package lib; /* * OpenSimplex Noise in Java. * by Kurt Spencer * * v1.1 (October 5, 2014) * - Added 2D and 4D implementations. * - Proper gradient sets for all dimensions, from a * dimensionally-generalizable scheme with an actual * rhyme and reason behind it. * - Removed default permutation array in favor of * default seed. * - Changed seed-based constructor to be independent * of any particular randomization library, so results * will be the same when ported to other languages. */ public class OpenSimplexNoise { private static final double STRETCH_CONSTANT_2D = -0.211324865405187; //(1/Math.sqrt(2+1)-1)/2; private static final double SQUISH_CONSTANT_2D = 0.366025403784439; //(Math.sqrt(2+1)-1)/2; private static final double STRETCH_CONSTANT_3D = -1.0 / 6; //(1/Math.sqrt(3+1)-1)/3; private static final double SQUISH_CONSTANT_3D = 1.0 / 3; //(Math.sqrt(3+1)-1)/3; private static final double STRETCH_CONSTANT_4D = -0.138196601125011; //(1/Math.sqrt(4+1)-1)/4; private static final double SQUISH_CONSTANT_4D = 0.309016994374947; //(Math.sqrt(4+1)-1)/4; private static final double NORM_CONSTANT_2D = 47; private static final double NORM_CONSTANT_3D = 103; private static final double NORM_CONSTANT_4D = 30; private static final long DEFAULT_SEED = 0; private short[] perm; private short[] permGradIndex3D; public OpenSimplexNoise() { this(DEFAULT_SEED); } public OpenSimplexNoise(short[] perm) { this.perm = perm; permGradIndex3D = new short[256]; for (int i = 0; i < 256; i++) { //Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. permGradIndex3D[i] = (short)((perm[i] % (gradients3D.length / 3)) * 3); } } //Initializes the class using a permutation array generated from a 64-bit seed. //Generates a proper permutation (i.e. doesn't merely perform N successive pair swaps on a base array) //Uses a simple 64-bit LCG. public OpenSimplexNoise(long seed) { perm = new short[256]; permGradIndex3D = new short[256]; short[] source = new short[256]; for (short i = 0; i < 256; i++) source[i] = i; seed = seed * 6364136223846793005l + 1442695040888963407l; seed = seed * 6364136223846793005l + 1442695040888963407l; seed = seed * 6364136223846793005l + 1442695040888963407l; for (int i = 255; i >= 0; i--) { seed = seed * 6364136223846793005l + 1442695040888963407l; int r = (int)((seed + 31) % (i + 1)); if (r < 0) r += (i + 1); perm[i] = source[r]; permGradIndex3D[i] = (short)((perm[i] % (gradients3D.length / 3)) * 3); source[r] = source[i]; } } //2D OpenSimplex Noise. public double eval(double x, double y) { //Place input coordinates onto grid. double stretchOffset = (x + y) * STRETCH_CONSTANT_2D; double xs = x + stretchOffset; double ys = y + stretchOffset; //Floor to get grid coordinates of rhombus (stretched square) super-cell origin. int xsb = fastFloor(xs); int ysb = fastFloor(ys); //Skew out to get actual coordinates of rhombus origin. We'll need these later. double squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D; double xb = xsb + squishOffset; double yb = ysb + squishOffset; //Compute grid coordinates relative to rhombus origin. double xins = xs - xsb; double yins = ys - ysb; //Sum those together to get a value that determines which region we're in. double inSum = xins + yins; //Positions relative to origin point. double dx0 = x - xb; double dy0 = y - yb; //We'll be defining these inside the next block and using them afterwards. double dx_ext, dy_ext; int xsv_ext, ysv_ext; double value = 0; //Contribution (1,0) double dx1 = dx0 - 1 - SQUISH_CONSTANT_2D; double dy1 = dy0 - 0 - SQUISH_CONSTANT_2D; double attn1 = 2 - dx1 * dx1 - dy1 * dy1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1); } //Contribution (0,1) double dx2 = dx0 - 0 - SQUISH_CONSTANT_2D; double dy2 = dy0 - 1 - SQUISH_CONSTANT_2D; double attn2 = 2 - dx2 * dx2 - dy2 * dy2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2); } if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0) double zins = 1 - inSum; if (zins > xins || zins > yins) { //(0,0) is one of the closest two triangular vertices if (xins > yins) { xsv_ext = xsb + 1; ysv_ext = ysb - 1; dx_ext = dx0 - 1; dy_ext = dy0 + 1; } else { xsv_ext = xsb - 1; ysv_ext = ysb + 1; dx_ext = dx0 + 1; dy_ext = dy0 - 1; } } else { //(1,0) and (0,1) are the closest two vertices. xsv_ext = xsb + 1; ysv_ext = ysb + 1; dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D; dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; } } else { //We're inside the triangle (2-Simplex) at (1,1) double zins = 2 - inSum; if (zins < xins || zins < yins) { //(0,0) is one of the closest two triangular vertices if (xins > yins) { xsv_ext = xsb + 2; ysv_ext = ysb + 0; dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D; dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D; } else { xsv_ext = xsb + 0; ysv_ext = ysb + 2; dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D; dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D; } } else { //(1,0) and (0,1) are the closest two vertices. dx_ext = dx0; dy_ext = dy0; xsv_ext = xsb; ysv_ext = ysb; } xsb += 1; ysb += 1; dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D; dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; } //Contribution (0,0) or (1,1) double attn0 = 2 - dx0 * dx0 - dy0 * dy0; if (attn0 > 0) { attn0 *= attn0; value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0); } //Extra Vertex double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; if (attn_ext > 0) { attn_ext *= attn_ext; value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext); } return value / NORM_CONSTANT_2D; } //3D OpenSimplex Noise. public double eval(double x, double y, double z) { //Place input coordinates on simplectic honeycomb. double stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D; double xs = x + stretchOffset; double ys = y + stretchOffset; double zs = z + stretchOffset; //Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. int xsb = fastFloor(xs); int ysb = fastFloor(ys); int zsb = fastFloor(zs); //Skew out to get actual coordinates of rhombohedron origin. We'll need these later. double squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D; double xb = xsb + squishOffset; double yb = ysb + squishOffset; double zb = zsb + squishOffset; //Compute simplectic honeycomb coordinates relative to rhombohedral origin. double xins = xs - xsb; double yins = ys - ysb; double zins = zs - zsb; //Sum those together to get a value that determines which region we're in. double inSum = xins + yins + zins; //Positions relative to origin point. double dx0 = x - xb; double dy0 = y - yb; double dz0 = z - zb; //We'll be defining these inside the next block and using them afterwards. double dx_ext0, dy_ext0, dz_ext0; double dx_ext1, dy_ext1, dz_ext1; int xsv_ext0, ysv_ext0, zsv_ext0; int xsv_ext1, ysv_ext1, zsv_ext1; double value = 0; if (inSum <= 1) { //We're inside the tetrahedron (3-Simplex) at (0,0,0) //Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest. byte aPoint = 0x01; double aScore = xins; byte bPoint = 0x02; double bScore = yins; if (aScore >= bScore && zins > bScore) { bScore = zins; bPoint = 0x04; } else if (aScore < bScore && zins > aScore) { aScore = zins; aPoint = 0x04; } //Now we determine the two lattice points not part of the tetrahedron that may contribute. //This depends on the closest two tetrahedral vertices, including (0,0,0) double wins = 1 - inSum; if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices. byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. if ((c & 0x01) == 0) { xsv_ext0 = xsb - 1; xsv_ext1 = xsb; dx_ext0 = dx0 + 1; dx_ext1 = dx0; } else { xsv_ext0 = xsv_ext1 = xsb + 1; dx_ext0 = dx_ext1 = dx0 - 1; } if ((c & 0x02) == 0) { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0; if ((c & 0x01) == 0) { ysv_ext1 -= 1; dy_ext1 += 1; } else { ysv_ext0 -= 1; dy_ext0 += 1; } } else { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1; } if ((c & 0x04) == 0) { zsv_ext0 = zsb; zsv_ext1 = zsb - 1; dz_ext0 = dz0; dz_ext1 = dz0 + 1; } else { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz_ext1 = dz0 - 1; } } else { //(0,0,0) is not one of the closest two tetrahedral vertices. byte c = (byte)(aPoint | bPoint); //Our two extra vertices are determined by the closest two. if ((c & 0x01) == 0) { xsv_ext0 = xsb; xsv_ext1 = xsb - 1; dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D; dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; } else { xsv_ext0 = xsv_ext1 = xsb + 1; dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; } if ((c & 0x02) == 0) { ysv_ext0 = ysb; ysv_ext1 = ysb - 1; dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; } else { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; } if ((c & 0x04) == 0) { zsv_ext0 = zsb; zsv_ext1 = zsb - 1; dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; } else { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; } } //Contribution (0,0,0) double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; if (attn0 > 0) { attn0 *= attn0; value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); } //Contribution (1,0,0) double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); } //Contribution (0,1,0) double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; double dz2 = dz1; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); } //Contribution (0,0,1) double dx3 = dx2; double dy3 = dy1; double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); } } else if (inSum >= 2) { //We're inside the tetrahedron (3-Simplex) at (1,1,1) //Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). byte aPoint = 0x06; double aScore = xins; byte bPoint = 0x05; double bScore = yins; if (aScore <= bScore && zins < bScore) { bScore = zins; bPoint = 0x03; } else if (aScore > bScore && zins < aScore) { aScore = zins; aPoint = 0x03; } //Now we determine the two lattice points not part of the tetrahedron that may contribute. //This depends on the closest two tetrahedral vertices, including (1,1,1) double wins = 3 - inSum; if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices. byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. if ((c & 0x01) != 0) { xsv_ext0 = xsb + 2; xsv_ext1 = xsb + 1; dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D; dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; } else { xsv_ext0 = xsv_ext1 = xsb; dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D; } if ((c & 0x02) != 0) { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; if ((c & 0x01) != 0) { ysv_ext1 += 1; dy_ext1 -= 1; } else { ysv_ext0 += 1; dy_ext0 -= 1; } } else { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D; } if ((c & 0x04) != 0) { zsv_ext0 = zsb + 1; zsv_ext1 = zsb + 2; dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D; } else { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D; } } else { //(1,1,1) is not one of the closest two tetrahedral vertices. byte c = (byte)(aPoint & bPoint); //Our two extra vertices are determined by the closest two. if ((c & 0x01) != 0) { xsv_ext0 = xsb + 1; xsv_ext1 = xsb + 2; dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; } else { xsv_ext0 = xsv_ext1 = xsb; dx_ext0 = dx0 - SQUISH_CONSTANT_3D; dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; } if ((c & 0x02) != 0) { ysv_ext0 = ysb + 1; ysv_ext1 = ysb + 2; dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; } else { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy0 - SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; } if ((c & 0x04) != 0) { zsv_ext0 = zsb + 1; zsv_ext1 = zsb + 2; dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; } else { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz0 - SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; } } //Contribution (1,1,0) double dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; double dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; double dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3); } //Contribution (1,0,1) double dx2 = dx3; double dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; double dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2); } //Contribution (0,1,1) double dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; double dy1 = dy3; double dz1 = dz2; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1); } //Contribution (1,1,1) dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; if (attn0 > 0) { attn0 *= attn0; value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); } } else { //We're inside the octahedron (Rectified 3-Simplex) in between. double aScore; byte aPoint; boolean aIsFurtherSide; double bScore; byte bPoint; boolean bIsFurtherSide; //Decide between point (0,0,1) and (1,1,0) as closest double p1 = xins + yins; if (p1 > 1) { aScore = p1 - 1; aPoint = 0x03; aIsFurtherSide = true; } else { aScore = 1 - p1; aPoint = 0x04; aIsFurtherSide = false; } //Decide between point (0,1,0) and (1,0,1) as closest double p2 = xins + zins; if (p2 > 1) { bScore = p2 - 1; bPoint = 0x05; bIsFurtherSide = true; } else { bScore = 1 - p2; bPoint = 0x02; bIsFurtherSide = false; } //The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer. double p3 = yins + zins; if (p3 > 1) { double score = p3 - 1; if (aScore <= bScore && aScore < score) { aScore = score; aPoint = 0x06; aIsFurtherSide = true; } else if (aScore > bScore && bScore < score) { bScore = score; bPoint = 0x06; bIsFurtherSide = true; } } else { double score = 1 - p3; if (aScore <= bScore && aScore < score) { aScore = score; aPoint = 0x01; aIsFurtherSide = false; } else if (aScore > bScore && bScore < score) { bScore = score; bPoint = 0x01; bIsFurtherSide = false; } } //Where each of the two closest points are determines how the extra two vertices are calculated. if (aIsFurtherSide == bIsFurtherSide) { if (aIsFurtherSide) { //Both closest points on (1,1,1) side //One of the two extra points is (1,1,1) dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; xsv_ext0 = xsb + 1; ysv_ext0 = ysb + 1; zsv_ext0 = zsb + 1; //Other extra point is based on the shared axis. byte c = (byte)(aPoint & bPoint); if ((c & 0x01) != 0) { dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; xsv_ext1 = xsb + 2; ysv_ext1 = ysb; zsv_ext1 = zsb; } else if ((c & 0x02) != 0) { dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; xsv_ext1 = xsb; ysv_ext1 = ysb + 2; zsv_ext1 = zsb; } else { dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; xsv_ext1 = xsb; ysv_ext1 = ysb; zsv_ext1 = zsb + 2; } } else {//Both closest points on (0,0,0) side //One of the two extra points is (0,0,0) dx_ext0 = dx0; dy_ext0 = dy0; dz_ext0 = dz0; xsv_ext0 = xsb; ysv_ext0 = ysb; zsv_ext0 = zsb; //Other extra point is based on the omitted axis. byte c = (byte)(aPoint | bPoint); if ((c & 0x01) == 0) { dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; xsv_ext1 = xsb - 1; ysv_ext1 = ysb + 1; zsv_ext1 = zsb + 1; } else if ((c & 0x02) == 0) { dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; xsv_ext1 = xsb + 1; ysv_ext1 = ysb - 1; zsv_ext1 = zsb + 1; } else { dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; xsv_ext1 = xsb + 1; ysv_ext1 = ysb + 1; zsv_ext1 = zsb - 1; } } } else { //One point on (0,0,0) side, one point on (1,1,1) side byte c1, c2; if (aIsFurtherSide) { c1 = aPoint; c2 = bPoint; } else { c1 = bPoint; c2 = aPoint; } //One contribution is a permutation of (1,1,-1) if ((c1 & 0x01) == 0) { dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D; dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; xsv_ext0 = xsb - 1; ysv_ext0 = ysb + 1; zsv_ext0 = zsb + 1; } else if ((c1 & 0x02) == 0) { dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D; dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; xsv_ext0 = xsb + 1; ysv_ext0 = ysb - 1; zsv_ext0 = zsb + 1; } else { dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D; xsv_ext0 = xsb + 1; ysv_ext0 = ysb + 1; zsv_ext0 = zsb - 1; } //One contribution is a permutation of (0,0,2) dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; xsv_ext1 = xsb; ysv_ext1 = ysb; zsv_ext1 = zsb; if ((c2 & 0x01) != 0) { dx_ext1 -= 2; xsv_ext1 += 2; } else if ((c2 & 0x02) != 0) { dy_ext1 -= 2; ysv_ext1 += 2; } else { dz_ext1 -= 2; zsv_ext1 += 2; } } //Contribution (1,0,0) double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); } //Contribution (0,1,0) double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; double dz2 = dz1; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); } //Contribution (0,0,1) double dx3 = dx2; double dy3 = dy1; double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); } //Contribution (1,1,0) double dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; double dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; double dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4; if (attn4 > 0) { attn4 *= attn4; value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4); } //Contribution (1,0,1) double dx5 = dx4; double dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; double dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5; if (attn5 > 0) { attn5 *= attn5; value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5); } //Contribution (0,1,1) double dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; double dy6 = dy4; double dz6 = dz5; double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6; if (attn6 > 0) { attn6 *= attn6; value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6); } } //First extra vertex double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0; if (attn_ext0 > 0) { attn_ext0 *= attn_ext0; value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); } //Second extra vertex double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1; if (attn_ext1 > 0) { attn_ext1 *= attn_ext1; value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); } return value / NORM_CONSTANT_3D; } //4D OpenSimplex Noise. public double eval(double x, double y, double z, double w) { //Place input coordinates on simplectic honeycomb. double stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D; double xs = x + stretchOffset; double ys = y + stretchOffset; double zs = z + stretchOffset; double ws = w + stretchOffset; //Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. int xsb = fastFloor(xs); int ysb = fastFloor(ys); int zsb = fastFloor(zs); int wsb = fastFloor(ws); //Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. double squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D; double xb = xsb + squishOffset; double yb = ysb + squishOffset; double zb = zsb + squishOffset; double wb = wsb + squishOffset; //Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin. double xins = xs - xsb; double yins = ys - ysb; double zins = zs - zsb; double wins = ws - wsb; //Sum those together to get a value that determines which region we're in. double inSum = xins + yins + zins + wins; //Positions relative to origin point. double dx0 = x - xb; double dy0 = y - yb; double dz0 = z - zb; double dw0 = w - wb; //We'll be defining these inside the next block and using them afterwards. double dx_ext0, dy_ext0, dz_ext0, dw_ext0; double dx_ext1, dy_ext1, dz_ext1, dw_ext1; double dx_ext2, dy_ext2, dz_ext2, dw_ext2; int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0; int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1; int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2; double value = 0; if (inSum <= 1) { //We're inside the pentachoron (4-Simplex) at (0,0,0,0) //Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest. byte aPoint = 0x01; double aScore = xins; byte bPoint = 0x02; double bScore = yins; if (aScore >= bScore && zins > bScore) { bScore = zins; bPoint = 0x04; } else if (aScore < bScore && zins > aScore) { aScore = zins; aPoint = 0x04; } if (aScore >= bScore && wins > bScore) { bScore = wins; bPoint = 0x08; } else if (aScore < bScore && wins > aScore) { aScore = wins; aPoint = 0x08; } //Now we determine the three lattice points not part of the pentachoron that may contribute. //This depends on the closest two pentachoron vertices, including (0,0,0,0) double uins = 1 - inSum; if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices. byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. if ((c & 0x01) == 0) { xsv_ext0 = xsb - 1; xsv_ext1 = xsv_ext2 = xsb; dx_ext0 = dx0 + 1; dx_ext1 = dx_ext2 = dx0; } else { xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1; } if ((c & 0x02) == 0) { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; dy_ext0 = dy_ext1 = dy_ext2 = dy0; if ((c & 0x01) == 0x01) { ysv_ext0 -= 1; dy_ext0 += 1; } else { ysv_ext1 -= 1; dy_ext1 += 1; } } else { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1; } if ((c & 0x04) == 0) { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; dz_ext0 = dz_ext1 = dz_ext2 = dz0; if ((c & 0x03) != 0) { if ((c & 0x03) == 0x03) { zsv_ext0 -= 1; dz_ext0 += 1; } else { zsv_ext1 -= 1; dz_ext1 += 1; } } else { zsv_ext2 -= 1; dz_ext2 += 1; } } else { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1; } if ((c & 0x08) == 0) { wsv_ext0 = wsv_ext1 = wsb; wsv_ext2 = wsb - 1; dw_ext0 = dw_ext1 = dw0; dw_ext2 = dw0 + 1; } else { wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1; } } else { //(0,0,0,0) is not one of the closest two pentachoron vertices. byte c = (byte)(aPoint | bPoint); //Our three extra vertices are determined by the closest two. if ((c & 0x01) == 0) { xsv_ext0 = xsv_ext2 = xsb; xsv_ext1 = xsb - 1; dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D; dx_ext2 = dx0 - SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x02) == 0) { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D; if ((c & 0x01) == 0x01) { ysv_ext1 -= 1; dy_ext1 += 1; } else { ysv_ext2 -= 1; dy_ext2 += 1; } } else { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x04) == 0) { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D; if ((c & 0x03) == 0x03) { zsv_ext1 -= 1; dz_ext1 += 1; } else { zsv_ext2 -= 1; dz_ext2 += 1; } } else { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x08) == 0) { wsv_ext0 = wsv_ext1 = wsb; wsv_ext2 = wsb - 1; dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - SQUISH_CONSTANT_4D; dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D; } } //Contribution (0,0,0,0) double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; if (attn0 > 0) { attn0 *= attn0; value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0); } //Contribution (1,0,0,0) double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); } //Contribution (0,1,0,0) double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; double dz2 = dz1; double dw2 = dw1; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); } //Contribution (0,0,1,0) double dx3 = dx2; double dy3 = dy1; double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; double dw3 = dw1; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); } //Contribution (0,0,0,1) double dx4 = dx2; double dy4 = dy1; double dz4 = dz1; double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; if (attn4 > 0) { attn4 *= attn4; value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); } } else if (inSum >= 3) { //We're inside the pentachoron (4-Simplex) at (1,1,1,1) //Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. byte aPoint = 0x0E; double aScore = xins; byte bPoint = 0x0D; double bScore = yins; if (aScore <= bScore && zins < bScore) { bScore = zins; bPoint = 0x0B; } else if (aScore > bScore && zins < aScore) { aScore = zins; aPoint = 0x0B; } if (aScore <= bScore && wins < bScore) { bScore = wins; bPoint = 0x07; } else if (aScore > bScore && wins < aScore) { aScore = wins; aPoint = 0x07; } //Now we determine the three lattice points not part of the pentachoron that may contribute. //This depends on the closest two pentachoron vertices, including (0,0,0,0) double uins = 4 - inSum; if (uins < aScore || uins < bScore) { //(1,1,1,1) is one of the closest two pentachoron vertices. byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. if ((c & 0x01) != 0) { xsv_ext0 = xsb + 2; xsv_ext1 = xsv_ext2 = xsb + 1; dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D; dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D; } if ((c & 0x02) != 0) { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; if ((c & 0x01) != 0) { ysv_ext1 += 1; dy_ext1 -= 1; } else { ysv_ext0 += 1; dy_ext0 -= 1; } } else { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D; } if ((c & 0x04) != 0) { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; if ((c & 0x03) != 0x03) { if ((c & 0x03) == 0) { zsv_ext0 += 1; dz_ext0 -= 1; } else { zsv_ext1 += 1; dz_ext1 -= 1; } } else { zsv_ext2 += 1; dz_ext2 -= 1; } } else { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D; } if ((c & 0x08) != 0) { wsv_ext0 = wsv_ext1 = wsb + 1; wsv_ext2 = wsb + 2; dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D; } } else { //(1,1,1,1) is not one of the closest two pentachoron vertices. byte c = (byte)(aPoint & bPoint); //Our three extra vertices are determined by the closest two. if ((c & 0x01) != 0) { xsv_ext0 = xsv_ext2 = xsb + 1; xsv_ext1 = xsb + 2; dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x02) != 0) { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c & 0x01) != 0) { ysv_ext2 += 1; dy_ext2 -= 1; } else { ysv_ext1 += 1; dy_ext1 -= 1; } } else { ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x04) != 0) { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c & 0x03) != 0) { zsv_ext2 += 1; dz_ext2 -= 1; } else { zsv_ext1 += 1; dz_ext1 -= 1; } } else { zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x08) != 0) { wsv_ext0 = wsv_ext1 = wsb + 1; wsv_ext2 = wsb + 2; dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D; } } //Contribution (1,1,1,0) double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; if (attn4 > 0) { attn4 *= attn4; value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); } //Contribution (1,1,0,1) double dx3 = dx4; double dy3 = dy4; double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); } //Contribution (1,0,1,1) double dx2 = dx4; double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; double dz2 = dz4; double dw2 = dw3; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); } //Contribution (0,1,1,1) double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; double dz1 = dz4; double dy1 = dy4; double dw1 = dw3; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); } //Contribution (1,1,1,1) dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; if (attn0 > 0) { attn0 *= attn0; value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0); } } else if (inSum <= 2) { //We're inside the first dispentachoron (Rectified 4-Simplex) double aScore; byte aPoint; boolean aIsBiggerSide = true; double bScore; byte bPoint; boolean bIsBiggerSide = true; //Decide between (1,1,0,0) and (0,0,1,1) if (xins + yins > zins + wins) { aScore = xins + yins; aPoint = 0x03; } else { aScore = zins + wins; aPoint = 0x0C; } //Decide between (1,0,1,0) and (0,1,0,1) if (xins + zins > yins + wins) { bScore = xins + zins; bPoint = 0x05; } else { bScore = yins + wins; bPoint = 0x0A; } //Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. if (xins + wins > yins + zins) { double score = xins + wins; if (aScore >= bScore && score > bScore) { bScore = score; bPoint = 0x09; } else if (aScore < bScore && score > aScore) { aScore = score; aPoint = 0x09; } } else { double score = yins + zins; if (aScore >= bScore && score > bScore) { bScore = score; bPoint = 0x06; } else if (aScore < bScore && score > aScore) { aScore = score; aPoint = 0x06; } } //Decide if (1,0,0,0) is closer. double p1 = 2 - inSum + xins; if (aScore >= bScore && p1 > bScore) { bScore = p1; bPoint = 0x01; bIsBiggerSide = false; } else if (aScore < bScore && p1 > aScore) { aScore = p1; aPoint = 0x01; aIsBiggerSide = false; } //Decide if (0,1,0,0) is closer. double p2 = 2 - inSum + yins; if (aScore >= bScore && p2 > bScore) { bScore = p2; bPoint = 0x02; bIsBiggerSide = false; } else if (aScore < bScore && p2 > aScore) { aScore = p2; aPoint = 0x02; aIsBiggerSide = false; } //Decide if (0,0,1,0) is closer. double p3 = 2 - inSum + zins; if (aScore >= bScore && p3 > bScore) { bScore = p3; bPoint = 0x04; bIsBiggerSide = false; } else if (aScore < bScore && p3 > aScore) { aScore = p3; aPoint = 0x04; aIsBiggerSide = false; } //Decide if (0,0,0,1) is closer. double p4 = 2 - inSum + wins; if (aScore >= bScore && p4 > bScore) { bScore = p4; bPoint = 0x08; bIsBiggerSide = false; } else if (aScore < bScore && p4 > aScore) { aScore = p4; aPoint = 0x08; aIsBiggerSide = false; } //Where each of the two closest points are determines how the extra three vertices are calculated. if (aIsBiggerSide == bIsBiggerSide) { if (aIsBiggerSide) { //Both closest points on the bigger side byte c1 = (byte)(aPoint | bPoint); byte c2 = (byte)(aPoint & bPoint); if ((c1 & 0x01) == 0) { xsv_ext0 = xsb; xsv_ext1 = xsb - 1; dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsb + 1; dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; } if ((c1 & 0x02) == 0) { ysv_ext0 = ysb; ysv_ext1 = ysb - 1; dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D; dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D; } else { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; } if ((c1 & 0x04) == 0) { zsv_ext0 = zsb; zsv_ext1 = zsb - 1; dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D; dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D; } else { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; } if ((c1 & 0x08) == 0) { wsv_ext0 = wsb; wsv_ext1 = wsb - 1; dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsb + 1; dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; } //One combination is a permutation of (0,0,0,2) based on c2 xsv_ext2 = xsb; ysv_ext2 = ysb; zsv_ext2 = zsb; wsv_ext2 = wsb; dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; if ((c2 & 0x01) != 0) { xsv_ext2 += 2; dx_ext2 -= 2; } else if ((c2 & 0x02) != 0) { ysv_ext2 += 2; dy_ext2 -= 2; } else if ((c2 & 0x04) != 0) { zsv_ext2 += 2; dz_ext2 -= 2; } else { wsv_ext2 += 2; dw_ext2 -= 2; } } else { //Both closest points on the smaller side //One of the two extra points is (0,0,0,0) xsv_ext2 = xsb; ysv_ext2 = ysb; zsv_ext2 = zsb; wsv_ext2 = wsb; dx_ext2 = dx0; dy_ext2 = dy0; dz_ext2 = dz0; dw_ext2 = dw0; //Other two points are based on the omitted axes. byte c = (byte)(aPoint | bPoint); if ((c & 0x01) == 0) { xsv_ext0 = xsb - 1; xsv_ext1 = xsb; dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; dx_ext1 = dx0 - SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsb + 1; dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x02) == 0) { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; if ((c & 0x01) == 0x01) { ysv_ext0 -= 1; dy_ext0 += 1; } else { ysv_ext1 -= 1; dy_ext1 += 1; } } else { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x04) == 0) { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; if ((c & 0x03) == 0x03) { zsv_ext0 -= 1; dz_ext0 += 1; } else { zsv_ext1 -= 1; dz_ext1 += 1; } } else { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; } if ((c & 0x08) == 0) { wsv_ext0 = wsb; wsv_ext1 = wsb - 1; dw_ext0 = dw0 - SQUISH_CONSTANT_4D; dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsb + 1; dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; } } } else { //One point on each "side" byte c1, c2; if (aIsBiggerSide) { c1 = aPoint; c2 = bPoint; } else { c1 = bPoint; c2 = aPoint; } //Two contributions are the bigger-sided point with each 0 replaced with -1. if ((c1 & 0x01) == 0) { xsv_ext0 = xsb - 1; xsv_ext1 = xsb; dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; dx_ext1 = dx0 - SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsb + 1; dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; } if ((c1 & 0x02) == 0) { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; if ((c1 & 0x01) == 0x01) { ysv_ext0 -= 1; dy_ext0 += 1; } else { ysv_ext1 -= 1; dy_ext1 += 1; } } else { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; } if ((c1 & 0x04) == 0) { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; if ((c1 & 0x03) == 0x03) { zsv_ext0 -= 1; dz_ext0 += 1; } else { zsv_ext1 -= 1; dz_ext1 += 1; } } else { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; } if ((c1 & 0x08) == 0) { wsv_ext0 = wsb; wsv_ext1 = wsb - 1; dw_ext0 = dw0 - SQUISH_CONSTANT_4D; dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsb + 1; dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; } //One contribution is a permutation of (0,0,0,2) based on the smaller-sided point xsv_ext2 = xsb; ysv_ext2 = ysb; zsv_ext2 = zsb; wsv_ext2 = wsb; dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; if ((c2 & 0x01) != 0) { xsv_ext2 += 2; dx_ext2 -= 2; } else if ((c2 & 0x02) != 0) { ysv_ext2 += 2; dy_ext2 -= 2; } else if ((c2 & 0x04) != 0) { zsv_ext2 += 2; dz_ext2 -= 2; } else { wsv_ext2 += 2; dw_ext2 -= 2; } } //Contribution (1,0,0,0) double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); } //Contribution (0,1,0,0) double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; double dz2 = dz1; double dw2 = dw1; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); } //Contribution (0,0,1,0) double dx3 = dx2; double dy3 = dy1; double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; double dw3 = dw1; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); } //Contribution (0,0,0,1) double dx4 = dx2; double dy4 = dy1; double dz4 = dz1; double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; if (attn4 > 0) { attn4 *= attn4; value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); } //Contribution (1,1,0,0) double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; if (attn5 > 0) { attn5 *= attn5; value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); } //Contribution (1,0,1,0) double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; if (attn6 > 0) { attn6 *= attn6; value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); } //Contribution (1,0,0,1) double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; if (attn7 > 0) { attn7 *= attn7; value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); } //Contribution (0,1,1,0) double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; if (attn8 > 0) { attn8 *= attn8; value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); } //Contribution (0,1,0,1) double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; if (attn9 > 0) { attn9 *= attn9; value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); } //Contribution (0,0,1,1) double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; if (attn10 > 0) { attn10 *= attn10; value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); } } else { //We're inside the second dispentachoron (Rectified 4-Simplex) double aScore; byte aPoint; boolean aIsBiggerSide = true; double bScore; byte bPoint; boolean bIsBiggerSide = true; //Decide between (0,0,1,1) and (1,1,0,0) if (xins + yins < zins + wins) { aScore = xins + yins; aPoint = 0x0C; } else { aScore = zins + wins; aPoint = 0x03; } //Decide between (0,1,0,1) and (1,0,1,0) if (xins + zins < yins + wins) { bScore = xins + zins; bPoint = 0x0A; } else { bScore = yins + wins; bPoint = 0x05; } //Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. if (xins + wins < yins + zins) { double score = xins + wins; if (aScore <= bScore && score < bScore) { bScore = score; bPoint = 0x06; } else if (aScore > bScore && score < aScore) { aScore = score; aPoint = 0x06; } } else { double score = yins + zins; if (aScore <= bScore && score < bScore) { bScore = score; bPoint = 0x09; } else if (aScore > bScore && score < aScore) { aScore = score; aPoint = 0x09; } } //Decide if (0,1,1,1) is closer. double p1 = 3 - inSum + xins; if (aScore <= bScore && p1 < bScore) { bScore = p1; bPoint = 0x0E; bIsBiggerSide = false; } else if (aScore > bScore && p1 < aScore) { aScore = p1; aPoint = 0x0E; aIsBiggerSide = false; } //Decide if (1,0,1,1) is closer. double p2 = 3 - inSum + yins; if (aScore <= bScore && p2 < bScore) { bScore = p2; bPoint = 0x0D; bIsBiggerSide = false; } else if (aScore > bScore && p2 < aScore) { aScore = p2; aPoint = 0x0D; aIsBiggerSide = false; } //Decide if (1,1,0,1) is closer. double p3 = 3 - inSum + zins; if (aScore <= bScore && p3 < bScore) { bScore = p3; bPoint = 0x0B; bIsBiggerSide = false; } else if (aScore > bScore && p3 < aScore) { aScore = p3; aPoint = 0x0B; aIsBiggerSide = false; } //Decide if (1,1,1,0) is closer. double p4 = 3 - inSum + wins; if (aScore <= bScore && p4 < bScore) { bScore = p4; bPoint = 0x07; bIsBiggerSide = false; } else if (aScore > bScore && p4 < aScore) { aScore = p4; aPoint = 0x07; aIsBiggerSide = false; } //Where each of the two closest points are determines how the extra three vertices are calculated. if (aIsBiggerSide == bIsBiggerSide) { if (aIsBiggerSide) { //Both closest points on the bigger side byte c1 = (byte)(aPoint & bPoint); byte c2 = (byte)(aPoint | bPoint); //Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1 xsv_ext0 = xsv_ext1 = xsb; ysv_ext0 = ysv_ext1 = ysb; zsv_ext0 = zsv_ext1 = zsb; wsv_ext0 = wsv_ext1 = wsb; dx_ext0 = dx0 - SQUISH_CONSTANT_4D; dy_ext0 = dy0 - SQUISH_CONSTANT_4D; dz_ext0 = dz0 - SQUISH_CONSTANT_4D; dw_ext0 = dw0 - SQUISH_CONSTANT_4D; dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D; dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D; dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D; if ((c1 & 0x01) != 0) { xsv_ext0 += 1; dx_ext0 -= 1; xsv_ext1 += 2; dx_ext1 -= 2; } else if ((c1 & 0x02) != 0) { ysv_ext0 += 1; dy_ext0 -= 1; ysv_ext1 += 2; dy_ext1 -= 2; } else if ((c1 & 0x04) != 0) { zsv_ext0 += 1; dz_ext0 -= 1; zsv_ext1 += 2; dz_ext1 -= 2; } else { wsv_ext0 += 1; dw_ext0 -= 1; wsv_ext1 += 2; dw_ext1 -= 2; } //One contribution is a permutation of (1,1,1,-1) based on c2 xsv_ext2 = xsb + 1; ysv_ext2 = ysb + 1; zsv_ext2 = zsb + 1; wsv_ext2 = wsb + 1; dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; if ((c2 & 0x01) == 0) { xsv_ext2 -= 2; dx_ext2 += 2; } else if ((c2 & 0x02) == 0) { ysv_ext2 -= 2; dy_ext2 += 2; } else if ((c2 & 0x04) == 0) { zsv_ext2 -= 2; dz_ext2 += 2; } else { wsv_ext2 -= 2; dw_ext2 += 2; } } else { //Both closest points on the smaller side //One of the two extra points is (1,1,1,1) xsv_ext2 = xsb + 1; ysv_ext2 = ysb + 1; zsv_ext2 = zsb + 1; wsv_ext2 = wsb + 1; dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; //Other two points are based on the shared axes. byte c = (byte)(aPoint & bPoint); if ((c & 0x01) != 0) { xsv_ext0 = xsb + 2; xsv_ext1 = xsb + 1; dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsb; dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x02) != 0) { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c & 0x01) == 0) { ysv_ext0 += 1; dy_ext0 -= 1; } else { ysv_ext1 += 1; dy_ext1 -= 1; } } else { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x04) != 0) { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c & 0x03) == 0) { zsv_ext0 += 1; dz_ext0 -= 1; } else { zsv_ext1 += 1; dz_ext1 -= 1; } } else { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; } if ((c & 0x08) != 0) { wsv_ext0 = wsb + 1; wsv_ext1 = wsb + 2; dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsb; dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; } } } else { //One point on each "side" byte c1, c2; if (aIsBiggerSide) { c1 = aPoint; c2 = bPoint; } else { c1 = bPoint; c2 = aPoint; } //Two contributions are the bigger-sided point with each 1 replaced with 2. if ((c1 & 0x01) != 0) { xsv_ext0 = xsb + 2; xsv_ext1 = xsb + 1; dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; } else { xsv_ext0 = xsv_ext1 = xsb; dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; } if ((c1 & 0x02) != 0) { ysv_ext0 = ysv_ext1 = ysb + 1; dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c1 & 0x01) == 0) { ysv_ext0 += 1; dy_ext0 -= 1; } else { ysv_ext1 += 1; dy_ext1 -= 1; } } else { ysv_ext0 = ysv_ext1 = ysb; dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; } if ((c1 & 0x04) != 0) { zsv_ext0 = zsv_ext1 = zsb + 1; dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; if ((c1 & 0x03) == 0) { zsv_ext0 += 1; dz_ext0 -= 1; } else { zsv_ext1 += 1; dz_ext1 -= 1; } } else { zsv_ext0 = zsv_ext1 = zsb; dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; } if ((c1 & 0x08) != 0) { wsv_ext0 = wsb + 1; wsv_ext1 = wsb + 2; dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; } else { wsv_ext0 = wsv_ext1 = wsb; dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; } //One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point xsv_ext2 = xsb + 1; ysv_ext2 = ysb + 1; zsv_ext2 = zsb + 1; wsv_ext2 = wsb + 1; dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; if ((c2 & 0x01) == 0) { xsv_ext2 -= 2; dx_ext2 += 2; } else if ((c2 & 0x02) == 0) { ysv_ext2 -= 2; dy_ext2 += 2; } else if ((c2 & 0x04) == 0) { zsv_ext2 -= 2; dz_ext2 += 2; } else { wsv_ext2 -= 2; dw_ext2 += 2; } } //Contribution (1,1,1,0) double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; if (attn4 > 0) { attn4 *= attn4; value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); } //Contribution (1,1,0,1) double dx3 = dx4; double dy3 = dy4; double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; if (attn3 > 0) { attn3 *= attn3; value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); } //Contribution (1,0,1,1) double dx2 = dx4; double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; double dz2 = dz4; double dw2 = dw3; double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; if (attn2 > 0) { attn2 *= attn2; value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); } //Contribution (0,1,1,1) double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; double dz1 = dz4; double dy1 = dy4; double dw1 = dw3; double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; if (attn1 > 0) { attn1 *= attn1; value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); } //Contribution (1,1,0,0) double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; if (attn5 > 0) { attn5 *= attn5; value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); } //Contribution (1,0,1,0) double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; if (attn6 > 0) { attn6 *= attn6; value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); } //Contribution (1,0,0,1) double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; if (attn7 > 0) { attn7 *= attn7; value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); } //Contribution (0,1,1,0) double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; if (attn8 > 0) { attn8 *= attn8; value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); } //Contribution (0,1,0,1) double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; if (attn9 > 0) { attn9 *= attn9; value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); } //Contribution (0,0,1,1) double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; if (attn10 > 0) { attn10 *= attn10; value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); } } //First extra vertex double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0; if (attn_ext0 > 0) { attn_ext0 *= attn_ext0; value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0); } //Second extra vertex double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1; if (attn_ext1 > 0) { attn_ext1 *= attn_ext1; value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1); } //Third extra vertex double attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2; if (attn_ext2 > 0) { attn_ext2 *= attn_ext2; value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2); } return value / NORM_CONSTANT_4D; } private double extrapolate(int xsb, int ysb, double dx, double dy) { int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E; return gradients2D[index] * dx + gradients2D[index + 1] * dy; } private double extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) { int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; return gradients3D[index] * dx + gradients3D[index + 1] * dy + gradients3D[index + 2] * dz; } private double extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) { int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC; return gradients4D[index] * dx + gradients4D[index + 1] * dy + gradients4D[index + 2] * dz + gradients4D[index + 3] * dw; } private static int fastFloor(double x) { int xi = (int)x; return x < xi ? xi - 1 : xi; } //Gradients for 2D. They approximate the directions to the //vertices of an octagon from the center. private static byte[] gradients2D = new byte[] { 5, 2, 2, 5, -5, 2, -2, 5, 5, -2, 2, -5, -5, -2, -2, -5, }; //Gradients for 3D. They approximate the directions to the //vertices of a rhombicuboctahedron from the center, skewed so //that the triangular and square facets can be inscribed inside //circles of the same radius. private static byte[] gradients3D = new byte[] { -11, 4, 4, -4, 11, 4, -4, 4, 11, 11, 4, 4, 4, 11, 4, 4, 4, 11, -11, -4, 4, -4, -11, 4, -4, -4, 11, 11, -4, 4, 4, -11, 4, 4, -4, 11, -11, 4, -4, -4, 11, -4, -4, 4, -11, 11, 4, -4, 4, 11, -4, 4, 4, -11, -11, -4, -4, -4, -11, -4, -4, -4, -11, 11, -4, -4, 4, -11, -4, 4, -4, -11, }; //Gradients for 4D. They approximate the directions to the //vertices of a disprismatotesseractihexadecachoron from the center, //skewed so that the tetrahedral and cubic facets can be inscribed inside //spheres of the same radius. private static byte[] gradients4D = new byte[] { 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, }; }