package squidpony.squidmath;
import squidpony.annotation.Beta;
import static squidpony.squidmath.PintRNG.determine;
import static squidpony.squidmath.PintRNG.determineBounded;
/**
* Another experimental noise class. Extends PerlinNoise and should have similar quality, but can be faster and has less
* periodic results. This is still considered experimental because the exact output may change in future versions, along
* with the scale (potentially) and the parameters it takes. In general, {@link #noise(double, double)} and
* {@link #noise(double, double, double)} should have similar appearance to {@link PerlinNoise#noise(double, double)}
* and {@link PerlinNoise#noise(double, double, double)}, but are not forced to a zoomed-in scale like PerlinNoise makes
* its results, are less likely to repeat sections of noise, and are also somewhat faster (a 20% speedup can be expected
* over PerlinNoise using those two methods). Sound good? This also performs minimal (if any) arithmetic on 64-bit long
* numbers, instead using double and int, a style that is ideal for GWT (this is true of PerlinNoise too).
* <br>
* Created by Tommy Ettinger on 12/14/2016.
*/
@Beta
public class WhirlingNoise extends PerlinNoise implements Noise.Noise2D, Noise.Noise3D, Noise.Noise4D {
public static final WhirlingNoise instance = new WhirlingNoise();
private static int fastFloor(double t) {
return t >= 0 ? (int) t : (int) t - 1;
}
private static int fastFloor(float t) {
return t >= 0 ? (int) t : (int) t - 1;
}
protected static final float root3 = 1.7320508f, root5 = 2.236068f,
F2f = 0.5f * (root3 - 1f),
G2f = (3f - root3) * 0.16666667f,
F3f = 0.33333334f,
G3f = 0.16666667f,
F4f = (root5 - 1f) * 0.25f,
G4f = (5f - root5) * 0.05f,
unit1_4f = 0.70710678118f, unit1_8f = 0.38268343236f, unit3_8f = 0.92387953251f;
protected static final float[][] grad2f = {
{1f, 0f}, {-1f, 0f}, {0f, 1f}, {0f, -1f},
{unit3_8f, unit1_8f}, {unit3_8f, -unit1_8f}, {-unit3_8f, unit1_8f}, {-unit3_8f, -unit1_8f},
{unit1_4f, unit1_4f}, {unit1_4f, -unit1_4f}, {-unit1_4f, unit1_4f}, {-unit1_4f, -unit1_4f},
{unit1_8f, unit3_8f}, {unit1_8f, -unit3_8f}, {-unit1_8f, unit3_8f}, {-unit1_8f, -unit3_8f}};
protected static float dotf(final float g[], final float x, final float y) {
return g[0] * x + g[1] * y;
}
protected static float dotf(final int g[], final float x, final float y, final float z) {
return g[0] * x + g[1] * y + g[2] * z;
}
/*
public static double interpolate(double t, double low, double high)
{
//debug
//return 0;
//linear
//return t;
//hermite
//return t * t * (3 - 2 * t);
//quintic
//return t * t * t * (t * (t * 6 - 15) + 10);
//t = (t + low + 0.5 - high) * 0.5;
//t = (t < 0.5) ? t * low : 1.0 - ((1.0 - t) * high);
//t = Math.pow(t, 1.0 + high - low);
//return (t + 0.5 + high - low) * 0.5;
return t * t * t * (t * (t * 6 - 15) + 10);
}
*/
/**
* 2D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double)} and this method. Roughly
* 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in chunks because
* it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized for the
* limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
*
* @param x X input; works well if between 0.0 and 1.0, but anything is accepted
* @param y Y input; works well if between 0.0 and 1.0, but anything is accepted
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoise(final double x, final double y) {
return noise(x, y);
}
/**
* Identical to {@link #getNoise(double, double)}; ignores seed.
* @param x X input; works well if between 0.0 and 1.0, but anything is accepted
* @param y Y input; works well if between 0.0 and 1.0, but anything is accepted
* @param seed ignored entirely.
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoiseWithSeed(final double x, final double y, final int seed) {
return noise(x, y);
}
/**
* 3D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double, double)} and this method.
* Roughly 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in chunks
* because it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized for the
* limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
* @param x X input
* @param y Y input
* @param z Z input
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoise(final double x, final double y, final double z) {
return noise(x, y, z);
}
/**
* Identical to {@link #getNoise(double, double, double)}; ignores seed.
* @param x X input
* @param y Y input
* @param z Z input
* @param seed ignored entirely.
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoiseWithSeed(final double x, final double y, final double z, final int seed) {
return noise(x, y, z);
}
/**
* 4D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double, double)} and this method.
* Roughly 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in chunks
* because it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized for the
* limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
* @param x X input
* @param y Y input
* @param z Z input
* @param w W input (fourth-dimension)
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoise(final double x, final double y, final double z, final double w) {
return noise(x, y, z, w);
}
/**
* Identical to {@link #getNoise(double, double, double, double)}; ignores seed.
* @param x X input
* @param y Y input
* @param z Z input
* @param w W input (fourth-dimension)
* @param seed ignored entirely.
* @return noise from -1.0 to 1.0, inclusive
*/
public double getNoiseWithSeed(final double x, final double y, final double z, final double w, final int seed) {
return noise(x, y, z, w);
}
/**
* 2D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double)} and this method. Roughly
* 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in chunks because
* it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized for the
* limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
*
* @param xin X input; works well if between 0.0 and 1.0, but anything is accepted
* @param yin Y input; works well if between 0.0 and 1.0, but anything is accepted
* @return noise from -1.0 to 1.0, inclusive
*/
public static double noise(final double xin, final double yin) {
//xin *= epi;
//yin *= epi;
double noise0, noise1, noise2; // from the three corners
// Skew the input space to determine which simplex cell we're in
double skew = (xin + yin) * F2; // Hairy factor for 2D
int i = fastFloor(xin + skew);
int j = fastFloor(yin + skew);
double t = (i + j) * G2;
double X0 = i - t; // Unskew the cell origin back to (x,y) space
double Y0 = j - t;
double x0 = xin - X0; // The x,y distances from the cell origin
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
double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y)
// unskewed coords
double y1 = y0 - j1 + G2;
double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y)
// unskewed coords
double y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
/*
int ii = i & 255;
int jj = j & 255;
int gi0 = perm[ii + perm[jj]] & 15;
int gi1 = perm[ii + i1 + perm[jj + j1]] & 15;
int gi2 = perm[ii + 1 + perm[jj + 1]] & 15;
*/
/*
int hash = (int) rawNoise(i + (j * 0x9E3779B9),
i + i1 + ((j + j1) * 0x9E3779B9),
i + 1 + ((j + 1) * 0x9E3779B9),
seed);
int gi0 = hash & 15;
int gi1 = (hash >>>= 4) & 15;
int gi2 = (hash >>> 4) & 15;
*/
int gi0 = determine(i + determine(j)) & 15;
int gi1 = determine(i + i1 + determine(j + j1)) & 15;
int gi2 = determine(i + 1 + determine(j + 1)) & 15;
// Calculate the contribution from the three corners
double t0 = 0.5 - x0 * x0 - y0 * y0;
if (t0 < 0) {
noise0 = 0.0;
} else {
t0 *= t0;
noise0 = t0 * t0 * dot(grad2[gi0], x0, y0);
// for 2D gradient
}
double t1 = 0.5 - x1 * x1 - y1 * y1;
if (t1 < 0) {
noise1 = 0.0;
} else {
t1 *= t1;
noise1 = t1 * t1 * dot(grad2[gi1], x1, y1);
}
double t2 = 0.5 - x2 * x2 - y2 * y2;
if (t2 < 0) {
noise2 = 0.0;
} else {
t2 *= t2;
noise2 = t2 * t2 * dot(grad2[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 * (noise0 + noise1 + noise2);
}
/**
* 2D simplex noise returning a float; extremely similar to {@link #noise(double, double)}, but this may be slightly
* faster or slightly slower. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result
* will be different when passing the same arguments to {@link PerlinNoise#noise(double, double)} and this method.
*
* @param x x input; works well if between 0.0 and 1.0, but anything is accepted
* @param y y input; works well if between 0.0 and 1.0, but anything is accepted
* @return noise from -1.0 to 1.0, inclusive
*/
public static float noiseAlt(double x, double y) {
//xin *= epi;
//yin *= epi;
float noise0, noise1, noise2; // from the three corners
float xin = (float)x, yin = (float)y;
// Skew the input space to determine which simplex cell we're in
float skew = (xin + yin) * F2f; // Hairy factor for 2D
int i = fastFloor(xin + skew);
int j = fastFloor(yin + skew);
float t = (i + j) * G2f;
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 + G2f; // Offsets for middle corner in (x,y)
// unskewed coords
float y1 = y0 - j1 + G2f;
float x2 = x0 - 1f + 2f * G2f; // Offsets for last corner in (x,y)
// unskewed coords
float y2 = y0 - 1f + 2f * G2f;
// Work out the hashed gradient indices of the three simplex corners
/*
int ii = i & 255;
int jj = j & 255;
int gi0 = perm[ii + perm[jj]] & 15;
int gi1 = perm[ii + i1 + perm[jj + j1]] & 15;
int gi2 = perm[ii + 1 + perm[jj + 1]] & 15;
*/
/*
int hash = (int) rawNoise(i + (j * 0x9E3779B9),
i + i1 + ((j + j1) * 0x9E3779B9),
i + 1 + ((j + 1) * 0x9E3779B9),
seed);
int gi0 = hash & 15;
int gi1 = (hash >>>= 4) & 15;
int gi2 = (hash >>> 4) & 15;
*/
int gi0 = PintRNG.determine(i + PintRNG.determine(j)) & 15;
int gi1 = PintRNG.determine(i + i1 + PintRNG.determine(j + j1)) & 15;
int gi2 = PintRNG.determine(i + 1 + PintRNG.determine(j + 1)) & 15;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0) {
noise0 = 0f;
} else {
t0 *= t0;
noise0 = t0 * t0 * dotf(grad2f[gi0], x0, y0);
// for 2D gradient
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0) {
noise1 = 0f;
} else {
t1 *= t1;
noise1 = t1 * t1 * dotf(grad2f[gi1], x1, y1);
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0) {
noise2 = 0f;
} else {
t2 *= t2;
noise2 = t2 * t2 * dotf(grad2f[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 70f * (noise0 + noise1 + noise2);
}
/**
* 3D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double, double)} and this method.
* Roughly 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in chunks
* because it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized for the
* limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
* @param xin X input
* @param yin Y input
* @param zin Z input
* @return noise from -1.0 to 1.0, inclusive
*/
public static double noise(final double xin, final double yin, final double zin) {
//xin *= epi;
//yin *= epi;
//zin *= epi;
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 = fastFloor(xin + s);
int j = fastFloor(yin + s);
int k = fastFloor(zin + s);
double t = (i + j + k) * G3;
double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j - t;
double Z0 = k - t;
double x0 = xin - X0; // The x,y,z distances from the cell origin
double y0 = yin - Y0;
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
if (y0 < z0) {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} // Z Y X order
else if (x0 < z0) {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} // Y Z X order
else {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // Y X Z order
}
// 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 + F3; // Offsets for third corner in
// (x,y,z) coords
double y2 = y0 - j2 + F3;
double z2 = z0 - k2 + F3;
double x3 = x0 - 0.5; // Offsets for last corner in
// (x,y,z) coords
double y3 = y0 - 0.5;
double z3 = z0 - 0.5;
// 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 = perm[ii + perm[jj + perm[kk]]] % 12;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
*/
int gi0 = determineBounded(i + determine(j + determine(k)), 12);
int gi1 = determineBounded(i + i1 + determine(j + j1 + determine(k + k1)), 12);
int gi2 = determineBounded(i + i2 + determine(j + j2 + determine(k + k2)), 12);
int gi3 = determineBounded(i + 1 + determine(j + 1 + determine(k + 1)), 12);
/*
int hash = (int) rawNoise(i + ((j + k * 0x632BE5AB) * 0x9E3779B9),
i + i1 + ((j + j1 + (k + k1) * 0x632BE5AB) * 0x9E3779B9),
i + i2 + ((j + j2 + (k + k2) * 0x632BE5AB) * 0x9E3779B9),
i + 1 + ((j + 1 + ((k + 1) * 0x632BE5AB)) * 0x9E3779B9),
seed);
int gi0 = (hash >>>= 4) % 12;
int gi1 = (hash >>>= 4) % 12;
int gi2 = (hash >>>= 4) % 12;
int gi3 = (hash >>> 4) % 12;
*/
//int hash = (int) rawNoise(i, j, k, seed);
//int gi0 = (hash >>>= 4) % 12, gi1 = (hash >>>= 4) % 12, gi2 = (hash >>>= 4) % 12, gi3 = (hash >>>= 4) % 12;
// Calculate the contribution from the four corners
double t0 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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);
}
/**
* 3D simplex noise returning a float; extremely similar to {@link #noise(double, double, double)}, but this may
* be slightly faster or slightly slower. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of
* the result will be different when passing the same arguments to {@link PerlinNoise#noise(double, double, double)}
* and this method.
*
* @param x X input
* @param y Y input
* @param z Z input
* @return noise from -1.0 to 1.0, inclusive
*/
public static float noiseAlt(double x, double y, double z) {
//xin *= epi;
//yin *= epi;
//zin *= epi;
float xin = (float)x, yin = (float)y, zin = (float)z;
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) * F3f; // 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) * G3f;
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
if (y0 < z0) {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} // Z Y X order
else if (x0 < z0) {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} // Y Z X order
else {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // Y X Z order
}
// 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 + G3f; // Offsets for second corner in (x,y,z)
// coords
float y1 = y0 - j1 + G3f;
float z1 = z0 - k1 + G3f;
float x2 = x0 - i2 + F3f; // Offsets for third corner in
// (x,y,z) coords
float y2 = y0 - j2 + F3f;
float z2 = z0 - k2 + F3f;
float x3 = x0 - 0.5f; // Offsets for last corner in
// (x,y,z) coords
float y3 = y0 - 0.5f;
float z3 = z0 - 0.5f;
// 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 = perm[ii + perm[jj + perm[kk]]] % 12;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
*/
int gi0 = PintRNG.determineBounded(i + PintRNG.determine(j + PintRNG.determine(k)), 12);
int gi1 = PintRNG.determineBounded(i + i1 + PintRNG.determine(j + j1 + PintRNG.determine(k + k1)), 12);
int gi2 = PintRNG.determineBounded(i + i2 + PintRNG.determine(j + j2 + PintRNG.determine(k + k2)), 12);
int gi3 = PintRNG.determineBounded(i + 1 + PintRNG.determine(j + 1 + PintRNG.determine(k + 1)), 12);
/*
int hash = (int) rawNoise(i + ((j + k * 0x632BE5AB) * 0x9E3779B9),
i + i1 + ((j + j1 + (k + k1) * 0x632BE5AB) * 0x9E3779B9),
i + i2 + ((j + j2 + (k + k2) * 0x632BE5AB) * 0x9E3779B9),
i + 1 + ((j + 1 + ((k + 1) * 0x632BE5AB)) * 0x9E3779B9),
seed);
int gi0 = (hash >>>= 4) % 12;
int gi1 = (hash >>>= 4) % 12;
int gi2 = (hash >>>= 4) % 12;
int gi3 = (hash >>> 4) % 12;
*/
//int hash = (int) rawNoise(i, j, k, seed);
//int gi0 = (hash >>>= 4) % 12, gi1 = (hash >>>= 4) % 12, gi2 = (hash >>>= 4) % 12, gi3 = (hash >>>= 4) % 12;
// Calculate the contribution from the four corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0) {
n0 = 0f;
} else {
t0 *= t0;
n0 = t0 * t0 * dotf(grad3[gi0], x0, y0, z0);
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0) {
n1 = 0f;
} else {
t1 *= t1;
n1 = t1 * t1 * dotf(grad3[gi1], x1, y1, z1);
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0) {
n2 = 0f;
} else {
t2 *= t2;
n2 = t2 * t2 * dotf(grad3[gi2], x2, y2, z2);
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0) {
n3 = 0f;
} else {
t3 *= t3;
n3 = t3 * t3 * dotf(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 32f * (n0 + n1 + n2 + n3);
}
/**
* 4D simplex noise. Unlike {@link PerlinNoise}, uses its parameters verbatim, so the scale of the result will be
* different when passing the same arguments to {@link PerlinNoise#noise(double, double, double, double)} and this
* method. Roughly 20-25% faster than the equivalent method in PerlinNoise, plus it has less chance of repetition in
* chunks because it uses a pseudo-random function (curiously, {@link PintRNG#determine(int)}, which is optimized
* for the limitations of GWT but is rather fast here) instead of a number chosen from a single 256-element array.
* @param x X input
* @param y Y input
* @param z Z input
* @param w W input (fourth-dimensional)
* @return noise from -1.0 to 1.0, inclusive
*/
public static double noise(double x, double y, double z, double w) {
// The skewing and unskewing factors are hairy again for the 4D case
// Skew the (x,y,z,w) space to determine which cell of 24 simplices
// we're in
double s = (x + y + z + w) * F4; // Factor for 4D skewing
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; // Factor for 4D unskewing
double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
double Y0 = j - t;
double Z0 = k - t;
double W0 = l - t;
double x0 = x - X0; // The x,y,z,w distances from the cell origin
double y0 = y - Y0;
double z0 = z - Z0;
double w0 = w - W0;
// 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.
// The method below is a good way of finding the ordering of x,y,z,w
// and
// then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each
// possible pair
// of the four coordinates, and the results are used to add up binary
// bits
// for an integer index.
int c = (x0 > y0 ? 32 : 0) | (x0 > z0 ? 16 : 0) | (y0 > z0 ? 8 : 0) |
(x0 > w0 ? 4 : 0) | (y0 > w0 ? 2 : 0) | (z0 > w0 ? 1 : 0);
// 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.
// The number 3 in the "simplex" array is at the position of the
// largest coordinate.
// The integer offsets for the second simplex corner
int i1 = simplex[c][0] >= 3 ? 1 : 0;
int j1 = simplex[c][1] >= 3 ? 1 : 0;
int k1 = simplex[c][2] >= 3 ? 1 : 0;
int l1 = simplex[c][3] >= 3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest
// coordinate.
// The integer offsets for the third simplex corner
int i2 = simplex[c][0] >= 2 ? 1 : 0;
int j2 = simplex[c][1] >= 2 ? 1 : 0;
int k2 = simplex[c][2] >= 2 ? 1 : 0;
int l2 = simplex[c][3] >= 2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest
// coordinate.
// The integer offsets for the fourth simplex corner
int i3 = simplex[c][0] >= 1 ? 1 : 0;
int j3 = simplex[c][1] >= 1 ? 1 : 0;
int k3 = simplex[c][2] >= 1 ? 1 : 0;
int l3 = simplex[c][3] >= 1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to
// look that up.
double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
double y1 = y0 - j1 + G4;
double z1 = z0 - k1 + G4;
double w1 = w0 - l1 + G4;
double x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
double y2 = y0 - j2 + 2.0 * G4;
double z2 = z0 - k2 + 2.0 * G4;
double w2 = w0 - l2 + 2.0 * G4;
double x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
double y3 = y0 - j3 + 3.0 * G4;
double z3 = z0 - k3 + 3.0 * G4;
double w3 = w0 - l3 + 3.0 * G4;
double x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
double y4 = y0 - 1.0 + 4.0 * G4;
double z4 = z0 - 1.0 + 4.0 * G4;
double w4 = w0 - 1.0 + 4.0 * G4;
int gi0 = determine(i + determine(j + determine(k + determine(l)))) & 31;
int gi1 = determine(i + i1 + determine(j + j1 + determine(k + k1 + determine(l + l1)))) & 31;
int gi2 = determine(i + i2 + determine(j + j2 + determine(k + k2 + determine(l + l2)))) & 31;
int gi3 = determine(i + i3 + determine(j + j3 + determine(k + k3 + determine(l + l3)))) & 31;
int gi4 = determine(i + 1 + determine(j + 1 + determine(k + 1 + determine(l + 1)))) & 31;
// Noise contributions from the five corners are n0 to n4
// Calculate the contribution from the five corners
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0, n0;
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, n1;
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, n2;
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, n3;
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, n4;
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);
}
/*
public static void main(String[] args)
{
long hash;
for (int x = -8; x < 8; x++) {
for (int y = -8; y < 8; y++) {
hash = rawNoise(x, y, 1);
System.out.println("x=" + x + " y=" + y);
System.out.println("normal=" +
(Float.intBitsToFloat(0x3F800000 | (int)(hash & 0x7FFFFF)) - 1.0));
System.out.println("tweaked=" +
(Float.intBitsToFloat(0x40000000 | (int)(hash & 0x7FFFFF)) - 3.0));
System.out.println("half=" +
(Float.intBitsToFloat(0x3F000000 | (int)(hash & 0x7FFFFF)) - 0.5));
}
}
}
*/
}