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KdotJPG/OpenSimplex2S.java

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Visually isotropic coherent noise algorithm based on alternate constructions of the A* lattice.
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OpenSimplex2S.java
/**
* K.jpg's OpenSimplex 2, smooth variant ("SuperSimplex")
*
* More language ports, as well as legacy 2014 OpenSimplex, can be found here:
* https://github.com/KdotJPG/OpenSimplex2
*/
public class OpenSimplex2S {
private static final long PRIME_X = 0x5205402B9270C86FL;
private static final long PRIME_Y = 0x598CD327003817B5L;
private static final long PRIME_Z = 0x5BCC226E9FA0BACBL;
private static final long PRIME_W = 0x56CC5227E58F554BL;
private static final long HASH_MULTIPLIER = 0x53A3F72DEEC546F5L;
private static final long SEED_FLIP_3D = -0x52D547B2E96ED629L;
private static final double ROOT2OVER2 = 0.7071067811865476;
private static final double SKEW_2D = 0.366025403784439;
private static final double UNSKEW_2D = -0.21132486540518713;
private static final double ROOT3OVER3 = 0.577350269189626;
private static final double FALLBACK_ROTATE3 = 2.0 / 3.0;
private static final double ROTATE3_ORTHOGONALIZER = UNSKEW_2D;
private static final float SKEW_4D = 0.309016994374947f;
private static final float UNSKEW_4D = -0.138196601125011f;
private static final int N_GRADS_2D_EXPONENT = 7;
private static final int N_GRADS_3D_EXPONENT = 8;
private static final int N_GRADS_4D_EXPONENT = 9;
private static final int N_GRADS_2D = 1 << N_GRADS_2D_EXPONENT;
private static final int N_GRADS_3D = 1 << N_GRADS_3D_EXPONENT;
private static final int N_GRADS_4D = 1 << N_GRADS_4D_EXPONENT;
private static final double NORMALIZER_2D = 0.05481866495625118;
private static final double NORMALIZER_3D = 0.2781926117527186;
private static final double NORMALIZER_4D = 0.11127401889945551;
private static final float RSQUARED_2D = 2.0f / 3.0f;
private static final float RSQUARED_3D = 3.0f / 4.0f;
private static final float RSQUARED_4D = 4.0f / 5.0f;
/*
* Noise Evaluators
*/
/**
* 2D OpenSimplex2S/SuperSimplex noise, standard lattice orientation.
*/
public static float noise2(long seed, double x, double y) {
// Get points for A2* lattice
double s = SKEW_2D * (x + y);
double xs = x + s, ys = y + s;
return noise2_UnskewedBase(seed, xs, ys);
}
/**
* 2D OpenSimplex2S/SuperSimplex 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,
* unless your map is centered around an equator. It's a slight
* difference, but the option is here to make it easy.
*/
public static float noise2_ImproveX(long seed, double x, double y) {
// Skew transform and rotation baked into one.
double xx = x * ROOT2OVER2;
double yy = y * (ROOT2OVER2 * (1 + 2 * SKEW_2D));
return noise2_UnskewedBase(seed, yy + xx, yy - xx);
}
/**
* 2D OpenSimplex2S/SuperSimplex noise base.
*/
private static float noise2_UnskewedBase(long seed, double xs, double ys) {
// Get base points and offsets.
int xsb = fastFloor(xs), ysb = fastFloor(ys);
float xi = (float)(xs - xsb), yi = (float)(ys - ysb);
// Prime pre-multiplication for hash.
long xsbp = xsb * PRIME_X, ysbp = ysb * PRIME_Y;
// Unskew.
float t = (xi + yi) * (float)UNSKEW_2D;
float dx0 = xi + t, dy0 = yi + t;
// First vertex.
float a0 = RSQUARED_2D - dx0 * dx0 - dy0 * dy0;
float value = (a0 * a0) * (a0 * a0) * grad(seed, xsbp, ysbp, dx0, dy0);
// Second vertex.
float a1 = (float)(2 * (1 + 2 * UNSKEW_2D) * (1 / UNSKEW_2D + 2)) * t + ((float)(-2 * (1 + 2 * UNSKEW_2D) * (1 + 2 * UNSKEW_2D)) + a0);
float dx1 = dx0 - (float)(1 + 2 * UNSKEW_2D);
float dy1 = dy0 - (float)(1 + 2 * UNSKEW_2D);
value += (a1 * a1) * (a1 * a1) * grad(seed, xsbp + PRIME_X, ysbp + PRIME_Y, dx1, dy1);
// Third and fourth vertices.
// Nested conditionals were faster than compact bit logic/arithmetic.
float xmyi = xi - yi;
if (t < UNSKEW_2D) {
if (xi + xmyi > 1) {
float dx2 = dx0 - (float)(3 * UNSKEW_2D + 2);
float dy2 = dy0 - (float)(3 * UNSKEW_2D + 1);
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp + (PRIME_X << 1), ysbp + PRIME_Y, dx2, dy2);
}
}
else
{
float dx2 = dx0 - (float)UNSKEW_2D;
float dy2 = dy0 - (float)(UNSKEW_2D + 1);
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp, ysbp + PRIME_Y, dx2, dy2);
}
}
if (yi - xmyi > 1) {
float dx3 = dx0 - (float)(3 * UNSKEW_2D + 1);
float dy3 = dy0 - (float)(3 * UNSKEW_2D + 2);
float a3 = RSQUARED_2D - dx3 * dx3 - dy3 * dy3;
if (a3 > 0) {
value += (a3 * a3) * (a3 * a3) * grad(seed, xsbp + PRIME_X, ysbp + (PRIME_Y << 1), dx3, dy3);
}
}
else
{
float dx3 = dx0 - (float)(UNSKEW_2D + 1);
float dy3 = dy0 - (float)UNSKEW_2D;
float a3 = RSQUARED_2D - dx3 * dx3 - dy3 * dy3;
if (a3 > 0) {
value += (a3 * a3) * (a3 * a3) * grad(seed, xsbp + PRIME_X, ysbp, dx3, dy3);
}
}
}
else
{
if (xi + xmyi < 0) {
float dx2 = dx0 + (float)(1 + UNSKEW_2D);
float dy2 = dy0 + (float)UNSKEW_2D;
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp - PRIME_X, ysbp, dx2, dy2);
}
}
else
{
float dx2 = dx0 - (float)(UNSKEW_2D + 1);
float dy2 = dy0 - (float)UNSKEW_2D;
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp + PRIME_X, ysbp, dx2, dy2);
}
}
if (yi < xmyi) {
float dx2 = dx0 + (float)UNSKEW_2D;
float dy2 = dy0 + (float)(UNSKEW_2D + 1);
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp, ysbp - PRIME_Y, dx2, dy2);
}
}
else
{
float dx2 = dx0 - (float)UNSKEW_2D;
float dy2 = dy0 - (float)(UNSKEW_2D + 1);
float a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if (a2 > 0) {
value += (a2 * a2) * (a2 * a2) * grad(seed, xsbp, ysbp + PRIME_Y, dx2, dy2);
}
}
}
return value;
}
/**
* 3D OpenSimplex2S/SuperSimplex 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 whatever your use case is.
* If Y is vertical in world coordinates, call noise3_ImproveXZ(x, z, Y) or use noise3_XZBeforeY.
* If Z is vertical in world coordinates, call noise3_ImproveXZ(x, y, Z).
* For a time varied animation, call noise3_ImproveXY(x, y, T).
*/
public static float noise3_ImproveXY(long seed, double x, double y, double z) {
// Re-orient the cubic lattices without skewing, so Z points up the main lattice diagonal,
// and the planes formed by XY are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
double xy = x + y;
double s2 = xy * ROTATE3_ORTHOGONALIZER;
double zz = z * ROOT3OVER3;
double xr = x + s2 + zz;
double yr = y + s2 + zz;
double zr = xy * -ROOT3OVER3 + zz;
// Evaluate both lattices to form a BCC lattice.
return noise3_UnrotatedBase(seed, xr, yr, zr);
}
/**
* 3D OpenSimplex2S/SuperSimplex 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 whatever your use case is.
* If Y is vertical in world coordinates, call noise3_ImproveXZ(x, Y, z).
* If Z is vertical in world coordinates, call noise3_ImproveXZ(x, Z, y) or use noise3_ImproveXY.
* For a time varied animation, call noise3_ImproveXZ(x, T, y) or use noise3_ImproveXY.
*/
public static float noise3_ImproveXZ(long seed, double x, double y, double z) {
// Re-orient the cubic lattices without skewing, so Y points up the main lattice diagonal,
// and the planes formed by XZ are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
double xz = x + z;
double s2 = xz * -0.211324865405187;
double yy = y * ROOT3OVER3;
double xr = x + s2 + yy;
double zr = z + s2 + yy;
double yr = xz * -ROOT3OVER3 + yy;
// Evaluate both lattices to form a BCC lattice.
return noise3_UnrotatedBase(seed, xr, yr, zr);
}
/**
* 3D OpenSimplex2S/SuperSimplex noise, fallback rotation option
* Use noise3_ImproveXY or noise3_ImproveXZ instead, wherever appropriate.
* They have less diagonal bias. This function's best use is as a fallback.
*/
public static float noise3_Fallback(long seed, double x, double y, double z) {
// Re-orient the cubic lattices via rotation, to produce a familiar look.
// Orthonormal rotation. Not a skew transform.
double r = FALLBACK_ROTATE3 * (x + y + z);
double xr = r - x, yr = r - y, zr = r - z;
// Evaluate both lattices to form a BCC lattice.
return noise3_UnrotatedBase(seed, 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 8 points.
*/
private static float noise3_UnrotatedBase(long seed, double xr, double yr, double zr) {
// Get base points and offsets.
int xrb = fastFloor(xr), yrb = fastFloor(yr), zrb = fastFloor(zr);
float xi = (float)(xr - xrb), yi = (float)(yr - yrb), zi = (float)(zr - zrb);
// Prime pre-multiplication for hash. Also flip seed for second lattice copy.
long xrbp = xrb * PRIME_X, yrbp = yrb * PRIME_Y, zrbp = zrb * PRIME_Z;
long seed2 = seed ^ -0x52D547B2E96ED629L;
// -1 if positive, 0 if negative.
int xNMask = (int)(-0.5f - xi), yNMask = (int)(-0.5f - yi), zNMask = (int)(-0.5f - zi);
// First vertex.
float x0 = xi + xNMask;
float y0 = yi + yNMask;
float z0 = zi + zNMask;
float a0 = RSQUARED_3D - x0 * x0 - y0 * y0 - z0 * z0;
float value = (a0 * a0) * (a0 * a0) * grad(seed,
xrbp + (xNMask & PRIME_X), yrbp + (yNMask & PRIME_Y), zrbp + (zNMask & PRIME_Z), x0, y0, z0);
// Second vertex.
float x1 = xi - 0.5f;
float y1 = yi - 0.5f;
float z1 = zi - 0.5f;
float a1 = RSQUARED_3D - x1 * x1 - y1 * y1 - z1 * z1;
value += (a1 * a1) * (a1 * a1) * grad(seed2,
xrbp + PRIME_X, yrbp + PRIME_Y, zrbp + PRIME_Z, x1, y1, z1);
// Shortcuts for building the remaining falloffs.
// Derived by subtracting the polynomials with the offsets plugged in.
float xAFlipMask0 = ((xNMask | 1) << 1) * x1;
float yAFlipMask0 = ((yNMask | 1) << 1) * y1;
float zAFlipMask0 = ((zNMask | 1) << 1) * z1;
float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f;
float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f;
float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f;
boolean skip5 = false;
float a2 = xAFlipMask0 + a0;
if (a2 > 0) {
float x2 = x0 - (xNMask | 1);
float y2 = y0;
float z2 = z0;
value += (a2 * a2) * (a2 * a2) * grad(seed,
xrbp + (~xNMask & PRIME_X), yrbp + (yNMask & PRIME_Y), zrbp + (zNMask & PRIME_Z), x2, y2, z2);
}
else
{
float a3 = yAFlipMask0 + zAFlipMask0 + a0;
if (a3 > 0) {
float x3 = x0;
float y3 = y0 - (yNMask | 1);
float z3 = z0 - (zNMask | 1);
value += (a3 * a3) * (a3 * a3) * grad(seed,
xrbp + (xNMask & PRIME_X), yrbp + (~yNMask & PRIME_Y), zrbp + (~zNMask & PRIME_Z), x3, y3, z3);
}
float a4 = xAFlipMask1 + a1;
if (a4 > 0) {
float x4 = (xNMask | 1) + x1;
float y4 = y1;
float z4 = z1;
value += (a4 * a4) * (a4 * a4) * grad(seed2,
xrbp + (xNMask & (PRIME_X * 2)), yrbp + PRIME_Y, zrbp + PRIME_Z, x4, y4, z4);
skip5 = true;
}
}
boolean skip9 = false;
float a6 = yAFlipMask0 + a0;
if (a6 > 0) {
float x6 = x0;
float y6 = y0 - (yNMask | 1);
float z6 = z0;
value += (a6 * a6) * (a6 * a6) * grad(seed,
xrbp + (xNMask & PRIME_X), yrbp + (~yNMask & PRIME_Y), zrbp + (zNMask & PRIME_Z), x6, y6, z6);
}
else
{
float a7 = xAFlipMask0 + zAFlipMask0 + a0;
if (a7 > 0) {
float x7 = x0 - (xNMask | 1);
float y7 = y0;
float z7 = z0 - (zNMask | 1);
value += (a7 * a7) * (a7 * a7) * grad(seed,
xrbp + (~xNMask & PRIME_X), yrbp + (yNMask & PRIME_Y), zrbp + (~zNMask & PRIME_Z), x7, y7, z7);
}
float a8 = yAFlipMask1 + a1;
if (a8 > 0) {
float x8 = x1;
float y8 = (yNMask | 1) + y1;
float z8 = z1;
value += (a8 * a8) * (a8 * a8) * grad(seed2,
xrbp + PRIME_X, yrbp + (yNMask & (PRIME_Y << 1)), zrbp + PRIME_Z, x8, y8, z8);
skip9 = true;
}
}
boolean skipD = false;
float aA = zAFlipMask0 + a0;
if (aA > 0) {
float xA = x0;
float yA = y0;
float zA = z0 - (zNMask | 1);
value += (aA * aA) * (aA * aA) * grad(seed,
xrbp + (xNMask & PRIME_X), yrbp + (yNMask & PRIME_Y), zrbp + (~zNMask & PRIME_Z), xA, yA, zA);
}
else
{
float aB = xAFlipMask0 + yAFlipMask0 + a0;
if (aB > 0) {
float xB = x0 - (xNMask | 1);
float yB = y0 - (yNMask | 1);
float zB = z0;
value += (aB * aB) * (aB * aB) * grad(seed,
xrbp + (~xNMask & PRIME_X), yrbp + (~yNMask & PRIME_Y), zrbp + (zNMask & PRIME_Z), xB, yB, zB);
}
float aC = zAFlipMask1 + a1;
if (aC > 0) {
float xC = x1;
float yC = y1;
float zC = (zNMask | 1) + z1;
value += (aC * aC) * (aC * aC) * grad(seed2,
xrbp + PRIME_X, yrbp + PRIME_Y, zrbp + (zNMask & (PRIME_Z << 1)), xC, yC, zC);
skipD = true;
}
}
if (!skip5) {
float a5 = yAFlipMask1 + zAFlipMask1 + a1;
if (a5 > 0) {
float x5 = x1;
float y5 = (yNMask | 1) + y1;
float z5 = (zNMask | 1) + z1;
value += (a5 * a5) * (a5 * a5) * grad(seed2,
xrbp + PRIME_X, yrbp + (yNMask & (PRIME_Y << 1)), zrbp + (zNMask & (PRIME_Z << 1)), x5, y5, z5);
}
}
if (!skip9) {
float a9 = xAFlipMask1 + zAFlipMask1 + a1;
if (a9 > 0) {
float x9 = (xNMask | 1) + x1;
float y9 = y1;
float z9 = (zNMask | 1) + z1;
value += (a9 * a9) * (a9 * a9) * grad(seed2,
xrbp + (xNMask & (PRIME_X * 2)), yrbp + PRIME_Y, zrbp + (zNMask & (PRIME_Z << 1)), x9, y9, z9);
}
}
if (!skipD) {
float aD = xAFlipMask1 + yAFlipMask1 + a1;
if (aD > 0) {
float xD = (xNMask | 1) + x1;
float yD = (yNMask | 1) + y1;
float zD = z1;
value += (aD * aD) * (aD * aD) * grad(seed2,
xrbp + (xNMask & (PRIME_X << 1)), yrbp + (yNMask & (PRIME_Y << 1)), zrbp + PRIME_Z, xD, yD, zD);
}
}
return value;
}
/**
* 4D SuperSimplex noise, with XYZ oriented like noise3_ImproveXY
* and W for an extra degree of freedom. W repeats eventually.
* Recommended for time-varied animations which texture a 3D object (W=time)
* in a space where Z is vertical
*/
public static float noise4_ImproveXYZ_ImproveXY(long seed, double x, double y, double z, double w) {
double xy = x + y;
double s2 = xy * -0.21132486540518699998;
double zz = z * 0.28867513459481294226;
double ww = w * 1.118033988749894;
double xr = x + (zz + ww + s2), yr = y + (zz + ww + s2);
double zr = xy * -0.57735026918962599998 + (zz + ww);
double wr = z * -0.866025403784439 + ww;
return noise4_UnskewedBase(seed, xr, yr, zr, wr);
}
/**
* 4D SuperSimplex noise, with XYZ oriented like noise3_ImproveXZ
* and W for an extra degree of freedom. W repeats eventually.
* Recommended for time-varied animations which texture a 3D object (W=time)
* in a space where Y is vertical
*/
public static float noise4_ImproveXYZ_ImproveXZ(long seed, double x, double y, double z, double w) {
double xz = x + z;
double s2 = xz * -0.21132486540518699998;
double yy = y * 0.28867513459481294226;
double ww = w * 1.118033988749894;
double xr = x + (yy + ww + s2), zr = z + (yy + ww + s2);
double yr = xz * -0.57735026918962599998 + (yy + ww);
double wr = y * -0.866025403784439 + ww;
return noise4_UnskewedBase(seed, xr, yr, zr, wr);
}
/**
* 4D SuperSimplex noise, with XYZ oriented like noise3_Fallback
* and W for an extra degree of freedom. W repeats eventually.
* Recommended for time-varied animations which texture a 3D object (W=time)
* where there isn't a clear distinction between horizontal and vertical
*/
public static float noise4_ImproveXYZ(long seed, double x, double y, double z, double w) {
double xyz = x + y + z;
double ww = w * 1.118033988749894;
double s2 = xyz * -0.16666666666666666 + ww;
double xs = x + s2, ys = y + s2, zs = z + s2, ws = -0.5 * xyz + ww;
return noise4_UnskewedBase(seed, xs, ys, zs, ws);
}
/**
* 4D SuperSimplex 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 static float noise4_ImproveXY_ImproveZW(long seed, double x, double y, double z, double w) {
double s2 = (x + y) * -0.28522513987434876941 + (z + w) * 0.83897065470611435718;
double t2 = (z + w) * 0.21939749883706435719 + (x + y) * -0.48214856493302476942;
double xs = x + s2, ys = y + s2, zs = z + t2, ws = w + t2;
return noise4_UnskewedBase(seed, xs, ys, zs, ws);
}
/**
* 4D SuperSimplex noise, fallback lattice orientation.
*/
public static float noise4_Fallback(long seed, double x, double y, double z, double w) {
// Get points for A4 lattice
double s = SKEW_4D * (x + y + z + w);
double xs = x + s, ys = y + s, zs = z + s, ws = w + s;
return noise4_UnskewedBase(seed, xs, ys, zs, ws);
}
/**
* 4D SuperSimplex noise base.
* Using ultra-simple 4x4x4x4 lookup partitioning.
* This isn't as elegant or SIMD/GPU/etc. portable as other approaches,
* but it competes performance-wise with optimized 2014 OpenSimplex.
*/
private static float noise4_UnskewedBase(long seed, double xs, double ys, double zs, double ws) {
// Get base points and offsets
int xsb = fastFloor(xs), ysb = fastFloor(ys), zsb = fastFloor(zs), wsb = fastFloor(ws);
float xsi = (float)(xs - xsb), ysi = (float)(ys - ysb), zsi = (float)(zs - zsb), wsi = (float)(ws - wsb);
// Unskewed offsets
float ssi = (xsi + ysi + zsi + wsi) * UNSKEW_4D;
float xi = xsi + ssi, yi = ysi + ssi, zi = zsi + ssi, wi = wsi + ssi;
// Prime pre-multiplication for hash.
long xsvp = xsb * PRIME_X, ysvp = ysb * PRIME_Y, zsvp = zsb * PRIME_Z, wsvp = wsb * PRIME_W;
// Index into initial table.
int index = ((fastFloor(xs * 4) & 3) << 0)
| ((fastFloor(ys * 4) & 3) << 2)
| ((fastFloor(zs * 4) & 3) << 4)
| ((fastFloor(ws * 4) & 3) << 6);
// Point contributions
float value = 0;
int secondaryIndexStartAndStop = LOOKUP_4D_A[index];
int secondaryIndexStart = secondaryIndexStartAndStop & 0xFFFF;
int secondaryIndexStop = secondaryIndexStartAndStop >> 16;
for (int i = secondaryIndexStart; i < secondaryIndexStop; i++) {
LatticeVertex4D c = LOOKUP_4D_B[i];
float dx = xi + c.dx, dy = yi + c.dy, dz = zi + c.dz, dw = wi + c.dw;
float a = (dx * dx + dy * dy) + (dz * dz + dw * dw);
if (a < RSQUARED_4D) {
a -= RSQUARED_4D;
a *= a;
value += a * a * grad(seed, xsvp + c.xsvp, ysvp + c.ysvp, zsvp + c.zsvp, wsvp + c.wsvp, dx, dy, dz, dw);
}
}
return value;
}
/*
* Utility
*/
private static float grad(long seed, long xsvp, long ysvp, float dx, float dy) {
long hash = seed ^ xsvp ^ ysvp;
hash *= HASH_MULTIPLIER;
hash ^= hash >> (64 - N_GRADS_2D_EXPONENT + 1);
int gi = (int)hash & ((N_GRADS_2D - 1) << 1);
return GRADIENTS_2D[gi | 0] * dx + GRADIENTS_2D[gi | 1] * dy;
}
private static float grad(long seed, long xrvp, long yrvp, long zrvp, float dx, float dy, float dz) {
long hash = (seed ^ xrvp) ^ (yrvp ^ zrvp);
hash *= HASH_MULTIPLIER;
hash ^= hash >> (64 - N_GRADS_3D_EXPONENT + 2);
int gi = (int)hash & ((N_GRADS_3D - 1) << 2);
return GRADIENTS_3D[gi | 0] * dx + GRADIENTS_3D[gi | 1] * dy + GRADIENTS_3D[gi | 2] * dz;
}
private static float grad(long seed, long xsvp, long ysvp, long zsvp, long wsvp, float dx, float dy, float dz, float dw) {
long hash = seed ^ (xsvp ^ ysvp) ^ (zsvp ^ wsvp);
hash *= HASH_MULTIPLIER;
hash ^= hash >> (64 - N_GRADS_4D_EXPONENT + 2);
int gi = (int)hash & ((N_GRADS_4D - 1) << 2);
return (GRADIENTS_4D[gi | 0] * dx + GRADIENTS_4D[gi | 1] * dy) + (GRADIENTS_4D[gi | 2] * dz + GRADIENTS_4D[gi | 3] * dw);
}
private static int fastFloor(double x) {
int xi = (int)x;
return x < xi ? xi - 1 : xi;
}
/*
* Lookup Tables & Gradients
*/
private static float[] GRADIENTS_2D;
private static float[] GRADIENTS_3D;
private static float[] GRADIENTS_4D;
private static int[] LOOKUP_4D_A;
private static LatticeVertex4D[] LOOKUP_4D_B;
static {
GRADIENTS_2D = new float[N_GRADS_2D * 2];
float[] grad2 = {
0.38268343236509f, 0.923879532511287f,
0.923879532511287f, 0.38268343236509f,
0.923879532511287f, -0.38268343236509f,
0.38268343236509f, -0.923879532511287f,
-0.38268343236509f, -0.923879532511287f,
-0.923879532511287f, -0.38268343236509f,
-0.923879532511287f, 0.38268343236509f,
-0.38268343236509f, 0.923879532511287f,
//-------------------------------------//
0.130526192220052f, 0.99144486137381f,
0.608761429008721f, 0.793353340291235f,
0.793353340291235f, 0.608761429008721f,
0.99144486137381f, 0.130526192220051f,
0.99144486137381f, -0.130526192220051f,
0.793353340291235f, -0.60876142900872f,
0.608761429008721f, -0.793353340291235f,
0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f,
-0.608761429008721f, -0.793353340291235f,
-0.793353340291235f, -0.608761429008721f,
-0.99144486137381f, -0.130526192220052f,
-0.99144486137381f, 0.130526192220051f,
-0.793353340291235f, 0.608761429008721f,
-0.608761429008721f, 0.793353340291235f,
-0.130526192220052f, 0.99144486137381f,
};
for (int i = 0; i < grad2.length; i++) {
grad2[i] = (float)(grad2[i] / NORMALIZER_2D);
}
for (int i = 0, j = 0; i < GRADIENTS_2D.length; i++, j++) {
if (j == grad2.length) j = 0;
GRADIENTS_2D[i] = grad2[j];
}
GRADIENTS_3D = new float[N_GRADS_3D * 4];
float[] grad3 = {
2.22474487139f, 2.22474487139f, -1.0f, 0.0f,
2.22474487139f, 2.22474487139f, 1.0f, 0.0f,
3.0862664687972017f, 1.1721513422464978f, 0.0f, 0.0f,
1.1721513422464978f, 3.0862664687972017f, 0.0f, 0.0f,
-2.22474487139f, 2.22474487139f, -1.0f, 0.0f,
-2.22474487139f, 2.22474487139f, 1.0f, 0.0f,
-1.1721513422464978f, 3.0862664687972017f, 0.0f, 0.0f,
-3.0862664687972017f, 1.1721513422464978f, 0.0f, 0.0f,
-1.0f, -2.22474487139f, -2.22474487139f, 0.0f,
1.0f, -2.22474487139f, -2.22474487139f, 0.0f,
0.0f, -3.0862664687972017f, -1.1721513422464978f, 0.0f,
0.0f, -1.1721513422464978f, -3.0862664687972017f, 0.0f,
-1.0f, -2.22474487139f, 2.22474487139f, 0.0f,
1.0f, -2.22474487139f, 2.22474487139f, 0.0f,
0.0f, -1.1721513422464978f, 3.0862664687972017f, 0.0f,
0.0f, -3.0862664687972017f, 1.1721513422464978f, 0.0f,
//--------------------------------------------------------------------//
-2.22474487139f, -2.22474487139f, -1.0f, 0.0f,
-2.22474487139f, -2.22474487139f, 1.0f, 0.0f,
-3.0862664687972017f, -1.1721513422464978f, 0.0f, 0.0f,
-1.1721513422464978f, -3.0862664687972017f, 0.0f, 0.0f,
-2.22474487139f, -1.0f, -2.22474487139f, 0.0f,
-2.22474487139f, 1.0f, -2.22474487139f, 0.0f,
-1.1721513422464978f, 0.0f, -3.0862664687972017f, 0.0f,
-3.0862664687972017f, 0.0f, -1.1721513422464978f, 0.0f,
-2.22474487139f, -1.0f, 2.22474487139f, 0.0f,
-2.22474487139f, 1.0f, 2.22474487139f, 0.0f,
-3.0862664687972017f, 0.0f, 1.1721513422464978f, 0.0f,
-1.1721513422464978f, 0.0f, 3.0862664687972017f, 0.0f,
-1.0f, 2.22474487139f, -2.22474487139f, 0.0f,
1.0f, 2.22474487139f, -2.22474487139f, 0.0f,
0.0f, 1.1721513422464978f, -3.0862664687972017f, 0.0f,
0.0f, 3.0862664687972017f, -1.1721513422464978f, 0.0f,
-1.0f, 2.22474487139f, 2.22474487139f, 0.0f,
1.0f, 2.22474487139f, 2.22474487139f, 0.0f,
0.0f, 3.0862664687972017f, 1.1721513422464978f, 0.0f,
0.0f, 1.1721513422464978f, 3.0862664687972017f, 0.0f,
2.22474487139f, -2.22474487139f, -1.0f, 0.0f,
2.22474487139f, -2.22474487139f, 1.0f, 0.0f,
1.1721513422464978f, -3.0862664687972017f, 0.0f, 0.0f,
3.0862664687972017f, -1.1721513422464978f, 0.0f, 0.0f,
2.22474487139f, -1.0f, -2.22474487139f, 0.0f,
2.22474487139f, 1.0f, -2.22474487139f, 0.0f,
3.0862664687972017f, 0.0f, -1.1721513422464978f, 0.0f,
1.1721513422464978f, 0.0f, -3.0862664687972017f, 0.0f,
2.22474487139f, -1.0f, 2.22474487139f, 0.0f,
2.22474487139f, 1.0f, 2.22474487139f, 0.0f,
1.1721513422464978f, 0.0f, 3.0862664687972017f, 0.0f,
3.0862664687972017f, 0.0f, 1.1721513422464978f, 0.0f,
};
for (int i = 0; i < grad3.length; i++) {
grad3[i] = (float)(grad3[i] / NORMALIZER_3D);
}
for (int i = 0, j = 0; i < GRADIENTS_3D.length; i++, j++) {
if (j == grad3.length) j = 0;
GRADIENTS_3D[i] = grad3[j];
}
GRADIENTS_4D = new float[N_GRADS_4D * 4];
float[] grad4 = {
-0.6740059517812944f, -0.3239847771997537f, -0.3239847771997537f, 0.5794684678643381f,
-0.7504883828755602f, -0.4004672082940195f, 0.15296486218853164f, 0.5029860367700724f,
-0.7504883828755602f, 0.15296486218853164f, -0.4004672082940195f, 0.5029860367700724f,
-0.8828161875373585f, 0.08164729285680945f, 0.08164729285680945f, 0.4553054119602712f,
-0.4553054119602712f, -0.08164729285680945f, -0.08164729285680945f, 0.8828161875373585f,
-0.5029860367700724f, -0.15296486218853164f, 0.4004672082940195f, 0.7504883828755602f,
-0.5029860367700724f, 0.4004672082940195f, -0.15296486218853164f, 0.7504883828755602f,
-0.5794684678643381f, 0.3239847771997537f, 0.3239847771997537f, 0.6740059517812944f,
-0.6740059517812944f, -0.3239847771997537f, 0.5794684678643381f, -0.3239847771997537f,
-0.7504883828755602f, -0.4004672082940195f, 0.5029860367700724f, 0.15296486218853164f,
-0.7504883828755602f, 0.15296486218853164f, 0.5029860367700724f, -0.4004672082940195f,
-0.8828161875373585f, 0.08164729285680945f, 0.4553054119602712f, 0.08164729285680945f,
-0.4553054119602712f, -0.08164729285680945f, 0.8828161875373585f, -0.08164729285680945f,
-0.5029860367700724f, -0.15296486218853164f, 0.7504883828755602f, 0.4004672082940195f,
-0.5029860367700724f, 0.4004672082940195f, 0.7504883828755602f, -0.15296486218853164f,
-0.5794684678643381f, 0.3239847771997537f, 0.6740059517812944f, 0.3239847771997537f,
-0.6740059517812944f, 0.5794684678643381f, -0.3239847771997537f, -0.3239847771997537f,
-0.7504883828755602f, 0.5029860367700724f, -0.4004672082940195f, 0.15296486218853164f,
-0.7504883828755602f, 0.5029860367700724f, 0.15296486218853164f, -0.4004672082940195f,
-0.8828161875373585f, 0.4553054119602712f, 0.08164729285680945f, 0.08164729285680945f,
-0.4553054119602712f, 0.8828161875373585f, -0.08164729285680945f, -0.08164729285680945f,
-0.5029860367700724f, 0.7504883828755602f, -0.15296486218853164f, 0.4004672082940195f,
-0.5029860367700724f, 0.7504883828755602f, 0.4004672082940195f, -0.15296486218853164f,
-0.5794684678643381f, 0.6740059517812944f, 0.3239847771997537f, 0.3239847771997537f,
0.5794684678643381f, -0.6740059517812944f, -0.3239847771997537f, -0.3239847771997537f,
0.5029860367700724f, -0.7504883828755602f, -0.4004672082940195f, 0.15296486218853164f,
0.5029860367700724f, -0.7504883828755602f, 0.15296486218853164f, -0.4004672082940195f,
0.4553054119602712f, -0.8828161875373585f, 0.08164729285680945f, 0.08164729285680945f,
0.8828161875373585f, -0.4553054119602712f, -0.08164729285680945f, -0.08164729285680945f,
0.7504883828755602f, -0.5029860367700724f, -0.15296486218853164f, 0.4004672082940195f,
0.7504883828755602f, -0.5029860367700724f, 0.4004672082940195f, -0.15296486218853164f,
0.6740059517812944f, -0.5794684678643381f, 0.3239847771997537f, 0.3239847771997537f,
//------------------------------------------------------------------------------------------//
-0.753341017856078f, -0.37968289875261624f, -0.37968289875261624f, -0.37968289875261624f,
-0.7821684431180708f, -0.4321472685365301f, -0.4321472685365301f, 0.12128480194602098f,
-0.7821684431180708f, -0.4321472685365301f, 0.12128480194602098f, -0.4321472685365301f,
-0.7821684431180708f, 0.12128480194602098f, -0.4321472685365301f, -0.4321472685365301f,
-0.8586508742123365f, -0.508629699630796f, 0.044802370851755174f, 0.044802370851755174f,
-0.8586508742123365f, 0.044802370851755174f, -0.508629699630796f, 0.044802370851755174f,
-0.8586508742123365f, 0.044802370851755174f, 0.044802370851755174f, -0.508629699630796f,
-0.9982828964265062f, -0.03381941603233842f, -0.03381941603233842f, -0.03381941603233842f,
-0.37968289875261624f, -0.753341017856078f, -0.37968289875261624f, -0.37968289875261624f,
-0.4321472685365301f, -0.7821684431180708f, -0.4321472685365301f, 0.12128480194602098f,
-0.4321472685365301f, -0.7821684431180708f, 0.12128480194602098f, -0.4321472685365301f,
0.12128480194602098f, -0.7821684431180708f, -0.4321472685365301f, -0.4321472685365301f,
-0.508629699630796f, -0.8586508742123365f, 0.044802370851755174f, 0.044802370851755174f,
0.044802370851755174f, -0.8586508742123365f, -0.508629699630796f, 0.044802370851755174f,
0.044802370851755174f, -0.8586508742123365f, 0.044802370851755174f, -0.508629699630796f,
-0.03381941603233842f, -0.9982828964265062f, -0.03381941603233842f, -0.03381941603233842f,
-0.37968289875261624f, -0.37968289875261624f, -0.753341017856078f, -0.37968289875261624f,
-0.4321472685365301f, -0.4321472685365301f, -0.7821684431180708f, 0.12128480194602098f,
-0.4321472685365301f, 0.12128480194602098f, -0.7821684431180708f, -0.4321472685365301f,
0.12128480194602098f, -0.4321472685365301f, -0.7821684431180708f, -0.4321472685365301f,
-0.508629699630796f, 0.044802370851755174f, -0.8586508742123365f, 0.044802370851755174f,
0.044802370851755174f, -0.508629699630796f, -0.8586508742123365f, 0.044802370851755174f,
0.044802370851755174f, 0.044802370851755174f, -0.8586508742123365f, -0.508629699630796f,
-0.03381941603233842f, -0.03381941603233842f, -0.9982828964265062f, -0.03381941603233842f,
-0.37968289875261624f, -0.37968289875261624f, -0.37968289875261624f, -0.753341017856078f,
-0.4321472685365301f, -0.4321472685365301f, 0.12128480194602098f, -0.7821684431180708f,
-0.4321472685365301f, 0.12128480194602098f, -0.4321472685365301f, -0.7821684431180708f,
0.12128480194602098f, -0.4321472685365301f, -0.4321472685365301f, -0.7821684431180708f,
-0.508629699630796f, 0.044802370851755174f, 0.044802370851755174f, -0.8586508742123365f,
0.044802370851755174f, -0.508629699630796f, 0.044802370851755174f, -0.8586508742123365f,
0.044802370851755174f, 0.044802370851755174f, -0.508629699630796f, -0.8586508742123365f,
-0.03381941603233842f, -0.03381941603233842f, -0.03381941603233842f, -0.9982828964265062f,
-0.3239847771997537f, -0.6740059517812944f, -0.3239847771997537f, 0.5794684678643381f,
-0.4004672082940195f, -0.7504883828755602f, 0.15296486218853164f, 0.5029860367700724f,
0.15296486218853164f, -0.7504883828755602f, -0.4004672082940195f, 0.5029860367700724f,
0.08164729285680945f, -0.8828161875373585f, 0.08164729285680945f, 0.4553054119602712f,
-0.08164729285680945f, -0.4553054119602712f, -0.08164729285680945f, 0.8828161875373585f,
-0.15296486218853164f, -0.5029860367700724f, 0.4004672082940195f, 0.7504883828755602f,
0.4004672082940195f, -0.5029860367700724f, -0.15296486218853164f, 0.7504883828755602f,
0.3239847771997537f, -0.5794684678643381f, 0.3239847771997537f, 0.6740059517812944f,
-0.3239847771997537f, -0.3239847771997537f, -0.6740059517812944f, 0.5794684678643381f,
-0.4004672082940195f, 0.15296486218853164f, -0.7504883828755602f, 0.5029860367700724f,
0.15296486218853164f, -0.4004672082940195f, -0.7504883828755602f, 0.5029860367700724f,
0.08164729285680945f, 0.08164729285680945f, -0.8828161875373585f, 0.4553054119602712f,
-0.08164729285680945f, -0.08164729285680945f, -0.4553054119602712f, 0.8828161875373585f,
-0.15296486218853164f, 0.4004672082940195f, -0.5029860367700724f, 0.7504883828755602f,
0.4004672082940195f, -0.15296486218853164f, -0.5029860367700724f, 0.7504883828755602f,
0.3239847771997537f, 0.3239847771997537f, -0.5794684678643381f, 0.6740059517812944f,
-0.3239847771997537f, -0.6740059517812944f, 0.5794684678643381f, -0.3239847771997537f,
-0.4004672082940195f, -0.7504883828755602f, 0.5029860367700724f, 0.15296486218853164f,
0.15296486218853164f, -0.7504883828755602f, 0.5029860367700724f, -0.4004672082940195f,
0.08164729285680945f, -0.8828161875373585f, 0.4553054119602712f, 0.08164729285680945f,
-0.08164729285680945f, -0.4553054119602712f, 0.8828161875373585f, -0.08164729285680945f,
-0.15296486218853164f, -0.5029860367700724f, 0.7504883828755602f, 0.4004672082940195f,
0.4004672082940195f, -0.5029860367700724f, 0.7504883828755602f, -0.15296486218853164f,
0.3239847771997537f, -0.5794684678643381f, 0.6740059517812944f, 0.3239847771997537f,
-0.3239847771997537f, -0.3239847771997537f, 0.5794684678643381f, -0.6740059517812944f,
-0.4004672082940195f, 0.15296486218853164f, 0.5029860367700724f, -0.7504883828755602f,
0.15296486218853164f, -0.4004672082940195f, 0.5029860367700724f, -0.7504883828755602f,
0.08164729285680945f, 0.08164729285680945f, 0.4553054119602712f, -0.8828161875373585f,
-0.08164729285680945f, -0.08164729285680945f, 0.8828161875373585f, -0.4553054119602712f,
-0.15296486218853164f, 0.4004672082940195f, 0.7504883828755602f, -0.5029860367700724f,
0.4004672082940195f, -0.15296486218853164f, 0.7504883828755602f, -0.5029860367700724f,
0.3239847771997537f, 0.3239847771997537f, 0.6740059517812944f, -0.5794684678643381f,
-0.3239847771997537f, 0.5794684678643381f, -0.6740059517812944f, -0.3239847771997537f,
-0.4004672082940195f, 0.5029860367700724f, -0.7504883828755602f, 0.15296486218853164f,
0.15296486218853164f, 0.5029860367700724f, -0.7504883828755602f, -0.4004672082940195f,
0.08164729285680945f, 0.4553054119602712f, -0.8828161875373585f, 0.08164729285680945f,
-0.08164729285680945f, 0.8828161875373585f, -0.4553054119602712f, -0.08164729285680945f,
-0.15296486218853164f, 0.7504883828755602f, -0.5029860367700724f, 0.4004672082940195f,
0.4004672082940195f, 0.7504883828755602f, -0.5029860367700724f, -0.15296486218853164f,
0.3239847771997537f, 0.6740059517812944f, -0.5794684678643381f, 0.3239847771997537f,
-0.3239847771997537f, 0.5794684678643381f, -0.3239847771997537f, -0.6740059517812944f,
-0.4004672082940195f, 0.5029860367700724f, 0.15296486218853164f, -0.7504883828755602f,
0.15296486218853164f, 0.5029860367700724f, -0.4004672082940195f, -0.7504883828755602f,
0.08164729285680945f, 0.4553054119602712f, 0.08164729285680945f, -0.8828161875373585f,
-0.08164729285680945f, 0.8828161875373585f, -0.08164729285680945f, -0.4553054119602712f,
-0.15296486218853164f, 0.7504883828755602f, 0.4004672082940195f, -0.5029860367700724f,
0.4004672082940195f, 0.7504883828755602f, -0.15296486218853164f, -0.5029860367700724f,
0.3239847771997537f, 0.6740059517812944f, 0.3239847771997537f, -0.5794684678643381f,
0.5794684678643381f, -0.3239847771997537f, -0.6740059517812944f, -0.3239847771997537f,
0.5029860367700724f, -0.4004672082940195f, -0.7504883828755602f, 0.15296486218853164f,
0.5029860367700724f, 0.15296486218853164f, -0.7504883828755602f, -0.4004672082940195f,
0.4553054119602712f, 0.08164729285680945f, -0.8828161875373585f, 0.08164729285680945f,
0.8828161875373585f, -0.08164729285680945f, -0.4553054119602712f, -0.08164729285680945f,
0.7504883828755602f, -0.15296486218853164f, -0.5029860367700724f, 0.4004672082940195f,
0.7504883828755602f, 0.4004672082940195f, -0.5029860367700724f, -0.15296486218853164f,
0.6740059517812944f, 0.3239847771997537f, -0.5794684678643381f, 0.3239847771997537f,
0.5794684678643381f, -0.3239847771997537f, -0.3239847771997537f, -0.6740059517812944f,
0.5029860367700724f, -0.4004672082940195f, 0.15296486218853164f, -0.7504883828755602f,
0.5029860367700724f, 0.15296486218853164f, -0.4004672082940195f, -0.7504883828755602f,
0.4553054119602712f, 0.08164729285680945f, 0.08164729285680945f, -0.8828161875373585f,
0.8828161875373585f, -0.08164729285680945f, -0.08164729285680945f, -0.4553054119602712f,
0.7504883828755602f, -0.15296486218853164f, 0.4004672082940195f, -0.5029860367700724f,
0.7504883828755602f, 0.4004672082940195f, -0.15296486218853164f, -0.5029860367700724f,
0.6740059517812944f, 0.3239847771997537f, 0.3239847771997537f, -0.5794684678643381f,
0.03381941603233842f, 0.03381941603233842f, 0.03381941603233842f, 0.9982828964265062f,
-0.044802370851755174f, -0.044802370851755174f, 0.508629699630796f, 0.8586508742123365f,
-0.044802370851755174f, 0.508629699630796f, -0.044802370851755174f, 0.8586508742123365f,
-0.12128480194602098f, 0.4321472685365301f, 0.4321472685365301f, 0.7821684431180708f,
0.508629699630796f, -0.044802370851755174f, -0.044802370851755174f, 0.8586508742123365f,
0.4321472685365301f, -0.12128480194602098f, 0.4321472685365301f, 0.7821684431180708f,
0.4321472685365301f, 0.4321472685365301f, -0.12128480194602098f, 0.7821684431180708f,
0.37968289875261624f, 0.37968289875261624f, 0.37968289875261624f, 0.753341017856078f,
0.03381941603233842f, 0.03381941603233842f, 0.9982828964265062f, 0.03381941603233842f,
-0.044802370851755174f, 0.044802370851755174f, 0.8586508742123365f, 0.508629699630796f,
-0.044802370851755174f, 0.508629699630796f, 0.8586508742123365f, -0.044802370851755174f,
-0.12128480194602098f, 0.4321472685365301f, 0.7821684431180708f, 0.4321472685365301f,
0.508629699630796f, -0.044802370851755174f, 0.8586508742123365f, -0.044802370851755174f,
0.4321472685365301f, -0.12128480194602098f, 0.7821684431180708f, 0.4321472685365301f,
0.4321472685365301f, 0.4321472685365301f, 0.7821684431180708f, -0.12128480194602098f,
0.37968289875261624f, 0.37968289875261624f, 0.753341017856078f, 0.37968289875261624f,
0.03381941603233842f, 0.9982828964265062f, 0.03381941603233842f, 0.03381941603233842f,
-0.044802370851755174f, 0.8586508742123365f, -0.044802370851755174f, 0.508629699630796f,
-0.044802370851755174f, 0.8586508742123365f, 0.508629699630796f, -0.044802370851755174f,
-0.12128480194602098f, 0.7821684431180708f, 0.4321472685365301f, 0.4321472685365301f,
0.508629699630796f, 0.8586508742123365f, -0.044802370851755174f, -0.044802370851755174f,
0.4321472685365301f, 0.7821684431180708f, -0.12128480194602098f, 0.4321472685365301f,
0.4321472685365301f, 0.7821684431180708f, 0.4321472685365301f, -0.12128480194602098f,
0.37968289875261624f, 0.753341017856078f, 0.37968289875261624f, 0.37968289875261624f,
0.9982828964265062f, 0.03381941603233842f, 0.03381941603233842f, 0.03381941603233842f,
0.8586508742123365f, -0.044802370851755174f, -0.044802370851755174f, 0.508629699630796f,
0.8586508742123365f, -0.044802370851755174f, 0.508629699630796f, -0.044802370851755174f,
0.7821684431180708f, -0.12128480194602098f, 0.4321472685365301f, 0.4321472685365301f,
0.8586508742123365f, 0.508629699630796f, -0.044802370851755174f, -0.044802370851755174f,
0.7821684431180708f, 0.4321472685365301f, -0.12128480194602098f, 0.4321472685365301f,
0.7821684431180708f, 0.4321472685365301f, 0.4321472685365301f, -0.12128480194602098f,
0.753341017856078f, 0.37968289875261624f, 0.37968289875261624f, 0.37968289875261624f,
};
for (int i = 0; i < grad4.length; i++) {
grad4[i] = (float)(grad4[i] / NORMALIZER_4D);
}
for (int i = 0, j = 0; i < GRADIENTS_4D.length; i++, j++) {
if (j == grad4.length) j = 0;
GRADIENTS_4D[i] = grad4[j];
}
int[][] lookup4DVertexCodes = {
new int[] { 0x15, 0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x15, 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xAA },
new int[] { 0x01, 0x05, 0x11, 0x15, 0x41, 0x45, 0x51, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA },
new int[] { 0x01, 0x15, 0x16, 0x45, 0x46, 0x51, 0x52, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x15, 0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA9, 0xAA },
new int[] { 0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xAA },
new int[] { 0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xAA },
new int[] { 0x05, 0x15, 0x16, 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xAA, 0xAB },
new int[] { 0x04, 0x05, 0x14, 0x15, 0x44, 0x45, 0x54, 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA },
new int[] { 0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA },
new int[] { 0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x9A, 0xAA },
new int[] { 0x05, 0x15, 0x16, 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x6A, 0x9A, 0xAA, 0xAB },
new int[] { 0x04, 0x15, 0x19, 0x45, 0x49, 0x54, 0x55, 0x58, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA, 0xAE },
new int[] { 0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x5E, 0x6A, 0x9A, 0xAA, 0xAE },
new int[] { 0x05, 0x15, 0x1A, 0x45, 0x4A, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x5E, 0x6A, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x15, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x11, 0x15, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xAA },
new int[] { 0x11, 0x15, 0x51, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x96, 0xA6, 0xAA },
new int[] { 0x11, 0x15, 0x16, 0x51, 0x52, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x96, 0xA6, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x99, 0xA5, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x9A, 0xA6, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x15, 0x16, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x6B, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x54, 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x99, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x9A, 0xAA },
new int[] { 0x15, 0x16, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x6B, 0x9A, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x19, 0x54, 0x55, 0x58, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x99, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x19, 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x6E, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x19, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x6E, 0x9A, 0xAA, 0xAE },
new int[] { 0x15, 0x1A, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x6B, 0x6E, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x10, 0x11, 0x14, 0x15, 0x50, 0x51, 0x54, 0x55, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x11, 0x15, 0x51, 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xAA },
new int[] { 0x11, 0x15, 0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0xA6, 0xAA },
new int[] { 0x11, 0x15, 0x16, 0x51, 0x52, 0x55, 0x56, 0x65, 0x66, 0x67, 0x6A, 0xA6, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x54, 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA6, 0xAA },
new int[] { 0x15, 0x16, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x6B, 0xA6, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xAA },
new int[] { 0x15, 0x16, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x6B, 0xAA, 0xAB },
new int[] { 0x14, 0x15, 0x19, 0x54, 0x55, 0x58, 0x59, 0x65, 0x69, 0x6A, 0x6D, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x19, 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x6E, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x19, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x6E, 0xAA, 0xAE },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x69, 0x6A, 0x6B, 0x6E, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x10, 0x15, 0x25, 0x51, 0x54, 0x55, 0x61, 0x64, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x11, 0x15, 0x25, 0x51, 0x55, 0x56, 0x61, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xAA, 0xBA },
new int[] { 0x11, 0x15, 0x25, 0x51, 0x55, 0x56, 0x61, 0x65, 0x66, 0x6A, 0x76, 0xA6, 0xAA, 0xBA },
new int[] { 0x11, 0x15, 0x26, 0x51, 0x55, 0x56, 0x62, 0x65, 0x66, 0x67, 0x6A, 0x76, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x14, 0x15, 0x25, 0x54, 0x55, 0x59, 0x64, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x25, 0x55, 0x65, 0x66, 0x69, 0x6A, 0x7A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x25, 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0x7A, 0xA6, 0xAA, 0xBA },
new int[] { 0x15, 0x26, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x6B, 0x7A, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x14, 0x15, 0x25, 0x54, 0x55, 0x59, 0x64, 0x65, 0x69, 0x6A, 0x79, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x25, 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x7A, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x25, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x7A, 0xAA, 0xBA },
new int[] { 0x15, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x6B, 0x7A, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x14, 0x15, 0x29, 0x54, 0x55, 0x59, 0x65, 0x68, 0x69, 0x6A, 0x6D, 0x79, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x15, 0x29, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x6E, 0x7A, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x15, 0x55, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x6E, 0x7A, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x6B, 0x6E, 0x7A, 0xAA, 0xAB, 0xAE, 0xBA, 0xBF },
new int[] { 0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xAA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x5A, 0x66, 0x95, 0x96, 0x9A, 0xA6, 0xAA },
new int[] { 0x41, 0x45, 0x46, 0x51, 0x52, 0x55, 0x56, 0x5A, 0x66, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x45, 0x46, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x5A, 0x69, 0x95, 0x99, 0x9A, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xAA },
new int[] { 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x96, 0x9A, 0x9B, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x49, 0x54, 0x55, 0x58, 0x59, 0x5A, 0x69, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x49, 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x99, 0x9A, 0x9E, 0xAA, 0xAE },
new int[] { 0x45, 0x4A, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x9A, 0x9B, 0x9E, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x95, 0x96, 0x99, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x59, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB },
new int[] { 0x51, 0x52, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xA7, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x56, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x15, 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x58, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAD, 0xAE },
new int[] { 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x66, 0x69, 0x95, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xAA },
new int[] { 0x51, 0x52, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x96, 0xA6, 0xA7, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xBA },
new int[] { 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0xA5, 0xA9, 0xAA },
new int[] { 0x15, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xBA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x9A, 0xA6, 0xA9, 0xAA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x58, 0x59, 0x65, 0x69, 0x6A, 0x99, 0xA9, 0xAA, 0xAD, 0xAE },
new int[] { 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x69, 0x6A, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x61, 0x64, 0x65, 0x66, 0x69, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x51, 0x55, 0x61, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x61, 0x65, 0x66, 0x6A, 0xA5, 0xA6, 0xAA, 0xB6, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x62, 0x65, 0x66, 0x6A, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x64, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA },
new int[] { 0x55, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x55, 0x56, 0x65, 0x66, 0x6A, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x59, 0x64, 0x65, 0x69, 0x6A, 0xA5, 0xA9, 0xAA, 0xB9, 0xBA },
new int[] { 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x15, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x68, 0x69, 0x6A, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA, 0xBE },
new int[] { 0x55, 0x59, 0x65, 0x69, 0x6A, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x15, 0x55, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0xAA, 0xAB, 0xAE, 0xBA, 0xBF },
new int[] { 0x40, 0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xAA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x95, 0x96, 0x9A, 0xA6, 0xAA },
new int[] { 0x41, 0x45, 0x46, 0x51, 0x52, 0x55, 0x56, 0x95, 0x96, 0x97, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA },
new int[] { 0x45, 0x46, 0x55, 0x56, 0x5A, 0x95, 0x96, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x95, 0x99, 0x9A, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xAA },
new int[] { 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9B, 0xAA, 0xAB },
new int[] { 0x44, 0x45, 0x49, 0x54, 0x55, 0x58, 0x59, 0x95, 0x99, 0x9A, 0x9D, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x49, 0x55, 0x59, 0x5A, 0x95, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9E, 0xAA, 0xAE },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x96, 0x99, 0x9A, 0x9B, 0x9E, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0x96, 0x99, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA },
new int[] { 0x51, 0x52, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA6, 0xA7, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xEA },
new int[] { 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA },
new int[] { 0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x58, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAD, 0xAE },
new int[] { 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xAE },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x96, 0x99, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA },
new int[] { 0x51, 0x52, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x51, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB },
new int[] { 0x54, 0x55, 0x58, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE },
new int[] { 0x54, 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x66, 0x69, 0x6A, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xAF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x61, 0x64, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB5, 0xBA },
new int[] { 0x51, 0x55, 0x61, 0x65, 0x66, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x61, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xB6, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x64, 0x65, 0x69, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA },
new int[] { 0x55, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x96, 0xA5, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x59, 0x64, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xB9, 0xBA },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA },
new int[] { 0x55, 0x56, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xBA, 0xBB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA, 0xBE },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x99, 0xA5, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x55, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xBA },
new int[] { 0x40, 0x45, 0x51, 0x54, 0x55, 0x85, 0x91, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x85, 0x91, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xAA, 0xEA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x85, 0x91, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xD6, 0xEA },
new int[] { 0x41, 0x45, 0x51, 0x55, 0x56, 0x86, 0x92, 0x95, 0x96, 0x97, 0x9A, 0xA6, 0xAA, 0xAB, 0xD6, 0xEA, 0xEB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x85, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x55, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xDA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xDA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x86, 0x95, 0x96, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB, 0xDA, 0xEA, 0xEB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x85, 0x94, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xD9, 0xEA },
new int[] { 0x45, 0x55, 0x59, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xDA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xAA, 0xDA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB, 0xDA, 0xEA, 0xEB },
new int[] { 0x44, 0x45, 0x54, 0x55, 0x59, 0x89, 0x95, 0x98, 0x99, 0x9A, 0x9D, 0xA9, 0xAA, 0xAE, 0xD9, 0xEA, 0xEE },
new int[] { 0x45, 0x55, 0x59, 0x89, 0x95, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE, 0xDA, 0xEA, 0xEE },
new int[] { 0x45, 0x55, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE, 0xDA, 0xEA, 0xEE },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9B, 0x9E, 0xAA, 0xAB, 0xAE, 0xDA, 0xEA, 0xEF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x91, 0x94, 0x95, 0x96, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x51, 0x55, 0x91, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xE6, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x91, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xE6, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x92, 0x95, 0x96, 0x9A, 0xA6, 0xA7, 0xAA, 0xAB, 0xE6, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xE9, 0xEA },
new int[] { 0x55, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x55, 0x56, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x55, 0x56, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x59, 0x94, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xE9, 0xEA },
new int[] { 0x55, 0x59, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x45, 0x55, 0x56, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x59, 0x95, 0x98, 0x99, 0x9A, 0xA9, 0xAA, 0xAD, 0xAE, 0xE9, 0xEA, 0xEE },
new int[] { 0x55, 0x59, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE },
new int[] { 0x45, 0x55, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xAA, 0xAB, 0xAE, 0xEA, 0xEF },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x91, 0x94, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xE5, 0xEA },
new int[] { 0x51, 0x55, 0x65, 0x91, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xE6, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x91, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xE6, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xE6, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x65, 0x94, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xE9, 0xEA },
new int[] { 0x55, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x94, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xE9, 0xEA },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x55, 0x56, 0x59, 0x65, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA },
new int[] { 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xEA, 0xEB },
new int[] { 0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xE9, 0xEA, 0xEE },
new int[] { 0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE },
new int[] { 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xEA },
new int[] { 0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0xA1, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB5, 0xBA, 0xE5, 0xEA, 0xFA },
new int[] { 0x51, 0x55, 0x65, 0x95, 0xA1, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA, 0xFA },
new int[] { 0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA, 0xFA },
new int[] { 0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA, 0xE6, 0xEA, 0xFB },
new int[] { 0x54, 0x55, 0x65, 0x95, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA, 0xFA },
new int[] { 0x55, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA },
new int[] { 0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA },
new int[] { 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xAB, 0xBA, 0xEA, 0xFB },
new int[] { 0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA, 0xFA },
new int[] { 0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA },
new int[] { 0x55, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA },
new int[] { 0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xBA, 0xEA },
new int[] { 0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA, 0xE9, 0xEA, 0xFE },
new int[] { 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAE, 0xBA, 0xEA, 0xFE },
new int[] { 0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xBA, 0xEA },
new int[] { 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xBA, 0xEA },
};
LatticeVertex4D[] latticeVerticesByCode = new LatticeVertex4D[256];
for (int i = 0; i < 256; i++) {
int cx = ((i >> 0) & 3) - 1;
int cy = ((i >> 2) & 3) - 1;
int cz = ((i >> 4) & 3) - 1;
int cw = ((i >> 6) & 3) - 1;
latticeVerticesByCode[i] = new LatticeVertex4D(cx, cy, cz, cw);
}
int nLatticeVerticesTotal = 0;
for (int i = 0; i < 256; i++) {
nLatticeVerticesTotal += lookup4DVertexCodes[i].length;
}
LOOKUP_4D_A = new int[256];
LOOKUP_4D_B = new LatticeVertex4D[nLatticeVerticesTotal];
for (int i = 0, j = 0; i < 256; i++) {
LOOKUP_4D_A[i] = j | ((j + lookup4DVertexCodes[i].length) << 16);
for (int k = 0; k < lookup4DVertexCodes[i].length; k++) {
LOOKUP_4D_B[j++] = latticeVerticesByCode[lookup4DVertexCodes[i][k]];
}
}
}
private static class LatticeVertex4D {
public final float dx, dy, dz, dw;
public final long xsvp, ysvp, zsvp, wsvp;
public LatticeVertex4D(int xsv, int ysv, int zsv, int wsv) {
this.xsvp = xsv * PRIME_X; this.ysvp = ysv * PRIME_Y;
this.zsvp = zsv * PRIME_Z; this.wsvp = wsv * PRIME_W;
float ssv = (xsv + ysv + zsv + wsv) * UNSKEW_4D;
this.dx = -xsv - ssv;
this.dy = -ysv - ssv;
this.dz = -zsv - ssv;
this.dw = -wsv - ssv;
}
}
}
Raw
OpenSimplexDemo.java
/*
* OpenSimplex2S Noise sample class.
*/
import java.awt.image.BufferedImage;
import javax.imageio.ImageIO;
import java.io.*;
public class OpenSimplexDemo
{
private static final long SEED = 0;
private static final int WIDTH = 512;
private static final int HEIGHT = 512;
private static final double FREQUENCY = 1.0 / 24.0;
public static void main(String[] args)
throws IOException {
BufferedImage image = new BufferedImage(WIDTH, HEIGHT, BufferedImage.TYPE_INT_RGB);
for (int y = 0; y < HEIGHT; y++)
{
for (int x = 0; x < WIDTH; x++)
{
double value = OpenSimplex2S.noise3_ImproveXY(SEED, x * FREQUENCY, y * FREQUENCY, 0.0);
int rgb = 0x010101 * (int)((value + 1) * 127.5);
image.setRGB(x, y, rgb);
}
}
ImageIO.write(image, "png", new File("noise.png"));
}
}
Raw
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@oloflarsson
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Here is another example of someone struggling with the "chance" problem:
http://stackoverflow.com/questions/3696747/generation-of-uniformly-distributed-random-noise

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ghost commented Apr 27, 2015

This is fantastic. Thank you! I am deff going to give you credit in my work.

@afonsolage
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Awesome work! This was exactly what I was looking for. I'll add to my project and, of course, keep your name on it!!!

@Asmageddon
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Bloody hell, this is a freaking long source. Any chance of a shorter implementation, perhaps a GLSL one?

@tyronx
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tyronx commented Feb 16, 2016

Shouldn't it generate noise between -1 and 1? For the 2d implementation it seems to generate more like within an area of -0.87 to +0.87

I thing the norm constants haven't been chosen quite right.

@CreamyCookie
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@KdotJPG There seem to be few unused assignments: smcameron/open-simplex-noise-in-c#4

Any idea?

@ghandhikus
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// Iterations: 100000000
2DOpenSimplexNoise speed: 6498.520513ms // this
2DSimplexNoise speed: 5000.267634ms // http://staffwww.itn.liu.se/~stegu/simplexnoise/SimplexNoise.java

// Iterations: 1000000
2DOpenSimplexNoise speed: 111.175103ms
2DSimplexNoise speed: 73.051068ms

////////////////////////////////////////////////////////////////
// After adding final to both implementation like so "public final class Name"
// Also I've separated the tests to avoid hot and cold scenario

// Iterations: 100000000
2DOpenSimplexNoise speed: 5702.409891ms
2DOpenSimplexNoise speed: 5675.584907ms
2DOpenSimplexNoise speed: 5863.16953ms
2DSimplexNoise speed: 4633.812286ms
2DSimplexNoise speed: 4524.991414ms
2DSimplexNoise speed: 4492.767565ms
2DSimplexNoise speed: 4649.350849ms
2DSimplexNoise speed: 4455.254193ms
2DSimplexNoise speed: 4633.330702ms
2DSimplexNoise speed: 4550.094936ms

// Best scenarios in this test
//
// 2DOpenSimplexNoise - 5675.584907ms
// 2DSimplexNoise - 4455.254193ms

// Worst scenarios in this test
//
// 2DOpenSimplexNoise - 5863.16953ms
// 2DSimplexNoise - 4649.350849ms

////////////////////////////////////////////////////////////////
// After removing final
2DOpenSimplexNoise speed: 5724.589568ms
2DOpenSimplexNoise speed: 5842.842763ms
2DOpenSimplexNoise speed: 5804.29675ms
2DOpenSimplexNoise speed: 5665.408102ms
2DSimplexNoise speed: 4581.063116ms
2DSimplexNoise speed: 4530.74752ms
2DSimplexNoise speed: 4590.37899ms
2DSimplexNoise speed: 4504.37333ms

// final seems to make no difference in this code

// Best scenarios in this test
//
// 2DOpenSimplexNoise - 5665.408102ms
// 2DSimplexNoise - 4504.37333ms

// Worst scenarios in this test
//
// 2DOpenSimplexNoise - 5842.842763ms
// 2DSimplexNoise - 4590.37899ms
////////////////////////////////////////////////////////////////

code:

public class SimplexNoisePerformanceTests {

	private static int iterations = 100000000;
	private static double x = 0.5447734756785486781d;
	private static double y = 0.4923141242323442d;
	
	public @Test void simplexNoise() {
		final double[] result = new double[iterations];
		final long start = System.nanoTime();
		for (int i = 0; i < iterations; i++)
			result[i] = SimplexNoise.noise(i*x, i*y);
		long end = System.nanoTime() - start;
		System.out.println("2DSimplexNoise speed: "+(end/1000000d)+"ms");
	}
	
	public @Test void openSimplexNoise() {
		final double[] result = new double[iterations];
		final OpenSimplexNoise simplex = new OpenSimplexNoise();
		long start = System.nanoTime();
		for (int i = 0; i < iterations; i++)
			result[i] = simplex.eval(i*x, i*y);
		long end = System.nanoTime() - start;
		System.out.println("2DOpenSimplexNoise speed: "+(end/1000000d)+"ms");
	}
}

@Porama6400
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Look like it's never touch -1 or 1
it's around -0.8 to +0.8

@Chovanec
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Chovanec commented Jun 1, 2017

agree with Porama6400 interval should be betwwn -1 to 1, how to change code to get correct values?

@blah1
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blah1 commented Jun 26, 2017

https://eev.ee/blog/2016/05/29/perlin-noise/
Near the bottom, under "Some properties"

Contrary to popular belief — one espoused even by Ken Perlin! — the output range of Perlin noise is not -1 to 1. It’s ±½√n, where n is the number of dimensions. So a 1-D plane can never extend beyond -½ or ½ (which I bet you could prove if you thought about it), and the familiar 2-D noise is trapped within ±½√2 ≈ ±0.707 (which is also provable by extending the same thought a little further). If you’re using Perlin noise and expecting to span a specific range, make sure to take this into account.

I believe this should explain your issues with the range on OpenSimplex Noise; for 3D noise it would have a amplitude of ~0.866.

@thecjharries
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What's the reason for shifting seed by 31 while permuting (source)? It seems like, for positive or negative seed, it would just shift the input up by 31, which could be taken care of in the LCG. I spent a decent amount of time researching that, and I couldn't find anything. Does it provide an extra layer of randomness on the off-chance the LCG aligns perfectly with the denominator?

@jearmstrong21
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I am doing eval(x,y,z,0) (4d noise with w=0) and it gives a range of about:

-0.6512914, 0.6200971
-0.77198315, 0.7699929
-0.6705122, 0.68826705

This is in a sample range of 16x256x16x0, or at point (x,y,z) the noise is eval(x,y,z,0).

Shouldnt it be +-(1/2)sqrt(4) = +-(1/2)2 = +-1?

@s5bug
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s5bug commented Oct 7, 2018

@KdotJPG Please explain what all the different constants mean, how you got to them, and why this code can't be generalized to n dimensions instead of just 2, 3, and 4. I want to write my own implementation in pure scala but this code is just a huge monster to tackle I can't really do it without explanation of the algorithm.

@cjburkey01
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@KdotJPG Please explain what all the different constants mean, how you got to them, and why this code can't be generalized to n dimensions instead of just 2, 3, and 4. I want to write my own implementation in pure scala but this code is just a huge monster to tackle I can't really do it without explanation of the algorithm.

The actual paper is here, but it requires some higher level mathematics to understand: http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf

OpenSimplex Noise, according to This Wikipedia Page, is slightly different in its implementation, though, in that:

  • It uses a stretched simplectic honeycomb instead of a hypercubic honeycomb
  • OpenSimplex noise uses a larger kernel size than Simplex noise, which results in slightly lost performance.

@nonchip
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nonchip commented Mar 23, 2019

@cjburkey01

the paper you linked explains perlin vs simplex, not opensimplex.

@Manuel3115
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Very good code thanks ! Only 1 question : how do you decrease the amplitude of the noise ? I'm getting a lot of big spikes in the values. I'd rather have bigger clusters of similar values. Thank you !

@benlmyers
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This is amazing!

@FoxSamu
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FoxSamu commented Jun 16, 2020

Amazing! I use a modified version of this implementation in a small procedural terrain generator library: https://github.com/RedGalaxySW/Noise. Thanks a lot!

@MarcoCiaramella
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Thanks!
I made an Android library version from the latest revision
https://github.com/MarcoCiaramella/OpenSimplexNoise

@KdotJPG
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Author

KdotJPG commented Jul 28, 2020

@MarcoCiaramella Very cool! Out of curiosity, why not use the optimized version or even OpenSimplex2S? Either way I like that you continued with the public domain license.

@MarcoCiaramella
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@KdotJPG ok good thanks for your advice, I will do that!

@MarcoCiaramella
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C implementation https://github.com/MarcoCiaramella/OpenSimplex2

@MarcoCiaramella
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GPU implementation in OpenCL https://github.com/MarcoCiaramella/OpenSimplex2/tree/main/GPU/OpenCL

@Pentagonist
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Thank you for this code!

@erik-alm
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agree with Porama6400 interval should be betwwn -1 to 1, how to change code to get correct values?

Normalization? (or even split normalization depending on above or below 0).

Isn't this supposed to be "random" from the seed? In that case it will never be -1 → 1 unless you normalize it to be that.

@bakabird
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This is amazing!!!

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