package net.glowstone.util.noise;
import java.util.Random;
/*
* A speed-improved simplex noise algorithm
*
* 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
*/
public class SimplexNoise extends PerlinNoise {
protected static final double SQRT_3 = Math.sqrt(3);
protected static final double F2 = 0.5 * (SQRT_3 - 1);
protected static final double G2 = (3 - SQRT_3) / 6;
protected static final double G22 = G2 * 2.0 - 1;
protected static final double F3 = 1.0 / 3.0;
protected static final double G3 = 1.0 / 6.0;
protected static final double G32 = G3 * 2.0;
protected static final double G33 = G3 * 3.0 - 1.0;
protected final int[] permMod12 = new int[512];
private static Grad[] grad3 = {new Grad(1, 1, 0), new Grad(-1, 1, 0), new Grad(1, -1, 0), new Grad(-1, -1, 0),
new Grad(1, 0, 1), new Grad(-1, 0, 1), new Grad(1, 0, -1), new Grad(-1, 0, -1),
new Grad(0, 1, 1), new Grad(0, -1, 1), new Grad(0, 1, -1), new Grad(0, -1, -1)};
public SimplexNoise(Random rand) {
super(rand);
for (int i = 0; i < 512; i++) {
permMod12[i] = perm[i] % 12;
}
}
public static int floor(double x) {
return x > 0 ? (int) x : (int) x - 1;
}
protected static double dot(Grad g, double x, double y) {
return g.x * x + g.y * y;
}
protected static double dot(Grad g, double x, double y, double z) {
return g.x * x + g.y * y + g.z * z;
}
@Override
protected double[] get2dNoise(double[] noise, double x, double z, int sizeX, int sizeY, double scaleX, double scaleY, double amplitude) {
int index = 0;
for (int i = 0; i < sizeY; i++) {
double zin = offsetY + (z + i) * scaleY;
for (int j = 0; j < sizeX; j++) {
double xin = offsetX + (x + j) * scaleX;
noise[index++] += simplex2D(xin, zin) * amplitude;
}
}
return noise;
}
@Override
protected double[] get3dNoise(double[] noise, double x, double y, double z, int sizeX, int sizeY, int sizeZ, double scaleX, double scaleY, double scaleZ, double amplitude) {
int index = 0;
for (int i = 0; i < sizeZ; i++) {
double zin = offsetZ + (z + i) * scaleZ;
for (int j = 0; j < sizeX; j++) {
double xin = offsetX + (x + j) * scaleX;
for (int k = 0; k < sizeY; k++) {
double yin = offsetY + (y + k) * scaleY;
noise[index++] += simplex3D(xin, yin, zin) * amplitude;
}
}
}
return noise;
}
@Override
public double noise(double xin, double yin) {
xin += offsetX;
yin += offsetY;
return simplex2D(xin, yin);
}
@Override
public double noise(double xin, double yin, double zin) {
xin += offsetX;
yin += offsetY;
zin += offsetZ;
return simplex3D(xin, yin, zin);
}
private double simplex2D(double xin, double yin) {
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 = floor(xin + s);
int j = floor(yin + s);
double t = (i + j) * G2;
double dX0 = i - t; // Unskew the cell origin back to (x,y) space
double dY0 = j - t;
double x0 = xin - dX0; // The x,y distances from the cell origin
double y0 = yin - dY0;
// 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; // lower triangle, XY order: (0,0)->(1,0)->(1,1)
j1 = 0;
} else {
i1 = 0; // upper triangle, YX order: (0,0)->(0,1)->(1,1)
j1 = 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 + G22; // Offsets for last corner in (x,y) unskewed coords
double y2 = y0 + G22;
// 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);
}
private double simplex3D(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
double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = floor(xin + s);
int j = floor(yin + s);
int k = floor(zin + s);
double t = (i + j + k) * G3;
double dX0 = i - t; // Unskew the cell origin back to (x,y,z) space
double dY0 = j - t;
double dZ0 = k - t;
double x0 = xin - dX0; // The x,y,z distances from the cell origin
double y0 = yin - dY0;
double z0 = zin - dZ0;
// 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; // X Y Z order
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} else if (x0 >= z0) {
i1 = 1; // X Z Y order
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
} else {
i1 = 0; // Z X Y order
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
} else { // x0<y0
if (y0 < z0) {
i1 = 0; // Z Y X order
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} else if (x0 < z0) {
i1 = 0; // Y Z X order
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} else {
i1 = 0; // Y X Z order
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
}
// 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 + G32; // Offsets for third corner in (x,y,z) coords
double y2 = y0 - j2 + G32;
double z2 = z0 - k2 + G32;
double x3 = x0 + G33; // Offsets for last corner in (x,y,z) coords
double y3 = y0 + G33;
double z3 = z0 + G33;
// 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 t0 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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]
return 32.0 * (n0 + n1 + n2 + n3);
}
// Inner class to speed up gradient computations
// (array access is a lot slower than member access)
private static class Grad {
public double x, y, z;
Grad(double x, double y, double z) {
this.x = x;
this.y = y;
this.z = z;
}
}
}