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noise.c
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#include <math.h>
#define F2 0.3660254037844386f
#define G2 0.21132486540518713f
#define F3 (1.0f / 3.0f)
#define G3 (1.0f / 6.0f)
#define ASSIGN(a, v0, v1, v2) (a)[0] = v0; (a)[1] = v1; (a)[2] = v2;
#define DOT3(v1, v2) ((v1)[0] * (v2)[0] + (v1)[1] * (v2)[1] + (v1)[2] * (v2)[2])
const static float GRAD3[16][3] = {
{ 1, 1, 0}, {-1, 1, 0}, { 1,-1, 0}, {-1,-1, 0},
{ 1, 0, 1}, {-1, 0, 1}, { 1, 0,-1}, {-1, 0,-1},
{ 0, 1, 1}, { 0,-1, 1}, { 0, 1,-1}, { 0,-1,-1},
{ 1, 0,-1}, {-1, 0,-1}, { 0,-1, 1}, { 0, 1, 1}
};
const static unsigned char PERM[] = {
151, 160, 137, 91, 90, 15, 131, 13,
201, 95, 96, 53, 194, 233, 7, 225,
140, 36, 103, 30, 69, 142, 8, 99,
37, 240, 21, 10, 23, 190, 6, 148,
247, 120, 234, 75, 0, 26, 197, 62,
94, 252, 219, 203, 117, 35, 11, 32,
57, 177, 33, 88, 237, 149, 56, 87,
174, 20, 125, 136, 171, 168, 68, 175,
74, 165, 71, 134, 139, 48, 27, 166,
77, 146, 158, 231, 83, 111, 229, 122,
60, 211, 133, 230, 220, 105, 92, 41,
55, 46, 245, 40, 244, 102, 143, 54,
65, 25, 63, 161, 1, 216, 80, 73,
209, 76, 132, 187, 208, 89, 18, 169,
200, 196, 135, 130, 116, 188, 159, 86,
164, 100, 109, 198, 173, 186, 3, 64,
52, 217, 226, 250, 124, 123, 5, 202,
38, 147, 118, 126, 255, 82, 85, 212,
207, 206, 59, 227, 47, 16, 58, 17,
182, 189, 28, 42, 223, 183, 170, 213,
119, 248, 152, 2, 44, 154, 163, 70,
221, 153, 101, 155, 167, 43, 172, 9,
129, 22, 39, 253, 19, 98, 108, 110,
79, 113, 224, 232, 178, 185, 112, 104,
218, 246, 97, 228, 251, 34, 242, 193,
238, 210, 144, 12, 191, 179, 162, 241,
81, 51, 145, 235, 249, 14, 239, 107,
49, 192, 214, 31, 181, 199, 106, 157,
184, 84, 204, 176, 115, 121, 50, 45,
127, 4, 150, 254, 138, 236, 205, 93,
222, 114, 67, 29, 24, 72, 243, 141,
128, 195, 78, 66, 215, 61, 156, 180,
151, 160, 137, 91, 90, 15, 131, 13,
201, 95, 96, 53, 194, 233, 7, 225,
140, 36, 103, 30, 69, 142, 8, 99,
37, 240, 21, 10, 23, 190, 6, 148,
247, 120, 234, 75, 0, 26, 197, 62,
94, 252, 219, 203, 117, 35, 11, 32,
57, 177, 33, 88, 237, 149, 56, 87,
174, 20, 125, 136, 171, 168, 68, 175,
74, 165, 71, 134, 139, 48, 27, 166,
77, 146, 158, 231, 83, 111, 229, 122,
60, 211, 133, 230, 220, 105, 92, 41,
55, 46, 245, 40, 244, 102, 143, 54,
65, 25, 63, 161, 1, 216, 80, 73,
209, 76, 132, 187, 208, 89, 18, 169,
200, 196, 135, 130, 116, 188, 159, 86,
164, 100, 109, 198, 173, 186, 3, 64,
52, 217, 226, 250, 124, 123, 5, 202,
38, 147, 118, 126, 255, 82, 85, 212,
207, 206, 59, 227, 47, 16, 58, 17,
182, 189, 28, 42, 223, 183, 170, 213,
119, 248, 152, 2, 44, 154, 163, 70,
221, 153, 101, 155, 167, 43, 172, 9,
129, 22, 39, 253, 19, 98, 108, 110,
79, 113, 224, 232, 178, 185, 112, 104,
218, 246, 97, 228, 251, 34, 242, 193,
238, 210, 144, 12, 191, 179, 162, 241,
81, 51, 145, 235, 249, 14, 239, 107,
49, 192, 214, 31, 181, 199, 106, 157,
184, 84, 204, 176, 115, 121, 50, 45,
127, 4, 150, 254, 138, 236, 205, 93,
222, 114, 67, 29, 24, 72, 243, 141,
128, 195, 78, 66, 215, 61, 156, 180
};
float noise2(float x, float y) {
int i1, j1, I, J, c;
float s = (x + y) * F2;
float i = floorf(x + s);
float j = floorf(y + s);
float t = (i + j) * G2;
float xx[3], yy[3], f[3];
float noise[3] = {0.0f, 0.0f, 0.0f};
int g[3];
xx[0] = x - (i - t);
yy[0] = y - (j - t);
i1 = xx[0] > yy[0];
j1 = xx[0] <= yy[0];
xx[2] = xx[0] + G2 * 2.0f - 1.0f;
yy[2] = yy[0] + G2 * 2.0f - 1.0f;
xx[1] = xx[0] - i1 + G2;
yy[1] = yy[0] - j1 + G2;
I = (int) i & 255;
J = (int) j & 255;
g[0] = PERM[I + PERM[J]] % 12;
g[1] = PERM[I + i1 + PERM[J + j1]] % 12;
g[2] = PERM[I + 1 + PERM[J + 1]] % 12;
for (c = 0; c <= 2; c++) {
f[c] = 0.5f - xx[c]*xx[c] - yy[c]*yy[c];
}
for (c = 0; c <= 2; c++) {
if (f[c] > 0) {
noise[c] = f[c] * f[c] * f[c] * f[c] *
(GRAD3[g[c]][0] * xx[c] + GRAD3[g[c]][1] * yy[c]);
}
}
return (noise[0] + noise[1] + noise[2]) * 70.0f;
}
float noise3(float x, float y, float z) {
int c, o1[3], o2[3], g[4], I, J, K;
float f[4], noise[4] = {0.0f, 0.0f, 0.0f, 0.0f};
float s = (x + y + z) * F3;
float i = floorf(x + s);
float j = floorf(y + s);
float k = floorf(z + s);
float t = (i + j + k) * G3;
float pos[4][3];
pos[0][0] = x - (i - t);
pos[0][1] = y - (j - t);
pos[0][2] = z - (k - t);
if (pos[0][0] >= pos[0][1]) {
if (pos[0][1] >= pos[0][2]) {
ASSIGN(o1, 1, 0, 0);
ASSIGN(o2, 1, 1, 0);
} else if (pos[0][0] >= pos[0][2]) {
ASSIGN(o1, 1, 0, 0);
ASSIGN(o2, 1, 0, 1);
} else {
ASSIGN(o1, 0, 0, 1);
ASSIGN(o2, 1, 0, 1);
}
} else {
if (pos[0][1] < pos[0][2]) {
ASSIGN(o1, 0, 0, 1);
ASSIGN(o2, 0, 1, 1);
} else if (pos[0][0] < pos[0][2]) {
ASSIGN(o1, 0, 1, 0);
ASSIGN(o2, 0, 1, 1);
} else {
ASSIGN(o1, 0, 1, 0);
ASSIGN(o2, 1, 1, 0);
}
}
for (c = 0; c <= 2; c++) {
pos[3][c] = pos[0][c] - 1.0f + 3.0f * G3;
pos[2][c] = pos[0][c] - o2[c] + 2.0f * G3;
pos[1][c] = pos[0][c] - o1[c] + G3;
}
I = (int) i & 255;
J = (int) j & 255;
K = (int) k & 255;
g[0] = PERM[I + PERM[J + PERM[K]]] % 12;
g[1] = PERM[I + o1[0] + PERM[J + o1[1] + PERM[o1[2] + K]]] % 12;
g[2] = PERM[I + o2[0] + PERM[J + o2[1] + PERM[o2[2] + K]]] % 12;
g[3] = PERM[I + 1 + PERM[J + 1 + PERM[K + 1]]] % 12;
for (c = 0; c <= 3; c++) {
f[c] = 0.6f - pos[c][0] * pos[c][0] - pos[c][1] * pos[c][1] -
pos[c][2] * pos[c][2];
}
for (c = 0; c <= 3; c++) {
if (f[c] > 0) {
noise[c] = f[c] * f[c] * f[c] * f[c] * DOT3(pos[c], GRAD3[g[c]]);
}
}
return (noise[0] + noise[1] + noise[2] + noise[3]) * 32.0f;
}
float simplex2(
float x, float y,
int octaves, float persistence, float lacunarity)
{
float freq = 1.0f;
float amp = 1.0f;
float max = 1.0f;
float total = noise2(x, y);
int i;
for (i = 1; i < octaves; i++) {
freq *= lacunarity;
amp *= persistence;
max += amp;
total += noise2(x * freq, y * freq) * amp;
}
return (1 + total / max) / 2;
}
float simplex3(
float x, float y, float z,
int octaves, float persistence, float lacunarity)
{
float freq = 1.0f;
float amp = 1.0f;
float max = 1.0f;
float total = noise3(x, y, z);
int i;
for (i = 1; i < octaves; ++i) {
freq *= lacunarity;
amp *= persistence;
max += amp;
total += noise3(x * freq, y * freq, z * freq) * amp;
}
return (1 + total / max) / 2;
}