4 in float element_sum_idx;
7 uniform sampler2D diff_flow_tex, smoothness_x_tex, smoothness_y_tex;
8 uniform usampler2D equation_tex;
9 uniform vec2 image_size;
12 // See pack_floats_shared() in equations.frag.
13 vec2 unpack_floats_shared(uint c)
15 // Recover the exponent, and multiply it in. Add one because
16 // we have denormalized mantissas, then another one because we
17 // already reduced the exponent by one. Then subtract 20, because
18 // we are going to shift up the number by 20 below to recover the sign bits.
19 float normalizer = uintBitsToFloat(((c >> 1) & 0x7f800000u) - (18 << 23));
20 normalizer *= (1.0 / 2047.0);
22 // Shift the values up so that we recover the sign bit, then normalize.
23 float a = int(uint(c & 0x000fffu) << 20) * normalizer;
24 float b = int(uint(c & 0xfff000u) << 8) * normalizer;
31 // Red-black SOR: Every other pass, we update every other element in a
32 // checkerboard pattern. This is rather suboptimal for the GPU, as it
33 // just immediately throws away half of the warp, but it helps convergence
34 // a _lot_ (rough testing indicates that five iterations of SOR is as good
35 // as ~50 iterations of Jacobi). We could probably do better by reorganizing
36 // the data into two-values-per-pixel, so-called “twinning buffering”,
37 // but it makes for rather annoying code in the rest of the pipeline.
38 int color = int(round(element_sum_idx)) & 1;
39 if (color != phase) discard;
41 uvec4 equation = texture(equation_tex, tc);
42 float inv_A11 = uintBitsToFloat(equation.x);
43 float A12 = uintBitsToFloat(equation.y);
44 float inv_A22 = uintBitsToFloat(equation.z);
45 vec2 b = unpack_floats_shared(equation.w);
47 // Subtract the missing terms from the right-hand side
48 // (it couldn't be done earlier, because we didn't know
49 // the values of the neighboring pixels; they change for
50 // each SOR iteration).
51 float smooth_l = textureOffset(smoothness_x_tex, tc, ivec2(-1, 0)).x;
52 float smooth_r = texture(smoothness_x_tex, tc).x;
53 float smooth_d = textureOffset(smoothness_y_tex, tc, ivec2( 0, -1)).x;
54 float smooth_u = texture(smoothness_y_tex, tc).x;
55 b += smooth_l * textureOffset(diff_flow_tex, tc, ivec2(-1, 0)).xy;
56 b += smooth_r * textureOffset(diff_flow_tex, tc, ivec2( 1, 0)).xy;
57 b += smooth_d * textureOffset(diff_flow_tex, tc, ivec2( 0, -1)).xy;
58 b += smooth_u * textureOffset(diff_flow_tex, tc, ivec2( 0, 1)).xy;
60 const float omega = 1.8; // Marginally better than 1.6, it seems.
61 diff_flow = texture(diff_flow_tex, tc).xy;
63 // From https://en.wikipedia.org/wiki/Successive_over-relaxation.
64 float sigma_u = A12 * diff_flow.y;
65 diff_flow.x += omega * ((b.x - sigma_u) * inv_A11 - diff_flow.x);
66 float sigma_v = A12 * diff_flow.x;
67 diff_flow.y += omega * ((b.y - sigma_v) * inv_A22 - diff_flow.y);