com.parzivail.util.noise.OpenSimplex2F Maven / Gradle / Ivy
package com.parzivail.util.noise;
import ;
import D;
import I;
import Z;
/**
* K.jpg's OpenSimplex 2, faster variant
*
* - 2D is standard simplex implemented using a lookup table.
* - 3D is "Re-oriented 4-point BCC noise" which constructs a
* congruent BCC lattice in a much different way than usual.
* - 4D constructs the lattice as a union of five copies of its
* reciprocal. It successively finds the closest point on each.
*
* Multiple versions of each function are provided. See the
* documentation above each, for more info.
*/
public class OpenSimplex2F
{
private static final int PSIZE = 2048;
private static final int PMASK = 2047;
private final short[] perm;
private final Grad2[] permGrad2;
private final Grad3[] permGrad3;
private final Grad4[] permGrad4;
public OpenSimplex2F(long seed)
{
perm = new short[PSIZE];
permGrad2 = new Grad2[PSIZE];
permGrad3 = new Grad3[PSIZE];
permGrad4 = new Grad4[PSIZE];
var source = new short[PSIZE];
for (short i = 0; i < PSIZE; i++)
source[i] = i;
for (var i = PSIZE - 1; i >= 0; i--)
{
seed = seed * 6364136223846793005L + 1442695040888963407L;
var r = (int)((seed + 31) % (i + 1));
if (r < 0)
r += (i + 1);
perm[i] = source[r];
permGrad2[i] = GRADIENTS_2D[perm[i]];
permGrad3[i] = GRADIENTS_3D[perm[i]];
permGrad4[i] = GRADIENTS_4D[perm[i]];
source[r] = source[i];
}
}
/*
* Noise Evaluators
*/
/**
* 2D Simplex noise, standard lattice orientation.
*/
public double noise2(double x, double y)
{
// Get points for A2* lattice
var s = 0.366025403784439 * (x + y);
double xs = x + s, ys = y + s;
return noise2_Base(xs, ys);
}
/**
* 2D Simplex noise, with Y pointing down the main diagonal.
* Might be better for a 2D sandbox style game, where Y is vertical.
* Probably slightly less optimal for heightmaps or continent maps.
*/
public double noise2_XBeforeY(double x, double y)
{
// Skew transform and rotation baked into one.
var xx = x * 0.7071067811865476;
var yy = y * 1.224744871380249;
return noise2_Base(yy + xx, yy - xx);
}
/**
* 2D Simplex noise base.
* Lookup table implementation inspired by DigitalShadow.
*/
private double noise2_Base(double xs, double ys)
{
xs %= Integer.MAX_VALUE;
ys %= Integer.MAX_VALUE;
double value = 0;
// Get base points and offsets
int xsb = fastFloor(xs), ysb = fastFloor(ys);
double xsi = xs - xsb, ysi = ys - ysb;
// Index to point list
var index = (int)((ysi - xsi) / 2 + 1);
var ssi = (xsi + ysi) * -0.211324865405187;
double xi = xsi + ssi, yi = ysi + ssi;
// Point contributions
for (var i = 0; i < 3; i++)
{
var c = LOOKUP_2D[index + i];
double dx = xi + c.dx, dy = yi + c.dy;
var attn = 0.5 - dx * dx - dy * dy;
if (attn <= 0)
continue;
int pxm = (xsb + c.xsv) & PMASK, pym = (ysb + c.ysv) & PMASK;
var grad = permGrad2[perm[pxm] ^ pym];
var extrapolation = grad.dx * dx + grad.dy * dy;
attn *= attn;
value += attn * attn * extrapolation;
}
return value;
}
/**
* 3D Re-oriented 4-point BCC noise, classic orientation.
* Proper substitute for 3D Simplex in light of Forbidden Formulae.
* Use noise3_XYBeforeZ or noise3_XZBeforeY instead, wherever appropriate.
*/
public double noise3_Classic(double x, double y, double z)
{
// Re-orient the cubic lattices via rotation, to produce the expected look on cardinal planar slices.
// If texturing objects that don't tend to have cardinal plane faces, you could even remove this.
// Orthonormal rotation. Not a skew transform.
var r = (2.0 / 3.0) * (x + y + z);
double xr = r - x, yr = r - y, zr = r - z;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* 3D Re-oriented 4-point BCC noise, with better visual isotropy in (X, Y).
* Recommended for 3D terrain and time-varied animations.
* The Z coordinate should always be the "different" coordinate in your use case.
* If Y is vertical in world coordinates, call noise3_XYBeforeZ(x, z, Y) or use noise3_XZBeforeY.
* If Z is vertical in world coordinates, call noise3_XYBeforeZ(x, y, Z).
* For a time varied animation, call noise3_XYBeforeZ(x, y, T).
*/
public double noise3_XYBeforeZ(double x, double y, double z)
{
// Re-orient the cubic lattices without skewing, to make X and Y triangular like 2D.
// Orthonormal rotation. Not a skew transform.
var xy = x + y;
var s2 = xy * -0.211324865405187;
var zz = z * 0.577350269189626;
double xr = x + s2 - zz, yr = y + s2 - zz;
var zr = xy * 0.577350269189626 + zz;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* 3D Re-oriented 4-point BCC noise, with better visual isotropy in (X, Z).
* Recommended for 3D terrain and time-varied animations.
* The Y coordinate should always be the "different" coordinate in your use case.
* If Y is vertical in world coordinates, call noise3_XZBeforeY(x, Y, z).
* If Z is vertical in world coordinates, call noise3_XZBeforeY(x, Z, y) or use noise3_XYBeforeZ.
* For a time varied animation, call noise3_XZBeforeY(x, T, y) or use noise3_XYBeforeZ.
*/
public double noise3_XZBeforeY(double x, double y, double z)
{
// Re-orient the cubic lattices without skewing, to make X and Z triangular like 2D.
// Orthonormal rotation. Not a skew transform.
var xz = x + z;
var s2 = xz * -0.211324865405187;
var yy = y * 0.577350269189626;
var xr = x + s2 - yy;
var zr = z + s2 - yy;
var yr = xz * 0.577350269189626 + yy;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* Generate overlapping cubic lattices for 3D Re-oriented BCC noise.
* Lookup table implementation inspired by DigitalShadow.
* It was actually faster to narrow down the points in the loop itself,
* than to build up the index with enough info to isolate 4 points.
*/
private double noise3_BCC(double xr, double yr, double zr)
{
xr %= Integer.MAX_VALUE;
yr %= Integer.MAX_VALUE;
zr %= Integer.MAX_VALUE;
// Get base and offsets inside cube of first lattice.
int xrb = fastFloor(xr), yrb = fastFloor(yr), zrb = fastFloor(zr);
double xri = xr - xrb, yri = yr - yrb, zri = zr - zrb;
// Identify which octant of the cube we're in. This determines which cell
// in the other cubic lattice we're in, and also narrows down one point on each.
int xht = (int)(xri + 0.5), yht = (int)(yri + 0.5), zht = (int)(zri + 0.5);
var index = (xht) | (yht << 1) | (zht << 2);
// Point contributions
double value = 0;
var c = LOOKUP_3D[index];
while (c != null)
{
double dxr = xri + c.dxr, dyr = yri + c.dyr, dzr = zri + c.dzr;
var attn = 0.5 - dxr * dxr - dyr * dyr - dzr * dzr;
if (attn < 0)
{
c = c.nextOnFailure;
}
else
{
int pxm = (xrb + c.xrv) & PMASK, pym = (yrb + c.yrv) & PMASK, pzm = (zrb + c.zrv) & PMASK;
var grad = permGrad3[perm[perm[pxm] ^ pym] ^ pzm];
var extrapolation = grad.dx * dxr + grad.dy * dyr + grad.dz * dzr;
attn *= attn;
value += attn * attn * extrapolation;
c = c.nextOnSuccess;
}
}
return value;
}
/**
* 4D OpenSimplex2F noise, classic lattice orientation.
*/
public double noise4_Classic(double x, double y, double z, double w)
{
// Get points for A4 lattice
var s = -0.138196601125011 * (x + y + z + w);
double xs = x + s, ys = y + s, zs = z + s, ws = w + s;
return noise4_Base(xs, ys, zs, ws);
}
/**
* 4D OpenSimplex2F noise, with XY and ZW forming orthogonal triangular-based planes.
* Recommended for 3D terrain, where X and Y (or Z and W) are horizontal.
* Recommended for noise(x, y, sin(time), cos(time)) trick.
*/
public double noise4_XYBeforeZW(double x, double y, double z, double w)
{
var s2 = (x + y) * -0.178275657951399372 + (z + w) * 0.215623393288842828;
var t2 = (z + w) * -0.403949762580207112 + (x + y) * -0.375199083010075342;
double xs = x + s2, ys = y + s2, zs = z + t2, ws = w + t2;
return noise4_Base(xs, ys, zs, ws);
}
/**
* 4D OpenSimplex2F noise, with XZ and YW forming orthogonal triangular-based planes.
* Recommended for 3D terrain, where X and Z (or Y and W) are horizontal.
*/
public double noise4_XZBeforeYW(double x, double y, double z, double w)
{
var s2 = (x + z) * -0.178275657951399372 + (y + w) * 0.215623393288842828;
var t2 = (y + w) * -0.403949762580207112 + (x + z) * -0.375199083010075342;
double xs = x + s2, ys = y + t2, zs = z + s2, ws = w + t2;
return noise4_Base(xs, ys, zs, ws);
}
/**
* 4D OpenSimplex2F noise, with XYZ oriented like noise3_Classic,
* and W for an extra degree of freedom. W repeats eventually.
* Recommended for time-varied animations which texture a 3D object (W=time)
*/
public double noise4_XYZBeforeW(double x, double y, double z, double w)
{
var xyz = x + y + z;
var ww = w * 0.2236067977499788;
var s2 = xyz * -0.16666666666666666 + ww;
double xs = x + s2, ys = y + s2, zs = z + s2, ws = -0.5 * xyz + ww;
return noise4_Base(xs, ys, zs, ws);
}
/**
* 4D OpenSimplex2F noise base.
* Current implementation not fully optimized by lookup tables.
* But still comes out slightly ahead of Gustavson's Simplex in tests.
*/
private double noise4_Base(double xs, double ys, double zs, double ws)
{
xs %= Integer.MAX_VALUE;
ys %= Integer.MAX_VALUE;
zs %= Integer.MAX_VALUE;
ws %= Integer.MAX_VALUE;
double value = 0;
// Get base points and offsets
int xsb = fastFloor(xs), ysb = fastFloor(ys), zsb = fastFloor(zs), wsb = fastFloor(ws);
double xsi = xs - xsb, ysi = ys - ysb, zsi = zs - zsb, wsi = ws - wsb;
// If we're in the lower half, flip so we can repeat the code for the upper half. We'll flip back later.
var siSum = xsi + ysi + zsi + wsi;
var ssi = siSum * 0.309016994374947; // Prep for vertex contributions.
var inLowerHalf = (siSum < 2);
if (inLowerHalf)
{
xsi = 1 - xsi;
ysi = 1 - ysi;
zsi = 1 - zsi;
wsi = 1 - wsi;
siSum = 4 - siSum;
}
// Consider opposing vertex pairs of the octahedron formed by the central cross-section of the stretched tesseract
double aabb = xsi + ysi - zsi - wsi, abab = xsi - ysi + zsi - wsi, abba = xsi - ysi - zsi + wsi;
double aabbScore = Math.abs(aabb), ababScore = Math.abs(abab), abbaScore = Math.abs(abba);
// Find the closest point on the stretched tesseract as if it were the upper half
int vertexIndex, via, vib;
double asi, bsi;
if (aabbScore > ababScore && aabbScore > abbaScore)
{
if (aabb > 0)
{
asi = zsi;
bsi = wsi;
vertexIndex = 0b0011;
via = 0b0111;
vib = 0b1011;
}
else
{
asi = xsi;
bsi = ysi;
vertexIndex = 0b1100;
via = 0b1101;
vib = 0b1110;
}
}
else if (ababScore > abbaScore)
{
if (abab > 0)
{
asi = ysi;
bsi = wsi;
vertexIndex = 0b0101;
via = 0b0111;
vib = 0b1101;
}
else
{
asi = xsi;
bsi = zsi;
vertexIndex = 0b1010;
via = 0b1011;
vib = 0b1110;
}
}
else
{
if (abba > 0)
{
asi = ysi;
bsi = zsi;
vertexIndex = 0b1001;
via = 0b1011;
vib = 0b1101;
}
else
{
asi = xsi;
bsi = wsi;
vertexIndex = 0b0110;
via = 0b0111;
vib = 0b1110;
}
}
if (bsi > asi)
{
via = vib;
var temp = bsi;
bsi = asi;
asi = temp;
}
if (siSum + asi > 3)
{
vertexIndex = via;
if (siSum + bsi > 4)
{
vertexIndex = 0b1111;
}
}
// Now flip back if we're actually in the lower half.
if (inLowerHalf)
{
xsi = 1 - xsi;
ysi = 1 - ysi;
zsi = 1 - zsi;
wsi = 1 - wsi;
vertexIndex ^= 0b1111;
}
// Five points to add, total, from five copies of the A4 lattice.
for (var i = 0; i < 5; i++)
{
// Update xsb/etc. and add the lattice point's contribution.
var c = VERTICES_4D[vertexIndex];
xsb += c.xsv;
ysb += c.ysv;
zsb += c.zsv;
wsb += c.wsv;
double xi = xsi + ssi, yi = ysi + ssi, zi = zsi + ssi, wi = wsi + ssi;
double dx = xi + c.dx, dy = yi + c.dy, dz = zi + c.dz, dw = wi + c.dw;
var attn = 0.5 - dx * dx - dy * dy - dz * dz - dw * dw;
if (attn > 0)
{
int pxm = xsb & PMASK, pym = ysb & PMASK, pzm = zsb & PMASK, pwm = wsb & PMASK;
var grad = permGrad4[perm[perm[perm[pxm] ^ pym] ^ pzm] ^ pwm];
var ramped = grad.dx * dx + grad.dy * dy + grad.dz * dz + grad.dw * dw;
attn *= attn;
value += attn * attn * ramped;
}
// Maybe this helps the compiler/JVM/LLVM/etc. know we can end the loop here. Maybe not.
if (i == 4)
break;
// Update the relative skewed coordinates to reference the vertex we just added.
// Rather, reference its counterpart on the lattice copy that is shifted down by
// the vector <-0.2, -0.2, -0.2, -0.2>
xsi += c.xsi;
ysi += c.ysi;
zsi += c.zsi;
wsi += c.wsi;
ssi += c.ssiDelta;
// Next point is the closest vertex on the 4-simplex whose base vertex is the aforementioned vertex.
var score0 = 1.0 + ssi * (-1.0 / 0.309016994374947); // Seems slightly faster than 1.0-xsi-ysi-zsi-wsi
vertexIndex = 0b0000;
if (xsi >= ysi && xsi >= zsi && xsi >= wsi && xsi >= score0)
{
vertexIndex = 0b0001;
}
else if (ysi > xsi && ysi >= zsi && ysi >= wsi && ysi >= score0)
{
vertexIndex = 0b0010;
}
else if (zsi > xsi && zsi > ysi && zsi >= wsi && zsi >= score0)
{
vertexIndex = 0b0100;
}
else if (wsi > xsi && wsi > ysi && wsi > zsi && wsi >= score0)
{
vertexIndex = 0b1000;
}
}
return value;
}
/*
* Utility
*/
private static int fastFloor(double x)
{
var xi = (int)x;
return x < xi ? xi - 1 : xi;
}
/*
* Definitions
*/
private static final LatticePoint2D[] LOOKUP_2D;
private static final LatticePoint3D[] LOOKUP_3D;
private static final LatticePoint4D[] VERTICES_4D;
static
{
LOOKUP_2D = new LatticePoint2D[4];
LOOKUP_3D = new LatticePoint3D[8];
VERTICES_4D = new LatticePoint4D[16];
LOOKUP_2D[0] = new LatticePoint2D(1, 0);
LOOKUP_2D[1] = new LatticePoint2D(0, 0);
LOOKUP_2D[2] = new LatticePoint2D(1, 1);
LOOKUP_2D[3] = new LatticePoint2D(0, 1);
for (var i = 0; i < 8; i++)
{
int i1, j1, k1, i2, j2, k2;
i1 = (i) & 1;
j1 = (i >> 1) & 1;
k1 = (i >> 2) & 1;
i2 = i1 ^ 1;
j2 = j1 ^ 1;
k2 = k1 ^ 1;
// The two points within this octant, one from each of the two cubic half-lattices.
var c0 = new LatticePoint3D(i1, j1, k1, 0);
var c1 = new LatticePoint3D(i1 + i2, j1 + j2, k1 + k2, 1);
// Each single step away on the first half-lattice.
var c2 = new LatticePoint3D(i1 ^ 1, j1, k1, 0);
var c3 = new LatticePoint3D(i1, j1 ^ 1, k1, 0);
var c4 = new LatticePoint3D(i1, j1, k1 ^ 1, 0);
// Each single step away on the second half-lattice.
var c5 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + k2, 1);
var c6 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + k2, 1);
var c7 = new LatticePoint3D(i1 + i2, j1 + j2, k1 + (k2 ^ 1), 1);
// First two are guaranteed.
c0.nextOnFailure = c0.nextOnSuccess = c1;
c1.nextOnFailure = c1.nextOnSuccess = c2;
// Once we find one on the first half-lattice, the rest are out.
// In addition, knowing c2 rules out c5.
c2.nextOnFailure = c3;
c2.nextOnSuccess = c6;
c3.nextOnFailure = c4;
c3.nextOnSuccess = c5;
c4.nextOnFailure = c4.nextOnSuccess = c5;
// Once we find one on the second half-lattice, the rest are out.
c5.nextOnFailure = c6;
c5.nextOnSuccess = null;
c6.nextOnFailure = c7;
c6.nextOnSuccess = null;
c7.nextOnFailure = c7.nextOnSuccess = null;
LOOKUP_3D[i] = c0;
}
for (var i = 0; i < 16; i++)
{
VERTICES_4D[i] = new LatticePoint4D((i) & 1, (i >> 1) & 1, (i >> 2) & 1, (i >> 3) & 1);
}
}
private static class LatticePoint2D
{
final int xsv;
final int ysv;
final double dx;
final double dy;
public LatticePoint2D(int xsv, int ysv)
{
this.xsv = xsv;
this.ysv = ysv;
var ssv = (xsv + ysv) * -0.211324865405187;
this.dx = -xsv - ssv;
this.dy = -ysv - ssv;
}
}
private static class LatticePoint3D
{
public final double dxr;
public final double dyr;
public final double dzr;
public final int xrv;
public final int yrv;
public final int zrv;
LatticePoint3D nextOnFailure, nextOnSuccess;
public LatticePoint3D(int xrv, int yrv, int zrv, int lattice)
{
this.dxr = -xrv + lattice * 0.5;
this.dyr = -yrv + lattice * 0.5;
this.dzr = -zrv + lattice * 0.5;
this.xrv = xrv + lattice * 1024;
this.yrv = yrv + lattice * 1024;
this.zrv = zrv + lattice * 1024;
}
}
private static class LatticePoint4D
{
final int xsv;
final int ysv;
final int zsv;
final int wsv;
final double dx;
final double dy;
final double dz;
final double dw;
double xsi, ysi, zsi, wsi;
final double ssiDelta;
public LatticePoint4D(int xsv, int ysv, int zsv, int wsv)
{
this.xsv = xsv + 409;
this.ysv = ysv + 409;
this.zsv = zsv + 409;
this.wsv = wsv + 409;
var ssv = (xsv + ysv + zsv + wsv) * 0.309016994374947;
this.dx = -xsv - ssv;
this.dy = -ysv - ssv;
this.dz = -zsv - ssv;
this.dw = -wsv - ssv;
this.xsi = xsi = 0.2 - xsv;
this.ysi = ysi = 0.2 - ysv;
this.zsi = zsi = 0.2 - zsv;
this.wsi = wsi = 0.2 - wsv;
this.ssiDelta = (0.8 - xsv - ysv - zsv - wsv) * 0.309016994374947;
}
}
/*
* Gradients
*/
private static class Grad2
{
double dx, dy;
public Grad2(double dx, double dy)
{
this.dx = dx;
this.dy = dy;
}
}
private static class Grad3
{
double dx, dy, dz;
public Grad3(double dx, double dy, double dz)
{
this.dx = dx;
this.dy = dy;
this.dz = dz;
}
}
private static class Grad4
{
double dx, dy, dz, dw;
public Grad4(double dx, double dy, double dz, double dw)
{
this.dx = dx;
this.dy = dy;
this.dz = dz;
this.dw = dw;
}
}
private static final double N2 = 0.01001634121365712;
private static final double N3 = 0.030485933181293584;
private static final double N4 = 0.009202377986303158;
private static final Grad2[] GRADIENTS_2D;
private static final Grad3[] GRADIENTS_3D;
private static final Grad4[] GRADIENTS_4D;
static
{
GRADIENTS_2D = new Grad2[PSIZE];
var grad2 = new Grad2[] {
new Grad2(0.130526192220052, 0.99144486137381),
new Grad2(0.38268343236509, 0.923879532511287),
new Grad2(0.608761429008721, 0.793353340291235),
new Grad2(0.793353340291235, 0.608761429008721),
new Grad2(0.923879532511287, 0.38268343236509),
new Grad2(0.99144486137381, 0.130526192220051),
new Grad2(0.99144486137381, -0.130526192220051),
new Grad2(0.923879532511287, -0.38268343236509),
new Grad2(0.793353340291235, -0.60876142900872),
new Grad2(0.608761429008721, -0.793353340291235),
new Grad2(0.38268343236509, -0.923879532511287),
new Grad2(0.130526192220052, -0.99144486137381),
new Grad2(-0.130526192220052, -0.99144486137381),
new Grad2(-0.38268343236509, -0.923879532511287),
new Grad2(-0.608761429008721, -0.793353340291235),
new Grad2(-0.793353340291235, -0.608761429008721),
new Grad2(-0.923879532511287, -0.38268343236509),
new Grad2(-0.99144486137381, -0.130526192220052),
new Grad2(-0.99144486137381, 0.130526192220051),
new Grad2(-0.923879532511287, 0.38268343236509),
new Grad2(-0.793353340291235, 0.608761429008721),
new Grad2(-0.608761429008721, 0.793353340291235),
new Grad2(-0.38268343236509, 0.923879532511287),
new Grad2(-0.130526192220052, 0.99144486137381)
};
for (var element : grad2)
{
element.dx /= N2;
element.dy /= N2;
}
for (var i = 0; i < PSIZE; i++)
{
GRADIENTS_2D[i] = grad2[i % grad2.length];
}
GRADIENTS_3D = new Grad3[PSIZE];
var grad3 = new Grad3[] {
new Grad3(-2.22474487139, -2.22474487139, -1.0),
new Grad3(-2.22474487139, -2.22474487139, 1.0),
new Grad3(-3.0862664687972017, -1.1721513422464978, 0.0),
new Grad3(-1.1721513422464978, -3.0862664687972017, 0.0),
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new Grad3(1.1721513422464978, 3.0862664687972017, 0.0)
};
for (var item : grad3)
{
item.dx /= N3;
item.dy /= N3;
item.dz /= N3;
}
for (var i = 0; i < PSIZE; i++)
{
GRADIENTS_3D[i] = grad3[i % grad3.length];
}
GRADIENTS_4D = new Grad4[PSIZE];
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new Grad4(0.508629699630796, -0.044802370851755174, 0.8586508742123365, -0.044802370851755174),
new Grad4(0.4321472685365301, -0.12128480194602098, 0.7821684431180708, 0.4321472685365301),
new Grad4(0.4321472685365301, 0.4321472685365301, 0.7821684431180708, -0.12128480194602098),
new Grad4(0.37968289875261624, 0.37968289875261624, 0.753341017856078, 0.37968289875261624),
new Grad4(0.03381941603233842, 0.9982828964265062, 0.03381941603233842, 0.03381941603233842),
new Grad4(-0.044802370851755174, 0.8586508742123365, -0.044802370851755174, 0.508629699630796),
new Grad4(-0.044802370851755174, 0.8586508742123365, 0.508629699630796, -0.044802370851755174),
new Grad4(-0.12128480194602098, 0.7821684431180708, 0.4321472685365301, 0.4321472685365301),
new Grad4(0.508629699630796, 0.8586508742123365, -0.044802370851755174, -0.044802370851755174),
new Grad4(0.4321472685365301, 0.7821684431180708, -0.12128480194602098, 0.4321472685365301),
new Grad4(0.4321472685365301, 0.7821684431180708, 0.4321472685365301, -0.12128480194602098),
new Grad4(0.37968289875261624, 0.753341017856078, 0.37968289875261624, 0.37968289875261624),
new Grad4(0.9982828964265062, 0.03381941603233842, 0.03381941603233842, 0.03381941603233842),
new Grad4(0.8586508742123365, -0.044802370851755174, -0.044802370851755174, 0.508629699630796),
new Grad4(0.8586508742123365, -0.044802370851755174, 0.508629699630796, -0.044802370851755174),
new Grad4(0.7821684431180708, -0.12128480194602098, 0.4321472685365301, 0.4321472685365301),
new Grad4(0.8586508742123365, 0.508629699630796, -0.044802370851755174, -0.044802370851755174),
new Grad4(0.7821684431180708, 0.4321472685365301, -0.12128480194602098, 0.4321472685365301),
new Grad4(0.7821684431180708, 0.4321472685365301, 0.4321472685365301, -0.12128480194602098),
new Grad4(0.753341017856078, 0.37968289875261624, 0.37968289875261624, 0.37968289875261624)
};
for (var value : grad4)
{
value.dx /= N4;
value.dy /= N4;
value.dz /= N4;
value.dw /= N4;
}
for (var i = 0; i < PSIZE; i++)
{
GRADIENTS_4D[i] = grad4[i % grad4.length];
}
}
}
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