92 lines
3.4 KiB
Plaintext
92 lines
3.4 KiB
Plaintext
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const int char_width = 8;
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const int char_height = 13;
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const int char_count = 95;
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const int char_pixels = char_width*char_height;
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const float2 char_dim = float2(char_width, char_height);
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const float2 font_scale = float2(1.0/float(char_width)/float(char_count), 1.0/float(char_height));
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void main()
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{
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float2 char_pos = floor(GetCoordinates()*GetResolution()/char_dim);
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float2 pixel_offset = floor(GetCoordinates()*GetResolution()) - char_pos*char_dim;
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// just a big number
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float mindiff = float(char_width*char_height) * 100.0;
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float minc = 0.0;
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float4 mina = float4(0.0, 0.0, 0.0, 0.0);
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float4 minb = float4(0.0, 0.0, 0.0, 0.0);
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for (int i=0; i<char_count; i++)
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{
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float4 ff = float4(0.0, 0.0, 0.0, 0.0);
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float4 f = float4(0.0, 0.0, 0.0, 0.0);
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float4 ft = float4(0.0, 0.0, 0.0, 0.0);
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float4 t = float4(0.0, 0.0, 0.0, 0.0);
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float4 tt = float4(0.0, 0.0, 0.0, 0.0);
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for (int x=0; x<char_width; x++)
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{
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for (int y=0; y<char_height; y++)
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{
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float2 tex_pos = char_pos*char_dim + float2(x,y) + 0.5;
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float4 tex = SampleLocation(tex_pos * GetInvResolution());
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float2 font_pos = float2(x+i*char_width, y) + 0.5;
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float4 font = SampleFontLocation(font_pos * font_scale);
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// generates sum of texture and font and their squares
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ff += font*font;
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f += font;
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ft += font*tex;
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t += tex;
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tt += tex*tex;
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}
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}
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// The next lines are a bit harder, hf :-)
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// The idea is to find the perfect char with the perfect background color and the perfect font color.
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// As this is an equation with three unknowns, we can't just try all chars and color combinations.
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// As criterion how "perfect" the selection is, we compare the "mean squared error" of the resulted colors of all chars.
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// So, now the big issue: how to calculate the MSE without knowing the two colors ...
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// In the next steps, "a" is the font color, "b" is the background color, "f" is the font value at this pixel, "t" is the texture value
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// So the square error of one pixel is:
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// e = ( t - a⋅f - b⋅(1-f) ) ^ 2
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// In longer:
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// e = a^2⋅f^2 - 2⋅a⋅b⋅f^2 + 2⋅a⋅b⋅f - 2⋅a⋅f⋅t + b^2⋅f^2 - 2⋅b^2⋅f + b^2 + 2⋅b⋅f⋅t - 2⋅b⋅t + t^2
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// The sum of all errors is: (as shortcut, ff,f,ft,t,tt are now the sums like declared above, sum(1) is the count of pixels)
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// sum(e) = a^2⋅ff - 2⋅a^2⋅ff + 2⋅a⋅b⋅f - 2⋅a⋅ft + b^2⋅ff - 2⋅b^2⋅f + b^2⋅sum(1) + 2⋅b⋅ft - 2⋅b⋅t + tt
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// To find the minimum, we have to derive this by "a" and "b":
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// d/da sum(e) = 2⋅a⋅ff + 2⋅b⋅f - 2⋅b⋅ff - 2⋅ft
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// d/db sum(e) = 2⋅a⋅f - 2⋅a⋅ff - 4⋅b⋅f + 2⋅b⋅ff + 2⋅b⋅sum(1) + 2⋅ft - 2⋅t
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// So, both equations must be zero at minimum and there is only one solution.
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float4 a = (f*ft - ff*t + f*t - ft*float(char_pixels)) / (f*f - ff*float(char_pixels));
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float4 b = (f*ft - ff*t) / (f*f - ff*float(char_pixels));
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float4 diff = a*a*ff + 2.0*a*b*f - 2.0*a*b*ff - 2.0*a*ft + b*b *(-2.0*f + ff + float(char_pixels)) + 2.0*b*ft - 2.0*b*t + tt;
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float diff_f = dot(diff, float4(1.0, 1.0, 1.0, 1.0));
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if (diff_f < mindiff)
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{
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mindiff = diff_f;
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minc = float(i);
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mina = a;
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minb = b;
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}
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}
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float2 font_pos_res = float2(minc * float(char_width), 0.0) + pixel_offset + 0.5;
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float4 col = SampleFontLocation(font_pos_res * font_scale);
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SetOutput(mina * col + minb * (float4(1.0,1.0,1.0,1.0) - col));
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}
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