# noise3D method

double noise3D (double xin, double yin, double zin)

## Implementation

``````double noise3D(double xin, double yin, double zin) {
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
final double s =
(xin + yin + zin) * _F3; // Very nice and simple skew factor for 3D
final int i = (xin + s).floor();
final int j = (yin + s).floor();
final int k = (zin + s).floor();
final double t = (i + j + k) * _G3;
final double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
final double Y0 = j - t;
final double Z0 = k - t;
final double x0 = xin - X0; // The x,y,z distances from the cell origin
final double y0 = yin - Y0;
final double z0 = zin - Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
if (x0 >= y0) {
if (y0 >= z0) {
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // X Y Z order
else if (x0 >= z0) {
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
} // X Z Y order
else {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
} // Z X Y order
} else {
// x0<y0
if (y0 < z0) {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} // Z Y X order
else if (x0 < z0) {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} // Y Z X order
else {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
final double x1 =
x0 - i1 + _G3; // Offsets for second corner in (x,y,z) coords
final double y1 = y0 - j1 + _G3;
final double z1 = z0 - k1 + _G3;
final double x2 =
x0 - i2 + 2.0 * _G3; // Offsets for third corner in (x,y,z) coords
final double y2 = y0 - j2 + 2.0 * _G3;
final double z2 = z0 - k2 + 2.0 * _G3;
final double x3 =
x0 - 1.0 + 3.0 * _G3; // Offsets for last corner in (x,y,z) coords
final double y3 = y0 - 1.0 + 3.0 * _G3;
final double z3 = z0 - 1.0 + 3.0 * _G3;
// Work out the hashed gradient indices of the four simplex corners
final int ii = i & 255;
final int jj = j & 255;
final int kk = k & 255;
final int gi0 = _permMod12[ii + _perm[jj + _perm[kk]]];
final int gi1 = _permMod12[ii + i1 + _perm[jj + j1 + _perm[kk + k1]]];
final int gi2 = _permMod12[ii + i2 + _perm[jj + j2 + _perm[kk + k2]]];
final int gi3 = _permMod12[ii + 1 + _perm[jj + 1 + _perm[kk + 1]]];
// Calculate the contribution from the four corners
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0)
n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * _dot3(_grad3[gi0], x0, y0, z0);
}
double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0)
n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * _dot3(_grad3[gi1], x1, y1, z1);
}
double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0)
n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * _dot3(_grad3[gi2], x2, y2, z2);
}
double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0)
n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * _dot3(_grad3[gi3], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0 * (n0 + n1 + n2 + n3);
}``````