diff options
Diffstat (limited to 'math.cginc')
| -rw-r--r-- | math.cginc | 151 |
1 files changed, 151 insertions, 0 deletions
@@ -1,6 +1,8 @@ #ifndef __MATH_INC
#define __MATH_INC
+#include "pema99.cginc"
+
#define PI 3.14159265358979323846264
#define TAU (2 * PI)
@@ -15,6 +17,155 @@ float wrapNoL(float NoL, float factor) { return pow(max(1E-4, (NoL + factor) / (1 + factor)), 1 + factor);
}
+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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