based on this paper: http://www.efg2.com/Lab/Library/ImageProcessing/DHALF.TXT
// Ordered dithering aka Bayer matrix dithering
uniform sampler2D bgl_RenderedTexture;
float Scale = 1.0;
float find_closest(int x, int  y, float c0)
{
int dither[8][8] = {
    { 0, 32,  8, 40,  2, 34, 10, 42},   /* 8x8 Bayer ordered dithering  */
    {48, 16, 56, 24, 50, 18, 58, 26},   /* pattern.  Each input pixel   */
    {12, 44,  4, 36, 14, 46,  6, 38},   /* is scaled to the 0..63 range */
    {60, 28, 52, 20, 62, 30, 54, 22},   /* before looking in this table */
    { 3, 35, 11, 43,  1, 33,  9, 41},   /* to determine the action.     */
    {51, 19, 59, 27, 49, 17, 57, 25},
    {15, 47,  7, 39, 13, 45,  5, 37},
    {63, 31, 55, 23, 61, 29, 53, 21} }; 
 
 float limit = 0.0;
 if(x < 8)
 {
  limit = (dither[x][y]+1)/64.0;
 }
 if(c0 < limit)
  return 0.0;
 return 1.0;
}
void main(void)
{
 vec4 lum = vec4(0.299, 0.587, 0.114, 0);
 float grayscale = dot(texture2D(bgl_RenderedTexture, gl_TexCoord[0].xy), lum);
 vec3 rgb = texture2D(bgl_RenderedTexture, gl_TexCoord[0].xy).rgb;
 
 vec2 xy = gl_FragCoord.xy * Scale;
 int x = int(mod(xy.x, 8));
 int y = int(mod(xy.y, 8));
 
 vec3 finalRGB;
 finalRGB.r = find_closest(x, y, rgb.r);
 finalRGB.g = find_closest(x, y, rgb.g);
 finalRGB.b = find_closest(x, y, rgb.b);
 
 float final = find_closest(x, y, grayscale);
 gl_FragColor = vec4(finalRGB, 1.0);
}
Comparison screenshots
original gradient

8x8 dither

4x4 dither

2x2 dither
 
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