Cartesian to Polar coordinates warp shader, for shadertoy.com

polarWarp.glsl

//To be used on shadertoy.com
//Uses the image at iChannel0 and warps it into polar coordinates
void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    vec2 relativePos = fragCoord.xy - (iResolution.xy / 2.0);
    vec2 polar;
    polar.y = sqrt(relativePos.x * relativePos.x + relativePos.y * relativePos.y);
    polar.y /= iResolution.x / 2.0;
    polar.y = 1.0 - polar.y;

    polar.x = atan(relativePos.y, relativePos.x);
    polar.x -= 1.57079632679;
    if(polar.x < 0.0){
		polar.x += 6.28318530718;
    }
    polar.x /= 6.28318530718;
    polar.x = 1.0 - polar.x;
    
    vec4 c = texture2D(iChannel0, polar);
	fragColor = vec4(c);
}