Non-euclidean virtual reality using ray marching
HTML-код
- Опубликовано: 21 окт 2024
- Non-euclidean virtual reality using ray marching
Try out the simulation at michaelwoodard....
The code is available at github.com/mtw...
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
ñ
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
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
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?
This makes me want the same thing but in hyperspherical geometry.
ruclips.net/video/yY9GAyJtuJ0/видео.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
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
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.
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
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?
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"
So easy to understand non euclidean geometry in vr. Awesome!!
Non-euclidean spaces always feel like something out of a cosmic horror. They're just so unnaturally unsettling.
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.
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
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.
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!)
Wow a digital ipecac! Fantastic!
In all seriousness, very impressive and fascinating work.
1:27 thats an amazing perfect circle
literally screamed when he drew a nearly perfect circle like it was nothing
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
Fascinating, the existence of truly unlimited virtual worlds is looking more and more possible.
This is so cool! Glad to be alive during the beginning of a new era of tech.
"Right-angled pentgon"
The fact that humans managed to emulate something like that is just... I dunno man I'm just really in awe
Honestly this is one of the more cooler things I've seen on youtube
I did this while on dmt and it was absolutely nuts
This Is the clearest explanation ever. I thought this topic would be difficult to understand but I was proved wrong.
The moment you ended up on a different cube but in the real world on the same spot made my brain melt.
I’ve had this video in my recommended for a year. I’ll watch it jesus
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.
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
This randomly showed up on my recommended and this blew my mind
I don't understand nor think I ever will understand this, but this is awesome.
Imagine being a part of the growth of this channel
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.
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
"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.
Incredibly creative and interesting, especially for anyone that was confused about the subject
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.
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.
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
Lets give him an additional respect for instantly drawing a perfect circle.
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 is cursed and amazing at the same time
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...
the narrative design potential 😩😤🤯 , Herald the mythic dawn
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!
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.
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.
I found this way more interesting then I thought I it was when I clicked on the video.
HE'S BACK!!
Holy cow! That's impressive!🖤
And so abstract!
Nice work, this was even cooler than I thought it would be!
Imagine now the horror of walking through non-Euclidean buildings and cities as described in Lovecraft. My… GOD
okay this is amazing, why did I discover this video just now
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.
Came here for ray marching and wound up seeing the best visual of non-Euclidean space
This used to be my recurring nightmare for like 5 years when I was a kid.
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.
@@Nauskills I am over here curious about the possibilities and you are curious about what exactly?
Is no one gonna talk how he did the circle Perfectly
I can feel my brain melting just from watching this, i can't imagine what it's like to see this in VR.
This was highly interested and I understand everything you're saying
You or someone should use this to in a puzzle game like portal or superliminal but for the VR, that would be so dope!
When I realised he walked around the pillar 4 times but hadn’t made a full way around it I literally audibly “wtf”d
This non- Euclidean vr is so cool. 😎
I legitimately spent hours today figuring out how to make one square shoot and kill another square in unity... this seems like the natural next step in my big brain adventure
I modded terraria items since its pretty much free (Aside the game) and takes smaller amount of time to sprite vs code. Baba is you is also a great game
@@ImLennz sounds cool... I’m just trying to learn some basic unity c# so that I can make my art sprites actually do things...
If I ever got good though I have so many ideas for things I’d like to make
Dang man you can make some trippy optical illusion games with this
This is a really unique way to demonstrate this subject, this is very interesting!
OMG! this means a lovecraftian VR game can be made INCLUDING non-euclidean goemetry, and we can all go insane! :D
looks like everyone is starting to get this now and I am suprisingly early for it
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.
This taught me more than school did
In 2022 humankind is able to create unrealistic, super cool mind-blowing video games.
Yet game developers decide to just make games more realistic.
I wish there was more games like this demo!
I love watching something I don't understand at the middle of the night
I wonder what path tracing in non-euclidean space looks like...
I can smell the sound of color and taste the speed of dark
This man has mastered geometry to the point his brain might as well be better than graphing apps
The next tool music video is gonna be non Euclidean and I'm stoked
I can imagine something like this inside Outer Wilds 2 if they make a sequel.
I thought the same
i wish that non-euclidian space wluld be used more in videogames especially in VR. Being able to pack tonnes of space into the virtual world inside of a room would be incredible. Most people have a 6x6ft (2x2m) room in their homes and if you could make a vr spacr that makes that 36sqft or 4sq meters into a square mile or square km that would be insane. Obviously youd need virtual barriers to prevent walking into a real life wall, but from what I understand you can have infinite 6x6ft "rooms" that you can walk in in the virtual world
Incredibly fascinating.
Oh my god and the fact that the brain doesn't give you your position correctly, amazing.
I dunno if this exact technique was used, but "Tea For God" Is a pretty good example of non-eucludian VR.
Quantum FPS splitgate really expanded my mind
Ive only just begun scraping at calculus so I have no idea how applicable this idea could be, but could non-euclidean marching be used to create expansive worlds within the euclidean space of a person’s room?
Like it wouldnt be too big of a world, but even a larger room could use non-euclidean space to create a larger-looking room in VR that is traversible, while irl you only have a smaller room.
With the negative curvature shown here, a euclidean representation of 5 lines worth of space was mapped within the confines of an irl 4 lines, with one overlayed on top of the first line. Get more efficient with this and could we see even more space generated overtop a smaller room? Now walking in a straight line would still be a challenge because both spaces have equal distancing with a single straight line, but i just wonder about the applications this could have is all.
Well if we can go from 4 corners to 5, what’s stopping us from continuing to 6, 10, infinity!
i have no idea what you're saying but it's very entertaining
I don't know what this is but it looks cool.
I love thinking about non-Euclidean space. My dreams will come true if a VR, hyperbolic, immersive WORLD is created.
Hyperbolica is a game using hyperbolic geometry that supports VR.
Absolutely brilliant, Henry. Thank you for showing us this.
This is so crazy bc u can kinda understand how disconcerting the weird non euclidean worlds in cthulhu mythos would be. Obviously we have the sphere and the color coded red and blue spaces to guide us and help us with direction here, as reference points, but can you image a world where you cannot perceive how far you have traveled, you cannot anticipate where you will be in space with general logic, and where there are no identifiable variations that you can understand that can aid you in getting around? The space without aid doesn't allow you to orient yourself at all, and without the handy landmarks and visualization, most people probably wouldn't even realize they're walking in pentagons. That would definitely be disconcerting lol
I am so glad I found this video, I feel like I know everything lol
Yea I ain’t gonna lie I have no idea what the title even is. The thumbnail just looked cool.
This would be amazing for a puzzle game
This is incredibly cool
I understand why HP Lovecraft spoke of this like it was something to fear. This is a little disturbing but very enjoyable
does this means that we can travel further in a VR space with limited physical space?
More games need this