Junferno you absolute buffoon why didn't you use Fourier series well I'll tell you why I
didn't use Fourier series you see in order to do Fourier series you need to be able to find
the constants for each vector that makes a circle to draw the shape in order to find those constants
you first need to actually already have the shape predetermined so that you can get the integral
of all the points and if you already have the shape represented in some other way then why
would you do it in Fourier series does Fourier series make it render at a higher resolution
no because it's approximated based off of the shape you already have at best it's going to
look like what you already have does it render faster also no because you need a near infinite
number of vectors to represent each shape which is not any better than just representing the shape
as the vectors that make it up in the first place and also since it is a path that you have to trace
you have to do even more rendering uh for each single frame can you represent each frame as a
single equation with Fourier series also no because Fourier series requires a closed shape
to draw since it's with periodic functions and so like look at this you're gonna need 50 for
your series this is Desmos I can't run this so yeah so that's why oh boy I sure am glad that
there's no more unnecessarily complex mathematical formulas for this pretty simple Desmos rendering
Tupper's self-referential formula it basically is just a counter from zero to a really large
number and then each number is representing some bitmap of zeros and ones that just represents
every single possible combination of pixels in kind of like a matrix however these numbers get
really big and so you can't really Desmos isn't very good with really really big numbers you know
any resolution that is higher than a few pixels and so and even if i wanted to make low resolution
pixel art on Desmos I'd just use a matrix so there's really no reason for why I would do that
now you may be saying Junferno you're you're just saying this because your version looks like PS1
graphics look at these linear approximations well I decided to redo the Desmos thing this time we're
using something called Bezier curves which is what an svg uses to render paths since in an svg
with if you just use linear approximations for example if you have like a round edge
then you're just going to have a lot of really tiny lines but with Bezier curves what it does is
it takes four coordinates one is a starting point one is ending point and then two that represent
the curvature and you can represent really almost any curve whether it's parabolic or or even like
a straight line you can represent it and so basically what we've done is we've made Desmos
into an svg renderer by converting each frame into a path of these curves that it can render
why did i choose a method that nobody commented about was it just to spite all of you for
you know making all these ludicrous suggestions yes anyways here's a preview
you