Move everything into a separate futatabi/ subdir, for the upcoming merge with Nageru.

[nageru] / futatabi / derivatives.frag

diff --git a/futatabi/derivatives.frag b/futatabi/derivatives.frag
new file mode 100644 (file)
index 0000000..0e2fd68
--- /dev/null
+++ b/futatabi/derivatives.frag
@@ -0,0 +1,32 @@
+#version 450 core
+
+in vec3 tc;
+out vec2 derivatives;
+out float beta_0;
+
+uniform sampler2DArray tex;
+
+void main()
+{
+       float x_m2 = textureOffset(tex, tc, ivec2(-2,  0)).x;
+       float x_m1 = textureOffset(tex, tc, ivec2(-1,  0)).x;
+       float x_p1 = textureOffset(tex, tc, ivec2( 1,  0)).x;
+       float x_p2 = textureOffset(tex, tc, ivec2( 2,  0)).x;
+
+       float y_m2 = textureOffset(tex, tc, ivec2( 0, -2)).x;
+       float y_m1 = textureOffset(tex, tc, ivec2( 0, -1)).x;
+       float y_p1 = textureOffset(tex, tc, ivec2( 0,  1)).x;
+       float y_p2 = textureOffset(tex, tc, ivec2( 0,  2)).x;
+
+       derivatives.x = (x_p1 - x_m1) * (2.0/3.0) + (x_m2 - x_p2) * (1.0/12.0);
+       derivatives.y = (y_p1 - y_m1) * (2.0/3.0) + (y_m2 - y_p2) * (1.0/12.0);
+
+       // The nudge term in the square root in the DeepFlow paper is ζ² = 0.1² = 0.01.
+       // But this is assuming a 0..255 level. Given the nonlinearities in the expression
+       // where β_0 appears, there's no 100% equivalent way to adjust this
+       // constant that I can see, but taking it to (0.1/255)² ~= 1.53e-7 ~=
+       // 1e-7 ought to be good enough. I guess the basic idea is that it
+       // will only matter for near-zero derivatives anyway. I am a tiny
+       // bit worried about fp16 precision when storing these numbers, but OK.
+       beta_0 = 1.0 / (derivatives.x * derivatives.x + derivatives.y * derivatives.y + 1e-7);
+}