Ocean waves simulation with Fast Fourier transform

[@peterhall6656]

You have done some good work on this issue. I am a retired expert in Fourier theory and it is interesting to see how the FFT still rocks on 50 years ago when I first used it.

[@warpigs330]

something tells me that we will be using fft for as long as we do computing. It is so fundamental.

[@ShatabdaRoy115]

holy moly. I'm 14 and I got alot to learn

[@Francesco_Armillotta]

Basically you can study whatever field in physics and fourier theorem is everywhere :)

[@zacharychristy8928]

I remember learning about it for the first time, and it totally changed how I thought about information. I used them like crazy in my next internship on software-defined radar systems. They're an insanely good tool to have.

[@Nekuzir]

@@ShatabdaRoy115 the e^2pi*i part is really just the number 1 e^pi*i is negative 1 e^(angle in radians)*i is the number on the complex unit circle distance 1 from the origin at the angle you put in

[@phillipjoyce8825]

Got about 7 minutes in until my brain rejected it. Stunning work, good on you for being so good at maths! I wish I could understand what you've done properly

[@dinosyr]

I made it about 6 mins i guess im more smooth brained lol

[@bekonix-b3s]

I feel this video is too condensed. There are multiple complicated math formulas appearing on the screen in 2-3s intervals at some point. It is certainly a good glimpse for someone looking for high level overview on how to generate oceanic waves, but to cover it completely clip would have to be 2h+. Kudos for making it though!

[@RileyGein]

@@bekonix-b3s the linked videos in the description help make a bit more sense of it. Not that it helped me much; I’m absolute garbage at math

[@santosmichelena3519]

I understood everything quite clearly but I think it's only because I and doing my masters in a very very closely related topic. The video is definitely very dense.

[@vladislavkornushenko]

well done, for me 4 min was enough)

[@papel6280]

Can’t believe I am learning Physics in a Unity tutorial-this is so well-made!

[@gamedevwithjacquelynnehei465]

I totally get what you mean! It's crazy how much math and science you use in game development. Watching videos like this just shows me how much I don't know.

[@damislav]

@@gamedevwithjacquelynnehei465 if one would know that math and physics can actually be fun and used for something, maybe I would bother to learn it in school xD

[@TheArrowster]

​@@gamedevwithjacquelynnehei465 Computers are all about math and science. Virtual environment is just a simplified version of real world.

[@NicholasSpies]

I was at a computer graphics company (on of the first doing commercial work) in 1987 and saw what was at the time an astounding, color still of a perspective view of the surface of a calm sea, bathed in the golden light of a sunset. It had taken hours, perhaps even over night, to render on a minicomputer. It was quite advanced at the time. I was told by the guy who modeled the scene that it involved sin/cos functions, which was more or less obvious because it was periodic but I didn't really understand how (and the source was FORTRAN, which had to be batch processed from a stack of Hollerith [IBM ]cards). So it was a pleasure to find this explanation.

[@tiporari]

I implemented your GitHub code in a unity project with XR enabled. These waves look awesome in VR. I assumed performance would be an issue, but it runs perfectly. Thanks for creating this. Giving me an awesome jumping off point for a novel VR experience.

[@FarhadHakimov]

Oh, thanks for the idea! I was hoping to implement it in Unreal, but VR in addition to ocean would be great. Here's hoping I won't get seasick xP

[@derp4581]

Man, youtube recommendations have been awesome lately! Finding all of these small but amazing channels left and right

[@joshko9030]

Amazing work man! Getting the feeling that this is gonna blow up

[@flatspinrc5262]

Hope there's more videos coming! They are all beautifully presented.

[@redsteph]

This is awesome, hope you’ll cover ocean shading, LOD management etc as you’ve said!

[@mooseriderwpg9586]

Maaaan KZbin always recommends videos explaining the gap in your understanding for an exam perfectly right after the exam XD

[@ltmcolen]

I've personally had instances when we were at anchor, the current came from the north and was stronger than the wind coming from the south. Pushing the ship with her stern towards the wind. The strangest part was that the waves also came from the south hitting the transom. It's like a huge bass drum being kicked irregularly

[@badradish2116]

THIS IS GREAT. THANK YOU!! its so hard to find detailed breakdowns of complex topics that arent targeted to specialists or total beginners. 100% sub'd and excited to see what else you have to offer! THANKS AGAIN.

[@flwi]

Well done! The result looks stunning.

[@wii3willRule]

Man, this is awesome. A bit dense/condensed, but an excellent high level overview-- I learned a lot. I'm completely new to FFT, so I know that I'm going to be checking out the 3B1B video next, but this was honestly the coolest introduction.

[@curiouspers]

This is very high quality content, thank you! I hope you're doing great and will return with more great stuff!

[@marshallross3373]

Great video! Thanks for covering the math and describing the issues involved.

[@farechildd]

Pretty cool to see the applications of what you learn in differential equations

[@stdcall]

if you do anything even mildly related to math/physics/computation in the future it will all be diffy qs

[@neuralworknet]

Omg this channel is insane! I really loved your videos. Keep up man!

[@DaveJ6515]

When something conceptually and mathematically so elegant works so well for so long in so many different fields, it probably holds some fundamental meaning.

[@omeryamanofficial]

Looks incredible, also you can add some underwater effects, water splashes for collisions and make it work with URP. Great research!

[@토이-q2i]

Could you please share the URP shader code?

[@Ahivo]

Never thought fourier transforms would work for me one day Dude the world is a better place with u in it So you could help people understand better and more tangible Great job Keep up the good work

[@superman39756]

What a great video! Thank you for going into the details and providing detailed references.

[@dariocardajoli6831]

Outstanding work . Speechless but still commenting seeing how underrated this vid is .

[@maki4041]

this video is just awesome.And I am really interested in topics the current video does not mention like ocean shader and mesh LOD.Looking forward to see more about these!

[@nesslange1833]

What a genius applying these advanced transforming things. Only thing you could have added is clouds /sky movement to make it even more vivid.

[@tefilobraga]

Excellent and fascinating work. It is very neat how you can synthesize a realistically-looking ocean based on rigorous physics of wave dynamics. I have one comment regarding the rendering, for example at 11:05. While the theory used is certainly for non-breaking waves, and therefore the waves by themselves would not produce foam, one can easily imagine a situation where the foam is pre-existing and the waves just move it around. Now, what happens in this animation extract is that the white patches (which I perceive as foam) move with the wave crests. In my opinion, you would get a more realistic effect if the foam remained on the air-water interface essentially at the same points in space horizontally, and the waves simply propagated over it. If you want to be maximally realistic, you could consider the back and forth motion associated with the horizontal oscillations produced by each wave cycle, and even, possibly, the slow drift, produced by the Stokes drift (although that latter aspect would not add much to the realism on the time scale of a few seconds).

[@JumpTrajectory]

Yeah, the foam definitely should be persitent. There are difficulties in meshing it with the cascades. There are two ways to do it, basically, and both are not perfect. Still working on it, actually. It is relatively easy to make it move with the wave cycles, though.

[@loganlee7510]

Very easy to understand :) Thank you for making this video

[@pyrit3863]

Looked at the code and have no idea what half the stuff does but I understand the concept. Really high quality waves though, looks amazing.

[@tupaicindjeke275]

Dude. Your video is great. Keep up the good work.

[@danielprovder]

Im not sure the accuracy of this, but I’ve read that there is something about pink noise as the spectrum of the ocean, it has a characteristic rise in amplitude as the frequency decreases. What’s interesting is that the pink noise is invariant under Fourier transform, and I wonder if applying this randomness instead of Gaussian would change the already beautiful results. Looking forward to more content!

[@adampy96]

Subscribed, you deserve more attention on youtube. Thanks for that video!

[@dolphin-sd]

Great explenation and visualisation!

[@hugo5097]

Your videos are honestly amazing! Thank you and keep it up!

[@JumpTrajectory]

Thanks! Working on it!

[@mrcao-fb9wx]

One of the best video on the topic!

[@GlorifiedPig]

wow this looks ultra realistic, good job!

[@anjoomfaisal]

This is so interesting. People like you make games beautiful. Thank you :)

[@cptray-steam]

Mind = blown, I'm probably gonna have to watch this like 30 times before I fully understand how it works.

[@norbertpape1993]

Beautiful work!

[@zetathix]

Thank you for good knowledge, I will try to digest it into use.

[@AlanZucconi]

This is the content I'm here for! 👏

[@roisanggung951]

What a very outstanding explanation, i love your work!

[@snbv5real]

Very nice video, definitely be interested in seeing the follow up on the other stuff you talked about. One thing I'll mention, is that when you exit the Unity world, those problems with "Pipelinestalls" and things aren't really issues. In API's like Vulkan, asynchronous execution of GPU commands is not only an option, its *expected and default behavior*. You can even separate the FFT step *entirely* from your rendering, have it be performed at a lower frame rate, and even *interpolate* the results by looking a head, but I digress. What you would probably do in this case is use double buffering, use the GPU to write the output in one buffer, and on the next frame use another buffer, allowing you to safely copy the information you need to your CPU while it is calculating the next buffer. No pipeline stalls period. What you would really want to do however, is calculate boyancy *on the GPU* instead, then copy *that* data to the host which is much much smaller.

[@JumpTrajectory]

Thank you for the advice! I would really like to dive into the graphics APIs at some point. The idea with GPU boyancy seems interesting. I think, as a bonus, all the GPU power can allow a more sofisticated boyancy model (voxel based maybe?)

[@oswaldcobblepot764]

@@JumpTrajectory It's funny you talk about this because i am actually trying to convert a buoyancy system (inspired by Habrador buoyancy tutorial) to compute shaders, in order to make it compatible with FFT ocean. So far it works pretty well with Gerstner waves (from CatlikeCoding tutorial), but i am dizzy when i read the fft ressources you linked because my math background is too weak to understand all this right now (I honnestly don't even really understand what FFT is).

[@CustomPhase]

This has nothing to do with Unity as is. Unity supports async gpu readback, async compute and all the other things you mentioned as well. You should research the topic before you embarass yourself in the future.

[@EnginAtik]

Very nice work! I thought the foam was a bit much on some of the waves. They gave the impression that they were hitting some rocks that were out of the frame. Then again there must be an indication of reflected waves if it was the case which I did not notice. It's amazing how we get attuned to how the sea behaves: our vestibular system starts doing some Fourier analysis after spending some time on the see and we get sea legs when we are back on land.

[@muhammednedimsahvelet4431]

Thank you so much. This video is so helpful.

[@josephseed9270]

dude you really deserve millions of subscribers

[@apurbabiswas7218]

This is amazing work - I'll be looking out for a Patreon page soon. I hope you keep making videos - subscribed!

[@WMPEXFBTLZYH]

Beautiful presentation. Subbed!

[@erikm9768]

Huge like to this , great explanation! bravo!

[@williamriddle9910]

Great topic and extremely detailed, such great work nice!

[@stephencarlson6297]

This is superb! Definitely subscribing!

[@TheGreatTimSheridan]

It's an amazing effort, I noticed there's also foam around the edge of the rowboat. It seems like there's a little too much uniformity and too much foam. It might look a little boring to remove some of that garnish, but it should look more realistic with less foam or maybe the foam triggers only a little more at the extremes

[@mrocean1293]

Super useful and very nicely done!

[@TwistedPresence]

Excellent video! Great job.

[@TopConductor]

Dude, you are legend!

[@soheil4471]

nice job man keep going amazing content!

[@СергейПупчин-ж7т]

It is nice to hear your slav accent

[@tolkienfan1972]

Fantastic! Wish I saw this earlier

[@abhishek.g0yal]

Awesome 🔥🔥🔥 Instantly attention captured

[@elialehman3052]

This vid skips over so much that it defines itself as a niche explanation for a niche mathematics crowd. Hope all u smarties are enjoying this more than I am!

[@BloedQS]

It's great work. Thank you!

[@Happen2Bme]

Thanks for the knowledge.

[@papaysailor1017]

This is so cool... I've gotta try this method in my Archipelago project! Thank you for posting!

[@GunnarLoeb]

Great work! Thanks!

[@slayerofwhales9720]

Where did you get the equation @ 10:19 from? I specifically wonder why we add 1 to the partial derivatives in the denominator. Why use this formula instead of forming tangent vectors with the partials and computing the cross product?

[@mauritsgli]

Fantastic work, thank you

[@raphaelklaussen1951]

It is fascinating that you can create a realistic effect without invoking the conservation laws.

[@sciencecompliance235]

Doesn't something that uses purely periodic functions assume conservation?

[@saliherenyuzbasoglu5819]

I hope one day I will be good enough computer scientist that I can understand the concepts in this video

[@whidzee]

Wow this is just amazing. most of the description went over my head but i am still very impressed. How would you go about combining this with onshore waves around an island? to have breaking waves coming from all angles?

[@JumpTrajectory]

Oh! That's a whole other thing! I've read some about it, but not much. Check outh this talk developer.download.nvidia.com/assets/gameworks/downloads/regular/events/cgdc15/CGDC2015_ocean_simulation_en.pdf

[@hexagon-77]

@@JumpTrajectory You should definitely make a video about this also, it's super interesting and probably more useful to a wider variety of devs. Great work so far, by the way!

[@catalingabrielpopa2696]

Amazing video!

[@vaakdemandante8772]

Cool video, quite dense in information and knowledge, so it would be nice if the formulas stayed a bit longer on screen, instead of vanishing like in 6:17 to show some not yet well defined parameter h0. Such fast format is a bit confusing, so if you could show the content on screen for longer and use some transforming animations to better explain how the formulas are linked to one another (like 3Blue1Brown does) it would come a long way in enhancing the understanding of key concepts.

[@adamstybrzynski3216]

Sir! Thank You for Your work! That's very valuable material and it is a matter of time for Your channel to go viral! I would be awesome if You could cover these topics in more details

[@MassimoRough]

It is not a matter of time for this channel to go viral. If only you could help this sharing the video in your social channels - that would make an impact, not just random noise.

[@anglewyrm3849]

I once worked on a lobster fishing boat 90 miles off the coast of North Carolina, and there were rare occasions where the ocean was amazingly flat, as depicted in this simulation. But most of the time there were rolling hills and even mountains of water.

[@JumpTrajectory]

Thank you for the observation! This is swell, I think. I didn't know how important it is for the look of the ocean at the time as I was making the video, but now I understand that it is present most of the time. Good news is that it is already supported in the code, I just didn't include in the scenes for the video.

[@b33blebrox]

Amazing! Can imagine what enormous computations are required to add there some solitons to simulate waves with negative slope...

[@oliverf.4235]

Great video.

[@__username__]

Гуд джоб, камрад! Ю а нот со нью ин шейдерс, ю ноу :)

[@zhehaoli1999]

really nice!

[@curtisnewton895]

sure that when you're busy playing a video game, you care SO MUCH about the realism of the ocean no doubt about that

[@CB-hn6pr]

Spectacular !

[@MarCuseus]

I see CG water, I press like. I see maths, my brain explodes.

[@jeancolapierrearmande3326]

You're a genius.............thank you!

[@KingofUshankas]

AMAZING!!

[@romanb2770]

Subbed, very nicely presented overview

[@robertfindley921]

Very nice. I'd have to brush off my MSEE brain cells to follow closely, but very interesting.

[@AlexSeligerX]

дуже хороше відео... правда десь на середині спати захотілось)

[@chadx8269]

Outstanding.

[@eryberto87]

astonishing

[@radcliffe2192]

Очень круто! Спасибо, что решил поделиться.

[@liluo7513]

pretty nice video ! thanks a lot !

[@Martin-se3ij]

mind boggling.

[@JinKee]

Acerola sent me here

[@kukunishad]

You should work for Rocket Industries, like SpaceX. They must have need a guy like you with this kind of applied mathematics knowledge.

[@evanburrows]

Great explanation!

[@christopherking6129]

Neat! I'm surprised inverse FFT isn't used in procedural generation more often.

[@galabolatory4905]

좋은 강의 영상입니다! 많은 도움이 되었습니다~! 정말 감사합니다.

[@WelshGuitarDude]

Can you do more deep dive into how to get the ocean to look visually nice as well like under water shader, SSS, foam etc etc.

[@JumpTrajectory]

I'm planning to do that (maybe not in the next video, but some time in the future)

[@Heknon]

@@JumpTrajectory Did you make the video already?

[@Heknon]

nope nvm

[@joshsvoss]

Really great content.

[@amerfilmstudios9292]

Hi, Can you sell a 1 minute length mp4 file video of ocean simulation of view scene ( camera view ) moving forward , static still scene... TQ

[@gamurarandrei2657]

amazing. Please do more videos like this

[@sitrakaforler8696]

It's incredible !!!!

[@alfiewhitson7726]

interesting stuff. Perhaps one alternative way to initially address the tiling issue would be to look at the tiling as a triangular tile of polygons wherein you take a random chunk of said triangle as a sample from the first "tile", re-randomise where the points are going to be drawn in 2d space and then take the edge most points and have it so they are what correlates the next tile to the one before it. So basically don't look at the grid as a grid but rather think of it as something that initially exists as a triangle of triangles but can potentially be manipulated to be an irregular triangle of triangles... think pyramid recursion wherein each pyramid of pyramids is manipulated via Perlin noise but then the gaussian random number generator you're already using is then manipulating in 3d space in the same manner in which you would manipulate Bezier curves where those points will actually be. Also in terms of the way in which you're generating the heightmap itself, have you considered, for a final phase in generating the actual heightmap, routing the 2 output textures through some sort of optical flow filter ? The reason I say this is because using this in order to influence the heightmap texture, could in essence apply a layer of recursion to the clumping affect going on within the heightmap texture itself. As far as actually doing the latter would be concerned, I suppose there'd be ways in which you could use the python API for MATLAB to take the actual heightmap texture itself, do optical flow shit in there and then replace the texture buffer that's storing the initial heightmap with the version of the heightmap with optical flow

[@JumpTrajectory]

I don't think I really follow what you are saying about tiling, but there is another reason to use the cascades, that I could have explained better in the video. The cascades greatly improve the dynamic range of the FFT. To represent a plausible water surface you need wavelengths from ~1cm up to the hundreds of meters in choppy sea. To cover this range of wavelengths you have to use multiple FFT domains, otherwise the required resolution becomes insane.