/*--------------------------------------------------------------------
Simplex Noise C++ implementation
Based on a public domain code by Stefan Gustavson.
(The original header is below)
--------------------------------------------------------------------*/
/*-- start of the original header --*/
/*
* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
*
* Based on example code by Stefan Gustavson (stegu@itn.liu.se).
* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
* Better rank ordering method by Stefan Gustavson in 2012.
*
* This could be speeded up even further, but it's useful as it is.
*
* Version 2012-03-09
*
* This code was placed in the public domain by its original author,
* Stefan Gustavson. You may use it as you see fit, but
* attribution is appreciated.
*
*/
/*-- end of the original header --*/
#include "iwa_simplexnoise.h"
#include <math.h> //sqrt
#include <iostream>
namespace
{
static Grad grad3[] = {Grad(1, 1, 0), Grad(-1, 1, 0), Grad(1, -1, 0), Grad(-1, -1, 0),
Grad(1, 0, 1), Grad(-1, 0, 1), Grad(1, 0, -1), Grad(-1, 0, -1),
Grad(0, 1, 1), Grad(0, -1, 1), Grad(0, 1, -1), Grad(0, -1, -1)};
static Grad grad4[] = {Grad(0, 1, 1, 1), Grad(0, 1, 1, -1), Grad(0, 1, -1, 1), Grad(0, 1, -1, -1),
Grad(0, -1, 1, 1), Grad(0, -1, 1, -1), Grad(0, -1, -1, 1), Grad(0, -1, -1, -1),
Grad(1, 0, 1, 1), Grad(1, 0, 1, -1), Grad(1, 0, -1, 1), Grad(1, 0, -1, -1),
Grad(-1, 0, 1, 1), Grad(-1, 0, 1, -1), Grad(-1, 0, -1, 1), Grad(-1, 0, -1, -1),
Grad(1, 1, 0, 1), Grad(1, 1, 0, -1), Grad(1, -1, 0, 1), Grad(1, -1, 0, -1),
Grad(-1, 1, 0, 1), Grad(-1, 1, 0, -1), Grad(-1, -1, 0, 1), Grad(-1, -1, 0, -1),
Grad(1, 1, 1, 0), Grad(1, 1, -1, 0), Grad(1, -1, 1, 0), Grad(1, -1, -1, 0),
Grad(-1, 1, 1, 0), Grad(-1, 1, -1, 0), Grad(-1, -1, 1, 0), Grad(-1, -1, -1, 0)};
// To remove the need for index wrapping, double the permutation table length
static short perm[512] =
{
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};
static short permMod12[512] =
{
7, 4, 5, 7, 6, 3, 11, 1, 9, 11, 0, 5, 2, 5, 7, 9,
8, 0, 7, 6, 9, 10, 8, 3, 1, 0, 9, 10, 11, 10, 6, 4,
7, 0, 6, 3, 0, 2, 5, 2, 10, 0, 3, 11, 9, 11, 11, 8,
9, 9, 9, 4, 9, 5, 8, 3, 6, 8, 5, 4, 3, 0, 8, 7,
2, 9, 11, 2, 7, 0, 3, 10, 5, 2, 2, 3, 11, 3, 1, 2,
0, 7, 1, 2, 4, 9, 8, 5, 7, 10, 5, 4, 4, 6, 11, 6,
5, 1, 3, 5, 1, 0, 8, 1, 5, 4, 0, 7, 4, 5, 6, 1,
8, 4, 3, 10, 8, 8, 3, 2, 8, 4, 1, 6, 5, 6, 3, 4,
4, 1, 10, 10, 4, 3, 5, 10, 2, 3, 10, 6, 3, 10, 1, 8,
3, 2, 11, 11, 11, 4, 10, 5, 2, 9, 4, 6, 7, 3, 2, 9,
11, 8, 8, 2, 8, 10, 7, 10, 5, 9, 5, 11, 11, 7, 4, 9,
9, 10, 3, 1, 7, 2, 0, 2, 7, 5, 8, 4, 10, 5, 4, 8,
2, 6, 1, 0, 11, 10, 2, 1, 10, 6, 0, 0, 11, 11, 6, 1,
9, 3, 1, 7, 9, 2, 11, 11, 1, 0, 10, 7, 1, 7, 10, 1,
4, 0, 0, 8, 7, 1, 2, 9, 7, 4, 6, 2, 6, 8, 1, 9,
6, 6, 7, 5, 0, 0, 3, 9, 8, 3, 6, 6, 11, 1, 0, 0,
7, 4, 5, 7, 6, 3, 11, 1, 9, 11, 0, 5, 2, 5, 7, 9,
8, 0, 7, 6, 9, 10, 8, 3, 1, 0, 9, 10, 11, 10, 6, 4,
7, 0, 6, 3, 0, 2, 5, 2, 10, 0, 3, 11, 9, 11, 11, 8,
9, 9, 9, 4, 9, 5, 8, 3, 6, 8, 5, 4, 3, 0, 8, 7,
2, 9, 11, 2, 7, 0, 3, 10, 5, 2, 2, 3, 11, 3, 1, 2,
0, 7, 1, 2, 4, 9, 8, 5, 7, 10, 5, 4, 4, 6, 11, 6,
5, 1, 3, 5, 1, 0, 8, 1, 5, 4, 0, 7, 4, 5, 6, 1,
8, 4, 3, 10, 8, 8, 3, 2, 8, 4, 1, 6, 5, 6, 3, 4,
4, 1, 10, 10, 4, 3, 5, 10, 2, 3, 10, 6, 3, 10, 1, 8,
3, 2, 11, 11, 11, 4, 10, 5, 2, 9, 4, 6, 7, 3, 2, 9,
11, 8, 8, 2, 8, 10, 7, 10, 5, 9, 5, 11, 11, 7, 4, 9,
9, 10, 3, 1, 7, 2, 0, 2, 7, 5, 8, 4, 10, 5, 4, 8,
2, 6, 1, 0, 11, 10, 2, 1, 10, 6, 0, 0, 11, 11, 6, 1,
9, 3, 1, 7, 9, 2, 11, 11, 1, 0, 10, 7, 1, 7, 10, 1,
4, 0, 0, 8, 7, 1, 2, 9, 7, 4, 6, 2, 6, 8, 1, 9,
6, 6, 7, 5, 0, 0, 3, 9, 8, 3, 6, 6, 11, 1, 0, 0};
};
//----------------------------------------
// 2D simplex noise
//----------------------------------------
double SimplexNoise::noise(double xin, double yin)
{
// Skewing and unskewing factors for 2 dimensions
static const double F2 = 0.5 * (sqrt(3.0) - 1.0);
static const double G2 = (3.0 - sqrt(3.0)) / 6.0;
double n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
double s = (xin + yin) * F2; // Hairy factor for 2D
int i = fastfloor(xin + s);
int j = fastfloor(yin + s);
double t = (i + j) * G2;
double X0 = i - t; // Unskew the cell origin back to (x,y) space
double Y0 = j - t;
double x0 = xin - X0; // The x,y distances from the cell origin
double y0 = yin - Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if (x0 > y0) {
i1 = 1;
j1 = 0;
} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else {
i1 = 0;
j1 = 1;
} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
double y1 = y0 - j1 + G2;
double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
double y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = permMod12[ii + perm[jj]];
int gi1 = permMod12[ii + i1 + perm[jj + j1]];
int gi2 = permMod12[ii + 1 + perm[jj + 1]];
// Calculate the contribution from the three corners
double t0 = 0.5 - x0 * x0 - y0 * y0;
if (t0 < 0)
n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
}
double t1 = 0.5 - x1 * x1 - y1 * y1;
if (t1 < 0)
n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
}
double t2 = 0.5 - x2 * x2 - y2 * y2;
if (t2 < 0)
n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return 70.0 * (n0 + n1 + n2);
}
//----------------------------------------
// 3D simplex noise
//----------------------------------------
double SimplexNoise::noise(double xin, double yin, double zin)
{
// Skewing and unskewing factors for 3 dimensions
static const double F3 = 1.0 / 3.0;
static const double G3 = 1.0 / 6.0;
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = fastfloor(xin + s);
int j = fastfloor(yin + s);
int k = fastfloor(zin + s);
double t = (i + j + k) * G3;
double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j - t;
double Z0 = k - t;
double x0 = xin - X0; // The x,y,z distances from the cell origin
double y0 = yin - Y0;
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.
double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
double y1 = y0 - j1 + G3;
double z1 = z0 - k1 + G3;
double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
double y2 = y0 - j2 + 2.0 * G3;
double z2 = z0 - k2 + 2.0 * G3;
double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
double y3 = y0 - 1.0 + 3.0 * G3;
double z3 = z0 - 1.0 + 3.0 * G3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int gi0 = permMod12[ii + perm[jj + perm[kk]]];
int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];
// Calculate the contribution from the four corners
double range = 0.6;
double t0 = range - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0)
n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
}
double t1 = range - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0)
n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
}
double t2 = range - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0)
n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
}
double t3 = range - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0)
n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * dot(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]
/*- 変更： [-0.5,0.5] の範囲にする -*/
return 16.0 * (n0 + n1 + n2 + n3);
//return 32.0*(n0 + n1 + n2 + n3);
}
//----------------------------------------
// 4D simplex noise
//----------------------------------------
double SimplexNoise::noise(double x, double y, double z, double w)
{
// Skewing and unskewing factors for 4 dimensions
static const double F4 = (sqrt(5.0) - 1.0) / 4.0;
static const double G4 = (5.0 - sqrt(5.0)) / 20.0;
// The skewing and unskewing factors are hairy again for the 4D case
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
double s = (x + y + z + w) * F4; // Factor for 4D skewing
int i = fastfloor(x + s);
int j = fastfloor(y + s);
int k = fastfloor(z + s);
int l = fastfloor(w + s);
double t = (i + j + k + l) * G4; // Factor for 4D unskewing
double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
double Y0 = j - t;
double Z0 = k - t;
double W0 = l - t;
double x0 = x - X0; // The x,y,z,w distances from the cell origin
double y0 = y - Y0;
double z0 = z - Z0;
double 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.
int rankx = 0;
int ranky = 0;
int rankz = 0;
int 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 look that up.
double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
double y1 = y0 - j1 + G4;
double z1 = z0 - k1 + G4;
double w1 = w0 - l1 + G4;
double x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
double y2 = y0 - j2 + 2.0 * G4;
double z2 = z0 - k2 + 2.0 * G4;
double w2 = w0 - l2 + 2.0 * G4;
double x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
double y3 = y0 - j3 + 3.0 * G4;
double z3 = z0 - k3 + 3.0 * G4;
double w3 = w0 - l3 + 3.0 * G4;
double x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
double y4 = y0 - 1.0 + 4.0 * G4;
double z4 = z0 - 1.0 + 4.0 * G4;
double w4 = w0 - 1.0 + 4.0 * G4;
// Work out the hashed gradient indices of the five simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int ll = l & 255;
int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
/*- パラメータ調整 -*/
double range = 0.66;
//double range = 0.6;
// Calculate the contribution from the five corners
double t0 = range - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if (t0 < 0)
n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
}
double t1 = range - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
if (t1 < 0)
n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
}
double t2 = range - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
if (t2 < 0)
n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
}
double t3 = range - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
if (t3 < 0)
n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
}
double t4 = range - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
if (t4 < 0)
n4 = 0.0;
else {
t4 *= t4;
n4 = t4 * t4 * dot(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);
}
/*----------------------------------------
セルまたぎを防ぐために、現在の所属セルを得る
----------------------------------------*/
CellIds SimplexNoise::getCellIds(double xin, double yin, double zin)
{
// Skew the input space to determine which simplex cell we're in
const double F3 = 1.0 / 3.0;
double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = fastfloor(xin + s);
int j = fastfloor(yin + s);
int k = fastfloor(zin + s);
const double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
double t = (i + j + k) * G3;
double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j - t;
double Z0 = k - t;
double x0 = xin - X0; // The x,y,z distances from the cell origin
double y0 = yin - Y0;
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
}
return CellIds(i, j, k, i1, j1, k1, i2, j2, k2);
}