Implementation
double noise4D(double x, double y, double z, double w) {
double n0, n1, n2, n3, n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
final s = (x + y + z + w) * _F4; // Factor for 4D skewing
final i = (x + s).floor();
final j = (y + s).floor();
final k = (z + s).floor();
final l = (w + s).floor();
final t = (i + j + k + l) * _G4; // Factor for 4D unskewing
final X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
final Y0 = j - t;
final Z0 = k - t;
final W0 = l - t;
final x0 = x - X0; // The x,y,z,w distances from the cell origin
final y0 = y - Y0;
final z0 = z - Z0;
final w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// Six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to rank the numbers.
var rankx = 0;
var ranky = 0;
var rankz = 0;
var rankw = 0;
if (x0 > y0) {
rankx++;
} else {
ranky++;
}
if (x0 > z0) {
rankx++;
} else {
rankz++;
}
if (x0 > w0) {
rankx++;
} else {
rankw++;
}
if (y0 > z0) {
ranky++;
} else {
rankz++;
}
if (y0 > w0) {
ranky++;
} else {
rankw++;
}
if (z0 > w0) {
rankz++;
} else {
rankw++;
}
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// Rank 3 denotes the largest coordinate.
i1 = rankx >= 3 ? 1 : 0;
j1 = ranky >= 3 ? 1 : 0;
k1 = rankz >= 3 ? 1 : 0;
l1 = rankw >= 3 ? 1 : 0;
// Rank 2 denotes the second largest coordinate.
i2 = rankx >= 2 ? 1 : 0;
j2 = ranky >= 2 ? 1 : 0;
k2 = rankz >= 2 ? 1 : 0;
l2 = rankw >= 2 ? 1 : 0;
// Rank 1 denotes the second smallest coordinate.
i3 = rankx >= 1 ? 1 : 0;
j3 = ranky >= 1 ? 1 : 0;
k3 = rankz >= 1 ? 1 : 0;
l3 = rankw >= 1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to compute that.
final x1 = x0 - i1 + _G4; // Offsets for second corner in (x,y,z,w) coords
final y1 = y0 - j1 + _G4;
final z1 = z0 - k1 + _G4;
final w1 = w0 - l1 + _G4;
final x2 =
x0 - i2 + 2.0 * _G4; // Offsets for third corner in (x,y,z,w) coords
final y2 = y0 - j2 + 2.0 * _G4;
final z2 = z0 - k2 + 2.0 * _G4;
final w2 = w0 - l2 + 2.0 * _G4;
final x3 =
x0 - i3 + 3.0 * _G4; // Offsets for fourth corner in (x,y,z,w) coords
final y3 = y0 - j3 + 3.0 * _G4;
final z3 = z0 - k3 + 3.0 * _G4;
final w3 = w0 - l3 + 3.0 * _G4;
final x4 =
x0 - 1.0 + 4.0 * _G4; // Offsets for last corner in (x,y,z,w) coords
final y4 = y0 - 1.0 + 4.0 * _G4;
final z4 = z0 - 1.0 + 4.0 * _G4;
final w4 = w0 - 1.0 + 4.0 * _G4;
// Work out the hashed gradient indices of the five simplex corners
final ii = i & 255;
final jj = j & 255;
final kk = k & 255;
final ll = l & 255;
final gi0 = _perm[ii + _perm[jj + _perm[kk + _perm[ll]]]] % 32;
final gi1 =
_perm[ii + i1 + _perm[jj + j1 + _perm[kk + k1 + _perm[ll + l1]]]] % 32;
final gi2 =
_perm[ii + i2 + _perm[jj + j2 + _perm[kk + k2 + _perm[ll + l2]]]] % 32;
final gi3 =
_perm[ii + i3 + _perm[jj + j3 + _perm[kk + k3 + _perm[ll + l3]]]] % 32;
final gi4 =
_perm[ii + 1 + _perm[jj + 1 + _perm[kk + 1 + _perm[ll + 1]]]] % 32;
// Calculate the contribution from the five corners
var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if (t0 < 0) {
n0 = 0.0;
} else {
t0 *= t0;
n0 = t0 * t0 * _dot4(_grad4[gi0], x0, y0, z0, w0);
}
var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
if (t1 < 0) {
n1 = 0.0;
} else {
t1 *= t1;
n1 = t1 * t1 * _dot4(_grad4[gi1], x1, y1, z1, w1);
}
var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
if (t2 < 0) {
n2 = 0.0;
} else {
t2 *= t2;
n2 = t2 * t2 * _dot4(_grad4[gi2], x2, y2, z2, w2);
}
var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
if (t3 < 0) {
n3 = 0.0;
} else {
t3 *= t3;
n3 = t3 * t3 * _dot4(_grad4[gi3], x3, y3, z3, w3);
}
var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
if (t4 < 0) {
n4 = 0.0;
} else {
t4 *= t4;
n4 = t4 * t4 * _dot4(_grad4[gi4], x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0 * (n0 + n1 + n2 + n3 + n4);
}