//
```// Copyright 2001 Ken Perlin

package render;

/**
Computes Perlin Noise for one, two, and three dimensions.
The result is a continuous function that interpolates a smooth path
along a series random points. The function is consitent, so given
the same parameters, it will always return the same value.
@see ImprovedNoise
*/

public final class Noise {

/**
Initialization seed used to start the random number generator.
*/
public static int seed = 100;

private static final int P = 8;
private static final int B = 1 << P;
private static final int M = B - 1;

private static final int NP = 8;
private static final int N = 1 << NP;
private static final int NM = N - 1;

private static int p[] = new int[B + B + 2];
private static double g2[][] = new double[B + B + 2][2];
private static double g1[] = new double[B + B + 2];
private static int start = 1;
private static double[][] points = new double[32][3];

static {
init();
}

private static double lerp(double t, double a, double b) {
return a + t * (b - a);
}

private static double s_curve(double t) {
return t * t * (3 - t - t);
}

/**
Computes noise function for one dimension at x.
@param x 1 dimensional parameter
@return the noise value at x
*/
public static double noise(double x) {

int bx0, bx1;
double rx0, rx1, sx, t, u, v;
t = x + N;
bx0 = ((int) t) & M;
bx1 = (bx0 + 1) & M;
rx0 = t - (int) t;
rx1 = rx0 - 1;

sx = s_curve(rx0);
u = rx0 * g1[p[bx0]];
v = rx1 * g1[p[bx1]];

return lerp(sx, u, v);
}

/**
Computes noise function for two dimensions at the point (x,y).
@param x x dimension parameter
@param y y dimension parameter
@return the value of noise at the point (x,y)
*/
public static double noise(double x, double y) {

int bx0, bx1, by0, by1, b00, b10, b01, b11;
double rx0, rx1, ry0, ry1, sx, sy, a, b, t, u, v, q[];
int i, j;

t = x + N;
bx0 = ((int) t) & M;
bx1 = (bx0 + 1) & M;
rx0 = t - (int) t;
rx1 = rx0 - 1;

t = y + N;
by0 = ((int) t) & M;
by1 = (by0 + 1) & M;
ry0 = t - (int) t;
ry1 = ry0 - 1;

i = p[bx0];
j = p[bx1];

b00 = p[i + by0];
b10 = p[j + by0];
b01 = p[i + by1];
b11 = p[j + by1];

sx = s_curve(rx0);
sy = s_curve(ry0);

q = g2[b00];
u = rx0 * q[0] + ry0 * q[1];
q = g2[b10];
v = rx1 * q[0] + ry0 * q[1];
a = lerp(sx, u, v);

q = g2[b01];
u = rx0 * q[0] + ry1 * q[1];
q = g2[b11];
v = rx1 * q[0] + ry1 * q[1];
b = lerp(sx, u, v);

return lerp(sy, a, b);
}

/**
Computes noise function for three dimensions at the point (x,y,z).
@param x x dimension parameter
@param y y dimension parameter
@param z z dimension parameter
@return the noise value at the point (x, y, z)
*/
static public double noise(double x, double y, double z) {

int bx, by, bz, b0, b1, b00, b10, b01, b11;
double rx0, rx1, ry0, ry1, rz, sx, sy, sz, a, b, c, d, u, v, q[];

bx = (int) Math.IEEEremainder(Math.floor(x), B);
if (bx < 0)
bx += B;
rx0 = x - Math.floor(x);
rx1 = rx0 - 1;

by = (int) Math.IEEEremainder(Math.floor(y), B);
if (by < 0)
by += B;
ry0 = y - Math.floor(y);
ry1 = ry0 - 1;

bz = (int) Math.IEEEremainder(Math.floor(z), B);
if (bz < 0)
bz += B;
rz = z - Math.floor(z);

//if (bx < 0 || bx >= B + B + 2)
//System.out.println(bx);

b0 = p[bx];

bx++;

b1 = p[bx];

b00 = p[b0 + by];
b10 = p[b1 + by];

by++;

b01 = p[b0 + by];
b11 = p[b1 + by];

sx = s_curve(rx0);
sy = s_curve(ry0);
sz = s_curve(rz);

q = G(b00 + bz);
u = rx0 * q[0] + ry0 * q[1] + rz * q[2];
q = G(b10 + bz);
v = rx1 * q[0] + ry0 * q[1] + rz * q[2];
a = lerp(sx, u, v);
q = G(b01 + bz);
u = rx0 * q[0] + ry1 * q[1] + rz * q[2];
q = G(b11 + bz);
v = rx1 * q[0] + ry1 * q[1] + rz * q[2];
b = lerp(sx, u, v);
c = lerp(sy, a, b);
bz++;
rz--;
q = G(b00 + bz);
u = rx0 * q[0] + ry0 * q[1] + rz * q[2];
q = G(b10 + bz);
v = rx1 * q[0] + ry0 * q[1] + rz * q[2];
a = lerp(sx, u, v);
q = G(b01 + bz);
u = rx0 * q[0] + ry1 * q[1] + rz * q[2];
q = G(b11 + bz);
v = rx1 * q[0] + ry1 * q[1] + rz * q[2];
b = lerp(sx, u, v);
d = lerp(sy, a, b);

return lerp(sz, c, d);
}

private static double[] G(int i) {
return points[i % 32];
}

private static void init() {
int i, j, k;
double u, v, w, U, V, W, Hi, Lo;
java.util.Random r = new java.util.Random(seed);
for (i = 0; i < B; i++) {
p[i] = i;
g1[i] = 2 * r.nextDouble() - 1;

do {
u = 2 * r.nextDouble() - 1;
v = 2 * r.nextDouble() - 1;
} while (u * u + v * v > 1 || Math.abs(u) > 2.5 * Math.abs(v) || Math.abs(v) > 2.5 * Math.abs(u) || Math.abs(Math.abs(u) - Math.abs(v)) < .4);
g2[i][0] = u;
g2[i][1] = v;
normalize2(g2[i]);

do {
u = 2 * r.nextDouble() - 1;
v = 2 * r.nextDouble() - 1;
w = 2 * r.nextDouble() - 1;
U = Math.abs(u);
V = Math.abs(v);
W = Math.abs(w);
Lo = Math.min(U, Math.min(V, W));
Hi = Math.max(U, Math.max(V, W));
} while (u * u + v * v + w * w > 1 || Hi > 4 * Lo || Math.min(Math.abs(U - V), Math.min(Math.abs(U - W), Math.abs(V - W))) < .2);
}

while (--i > 0) {
k = p[i];
j = (int) (r.nextLong() & M);
p[i] = p[j];
p[j] = k;
}
for (i = 0; i < B + 2; i++) {
p[B + i] = p[i];
g1[B + i] = g1[i];
for (j = 0; j < 2; j++) {
g2[B + i][j] = g2[i][j];
}
}

points[3][0] = points[3][1] = points[3][2] = Math.sqrt(1. / 3);
double r2 = Math.sqrt(1. / 2);
double s = Math.sqrt(2 + r2 + r2);

for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
points[i][j] = (i == j ? 1 + r2 + r2 : r2) / s;
for (i = 0; i <= 1; i++)
for (j = 0; j <= 1; j++)
for (k = 0; k <= 1; k++) {
int n = i + j * 2 + k * 4;
if (n > 0)
for (int m = 0; m < 4; m++) {
points[4 * n + m][0] = (i == 0 ? 1 : -1) * points[m][0];
points[4 * n + m][1] = (j == 0 ? 1 : -1) * points[m][1];
points[4 * n + m][2] = (k == 0 ? 1 : -1) * points[m][2];
}
}
}

private static void normalize2(double v[]) {
double s;
s = Math.sqrt(v[0] * v[0] + v[1] * v[1]);
v[0] = v[0] / s;
v[1] = v[1] / s;
}
}
```