X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;f=futatabi%2Fderivatives.frag;fp=futatabi%2Fderivatives.frag;h=0e2fd687c9cd483ba2f33d5ca40f40046c0eea80;hb=6e116a6bbeb2c047a3bfb084395ec601ce211e6c;hp=0000000000000000000000000000000000000000;hpb=ce2e0615420b706e1ff2405fffcedfba37a9adac;p=nageru

diff --git a/futatabi/derivatives.frag b/futatabi/derivatives.frag
new file mode 100644
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);
+}