Non-euclidean virtual reality using ray marching
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- Опубліковано 28 лют 2019
- Non-euclidean virtual reality using ray marching
Try out the simulation at michaelwoodard.net/hypVR-Ray
The code is available at github.com/mtwoodard/hypVR-Ray
Joint work with Roice Nelson and Michael Woodard.
This video demonstrates a virtual reality simulation of a non-euclidean, negatively curved space.
Suppose that I walk in a straight line, then turn left by 90 degrees, and then repeat these steps until I get back to where I started. In a flat space with no curvature, I have just walked around a square. In a positively curved space, like the surface of a sphere, I could instead have walked around a right-angled triangle: I could start on the equator and walk a quarter the way around the sphere, then turn left and go up to the north pole, then turn left again and walk down to my starting point. In this video I am (virtually) in a negatively curved space; here I walk around a right-angled pentagon.
The study of negatively curved spaces like this (more specifically, hyperbolic space) is an intense area of research in three-dimensional geometry and topology. This has grown from the seminal work of William Thurston, who showed that "most" three-dimensional spaces are hyperbolic - the flat, euclidean spaces are the unusual ones!
We created this simulation to make non-euclidean spaces more accessible to the general public: The simulation is available at michaelwoodard.net/hypVR-Ray and works in any web-browser - there is even a version for iOS and Android devices. In the future, we hope to implement simulations of other non-euclidean spaces, including some of the other geometries described by Thurston in his foundational "geometrization conjecture", which was proved by Grigori Perelman in 2003. We also plan to integrate our visualization work into software used by other researchers, such as the program "SnapPy", which is used to study hyperbolic manifolds.
Our simulation is programmed using ray-marching, a graphics technique similar to ray-tracing. For each pixel of the screen, the program decides how to colour the pixel by tracing a ray of light from the pixel out into the world of the simulation and seeing which object it hits. As described in the video, an implementation of ray-marching requires very little knowledge about the space we are simulating, only:
1) A way to write down points in the space (i.e. a model for the space),
2) signed distance functions for the objects in the world, and
3) a way to move a given distance along a ray.
This should help us generalise the technique to other, even weirder spaces.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Amazing application of ray marching! It's so much more satisfying to see into infinity without the rendering limitations.
This was a start of something awesome, I imagine.
@@Cheesewiz247 yep
Yeah I can’t wait to see hyperbolica and maybe you 2 could work together on a hyperbolic VR game
@@Cheesewiz247 ñó
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A game or puzzle made with this would be a wonderful challenge for someone with a natural aptitude for Spatial Awareness and wayfinding. Perhaps as a way of expanding upon their abilities outside of Euclidean space while still being obligated to abide by it in the physical world.
The idea of reaching places in the virtual world while abiding the real world walls sounds interesting. But I do not think this would make a good puzzle game in VR, because it would depend on the physical space you are in, and also I think puzzles work better on a grid (in a continuous world, you could change your facing direction in a virtual non-Euclidean world by spinning your head, and you could use that to solve any such puzzle easily).It sound sounds a bit like mimics in DROD, who mirror your movement (if possible) and typical puzzles are where you have to get them to a specific place without moving your real body into a wall. HyperRogue also has mimics who work similarly (but in non-Euclidean space). It could be fun to add a puzzle where one entity lives on a non-Euclidean grid and the other one lives on an Euclidean one, and you have to synchronize your movements.
You may be interested in this game: miegakure.com/
porky11 miegakure is not at all related to non Euclidean geometry, it’s Euclidean space with an extra spatial dimension but I guess it would work just as well
You're totally in luck, there's an indie game being developed right now known as hyperbolica that takes place in non-euclidian space. (It's also supposed to be released in VR)
There is Antimatter
Man, that's trippy. I wonder what other crazy shape concepts VR will help people visualize in the future.
Imagine being on weed for this
@@kmflowtimelordmal5446 probably more like shrooms. Smoking weed or taking edibles doesn't really work in VR because vr requires alot of energy and coordination. When you are high thats the opposite of what you want.
Whatever VR it ends up being, I'm sprinting in it while drunk
@@kmflowtimelordmal5446 Imagine referring to _being high_ as _being on weed_ 💀
This is DMT space
I love how everyone is talking about that nobody is talking about the near perfect circle he draws. Truly a non euclidian experience
Just scroll down
I read this comment as soon as he made the circle
that wasnt even good, are you blind? the circle literally doesnt even connect lmao
@@creamypeanutbutter6269 alright creamy peanut butter draw a perfect circle right now
@@mr.nazareth4501 i was about to ask you why you called them that then i realized it was their username
This is so weird, it’s like you’re traversing another dimension and our reality at the same time. Like a few steps in our reality leads you to square one, but a few steps in that plane leads you further from the starting point.
Math can be weird and cool baby
Reminds me of when i was 16-17 huffing gasoline like an idiot. I had the most terrifying hallucination that i was falling down through an infinite grid of squares like this. Felt like i was there for a lifetime in that space.
Damn that seems pretty fun
نه هر چند بله هر چند نه چندان
@@gabs1400 time to go huff gasoline
Average Midwest/Eastern Europe dweller
am I the only one who's very very alarmed by this?
Video is cool and all but is no one even going to mention how effortless his circle was? Cmon, that was clean
no
I can hear aphex twin
well it was a speed up footage so we cant be sure about how effortless it was
@@theboyothatcalledzabe7307 on the whiteboard
@@TheArcticFoxxo yes on the whiteboard while he is drawing u can notice footage goes on a higher speed than normal thats like that probably because while editing he didnt make us wait for him to draw circles
This makes me want the same thing but in hyperspherical geometry.
ua-cam.com/video/yY9GAyJtuJ0/v-deo.html
neopalm2050 I know I watch that channel. I’m so happy we finally got to see that.
hypershwat? i thought spheres have same geometry in all geometries
@@kimapr3817 No, there are definitely different geometries. A pretty fundamental difference would be a difference in dimension.
ah wait. I thought you were talking spheres in hyperbolic geometry. I see you meant higher dimensional spheres. In hyperbolic geometry there are hyperspheres which are basically just infinite spheres. They have euclidean geometry in them (note: sphere=surface of a ball)
EDIT: i meant horospheres. Hyperspheres are larger than infinite and i don't know what geometry they are
That is one of the best circles I have ever seen. He also does it so effortlesly.
1:26
This guy, knows how to draw a perfect circle
My drawed circle: B
No
You clearly haven't seen any freehand circle drawing competitions, this is an amateur circle
How awesome would be to see some actual games based on this and on other non-euclidean effects.
Hyperrogue is game that literally added 3D hyperbolic geometry this week. I don't think its released yet, but it has had 2D hyperbolic geometry for years that is quite mature.
I believe the Ayuascha vr experience utilizes some of these techniques in its rendering, I'm not sure though
It is strangely hard to see the icosahedral vertex figure in this visualization: vertices look very similar to {4,3,4} unless you look very carefully. On the other hand, in HyperRogue {4,3,5} it is strikingly clear that you see a different cell to the left and right side of a beam -- if one of them is filled with a wall and the other one is not, it appears as if there should be a wall but it is not drawn for some reason (and then you go to explore it and see the reason).
What reason?
I do get a sense of dread seeing you exist in a space such as this. One of my greatest fears are slowly drifting into a black hole in space and seeing the ever expanding abyss swallowing you. This gives of similar vibes, but in a smaller scope for some reason..
Then most definitely do not take DMT because you will experience exactly that
Do not take dmt or ketamine or salvia divinorum
Do not take Tarianium IV
@@sa-amirel-hayeed699 Or any psychedelics, period.
Non-euclidean spaces always feel like something out of a cosmic horror. They're just so unnaturally unsettling.
So easy to understand non euclidean geometry in vr. Awesome!!
literally screamed when he drew a nearly perfect circle like it was nothing
Non-Euclidean SDF ray-marching!! You really are one of my favorite people :) I'm going to read the code right this second! (Thanks so much for sharing that online!)
It always feels like he's walking up to a wall that's the same as his surroundings, would be great to see this be used in VR horror.
This sounds terrifying to experience in any more than just walking in a square (or pentagon in vr) because motion sickness is already an issue in normal world vr, but it's also terrifying because why did they make the rods look like that? They look all rusty and the lighting is so gloomy, it's like you're in some abandoned non Euclidean scaffolding project
Could these be applied in the virtual space such that a user believes themselves to be making forward progress in the VR world, but having only moved a small/repeatable distance in our reality?
a year late on the reply, but i did something like this for a uni project years ago and it worked pretty well. rather than raymarching or non euclidean space, i set up a euclidean space much larger than the real play area, but with a custom camera and very specific angles and such. the camera turned less than the real human, so people would be walking back and forth in the real world while progressing along a zig-zag path in VR.
it worked surprisingly well, and people were fooled into feeling like they were in a much larger space than they actually were. we didn't tell the subjects what the experiment was about until afterwards, and a lot of people were like "oh yeah this room really isn't that big now that i think about it"
Just stumbled on this video. Pretty cool, and unnerving. Weirdest being how in this strange non-euclidian world there's an abundance of Old Oklahoma State University logos.
"Right-angled pentgon"
The fact that humans managed to emulate something like that is just... I dunno man I'm just really in awe
i love this because it fits an entire world into the size of a vr play area. I've always wanted to see this applied to vr when i learned about non euclidian world's
This is so cool! Glad to be alive during the beginning of a new era of tech.
Fascinating, the existence of truly unlimited virtual worlds is looking more and more possible.
Incredibly creative and interesting, especially for anyone that was confused about the subject
This Is the clearest explanation ever. I thought this topic would be difficult to understand but I was proved wrong.
Honestly this is one of the more cooler things I've seen on youtube
I’ve had this video in my recommended for a year. I’ll watch it jesus
this is the perfect way for people to understand curved space
Nice work, this was even cooler than I thought it would be!
The moment you ended up on a different cube but in the real world on the same spot made my brain melt.
gorgeously trippy
I play a game called Vrchat using either my computer and my quest ll, and very recently I started making my own avatars in unity and using raymarching shaders like these are my favorite, it is so fun to look down at my hands and somehow be looking into an infinite void of lava or galaxies, (both of which can be made by using the starnest shader) but just on the other side of my hands is the floor a few feet away
I don't understand nor think I ever will understand this, but this is awesome.
This randomly showed up on my recommended and this blew my mind
This is awesome! I have planned to do this with part of my dream game, and this'll make it so much easier when I do!
Now to figure out how to hide the corners of the square when the player gets close.
"Parker slipped as the other three were plunging frenziedly over endless vistas of green-crusted rock to the boat, and Johansen swears he was swallowed up by an angle of masonry which shouldn’t have been there; an angle which was acute, but behaved as if it were obtuse." Lovecraft had some insight into this, it seems.
HE'S BACK!!
Wow a digital ipecac! Fantastic!
In all seriousness, very impressive and fascinating work.
Now imagine this is a legit fractal with infinite colors, and shapes, and pockets. Then imagine flying around in it just like this, room to room. That's a DMT breakthrough.
The NSF ending was so smooth
I haven't got a clue what use this has or a word of how it works, but man, that is super cool.
This was highly interested and I understand everything you're saying
This is cursed and amazing at the same time
Holy cow! That's impressive!🖤
And so abstract!
Lets give him an additional respect for instantly drawing a perfect circle.
okay this is amazing, why did I discover this video just now
Incredibly fascinating.
Imagine being a part of the growth of this channel
I'm really good at finding my way around places/areas
I never get lost wherever i go and can always find my way back to where i started, in games and real life
So i'd really like to try an exploration game with elements like these to feel what it's like to be completely lost and dissoriented lol
I did this while on dmt and it was absolutely nuts
the narrative design potential 😩😤🤯 , Herald the mythic dawn
This non- Euclidean vr is so cool. 😎
1:27 thats an amazing perfect circle
I have no idea what he is talking about. But I just can't stop watching these videos as if I was about to take a test from physics.
Imagine now the horror of walking through non-Euclidean buildings and cities as described in Lovecraft. My… GOD
This was fascinating!
This is a really unique way to demonstrate this subject, this is very interesting!
Absolutely brilliant, Henry. Thank you for showing us this.
this is awesome to watch. just...wow
It is very cool! I have no words.
I found this way more interesting then I thought I it was when I clicked on the video.
This is incredibly cool
As a kid i dreamt about playing tag with a friend in something like this. I woke up with a healthy fear of how large the universe was. Thanks maths!
Subbd because I cannot get enough of this!
Holy shit the first half of the circle he drew was one of the most impressive things I've ever seen
Get out more often.
Beautiful!
Is there any way I could simply download the simulation you were using for the VR head set I'm always looking for neat vr experiences and this is right up there
I am so glad I found this video, I feel like I know everything lol
Is no one gonna talk how he did the circle Perfectly
I have tried for ages but I can’t seem to use this with my quest. I’ve used virtual desktop and link and native in the quest but I can’t play this amazing VR masterpiece. I love hyperbolic geometry so if you know a way I can play it then please let me know.
this makes explaining Non-Euclidean much easier
normal space is also non euclidean, for the record. a non euclidean space means that 2 parallel lines must follow a curved path to be parallel. this video specifically demonstrates hyperbolic space, a space where a square grid connects on 5 fronts rather the the typical 4. that's why it takes 5 90 degree turns to return to his starting position, each 90 degree turn is warranted by one square that is adjacent to the starting square.
pardon the reply to a year old comment, by the way.
looks like everyone is starting to get this now and I am suprisingly early for it
I can imagine something like this inside Outer Wilds 2 if they make a sequel.
I thought the same
1:27 nobody gonna talk about how this man just drew a near perfect circle
literally the first thing that sent me to the comments haha
several people already did, so...
This taught me more than school did
Came here for ray marching and wound up seeing the best visual of non-Euclidean space
More games need this
Dang man you can make some trippy optical illusion games with this
Quantum FPS splitgate really expanded my mind
OMG! this means a lovecraftian VR game can be made INCLUDING non-euclidean goemetry, and we can all go insane! :D
This would be amazing for a puzzle game
Fascinating
Amazing work, I'll try this out with the Vive. D:
This is so cool
The next tool music video is gonna be non Euclidean and I'm stoked
Very cool :) thank you for the explanation!
You or someone should use this to in a puzzle game like portal or superliminal but for the VR, that would be so dope!
That is so cool!
Tbh, this is the closest to what I remember seeing my first time trying DMT.
It was more wirey, darker at areas but neon green rather than grey.
It was intensely beautiful.
So we basically already have the core essentials for making a Mystery Flesh Pit National Park game, and I can't help but feel that's what put this into motion in the first place.
Thanks for sharing.
I love watching something I don't understand at the middle of the night
i have no idea what you're saying but it's very entertaining
This is so cool!
this is sick
This is so above my paygrade. All I want to know is how this helps humanity.
It doesn't, but people can make things that doesn't help humanity. Your comment for exemple doesn't, and yet here you are.
@@bugplayer I am over here curious about the possibilities and you are curious about what exactly?
That's cool as hell
Terrifyingly awesome!
Oh my god and the fact that the brain doesn't give you your position correctly, amazing.