Post-processing for polar coordinates / planet effect

interpolated-polar-coordinates-shader.frag

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    // Normalized pixel coordinates (from 0 to 1)
    vec2 uv = fragCoord/iResolution.xy;
    vec2 originalUv = uv;
    
    uv -= 0.5;
    
    vec2 n = normalize(uv);
    
    float a = atan(-uv.y, uv.x) + 3.1415926 / 2.0;
    float r = pow(length(uv), 1.0 / sqrt(3.1415926));
    
    float y = r;
    float x = fract((1.0 + a / 3.1415926) / 2.0);
    
    vec2 polarUv = vec2(x, y);
    
    float i = iTime;
    
    uv = mix(originalUv, polarUv, fract(iTime));

    // Time varying pixel color
    vec4 col = texture(iChannel0, uv);

    // Output to screen
    // fragColor = vec4(r, a, 0.0, 1.0);
    fragColor = col;
}