package monkstone.noise;
/**
* 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 FastTerrain implements Noise {
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 FastTerrain(long seed) {
perm = new short[PSIZE];
permGrad2 = new Grad2[PSIZE];
permGrad3 = new Grad3[PSIZE];
permGrad4 = new Grad4[PSIZE];
short[] source = new short[PSIZE];
for (short i = 0; i < PSIZE; i++) {
source[i] = i;
}
for (int i = PSIZE - 1; i >= 0; i--) {
seed = seed * 6364136223846793005L + 1442695040888963407L;
int 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.
*
* @param x
* @param y
* @return
*/
public double noise2(double x, double y) {
// Get points for A2* lattice
double 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.
*
* @param x
* @param y
* @return
*/
public double noise2_XBeforeY(double x, double y) {
// Skew transform and rotation baked into one.
double xx = x * 0.7071067811865476;
double 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) {
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
int index = (int) ((ysi - xsi) / 2 + 1);
double ssi = (xsi + ysi) * -0.211324865405187;
double xi = xsi + ssi, yi = ysi + ssi;
// Point contributions
for (int i = 0; i < 3; i++) {
LatticePoint2D c = LOOKUP_2D[index + i];
double dx = xi + c.dx, dy = yi + c.dy;
double attn = 0.5 - dx * dx - dy * dy;
if (attn <= 0) {
continue;
}
int pxm = (xsb + c.xsv) & PMASK, pym = (ysb + c.ysv) & PMASK;
Grad2 grad = permGrad2[perm[pxm] ^ pym];
double extrapolation = grad.dx * dx + grad.dy * dy;
attn *= attn;
value += attn * attn * extrapolation;
}
return value;
}
/**
* 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).
*
* @param x
* @param y
* @param z
* @return
*/
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.
double xy = x + y;
double s2 = xy * -0.211324865405187;
double zz = z * 0.577350269189626;
double xr = x + s2 - zz, yr = y + s2 - zz;
double 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.
*
* @param x
* @param y
* @param z
* @return
*/
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.
double xz = x + z;
double s2 = xz * -0.211324865405187;
double yy = y * 0.577350269189626;
double xr = x + s2 - yy;
double zr = z + s2 - yy;
double 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) {
// 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);
int index = (xht) | (yht << 1) | (zht << 2);
// Point contributions
double value = 0;
LatticePoint3D c = LOOKUP_3D[index];
while (c != null) {
double dxr = xri + c.dxr, dyr = yri + c.dyr, dzr = zri + c.dzr;
double 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;
Grad3 grad = permGrad3[perm[perm[pxm] ^ pym] ^ pzm];
double extrapolation = grad.dx * dxr + grad.dy * dyr + grad.dz * dzr;
attn *= attn;
value += attn * attn * extrapolation;
c = c.nextOnSuccess;
}
}
return value;
}
/**
* 4D FastTerrain 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.
*
* @param x
* @param y
* @param z
* @param w
* @return
*/
public double noise4_XYBeforeZW(double x, double y, double z, double w) {
double s2 = (x + y) * -0.178275657951399372 + (z + w) * 0.215623393288842828;
double 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 FastTerrain 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)
*
* @param x
* @param y
* @param z
* @param w
* @return
*/
public double noise4_XYZBeforeW(double x, double y, double z, double w) {
double xyz = x + y + z;
double ww = w * 0.2236067977499788;
double 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 FastTerrain 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) {
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.
double siSum = xsi + ysi + zsi + wsi;
double ssi = siSum * 0.309016994374947; // Prep for vertex contributions.
boolean 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;
double 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 (int i = 0; i < 5; i++) {
// Update xsb/etc. and add the lattice point's contribution.
LatticePoint4D 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;
double 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;
Grad4 grad = permGrad4[perm[perm[perm[pxm] ^ pym] ^ pzm] ^ pwm];
double 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.
double 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) {
int 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 (int 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.
LatticePoint3D c0 = new LatticePoint3D(i1, j1, k1, 0);
LatticePoint3D c1 = new LatticePoint3D(i1 + i2, j1 + j2, k1 + k2, 1);
// Each single step away on the first half-lattice.
LatticePoint3D c2 = new LatticePoint3D(i1 ^ 1, j1, k1, 0);
LatticePoint3D c3 = new LatticePoint3D(i1, j1 ^ 1, k1, 0);
LatticePoint3D c4 = new LatticePoint3D(i1, j1, k1 ^ 1, 0);
// Each single step away on the second half-lattice.
LatticePoint3D c5 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + k2, 1);
LatticePoint3D c6 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + k2, 1);
LatticePoint3D 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 (int i = 0; i < 16; i++) {
VERTICES_4D[i] = new LatticePoint4D((i) & 1, (i >> 1) & 1, (i >> 2) & 1, (i >> 3) & 1);
}
}
@Override
public float noise(float x, float y){
return (float)noise2_XBeforeY(x, y);
}
@Override
public float noise(float x, float y, float z) {
return (float)noise3_XYBeforeZ(x, y, z);
}
@Override
public float noise(float x, float y, float z, float w) {
return (float)noise4_XYBeforeZW(x, y, z, w);
}
@Override
public void noiseMode(NoiseMode mode) {
}
@Override
public void noiseSeed(long seed) {
}
private static class LatticePoint2D {
int xsv, ysv;
double dx, dy;
public LatticePoint2D(int xsv, int ysv) {
this.xsv = xsv;
this.ysv = ysv;
double ssv = (xsv + ysv) * -0.211324865405187;
this.dx = -xsv - ssv;
this.dy = -ysv - ssv;
}
}
private static class LatticePoint3D {
public double dxr, dyr, dzr;
public int xrv, yrv, 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 {
int xsv, ysv, zsv, wsv;
double dx, dy, dz, dw;
double xsi, ysi, zsi, wsi;
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;
double 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];
Grad2[] 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 (Grad2 grad21 : grad2) {
grad21.dx /= N2;
grad21.dy /= N2;
}
for (int i = 0; i < PSIZE; i++) {
GRADIENTS_2D[i] = grad2[i % grad2.length];
}
GRADIENTS_3D = new Grad3[PSIZE];
Grad3[] 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),
new Grad3(-2.22474487139, -1.0, -2.22474487139),
new Grad3(-2.22474487139, 1.0, -2.22474487139),
new Grad3(-1.1721513422464978, 0.0, -3.0862664687972017),
new Grad3(-3.0862664687972017, 0.0, -1.1721513422464978),
new Grad3(-2.22474487139, -1.0, 2.22474487139),
new Grad3(-2.22474487139, 1.0, 2.22474487139),
new Grad3(-3.0862664687972017, 0.0, 1.1721513422464978),
new Grad3(-1.1721513422464978, 0.0, 3.0862664687972017),
new Grad3(-2.22474487139, 2.22474487139, -1.0),
new Grad3(-2.22474487139, 2.22474487139, 1.0),
new Grad3(-1.1721513422464978, 3.0862664687972017, 0.0),
new Grad3(-3.0862664687972017, 1.1721513422464978, 0.0),
new Grad3(-1.0, -2.22474487139, -2.22474487139),
new Grad3(1.0, -2.22474487139, -2.22474487139),
new Grad3(0.0, -3.0862664687972017, -1.1721513422464978),
new Grad3(0.0, -1.1721513422464978, -3.0862664687972017),
new Grad3(-1.0, -2.22474487139, 2.22474487139),
new Grad3(1.0, -2.22474487139, 2.22474487139),
new Grad3(0.0, -1.1721513422464978, 3.0862664687972017),
new Grad3(0.0, -3.0862664687972017, 1.1721513422464978),
new Grad3(-1.0, 2.22474487139, -2.22474487139),
new Grad3(1.0, 2.22474487139, -2.22474487139),
new Grad3(0.0, 1.1721513422464978, -3.0862664687972017),
new Grad3(0.0, 3.0862664687972017, -1.1721513422464978),
new Grad3(-1.0, 2.22474487139, 2.22474487139),
new Grad3(1.0, 2.22474487139, 2.22474487139),
new Grad3(0.0, 3.0862664687972017, 1.1721513422464978),
new Grad3(0.0, 1.1721513422464978, 3.0862664687972017),
new Grad3(2.22474487139, -2.22474487139, -1.0),
new Grad3(2.22474487139, -2.22474487139, 1.0),
new Grad3(1.1721513422464978, -3.0862664687972017, 0.0),
new Grad3(3.0862664687972017, -1.1721513422464978, 0.0),
new Grad3(2.22474487139, -1.0, -2.22474487139),
new Grad3(2.22474487139, 1.0, -2.22474487139),
new Grad3(3.0862664687972017, 0.0, -1.1721513422464978),
new Grad3(1.1721513422464978, 0.0, -3.0862664687972017),
new Grad3(2.22474487139, -1.0, 2.22474487139),
new Grad3(2.22474487139, 1.0, 2.22474487139),
new Grad3(1.1721513422464978, 0.0, 3.0862664687972017),
new Grad3(3.0862664687972017, 0.0, 1.1721513422464978),
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)
};
for (Grad3 grad31 : grad3) {
grad31.dx /= N3;
grad31.dy /= N3;
grad31.dz /= N3;
}
for (int i = 0; i < PSIZE; i++) {
GRADIENTS_3D[i] = grad3[i % grad3.length];
}
GRADIENTS_4D = new Grad4[PSIZE];
Grad4[] grad4 = {
new Grad4(-0.753341017856078, -0.37968289875261624, -0.37968289875261624, -0.37968289875261624),
new Grad4(-0.7821684431180708, -0.4321472685365301, -0.4321472685365301, 0.12128480194602098),
new Grad4(-0.7821684431180708, -0.4321472685365301, 0.12128480194602098, -0.4321472685365301),
new Grad4(-0.7821684431180708, 0.12128480194602098, -0.4321472685365301, -0.4321472685365301),
new Grad4(-0.8586508742123365, -0.508629699630796, 0.044802370851755174, 0.044802370851755174),
new Grad4(-0.8586508742123365, 0.044802370851755174, -0.508629699630796, 0.044802370851755174),
new Grad4(-0.8586508742123365, 0.044802370851755174, 0.044802370851755174, -0.508629699630796),
new Grad4(-0.9982828964265062, -0.03381941603233842, -0.03381941603233842, -0.03381941603233842),
new Grad4(-0.37968289875261624, -0.753341017856078, -0.37968289875261624, -0.37968289875261624),
new Grad4(-0.4321472685365301, -0.7821684431180708, -0.4321472685365301, 0.12128480194602098),
new Grad4(-0.4321472685365301, -0.7821684431180708, 0.12128480194602098, -0.4321472685365301),
new Grad4(0.12128480194602098, -0.7821684431180708, -0.4321472685365301, -0.4321472685365301),
new Grad4(-0.508629699630796, -0.8586508742123365, 0.044802370851755174, 0.044802370851755174),
new Grad4(0.044802370851755174, -0.8586508742123365, -0.508629699630796, 0.044802370851755174),
new Grad4(0.044802370851755174, -0.8586508742123365, 0.044802370851755174, -0.508629699630796),
new Grad4(-0.03381941603233842, -0.9982828964265062, -0.03381941603233842, -0.03381941603233842),
new Grad4(-0.37968289875261624, -0.37968289875261624, -0.753341017856078, -0.37968289875261624),
new Grad4(-0.4321472685365301, -0.4321472685365301, -0.7821684431180708, 0.12128480194602098),
new Grad4(-0.4321472685365301, 0.12128480194602098, -0.7821684431180708, -0.4321472685365301),
new Grad4(0.12128480194602098, -0.4321472685365301, -0.7821684431180708, -0.4321472685365301),
new Grad4(-0.508629699630796, 0.044802370851755174, -0.8586508742123365, 0.044802370851755174),
new Grad4(0.044802370851755174, -0.508629699630796, -0.8586508742123365, 0.044802370851755174),
new Grad4(0.044802370851755174, 0.044802370851755174, -0.8586508742123365, -0.508629699630796),
new Grad4(-0.03381941603233842, -0.03381941603233842, -0.9982828964265062, -0.03381941603233842),
new Grad4(-0.37968289875261624, -0.37968289875261624, -0.37968289875261624, -0.753341017856078),
new Grad4(-0.4321472685365301, -0.4321472685365301, 0.12128480194602098, -0.7821684431180708),
new Grad4(-0.4321472685365301, 0.12128480194602098, -0.4321472685365301, -0.7821684431180708),
new Grad4(0.12128480194602098, -0.4321472685365301, -0.4321472685365301, -0.7821684431180708),
new Grad4(-0.508629699630796, 0.044802370851755174, 0.044802370851755174, -0.8586508742123365),
new Grad4(0.044802370851755174, -0.508629699630796, 0.044802370851755174, -0.8586508742123365),
new Grad4(0.044802370851755174, 0.044802370851755174, -0.508629699630796, -0.8586508742123365),
new Grad4(-0.03381941603233842, -0.03381941603233842, -0.03381941603233842, -0.9982828964265062),
new Grad4(-0.6740059517812944, -0.3239847771997537, -0.3239847771997537, 0.5794684678643381),
new Grad4(-0.7504883828755602, -0.4004672082940195, 0.15296486218853164, 0.5029860367700724),
new Grad4(-0.7504883828755602, 0.15296486218853164, -0.4004672082940195, 0.5029860367700724),
new Grad4(-0.8828161875373585, 0.08164729285680945, 0.08164729285680945, 0.4553054119602712),
new Grad4(-0.4553054119602712, -0.08164729285680945, -0.08164729285680945, 0.8828161875373585),
new Grad4(-0.5029860367700724, -0.15296486218853164, 0.4004672082940195, 0.7504883828755602),
new Grad4(-0.5029860367700724, 0.4004672082940195, -0.15296486218853164, 0.7504883828755602),
new Grad4(-0.5794684678643381, 0.3239847771997537, 0.3239847771997537, 0.6740059517812944),
new Grad4(-0.3239847771997537, -0.6740059517812944, -0.3239847771997537, 0.5794684678643381),
new Grad4(-0.4004672082940195, -0.7504883828755602, 0.15296486218853164, 0.5029860367700724),
new Grad4(0.15296486218853164, -0.7504883828755602, -0.4004672082940195, 0.5029860367700724),
new Grad4(0.08164729285680945, -0.8828161875373585, 0.08164729285680945, 0.4553054119602712),
new Grad4(-0.08164729285680945, -0.4553054119602712, -0.08164729285680945, 0.8828161875373585),
new Grad4(-0.15296486218853164, -0.5029860367700724, 0.4004672082940195, 0.7504883828755602),
new Grad4(0.4004672082940195, -0.5029860367700724, -0.15296486218853164, 0.7504883828755602),
new Grad4(0.3239847771997537, -0.5794684678643381, 0.3239847771997537, 0.6740059517812944),
new Grad4(-0.3239847771997537, -0.3239847771997537, -0.6740059517812944, 0.5794684678643381),
new Grad4(-0.4004672082940195, 0.15296486218853164, -0.7504883828755602, 0.5029860367700724),
new Grad4(0.15296486218853164, -0.4004672082940195, -0.7504883828755602, 0.5029860367700724),
new Grad4(0.08164729285680945, 0.08164729285680945, -0.8828161875373585, 0.4553054119602712),
new Grad4(-0.08164729285680945, -0.08164729285680945, -0.4553054119602712, 0.8828161875373585),
new Grad4(-0.15296486218853164, 0.4004672082940195, -0.5029860367700724, 0.7504883828755602),
new Grad4(0.4004672082940195, -0.15296486218853164, -0.5029860367700724, 0.7504883828755602),
new Grad4(0.3239847771997537, 0.3239847771997537, -0.5794684678643381, 0.6740059517812944),
new Grad4(-0.6740059517812944, -0.3239847771997537, 0.5794684678643381, -0.3239847771997537),
new Grad4(-0.7504883828755602, -0.4004672082940195, 0.5029860367700724, 0.15296486218853164),
new Grad4(-0.7504883828755602, 0.15296486218853164, 0.5029860367700724, -0.4004672082940195),
new Grad4(-0.8828161875373585, 0.08164729285680945, 0.4553054119602712, 0.08164729285680945),
new Grad4(-0.4553054119602712, -0.08164729285680945, 0.8828161875373585, -0.08164729285680945),
new Grad4(-0.5029860367700724, -0.15296486218853164, 0.7504883828755602, 0.4004672082940195),
new Grad4(-0.5029860367700724, 0.4004672082940195, 0.7504883828755602, -0.15296486218853164),
new Grad4(-0.5794684678643381, 0.3239847771997537, 0.6740059517812944, 0.3239847771997537),
new Grad4(-0.3239847771997537, -0.6740059517812944, 0.5794684678643381, -0.3239847771997537),
new Grad4(-0.4004672082940195, -0.7504883828755602, 0.5029860367700724, 0.15296486218853164),
new Grad4(0.15296486218853164, -0.7504883828755602, 0.5029860367700724, -0.4004672082940195),
new Grad4(0.08164729285680945, -0.8828161875373585, 0.4553054119602712, 0.08164729285680945),
new Grad4(-0.08164729285680945, -0.4553054119602712, 0.8828161875373585, -0.08164729285680945),
new Grad4(-0.15296486218853164, -0.5029860367700724, 0.7504883828755602, 0.4004672082940195),
new Grad4(0.4004672082940195, -0.5029860367700724, 0.7504883828755602, -0.15296486218853164),
new Grad4(0.3239847771997537, -0.5794684678643381, 0.6740059517812944, 0.3239847771997537),
new Grad4(-0.3239847771997537, -0.3239847771997537, 0.5794684678643381, -0.6740059517812944),
new Grad4(-0.4004672082940195, 0.15296486218853164, 0.5029860367700724, -0.7504883828755602),
new Grad4(0.15296486218853164, -0.4004672082940195, 0.5029860367700724, -0.7504883828755602),
new Grad4(0.08164729285680945, 0.08164729285680945, 0.4553054119602712, -0.8828161875373585),
new Grad4(-0.08164729285680945, -0.08164729285680945, 0.8828161875373585, -0.4553054119602712),
new Grad4(-0.15296486218853164, 0.4004672082940195, 0.7504883828755602, -0.5029860367700724),
new Grad4(0.4004672082940195, -0.15296486218853164, 0.7504883828755602, -0.5029860367700724),
new Grad4(0.3239847771997537, 0.3239847771997537, 0.6740059517812944, -0.5794684678643381),
new Grad4(-0.6740059517812944, 0.5794684678643381, -0.3239847771997537, -0.3239847771997537),
new Grad4(-0.7504883828755602, 0.5029860367700724, -0.4004672082940195, 0.15296486218853164),
new Grad4(-0.7504883828755602, 0.5029860367700724, 0.15296486218853164, -0.4004672082940195),
new Grad4(-0.8828161875373585, 0.4553054119602712, 0.08164729285680945, 0.08164729285680945),
new Grad4(-0.4553054119602712, 0.8828161875373585, -0.08164729285680945, -0.08164729285680945),
new Grad4(-0.5029860367700724, 0.7504883828755602, -0.15296486218853164, 0.4004672082940195),
new Grad4(-0.5029860367700724, 0.7504883828755602, 0.4004672082940195, -0.15296486218853164),
new Grad4(-0.5794684678643381, 0.6740059517812944, 0.3239847771997537, 0.3239847771997537),
new Grad4(-0.3239847771997537, 0.5794684678643381, -0.6740059517812944, -0.3239847771997537),
new Grad4(-0.4004672082940195, 0.5029860367700724, -0.7504883828755602, 0.15296486218853164),
new Grad4(0.15296486218853164, 0.5029860367700724, -0.7504883828755602, -0.4004672082940195),
new Grad4(0.08164729285680945, 0.4553054119602712, -0.8828161875373585, 0.08164729285680945),
new Grad4(-0.08164729285680945, 0.8828161875373585, -0.4553054119602712, -0.08164729285680945),
new Grad4(-0.15296486218853164, 0.7504883828755602, -0.5029860367700724, 0.4004672082940195),
new Grad4(0.4004672082940195, 0.7504883828755602, -0.5029860367700724, -0.15296486218853164),
new Grad4(0.3239847771997537, 0.6740059517812944, -0.5794684678643381, 0.3239847771997537),
new Grad4(-0.3239847771997537, 0.5794684678643381, -0.3239847771997537, -0.6740059517812944),
new Grad4(-0.4004672082940195, 0.5029860367700724, 0.15296486218853164, -0.7504883828755602),
new Grad4(0.15296486218853164, 0.5029860367700724, -0.4004672082940195, -0.7504883828755602),
new Grad4(0.08164729285680945, 0.4553054119602712, 0.08164729285680945, -0.8828161875373585),
new Grad4(-0.08164729285680945, 0.8828161875373585, -0.08164729285680945, -0.4553054119602712),
new Grad4(-0.15296486218853164, 0.7504883828755602, 0.4004672082940195, -0.5029860367700724),
new Grad4(0.4004672082940195, 0.7504883828755602, -0.15296486218853164, -0.5029860367700724),
new Grad4(0.3239847771997537, 0.6740059517812944, 0.3239847771997537, -0.5794684678643381),
new Grad4(0.5794684678643381, -0.6740059517812944, -0.3239847771997537, -0.3239847771997537),
new Grad4(0.5029860367700724, -0.7504883828755602, -0.4004672082940195, 0.15296486218853164),
new Grad4(0.5029860367700724, -0.7504883828755602, 0.15296486218853164, -0.4004672082940195),
new Grad4(0.4553054119602712, -0.8828161875373585, 0.08164729285680945, 0.08164729285680945),
new Grad4(0.8828161875373585, -0.4553054119602712, -0.08164729285680945, -0.08164729285680945),
new Grad4(0.7504883828755602, -0.5029860367700724, -0.15296486218853164, 0.4004672082940195),
new Grad4(0.7504883828755602, -0.5029860367700724, 0.4004672082940195, -0.15296486218853164),
new Grad4(0.6740059517812944, -0.5794684678643381, 0.3239847771997537, 0.3239847771997537),
new Grad4(0.5794684678643381, -0.3239847771997537, -0.6740059517812944, -0.3239847771997537),
new Grad4(0.5029860367700724, -0.4004672082940195, -0.7504883828755602, 0.15296486218853164),
new Grad4(0.5029860367700724, 0.15296486218853164, -0.7504883828755602, -0.4004672082940195),
new Grad4(0.4553054119602712, 0.08164729285680945, -0.8828161875373585, 0.08164729285680945),
new Grad4(0.8828161875373585, -0.08164729285680945, -0.4553054119602712, -0.08164729285680945),
new Grad4(0.7504883828755602, -0.15296486218853164, -0.5029860367700724, 0.4004672082940195),
new Grad4(0.7504883828755602, 0.4004672082940195, -0.5029860367700724, -0.15296486218853164),
new Grad4(0.6740059517812944, 0.3239847771997537, -0.5794684678643381, 0.3239847771997537),
new Grad4(0.5794684678643381, -0.3239847771997537, -0.3239847771997537, -0.6740059517812944),
new Grad4(0.5029860367700724, -0.4004672082940195, 0.15296486218853164, -0.7504883828755602),
new Grad4(0.5029860367700724, 0.15296486218853164, -0.4004672082940195, -0.7504883828755602),
new Grad4(0.4553054119602712, 0.08164729285680945, 0.08164729285680945, -0.8828161875373585),
new Grad4(0.8828161875373585, -0.08164729285680945, -0.08164729285680945, -0.4553054119602712),
new Grad4(0.7504883828755602, -0.15296486218853164, 0.4004672082940195, -0.5029860367700724),
new Grad4(0.7504883828755602, 0.4004672082940195, -0.15296486218853164, -0.5029860367700724),
new Grad4(0.6740059517812944, 0.3239847771997537, 0.3239847771997537, -0.5794684678643381),
new Grad4(0.03381941603233842, 0.03381941603233842, 0.03381941603233842, 0.9982828964265062),
new Grad4(-0.044802370851755174, -0.044802370851755174, 0.508629699630796, 0.8586508742123365),
new Grad4(-0.044802370851755174, 0.508629699630796, -0.044802370851755174, 0.8586508742123365),
new Grad4(-0.12128480194602098, 0.4321472685365301, 0.4321472685365301, 0.7821684431180708),
new Grad4(0.508629699630796, -0.044802370851755174, -0.044802370851755174, 0.8586508742123365),
new Grad4(0.4321472685365301, -0.12128480194602098, 0.4321472685365301, 0.7821684431180708),
new Grad4(0.4321472685365301, 0.4321472685365301, -0.12128480194602098, 0.7821684431180708),
new Grad4(0.37968289875261624, 0.37968289875261624, 0.37968289875261624, 0.753341017856078),
new Grad4(0.03381941603233842, 0.03381941603233842, 0.9982828964265062, 0.03381941603233842),
new Grad4(-0.044802370851755174, 0.044802370851755174, 0.8586508742123365, 0.508629699630796),
new Grad4(-0.044802370851755174, 0.508629699630796, 0.8586508742123365, -0.044802370851755174),
new Grad4(-0.12128480194602098, 0.4321472685365301, 0.7821684431180708, 0.4321472685365301),
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 (Grad4 grad41 : grad4) {
grad41.dx /= N4;
grad41.dy /= N4;
grad41.dz /= N4;
grad41.dw /= N4;
}
for (int i = 0; i < PSIZE; i++) {
GRADIENTS_4D[i] = grad4[i % grad4.length];
}
}
}