package monkstone.noise; /** * K.jpg's OpenSimplex 2, smooth variant ("SuperSimplex") * * - 2D is standard simplex, modified to support larger kernels. Implemented * using a lookup table. - 3D is "Re-oriented 8-point BCC noise" which * constructs a congruent BCC lattice in a much different way than usual. - 4D * uses a naïve pregenerated lookup table, and averages out to the expected * performance. * * Multiple versions of each function are provided. See the documentation above * each, for more info. */ public class OpenSimplex2S { 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 OpenSimplex2S(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 SuperSimplex 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 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. * * @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 SuperSimplex 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 a = (int) (xsi + ysi); int index = (a << 2) | (int) (xsi - ysi / 2 + 1 - a / 2.0) << 3 | (int) (ysi - xsi / 2 + 1 - a / 2.0) << 4; double ssi = (xsi + ysi) * -0.211324865405187; double xi = xsi + ssi, yi = ysi + ssi; // Point contributions for (int i = 0; i < 4; i++) { LatticePoint2D c = LOOKUP_2D[index + i]; double dx = xi + c.dx, dy = yi + c.dy; double attn = 2.0 / 3.0 - 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 8-point BCC noise, classic orientation Proper substitute * for what 3D SuperSimplex would be, 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 8-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 z * @param y * @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 8-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 8 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 = 0.75 - 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 SuperSimplex noise, classic lattice orientation. * * @param x * @param y * @param z * @param w * @return */ public double noise4_Classic(double x, double y, double z, double w) { // Get points for A4 lattice double s = 0.309016994374947 * (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 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. * * @param x * @param y * @param z * @param w * @return */ public double noise4_XYBeforeZW(double x, double y, double z, double w) { double s2 = (x + y) * -0.28522513987434876941 + (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_Base(xs, ys, zs, ws); } /** * 4D SuperSimplex 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 y * @param z * @param w * @return */ public double noise4_XZBeforeYW(double x, double y, double z, double w) { double s2 = (x + z) * -0.28522513987434876941 + (y + w) * 0.83897065470611435718; double t2 = (y + w) * 0.21939749883706435719 + (x + z) * -0.48214856493302476942; double xs = x + s2, ys = y + t2, zs = z + s2, ws = w + t2; return noise4_Base(xs, ys, zs, ws); } /** * 4D SuperSimplex noise, with XYZ oriented like noise3_Classic, and W for * an extra degree of freedom.Recommended for time-varied animations which * texture a 3D object (W=time) * * @param x * @param y * @param z * @param w * @return */ public double noise4_XYZBeforeW(double x, double y, double z, double w) { double xyz = x + y + z; double ww = w * 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_Base(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 does compete performance-wise with optimized * OpenSimplex1. */ 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; // Unskewed offsets double ssi = (xsi + ysi + zsi + wsi) * -0.138196601125011; double xi = xsi + ssi, yi = ysi + ssi, zi = zsi + ssi, wi = wsi + ssi; int index = ((fastFloor(xs * 4) & 3)) | ((fastFloor(ys * 4) & 3) << 2) | ((fastFloor(zs * 4) & 3) << 4) | ((fastFloor(ws * 4) & 3) << 6); // Point contributions for (LatticePoint4D c : LOOKUP_4D[index]) { double dx = xi + c.dx, dy = yi + c.dy, dz = zi + c.dz, dw = wi + c.dw; double attn = 0.8 - dx * dx - dy * dy - dz * dz - dw * dw; if (attn > 0) { attn *= attn; int pxm = (xsb + c.xsv) & PMASK, pym = (ysb + c.ysv) & PMASK; int pzm = (zsb + c.zsv) & PMASK, pwm = (wsb + c.wsv) & PMASK; Grad4 grad = permGrad4[perm[perm[perm[pxm] ^ pym] ^ pzm] ^ pwm]; double extrapolation = grad.dx * dx + grad.dy * dy + grad.dz * dz + grad.dw * dw; value += attn * attn * extrapolation; } } 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[][] LOOKUP_4D; static { LOOKUP_2D = new LatticePoint2D[8 * 4]; LOOKUP_3D = new LatticePoint3D[8]; LOOKUP_4D = new LatticePoint4D[256][]; for (int i = 0; i < 8; i++) { int i1, j1, i2, j2; if ((i & 1) == 0) { if ((i & 2) == 0) { i1 = -1; j1 = 0; } else { i1 = 1; j1 = 0; } if ((i & 4) == 0) { i2 = 0; j2 = -1; } else { i2 = 0; j2 = 1; } } else { if ((i & 2) != 0) { i1 = 2; j1 = 1; } else { i1 = 0; j1 = 1; } if ((i & 4) != 0) { i2 = 1; j2 = 2; } else { i2 = 1; j2 = 0; } } LOOKUP_2D[i * 4 + 0] = new LatticePoint2D(0, 0); LOOKUP_2D[i * 4 + 1] = new LatticePoint2D(1, 1); LOOKUP_2D[i * 4 + 2] = new LatticePoint2D(i1, j1); LOOKUP_2D[i * 4 + 3] = new LatticePoint2D(i2, j2); } 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); // (1, 0, 0) vs (0, 1, 1) away from octant. LatticePoint3D c2 = new LatticePoint3D(i1 ^ 1, j1, k1, 0); LatticePoint3D c3 = new LatticePoint3D(i1, j1 ^ 1, k1 ^ 1, 0); // (1, 0, 0) vs (0, 1, 1) away from octant, on second half-lattice. LatticePoint3D c4 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + k2, 1); LatticePoint3D c5 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + (k2 ^ 1), 1); // (0, 1, 0) vs (1, 0, 1) away from octant. LatticePoint3D c6 = new LatticePoint3D(i1, j1 ^ 1, k1, 0); LatticePoint3D c7 = new LatticePoint3D(i1 ^ 1, j1, k1 ^ 1, 0); // (0, 1, 0) vs (1, 0, 1) away from octant, on second half-lattice. LatticePoint3D c8 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + k2, 1); LatticePoint3D c9 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + (k2 ^ 1), 1); // (0, 0, 1) vs (1, 1, 0) away from octant. LatticePoint3D cA = new LatticePoint3D(i1, j1, k1 ^ 1, 0); LatticePoint3D cB = new LatticePoint3D(i1 ^ 1, j1 ^ 1, k1, 0); // (0, 0, 1) vs (1, 1, 0) away from octant, on second half-lattice. LatticePoint3D cC = new LatticePoint3D(i1 + i2, j1 + j2, k1 + (k2 ^ 1), 1); LatticePoint3D cD = new LatticePoint3D(i1 + (i2 ^ 1), j1 + (j2 ^ 1), k1 + k2, 1); // First two points are guaranteed. c0.nextOnFailure = c0.nextOnSuccess = c1; c1.nextOnFailure = c1.nextOnSuccess = c2; // If c2 is in range, then we know c3 and c4 are not. c2.nextOnFailure = c3; c2.nextOnSuccess = c5; c3.nextOnFailure = c4; c3.nextOnSuccess = c4; // If c4 is in range, then we know c5 is not. c4.nextOnFailure = c5; c4.nextOnSuccess = c6; c5.nextOnFailure = c5.nextOnSuccess = c6; // If c6 is in range, then we know c7 and c8 are not. c6.nextOnFailure = c7; c6.nextOnSuccess = c9; c7.nextOnFailure = c8; c7.nextOnSuccess = c8; // If c8 is in range, then we know c9 is not. c8.nextOnFailure = c9; c8.nextOnSuccess = cA; c9.nextOnFailure = c9.nextOnSuccess = cA; // If cA is in range, then we know cB and cC are not. cA.nextOnFailure = cB; cA.nextOnSuccess = cD; cB.nextOnFailure = cC; cB.nextOnSuccess = cC; // If cC is in range, then we know cD is not. cC.nextOnFailure = cD; cC.nextOnSuccess = null; cD.nextOnFailure = cD.nextOnSuccess = null; LOOKUP_3D[i] = c0; } int[][] lookup4DPregen = { {0x15, 0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA}, {0x15, 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xAA}, {0x01, 0x05, 0x11, 0x15, 0x41, 0x45, 0x51, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA}, {0x01, 0x15, 0x16, 0x45, 0x46, 0x51, 0x52, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xA6, 0xAA, 0xAB}, {0x15, 0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA9, 0xAA}, {0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xAA}, {0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xAA}, {0x05, 0x15, 0x16, 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x96, 0x9A, 0xAA, 0xAB}, {0x04, 0x05, 0x14, 0x15, 0x44, 0x45, 0x54, 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA}, {0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA}, {0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x9A, 0xAA}, {0x05, 0x15, 0x16, 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x6A, 0x9A, 0xAA, 0xAB}, {0x04, 0x15, 0x19, 0x45, 0x49, 0x54, 0x55, 0x58, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xA9, 0xAA, 0xAE}, {0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA, 0xAE}, {0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x5E, 0x6A, 0x9A, 0xAA, 0xAE}, {0x05, 0x15, 0x1A, 0x45, 0x4A, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x5E, 0x6A, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF}, {0x15, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9, 0xAA}, {0x11, 0x15, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xAA}, {0x11, 0x15, 0x51, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x96, 0xA6, 0xAA}, {0x11, 0x15, 0x16, 0x51, 0x52, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x96, 0xA6, 0xAA, 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0xEA}, {0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xE6, 0xEA, 0xEB}, {0x54, 0x55, 0x65, 0x94, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xE9, 0xEA}, {0x55, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA}, {0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA}, {0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB}, {0x54, 0x55, 0x59, 0x65, 0x69, 0x94, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xE9, 0xEA}, {0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA}, {0x55, 0x56, 0x59, 0x65, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA}, {0x55, 0x56, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xEA, 0xEB}, {0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xE9, 0xEA, 0xEE}, {0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE}, {0x55, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE}, {0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xEA}, {0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0xA1, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB5, 0xBA, 0xE5, 0xEA, 0xFA}, {0x51, 0x55, 0x65, 0x95, 0xA1, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA, 0xFA}, {0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA, 0xFA}, {0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA, 0xE6, 0xEA, 0xFB}, {0x54, 0x55, 0x65, 0x95, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA, 0xFA}, {0x55, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA}, {0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA}, {0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xAB, 0xBA, 0xEA, 0xFB}, {0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA, 0xFA}, {0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA}, {0x55, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA}, {0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xBA, 0xEA}, {0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA, 0xE9, 0xEA, 0xFE}, {0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAE, 0xBA, 0xEA, 0xFE}, {0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xBA, 0xEA}, {0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE, 0xBA, 0xEA},}; LatticePoint4D[] latticePoints = new LatticePoint4D[256]; for (int i = 0; i < 256; i++) { int cx = ((i) & 3) - 1; int cy = ((i >> 2) & 3) - 1; int cz = ((i >> 4) & 3) - 1; int cw = ((i >> 6) & 3) - 1; latticePoints[i] = new LatticePoint4D(cx, cy, cz, cw); } for (int i = 0; i < 256; i++) { LOOKUP_4D[i] = new LatticePoint4D[lookup4DPregen[i].length]; for (int j = 0; j < lookup4DPregen[i].length; j++) { LOOKUP_4D[i][j] = latticePoints[lookup4DPregen[i][j]]; } } } 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; public LatticePoint4D(int xsv, int ysv, int zsv, int wsv) { this.xsv = xsv; this.ysv = ysv; this.zsv = zsv; this.wsv = wsv; double ssv = (xsv + ysv + zsv + wsv) * -0.138196601125011; this.dx = -xsv - ssv; this.dy = -ysv - ssv; this.dz = -zsv - ssv; this.dw = -wsv - ssv; } } /* * 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 = 0.05481866495625118; private static final double N3 = 0.2781926117527186; private static final double N4 = 0.11127401889945551; 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) }; Grad2[] grad2XBeforeY = new Grad2[grad2.length]; 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, 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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, 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