//
```// JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN.

package render;

/**
Improved version of {@link Noise}.

Algorithm:
Find unit cube that contains point (x, y, z).
Find the relative x,y,z of the point in the cube.
Compute the fade curves for each of x,y,z.
Hash coordinates of the eight cube corners and add blended results from the
eight corners of the cube.
Return the sum.
@author Ken Perlin 2001
*/

public final class ImprovedNoise {
/**
Computes the Perlin noise function value at the point (x, y, z).
@param x x coordinate
@param y y coordinate
@param z z coordinate
@return the noise function value at (x, y, z)
*/
static public double noise(double x, double y, double z) {
int X = (int) Math.floor(x) & 255, // FIND UNIT CUBE THAT
Y = (int) Math.floor(y) & 255, // CONTAINS POINT.
Z = (int) Math.floor(z) & 255;
x -= Math.floor(x); // FIND RELATIVE X,Y,Z
y -= Math.floor(y); // OF POINT IN CUBE.
z -= Math.floor(z);
double u = fade(x), // COMPUTE FADE CURVES
v = fade(y), // FOR EACH OF X,Y,Z.
int A = p[X] + Y, AA = p[A] + Z, AB = p[A + 1] + Z, // HASH COORDINATES OF
B = p[X + 1] + Y, BA = p[B] + Z, BB = p[B + 1] + Z; // THE 8 CUBE CORNERS,

return lerp(w, lerp(v, lerp(u, grad(p[AA], x, y, z), // AND ADD
grad(p[BA], x - 1, y, z)), // BLENDED
lerp(u, grad(p[AB], x, y - 1, z), // RESULTS
grad(p[BB], x - 1, y - 1, z))), // FROM  8
lerp(v, lerp(u, grad(p[AA + 1], x, y, z - 1), // CORNERS
grad(p[BA + 1], x - 1, y, z - 1)), // OF CUBE
lerp(u, grad(p[AB + 1], x, y - 1, z - 1), grad(p[BB + 1], x - 1, y - 1, z - 1))));
}
static double fade(double t) {
return t * t * t * (t * (t * 6 - 15) + 10);
}
static double lerp(double t, double a, double b) {
return a + t * (b - a);
}
static double grad(int hash, double x, double y, double z) {
int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
double u = h < 8 || h == 12 || h == 13 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h < 4 || h == 12 || h == 13 ? y : z;
return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
}
static final int p[] = new int[512], permutation[] = { 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 };
static {
for (int i = 0; i < 256; i++)
p[256 + i] = p[i] = permutation[i];
}
}
```