/OpenSimplexNoise.java
Last active Oct 15, 2019
Visually axis-decorrelated coherent noise algorithm based on the Simplectic honeycomb.
| /* | |
| * 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, | |
| }; | |
| } |
| /* | |
| * OpenSimplex Noise sample class. | |
| */ | |
| import java.awt.image.BufferedImage; | |
| import javax.imageio.ImageIO; | |
| import java.io.*; | |
| public class OpenSimplexNoiseTest | |
| { | |
| private static final int WIDTH = 512; | |
| private static final int HEIGHT = 512; | |
| private static final double FEATURE_SIZE = 24; | |
| public static void main(String[] args) | |
| throws IOException { | |
| OpenSimplexNoise noise = new OpenSimplexNoise(); | |
| BufferedImage image = new BufferedImage(WIDTH, HEIGHT, BufferedImage.TYPE_INT_RGB); | |
| for (int y = 0; y < HEIGHT; y++) | |
| { | |
| for (int x = 0; x < WIDTH; x++) | |
| { | |
| double value = noise.eval(x / FEATURE_SIZE, y / FEATURE_SIZE, 0.0); | |
| int rgb = 0x010101 * (int)((value + 1) * 127.5); | |
| image.setRGB(x, y, rgb); | |
| } | |
| } | |
| ImageIO.write(image, "png", new File("noise.png")); | |
| } | |
| } |
| This is free and unencumbered software released into the public domain. | |
| Anyone is free to copy, modify, publish, use, compile, sell, or | |
| distribute this software, either in source code form or as a compiled | |
| binary, for any purpose, commercial or non-commercial, and by any | |
| means. | |
| In jurisdictions that recognize copyright laws, the author or authors | |
| of this software dedicate any and all copyright interest in the | |
| software to the public domain. We make this dedication for the benefit | |
| of the public at large and to the detriment of our heirs and | |
| successors. We intend this dedication to be an overt act of | |
| relinquishment in perpetuity of all present and future rights to this | |
| software under copyright law. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, | |
| EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF | |
| MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. | |
| IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR | |
| OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, | |
| ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR | |
| OTHER DEALINGS IN THE SOFTWARE. |
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tliron
commented
Oct 6, 2014
|
Any chance you can make periodic versions? |
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oloflarsson
commented
Feb 27, 2015
|
I would like to see a 1 dimension implementation as well. |
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oloflarsson
commented
Mar 3, 2015
|
Here is another example of someone struggling with the "chance" problem: |
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ghost
commented
Apr 27, 2015
|
This is fantastic. Thank you! I am deff going to give you credit in my work. |
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afonsolage
commented
Jun 13, 2015
|
Awesome work! This was exactly what I was looking for. I'll add to my project and, of course, keep your name on it!!! |
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Asmageddon
commented
Jun 18, 2015
|
Bloody hell, this is a freaking long source. Any chance of a shorter implementation, perhaps a GLSL one? |
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tyronx
commented
Feb 16, 2016
|
Shouldn't it generate noise between -1 and 1? For the 2d implementation it seems to generate more like within an area of -0.87 to +0.87 I thing the norm constants haven't been chosen quite right. |
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CreamyCookie
commented
Jun 17, 2016
|
@KdotJPG There seem to be few unused assignments: smcameron/open-simplex-noise-in-c#4 Any idea? |
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ghandhikus
commented
Nov 18, 2016
// Iterations: 100000000
2DOpenSimplexNoise speed: 6498.520513ms // this
2DSimplexNoise speed: 5000.267634ms // http://staffwww.itn.liu.se/~stegu/simplexnoise/SimplexNoise.java
// Iterations: 1000000
2DOpenSimplexNoise speed: 111.175103ms
2DSimplexNoise speed: 73.051068ms
////////////////////////////////////////////////////////////////
// After adding final to both implementation like so "public final class Name"
// Also I've separated the tests to avoid hot and cold scenario
// Iterations: 100000000
2DOpenSimplexNoise speed: 5702.409891ms
2DOpenSimplexNoise speed: 5675.584907ms
2DOpenSimplexNoise speed: 5863.16953ms
2DSimplexNoise speed: 4633.812286ms
2DSimplexNoise speed: 4524.991414ms
2DSimplexNoise speed: 4492.767565ms
2DSimplexNoise speed: 4649.350849ms
2DSimplexNoise speed: 4455.254193ms
2DSimplexNoise speed: 4633.330702ms
2DSimplexNoise speed: 4550.094936ms
// Best scenarios in this test
//
// 2DOpenSimplexNoise - 5675.584907ms
// 2DSimplexNoise - 4455.254193ms
// Worst scenarios in this test
//
// 2DOpenSimplexNoise - 5863.16953ms
// 2DSimplexNoise - 4649.350849ms
////////////////////////////////////////////////////////////////
// After removing final
2DOpenSimplexNoise speed: 5724.589568ms
2DOpenSimplexNoise speed: 5842.842763ms
2DOpenSimplexNoise speed: 5804.29675ms
2DOpenSimplexNoise speed: 5665.408102ms
2DSimplexNoise speed: 4581.063116ms
2DSimplexNoise speed: 4530.74752ms
2DSimplexNoise speed: 4590.37899ms
2DSimplexNoise speed: 4504.37333ms
// final seems to make no difference in this code
// Best scenarios in this test
//
// 2DOpenSimplexNoise - 5665.408102ms
// 2DSimplexNoise - 4504.37333ms
// Worst scenarios in this test
//
// 2DOpenSimplexNoise - 5842.842763ms
// 2DSimplexNoise - 4590.37899ms
////////////////////////////////////////////////////////////////code: public class SimplexNoisePerformanceTests {
private static int iterations = 100000000;
private static double x = 0.5447734756785486781d;
private static double y = 0.4923141242323442d;
public @Test void simplexNoise() {
final double[] result = new double[iterations];
final long start = System.nanoTime();
for (int i = 0; i < iterations; i++)
result[i] = SimplexNoise.noise(i*x, i*y);
long end = System.nanoTime() - start;
System.out.println("2DSimplexNoise speed: "+(end/1000000d)+"ms");
}
public @Test void openSimplexNoise() {
final double[] result = new double[iterations];
final OpenSimplexNoise simplex = new OpenSimplexNoise();
long start = System.nanoTime();
for (int i = 0; i < iterations; i++)
result[i] = simplex.eval(i*x, i*y);
long end = System.nanoTime() - start;
System.out.println("2DOpenSimplexNoise speed: "+(end/1000000d)+"ms");
}
} |
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Porama6400
commented
Dec 8, 2016
|
Look like it's never touch -1 or 1 |
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Chovanec
commented
Jun 1, 2017
|
agree with Porama6400 interval should be betwwn -1 to 1, how to change code to get correct values? |
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blah1
commented
Jun 26, 2017
|
https://eev.ee/blog/2016/05/29/perlin-noise/
I believe this should explain your issues with the range on OpenSimplex Noise; for 3D noise it would have a amplitude of ~0.866. |
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thecjharries
commented
Aug 27, 2017
|
What's the reason for shifting |
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mackycheese
commented
Jan 23, 2018
|
I am doing eval(x,y,z,0) (4d noise with w=0) and it gives a range of about: -0.6512914, 0.6200971 This is in a sample range of 16x256x16x0, or at point (x,y,z) the noise is eval(x,y,z,0). Shouldnt it be +-(1/2)sqrt(4) = +-(1/2)2 = +-1? |
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sorenbug
commented
Oct 7, 2018
|
@KdotJPG Please explain what all the different constants mean, how you got to them, and why this code can't be generalized to |
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cjburkey01
commented
Mar 14, 2019
The actual paper is here, but it requires some higher level mathematics to understand: http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf OpenSimplex Noise, according to This Wikipedia Page, is slightly different in its implementation, though, in that:
|
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nonchip
commented
Mar 23, 2019
|
the paper you linked explains perlin vs simplex, not opensimplex. |
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Manuel3115
commented
Apr 9, 2019
|
Very good code thanks ! Only 1 question : how do you decrease the amplitude of the noise ? I'm getting a lot of big spikes in the values. I'd rather have bigger clusters of similar values. Thank you ! |
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ecumene commentedSep 23, 2014
Wow, great work!