Calculus of Variations (in Blender) // Optimization Simulations

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[@andrewphoto4750]

Bro a shapeshifter every time he post

[@gnome3d750]

😂

[@sasodoma]

One thing to note about this iterative optimization is that it doesn't necessarily find the most optimal result, just the one that is better than all of the nearby ones. So for example with the two mountains, you would probably never get the line to cross a mountain and find the best path around, because when it tries to go over a mountain, the middle is still comparatively better.

[@OGPatriot03]

That just depends on your math, for example you could multiply any z axis distance by some arbitrary value to weight inclines more heavily. If the noise distortion is sufficient then one of the random paths would probably eventually skirt around to either side and that would become the new shortest path.

[@globglob3d]

​@@OGPatriot03 but if the noise is too strong and big you'll get poor accuracy toward the end. Ideally the noise scaling and strength should decrease overtime in order to get good exploration at the start and small distortion in the end.

[@user-sl6gn1ss8p]

one approach to help with that which wouldn't be too hard to fit into this would be to always accept changes which reduce the length, but also possibly accept changes which increase it, but with a chance which goes down the larger the increase, instead of simply adding more noise. This means the path still strongly favors becoming shorter, but still retains some chance to wander about. You could also keep track of what the shortest path found was, besides the current path.

[@namor_votilav]

Exactly, why not just blur position while «pinning» endpoints with spline parameter?

[@user-sl6gn1ss8p]

@@namor_votilav that won't work for most metrics, will it? Like, if you're using euclidian, which is the usual, it should work, but for anything else I think it would fail

[@jonathan6296]

I feel like an idiot watching this.

[@drokolesko12]

But in every task you somehow find a smart solution!

[@NotGarrettT]

I feel like an idiot watching all of his videos

[@Casey-nz7xl]

Just in case you are not aware, you can uncheck "Normalize" on the "Noise Texture" to change the range from (0, 1) -> (-1, 1) which would have the same effect as the "Subtract" vector node. (But with a factor of 2)🙂

[@gwentarinokripperinolkjdsf683]

thanks for saving me using map range everywhere

[@omidpakbin]

I don't think I will ever going to use this technique, but I still sat through the whole thing, because this is one of my top favorite channels. Dude wastes no time. So on point. Love it.

[@shadamethyst1258]

It's a technique used in other areas of computer science, and there are many variations to try to find better extremas

[@uriinbar6046]

to invert the endpoint selection, i think using a boolean 'not' node is simpler and more elegant than subtracting from 1

[@13thxenos]

Damn this is amazing. I had a flashback to my machine learning class where we optimize a function. This could be an amazing learning aid, if a teacher can actually use blender as well as you. And you can actually use better optimizing functions instead of random. Though even in this simple form I had a hard time following.

[@fredrik3685]

In order to reach optimal target faster you can add "temperature" to the simulation. At start the added noise can be high but as the simulation continues it can cool down i.e. the added noise can become smaller and smaller.

[@hakankosebas2085]

Could you tell in detail how would implementation be exactly?

[@XXXMakabaka1880]

@@hakankosebas2085 You could actually find some course on ML, it might talks about it

[@juliusfucik4011]

Definately going to use this. This has so many uses in modeling and visualization. 👍

[@steamer2k319]

Pro-tip: decrease the scale of the exploratory offset you use in each iteration. Extreme pro-tip: try to identify linear or convex aspects of the particular problem and then exploit that. In the case of the bubbles, try to minimize tension. Instead of moving each vertex in a random direction, weight each vertice's movement towards neighbors which are near longer-than-average edges.

[@AKA-f7p]

Nice way to teach Lagrangian mechanics. Can you please do hemeltonian mechanics. Not for me for science.

[@Ali-s-s-s]

I don't know what this channel is about anymore man but I'm always watching nonetheless, this is magnificent.

[@harryblends]

"It's always the useless things that end up being the most useful" - my mum

[@MysteryPancake]

can't wait for episode 2 neural network in blender

[@samk9632]

People have already done this in shader nodes

[@MysteryPancake]

@@samk9632 lol i'm not surprised

[@_spartan11796]

Great stuff as always!

[@gower1973]

That last example reminds me of that thing you can do on graph paper, where you draw a line from x1 to y10, then x2 to y9 and so on and it ends up tracing out a curve.

[@user-sl6gn1ss8p]

what do you mean by x1, y10, etc?

[@rubenoconnor198]

@@user-sl6gn1ss8p As in draw a line between the points 1,0 to 0,10 then again between 2,0 and 0,9 and again from 3,0 to 0,8 etc.. If you then imagined drawing an infinite amount of these lines (in this case the step =1) but if we used a step that was infinitely small we would get a smooth curve. And also im pretty sure the name of this curve will be a quadratic Bézier curve since what you are doing is essentially evaluating nested lerp functions. It is pretty much a geometric interpretation of De Casteljau's algorithm on paper - very cool imo and hope this helps :)

[@user-sl6gn1ss8p]

@@rubenoconnor198 I think I'm misundertanding something, the way I got it this would make a curve mirrored in the y axis. Which is still kinda cool tho

[@potaatobaked7013]

yo calculus!

[@infectioussneeze9099]

ai......

[@echauz1]

Very nice, but there's no calculus of variations here; that was non-guided random search

[@skop6321]

math is math it is calc of var at its core sure, its basically a minimization function but it gives results consistent with calc of var

[@hakankosebas2085]

Yeah thought same thing, do you know any better algorithm to that else? Any tutorial source?

[@sikliztailbunch]

Maxon! Take notes. Why is Blender better in so many features. I just figured you cannot measure surface area in C4D. Lame! Thanks for this great video!

[@MooImABunny]

I really love the thought process here, you learned a very important math/physics tool, and you thought "I wonder if I can do this in Blender?" can't wait to see what you can do with the spectral theorem or like Cauchy's integral formula, or the prime number theorem XD

[@maxungar516]

just watched physics for the birds / the double bubble theorem. you may be interested in ideating on that general topic

[@repositorytutorial3d50]

what about shrinking the edges? wouldn't it make it smoother? I feel that adding a noise will really never converge into the smooth shape that you are looking for.

[@panz1skate]

Great tutorial, as always! It seems that the algorithm converges to the local optimum and not to the global optimum. on a flat surface they're the same, but we cannot be sure for other geometry.

[@gwentarinokripperinolkjdsf683]

This is useful, but you can get similar results by applying a smoothing operation instead of random noise, then you don't even need to test that the surface area is going down. much less general though i suppose

[@Jebarrda00]

also fyi u may want to experiment with decreaseing noise amplitude with frame number to get cleaner convergence to a straight line

[@Jebarrda00]

ok this is cool. lots of cool stuff. iterative optimization is very cool and swaggy

[@DesignTWO]

boomer here. Love your videos, but I have to listen to them at half speed cause I'm old af.

[@muniz9046]

it would be pretty interesting to see that setup used to wrap around a second object in a more interesting way than the ways we do IRL, i bet it can get a ship in a bottle kinda vibe

[@004307ec]

Basically a evolution algorithm in blender, nice❤

[@PCgmesforever]

Question. 3:27 is there a benefit of subtracting the end point Boolean from one opposed to using "not" node ?

[@PnkBabyZebra]

when you stroll by and theres a hyperbolic paraboloid in the thumbnail

[@suhailabdulla3075]

how to create pyro solver in blender's geometry nodes?

[@bimalpandey9736]

Look what 16 microseconds of node editor does to a man.

[@FORTHEGAME-c1n]

Why am i feeling Nostalgic?

[@deedyago]

When does this channel shift to a math one?👀

[@lennon163]

AI will replace us? :(

[@rafliadharivaldy883]

bro just like a mad scientist

[@drokolesko12]

My personal genius

[@fals_volks3127]

Oww just 10mnt Vid 🤔

[@GaryParris]

excellent use of math

[@sanketsbrush]

nice👍👍

[@89ZY]

Great

[@skop6321]

man explained calc of var in like a minute and my physics professor never could get anyone in class to understand lol This is very cool, I've always liked calc of var. it creates some very cool shapes

[@grantmcgregor1571]

I really apricated this, I tried doing lattices in blender and was stuck with geometry nodes without using Booleans. This helped.

[@pranjalrathor]

i love u

[@mod3528]

Why just do not use Blur Attribute node instead...\

[@hakankosebas2085]

Sorry to be greedy but it doesn't make a smooth perfect surface, needs too many iteration, is there a better algorithm?

[@steamer2k319]

Yes. Convex optimization + gradient descent.

[@hakankosebas2085]

@@steamer2k319 how is that, could share node setup of it with me?

[@steamer2k319]

@@hakankosebas2085 Unfortunately, no node group. kzbin.info/www/bejne/d36Zc4xql9mdY68

[@dwellersart7538]

🙌

[@edwardedward6130]

This is great! You're the best! Thanks!

[@StarkRaveness]

nice work