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Diffstat (limited to 'Shaders/parallax/math.cginc')
| -rw-r--r-- | Shaders/parallax/math.cginc | 77 |
1 files changed, 77 insertions, 0 deletions
diff --git a/Shaders/parallax/math.cginc b/Shaders/parallax/math.cginc new file mode 100644 index 0000000..68ff9a1 --- /dev/null +++ b/Shaders/parallax/math.cginc @@ -0,0 +1,77 @@ +#ifndef __MATH_INC +#define __MATH_INC + +#include "pema99.cginc" + +// 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(float3 p) +{ + return frac(sin(dot(p, float2(561.0, 885.0))) * 776.2) / 2.0; +} + +// Generate a random number on [0, 1]. +float rand3(float3 p) +{ + return frac(sin(dot(p, float3(897.0, 367.0, 197.0))) * 1073.6) / 2.0; +} + +// 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(frac(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; + } + return res; +} + +#endif // __MATH_INC + |
