com.rafaskoberg.gdx.typinglabel.utils.SimplexNoise Maven / Gradle / Ivy
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package com.rafaskoberg.gdx.typinglabel.utils;
import com.badlogic.gdx.math.MathUtils;
/**
* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
*
* Based on example code by Stefan Gustavson ([email protected]). Optimisations by Peter Eastman
* ([email protected]). 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.
*/
public class SimplexNoise { // Simplex noise in 2D, 3D and 4D
private static Grad[] grad3;
private static Grad[] grad4;
private static short[] p;
private static short[] perm;
private static short[] permMod12;
static {
grad3 = new Grad[]{
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)
};
grad4 = new Grad[]{
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)
};
p = new short[]{
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
};
// To remove the need for index wrapping, float the permutation table length
perm = new short[512];
permMod12 = new short[512];
for(int i = 0; i < 512; i++) {
perm[i] = p[i & 255];
permMod12[i] = (short) (perm[i] % 12);
}
}
// Skewing and unskewing factors for 2, 3, and 4 dimensions
private static final float F2 = (float) (0.5 * (Math.sqrt(3.0) - 1.0));
private static final float G2 = (float) ((3.0 - Math.sqrt(3.0)) / 6.0);
private static final float F3 = (float) (1.0 / 3.0);
private static final float G3 = (float) (1.0 / 6.0);
private static final float F4 = (float) ((Math.sqrt(5.0) - 1.0) / 4.0);
private static final float G4 = (float) ((5.0 - Math.sqrt(5.0)) / 20.0);
// Instance variables for consistency and randomness
private final int octaves;
private final float roughness;
private final float scale;
private float offset;
private int xCursor;
private int yCursor;
public SimplexNoise() {
this(4, 1f, 1f);
}
public SimplexNoise(int octaves, float roughness, float scale) {
this.octaves = octaves;
this.roughness = roughness;
this.scale = scale;
generateNewOffset();
}
public SimplexNoise(int octaves, float roughness, float scale, float offset) {
this.octaves = octaves;
this.roughness = roughness;
this.scale = scale;
this.offset = offset;
}
public void generateNewOffset() {
this.offset = Short.MAX_VALUE * MathUtils.random(-1f, 1f);
}
public float getRawNoise(float x, float y) {
return noise(x + offset, y + offset);
}
public float getRawNoise(float x, float y, float z) {
return noise(x + offset, y + offset, z + offset);
}
public float getRawNoise(float x, float y, float z, float w) {
return noise(x + offset, y + offset, z + offset, w + offset);
}
public float getNoise(float x, float y) {
return octavedNoise(x + offset, y + offset, octaves, roughness, scale);
}
public float getNoise(float x, float y, float z) {
return octavedNoise(x + offset, y + offset, z + offset, octaves, roughness, scale);
}
public float getNoise(float x, float y, float z, float w) {
return octavedNoise(x + offset, y + offset, z + offset, w + offset, octaves, roughness, scale);
}
public float nextNoiseX() {
return getNoise(xCursor++, 0);
}
public float nextNoiseY() {
return getNoise(0, yCursor++);
}
// This method is a *lot* faster than using (int)Math.floor(x)
private static int fastfloor(float x) {
int xi = (int) x;
return x < xi ? xi - 1 : xi;
}
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
public static float noise(float xin, float yin) {
float n0, n1, 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 = fastfloor(xin + s);
int j = fastfloor(yin + s);
float t = (i + j) * G2;
float X0 = i - t; // Unskew the cell origin back to (x,y) space
float Y0 = j - t;
float x0 = xin - X0; // The x,y distances from the cell origin
float 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
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
public static float noise(float xin, float yin, float zin) {
float n0, n1, n2, 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 = fastfloor(xin + s);
int j = fastfloor(yin + s);
int k = fastfloor(zin + s);
float t = (i + j + k) * G3;
float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
float Y0 = j - t;
float Z0 = k - t;
float x0 = xin - X0; // The x,y,z distances from the cell origin
float y0 = yin - Y0;
float 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)
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= 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 = 0.0f;
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);
}
public static float octavedNoise(float xin, float yin, int octaves, float roughness, float scale) {
float noiseSum = 0;
float layerFrequency = scale;
float layerWeight = 1;
float weightSum = 0;
for(int octave = 0; octave < octaves; octave++) {
noiseSum += SimplexNoise.noise(xin * layerFrequency, yin * layerFrequency) * layerWeight;
layerFrequency *= 2;
weightSum += layerWeight;
layerWeight *= roughness;
}
return noiseSum / weightSum;
}
public static float octavedNoise(float xin, float yin, float zin, int octaves, float roughness, float scale) {
float noiseSum = 0;
float layerFrequency = scale;
float layerWeight = 1;
float weightSum = 0;
for(int octave = 0; octave < octaves; octave++) {
noiseSum += noise(xin * layerFrequency, yin * layerFrequency, zin * layerFrequency) * layerWeight;
layerFrequency *= 2;
weightSum += layerWeight;
layerWeight *= roughness;
}
return noiseSum / weightSum;
}
public static float octavedNoise(float xin, float yin, float zin, float win, int octaves, float roughness, float scale) {
float noiseSum = 0;
float layerFrequency = scale;
float layerWeight = 1;
float weightSum = 0;
for(int octave = 0; octave < octaves; octave++) {
noiseSum += noise(xin * layerFrequency, yin * layerFrequency, zin * layerFrequency, win * layerFrequency) *
layerWeight;
layerFrequency *= 2;
weightSum += layerWeight;
layerWeight *= roughness;
}
return noiseSum / weightSum;
}
// Inner class to speed upp gradient computations
// (array access is a lot slower than member access)
private static class Grad {
float x, y, z, 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;
}
}
}