vec2 x=tc - vec2(0.5,0.5);
 float radius=length(x);
 float angle=atan(x.y, x.x);

#version ...
precision ...

varying vec2 tc; // texcoords from vertex shader
uniform sampler2D tex;

#define PI 3.14159265358979323844

void main ()
{
    const float r_inner=0.25;
    const float t_outer=0.5;

    vec2 x = v_tex - vec2(0.5);
    float radius = length(x);
    float angle = atan(x.y, x.x);

    vec2 tc_polar; // the new polar texcoords
    // map radius so that for r=r_inner -> 0 and r=r_outer -> 1
    tc_polar.s = ( radius - r_inner) / (r_outer - r_inner);

    // map angle from [-PI,PI] to [0,1]
    tc_polar.t = angle * 0.5 / PI + 0.5;

    // texture mapping
    gl_FragColor = texture2D(tex, tc_polar);
}

uniform float Angle; // range 2pi / 100000.0 to 1.0 (rounded down), exponential
uniform float AngleMin; // range -3.2 to 3.2
uniform float AngleWidth; // range 0.0 to 6.4
uniform float Radius; // range -10000.0 to 1.0
uniform float RadiusMin; // range 0.0 to 2.0
uniform float RadiusWidth; // range 0.0 to 2.0
uniform vec2 Center; // range: -1.0 to 3.0

uniform sampler2D Texture;

void main()
{
    // Normalised texture coords
    vec2 texCoord = gl_TexCoord[0].xy;
    // Shift origin to texture centre (with offset)
    vec2 normCoord;
    normCoord.x = 2.0 * texCoord.x – Center.x;
    normCoord.y = 2.0 * texCoord.y – Center.y;
    // Convert Cartesian to Polar coords
    float r = length(normCoord);
    float theta = atan(normCoord.y, normCoord.x);

    // The actual effect
    r = (r < RadiusMin) ? r : (r > RadiusMin + RadiusWidth) ? r : ceil(r / Radius) * Radius;
    theta = (theta < AngleMin) ? theta : (theta > AngleMin + AngleWidth) ? theta : floor(theta / Angle) * Angle;

    // Convert Polar back to Cartesian coords
    normCoord.x = r * cos(theta);
    normCoord.y = r * sin(theta);
    // Shift origin back to bottom-left (taking offset into account)
    texCoord.x = normCoord.x / 2.0 + (Center.x / 2.0);
    texCoord.y = normCoord.y / 2.0 + (Center.y / 2.0);

    // Output
    gl_FragColor = texture2D(Texture, texCoord);
}