Projecting Space - Hyperbolica Devlog #4

In this 4th installment, we'll go beyond the camera and dive into the tricky
nuances of dealing with hyperbolic and spherical rendering, how to achieve them in a traditional rendering pipeline, and working with gravity in a hyperbolic world.
Previous Devlogs:
Devlog #1: • Non-Euclidean Geometry...
Devlog #2: • Spherical Geometry Is ...
Devlog #3: • Rendering Hyperbolic S...
Hyperbolica on Steam: store.steampowered.com/app/12...
Trailer: • Hyperbolica: A Non-Euc...
Discord Server: / discord
Merch: crowdmade.com/collections/cod...
If you like the things I do and want to support the channel:
/ codeparade
ko-fi.com/codeparade
Music:
Jesse Spillane - No Disclaimer
jessespillane.bandcamp.com/al...

[@AgentM124]

He can just show his code and dev progress without the fear of anyone making a clone or stealing his idea, because nobody understands even remotely what he's doing.

[@linklayer1318]

Ah yes, that Code is made of Code

[@bhanusri3732]

Yes so true

[@soldier6173]

He knows that the unworthy who will try to decode it will lose their sanity in the process so he doesn't have to worry

[@ultimatedude5686]

I get what he's saying but I have no idea how this'd be put into code, I'm not really skilled at this type of thing. If I remember correctly he's making the engine open-source anyway

[@AgentM124]

@@linklayer1318 actually the Code is all Cake. Everything is cake. This comment is cake. 🍰

[@nutzeeer]

I find the increase in curvature on high objects nice. its like they bow their shape to the roundness of the world. fits right in!

[@Nerdule]

Sort of, except the world in hyperbolic space *isn't round!* (In fact, it's very much the opposite of spherical). It just kind of *looks* like it due to some trickiness about the way light rays move in hyperbolic space.

[@mattontop]

@@Nerdule yeah i think that op knows that. The world just looks like a sphere but it isn't one.

[@freedomofspeech2867]

it would be nice if the center of the worlds "bendiness" followed the player tho.

[@omnificatorg4426]

That's questionable. Maybe only large objects (buildings etc.) should be curved as altitude rises. In a hyperbolic world, you can build a tower on a small piece of ground, and the higher you build it, the wider it becomes. Each floor of the building represents a piece of hypersphere, the convex surface equidistant to the ground plane. Or, if you dig under the ground, you will get concave floors. Unlike buildings, small objects (crates etc.) should retain their shape, regardless of the altitude where you find them.

[@pietrocelano23]

shouldnt they curve the other way around? like how the fence always looks like it bends away from you?

[@DrakiniteOfficial]

I'm glad you recognized that the demographic of people who are interested in this game (your viewers) are also going to be just as interested in all the technical challenges you faced along the way. This is way more fascinating than JUST seeing the finished product.

[@-jadepink-500]

So true ;v;

[@Christer2222]

Moving around in VR makes most people motion sick, but I can't imagine how sick you would get it hyperbolic VR lol

[@rt_w1456]

Need anti nausa meds just thinking about it

[@tekbox7909]

Not most people to my knowledge and a lot just comes down to the kind of game one is playing in vr as well as how well movement is handled.

[@mibdev]

@Tekbox is right on the money. I've tried the demo shown and since it never *moves* you, there's no real chance of getting motion sick.

[@The_SOB_II]

@@mibdev For some people, there's always a chance of getting motion sickness. Even if the game isn't moving you

[@Griffin12536]

I'm poping dramamine just to watch his devlogs. I think I'll pass on a vr version.

[@kindoflame]

CodeParade: "This comes with a weird compromise... As you increase in elevation, you end up moving faster the higher up you go." Speedrunners: "Its not a bug, its a feature!"

[@reizinhodojogo3956]

spam jump run

[@justrecentlyi5444]

"You move faster the higher up you are" *Speedrunners perk up*

[@xp7108]

Bhop time

[@_Killkor]

Hyperbolica Skyhop any% Glitchless

[@_Killkor]

@@corb805 Yeah, we know. It was a speedrunning joke.

[@data_5674]

i bet the main strat is to constantly jump to get that slightly faster movement speed

[@RoboSkyrat]

I'm not even a speedrunner and I still perked up at it

[@Maxi25554]

Honestly cannot wait to play this game when it releases :D

[@ozzymetalface7363]

Same

[@gibbz115]

same

[@bloooops]

Same

[@vvill-ga]

Don't forget to wishlist the game on Steam! store.steampowered.com/app/1256230/Hyperbolica

[@thechosenone9910]

Same

[@SaplingxAura]

If you move faster while higher, and then slower while close to the ground, are you decelerating as you fall?

[@leleo53000]

you move faster on the horizontal plane as you go higher, but your speed isn't impacted on the vertical axis.

[@thegaspatthegateway]

@Questa Semplice Animazione that really turns my stomach. literally!

[@DragonWinter36]

Horizontally, yes, but not vertically

[@Edwing77]

@@thegaspatthegateway nice 1

[@leonidmeleshin4227]

No, because Y-axis uses euclidian physics

[@Grimfoon]

my brain hurts but i think that's a good sign you've developed something special

[@mRmAN-jl1jh]

I made this comment 69 likes

[@Charcoal190]

"The higher you are, the faster you go" is basically the equivalent of picking the top route in Sonic games.

[@juliewinchester1488]

The avatar checks out

[@GameVyse]

I can't wait for speedrunners to get ahold of this game.

[@henrikljungstrand2036]

Speedrunners always learn to master and tweak any game popular enough. Just look at speedruns for various quests in Hyper Rogue!

[@diribigal]

Weird. Speedrunners have already gotten ahold of the Minkowski space level of this game in my reference frame.

[@randomcatdude]

Just imagine what will happen once they find some kind of out-of-bounds bug.

[@nemesisurvivorleon]

I can't wait to watch their speedruns and vomit from disorientation.

[@woosix7735]

No one: Speedruners: you can go faster on a curved trajectory than on a straight line

[@freedomofspeech2867]

This is what happens when you make acid illegal. People just find alternatives.

[@dark5358]

Real talk, they just keep finding acid. Making harmless drugs illegal accomplishes nothing useful.

[@freedomofspeech2867]

@@dark5358 It's not harmless but yes, making it illegal is a small brain move.

[@nodros1]

@@freedomofspeech2867 shout out to Oregon

[@dungeonmaster217]

@@dark5358 science can by way more trippy than psychedelics.

[@tristenarctician6910]

But hyperbolica has a minimap, and that needs different projections to make it easier to read

[@ShamikShah]

I think that the increase in speed and curvature at higher elevations sounds like a feature, not a bug. It sounds super awesome, like maybe there's a thing that you can only do at a higher elevation that you can't do at a lower one or something.

[@Izzythemaker127]

The faster speed doesn't mean anything because platforms are also bigger at higher heights, and because of the speed change, you accelerate(horizontally) as you get higher, and decelerate as you get lower.

[@megalunalexi5601]

This music is completely perfect for the trippy weirdness going on, I *adore* it

[@oh_tassos]

i like the consequences of using euclidean height, it feels... like an interesting gimmick i dont know what its meant to look like normally nor can i imagine that but it looks cool the way you have done it

[@CedarAce1000]

The dev logs are always appreciated! You always bring up issues I never would have imagined would exist :)

[@OneShot_cest_mieux]

Niko power

[@gjkdshgkjshjkgdfg]

Niko power

[@rolandkatsuragi]

3:22 Does geometry from both hemispheres have a risk of colliding into each other?

[@CodeParade]

The split into hemispheres is just a rendering thing, physical objects exist in only 1 space, so there's no problems with collisions. If you mean overlapping geometry, then yes, but it's okay because both hemispheres should be drawing the same thing at the equator.

[@ThatGuyCanmanNC]

@@CodeParade ah yes, words

[@jojojorisjhjosef]

This madlad not only tried every perspective possible, he seamlessly transitions between them, just for a few frames for a video. Gucci gang aint got nothing on this lvl of flexing.

[@CodeParade]

I already had the smooth transitions from the in-game map, so I didn't have to add that much to make the video.

[@ZenoRogue]

This is actually very simple: the Beltrami-Klein projection, Poincaré projection, and Gans projection are all obtained from the hyperboloid model by projecting from different points (respectively 0, -1, and -infinity). The intermediate values yield intermediate projections. (Exactly the same holds for their spherical analogs: gnomonic, stereographic and orthographic.) Far from every perspective possible, there are dozens more, just like there are dozens of spherical projections -- then transitioning is harder, but still possible in many cases. (see e.g. my video "Hyperbolic analogs of spherical projections")

[@Lucky10279]

@@ZenoRogue I think we have different definitions of "very simple."

[@ZenoRogue]

​@@Lucky10279 Well, if you already did implement all these projections, and did it correctly, then the transitions are very simple :)

[@Lucky10279]

@@ZenoRogue So basically, you're saying that it's simple _after_ you've already done all the complicated stuff?

[@DenisShiryaev]

Great video, as usual, looking forward to star playing it

[@Fleechin]

Last I was this early Euclid had just made his fifth postulate

[@valarikjeffeerson7226]

oof

[@jonwallace6204]

Sick reference bro

[@Fleechin]

@Michael Darrow Maybe I was

[@notanimposter]

These devlogs are straight up some of the most interesting videos on KZbin right now

[@Driesipops]

i like to pretend to understand what he is saying

[@arnavdas3139]

Bruh u mah soul or something ?

[@Gejam_GameDev]

Me 2

[@morkovija]

indeed!

[@zyansheep]

Oh, he used 2 hyperbolic dimensions and one euclidean dimension for physics to prevent weird spacial camera movement? yes, I know *exactly* what that means.

[@theawesome1883]

I watch his videos to pretend that I am good at programing and understand complex programing things

[@NStripleseven]

These videos are really interesting, and they bring up problems that you would never encounter in a normal game.

[@LeoStaley]

Just waiting for ZenoTheRogue, the internet's expert on non-euclidean gaming, to weigh in, like he did on the Las one.

[@ZenoRogue]

Not much to talk about on this one, although it seems that correct S3 rendering can be done better than explained here. In HyperRogue we just make four passes based on gnomonic projection (distances 0 to 90deg, 90 to 180, 180 to 270, 270 to 360) and it just works, without any discontinuities. I believe Jeff Weeks explains in his papers how to do this with just two passes -- but the spherical spaces are small, so there is no need to optimize much.

[@omnificatorg4426]

@@ZenoRogue is it just a kind of cubemap? (sorry, I'm noob in spherical geometry)

[@ZenoRogue]

@@omnificatorg4426 No, I do not think cubemaps are related. In spherical geometry you can measure the distances using angle measures, i.e., degrees. If you feed the sphere model coordinates* to OpenGL, IIRC it will correctly render what is in front of you, but only up to 90 degrees from you; anything else won't be rendered. But you can do this four times, to also render 90 to 180 degrees (in front of you but on the other hemisphere), 180 to 270 (behind the antipodal point), and 270 to 360 (behind you, but still visible because the sphere wraps around). And there are no holes that way. * (x,y,z,w) such that x²+y²+z²+w²=1

[@omnificatorg4426]

@@ZenoRogue Gnomonic projection is the only one that keeps lines straight, am I right? But if you project a hemisphere onto a plane, the equator goes to infinity. The equator itself is a place where geodesics (i.e. camera rays) become "parallel". How can you render areas beyond the equator, where the rays start to converge, without distorting all the nearby hemisphere? Or it needs to be compressed in a kind of way?

[@ZenoRogue]

@@omnificatorg4426 Yes, that's why this projection renders only distances up to 90 degrees (the equator is at 90 degrees). But all the four sections can be rendered in the same way, so you first render the furthest section, clear the depth buffer, render the second further, clear the depth buffer, etc.

[@nextProgram]

I swear this has to be the most technical game ever

[@abyvs]

Yes! I’ve been patiently waiting for the next update. I’m so excited to see how this game turns out

[@michaelchikos4551]

The sheer challenge of this is so interesting to watch. This is uncharted territory. I don’t understand half of what you’re saying, but the shapes you’re making are awesome. The solution at 3:17 makes me reimagine how alien it really would be to be in that world. It reminds me of how hyperbolic crochet looks, or how some 3d models show the hyperbolic plane as a reverse sphere.

[@alexandersolodovnikov4840]

So basically your game will have a hybrid world with geometry from one space but with physics from the other?

[@HinnerkHesse]

I think the increased movement speed higher up could be a nice part of level design !

[@yommish]

The thought of troubleshooting these issues tickles my brain and sounds really fun but also maddeningly difficult. Very cool that someone is able to do it.

[@micahgilbert8019]

I personally like the look of the curvature on the boxes higher up.

[@HarhaMedia]

This is a very very interesting series!

[@benwaffleiron]

babe wake up, new codeparade video

[@AidenOcelot]

OH wow, I was wondering a few days ago if the vertical axis was also hyperbolic

[@iestynne]

Fascinating! Thank you for making this series and for covering technical issues in such detail.

[@shadowdude101]

Your devlogs are an absolute blessing. You are a wondrous pioneer in the future of video games.

[@builder1013]

I don’t know what he’s talking about; I just like watching him play the game.

[@hashasbashbash2724]

Lel same

[@eftorq]

All of this makes so much sense! Please keep this Devlog going forever!

[@ThatCardTi]

first video I've seen of yours. I subscribed right away. Impressive dude, Keep up the good work!

[@zenu903]

Even though I don't understand half of the things being presented here I love watching these devlogs! Hyberbolica seems so fascinating and mesmerizing, I can't wait to see more!

[@joshuaolian7732]

your ability to understand all of this stuff and apply it to your coding is so awesome!

[@stanley8006]

damn no the visual increase in curvature the higher you go looks amazing, and it's yet another thing players could get there head around. It would be fun! Plus it just adds to the charm of the weirdness

[@WhipinsnapperYT]

LET'S GOOOOO I'm so hyped for this

[@TheAechBomb]

I'm hyperbolic for this game too

[@danielkjm]

*Your game its Awesome, and i am spreading to everyone i know, friends, KZbinrs, Streamers, and several game design foruns. Your game will change how we think and create games, you are an Inspiration*

[@Thrustmaster64]

I'm incredibly glad this exists, thank you.

[@madscience6283]

I look so forward to this series, because I hope to one day be able to do these concepts myself. Thank-you!

[@itisALWAYSR.A.]

I love these vids and I'm super happy you're continuing this project. I've got a soft-spot for non-Euc geometry concepts (I tried to imagine a flatland world which is also a Mobius strip and how sunlight would work in it and my brain 404'd). Also I'm just beginning my journey into programming/coding, so these vids are extra satisfying :)

[@cs.shorts]

These videos always make my day and blow my mind!

[@dozerrrrr]

this is such a ridiculously big idea, you could sell this to a metaverse or make one yourself. in vr, this is going to change the way people think... im in love

[@vantahku7211]

I love this dev vlog series. Thanks!

Man, you're such a warrior, really, that's insane, I can only say "great job"!!

[@danharris2917]

Love these devlogs :)

[@catherinepoteat]

Damn, I just finished an essay about hyperbolic geometry and I should have watched this final video where you show the different projection. I love your work and can't wait for the game to come out. Good luck!

[@JelleVermandere]

nice work, looking forward to next episode for some juicy 3D models!

[@ruolbu]

It's a lovely look into whats going on with this beautiful presentation. And honestly, while the comments make it sound like your talking in cryptic tongues, I thought it was very doable to follow your explanations. Well done not just in building this but also breaking it down for others to understand.

[@ZackLondres]

This guy's just too crazy. Actually blowing my mind. I just feel inept

[@gabeolive516]

I would've gone insane at this point, good work! Keep going, dude.

[@0_-]

Today i literally just got recommend of your devlogs and in the same day a new one has released lol

[@DevashishGuptaOfficial]

So insightful! ❤️

[@Skeffles]

Wow. This is fascinating to hear about. I can't wait to see how you tackle 3D modelling.

[@sophietheinfallible8907]

These videos are insanely interesting

[@juanKme]

Amazing work man!!! congrats and keep the great work. I am looking forward to play your game

[@jvcmarc]

the music matches the concept of this game so much

[@crunglemcbungley]

This game is like an evolved version of Antichamber but with more math and horrifying geometry and I love it

[@Lucky10279]

How is the geometry horrifying?

[@trymbruset3868]

Wow, I absolutely love these devlog videos! I fell in love with hyperbolic geometry when I took a course in it for my Master's, but realized when I got into more general manifolds that things can get very weird. I think it's a good idea to use H2xE, and I can't wait to see how you actually rig the models.

[@Name_Happrycorn]

Потрясающе!

[@S1lentG4mer]

I absolutely adore your videos

[@Schmidtstone]

A beautiful solution for a beautiful problem.

[@dannythrust]

You seem staggeringly intelligent aha, Had your game on my wish list for a long time! cannot wait to buy!

[@prototypeinheritance515]

nice first sebastian lague uploads, then a few hours later a new hyperbolica update. today is an awesome day!

[@traderslick9763]

You have my respect. Hope I`ll learn enough to clearly understand it.

[@red_juan]

Beautiful.

[@DasParedes]

maaan, this project is amazing. Look like you needed to study a lot of math to make this work, and already look incredible. I want so much to experience your game. I am "anxious" to see the next devlog and how you solved the problem of creating 3d maps for this project. Good Luck with the game.

[@Lavamar]

Can't wait! Looks sick

[@gibbz115]

yooooo, new devlogggggg!!!! CodeParade, i love this game, keep up the good work.

[@fxvntp]

I can't wait this been on my wishlist since you first announced it

[@iwbmo]

lets just appreciate how this person used like every single type of rendering that he is talking about, actually doing this so many times in so many different ways is insane

[@pureplay7]

Thanks a lot for sharing this with us. It's extremely interesting to try to think in non-euclidean space while looking at the problems and solutions you show us. You should do similar dev-logs more often! :D (if it doesn't affects the development, of course) ;)

[@LOogt]

Dude I love this

[@nateshrager512]

Well done!! Keep it up

[@kingkoollgs]

I have absolutely no clue what he is talking about but looks dope

[@beanmcknee1610]

I’m so looking forward to this

[@TheConnor12500]

This is amazing.

[@angeldude101]

With the Gnomonic projection, i think the artifacts you saw are from the Gnomonic projection actually being better for _elliptic_ space rather than _spherical_ space. The difference is that in elliptical space, opposing ends of the hypersphere are treated as the same point, rather than as distinct points as in spherical space. The same thing technically still exists for euclidean space and the Klein projection of hyperbolic space, but the difference there is that there's no smooth transition that can bring you from the w = 1 hyperplane to the w = -1 hyperplane, of from the positive hyperboloid to the negative hyperboloid, so it's easier to forget that the negative sides still exist like it does in spherical and elliptical geometry.

[@aneemahach]

Incredible.

[@theartsywhale]

This is so freakin cool!

[@antediluvial]

VR baby! Man what a time to be alive

[@kayturs]

Another awesome video! I want to get H3 rendering with H2xE physics in HyperBlock as well; it seems like a great compromise! As you elevated, the change in speed and scale balanced each other out really naturally

[@CodeParade]

Thanks! I like the way you have it already, I think it works for the game. The main disadvantage with H3 for a H2xE block game is that the blocks get squished in the vertical direction, so they'll start to look more flat and paper-like as you get higher up (or down) and the increase in curvature will limit your view more. I can compensate for this with the 3D modeling step, but you won't have that flexibility with blocks.

[@deoxyplasmic]

Well done! I don't understand a lot of this, but I love the process. Keep up the good work. It reminds me of a KZbinr (BIB) who used a program to make a fractal landscape. It basically looked like 4-dimensional landscape rendered in 3 dimensions, on a 2-dimensional screen. Fun stuff.

[@adlsfreund]

Fascinating!

[@DanielLCarrier]

I toyed around with something like this a while ago, and one interesting thing I did with the holonomy is build a "house" in spherical geometry where each room is a tetrahedron with all right angles. You can pass through the walls (I haven't implemented doors) or use elevators at the edges of each room to go up or down a floor. The physics is normally S^2 x R like what you did, except when you take an elevator. That way, you can walk on any wall of any room. I also made one in hyperbolic geometry inspired by the Poincaré dodecahedron, except that instead of looping around with a 36 degree twist it's a 108 degree twist (if I remember it right). And I made it so you're in a smaller dodecahedron within the one that loops around, in order to make it so you hit the faces that loop you around at right angles instead of 60 degree angles. Unfortunately I'm nowhere near as good at documenting this stuff and explaining it as you. I wanted to make it something I'd let other people use, but I doubt other people would be able to use it.

[@CodeParade]

That sounds really interesting, do you have any video or demo of that project? It would be cool to see even if you didn't document it.

[@aniksamiurrahman6365]

Man you are a legend.

[@lankyduck8576]

Can't wait to play this game!

[@sumorley7267]

not only does my head hurt from the visuals but also the words too!

[@NonTwinBrothers]

Oooh now this is exciting

[@corvusbright]

3:39 the fact that he figured out this method would fix the draw issues is incredible. big brain move

[@alfinnizar6208]

Amazing 👍👍

[@guilldea]

you are an absolute unit

[@kaninepete]

Can't wait for the next one!

[@vitormbertani]

Great soundtrack choice, man