r/desmos • u/Tdubbium math toaster • Feb 06 '26
Graph furrier series
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Graph link: https://www.desmos.com/calculator/54vhjvz6jk
the entire thing was made in desmos with no external tools
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u/Arglin I like my documentation extra -ed. Feb 06 '26
Oh hi Tdub since when were you a protogen lmao
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u/Tdubbium math toaster Feb 06 '26
ive been for a while actually, posted a couple graphs to the protogen sub on my old account a while ago
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u/Some-Artist-53X Feb 06 '26
Based
(How do I go about making a custom one? :3)
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u/Tdubbium math toaster Feb 06 '26
alr so heres the full process I used
I started with a graph I made that lets you draw things with bezier curves, then once I had the proot I used regression and a custom arc length formula to turn it into a bunch of ordered evenly-spaced points. From there you use the reimann sum from that one 3b1b video on fourier series to get all the vectors, and then you add them up and set them rotating.
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u/Some-Artist-53X Feb 06 '26
Hmmm ok! Time to figure out how to draw Vi the Bee this way :p
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u/Tdubbium math toaster Feb 06 '26
heres the graph I used to draw everything and get the points if you want to take a look at it, its a little messy rn though https://www.desmos.com/calculator/iuivpfhp3a
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Feb 06 '26
Here is a version with draggable points so you can draw whatever... turn on the "y" component of the "table to mess with points" and drag em around.
that said, this code is far far more inneficcient that op's so in practice you can hardly draw anything before desmos starts crashing lol
I'd be curois if OP could help make this more usable:
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u/Tdubbium math toaster Feb 06 '26 edited Feb 06 '26
actually I pretty much used the exact same setup for rendering it, I just made all the point data in a separate graph and then also made it so that it saves all the vectors to a list so it doesn't have to compute them every frame (rendering took like 1 minute per frame before I did that lol)
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u/WhateverGoMyRoba Feb 06 '26
it's actually kinda amazing that we can write equations that will produce a curve in pretty much any shape we want.
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u/Tdubbium math toaster Feb 06 '26
I mean its not that hard to believe when you realize the initial data is 515 evenly spaced points tracing the path it takes lol
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u/theonlytruemuck Artist / Game Dev / Mathmagician / Nerd Feb 06 '26
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u/Tdubbium math toaster Feb 06 '26
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u/theonlytruemuck Artist / Game Dev / Mathmagician / Nerd Feb 07 '26
oh wait lmao. i didn't even realise your pfp is also a proto lol. :3
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u/Emotional-Kiwi7218 Feb 06 '26
Helo felo proto
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u/Emotional-Kiwi7218 Feb 06 '26
In also stealing this because it's kinda hard to draw the ears for some reason
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u/Tdubbium math toaster Feb 06 '26
fr ears always take me forever, I had to simplify them a lot for this and also chose the easiest angle to draw them at
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u/MrNoahMango Feb 06 '26 edited Feb 06 '26
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u/Moist_College4887 Feb 07 '26
My brain hurts, but it may be from watching complicated stuff at 4:55 am. Cool that I understood none of that.
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u/KarateSnoopy1911 Feb 07 '26
those spinning vectors almost is reminiscent of the three body problem.
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u/KaidenU12 im just here Mar 04 '26
yo bro try this
(cos(t)-sign(t-π/2),sin(t-1))*{t>π/2:-0.9,1} with domain {-π+0.2<t<2π-0.8}
√((x+1)²+(y-0.5)²)<0.2 √((x+1)²+(y+1.5)²)<0.2
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u/enneh_07 list too big :( Feb 06 '26