How do non-euclidean games work? | Bitwise

I'm a professional programmer who works on games, web and VR/AR applications. With my videos I like to share the wonderful world of programming with everyone!
What are "non-euclidean" games and how do they work? We'll discuss the inner workings of games like Antichamber and Superliminal as well as discussing the theory behind non-euclidean geometry.
References
HyperRogue trailer • HyperRogue trailer
Zeno Rogue / 1245367263936512001
Unity stencil buffer tutorial www.alanzucconi.com/2015/12/0...
No! Euclid! GPY Ray Tracer game • "No! Euclid!" GPU Ray ...
Channel CNLohr / @cnlohr
Hyperbolica trailer • Hyperbolica: A Non-Euc...
Hyperbolica devlog #1 • Non-Euclidean Geometry...
Channel CodeParade / @codeparade
Antichamber store.steampowered.com/app/21...
Superliminal store.steampowered.com/app/10...
Hyperbolica store.steampowered.com/app/12...
HyperRogue store.steampowered.com/app/34...
Music in in outro:
Besus y Abrazor - Rolemusic: freemusicarchive.org/music/Ro... available under a Creative Commons Attribution license creativecommons.org/licenses/...

[@ZenoRogue]

Thanks for the shout-out! Here are some comments: * you say that "the shortest line on a sphere is not necessarily a straight line" but what is a straight line? It is a kind of meaningless concept until you define it. In my opinion a straight line is one that is (locally) shortest, making this "axiom" a definition. For a creature actually living in a non-Euclidean world, the shortest lines are indeed straight. If you are a creature living in a (two-dimensional) spherical geometry, the third dimension simply does not exist for you, and the great circles are perfectly straight lines, because they curve neither to the left nor to the right. Also, if you try a computer simulation of a spherical or hyperbolic three-dimensional space, the shortest lines will look straight (this is not the case in non-isotropic geometries though). * I definitely agree that all the games are just tricks. However, it does not matter! It is the effect which is important, not how it was achieved. The problem with games such as Antichamber or Superliminal is that they do not give a feeling of being in a non-Euclidean space at all. You do not see the visual or geometric effects typical for non-Euclidean geometry when playing these games. The effects you see have nothing to do with non-Euclidean geometry. * you sound as if non-Euclidean geometry was something accessible only to geniuses, and game development was easy. Most people are born with great math skills, which then deteriorate because of bad teaching. The math of non-Euclidean geometry is not really much more difficult than the Pythagorean theorem or trigonometry. The bigger problem is conceptual, not mathematical: people have their Euclidean intuitions so deeply ingrained that if you show them that they are wrong, they will not believe you and make the same Euclidean assumption again. * Also it is the best to just play a true non-Euclidean game and see for yourself. That is way better than watching videos or reading books. Everything can be experienced in HyperRogue.

[@Alayric]

Moreover, HyperRogue is a great game in itself!

[@MatthijsvanDuin]

It annoys me when people call things "non-euclidean" when they're really just euclidean (zero curvature) with somewhat weird global geometry

[@DigiDigger]

Thanks for checking out my video! I keep underestimating what a reach my videos can have, I think it's awesome that you found my video. Sorry for not including HyperRogue as an example, not sure how I forgot to include it in the video. I at least added a reference card and added a link to the description. Thank you for the insightful comments, I'll pin it in the hopes more people will read it :)

[@TomtheMagician21]

I agree because longitude lines aren’t even straight like the example in 2:55 but everything else was great

[@creativenametxt2960]

@@MatthijsvanDuin well, non Euclidean means some of the axioms don't work. Normally the axioms that don't work out lead to a non-zero curvature geometry. But any geometry that doesn't follow the axioms is non Euclidean. Even if all the axioms do work locally.

[@RealRalsei]

The original non euclidean space is the infinite staircase in Mario 64

[@Jummmpy]

lol

[@Twisted_Code]

well considering it uses that teleport trick (this is part of the reason the Bowser paintings on the side repeat periodically), I see no issue with this

[@miguelbaltazar7606]

Why portal? Why? WHY? W H Y

[@Mirthful_Midori]

Duke Nukem 3D had a secret level before that called "Tier Drops".

[@donflamingo795]

I believe it is pacman You got teleported back to the right if you go to left and vice versa The same goes to up and down

[@Terra-Antares]

Before portal 2, valve experimented with a concept called "f-stop" it basically had the same rules as the game seen near the end. You had a "magic" camera that takes pictures, take a picture of an object and suddenly you can place a much larger or smaller version of that object by just using the portrait. It was an interesting concept that never saw the light of day but at least its idea exists in many games today.

[@darkhoodchief]

Actually, I think that was supposed to be the premise of Portal 2. But playtesters got confused when a game named "portal" has no portals in it.

[@zarrowthehorse]

A bit off topic but Portal 2 is an amazing game

[@gamertherapyconsoleyoursel5804]

Seems a lot like Superliminal, definitely a head trip of a game.

[@_sam29]

@Julia Li sadly, no

[@MrCalhoun556]

@@Vindextra Viewfinder.

[@sonicnaruto12345]

Hyperbolica is an actual true Non-Euclidean game with curved space instead of a locally Euclidean game which occasionally breaks it's own space

[@godlyvex5543]

Hyperrogue as well. Hyperbolica sorta dropped the ball. Hyperrogue shows off tons of concepts explorable in-depth, while hyperbolica only briefly touches on most concepts.

[@louisrobitaille5810]

@@godlyvex5543 Code Parade documented how he made Hyperbolica. Idk if the Hyperrogue dev did too 🤔.

[@godlyvex5543]

@@louisrobitaille5810 Not sure, but hyperrogue is open source and has been used in research for applied hyperbolic geometry. It's clunky to use, but it has so many more features than hyperbolica. It has support for various tilings of the plane, including even spherical tilings, or 4d hypercrystal tilings.

[@SpydrXIII]

yeah the incorrect use of "non-euclidean" irks me. when someone says non-euclidean they almost always mean escherian.

[@duilinn]

Hyperbolica was fun to play but limiting the game world's size kind of makes it just feel like it's all just set in a town where everything is set really far apart even though it's technically close (perhaps inspired by American urban planning :P). I found myself using the minimap much of the time as my primary mode of navigation, thus turning it into a top-down 2d game like HyperRogue.

[@lightningmchick8948]

Dude, if my geometry teacher explained it like this, I wouldn't have done summer school

[@emmathomas1869]

Allot of KZbinrs are better teachers than real teachers

[@SpaceAgeDave]

Jim??

[@Thor_the_Doge]

Summer school? I feel bad for you...

[@lightningmchick8948]

@@Thor_the_Doge Twice man, and don't I was pretty lazy as hell

[@trentonharrower1854]

Lol Same.

[@markgearing]

Q: How can games be non-Euclidian? A: It’s software. It doesn’t have to model the real world.

[@markgearing]

pyropulse - If the title had been “How can a Euclidean game engine be tricked into providing a non-Euclidian game experience” you might have a point, no matter how triggered you come across as being. I invite you to watch the video again and see if the games shown model any real world experience you have ever had. However, the video title is “How do non-euclidian games work?”, and the true answer to that is better reflected by my comment than the content of the video. That’s a professional opinion, BTW. pyropulse, chill mate. Take a break if you’re stressed. 2020 will finally end and hopefully the world can become a friendly place again. Stay well until then.

[@bergkajian1257]

The non Euclidean world demo that shows at 5:09 is pretty close to what a non Euclidean world would really be like, but I get your point, there are no laws of physics to follow. you can do allmost anything with software, but still by definition the games shown are non Euclidean, some of them at least

[@tonydai782]

​@pyropulse The comment is meant to communicate the following: Software needn't follow what us humans see as normal. I don't see a reason to be toxic about the comment.

[@random-b-i2480]

@pyropulse oh my god you're so stupid

[@trevorthieme5157]

@@markgearing Well at the rate 2020 is going some science experiment will go haywire and break into the 4th or 5th dimension and we will be able to go beyond our euclidean realm while inviting aliens from some place like control...

[@algodude8713]

4:34 So my early 3d drawing program wasn't faulty, it was just simulating spherical space

[@stevecarter8810]

I love the way these "impossible" things are happening in a world that has taken decades to tune so that it didn't routinely do these kinds of reality-breaking things.

[@japanpanda2179]

Yeah it would be quite fun if these things actually did happen IRL though.

[@shadowcween7890]

I had to keep reading this be cause my brain just didn't understand it

[@jordanwardan7588]

the "world" they mean is the medium of video games

[@stevecarter8810]

@@jordanwardan7588 right. And 3d graphics, where we had to figure out projections that looked realistic, how to avoid drawing the backs of things, how to avoid drawing things that had other things in front of them, how to rotate things in such a way that they didn't lose all their integrity, the right way to move a camera so as not to spoil the illusion, etc.

[@reizinhodojogo3956]

@@japanpanda2179 yes, if we become able to make wormholes that have inertia we can make non euclidean spaces in earth, or a portal to the moon or something

[@darkhoodchief]

TL,DR: Euclidean: "Makes sense to me" Non-Euclidean: "How tf does that work?"

[@CypressConroy]

Thanks

[@evad.5174]

pyropulse dude no need to trash this person with your pseudo-intellectualism just because they don’t fully get a relatively complicated math concept. Everyone’s mind works differently.

[@darkhoodchief]

@pyropulse Wow, can't believe someone is taking comments too seriously. Maybe you should blow off a little steam if a dumb comment upsets you so much.

[@slendervendetta6229]

So, are women non-euclidean? Lel

[@ryno4ever433]

@pyropulse I'm impressed that you wrote this much without explaining anything, and instead managed to only insult people.

[@matthewschad6649]

For a moment I thought CodeParade uploaded when I saw a non-euclidean themed video.

[@fagelhd]

Same. Im glad he mentioned Hyperbolica

[@GlanVonBrylan]

It's funny how so many people imagine weird, eldritch stuff when hearing "non-euclidean"... Scared of a term they don't know, like with chemicals. Not realising they encounter non-euclidean geometry on a daily basis. Drew a face on a balloon? Had a tattoo? Congratulations, you made non-euclidian geometry. I guess we partly have to blame Lovecraft for that.

[@andersnaugle4105]

Glân von Brylân or maybe schools that don’t teach us this. You would expect a school to teach you more than KZbin can, but what can ya do. I still need to know the names of the wives a king killed thousands of years ago. Memorizing their names is far more important.

[@maskettaman1488]

@@andersnaugle4105 History is far more important for regular life than understanding non-euclidean geometry. I bet you've managed to draw a smiley face on a balloon before without ever being taught how.

[@andersnaugle4105]

Masketta Man yeah I guess you’re right. Just yesterday I communicated with some ancient polytheistic gods. None of my friends knew their names, but luckily I had learned to tell, the difference between the Greek and Norse gods. We all would have been struck down if not for my extensive knowledge of what I had previously thought were two dead religions. How amazingly lucky I was to have learned that in school. I admit that learning Euclidean geometry is pretty useless, but I think learning about fake gods from a dead religion that is now only relevant in statues and literature trumps that. So does learning the legal system of a dead civilization just so I can understand the origins of the term “an eye for an eye”. I could be learning how to do taxes or a business runs but instead I’m learning about... ziggurats. Instead of learning something useful I now know every single one of Heracles’ trials, as well as why he did them and how he died. I repeat, I learned the life story of a fake person from literally millennia ago before I learned how vote. Like seriously WTF?!?! Our society prioritized the life cycle of a butterfly before it’s own legal system!

[@GlanVonBrylan]

@@andersnaugle4105 History helps understanding today's world, but if you don't know History, I guess you can't realise that. Or maybe you simply don't care, in which case we don't need to further this conversation, since it obviously won't lead anywhere.

[@andersnaugle4105]

Glân von Brylân I understand WHY we learn history. I understand that we learn why Henry VIII killed his women because the ability to get a divorce was a significant event in women’s rights, and it also sparked the beginning of a newish religion. What I don’t understand is why we need to get quizzed on their names. I understand the impact the Greeks and Romans had on our governments, architecture, and more. I understand that a lot of that is because of their mythology and that we can understand more about them because of their mythology. What I don’t understand is why I need to know about Janus, god of doors. Wtf does a door have to do with anything. They literally already have a goddess of cross roads, why would they need another? He’s the most pointless, boring, and all around useless god ever. Why would I need to memorize his name for a test? I understand why we should learn about the history of native Americans. What I don’t understand is why I DIDN’T learn about all the amazing things that Geronimo did and all the hundreds and thousands of people who died because of the negligence of the US government. Learn from your mistakes and al, that right? Isn’t it all about that one quote “he who doesn’t know his history is doomed to repeat it” or something? But nooooo. It’s not like everyone knows his name without knowing any of his absolutely amazing bravery fighting for his people or anything. He’s not famous at all. I understand why I’m learning a lot of these things, but only generally. Most of the specifics are utterly useless and waste hundreds of hours teaching completely pointless garbage that will never be used by anyone in any context.

[@zzasdfwas]

There's multiple ways of being non-Euclidean. Portal and Antichamber are mostly flat and Euclidean as long as you aren't close to a portal, but globally are not simply connected and so the axioms don't hold. But hyperbolic and spherical spaces are curved, and so the axioms don't hold. I wouldn't say one is more truly non-Euclidean. But the former are not even smooth manifolds, having sharp edges where space breaks down. If you were to stand in a Portal portal and move sideways, would you be sliced in half by the sharp edges of space?

[@Kitulous]

I personally think you would still collide with the wall, even though the wall should be supposed to be infinitely thin. If you push yourself hard enough you would slice yourself I guess.

[@robbierotten2024]

There is an orange and blue portal frame around the portals, perhaps that provides a buffer between being cut in half.

[@thegaspatthegateway]

i ask myself that every day

[@eryxyre]

There are multiple ways of being non-Euclidean, you are correct about that. However, this word has a specific meaning in mathematics, and Portal and Antichamber do not conform to this meaning. Portals and Antichamber tricks change topology, but the geometry remains Euclidean.

[@eryxyre]

@pyropulse "Euclidean space" usually means this specific thing: en.wikipedia.org/wiki/Euclidean_space However, "non-Euclidean" means "Riemannian manifold which is not an Euclidean manifold" i.e. "Riemannian manifold whose geometry is not Euclidean". So Portal is an Euclidean manifold, but not the three-dimensional Euclidean space, and it is not non-Euclidean.

[@ShawnTheMidget]

He’s back boys! So excited to watch

[@shadowblood95]

Anti-Chamber was so fun. My favorite mechanic is finding out that you are expected to break the game. Set aside proper notions and see how often you have to do the exact opposite of what you think.

[@ripleyhero8245]

We were discussing the basic Euclidian Geometry in class, and I mentioned how some video games use their platform in creative ways to bend those Euclidian rules. I shared this video with the teacher, and made a 10 point extra credit assignment for the class if we could give a 150 word reaction of this video, discussing the stuff you went over.

[@wakacyjnakostnica4794]

Non-euclidian geometry: hi, whats up! My brain: *panic*

[@wakacyjnakostnica4794]

@pyropulse everyone doesnt care what did you hate, sorry

[@happinesstan]

@pyropulse I guess it beats hating yourself.

[@kriszenn1125]

stop worrying about non-euclidean geometry. it is just different curvatures. ever written a face on a balloon before? congrats, you made non-euclidean space

[@NiepKiep]

And he came back when we least expected him

[@plebisMaximus]

This is one trick where explaining the magic has only made it cooler. Simple, yet extremely effective.

[@alpik44]

actually, it was disappointing to know that non-euclidean games are actually euclidean lol

[@ipaqmaster]

It was annoying hearing them referred to as such when they were not.

[@davidkonevky7372]

I always knew that so it isn't that bad

[@user-ne1nw6hw2q]

The good thing is that there exists some real non-Euclidean games and you can play it. See HyperRogue for example. It is even free when it's without some minor bonuses.

[@zzasdfwas]

They aren't Euclidean. He even said that going by the axioms of Euclid, they violate them. But he suggested that they were less legitimate somehow. Which is a wrong way to put it. What he should have said is that they are non-Euclidean in different ways compared to the non-Euclidean games based on hyperbolic or spherical geometry.

[@anlumo1]

@@zzasdfwas They only violate these rules in very specific circumstances.

[@rambleroodle2369]

Imagine being so legendary that even after 2500 years they use your theories to describe geometry.

[@vorpal22]

Well, the Greeks formed a lot of the basis of modern mathematics. Look at how important the Pythagorean theorem is.

[@zokushatech]

@@vorpal22 fun fact Pythagoras was a crazy spiritual leader guy who created a cult and had nothing to do with mathematics. “His” theorem was well known for almost 1300 years before he was even born

[@vorpal22]

@@zokushatech It has been discovered by different cultures at different points throughout history, but the ancient Greeks had a system of logic in place that allowed for proving things rigorously, and made many important mathematical discoveries. While I already knew that Pythagoras was a "spiritual leader," that fact doesn't matter to me when discussing math. History is littered with charismatic people who started a religion / who a religion was started around. I mean, look at Christianity and Islam... both incredibly stupid religions, one started around a figurehead, and one started because of a figurehead. Same with Mormonism, Scientology, and many others. The fact that Catholics believe that the Pope is the spokesperson for their god is just as ridiculous, especially since each Pope has advocated for different things, and the mind of their god Yahweh is supposed to be unchanging and yet it clearly changed according to all branches of Christianity when Jesus died, and according to Catholicism, keeps on changing.

[@vorpal22]

@@zokushatech (I did not know about Plimpton 322 formerly, though, so thank you for indirectly teaching me something new.)

[@thisrandomdude2846]

YOOOOOO I suggested this a while back, glad to say it so beautifully explained!

[@crispybacon4240]

lIteRaLlY?

[@Andrew-rd9zq]

Literally literal

[@saffetsinanoglu2631]

Bro you're giving us hope like this, making amazing videos and whatnot

[@saffetsinanoglu2631]

Dont leave again? Deal.

[@happinesstan]

Really? Your hope lies in computer games? Welcome to the simulation, sir.

[@Xonatron]

2:51 - Actually... a straight line is still the shortest in the curved space shown (sphere). The curve you see is extra-dimensional and is not an actual curve within the curved space.

[@happinesstan]

And then he doesn't pick two parallel lines. 3 mins in and I'm already wondering what the game is.

[@NitzanBueno]

@@happinesstan The lines are actually parallel

[@illeatthat]

If you imagine the 3D sphere - cutting through the sphere (the straight line) IS still the shortest, just the diagram shows the line along the surface as opposed to cutting through

[@illeatthat]

Nitzan Bueno they’re 2d lines on a 3D object - they’re parallel in terms of their dimensions - but in a 3D object, they’re not actually parallel. They’d have to cut through the sphere

[@illeatthat]

I think we said the same thing - please regard my response as moot aha 😅

[@sargentjayro715]

This video coming into existence at this point in my life has made my week

[@benthomason3307]

"Hey vsaue, michale here. These games are non-euclidean. _or are they?_ "

[@Brahvim]

OOf xDDD

[@NovaGamma_]

What a great video, just like the other of the bitwise series, I always love to see and understand how these games mechanics works with a great explanation and plenty of examples

[@wswanberg]

"On spherical surfaces parallel lines converge." Latitude lines: Am I a joke to you?

[@cringium]

are you sure its a line or a circle.

[@CatNolara]

those aren't straight in spherical space tho

[@dannygjk]

ikr

[@trueriver1950]

Correct. The axiom should refer to straight lines. The oddest thing about latitude lines (from a Euclidean perspective) is that two latitude lines are everywhere parallel even though they are curved with different radii. Two latitude lines in opposite hemispheres are parallel even though they are curved "away" from each other. The oddest example is the equator and any other latitude line. There we have a straight line that is parallel everywhere along its length to a curved one.

[@TheNinthGenerarion]

@@trueriver1950 although the latitude lines do curve when they’re not at the equator, if they were straight lines they would converge

[@rodneylives]

You mentioned Zeno Rogue! He's awesome, and his game Hyperrogue is a way to help wrap your head around what hyperbolic planes are like interactively.

[@AvarFeralfang]

Their teleportation had to be on point, literally. They make sure that you teleport not only to the hallway but to the corresponding position in the destination hallway. I love these games!

[@iamwhatitorture6072]

It may sound difficult, but you really just always teleport the same distance on every axis and the distance is simply dependend on the size of the map

[@RafaelMunizYT]

@@iamwhatitorture6072 the maps could also be on top of each other so you only change the Y position

[@RadeticDaniel]

@@RafaelMunizYT that was my first thought too some clever alignment and you are good to go for a prototype

[@ItsLumina]

AN UPLOAD! THIS MUST BE WHAT THE PROPHECY WAS SPEAKING OF

[@Tuntor689]

“The fastest way to get from one point to another is a straight line with no curvature” Bhoppers: Well, yes but actually no

[@atumaIaca]

ayyy, glad to know you're back dude!! hope you continue with your work in these videos, they are really great. Have fun making them, 'cause we're sure having fun watching 'em

[@alexdiez993]

Nobody: Christopher Nolan: lets write a film around this

[@defectivepikachu4582]

plot twist christopher nolan made these games

[@japanpanda2179]

Is that Inception you mean?

[@invghost]

I love non-euclidean puzzle games. Working out something that breaks everything you're meant to know is immensely satisfying.

[@Jay-ln1co]

I remember an old Duke Nukem 3D map, where there's two skyscrapers with pools on top. There's a vent in each pool that you can swim through to get from one pool to another. But there's no structure between the buildings connecting them. The buildings aren't even the same height, but the tunnel from one pool to the next is a straight line.

[@Mate_Antal_Zoltan]

that game already uses teleports to sell the illusion of rooms stacked on top of one another

[@ubergnu]

This is so much fun to play with! I'm doing an infinitive rooms walk, the gimmick is that everything you did in previous rooms is saved. And the rooms loops back in an illogical manner, so you can't draw a map of it. With a 2x10^6 rooms I don't know how to make a game of this or how to make it interesting, but the technical aspect of it is fun!

[@krawutz6515]

Yay, you're back! Thanks! :D

[@arnau02]

I don't know why youtube has recomended this to me, but, man, thank you. This is amazing.

[@EarnestKane]

Such a great introduction of how physical geometry could work in game engine. Inspiring and fantastic, appreciate your work:)

[@Cyberian_Khatru]

"you don't have to be incredibly smart or talented to create one of these things" lol what a backhanded compliment though I agree

[@coyraig8332]

It's accurate, but it still takes a bit of creativity to come up with

[@vorpal22]

This was a fun video, especially since I just finished writing a ray tracer yesterday, and I have a PhD in math and have worked a lot with non-Euclidean geometries. People should keep in mind that we're (basically) living on a spherical geometry: it's just a topological manifold as it's locally Euclidean (i.e. we get all the effects of Euclidean geometries on small scales: if you draw a triangle with chalk on the ground, it's going to look like the angles add up to 180 degrees even though in reality it's going to be 180 + epsilon for some very tiny value epsilon), and it's large enough that we can't usually detect that it's not Euclidean. When you fly, though, as you said, the shortest distance between two points is actually the great circle between them (take those two points and draw a circle passing through both of them that is just the equator transformed) and lines on a sphere are all great circles, where as you say, parallel lines intersect. We perceive ourselves to be living in 3D, but the surface of a sphere is a 2D geometry. It's also part of the reason why making accurate maps are so hard: you can't "unfold" the earth into a rectangle (basically a plane which would be a Euclidean geometry), since the surface of the Earth is non-Euclidean. As for the cube room, this could just be done with projective geometries. You're basically living in a projective geometry if you close one eye and it's what ray tracing is based on, as are, say, movies watched on a flat surface: you're watching a projection of a 3D world onto a 2D one... so those cubes you saw could just be like a "six sided LCD screen" with each side being a unique projective geometry onto a completely different scene. When I play a game like Boggle, I always feel cheated that it's played on a 4x4 grid, since the letters in the corners are only adjacent to three other letters, the letters on a side are adjacent to five, and the letters not on corners or sides are adjacent to nine... so I play Boggle on the surface of a torus instead (which is essentially a donut): you can "roll over" the top of the grid to the bottom (pretend they're glued together), and if you think of it that way, then you turn the surface of the board into a cylinder. If you then do the same thing to glue the left and right sides of the board, you take that cylinder of finite length, curve it around, and connect the ends, which gives you the "donut" shape of a torus. A real mindf*ck is to try to play Boggle on the surface of a finite projective geometry: take the top of the board, flip it around, and glue it to the bottom of the board: they you get a Möbius strip. Do the same thing with the left and right sides and you get a shape that you can't even really imagine. I worked on an app where you can choose the surface you want to play Boggle on, and when you click a letter, it shows what letters are considered adjacent to it... playing on a torus feels really natural, but playing on a finite projective geometry is very disorienting. Fun stuff and good video.

[@fim-43redeye31]

That sounds absurd. Is that app public? I bet people would love to try it.

[@vorpal22]

@@fim-43redeye31 I never quite finished it... most of the logic is in place (and it has a border around the board that shows the across-board adjacencies so you can wrap your head around the different geometries), but I never got to the scoring or the configuration UI, and then I ended up moving on because it was in Java using JavaFX. I might go back to it at some point. Here's a video that shows how it's laid out, if you're interested: kzbin.info/www/bejne/joSlmpekhZ19nZI

[@scrithen2836]

Everytime i see antichamber i get reminded of when someone posted a “Portal 3 Gameplay” video and it was just antichamber

[@auhsojacosta1672]

Oof

[@timchanux]

Welcome back! High quality content as always

[@whynotanyting]

I was really impressed with superliminal when it came out. Literally didn't know how it was achieved. Now it looks so simple, but it's great.

[@brunoo_dgs2195]

so nice this video, has explaned so many of my questions.

[@beeboi5467]

"a love to create and a passion to learn" I thought you were gonna transition into a skillshare sponsorship

[@nyuppo]

He's back! Always love to see content from this channel

[@malul_dog-trainer]

First video I checked out from you. Loved it and I'm here to stay, will be looking out for what ever you put out ther

[@madesta3667]

Great video! You teach people by using an unusual and most importantly an interesting example - games. As a 15 year old student, I am VERY interesting to watch this, thanks. I played Antichamber almost 5 year old, but still remember that masterpiece, i should play it again!

[@Nonkel_Jef]

Really interesting games. Highly recommend Monument Valley as well. It uses isometric perspective with Escher-like tricks, where things that look connected are corrected.

[@SpunerPlay]

Your content is truly amazing. I wish there was more of it.

[@yeehaw142]

I love this content man, incredible work.

[@kobeneilson6717]

Hey, around 1:35, perspective geometry claims that parallel lines intersect at infinity. On another note, there is another game similar to those showcased in which the player has a camera that takes photos, then can put the picture anywhere, and the picture becomes physical.

[@KindOldRaven]

I agree that we can't really fault '3D' videogames (or VR games) for trickery since it's literally all trickery in the first place ;p ''3D'' games aren't truly 3D, visually speaking, as we all know and VR is possibly even more trickery and illusion. Adding in more clever illusions to portray concepts such as non-euclidian geometry is brilliant. There's a few VR titles that mildly lend from these concepts as well. It's mostly portal/movement speed trickery in those, but still very clever and weird to experience. Whether it's ''Tea for God'' or ''Shattered Lights'' (both of which you will walk around your own playspace, despite traveling larger distances in game) or other roomspace/playspace trickery it's quite weird experience.

[@errantoverflow4828]

This was a very interesting topic to cover. You always deliver with your videos!

[@JaggerMcClaw]

Great video! I definitely think the in engine examples you show put your vid a step above other explanations that I've seen of antichamber.

[@idna832]

*watches whole vid* Digi: "Now youre a "bit wiser" me: "Ohhhhhhhhhhhhhh"

[@christopherking6129]

You forgot to mention Hyperrogue, one of the original noneuclidean geometry games.

[@miguelbaltazar7606]

What is Hyperrouge?

[@christopherking6129]

@@miguelbaltazar7606 a Hyperbolic rogue like. There is even a free version.

[@bearlykoalafied9821]

Bro throughout all of highschool i struggled with finding angles in triangles cause i never understood and you literally just helped me figure it out in less than 3 seconds

[@EpicStealthyNinja]

Love your content. Glad you are still posting.

[@daniellopespvh2]

0:46 maybe the most famous Brazilian meme good taste

[@LeftSoulz]

Excuse-me, what the porra kkk zoa, é de fucker msm

[@murilorocha531]

very fuck

[@feliperafael8104]

cuma? rsrsrsr

[@luiz.brandao]

Eu tava procurando este comentário kkkkk

[@brunovaz]

Brasileiro, o povo mais carente do mundo

[@DarkKnightDad]

"You could say you are a bit wiser" 😅❤❤❤

[@louiebeatty3667]

Always a joy when you upload

[@_bruddy]

This video is worth more than it sets itself out to be. Thank you!!!

[@Firestar19]

Wouldn't be surprised if he just said "First, we need to talk about parallel universes." Then just started talking about SM64

[@raphaelcardoso7927]

0:46 a brazilian meme! here's my like

[@blueninja012]

I love these videos so much I'm so glad you're making more

[@TheBloodRedDane]

Really appreciate this vid. it's something I've wondered about for years.

[@connorconnor2421]

"Light rays hate your eyes"

[@connorconnor2421]

5:24

[@cassied9327]

Stop that 🛑 😂 ✋

[@Exile5796]

I’m going to buy Superliminal on the Epic Games Store after having seen this video. Do you have an Epic Games Store creator tag?

[@syynti]

materiał jak zawsze przyjemny w odbiorze. czekam na kolejną część!

[@eriodas4802]

this is actually very helpful, thanks for the great explanation!!

[@iangabriel5536]

As a brazilian, it's fun to see a Nazaré Tadesco(the math woman) meme.

[@luiz.brandao]

kkkkkkkkkkkkkkk HU3HU3HU3HU3HU3 BR

[@nerszi8479]

SIM KSKAKW

[@sinom]

2:59 that point doesn't really work. We can't tell that thee shortest paths aren't straight lines just by looking at them, because for the space to be non Euclidian, this 2D space isn't allowed to be 3D, so any curvature into the third dimension doesn't matter. That's why using a sphere as an illustration is kinda bad. Edit. Ok I was too stupid to read the pinned comment. That already talked about that problem.

[@kiroshi7364]

Omg! I just watched your portal video like 2-3 months ago and got so sad you haven’t posted in 3 years! I’m happy to see you back

[@craigpowell4142]

One of the first examples of non-euclidean geometry in a game that I recall seeing was a deathmatch map in Bungie's game Marathon in the mid-90's. I believe it was called "4D Space". Was a fun one to play. Possible or even likely there were examples prior, but that was my introduction to warping the 3D world in this fashion.

[@frankbruder3097]

I'm sure some are looking for this and were disappointed that it's not provided in the video. So: Use Möbius transformations of quaternions. (Look it up if it's new to you. I won't give full explanations here.) Quaternion rotations are represented as Möbius transformations of the form q 0 0 q A parallel transport (translation) of distance s in the direction of unit vector v is... in a flat Euclidean space: 1 sv 0 1 in a spherical space of curvature 1: cos(s) sin(s)v sin(s)v cos(s) in a hyperblic space of curvature -1: cosh(s) sinh(s)v -sinh(s)v cosh(s) This works with coordinates in a polar projection for spherical and a Poincaré disk for hyperbolic space. Geodesic surfaces are represented as surfaces of constant curvature (spheres and planes). If you want to use standard Z-buffer based 3d graphics, then for rendering you need to transform the hyperbolic coordinates to the Beltrami-Klein model and the spherical coordinates to a central projection. The central projection can only map half of the sphere, and that's ignoring limits of floating point precision. So you'd need think about how you can slice and dice your frustrum to render beyond that. In all of this we use the imaginary space of the quaternions as our three-dimensional world. But we're using four-dimensional quaternions internally. So this can easily be expanded to a four-dimensional world by allowing rotations into the real-valued axis of the form q 0 0 q* (where q* is the conjugate of q) and allowing v to have non-zero real values.

[@desmonddart5163]

You gotta play "manifold garden", this game is mesmerizing af

[@digimaks]

Trippyyyy!! I kinda did that effect in Unreal Tournament long time ago, when they had "portal" zoning mechanics. It did exactly that by a geometry plane displaying the other geometry plane in another part of the map. So you could literally walk from one part of the map to the other without noticing space bending.

[@Isami510]

Welcome back, dude Great vid, as always

[@Favmir]

2:54 nitpicking, but that's not the shortest line!

[@MarkArandjus]

"Luckily the answer isn't every complex" He said as if it didn't take mathematicians hundreds of years to figure it out :D

[@OP-lk4tw]

funny you just mentioned my 3 favorite games at the start of the video xD, i love the immersion in these trippy worlds

[@ricardocardenas186]

Thank you for making us a bit wiser!

[@Yipper64]

Theres one game you didnt mention but it also does this, almost identically to antichamber. Its called "the Stanley parable" it doesnt focus on these instances, but rather just casually has them strewn about the world making it feel just that more surreal.

[@Potatinized]

"You dont have to be super smart to create games like these" Gamers, playing these games: Holy sheeeitttt!!! The guys who made this must be lvl 255 wizards!

[@fomalhaut3451]

I follow hyperbolica's development, trust me when I say that dude IS a wizard

[@sumitrana2420]

They are as smart as coders must be. The great thing is the innovative mindset to use the same tools. Those other coders could also make this once they know the tricks. But there are sometimes some really smart stuff needed to be done for things that gamers like us just ignore on first hand basis.

[@Aragubas]

i love the videos on this channel and how you explain things!

[@TechNinjaSigma]

glad you're back Digi, great video!

[@TheCaptainLulz]

9:33 - Or they designed a virtual mirror image box. They sell these for real. Its half an image on one side of the v and mirror on the other, so it looks like a whole image, but you can have up to 4 images, one on each size.

[@TheGroxCS]

although it has sense, that doesn't work pretty well in the final result.

[@HironixGamer]

I was just looking for a different game to play and now I'm a phd in physics

[@whypper8427]

I found this video very well explained and the examples were very helpful!

[@falxie_]

I want more games that explore this concept because it's so neat

[@RealRalsei]

And then there's me who has never heard of antichamber

[@eramires]

I talk to some people about this kind of thing and they actually think games should simulate 100% accurate real world rules, but the game don't actually need to do that, cause you can totally fake it in the code and the player wont ever notice the difference if done right, and in the end you save some performance. I was discussing about orbital mechanics and FTL drives and the dude went nuts saying the FTL should totally calculate the velocity + orbit change + gravitational pull, etc, etc, i just said like: all it need to do is make the ship move forward in a straight line, lerping the movement, that's all. But he insisted it should be applied real formulas, i was like omg dude you over complicating this xD

[@Flightcoach]

Wow! Blew my mind with the clear explanation and visuals. Did you make those explainer clips yourself as well? Must have been a lot of work! Liked and subbed!

[@Gale42]

in fact i tought this was a code parade video, until i saw the thumbnail, and i was happy to see your channel with a new video

[@IthinkitsaDanny]

The non Euclidean games really make me feel uncomfortable. Especially that ray tracing game ahhhh it makes my skin crawl.

[@EBTS-3]

Yeah that ray tracing one reminds me of fever dream memories

[@AllvezTV]

0:46 Nazaré Tedesco rainha dos memes 🥰❤️🇧🇷

[@daniel_argolo]

The math meme earned you an easy like haha, and the content is pretty well produced, thank you.

[@dominikcygan2664]

these are my favourite type of games and i never knew what they're called, so glad i found this video