package com.voxel.engine.core.Noise;
/**
* Simplex Noise in 2D, 3D and 4D. Based on the example code of this paper:
* http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
*
* @author Stefan Gustavson, Linkping University, Sweden (stegu at itn dot liu
* dot se)
*
* Slight optimizations & restructuring by
* @author Karsten Schmidt (info at toxi dot co dot uk)
*
*/
public class SimplexNoise {
private static final double SQRT3 = Math.sqrt(3.0);
private static final double SQRT5 = Math.sqrt(5.0);
private static final double F2 = 0.5 * (SQRT3 - 1.0);
private static final double G2 = (3.0 - SQRT3) / 6.0;
private static final double G22 = G2 * 2.0 - 1.0;
private static final double F3 = 1.0 / 3.0;
private static final double G3 = 1.0 / 6.0;
private static final double G32 = G3 * 2.0;
private static final double G33 = G3 * 3.0 - 1.0;
private static final double F4 = (SQRT5 - 1.0) / 4.0;
private static final double G4 = (5.0 - SQRT5) / 20.0;
private static final double G42 = G4 * 2.0;
private static final double G43 = G4 * 2.0;
private static final double G44 = G4 * 4.0 - 1.0;
private static final 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 final 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}, {0, -1, -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}};
private static 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 };
private static int perm[] = new int[0x200];
static {
for(int i = 0;i < 0x100;i++){
perm[i] = p[i & 0xff];
}
}
private static final 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 final int fastFloor(double x){
return x > 0 ? (int) x : (int) x -1;
}
private static double dot(int g[], double x, double y){
return g[0] * x + g[1] * y;
}
private static double dot(int g[], double x, double y, double z){
return g[0] * x + g[1] * y + g[2] * z;
}
private static double dot(int g[], double x, double y, double z, double w){
return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
}
public static double noise(double x, double y){
double n0, n1, n2;
double s = (x + y) * F2;
int i = fastFloor(x + s);
int j = fastFloor(y + s);
double t = (i + j) * G2;
double x0 = x - (i - t);
double y0 = y - ( i - t);
int i1, j1;
if(x0 > y0){
i1 = 1;
j1 = 0;
}else{
i1 = 0;
j1 = 1;
}
double x1 = x0 - i1 + G2;
double y1 = y0 - j1 + G2;
double x2 = x0 + G22;
double y2 = y0 + G22;
int ii = i & 0xff;
int jj = j & 0xff;
double t0 = 0.5 - x0 * x0 - y0 * y0;
if(t0 < 0){
n0 = 0.0;
}else{
t0 *= t0;
int gi0 = perm[ii + perm[jj]] % 12;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0);
}
double t1 = 0.5 - x1 * x1 - y1 * y1;
if(t1 < 0){
n1 = 0.0;
}else{
t1 *= t1;
int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
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;
int gi2 = perm[ii + 1 + perm[jj + 1]] % 12;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
}
return 70.0 * (n0 + n1 + n2);
}
public static double noise(double x, double y, double z){
double n0, n1, n2, n3;
double s = (x + y + z) * F3;
int i = fastFloor(x + s);
int j = fastFloor(y + s);
int k = fastFloor(z + s);
double t = (i + j + k) * G3;
double x0 = x - (i - t);
double y0 = y - (j - t);
double z0 = z - (k - t);
int i1, j1, k1;
int i2, j2, k2;
if(x0 >= y0){
if(y0 >= z0){
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}else if(x0 >= z0){
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}else{
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
}else{
if(y0 < z0){
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
}else if(x0 < z0){
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
}else{
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
}
double x1 = x0 - i1 + G3;
double y1 = y0 - j1 + G3;
double z1 = z0 - k1 + G3;
double x2 = x0 - i2 + G3;
double y2 = y0 - j2 + G32;
double z2 = z0 - k2 + G32;
double x3 = x0 + G33;
double y3 = y0 + G33;
double z3 = z0 + G33;
int ii = i & 0xff;
int jj = j & 0xff;
int kk = k & 0xff;
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
if(t0 < 0){
n0 = 0.0;
}else{
t0 *= t0;
int gi0 = perm[ii + perm[jj + perm[kk]]] % 12;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
}
double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0){
n1 = 0.0;
}else{
t1 *= t1;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
}
double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0){
n2 = 0.0;
}else{
t2 *= t2;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
}
double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0){
n3 = 0.0;
}else{
t3 *= t3;
int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
}
return 32.0 * (n0 + n1 + n2 + n3);
}
public static double noise(double x, double y, double z, double w) {
double n0, n1, n2, n3, n4;
double s = (x + y + z + w) * F4;
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;
double x0 = x - (i - t);
double y0 = y - (j - t);
double z0 = z - (k - t);
double w0 = w - (l - t);
int c = 0;
if (x0 > y0){
c = 0x20;
}
if (x0 > z0){
c |= 0x10;
}
if (y0 > z0){
c |= 0x08;
}
if (x0 > w0){
c |= 0x04;
}
if (y0 > w0){
c |= 0x02;
}
if (z0 > w0){
c |= 0x01;
}
int i1, j1, k1, l1;
int i2, j2, k2, l2;
int i3, j3, k3, l3;
int[] sc = simplex[c];
i1 = sc[0] >= 3 ? 1 : 0;
j1 = sc[1] >= 3 ? 1 : 0;
k1 = sc[2] >= 3 ? 1 : 0;
l1 = sc[3] >= 3 ? 1 : 0;
i2 = sc[0] >= 2 ? 1 : 0;
j2 = sc[1] >= 2 ? 1 : 0;
k2 = sc[2] >= 2 ? 1 : 0;
l2 = sc[3] >= 2 ? 1 : 0;
i3 = sc[0] >= 1 ? 1 : 0;
j3 = sc[1] >= 1 ? 1 : 0;
k3 = sc[2] >= 1 ? 1 : 0;
l3 = sc[3] >= 1 ? 1 : 0;
double x1 = x0 - i1 + G4;
double y1 = y0 - j1 + G4;
double z1 = z0 - k1 + G4;
double w1 = w0 - l1 + G4;
double x2 = x0 - i2 + G42;
double y2 = y0 - j2 + G42;
double z2 = z0 - k2 + G42;
double w2 = w0 - l2 + G42;
double x3 = x0 - i3 + G43;
double y3 = y0 - j3 + G43;
double z3 = z0 - k3 + G43;
double w3 = w0 - l3 + G43;
double x4 = x0 - 1.0 + G44;
double y4 = y0 + G44;
double z4 = z0 + G44;
double w4 = w0 + G44;
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int ll = l & 255;
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if (t0 < 0){
n0 = 0.0;
}else {
t0 *= t0;
int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
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;
int gi1 = perm[ii + i1
+ perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
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;
int gi2 = perm[ii + i2
+ perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
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;
int gi3 = perm[ii + i3
+ perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
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;
int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
}
return 27.0 * (n0 + n1 + n2 + n3 + n4);
}
}