CodeParade - 2020-09-01
This is the 3rd devlog for Hyperbolica where I talk about how I build and render hyperbolic worlds. If you haven't seen the first 2 videos in the series, make sure you watch them first or else this may be confusing. Devlog #1: https://www.youtube.com/watch?v=zQo_S3yNa2w Devlog #2: https://www.youtube.com/watch?v=yY9GAyJtuJ0 Hyperbolica on Steam: https://store.steampowered.com/app/1256230/Hyperbolica/ Trailer: https://www.youtube.com/watch?v=EMKLeS-Uq_8 Discord Server: https://discord.gg/7fAwnYV If you like the things I do and want to support the channel: https://www.patreon.com/codeparade https://ko-fi.com/codeparade **CORRECTIONS:** I just found out that Gyrovectors are indeed associative. I misunderstood the context of the claim in the paper, which was referring to mobius addition, not the full gyrovector addition which corrects the associativity. I apologize for the mistake! Other references from video: Miegakure: https://miegakure.com/ Ungar's original paper about Gyrovector Spaces: https://www.researchgate.net/publication/268710591_Gyrovector_spaces_and_their_differential_geometry Music: Horrible - Mela https://melagroup.bandcamp.com/album/mela-two
CodeParade: Gyrovector translations aren't commutative
Me: Yeah, sure, I can deal with that.
Codeparade: ... or associative.
Me: wait
@f 5673 Associativity breaks down when we don't just compose functions but instead combine them with each other using certain projections, like those of observation in quantum mechanics, which form what is called a Jordan algebra.
Octonion multiplication is another example of function combination that is more complex than composition, and non-associative as a reault. If we represent octonions first as 8-dimensional vectors, and then represent left multiplications and right multiplications with specific octonions as matrices acting on these vectors from the left. Funny thing is that even though f * g =/= f o g in general, f * g * f = f o g o f always. For f and g both representing left multiplications with octonions (or both right multiplications). "*" signifies octonion multiplication, while "o" is composition i.e. ordinary matrix multiplication.
It is true for octonions, and all Moufang loops, that (f * g) * f = f * (g * f) always, though (f * g) * h =/= f * (g * h) in general. It is also true that (f * f) * g = f * (f * g) and (g * f) * f = g * (f * f).
@tosterm "I don't know" "what any of that means" is different from "I don't know what" "any of that means". Now you know what it means.
@IIAOPSW This is what's called a pro gamer move.
me programming with a math background: *flips table
what's so hard ? any function in non-pure programming language is like that. you can't just switch the order of anything without getting "bugs".
In one of the levels you should place a large rock at coordinate "ULURU"
Ha
...why?
@ninjacat230 uluru is a big rock in the middle of Australia
@old channel yus
@old channel but then everyone else wouldn't be able to have any fun with the stone!
gotta say, programming a true non-euclidean game without overuse of portals is itself a puzzle.
@kayturs x: 4 y: 7 z: 8 a: 4̷̨̢̡̢̢̭͓̞̫̬͉̮͙͚̩̻̤͇̻̠͕̱͇̘̹̣̼͔̫̻̟̗̰̭͍̠͎̯͇̤̼̥̭̦̥̝̫̰͈̘͓̻͈͇̠͚̗̭͓̖̗̗͓̲̹͚͈͎̗͓̠̤͎̗͉̌͊̔̄̽̋̚͜͜͝ͅͅͅ3̴̧̧̧̛̛̛͔̭̬̬̣̯̙͇͓̗̥͙͚̩͉̞̄̆̀̾̊̄̋̎̎̂́̎̀̊͑̊͌̐̃͆͐̉̈́́̈́̃̆̈͋̊͐̄̽̂͊̈́̇͂͌̈̓̑̅̑̏̒̍̍͊̉̅͛͗̿͛̚͘̕̕̚͠ͅ8̴̢̨̢̡̡̢̡̢̛̛̬̭͎͍̥̺̝̬̜͚̪̥̗̥̰̭͖̬̩̱̲̮͓͙̰̦͇̖̙͍͓̺̪̺̜̯̪͉̖͉̖̹͔͍̠̦͔̜̹̲̱͓̪͚̼͍̼͓̮̮̦̟̩̺͎̙̬͔̝̞̭̫̞͕͍̠̬̭̮̘̋̅͗͐̏͛̄͐̈́͊̾͗̃̃͒̄́͂̄̂͛̒͒͌́̍̀̽̎̋̕̚̚̚͝͠͠ͅͅ2̴̧̨̛̛̛̛̛̛̝̺̫̬̳͔̟̬̩͙̠̘̮̹͕̗̯̙̗͍̻͓̜̰̹̩̣͇̦̙̻̱͍̹͙̳͒̀͛̈̀͌͆́́̐̑̀̂̽̀̐̔̈́̀̇̓̎͛̄͆̅͆̔̆͊͊̾̔̿́͐͆̆̀̏̉̀͒́̅̒̓̆͛́͊̂͛͐̍̾̃̍̕̚͘͘̕̚̚͠ͅͅ9̶̨̢̧̢̨̨̧̢̜̱͇͓̘͔̪̱̞̳͔̻̟̘̮͚̫͉̲̰̘̝̙̙̪͚͓͇̮̬̯͔͇̭̹̟̫̰͖͉͕̹̹̠͙͍̗͍̳̺͈͉͕̰͓̹̦̳̘͍̺̞͈̥̲͕̥̗̙̜͎̩̰̤̱͖͍̦͚̮̉͋͛̒͌̏̾̄̑́͒̔͐͗́̽̽̈͗̅͑̈́̀̌̂́̐̃̈́̉͋͒̀̌͂̐̈̂̎̋͂̄͂͊̽̂́̃̊̎̋̏̓̾̈͛̎̅͐̒͌̋̓͌͂̇̎͘̕͘͘͘͘͘͘͝͠͠͝ͅͅͅ
yeah, this is the real big boy leagues
Are you telling me that you can walk forwards 19 meters.... without portals???
@Racon Vid at least its meters, I know those. it doesn't matter its a gyrovector made of 2 quaternions and 1 "thing" that's a complex number
still easy than imperial
"If you haven't seen the first 2 videos in the series, make sure you watch them first or else this may be confusing."
Oh, don't worry, this is definitely still flying over most of our heads anyways...
I just watch it because it's trippy especially the spherical geometry one
only people that focused in school can understand this big brain stuff
"And, though it was perhaps unsurprising that Cameron should be unenthusiastic about Juncker's candidacy, the vehemence of his opposition was extraordinary."
I'm a mathematician, and when he started talking about Gyrovectors, my brain told me to go look that up. The Operation that's described in the paper he puts on screen is a fucking monster, as well. Although, it kind-of sounds like he's describing Quarternions, so "gyrovector" could just be a generalized term for the algebraic structure that quarternions operate in. Although, the non-associativity is definitely not something that Quarternions do, and it presents a major problem for anyone who wants to do algebra with them, since inverse operations are difficult at best.
The most fascinating part of these videos is that despite my fear of these topics flying over my head, the explanations are so carefully presented that I still feel like I understand. This person is a great teacher.
Yeah, his animations about how walking a path in a different order leads you to different locations, or how moving can add unexpected rotation, really grounded the abstract rules of the gyrovectors in a neat way.
I think a great teacher should make the student actually understand the topics, not "feel they understand".
(While it is of course impossible to explain non-Euclidean rendering to a 5yo in five minutes, gyrovectors are not the simplest way to do it.)
Virtual Reality mode
This is already amazing, but I feel like these types of games are an even bigger boom in VR. And theoretically, I don't think you would need to change the rendering pipeline too much to add a VR mode. I'm not sure what type of user interactions you wanna add, but Unity has really good VR tools. And I really think it would boost the game's visibility, since there aren't many VR games yet, especially as unique looking as this.
And actually feeling the distance of things change would I think add a whole another dimension (literally) to the visuals.
While we can adapt, it's hard. I never got motion sickness from videos until after I played VR. After I played VR, I can no longer watch VR videos on YouTube without suffering motion sickness. It's hard to train out several hundred million years of specialized gray matter trying to process what it's seeing. Some people will be very sensitive to distortions. I know I can typically see an 89 degree angle and be able to understand it's off by 1 degree. Humans are good at seeing right angles and knowing what they are. Some are even better at it and have an eye for exact proportions. That kind of hyper-specialization is detrimental to accepting even the slightest of off-kilter imagery, especially when it's where you're basing your sense of motion partially.
When trying to visualize parabolic space mentally, I have the same reaction to seeing or imagining VR. I imagine many people will have this issue more-so with this game in VR as it's such a disconnect between understanding what you SHOULD be seeing and knowing how parabolic space works, and then actually seeing it and maneuvering around it. I think it's two different parts of the brain working against each other. I honestly wouldn't be surprised to hear of someone suffering a seizure from such an occurrence.
@GreenDave113 I don't know if your personal anecdotal experience can be extended to the general population, though. My personal anecdotal experience is that I have been a VR fanatic for about a decade now, and about 120 seconds of smooth locomotion can STILL put me on my ass for several hours.
The last time I dabbled in it, I couldn't look at a 2D screen without feeling nauseous the next day, either.
@Natan Getschel i have motion sickness just watching the devlogs, i can't imagine with VR on
@Natan Getschel i would disagree, I have a vr headset and I never get motionsick
Imagine a game like Pavlov in hyperbolic space, that would be wild
This is one of the few things making me not hate my Linar algebra and Calculus classes anymore.
@Sillygoose210 _ for me math is fun once i understand it, but getting there is a real pain in the ass.
I love algebra and league ❤️.. calculus just a little 🤭
There is such a thing as "Tensor Calculus" :-P :-) and apparently tensors often contain a nested structure of lesser tensors rather than just being of scalars/reals/complex.
Sillygoose210 _ if ur a loser with no life and can’t afford weed
@I’m stupid, but calculus and weed are the best combo, wtf are you on about?
I came for answers, and... boy did I get them.
So that’s why Miegakure’s been in development for so long? Yeah, I sure realize why now!
And I like how you reused your spherical geometry map, the one with the house and the fence, in demonstrating constructing hyperbolic geometry maps!
i'm so confused on all of this stuff.....
it really does explain a lot, in fact for me it actually kinda made me feel stupid about myself because the answer is so... SOO simple, just makes me think on how i didnt think of it
of course its been in develpment for over 10 years, go ahead and tell me a game engine that can run 4 dimensions
oh, well i'm actually relatively new to all of this stuff so it makes sense i'm confused. i like the videos though, they're cool(at least, the parts i can understand)
Noticed the Minecraft pig in your picture. Thought I should let you know I'm working on a hyperbolic minecraft game :)
Why don't you just use Cinema 4D for the 4D game???
because it's a toy, just like blender and gimp.
ill use Cinema 5D
ba dum tss
@chodari by 23exe its not expensive, you use 4D money to buy it, not 3D normal money
@xl we spotted the Maya user...
Yay another devlog hyperbolica is epic.
Hyperbolica*
Yes. Keep it coming. Please. I beg you!
Big epic by hurting my brain xD
,
@General Durchbruchmüller Ecks deeeeeeeeeee
And here I am staring at my calculus problems for school and going “wtf why are there more letters than numbers?”
Jesus Christ, I’m looking forward to trying to play this game!
Really love how the game is coming along so far. For whatever reason, I kind of dig being disoriented in the hyperbolic space and having to relearn a lot seems kinda fun & a challenge. Looking forward to the final game, you're doing God's work son
Love this series. The perfect blend of Math and Code to produce literally a new perspective.
"It's hard to draw 4D scenes on 2D paper"
Then maybe 4D scenes could be drawn on 3D paper.
Your monitol is still 2D tho
@Ascyt no mine is ULURU
Among the coolest and informative stuff I've seen this year. Thanks for explaining the Miegakure challenges, I've been checking out the progress several times a year.
I had numerics as an engineer... this is the E student watching the A student understanding and finding use of what I just accepted, memorized as algorithms and didn't find useful or interesting at all...
I hope you put more architecture in the game! Like multi-floor buildings with confusing corridors, staircases, and walkways in and between them.
This geometry really lends itself well to that as opposed to just open environments.
I love this kind of vlogs. You don't realize how much time consuming this is until you actually start doing it. Also, since there's not a lot of youtube videos on the matter, documenting this kind of stuff could be really helpful for someone trying to do something similar.
There is a way to store locations in non-Euclidean space. You just need to use metric tensors[ https://en.wikipedia.org/wiki/Metric_tensor ]. For a 3D space, the metric tensor would be 3x3. In your case, there's no curvature up or down. As such the metric tensor could probably simplify to a 2D-esque form[ https://en.wikipedia.org/wiki/Poincar%C3%A9_metric ]. Essentially, metric tensors tell you how much space is expanded or contracted in any given direction at any point. They can describe curved, non-Euclidean space extremely well.
In order to get the components of the metric tensor you still need a coordinate system, and a poor choice of coordinates will make the metric tensor components very complicated, so this doesn't avoid the coordinate system issue.
By the way, I think the game also has curvature up and down.
big brain man
I get a feeling that you have all the tools and ideas at your disposal to solve all the problems of current day Virtual Reality.
When you realise that code parade is the first person to talk about gyrovectors on yt
I love the idea of this game and i admire all the effort you're putting in this, i'll surely buy it.
P.s: This series definitely needs more views
Can we visit such a debug level in the game? This could enable us to learn more about how hyperbolic and spheric geometries work.
this looks amazing man, probably the most unique game i’ve ever heard of, how has this not been mass invested in yet? non euclidean gaming, genius
I didn’t realise it was so complicated to figure out how to walk around in hyperbolic space
me too. thought you'd just do some trickery with the output view
Imagine this being an online game, and being able to play the game like a shooter in hyperbolic space
oh sh-
You're the reason I've begun to lean forward building my own game, inspired avidly🥰
"You can multiply these matrices together..."
Me, a mathematician: yes... 'Multiply'.
I believe the technical term is "smoosh".
@OriginalPiMan Fusion is just a cheap tactic to make weak matrices stronger
Ok, let's throw aside the technical stuff for a min,
Is there a story to this game? And if so, what would it be?
You're a pioneer to the next step in the evolution of gaming.
This man's taking flat earth to whole new dimensions
I’m imagining a hyperbolic shooter and I think that would be dope
everyone: "with the exception of outer space, there is no such things like uncharted territories!"
CodeParade: "Hold my Euclidean geometry..."
Man, can't wait to blow my mind with Hyperbolica!!! Thanks for this logs, super interesting!
This game is gonna be a 1 of a kind when it comes out, and is inspiring a lot of people including myself.
But 1 question, is there going to be a deep story or will the game focus more on the Hyperbolic world aspect?
It will do both :)
Hey, you found a great way to make levels! I had a similar problem when I tried to make levels for my 4d game, basically being locked to using only primitives to create anything
I do kinda hope we can mess around with the geometry, I'd love to see what people make in higher geometry and how it looks cool
I love how uncanny the hyperbolic perspective looks. I'd love to see an environment rendered with lifelike textures, atmosphere and geography, but in hyperbolic space. I'm sure that would take a ton of resources and isn't really the point of Hyperbolica, but imagine the uncanniness.
I really want to see what this type of rendering could do for visual effects in movies to depict time travel, or passage through a wormhole. And imagine combining ray tracing into this kind of rendering.
Man this could really be a big step in videogames. Imagine the FC4 drug missions with this kind of stuff.
Woo! I'm so glad we get to watch the development, it definitely makes it seem like it's not going to go the way of Miegakure and stall out.
Let's just take a moment how one day this is going to be an amazing niche Indi game and we get to watch the development... That is down right amazing!!!!
I've been thinking. Objects in spherical space should look darker in the distance than nearby.
Because objects far away are stretched, they emit less light that reaches each of the pixels on screen. This means objects stretched 2x would look 4x darker because each pixel we would normally see would be spreading it's light across 4 pixels.
This would somewhat be counteracted by a different effect where pixels on object textures would be visible from bigger viewing angles. This would increase amount of light we would be able to see. So in spherical space every pixel on flat surface when viewed from maximum distance would be visible from 180 degree which would allow us to see every light ray it emits, but these light rays would also be stretched across entire sky, so the end result should be darker sky.
I think reverse should be true for hyperbolic space. More pixels would be firing light rays at us, but they would be doing so at smaller angle.
This project looks amazing to me. I wish it would also come out for VR, that would be mindblowing to actually experience hyperbolic space.
Thank you for sharing your work! This is fascinating stuff. I loved your 4D video, and I look forward to seeing more videos! :)
2:12 Getting flashbacks to making a Rubik's cube solver
@Sandy Ross Oh god I wonder what THAT would look like
@OrangeC7 What's tricky about this is there's no good way to add points on hyperbolic space together. In order to think of scrambles as points in hyperbolic space, you'd need points associated to 2 different scrambles to "sum" to a new point which corresponds to the composition of the 2 scrambles. That would mean the structure of the scrambles and their corresponding points would be the same. Unfortunately, there's no structure on hyperbolic space.
What you CAN do is map each scramble to a transformation of a hyperbolic space. These could be rotations, scalings, etc. Composing two transformations gives you a new transformation, just like composing two scrambles gives you a new scramble! However, To fully capture all the different ways to scramble a Rubiks cube, you'd probably need to consider hyperbolic spaces with more than 3 dimensions.
A similar line of thinking (mapping groups onto transformations of euclidian space) constitutes a whole field of math called "representation theory", which surprisingly enough is a vital part of modern physics!
OrangeC7 Don't we have URD=RU in hyperbolic space but not on a Rubik's cube? As well as UUUU=ø on a Rubiks cube but not in hyperbolic space
@columbus8myhw Yeah
@Sandy Ross oh
Surely you must be aware of the hyperbolic game engine made for hyper rogue, right?
Can’t wait to see more videos on this game. It’s such an interesting concept
I’ve been looking for 3d graphing tools, and was surprised to find out how limited they were, despite how common 3d modeling is. I went up to 4d graphs (because I need to represent a complex data set) and omg, there is Nothing!!
Can’t wait for full game and walkthrough, I wonder if there will be a boss or if this is a puzzle game? 🤔
This series is awesome! I love the idea of a spacially compactified mini-map. Not sure if that's technically what I was seeing go on, But that's best I can express the thought.
Klondike 2: the musical - 2020-09-01
This is literally the coolest game I have ever seen. I will be buying it as soon as it comes out!
Northwest passage - 2021-03-15
Yeah as appears to being figuratively the coolest game.
1marcelfilms - 2021-03-20
"buying"
x - 2021-04-24
@I'm not fucking using this account anymore Imagine being too much of a cheapskate leech to financially support creators you respect
Diego Bucarey - 2021-06-19
You can play Superliminal while you wait ;)
silent-lee - 2021-12-25
Same