Fish-eye Shader for Love 2D

fisheye.frag

const float PI = 3.1415926535;

vec4 effect( vec4 color, Image texture, vec2 texture_coords, vec2 screen_coords)
{
  float aperture = 178.0;
  float apertureHalf = 0.5 * aperture * (PI / 180.0);
  float maxFactor = sin(apertureHalf);
  
  vec2 uv;
  vec2 xy = 2.0 * texture_coords.xy - 1.0;
  float d = length(xy);
  if (d < (2.0-maxFactor))
  {
    d = length(xy * maxFactor);
    float z = sqrt(1.0 - d * d);
    float r = atan(d, z) / PI;
    float phi = atan(xy.y, xy.x);
    
    uv.x = r * cos(phi) + 0.5;
    uv.y = r * sin(phi) + 0.5;
  }
  else
  {
    uv = texture_coords.xy;
  }
  vec4 c = texture2D(texture, uv);
  return c;
}

fisheye.vert

vec4 position( mat4 transform_projection, vec4 vertex_position )
{
    return transform_projection * vertex_position;
}

Based on http://www.geeks3d.com/20140213/glsl-shader-library-fish-eye-and-dome-and-barrel-distortion-post-processing-filters/