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#ifndef __MATH_INC
#define __MATH_INC
#include "pema99.cginc"
#define PI 3.14159265358979323846264
#define TAU (2 * PI)
float pow5(float x)
{
float tmp = x * x;
return (tmp * tmp) * x;
}
float wrapNoL(float NoL, float factor) {
// https://www.iro.umontreal.ca/~derek/files/jgt_wrap_final.pdf
return pow(max(1E-4, (NoL + factor) / (1 + factor)), 1 + factor);
}
float halfLambertianNoL(float NoL) {
// https://www.iro.umontreal.ca/~derek/files/jgt_wrap_final.pdf
float tmp = (NoL + 1) * 0.5;
return tmp * tmp;
}
float rand1(float p)
{
return frac(sin(p) * 43758.5453123);
}
float rand2(float2 p)
{
return frac(sin(dot(p, float2(12.9898, 78.233))) * 43758.5453123);
}
inline float rand3_dot(float3 p)
{
return dot(p, float3(151.0, 157.0, 163.0));
}
float3 rand3_hash(float3 p)
{
// Improved Murmurhash3 by Squirrel Eiserloh (GDC 2017)
p = float3(dot(p, float3(127.1, 311.7, 74.7)),
dot(p, float3(269.5, 183.3, 246.1)),
dot(p, float3(113.5, 271.9, 124.6)));
return -1.0 + 2.0 * frac(sin(p) * 43758.5453123);
}
float rand3(float3 p)
{
return frac(rand3_hash(p).x);
}
float2 domainWarp1(float x, uint octaves, float strength, float scale)
{
[loop]
for (uint i = 0; i < octaves; i++) {
x += strength * frac(sin(float2(
dot(x * scale, float2(12.9898, 78.233)),
dot(x * scale + 1, float2(12.9898, 78.233))) * 43758.5453123));
}
return x;
}
float2 domainWarp2(float2 uv, uint octaves, float strength, float scale)
{
[loop]
for (uint i = 0; i < octaves; i++) {
uv += strength * frac(sin(float2(
dot(uv * scale, float2(12.9898, 78.233)),
dot(uv * scale + 1, float2(12.9898, 78.233))) * 43758.5453123));
}
return uv;
}
float determinant(float3x3 m)
{
return (m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
- m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0]))
+ m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
}
float3x3 inverse(float3x3 m)
{
float det = determinant(m);
float3x3 adj;
adj[0][0] = (m[1][1] * m[2][2] - m[1][2] * m[2][1]);
adj[0][1] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]);
adj[0][2] = (m[0][1] * m[1][2] - m[0][2] * m[1][1]);
adj[1][0] = -(m[1][0] * m[2][2] - m[1][2] * m[2][0]);
adj[1][1] = (m[0][0] * m[2][2] - m[0][2] * m[2][0]);
adj[1][2] = -(m[0][0] * m[1][2] - m[0][2] * m[1][0]);
adj[2][0] = (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
adj[2][1] = -(m[0][0] * m[2][1] - m[0][1] * m[2][0]);
adj[2][2] = (m[0][0] * m[1][1] - m[0][1] * m[1][0]);
return adj * (1.0 / det);
}
float3 domainWarp3(float3 pos, uint octaves, float strength, float scale, float offset)
{
[loop]
for (uint i = 0; i < octaves; i++) {
pos += strength * frac(sin(float3(
rand3_dot(pos * scale + offset),
rand3_dot(pos * scale + offset + 1),
rand3_dot(pos * scale + offset + 2)) * 43758.5453123));
}
return pos;
}
void domainWarp3Normals(inout float3 normal, inout float3 tangent, float3 basePos, uint octaves, float strength, float scale, float offset)
{
// Use the actual vertex position for correct derivative evaluation.
float3 p = basePos;
// Start with the identity matrix for the total Jacobian.
float3x3 J = float3x3(
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0
);
const float k = 43758.5453123;
// Updated constant vector to match that of rand3_dot (used in domainWarp3)
const float3 c = float3(151.0, 157.0, 163.0);
for (uint i = 0; i < octaves; i++)
{
// Compute the vector v using the same offsetting as in domainWarp3.
float3 v = float3(
dot(p * scale + float3(offset, offset, offset), c),
dot(p * scale + float3(offset + 1.0, offset + 1.0, offset + 1.0), c),
dot(p * scale + float3(offset + 2.0, offset + 2.0, offset + 2.0), c)
);
// Compute the warp offset with frac.
float3 f_val = frac(sin(v) * k);
float3 warpOffset = strength * f_val;
// Compute the derivative (Jacobian) of the offset.
float3 cos_v = cos(v);
float3x3 D = float3x3(
strength * k * scale * cos_v.x * c.x, strength * k * scale * cos_v.x * c.y, strength * k * scale * cos_v.x * c.z,
strength * k * scale * cos_v.y * c.x, strength * k * scale * cos_v.y * c.y, strength * k * scale * cos_v.y * c.z,
strength * k * scale * cos_v.z * c.x, strength * k * scale * cos_v.z * c.y, strength * k * scale * cos_v.z * c.z
);
// The per–octave Jacobian is I + D.
float3x3 iterJacobian = float3x3(
1.0 + D[0][0], D[0][1], D[0][2],
D[1][0], 1.0 + D[1][1], D[1][2],
D[2][0], D[2][1], 1.0 + D[2][2]
);
// Chain this iteration's Jacobian.
J = mul(iterJacobian, J);
// Update p for the next iteration.
p += warpOffset;
}
// Transform the normal via the inverse-transpose of the total Jacobian.
float3x3 invTransJ = transpose(inverse(J));
normal = normalize(mul(invTransJ, normal));
// Transform the tangent via the forward total Jacobian.
tangent = normalize(mul(J, tangent));
}
#endif // __MATH_INC
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