Shadertoy / Inverse Barrel Distortion

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The inverse of a Barrel Distortion.

I couldn't find this function online, so I derived it myself. A surprisingly complex formula ;-).

uv -= .5;

float b = distortion;
float l = length(uv);

float x0 = pow(9.*b*b*l + sqrt(3.) * sqrt(27.*b*b*b*b*l*l + 4.*b*b*b), 1./3.);
float x = x0 / (pow(2., 1./3.) * pow(3., 2./3.) * b) - pow(2./3., 1./3.) / x0;

return uv * (x / l) + .5;

Source code

You can find (the full source of) Inverse Barrel Distortion on Shadertoy.