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 OpenSimplex2F { private static final int PSIZE = 2048; private static final int PMASK = 2047; private final short[] perm; private final Grad2[] permGrad2; private final Grad3[] permGrad3; private final Grad4[] permGrad4; /** * * @param seed */ public OpenSimplex2F(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, classic orientation.Proper substitute * for 3D Simplex in light of Forbidden Formulae.Use noise3_XYBeforeZ or * noise3_XZBeforeY instead, wherever appropriate. * * @param x * @param y * @param z * @return */ public double noise3_Classic(double x, double y, double z) { // Re-orient the cubic lattices via rotation, to produce the expected look on cardinal planar slices. // If texturing objects that don't tend to have cardinal plane faces, you could even remove this. // Orthonormal rotation. Not a skew transform. double r = (2.0 / 3.0) * (x + y + z); double xr = r - x, yr = r - y, zr = r - z; // Evaluate both lattices to form a BCC lattice. return noise3_BCC(xr, yr, zr); } /** * 3D Re-oriented 4-point BCC noise, with better visual isotropy in (X, * Y).Recommended for 3D terrain and time-varied animations.The Z coordinate * should always be the "different" coordinate in your use case.If Y is * vertical in world coordinates, call noise3_XYBeforeZ(x, z, Y) or use * noise3_XZBeforeY.If Z is vertical in world coordinates, call * noise3_XYBeforeZ(x, y, Z). For a time varied animation, call * noise3_XYBeforeZ(x, y, T). * * @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 OpenSimplex2F noise, classic lattice orientation. * * @param x * @param y * @param w * @param z * @return */ public double noise4_Classic(double x, double y, double z, double w) { // Get points for A4 lattice double s = -0.138196601125011 * (x + y + z + w); double xs = x + s, ys = y + s, zs = z + s, ws = w + s; return noise4_Base(xs, ys, zs, ws); } /** * 4D OpenSimplex2F noise, with XY and ZW forming orthogonal * triangular-based planes.Recommended for 3D terrain, where X and Y (or Z * and W) are horizontal.Recommended for noise(x, y, sin(time), cos(time)) * trick. * * @param x * @param z * @param y * @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 OpenSimplex2F noise, with XZ and YW forming orthogonal * triangular-based planes.Recommended for 3D terrain, where X and Z (or Y * and W) are horizontal. * * @param x * @param z * @param y * @param w * @return */ public double noise4_XZBeforeYW(double x, double y, double z, double w) { double s2 = (x + z) * -0.178275657951399372 + (y + w) * 0.215623393288842828; double t2 = (y + w) * -0.403949762580207112 + (x + z) * -0.375199083010075342; double xs = x + s2, ys = y + t2, zs = z + s2, ws = w + t2; return noise4_Base(xs, ys, zs, ws); } /** * 4D OpenSimplex2F noise, with XYZ oriented like noise3_Classic, and W for * an extra degree of freedom.W repeats eventually.Recommended for * time-varied animations which texture a 3D object (W=time) * * @param x * @param w * @param y * @param z * @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 OpenSimplex2F noise base. Current implementation not fully optimized * by lookup tables. But still comes out slightly ahead of Gustavson's * Simplex in tests. */ private double noise4_Base(double xs, double ys, double zs, double ws) { 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); } } 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 = 0.2 - xsv; this.ysi = 0.2 - ysv; this.zsi = 0.2 - zsv; this.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, 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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, 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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]; } } }