1 files changed, 89 insertions, 0 deletions
diff --git a/Shaders/cloud/math.cginc b/Shaders/cloud/math.cginc
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+++ b/Shaders/cloud/math.cginc
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+#ifndef __MATH_INC
+#define __MATH_INC
+
+#include "pema99.cginc"
+
+#define PI 3.14159265
+
+// Differentiable approximation of the standard `max` function.
+float dmax(float a, float b, float k)
+{
+  return log2(exp2(k * a) + exp2(k * b)) / k;
+}
+
+// Differentiable approximation of the standard `min` function.
+float dmin(float a, float b, float k)
+{
+  return -1.0 * dmax(-1.0 * a, -1.0 * b, k);
+}
+
+// Generate a random number on [0, 1].
+float rand2(float2 p)
+{
+  return glsl_mod(sin(dot(p, float2(561.0, 885.0))) * 776.2, 1.0);
+}
+
+// Generate a random number on [0, 1].
+float rand3(float3 p)
+{
+  return glsl_mod(sin(dot(p, float3(897.0, 367.0, 197.0))) * 1073.6
+      + sin(dot(p, float3(473.0, 599.0, 1093.0))) * 12.6, 1.0);
+}
+
+// 3 dimensional value noise. `p` is assumed to be a point inside a unit cube.
+// Theory: https://en.wikipedia.org/wiki/Value_noise
+float vnoise3d(float3 p)
+{
+  float3 pu = floor(p);
+  float3 pv = glsl_mod(p, 1.0);
+
+  // Assign random numbers to the corner of a cube.
+  float n000 = rand3(pu + float3(0,0,0));
+  float n001 = rand3(pu + float3(0,0,1));
+  float n010 = rand3(pu + float3(0,1,0));
+  float n011 = rand3(pu + float3(0,1,1));
+  float n100 = rand3(pu + float3(1,0,0));
+  float n101 = rand3(pu + float3(1,0,1));
+  float n110 = rand3(pu + float3(1,1,0));
+  float n111 = rand3(pu + float3(1,1,1));
+
+  float n00 = lerp(n000, n001, pv.z);
+  float n01 = lerp(n010, n011, pv.z);
+  float n10 = lerp(n100, n101, pv.z);
+  float n11 = lerp(n110, n111, pv.z);
+
+  float n0 = lerp(n00, n01, pv.y);
+  float n1 = lerp(n10, n11, pv.y);
+
+  float n = lerp(n0, n1, pv.x);
+
+  return n;
+}
+
+float fbm(float3 p, const int n_octaves, float w)
+{
+  float g = exp2(-w);
+  float a = 1.0;
+  float p_scale = 1.0;
+
+  float res = 0.0;
+  for (int i = 0; i < n_octaves; i++) {
+    res += a * vnoise3d(p * p_scale);
+
+    p_scale /= w;
+    a *= g;
+  }
+
+  // On average, vnoise3d returns 0.5.
+  // Sum of any geometric series is, for growth parameter r and constant a,
+  // a / (1 - r).
+  // We want to map onto [0, 1], so divide by this expected sum.
+  // Use a = 1, to account for the worst-case possibility that every call to
+  // vnoise3d() returns 1.
+  res /= (1 / (1 - g));
+
+  return res;
+}
+
+#endif  // __MATH_INC
+