Thank you! It took me way too much time :D

@@PezzzasWork But really how did you do the Paint Dispenser it looked so good?!

Thank you! My background isn’t about mathematics, that might be why :)

Thank you for your comment, I didn’t know about this, I will have a look!

3b1b actually has a couple of very similar videos (including pretty similar animations), so I don’t think this would be a good entry for SoME (as I think being a somewhat novel explainer is part of the judgement criteria). I know of at least 4 major STEM KZfaq channels who have done this topic (focusing on using the FFT/DFT to draw). However, I totally think this channel should consider coming up with an entry. The videos are very polished and the explanations are clear.

I've seen these Fourier drawings on 3b1b before

It would be good for SoME, but he already has that type of video

Thank you! Glad you appreciate the details, it is what takes most of the time :)

Thank you!

Thank you! Yes indeed! I wanted to redo it for a long time since I truly find this fascinating :)

fr

Thank you! It’s hand made and runs in real time during the signal reconstruction. It is based on the XPBD method, the scientific paper is amazing and makes it very easy to implement.

Thank you very much for the nice comment :)

Xerne5 clone? Lol

Merci beaucoup ! :)

Who is the other one you are referring to? Sebastian Lague?

Ok

Yep sme

Thank you for your support!

Thank you!

so fearless

Thank you very much for the nice comment!

Thank you!

Thank you! I will do some videos about my way of doing animations as it seems there is a demand for it.

Data fitting was why the DFT was originally invented. The FFT, a fast algorithm for performing the DFT, was originally discovered by Gauss while trying to predict the orbits of asteroids.

@@CliffHanger-fg6uy Pretty cool!

He never actually used a 2D DFT. The DFT by default allows for a complex-valued signal. You can just set the real and imaginary parts of each entry to the x and y coordinates of each sample. Typical generalizations to higher dimensions rely on adding up plane waves, which certainly wouldn’t create a comparable graphic. For that reason, generalizing this sort of animation to 3D would be significantly tricky. Apparently there’s such a thing as a quaternion Fourier transform. Maybe that would do it? I’ve never studied them, though, so I don’t know.

@@CliffHanger-fg6uy Yes, you can sum plane waves, but in every actual use I've ever seen it's done by decomposition... just like in this video.

Signed distance function is more suitable for 3D I think.

Is there an algorithm for turning a curve into a bunch of stitched together Bezier curves? I am under the impression that Bezier curves are typically made by hand.

Thank you!

Thank you! I am using my own animation framework I wrote in C++

if you put the circles that made the y signal on top of the circles that made the x signal or vice versa they simply combine, that's all, if this were real life u literally just stick them on top of each other (obviously aligned correctly) yes he could've done it by altering the circles and likely did as this would make it look more satisfying but it is not necessary, the order of the circles don't matter it just looks nicer when it decreases in size

i believe it works by feeding the positions as complex numbers (x+iy) into the formula.

In the code the circles are really represented as complex numbers, But I'll still frame my comment here in terms of those circles, and sine/cosine. Also my notation here won't necessarily match the video. I don't think he computed x circles and y circles individually. For each frequency component, there is a single circle that handles both x and y. Still, if you do have a set of circles for x and y here is how you can combine them. Each circle will have some radius r, some speed ω, and some offset(phase) ϕ. So a point moving in a circle around the origin can be described as two functions x(t) = r⋅cos(ω(t-ϕ)) and y(t) = r⋅sin(ω(t-ϕ)) The x circles and y circles will have circles of possibly different sizes and phases, but same speeds. By which I mean, if the x circles will have one with a speed of 5, so too will the y circle. (Actually the speeds will be a multiple of 2*pi/N but whatever). Let's say the x circles include one with radius a, speed ω, and phase ϕ_1, and the y circles include one with radius b, speed ω, and phase ϕ_2. We can add these two circles to get a single circle. To do so, you can plug in t=0 to get the x,y values of one point from each circle, let's label them (x1,y1) and (x2,y2). Add these points component-wise to get a new point. So (x3,y3) = (x1+x2,y1+y2) . The radius of our resulting circle will be the distance of (x3,y3) from the origin, so sqrt(x3^2 + y3^2). The phase of our resulting circle will be the angle that (x3,y3) makes with the origin and the x axis, so atan2(y3,x3). And finally the speed will stay the same.

Thank you! And I think I recognize your profile picture from GitHub, so I take the opportunity to thank you very much for your generous support!

Thank you!

Thank you!

Thank you! I hope this will help you :) I am using my own C++ framework !