does anyone know how images like this are made? (or who is making most of them)
from what I've looked at so far I'm guessing it's something like Mathematica's ImageTransformation with an alternate coordinate system
I don't have Mathematica so I plan to write my own script that does it (and works with GIFs as well), but complex math like this really isn't my strong point. I've only gotten as far as understanding log-polar transforms like http://mathematica.stackexchange.com/a/24649
if anyone's curious, I at least figured out bipolar coordinates, which the first image doesn't seem to be, at least not in the way i did.
first you have to map the output image pixel coordinates to a cartesian plane, e.g. [-2, 2] on both axes. then for each pixel transform into bipolar coordinates where the poles are on the x-axis at -a and a like:
float[] bipolar(float a, float x, float y) {
float t = 0.5*log((pow(x+a, 2)+y*y)/(pow(x-a, 2)+y*y));
float o = PI-2*atan(2*a*y/(a*a-x*x-y*y+sqrt(pow(a*a-x*x-y*y, 2)+4*a*a+y*y)));
return new float[] {t, o};
}
i haven't calculated the axes' ranges on that, but you then need to map each to a positive range e.g. 0-10 and then modulo-1 the coordinates to get x- and y-coordinates in [0, 1)
then just multiply that by the image dimensions and wa la!
I believe this is a more general version of the transform in the OP, that i found on a random blog without much context
Holy, i want to know this too.
Sadly i cannot help you.
At least do you know how images like this are called?
>>143665
No idea, though I think I figured it out. I think I misinterpreted the wiki page on bipolar coordinates and got the transform for σ incorrect. This resulted in the preservation of horizontal lines but didn't give the vertical arcs like in the previous picture.
So I got that right, and then when setting the a-points to near 0 and the scale factor really high to compensate, the result does look like the previous picture. Funnily, I found the author of the original picture, and it's not an image projection, actually just drawing the arcs manually.
I think the first image is using multiple projections of the type I figured out, but without knowing who made it it's hard to say. Pic related is what I can do now. I will post code when I'm home from work
>>143704
that seems like the kaleidoscope effect on after effects.
https://www.youtube.com/watch?v=HL4TNF--lss
>>143704
as promised
https://mega.nz/#!nEY2RC6R!AVn10CRED6_a9D1eFV5_D5bv3Up8eFgka1NHraDRV20
runs in Processing 3 and I tried to comment everything so the transformations are clear
>>143860
not op but thanks i'll try it later since i'm familiar with processing.
