3 in vec2 tc, tc_left, tc_down;
4 in vec2 equation_tc_assuming_left, equation_tc_assuming_right;
5 in float element_x_idx, element_sum_idx;
8 uniform sampler2D diff_flow_tex, diffusivity_tex;
9 uniform usampler2D equation_red_tex, equation_black_tex;
12 uniform bool zero_diff_flow;
14 // See pack_floats_shared() in equations.frag.
15 vec2 unpack_floats_shared(uint c)
17 // Recover the exponent, and multiply it in. Add one because
18 // we have denormalized mantissas, then another one because we
19 // already reduced the exponent by one. Then subtract 20, because
20 // we are going to shift up the number by 20 below to recover the sign bits.
21 float normalizer = uintBitsToFloat(((c >> 1) & 0x7f800000u) - (18 << 23));
22 normalizer *= (1.0 / 2047.0);
24 // Shift the values up so that we recover the sign bit, then normalize.
25 float a = int(uint(c & 0x000fffu) << 20) * normalizer;
26 float b = int(uint(c & 0xfff000u) << 8) * normalizer;
31 float zero_if_outside_border(vec4 val)
34 // We hit the border (or more like half-way to it), so zero smoothness.
43 // Red-black SOR: Every other pass, we update every other element in a
44 // checkerboard pattern. This is rather suboptimal for the GPU, as it
45 // just immediately throws away half of the warp, but it helps convergence
46 // a _lot_ (rough testing indicates that five iterations of SOR is as good
47 // as ~50 iterations of Jacobi). We could probably do better by reorganizing
48 // the data into two-values-per-pixel, so-called “twinning buffering”,
49 // but it makes for rather annoying code in the rest of the pipeline.
50 int color = int(round(element_sum_idx)) & 1;
51 if (color != phase) discard;
55 if ((int(round(element_x_idx)) & 1) == 0) {
56 equation_tc = equation_tc_assuming_left;
58 equation_tc = equation_tc_assuming_right;
61 equation = texture(equation_red_tex, equation_tc);
63 equation = texture(equation_black_tex, equation_tc);
65 float inv_A11 = uintBitsToFloat(equation.x);
66 float A12 = uintBitsToFloat(equation.y);
67 float inv_A22 = uintBitsToFloat(equation.z);
68 vec2 b = unpack_floats_shared(equation.w);
71 diff_flow = vec2(0.0f);
73 // Subtract the missing terms from the right-hand side
74 // (it couldn't be done earlier, because we didn't know
75 // the values of the neighboring pixels; they change for
76 // each SOR iteration).
77 float smooth_l = zero_if_outside_border(texture(diffusivity_tex, tc_left));
78 float smooth_r = zero_if_outside_border(textureOffset(diffusivity_tex, tc_left, ivec2(1, 0)));
79 float smooth_d = zero_if_outside_border(texture(diffusivity_tex, tc_down));
80 float smooth_u = zero_if_outside_border(textureOffset(diffusivity_tex, tc_down, ivec2(0, 1)));
81 b += smooth_l * textureOffset(diff_flow_tex, tc, ivec2(-1, 0)).xy;
82 b += smooth_r * textureOffset(diff_flow_tex, tc, ivec2( 1, 0)).xy;
83 b += smooth_d * textureOffset(diff_flow_tex, tc, ivec2( 0, -1)).xy;
84 b += smooth_u * textureOffset(diff_flow_tex, tc, ivec2( 0, 1)).xy;
85 diff_flow = texture(diff_flow_tex, tc).xy;
88 const float omega = 1.8; // Marginally better than 1.6, it seems.
90 // From https://en.wikipedia.org/wiki/Successive_over-relaxation.
91 float sigma_u = A12 * diff_flow.y;
92 diff_flow.x += omega * ((b.x - sigma_u) * inv_A11 - diff_flow.x);
93 float sigma_v = A12 * diff_flow.x;
94 diff_flow.y += omega * ((b.y - sigma_v) * inv_A22 - diff_flow.y);