I Tried Simulating The Entire Ocean

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Sea of Thieves boasts some very beautiful water, perhaps the best looking water in gaming history! But, how does it work? Did they even do it first? Can I do better with current hardware? Who knows!
Topics covered include: Fourier series, fourier transform, frequency and time domain, oceanographic spectra, discrete fourier transform, fast fourier transform, approximate subsurface scattering, simulating foam, leveraging multiple frequency bands
Check out Jump Trajectory's channel!
/ @jumptrajectory
Support me on Patreon!
/ acerola_t
Socials:
Twitter: / acerola_t
Twitch: / acerola_t
Discord: / discord
Code: github.com/GarrettGunnell/Water
References:
There are way too many references please just go to the code link above and scroll to the bottom of the readme for all my references there
Music:
Afternoon Break - Persona 3 OST
This Mysterious Feeling - Persona 3 OST
Midori Eyes - Paradise Killer OST
During The Test - Persona 3 OST
Junes Theme - Persona 4 OST
New Game - WORLD OF HORROR OST
In A Moment's Time - Skullgirls OST
A New Frontier - VA-11 Hall-A OST
Climactic Reasoning - Danganronpa 2 OST
Every Day Is Night - VA-11 Hall-A OST
Those Who Dwell In The Shadows - VA-11 Hall-A OST
Empty Ocean - Loop Hero OST
Joy - Persona 3 OST
Underground Club - VA-11 Hall-A OST
Your Love Is A Drug - VA-11 Hall-A OST
GO!GO!STYLE - Paradise Killer OST
Like A Dream Come True - Persona 4 OST
Thanks for watching!
This video is dedicated to my friend, Alotryx.
#acerola #graphics #gamedev #unity3d #graphics #shaders

[@Acerola_t]

Get a free 30 day trial and 20% off an annual plan at brilliant.org/acerola #ad The Unity Awards nomination voting is live! It'd make me super happy if you submitted my name (if you think I am deserving). unity.com/awards?

[@djjudd566]

Wooo! My boy Acerola got. that. sponsorship. Lets gooooooo

[@PlanetComputer]

thanks, employed "_t" Acerola, you brilliant goblin

[@NotGabe001]

is that the real Dan Salvato at 25:02?

[@Acerola_t]

@@NotGabe001 yeah we are moots on twt

[@Gabriel38196]

@@Acerola_t done, thanks for the tutorial, I'll try to implement this myself!

[@eefflie]

99% of graphics programmers quit right before a 0.001% increase in performance

[@nightlight0x07cc]

LOL

[@NILLANEAB]

literally me except I quit when I get an opengl error before starting

[@ryusdarling]

release quote

[@stevenshea990]

@@NILLANEAB Or with vulkan/dx12, when you get a fatal memory error before you've even initialized the gpu device object.

[@codeninja1832]

I use the same logic for gambling.

[@otheusma]

I don't understand 95% of the things you say but I always find it fascinating.

[@Brunoenribeiro]

Chilling with Persona songs and hard math

[@spookbag24]

i like your funny words magic man

[@ThePandaAgenda]

I understand maybe 75% of what he’s saying and I am still amazed by this guy’s creativity

[@DemoniteBL]

I don't really care about any of this, my monkey brain just clicks on random videos.

[@ThePandaAgenda]

@@DemoniteBL vibe

[@anonelusive340]

It’s kind of ironic how Fourier actually invented his famous formula to predict when/how the tides of the ocean would occur and now in recent times people rediscovered that it could be used to simulate the very same thing it was meant to describe all along Edit: What I meant to say was that one of the very first uses of the Fourier Series was to predict tidal motion (Sir Kelvin was the one who actually did the thing alongside the mechanical integrator! It's a very cool story too! )

[@BenGroebe]

My understanding is that Fourier created the method for solving the differential equations involved in modelling heat diffusion in metal plates? I don't think this is correct :/ Citation: Mémoire sur la propagation de la chaleur dans les corps solides (1807)

[@_zedsdead_]

I think it was Kelvin that used the formula to predict waves

[@jimsmith3715]

Well of course it could that's just basic correlation isn't it? Many mathematical formulas can work the same

[@stevenshea990]

@@_zedsdead_ Yes, Fourier invented the Fourier series to develop an equation for how heat diffuses through a metal plate, then for a general heat equation.

[@LouSaydus]

The Fourier transform is pretty ubiquitous in any situation dealing with waves, and a LOT of things can be broken down by describing them as waves.

[@jbritain]

using Jack Quaid as the onscreen representation for Richard Feynman made me laugh harder than it had any right to

[@paninisauce6949]

I know who neither of these people are 👍💯‼️💯

[@jbritain]

@@paninisauce6949 Richard Feynman was a physicist. Jack Quaid played him in Oppenheimer (albeit briefly) but is more known for playing Hughie in The Boys

[@purple-flowers]

@@jbritain Richard Feynman was such a guy. I'd recommend reading his memoir where he details breaking into classified desks at Los Alamos and leaving silly notes for fun, being obsessed with the bongos, and much more.

[@jbritain]

@@purple-flowers my physics teacher used to tell us stories about some of the funnier stuff he did, will look into that

[@XxyGoddam]

came to say the same. I laughed way too much from it :D

[@jarred7721]

I've gotta hand it to you. You have some of the best shader content anywhere on the internet. It's digestible, entertaining, and informative.

[@stevenmathews7621]

not to mention his aesthetic absolutely love his video style

[@uninable]

@@stevenmathews7621_Black Scene_

[@Kwauhn.]

Right!? I wish I had this when I was first getting into computer graphics in highschool.

[@vjcodec]

The meme way of learning!

[@charactername263]

You can apply almost the same FFT for waves for grass blowing in the wind without obvious tiling.

[@filiformis]

I can't imagine how validating it must be to have your opinion backed by the Oceanographic Literature.

[@TechJolt3d]

17:15 This image and the line "in truth, this is because our lighting model forgot how light works" Is making me laugh a lot

[@CentaurionArcher]

FFT really is like magic. I spent like two months understanding it a few years ago and now I've completely forgotten

[@Meoiswa]

It would be cool to have this as a live wallpaper, with the wave parameters slowly changing over time (or perhaps using weather data?) so the ocean looks somewhat different every time you get to see it.

[@TheShinyZoroark_]

Nice wallpaper engine idea

[@YdenPL]

That's absolutely doable, if I ever get around to installing Unity, maybe I could modify the project to pull weather data and package it up into a Wallpaper Engine wallpaper.

[@DeletedDevilDeletedAngel]

@@YdenPL is it done?

[@mu4784]

Honestly, 2 things I very recently learned upon doing 3D are just how weak computers are compared to what I had in my mind (which was at the level of "just generate noise in real time and it will take 0.1% of CPU kek") and at the same time just how insanely optimized any game is and how many smart solutions have to be built in order to get gorgeous visuals while maintaining performance!

[@prismalglue]

we need organic computers NOW! xD

[@yaman.]

donate your brains@@prismalglue

[@eeee69]

i just finished a class on numerical methods a few days ago and already i am getting flashbacks also the way you "removed" tiling at the end was really impressive

[@stanleyyyyyyyyyyy]

it was quite clear what needed to be done to everyone who understood the topic.

[@Good_Hot_Chocolate]

​@@stanleyyyyyyyyyyyGet off your high horse. There's no reason to put down other people's understanding, especially when the one in question was still learning.

[@PokiniGames]

I can not thank you enough for your contributions to the Unity shader coding scene. I have been wanting to add more water/flooded areas to my game, but have been avoiding it due to the performance impact/obvious tiling issues that existing water simulations on the marketplace have.

[@fablearchitect7645]

I think you should continue to use your 1660 to benchmark your projects to prevent the rebound effect on optimization caused by newer and faster hardware

[@Acerola_t]

when i get a new pc yeah i'll keep the 1660 around hopefully

[@jacobcowan3599]

Another banger from the funniest technical artist on KZbin. You do such a great job telling a story and providing dense info in a super digestible manner. I am so ready for that principled BRDF video!

[@E-dart]

Babe wake up, acerola released a new video

[@pi0neer758]

I was looking if someone already said this, but I wasn't expecting it within *3 minutes* you're insane (in a good way)

[@Soundy777]

This got me good

[@bastian3461]

that was fast

[@ceilidhDwy]

Excellent video as always! It looks so impressive in the end and honestly working with enterprise software (that takes 45 second to load a single page of 20 customer requests) I tend to forget that computers can do this kind of magic! Your videos kinda make me motivated towards programming On another note, that transition to sponsor is very good

[@bondthefifth]

Working in backend did that to you, but also I think acerola said in his pixel sorting algorithm video that a CPU, which you and I used everyday in enterprise software is Smarter Slower, but a GPU which he uses in the shader program is Stupid Faster (and yet it can still do a mind blowing approximation of an entire ocean waves in real time)

[@yan-amar]

And then you have entreprise software which is Stupid Slower. Really, running on the CPU is no excuse for modern software being slow.

[@kylebelle246]

​​@@yan-amarits probably due partly to network requests, which realistically is not something that can be solved. Many times even the server you make network requests to have to make other network/api request. But yes some software is just terrible as well

[@mauriciosmit1232]

Especially since on a higher-range laptop's CPU, you can run a rough equivalent of a local ChatGPT now, and still have resources for other stuff. It's crazy what our chips are capable of when programs are optimized for them.

[@BeatCrazey]

This video (and the previous) COMPLETELY sold me on Fourier Transforms and FFT. I'm going to Uni so I hope I'll have the opportunity to learn more about them (and maybe make an ocean a quarter as good as yours)

[@lbgstzockt8493]

Your videos became a lot easier to understand after going to college for a few semesters.

[@kojumble]

i think this counts as the best follow up video of all time

[@thespycrab8305]

I love how all the math I learned in my Physics studies shows up in unexpected places like real time rendering. Never thought I'd hear about the Jacobian outisde of my simulations and modeling course.

[@filoteo]

It’s so cool seeing these otherwise abstract tools of vector calculus and differential equations I’ve learned about or heard about throughout college in such a creative and artistic context. Never stop!

[@polic72andDrD3ath]

this is the hardest my minor in applied math has ever had to work, and I'm not even trying to implement it myself yet...at least I actually recognized 90% of the terms you said without having to look them up! amazing video!

[@JamEngulfer]

This is amazing! Reducing tiling by throwing more FFTs at it was really interesting as well. I’m now thinking about what could be done to further improve the sea foam, because the solution was (relatively) simple, so I think there’s room for some neat additions. Maybe a vertical offset of some kind to give it the impression of having volume and adjusting the rate at which it appears and fades to make it a bit more ‘sticky’?

[@Acerola_t]

Probably experimenting with different decay functions would be the easiest way. I didn't really spend much time innovating the foam cause it's kinda tacked on. It is the same method that every game uses as far as I'm aware, the biggest difference between mine and others is that since I don't use a texture for the foam appearance I don't blur the accumulated foam tex in order to keep it noisy and pseudo detailed to prevent it from obviously being a flat color.

[@miles6910]

@@Acerola_t seems like you'd want to adjust the material properties for the foam as well. do you apply the compliment of the fresnel to your scattered light component of your surface material? i think that is warranted, but maybe it's all bs enough to not matter.

[@onechippyboi]

You're by far the most entertaining resource on how complex shaders and simulations work but you still maintain a very professional quality in results. There are others who make the same kind of content but you have knowledge and skills on par with AAA devs when it comes to what you do.

[@Acerola_t]

To be fair it's cause I was a AAA dev

[@onechippyboi]

@@Acerola_t I know, I just wanted to say that you're giving people free education on things that take years of school and industry experience. It's a real talent to make graphics optimization and math as entertaining as you do. 👍

[@Ataraxia0]

its insane how much better it looks while also improving the performance as a music producer its really interesting to me how working in the frequency domain is so much better than the time domain as when working with music you have to sample the waveform in time before you can start working in frequency, so i would have initially assumed the exact opposite. thinking about it now though, it definitely makes sense why its so powerful since any conceivable wave can be represented by a set of frequencies and phases i'd love to see more like this, its really interesting to see how waves can be used in graphics and not just audio

[@gameworkerty]

Love the thoughtful detailed breakdown of these effects

[@xeuxixiliak8417]

Okay, the notification Acerola: Simulating the Entire Ocean definitely looked to me at a glance like 'Stimulating the entire Areola'

[@kodinamsinh1267]

i need that tutorial

[@IstyManame]

Your vids are genuinely great for falling asleep

[@Acerola_t]

only a little insulting!

[@jeb123]

FFT's are still continues to amaze me, seriously. Our life would be very different without them. Also your channel amazes me too! Your use of math with Unity is insane. There are few questions i want to ask, how did you learn all of this? At school or all by yourself? If at school what was your major?

[@Acerola_t]

I have a bachelors in computer science but I taught myself most of this stuff

[@jeb123]

@@Acerola_t Thanks for the reply! Your channel is really amazing, so much to learn.

[@ufalsalman]

I love you mentioned Euler's formula, because you also took the reference from Monogatari Series as your brand and Euler was mentioned in Zoku Owarimonogatari too. Cool video btw, I like it (despite I studied in food technology field lmao)

[@MCLooyverse]

On the comment about the conventional math summing notation being inclusive, I usually write `sum{k = 0;

[@ChaonicMew]

Thank you for being a technical artist to all of us! What you're doing will enable the rest of us to make MUCH better games!

[@PuppyGamerYT]

Amazing video acerola! Every video I watch makes me want to learn more about shader programming!

[@TheLaxOne]

This whole wave simulation series and channel as a whole has gotten me super interested in shaders when I'd never given it much of any thought before. The way you outline all of the math behind the graphics along with the humor in your presentation just makes for great edutainment. I also super appreciate all of the sources so those who want to see the nitty-gritty math can do so!

[@SylvanSerenity]

Super interesting video! Very detailed, on topic, and the humor and analogies really help pull it together. Very happy to have found your channel. Thank you for the content!

[@thelegalsystem]

Black Flag had the first ocean in a videogame that felt believeable to me

[@torikenyon]

so much of this happens to line up with what i'm learning in my digital audio theory class

[@James-Calvin]

This is absolutely amazing. GG Acerola. You go into just the right amount of detail to introduce topics and be entertaining. And you're just really funny. Thanks for making this video!

[@0osk]

Very cool Mr. Rola. Even if I usually don't understand the nitty gritty details, I appreciate how your videos always make it easy for someone like me to at least understand the basic idea of how these things work and the thought process behind it.

[@LighthoofDryden]

It’s been like ten years since I first heard about Fourier Transforms and because of you I finally know what they are ❤

[@Crovea]

Great video Rōra Hime if you could do river water flow shader stuff in the future that would be epic! and maybe even how to have it flow seamlessly into oceans

[@iliya-malecki]

im so happy for you to finally go ballistic with the view counts! you are the best! im learning so much useful stuff directly applicable to my field, and im not even a game dev but a data scientist

[@stargazersdance]

Idk when I discovered your channel but I've been watching for a pretty decent time. I think what got me hooked at first was the Persona 2 music in one of your videos. Then the Monogatari styled editing pulled me in even further. What sealed the deal was the topics you talked about. Hope you keep it up, Acerola. Frfr

[@SpottedEgg]

I appreciate the effort you put into your videos Acerola

[@gehtsiegarnixan]

Very impressive and fascinating. And it explaines why oceans in movies and games always look so fundamentally wrong. I have been sailing for my entire life and leanred how to read waves. True waves are curved from above too and have directional waves in different regions all of which you can see from pretty far away to the smallest detail.

[@oystercatcher943]

That’s super impressive! Loved how you explained it, especially the touches like foam

[@mrbonono2951]

I can’t wait for even more content, your stuff is so good and you can’t find anything else like it

[@ricardo.mazeto]

24:12, you could dig a little deeper on the frequencies used here. If you use prime numbers for frequencies, they will tile on a much larger square, because prime numbers have the biggest LCM (Least Common Multiple). I use this trick for procedurally generate huge tiling textures from tiny samples.

[@Acerola_t]

the tiling is actually gated by the resolution of the textures, since all of this is being precomputed into textures that the ocean mesh then samples. If GPUs are ever fast enough to calculate the fft per vertex, then yeah this would be applicable knowledge, but we'll probably die first.

[@ricardo.mazeto]

@@Acerola_t No, you got it wrong. There's no need for FFT. If you sample the textures, such that for each vertex v, for each texture t, the height of the vertex, or color of the pixel, is equal to the sum of t_i mod t_i_len, the size of the "tiles" is equal to LCM(t_1, ..., t_n). If the sizes of the textures are prime number length, which is the optimal length for this technique, you can get huge tiles with tiny textures. It's a well known technique.

[@simonstrandgaard5503]

Beautiful result. Well explained. Well produced video. Thank you for making this.

[@DoggHounder]

Just wanted to say that this is one of the most interesting videos on solving complex problems in game dev I've seen on youtube! subbed and i'm curious for your next videos

[@nynx8269]

Yes another acerola video

[@Gokanaru]

WOW this is beautiful.

[@Acerola_t]

thanks king

[@SergeyLergDev]

Great as usual. Helps a lot with understanding intricate rendering techniques. I'm also currently working on a rendering project for youtube, it's not water but similar. And your videos are quite inspirational, thanks!

[@RecOgMission]

I came across your videos this week only, and am enjoying them immensely! Any ideas of how to tone down the waves along a shore (or similar)?

[@RecOgMission]

I've got something working :)

[@gamingshowerthoughts9723]

I'm really curious how good the new built-in water system is in Unity HDRP. It seems to do ....most of what you showed.

[@danielgysi5729]

Recreating effects from huge titles like you do in this series and with the smoke video is definitely really interesting and informative and I'm so grateful for it That said, would you ever consider trying to make a video around an original effect rather than copying one from the literature? Seeing how you approach something like that would be really useful I think. Either way though I'm a huge fan of you work. Cheers!

[@Acerola_t]

My pixel sort video is essentially an original effect as I invented that algorithm (the one presented in the vid, not the concept itself)

[@forest-goddess]

finally got around to watching this one, as always, incredibly good video. really great at explaining these topics a bit in extremey enjoyable ways.

[@LambOfDemyelination]

really impressive videos one after the other! hope you're balancing work well ❤

[@katie.d0905]

But acerola !!

[@NunSuperior]

Warning : Adult Mathematics (That's some tasty water right there)

[@andrewallbright658]

I’m rewatching this with the experience of more game dev knowledge. I appreciate the attempts to translate the complex (ha) math topics into something more legible to a wider audience. Great work on foreshadowing the evolution of technique. I’m happy you create content on these subjects. Looking forward to the next vid :3

[@TigerMax96]

I just love your content! It's informative, concise and interesting to watch. Keep it up!

[@henrysteven137]

you sir are on a different level of talent with shaders. amazing work

[@JiraMelaj]

Thank you ever so much! I found myself in the position of needing to write my own water math, and was feeling apprehensive... I feel encouraged & so much better now! :D

[@LoyalSage]

12:45 That’s a really good way to describe a lot of things where complex functions are used to produce real results (at least for people who have heard of Plato’s Cave).

[@OrangeJambo]

Luv u, thanks Acerola. Enjoy everything you cover, always insightful!

[@RedekerEleven]

first of all, thank you for being awesome. you help break down complex subjects that i'd need a semester of college to understand otherwise and i'm endlessly grateful for that secondly, i'd like to request some topics! #1 a summary of common optimization techniques, or #2 mobile GPUs/APIs/mobile gfx in general

[@JordanMarshDev]

Incredible work! Most of the math of shaders goes right over my head, but the end result here was damn impressive. If you do continue this project I would love to see you push the limits of a CPU based underwater ecosystem - that would be quite an addition! Earned a subscriber in me cheers.

[@morgan0]

something i came across between the last video and this one is some tiling techniques inigo quilez came up with years ago. basically instead of repeating it in a grid, you use some other positioning for bits of the texture and blend them in between. maybe it could be applied here for further tiling reduction, maybe allowing for lower size textures and fewer of them with comparable quality

[@ggavilan]

So inspiring!! I always get some new math concepts to apply on my own blender shaders

[@nathanbarraud4349]

Man every single video you make are amazing ! Thanks for your work, it is very inspiring!

[@zactron1997]

Excellent video. You should look into introducing player induced displacement into your simulation as a bonus challenge. Since you know a player has minimal mass compared to the ocean, you know their impact on the ocean can be limited to a very small region of space, but with a high impact. Since the spectrum is also a linear space, you can sum the player induced displacement with the natural simulation, and it should look pretty convincing. Ocean spray would also be nice, but I don't think it's as important.

[@basiliotornado]

Awesome video, the fft is one of my favorite math functions. my favorite project with it so far has been turning an entire audio file into a midi. Originally made it in python (have clips uploaded (don't judge)), and tried to convert it to rust, but i had problems generating the spectrogram correctly. I love this project and kinda want to try it for myself

[@Aliberation]

Awesome video, as always. Thank you for your hard work!

[@brownshoes5225]

The Va-11 Hall-A music in the background was a nice touch.

[@EndlessNameless5]

Awesome video! I will share with my students that are learning to use Fourier transform

[@ashtonmadsen9278]

Ahhhh! Do another ocean simulation! I want to see how far you can take this! By far the best real time I’ve ever seen

[@rallymax2]

Just discovered the channel. This was a fantastic video. I can’t wait to give it a try myself. I wonder if quadtree culling could be used to make it more efficient?

[@Dadointdetrip]

the forest creators really worked on the ocean. even at that time you can see many little parts of it but one small problem is it locked at some frame rate so if you have 60 fps water will look like a slide show

[@jelledgecg]

Videos like these are what inspire me to keep learning and working toward becoming a graphics programmer. Wish I could like twice, wonderful content.

[@Helios.vfx.]

Glad to have found this channel. Great stuff

[@DevJorvan]

Man, I watch a lot of youtube and want to tell you that I really love your videos (great content with a nice amount of comedy). Thanks for sharing, mate 🤝

[@tastycake5465]

7:01 love how timed this music is to the graph

[@Cluvr]

Just discovered your content and it's awesome. Time to start binging

[@blarvinius]

@Acerola I have this idea to get around the tiling problem in all sorts of shaders and texturing: APERIODIC TILING! But it's beyond me to implement. The world needs someone like you to look into this.

[@ortxxxm]

@Acerola_t thanks to your inspiration, I've enrolled into an intro to image processing class for this semester! thank you :]

[@DFX2KX]

that is insanely impressive. I didn't realize it was feasable to push the detail THAT high.

[@o_2731]

Congrats to getting sponsored by brilliant! I love this channel and watching it grow :D

[@simpli_A]

I love your videos! Mist people that do similar stuff to this treat is as a video about making a cool with with a bonus being if the viewer can learn something… but your videos are about teaching us how to do these, with you also getting a bonus cool thing!

[@CasMcAss]

The cat video during the sponsorship was absolutely brilliant! made it so much easier to not fast forward.

[@ottley32]

I’m glad you mentioned Atlas’s ocean system. I thought it was cutting edge for it’s time, and holds up very well today.

[@danmerillat]

Great followup. It will break down when it interacts with land though, which might make for another interesting topic on how to deal with that.

[@Acerola_t]

Well, this is an ocean spectra which simulates how waves behave thousands of miles away from shore, so a shoreline is contextually irrelevant. But yeah that will come up when I do terrain gen or something.

[@danmerillat]

@@Acerola_tI was just thinking if the same algorithm works if the shore casts a 'shadow' on the frequency domain, effectively removing waves in a specific direction.

[@jfalk6500]

I gotta say I really enjoy your monogatari style editing, it's very satisfying and fun

[@callofdutyfreak10123]

I remember learning this math in my linear circuits 1 class, it’s useful for modeling phaser, cool to see the math reimplemented here!

[@SuperLlama88888]

Didn't think I'd enjoy this, but great job! Ended up really enjoying the explanation!

[@Acerola_t]

lol I totally understand if this one comes off like clickbait

[@EpicGamer-ux1tu]

Amazing video, thank you Acerola for your hard work!

[@xenen9797]

Another Acerola W. i never understand the videos the first watch through but, they are always interesting. Keep it up!

[@davidriosg]

Great video as always