Godot Fisheye (Screen-Space)

// A simple (screen space) fisheye shader for Godot, based on: https://gist.github.com/aggregate1166877/a889083801d67917c26c12a98e7f57a7
// It's calibrated to convert a square screen space into a sphere

shader_type canvas_item;

const float crop_amount = 0.9;

vec2 distort(vec2 p)
{
    float d = length(p);
    float z = sqrt(1.0 + d * d * -1.0);
    float r = atan(d, z) / 3.1415926535;
    float phi = atan(p.y, p.x);
    return vec2(r*cos(phi)+.5,r*sin(phi)+.5);
}

void fragment()
{
    vec2 xy = (2.0 * SCREEN_UV);
    xy.x = xy.x - 1.0;
    xy.y = xy.y - 1.0;

    vec4 tex;
    float d = length(xy);
    if (d < 1.0) {
        xy = distort(xy);
        tex = texture(SCREEN_TEXTURE, xy);
        COLOR = tex;
        COLOR.a = 0.999;
    }

    // crop.
    if (d > crop_amount) {
        COLOR = vec4(0,0,0,1);
    }
}