/*
* Copyright 2013 MovingBlocks
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.terasology.utilities.procedural;
import org.terasology.math.TeraMath;
import org.terasology.utilities.random.FastRandom;
/**
* A speed-improved simplex noise algorithm for Simplex noise in 2D, 3D and 4D.
* <br><br>
* 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.
* <br><br>
* This could be speeded up even further, but it's useful as it is.
* <br><br>
* Version 2012-03-09
* <br><br>
* 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.
* <br><br>
* See http://staffwww.itn.liu.se/~stegu/
* <br><br>
* msteiger: Introduced seed value
*/
public class SimplexNoise extends AbstractNoise implements Noise2D, Noise3D {
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)};
private static Grad[] grad4 = {
new Grad(0, 1, 1, 1), new Grad(0, 1, 1, -1), new Grad(0, 1, -1, 1), new Grad(0, 1, -1, -1),
new Grad(0, -1, 1, 1), new Grad(0, -1, 1, -1), new Grad(0, -1, -1, 1), new Grad(0, -1, -1, -1),
new Grad(1, 0, 1, 1), new Grad(1, 0, 1, -1), new Grad(1, 0, -1, 1), new Grad(1, 0, -1, -1),
new Grad(-1, 0, 1, 1), new Grad(-1, 0, 1, -1), new Grad(-1, 0, -1, 1), new Grad(-1, 0, -1, -1),
new Grad(1, 1, 0, 1), new Grad(1, 1, 0, -1), new Grad(1, -1, 0, 1), new Grad(1, -1, 0, -1),
new Grad(-1, 1, 0, 1), new Grad(-1, 1, 0, -1), new Grad(-1, -1, 0, 1), new Grad(-1, -1, 0, -1),
new Grad(1, 1, 1, 0), new Grad(1, 1, -1, 0), new Grad(1, -1, 1, 0), new Grad(1, -1, -1, 0),
new Grad(-1, 1, 1, 0), new Grad(-1, 1, -1, 0), new Grad(-1, -1, 1, 0), new Grad(-1, -1, -1, 0)};
// Skewing and unskewing factors for 2, 3, and 4 dimensions
private static final float F2 = 0.5f * (float) (Math.sqrt(3.0f) - 1.0f);
private static final float G2 = (3.0f - (float) Math.sqrt(3.0f)) / 6.0f;
private static final float F3 = 1.0f / 3.0f;
private static final float G3 = 1.0f / 6.0f;
private static final float F4 = ((float) Math.sqrt(5.0f) - 1.0f) / 4.0f;
private static final float G4 = (5.0f - (float) Math.sqrt(5.0f)) / 20.0f;
private final short[] perm = new short[512];
private final short[] permMod12 = new short[512];
/**
* Initialize permutations with a given seed
*
* @param seed a seed value used for permutation shuffling
*/
public SimplexNoise(long seed) {
FastRandom rand = new FastRandom(seed);
short[] p = new short[256];
// Initialize with all values [0..255]
for (short i = 0; i < 256; i++) {
p[i] = i;
}
// Shuffle the array
for (int i = 0; i < 256; i++) {
int j = rand.nextInt(256);
short swap = p[i];
p[i] = p[j];
p[j] = swap;
}
for (int i = 0; i < 512; i++) {
perm[i] = p[i & 255];
permMod12[i] = (short) (perm[i] % 12);
}
}
// This method is a *lot* faster than using (int)Math.floor(x)
private static float dot(Grad g, float x, float y) {
return g.x * x + g.y * y;
}
private static float dot(Grad g, float x, float y, float z) {
return g.x * x + g.y * y + g.z * z;
}
private static float dot(Grad g, float x, float y, float z, float w) {
return g.x * x + g.y * y + g.z * z + g.w * w;
}
/**
* 2D simplex noise
*
* @param xin the x input coordinate
* @param yin the y input coordinate
* @return a noise value in the interval [-1,1]
*/
@Override
public float noise(float xin, float yin) {
float n0;
float n1;
float n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float s = (xin + yin) * F2; // Hairy factor for 2D
int i = TeraMath.floorToInt(xin + s);
int j = TeraMath.floorToInt(yin + s);
float t = (i + j) * G2;
float xo0 = i - t; // Unskew the cell origin back to (x,y) space
float yo0 = j - t;
float x0 = xin - xo0; // The x,y distances from the cell origin
float y0 = yin - yo0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1; // Offsets for second (middle) corner of simplex in (i,j) coords
int j1;
if (x0 > y0) { // lower triangle, XY order: (0,0)->(1,0)->(1,1)
i1 = 1;
j1 = 0;
} else { // upper triangle, YX order: (0,0)->(0,1)->(1,1)
i1 = 0;
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
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * 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
float t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0) {
n0 = 0.0f;
} else {
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0) {
n1 = 0.0f;
} else {
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0) {
n2 = 0.0f;
} 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 70.0f * (n0 + n1 + n2);
}
/**
* 3D simplex noise
*
* @param xin the x input coordinate
* @param yin the y input coordinate
* @param zin the z input coordinate
* @return a noise value in the interval [-1,1]
*/
@Override
public float noise(float xin, float yin, float zin) {
float n0;
float n1;
float n2;
float n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
float s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = TeraMath.floorToInt(xin + s);
int j = TeraMath.floorToInt(yin + s);
int k = TeraMath.floorToInt(zin + s);
float t = (i + j + k) * G3;
float xo0 = i - t; // Unskew the cell origin back to (x,y,z) space
float yo0 = j - t;
float zo0 = k - t;
float x0 = xin - xo0; // The x,y,z distances from the cell origin
float y0 = yin - yo0;
float z0 = zin - zo0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1;
int j1;
int k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2;
int j2;
int k2; // Offsets for third corner of simplex in (i,j,k) coords
if (x0 >= y0) {
if (y0 >= z0) { // X Y Z order
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} else if (x0 >= z0) { // X Z Y order
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
} else { // Z X Y order
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
} else { // x0<y0
if (y0 < z0) { // Z Y X order
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} else if (x0 < z0) { // Y Z X order
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} else { // Y X Z order
i1 = 0;
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.
float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
float y2 = y0 - j2 + 2.0f * G3;
float z2 = z0 - k2 + 2.0f * G3;
float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
float y3 = y0 - 1.0f + 3.0f * G3;
float z3 = z0 - 1.0f + 3.0f * 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
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0) {
n0 = 0.0f;
} else {
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0) {
n1 = 0.0f;
} else {
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0) {
n2 = 0.0f;
} else {
t2 *= t2;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0) {
n3 = 0.0f;
} 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 32.0f * (n0 + n1 + n2 + n3);
}
/**
* 4D simplex noise, better simplex rank ordering method 2012-03-09
*
* @param xin the x input coordinate
* @param yin the y input coordinate
* @param zin the z input coordinate
* @return a noise value in the interval [-1,1]
*/
public float noise(float xin, float yin, float zin, float win) {
float n0;
float n1;
float n2;
float n3;
float n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = (xin + yin + zin + win) * F4; // Factor for 4D skewing
int i = TeraMath.floorToInt(xin + s);
int j = TeraMath.floorToInt(yin + s);
int k = TeraMath.floorToInt(zin + s);
int l = TeraMath.floorToInt(win + s);
float t = (i + j + k + l) * G4; // Factor for 4D unskewing
float xo0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float yo0 = j - t;
float zo0 = k - t;
float wo0 = l - t;
float x0 = xin - xo0; // The x,y,z,w distances from the cell origin
float y0 = yin - yo0;
float z0 = zin - zo0;
float w0 = win - wo0;
// 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;
int j1;
int k1;
int l1; // The integer offsets for the second simplex corner
int i2;
int j2;
int k2;
int l2; // The integer offsets for the third simplex corner
int i3;
int j3;
int k3;
int 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.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f * G4;
float z2 = z0 - k2 + 2.0f * G4;
float w2 = w0 - l2 + 2.0f * G4;
float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f * G4;
float z3 = z0 - k3 + 3.0f * G4;
float w3 = w0 - l3 + 3.0f * G4;
float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f * G4;
float z4 = z0 - 1.0f + 4.0f * G4;
float w4 = w0 - 1.0f + 4.0f * 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;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if (t0 < 0) {
n0 = 0.0f;
} else {
t0 *= t0;
n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
if (t1 < 0) {
n1 = 0.0f;
} else {
t1 *= t1;
n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
if (t2 < 0) {
n2 = 0.f;
} else {
t2 *= t2;
n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
if (t3 < 0) {
n3 = 0.0f;
} else {
t3 *= t3;
n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
}
float t4 = 0.6f - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
if (t4 < 0) {
n4 = 0.0f;
} 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 27.0f * (n0 + n1 + n2 + n3 + n4);
}
// Inner class to speed up gradient computations
// (array access is a lot slower than member access)
private static class Grad {
float x;
float y;
float z;
float w;
Grad(float x, float y, float z) {
this.x = x;
this.y = y;
this.z = z;
}
Grad(float x, float y, float z, float w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
}
}