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/**
* Copyright (c) 2008-2012 Ardor Labs, Inc.
*
* This file is part of Ardor3D.
*
* Ardor3D is free software: you can redistribute it and/or modify it
* under the terms of its license which may be found in the accompanying
* LICENSE file or at .
*/
package com.ardor3d.math.functions;
import java.util.BitSet;
import com.ardor3d.math.MathUtils;
/**
* Simplex noise in 2D, 3D and 4D
*
* Based on the implementation of Ken Perlin's Simplex Noise done by Stefan Gustavson in 2005. See the paper at
* http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
*
*/
public class SimplexNoise {
private static int grad3[][] = { { 1, 1, 0 }, { -1, 1, 0 }, { 1, -1, 0 }, { -1, -1, 0 }, { 1, 0, 1 }, { -1, 0, 1 },
{ 1, 0, -1 }, { -1, 0, -1 }, { 0, 1, 1 }, { 0, -1, 1 }, { 0, 1, -1 }, { 0, -1, -1 } };
private static int grad4[][] = { { 0, 1, 1, 1 }, { 0, 1, 1, -1 }, { 0, 1, -1, 1 }, { 0, 1, -1, -1 },
{ 0, -1, 1, 1 }, { 0, -1, 1, -1 }, { 0, -1, -1, 1 }, { 0, -1, -1, -1 }, { 1, 0, 1, 1 }, { 1, 0, 1, -1 },
{ 1, 0, -1, 1 }, { 1, 0, -1, -1 }, { -1, 0, 1, 1 }, { -1, 0, 1, -1 }, { -1, 0, -1, 1 }, { -1, 0, -1, -1 },
{ 1, 1, 0, 1 }, { 1, 1, 0, -1 }, { 1, -1, 0, 1 }, { 1, -1, 0, -1 }, { -1, 1, 0, 1 }, { -1, 1, 0, -1 },
{ -1, -1, 0, 1 }, { -1, -1, 0, -1 }, { 1, 1, 1, 0 }, { 1, 1, -1, 0 }, { 1, -1, 1, 0 }, { 1, -1, -1, 0 },
{ -1, 1, 1, 0 }, { -1, 1, -1, 0 }, { -1, -1, 1, 0 }, { -1, -1, -1, 0 } };
// A lookup table to traverse the simplex around a given point in 4D.
// Details can be found where this table is used, in the 4D noise method.
private static int simplex[][] = { { 0, 1, 2, 3 }, { 0, 1, 3, 2 }, { 0, 0, 0, 0 }, { 0, 2, 3, 1 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 1, 2, 3, 0 }, { 0, 2, 1, 3 }, { 0, 0, 0, 0 }, { 0, 3, 1, 2 },
{ 0, 3, 2, 1 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 1, 3, 2, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 1, 2, 0, 3 }, { 0, 0, 0, 0 }, { 1, 3, 0, 2 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 2, 3, 0, 1 }, { 2, 3, 1, 0 }, { 1, 0, 2, 3 }, { 1, 0, 3, 2 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 2, 0, 3, 1 }, { 0, 0, 0, 0 }, { 2, 1, 3, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 2, 0, 1, 3 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 3, 0, 1, 2 },
{ 3, 0, 2, 1 }, { 0, 0, 0, 0 }, { 3, 1, 2, 0 }, { 2, 1, 0, 3 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
{ 0, 0, 0, 0 }, { 3, 1, 0, 2 }, { 0, 0, 0, 0 }, { 3, 2, 0, 1 }, { 3, 2, 1, 0 } };
private static double dot(final int g[], final double x, final double y) {
return g[0] * x + g[1] * y;
}
private static double dot(final int g[], final double x, final double y, final double z) {
return g[0] * x + g[1] * y + g[2] * z;
}
private static double dot(final int g[], final double x, final double y, final double z, final double w) {
return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
}
// To remove the need for index wrapping, double the permutation table length
private final int perm[] = new int[512];
public SimplexNoise() {
final int p[] = { 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 };
setPermutations(p);
}
public void setPermutations(final int[] permutations) {
if (permutations.length != 256) {
throw new IllegalArgumentException(
"not enough data, permutations should contain 0 thru 255 each exactly once");
}
final BitSet set = new BitSet(256);
for (final int i : permutations) {
set.set(i);
}
if (set.cardinality() != 256) {
throw new IllegalArgumentException("permutations should contain 0 thru 255 each exactly once");
}
resetPerm(permutations);
}
private void resetPerm(final int[] p) {
for (int i = 0; i < 512; i++) {
perm[i] = p[i & 255];
}
}
// 2D simplex noise
public double noise(final double xin, final double yin) {
double n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
final double s = (xin + yin) * F2; // Hairy factor for 2D
final int i = (int) MathUtils.floor(xin + s);
final int j = (int) MathUtils.floor(yin + s);
final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
final double t = (i + j) * G2;
final double X0 = i - t; // Unskew the cell origin back to (x,y) space
final double Y0 = j - t;
final double x0 = xin - X0; // The x,y distances from the cell origin
final 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
final double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
final double y1 = y0 - j1 + G2;
final double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
final double y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
final int ii = i & 255;
final int jj = j & 255;
final int gi0 = perm[ii + perm[jj]] % 12;
final int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
final int gi2 = perm[ii + 1 + perm[jj + 1]] % 12;
// 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
public double noise(final double xin, final double yin, final 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 F3 = 1.0 / 3.0;
final double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
final int i = (int) MathUtils.floor(xin + s);
final int j = (int) MathUtils.floor(yin + s);
final int k = (int) MathUtils.floor(zin + s);
final double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
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) ? 32 : 0;
final int c2 = (x0 > z0) ? 16 : 0;
final int c3 = (y0 > z0) ? 8 : 0;
final int c4 = (x0 > w0) ? 4 : 0;
final int c5 = (y0 > w0) ? 2 : 0;
final int c6 = (z0 > w0) ? 1 : 0;
final int c = c1 + c2 + c3 + c4 + c5 + c6;
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= 3 ? 1 : 0;
j1 = simplex[c][1] >= 3 ? 1 : 0;
k1 = simplex[c][2] >= 3 ? 1 : 0;
l1 = simplex[c][3] >= 3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0] >= 2 ? 1 : 0;
j2 = simplex[c][1] >= 2 ? 1 : 0;
k2 = simplex[c][2] >= 2 ? 1 : 0;
l2 = simplex[c][3] >= 2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0] >= 1 ? 1 : 0;
j3 = simplex[c][1] >= 1 ? 1 : 0;
k3 = simplex[c][2] >= 1 ? 1 : 0;
l3 = simplex[c][3] >= 1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
final double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
final double y1 = y0 - j1 + G4;
final double z1 = z0 - k1 + G4;
final double w1 = w0 - l1 + G4;
final double x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
final double y2 = y0 - j2 + 2.0 * G4;
final double z2 = z0 - k2 + 2.0 * G4;
final double w2 = w0 - l2 + 2.0 * G4;
final double x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
final double y3 = y0 - j3 + 3.0 * G4;
final double z3 = z0 - k3 + 3.0 * G4;
final double w3 = w0 - l3 + 3.0 * G4;
final double x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
final double y4 = y0 - 1.0 + 4.0 * G4;
final double z4 = z0 - 1.0 + 4.0 * G4;
final double w4 = w0 - 1.0 + 4.0 * G4;
// Work out the hashed gradient indices of the five simplex corners
final int ii = i & 255;
final int jj = j & 255;
final int kk = k & 255;
final int ll = l & 255;
final int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
final int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
final int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
final int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
final int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
// Calculate the contribution from the five corners
double t0 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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);
}
}