vtubers: The 2 Sides of Self Discovery
Next episode How to be a Virtual Youtuber! Complete 2020 Guide
Link YouTube

Impossible Geometry will change VR forever is the thirteenth episode of The Virtual Reality Show. It discusses the concept of non-Euclidean geometry, and how it can be utilized in virtual reality. The episode features the special guest CodeParade.


Video description

Episode 13 of TVRS is about non-euclidean geometry inside of VR. Some people may think the only way to walk endlessly without breaking immersion is with omni-directional treadmills, but using impossible geometry means you can do some really crazy things without ever leaving your playspace. In this video, I explain what non-euclidean is and do an interview with fellow YouTuber CodeParade, someone whose knowledge on the subject is “unparalleled.”


PHIA: Hey guys and welcome back to The Virtual Reality Show where we talk about any and all things related to virtual reality inside...virtual reality! (laughs) I'm your host, PHIA. Math is the coding and the structure that makes up our universe. It gives us laws and theories to guide us in how we navigate the plane of which we exist on. The equations that make up nature are mirrored in the equations we program into computers to create our own cyberverse. We use it to simulate the familiar world and laws of which we are so used to, but in the cyber world, we can experience things that we are very much not familiar with. This is non-Euclidean geometry. It's mind-bending and it really intrigued me when I first found out about it, and I want to try and explain why this is so revolutionary for VR.

So what makes something non-Euclidean? Most of us learn geometry in our teen years because most schools require it, but what you learn in a basic level geometry class is actually only one type of geometry, Euclidean geometry. It is defined by what are called the five postulates. They were put together by this really smart guy Euclid. It's mostly pretty basic stuff saying that all right angles are congruent and that a straight line can be drawn one point to another, but the fifth one is the most interesting, because it raises some problems. The fifth postulate put simply is the parallel postulate saying that if you have a straight line and then two lines angled towards each other overlapping, at some point they are guaranteed to cross. So this pretty much implies that any parallel lines won't ever cross and that lines pointing away from each other will always get further apart.

However, this only works when you are drawing them on a plane that does not bend or contort which is where we get non-Euclidean geometry. For example, if you have lines of latitude on a globe despite being parallel, they will in fact meet at the north and south poles. This is because the plane they exist on is a sphere. It's elliptical. On the opposite spectrum, we could have planes that are hyperbolic and extend in the opposite direction meaning that the form is shaped quite similar to what we see in wormholes. The hyperbolic plane extends out and gives us a larger line of sight as to what we see, meaning you can peer into more of space itself. This seems quite abstract in comparison to what we typically think about math, but we know that our universe because of the space-time continuum isn't even a flat plane itself. Our universe curves and contorts very visibly around objects like black holes, but in our day-to-day real world experience, we don't get explore this kind of geometry. But what about in the virtual world?

I reached out to someone named CodeParade, someone I would call an expert in non-Euclidean geometry as he put out a video back in 2018 showing off his non-Euclidean Worlds Engine he created himself. What this features is something called impossible geometry, a type non-Euclidean that bends and connects space where it similarly shouldn't.

CodeParade: Yeah, so there. Like I said, there's kind of two different notions of non-Euclidean. There's the more formal geometry which is a lot more math intensive, and then there's the non-Euclidean in the sense of, you know, the space is not connected in the same way that you would expect. So in the second case, you could also do it by just kinda imagining portals. So like, this portal over here connects to this area over here, and this part of the map connects to this part of the map. And it's not too difficult to do that in an engine that can support it. As far as like the hyperbolic geometries and things like those types of non-Euclidean things, those are a lot more difficult because rather than connecting this area to this area or something, the entire space is continuously non-Euclidean. So every point in space contains more space than you would expect.

PHIA: There are some great examples of games out there that you're probably already familiar with that use this kind of method, like Portal or the Stanley Parable. But CodeParade recommended some VR games that are still in their betas to try out for myself so that I could full dive into these impossible spaces firsthand. Right off the bat, I realized I was going to need a lot more space in my play area than what I typically use in my room. None of these games allowed me to move around with a joystick or teleport anywhere I wanted to go. I had to move towards them physically. So I cleared out a six and a half by six and a half foot space and jumped into the game Tea for God.

What I found inside were winding impossible hallways. They were randomly generated each time I entered the game, leading me through unique spaces that challenged my sense of direction. It was unnerving and I could feel myself becoming uncomfortable, yet intrigued by what was going on. This was exemplified inside of the pyramid part of the game Out-or-Dead, which was a labyrinth that fit inside impossible space, challenging what I thought I knew about direction and sense of place.

CodeParade: We build mental maps in our head as we walk around or drive around or travel or whatever. We kinda have this internal compass, and it kinda helps you if you're walking through the forest, you'll kinda remember how you got back. But it's a combination of, like, seeing different landmarks and different objects and remembering the actual direction of the spaces. But if you take away part of at least one of those, then you start getting these weird effects where it's like, um, it becomes more difficult to navigate. So for instance, in like "Tea for God" or something, there aren't really any landmarks, right? I think the same with the other game I sent you, they're mostly dungeons that are all very similar. Like every wall, every corner. You can't really tell them apart. You lose that kind of landmark. And in addition to that, you also lose this actual direction, because as you move around, the world's constantly changing and generating.

PHIA: Hmm...

CodeParade: You can't really remember how you got back or there. There's just, like, too many directions.

PHIA: What I realized from wandering around these impossible spaces is that I was never feeling like I was limited by the space in my room. I always kept voyaging forward.

CodeParade: As far as VR, I think having the ability to fit more space in less space is very useful, but we'll probably will see that there's more of that in the future.

PHIA: Mmm-hmmm, I definitely agree. I definitely think that that's like the main pull for the non-Euclidean stuff kinda connecting to VR. It's this idea that we can fit more in such little space.

Being able to create large virtual worlds that you can walk through seamlessly has huge, untapped potential for creating a more immersive experience for a household VR user. Right now, there's not a lot of games that utilize the potentials of impossible geometry in VR, and I hope that maybe new game developers will start realizing the potentials of just how beneficial it can be and incorporate it in new, inventive ways in the near future. The virtual world truly is unparalleled if you know what I mean.

If you enjoyed this video, then please give it a big thumbs up and subscribe to The Virtual Reality Show channel for a new video every single week. Special thanks to CodeParade for being willing to interview with me on this topic which if you want to talk more about, then go ahead and join my Discord link in the description. I've been your host PHIA, and I'll see you on next week's episode! Bye!~.


  • The internal file name for this episode's thumnbnail is "E--PHIA-Phia Master Assets Folder-Thumbnails-DIS BITCH NONEUCLIDEANNN.jpg".