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#ifndef __SSFD_INC
#define __SSFD_INC
#include "globals.cginc"
float ssfd(float2 uv, float scale, float max_fwidth, float2 uv_offset, texture3D noise)
{
//float uv_fw = fwidth(uv.x) + fwidth(uv.y);
// Original paper uses SVD instead of fwidth.
float2x2 M = float2x2(ddx(uv), ddy(uv));
float2x2 MtM = mul(transpose(M), M);
float trace = MtM[0][0] + MtM[1][1];
float det = determinant(MtM);
// Calculate eigenvalues using quadratic formula.
float tmp = sqrt(trace * trace - 4 * det);
float e1 = (trace + tmp) * 0.5;
float e2 = (trace - tmp) * 0.5;
float2 singular_values = sqrt(float2(e1, e2));
// Logic from original paper: the smaller eigenvalue corresponds to the
// largest amount of stretching, so we use it to determine when to
// subdivide.
float uv_fw = singular_values.y;
uv_fw *= scale;
uint width, height, depth;
noise.GetDimensions(width, height, depth);
float bayer_res = sqrt(depth);
// Suppose max_fwidth is 1.
// uv_fw is 16. That means UV is changing a lot per pixel. That means we want to shrink the scale of the UV.
// Factor is 16.
// log_2(factor) is 4.
// Divide original by 16.
float fw_factor = uv_fw / max_fwidth;
// log_b(x) = log_a(x) / log_a(b)
float fractal_level = log2(fw_factor) / log2(bayer_res);
float fractal_level_floor = floor(fractal_level);
float fractal_remainder = fractal_level - fractal_level_floor;
uv *= pow(bayer_res, -fractal_level_floor);
uv += uv_offset * pow(bayer_res, -fractal_level_floor);
float n_layers = depth;
float not_used_lo = 1/(n_layers*2);
float not_used_hi = 1 - not_used_lo;
float uvw = (not_used_hi - not_used_lo) * (1 - fractal_remainder) + not_used_lo;
float3 uv_3d = float3(uv, uvw);
float dither = noise.SampleLevel(linear_repeat_s, uv_3d, 0);
return dither;
}
#endif // __SSFD_INC
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