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author | Dinnerbone <dinnerbone@dinnerbone.com> | 2011-06-26 17:41:25 +0100 |
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committer | Dinnerbone <dinnerbone@dinnerbone.com> | 2011-06-26 17:41:25 +0100 |
commit | 9e51583ca29feed5bbd9b8f70128fafa01911cbd (patch) | |
tree | 2b953e65bc37eaf2774d5116253c867d3f9d514f /src | |
parent | d8f0f0d17c790c066e68c69cf1dbf1191d157db1 (diff) | |
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Added a Perlin and Simplex noise generator for utils
Diffstat (limited to 'src')
3 files changed, 843 insertions, 0 deletions
diff --git a/src/main/java/org/bukkit/util/noise/NoiseGenerator.java b/src/main/java/org/bukkit/util/noise/NoiseGenerator.java new file mode 100644 index 00000000..823528fc --- /dev/null +++ b/src/main/java/org/bukkit/util/noise/NoiseGenerator.java @@ -0,0 +1,120 @@ + +package org.bukkit.util.noise; + +/** + * Base class for all noise generators + */ +public abstract class NoiseGenerator { + protected final int perm[] = new int[512]; + protected double offsetX; + protected double offsetY; + protected double offsetZ; + + /** + * Speedy floor, faster than (int)Math.floor(x) + * + * @param x Value to floor + * @return Floored value + */ + public static int floor(double x) { + return (int)Math.floor(x); + } + + protected static double fade(double x) { + return x * x * x * (x * (x * 6 - 15) + 10); + } + + protected static double lerp(double x, double y, double z) { + return y + x * (z - y); + } + + protected static double grad(int hash, double x, double y, double z) { + hash &= 15; + double u = hash < 8 ? x : y; + double v = hash < 4 ? y : hash == 12 || hash == 14 ? x : z; + return ((hash & 1) == 0 ? u : -u) + ((hash & 2) == 0 ? v : -v); + } + + /** + * Computes and returns the 1D noise for the given coordinate in 1D space + * + * @param x X coordinate + * @return Noise at given location, from range -1 to 1 + */ + public double noise(double x) { + return noise(x, 0, 0); + } + + /** + * Computes and returns the 2D noise for the given coordinates in 2D space + * + * @param x X coordinate + * @param y Y coordinate + * @return Noise at given location, from range -1 to 1 + */ + public double noise(double x, double y) { + return noise(x, y, 0); + } + + /** + * Computes and returns the 3D noise for the given coordinates in 3D space + * + * @param x X coordinate + * @param y Y coordinate + * @param z Z coordinate + * @return Noise at given location, from range -1 to 1 + */ + public abstract double noise(double x, double y, double z); + + /** + * Generates noise for the 1D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public double noise(double x, int octaves, double frequency, double amplitude) { + return noise(x, 0, 0, octaves, frequency, amplitude); + } + + /** + * Generates noise for the 2D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param y Y-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public double noise(double x, double y, int octaves, double frequency, double amplitude) { + return noise(x, y, 0, octaves, frequency, amplitude); + } + + /** + * Generates noise for the 3D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param y Y-coordinate + * @param z Z-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public double noise(double x, double y, double z, int octaves, double frequency, double amplitude) { + double result = 0; + double amp = 1; + double freq = 1; + + for (int i = 0; i < octaves; i++) { + result += noise(x * freq, y * freq, z * freq) * amp; + freq *= frequency; + amp *= amplitude; + } + + return result; + } +} diff --git a/src/main/java/org/bukkit/util/noise/PerlinNoiseGenerator.java b/src/main/java/org/bukkit/util/noise/PerlinNoiseGenerator.java new file mode 100644 index 00000000..1ac77420 --- /dev/null +++ b/src/main/java/org/bukkit/util/noise/PerlinNoiseGenerator.java @@ -0,0 +1,210 @@ +package org.bukkit.util.noise; + +import java.util.Random; +import org.bukkit.World; + +/** + * Generates noise using the "classic" perlin generator + * + * @see SimplexNoiseGenerator "Improved" and faster version with slighly different results + */ +public class PerlinNoiseGenerator extends NoiseGenerator { + protected static final int grad3[][] = {{1, 1, 0}, {-1, 1, 0}, {1, -1, 0}, {-1, -1, 0}, + {1, 0, 1}, {-1, 0, 1}, {1, 0, -1}, {-1, 0, -1}, + {0, 1, 1}, {0, -1, 1}, {0, 1, -1}, {0, -1, -1}}; + private static final PerlinNoiseGenerator instance = new PerlinNoiseGenerator(); + + protected PerlinNoiseGenerator() { + int p[] = {151, 160, 137, 91, 90, 15, 131, 13, 201, + 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, + 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, + 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, + 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, + 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, + 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, + 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, + 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, + 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, + 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, + 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, + 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, + 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, + 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, + 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, + 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, + 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180}; + + for (int i = 0; i < 512; i++) { + perm[i] = p[i & 255]; + } + } + + /** + * Creates a seeded perlin noise generator for the given world + * + * @param world World to construct this generator for + */ + public PerlinNoiseGenerator(World world) { + this(new Random(world.getSeed())); + } + + /** + * Creates a seeded perlin noise generator for the given seed + * + * @param seed Seed to construct this generator for + */ + public PerlinNoiseGenerator(long seed) { + this(new Random(seed)); + } + + /** + * Creates a seeded perlin noise generator with the given Random + * + * @param rand Random to construct with + */ + public PerlinNoiseGenerator(Random rand) { + offsetX = rand.nextDouble() * 256; + offsetY = rand.nextDouble() * 256; + offsetZ = rand.nextDouble() * 256; + + for (int i = 0; i < 256; i++) { + perm[i] = i; + } + + for (int i = 0; i < 256; i++) { + int pos = rand.nextInt(256 - i) + i; + int old = perm[i]; + + perm[i] = perm[pos]; + perm[pos] = old; + perm[i + 256] = perm[i]; + } + } + + /** + * Computes and returns the 1D unseeded perlin noise for the given coordinates in 1D space + * + * @param x X coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double x) { + return instance.noise(x); + } + + /** + * Computes and returns the 2D unseeded perlin noise for the given coordinates in 2D space + * + * @param x X coordinate + * @param y Y coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double x, double y) { + return instance.noise(x, y); + } + + /** + * Computes and returns the 3D unseeded perlin noise for the given coordinates in 3D space + * + * @param x X coordinate + * @param y Y coordinate + * @param z Z coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double x, double y, double z) { + return instance.noise(x, y, z); + } + + /** + * Gets the singleton unseeded instance of this generator + * + * @return Singleton + */ + public static PerlinNoiseGenerator getInstance() { + return instance; + } + + @Override + public double noise(double x, double y, double z) { + x += offsetX; + y += offsetY; + z += offsetZ; + + int floorX = floor(x); + int floorY = floor(y); + int floorZ = floor(z); + + // Find unit cube containing the point + int X = floorX & 255; + int Y = floorY & 255; + int Z = floorZ & 255; + + // Get relative xyz coordinates of the point within the cube + x -= floorX; + y -= floorY; + z -= floorZ; + + // Compute fade curves for xyz + double fX = fade(x); + double fY = fade(y); + double fZ = fade(z); + + // Hash coordinates of the cube corners + int A = perm[X] + Y; + int AA = perm[A] + Z; + int AB = perm[A + 1] + Z; + int B = perm[X + 1] + Y; + int BA = perm[B] + Z; + int BB = perm[B + 1] + Z; + + return lerp(fZ, lerp(fY, lerp(fX, grad(perm[AA], x, y, z), + grad(perm[BA], x - 1, y, z)), + lerp(fX, grad(perm[AB], x, y - 1, z), + grad(perm[BB], x - 1, y - 1, z))), + lerp(fY, lerp(fX, grad(perm[AA + 1], x, y, z - 1), + grad(perm[BA + 1], x - 1, y, z - 1)), + lerp(fX, grad(perm[AB + 1], x, y - 1, z - 1), + grad(perm[BB + 1], x - 1, y - 1, z - 1)))); + } + + /** + * Generates noise for the 1D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public static double getNoise(double x, int octaves, double frequency, double amplitude) { + return instance.noise(x, octaves, frequency, amplitude); + } + + /** + * Generates noise for the 2D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param y Y-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public double getNoise(double x, double y, int octaves, double frequency, double amplitude) { + return instance.noise(x, y, octaves, frequency, amplitude); + } + + /** + * Generates noise for the 3D coordinates using the specified number of octaves and parameters + * + * @param x X-coordinate + * @param y Y-coordinate + * @param z Z-coordinate + * @param octaves Number of octaves to use + * @param frequency How much to alter the frequency by each octave + * @param amplitude How much to alter the amplitude by each octave + * @return Resulting noise + */ + public double getNoise(double x, double y, double z, int octaves, double frequency, double amplitude) { + return instance.noise(x, y, z, octaves, frequency, amplitude); + } +} diff --git a/src/main/java/org/bukkit/util/noise/SimplexNoiseGenerator.java b/src/main/java/org/bukkit/util/noise/SimplexNoiseGenerator.java new file mode 100644 index 00000000..c5e5781c --- /dev/null +++ b/src/main/java/org/bukkit/util/noise/SimplexNoiseGenerator.java @@ -0,0 +1,513 @@ +package org.bukkit.util.noise; + +import java.util.Random; +import org.bukkit.World; + +/** + * Generates simplex-based noise. + * + * This is a modified version of the freely published version in the paper by + * Stefan Gustavson at http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf + */ +public class SimplexNoiseGenerator extends PerlinNoiseGenerator { + protected static final double SQRT_3 = Math.sqrt(3); + protected static final double SQRT_5 = Math.sqrt(5); + protected static final double F2 = 0.5 * (SQRT_3 - 1); + protected static final double G2 = (3 - SQRT_3) / 6; + protected static final double G22 = G2 * 2.0 - 1; + protected static final double F3 = 1.0 / 3.0; + protected static final double G3 = 1.0 / 6.0; + protected static final double F4 = (SQRT_5 - 1.0) / 4.0; + protected static final double G4 = (5.0 - SQRT_5) / 20.0; + protected static final double G42 = G4 * 2.0; + protected static final double G43 = G4 * 3.0; + protected static final double G44 = G4 * 4.0 - 1.0; + protected static final int grad4[][] = {{0, 1, 1, 1}, {0, 1, 1, -1}, {0, 1, -1, 1}, {0, 1, -1, -1}, + {0, -1, 1, 1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {0, -1, -1, -1}, + {1, 0, 1, 1}, {1, 0, 1, -1}, {1, 0, -1, 1}, {1, 0, -1, -1}, + {-1, 0, 1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1}, {-1, 0, -1, -1}, + {1, 1, 0, 1}, {1, 1, 0, -1}, {1, -1, 0, 1}, {1, -1, 0, -1}, + {-1, 1, 0, 1}, {-1, 1, 0, -1}, {-1, -1, 0, 1}, {-1, -1, 0, -1}, + {1, 1, 1, 0}, {1, 1, -1, 0}, {1, -1, 1, 0}, {1, -1, -1, 0}, + {-1, 1, 1, 0}, {-1, 1, -1, 0}, {-1, -1, 1, 0}, {-1, -1, -1, 0}}; + protected static final int simplex[][] = { + {0, 1, 2, 3}, {0, 1, 3, 2}, {0, 0, 0, 0}, {0, 2, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 3, 0}, + {0, 2, 1, 3}, {0, 0, 0, 0}, {0, 3, 1, 2}, {0, 3, 2, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 3, 2, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {1, 2, 0, 3}, {0, 0, 0, 0}, {1, 3, 0, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 3, 0, 1}, {2, 3, 1, 0}, + {1, 0, 2, 3}, {1, 0, 3, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 0, 3, 1}, {0, 0, 0, 0}, {2, 1, 3, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {2, 0, 1, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 0, 1, 2}, {3, 0, 2, 1}, {0, 0, 0, 0}, {3, 1, 2, 0}, + {2, 1, 0, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 1, 0, 2}, {0, 0, 0, 0}, {3, 2, 0, 1}, {3, 2, 1, 0}}; + protected static double offsetW; + private static final SimplexNoiseGenerator instance = new SimplexNoiseGenerator(); + + protected SimplexNoiseGenerator() { + super(); + } + + /** + * Creates a seeded simplex noise generator for the given world + * + * @param world World to construct this generator for + */ + public SimplexNoiseGenerator(World world) { + this(new Random(world.getSeed())); + } + + /** + * Creates a seeded simplex noise generator for the given seed + * + * @param seed Seed to construct this generator for + */ + public SimplexNoiseGenerator(long seed) { + this(new Random(seed)); + } + + /** + * Creates a seeded simplex noise generator with the given Random + * + * @param rand Random to construct with + */ + public SimplexNoiseGenerator(Random rand) { + super(rand); + offsetW = rand.nextDouble() * 256; + } + + protected static double dot(int g[], double x, double y) { + return g[0] * x + g[1] * y; + } + + protected static double dot(int g[], double x, double y, double z) { + return g[0] * x + g[1] * y + g[2] * z; + } + + protected static double dot(int g[], double x, double y, double z, double w) { + return g[0] * x + g[1] * y + g[2] * z + g[3] * w; + } + + /** + * Computes and returns the 1D unseeded simplex noise for the given coordinates in 1D space + * + * @param xin X coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double xin) { + return instance.noise(xin); + } + + /** + * Computes and returns the 2D unseeded simplex noise for the given coordinates in 2D space + * + * @param xin X coordinate + * @param yin Y coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double xin, double yin) { + return instance.noise(xin, yin); + } + + /** + * Computes and returns the 3D unseeded simplex noise for the given coordinates in 3D space + * + * @param xin X coordinate + * @param yin Y coordinate + * @param zin Z coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double xin, double yin, double zin) { + return instance.noise(xin, yin, zin); + } + + /** + * Computes and returns the 4D simplex noise for the given coordinates in 4D space + * + * @param x X coordinate + * @param y Y coordinate + * @param z Z coordinate + * @param w W coordinate + * @return Noise at given location, from range -1 to 1 + */ + public static double getNoise(double x, double y, double z, double w) { + return instance.noise(x, y, z, w); + } + + @Override + public double noise(double xin, double yin, double zin) { + xin += offsetX; + yin += offsetY; + zin += offsetZ; + + double n0, n1, n2, n3; // Noise contributions from the four corners + + // Skew the input space to determine which simplex cell we're in + double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D + int i = floor(xin + s); + int j = floor(yin + s); + int k = floor(zin + s); + double t = (i + j + k) * G3; + double X0 = i - t; // Unskew the cell origin back to (x,y,z) space + double Y0 = j - t; + double Z0 = k - t; + double x0 = xin - X0; // The x,y,z distances from the cell origin + double y0 = yin - Y0; + double z0 = zin - Z0; + + // For the 3D case, the simplex shape is a slightly irregular tetrahedron. + + // Determine which simplex we are in. + int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords + int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords + if (x0 >= y0) { + if (y0 >= z0) { + i1 = 1; + j1 = 0; + k1 = 0; + i2 = 1; + j2 = 1; + k2 = 0; + } // X Y Z order + else if (x0 >= z0) { + i1 = 1; + j1 = 0; + k1 = 0; + i2 = 1; + j2 = 0; + k2 = 1; + } // X Z Y order + else { + i1 = 0; + j1 = 0; + k1 = 1; + i2 = 1; + j2 = 0; + k2 = 1; + } // Z X Y order + } else { // x0<y0 + if (y0 < z0) { + i1 = 0; + j1 = 0; + k1 = 1; + i2 = 0; + j2 = 1; + k2 = 1; + } // Z Y X order + else if (x0 < z0) { + i1 = 0; + j1 = 1; + k1 = 0; + i2 = 0; + j2 = 1; + k2 = 1; + } // Y Z X order + else { + i1 = 0; + j1 = 1; + k1 = 0; + i2 = 1; + j2 = 1; + k2 = 0; + } // Y X Z order + } + + // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), + // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and + // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where + // c = 1/6. + double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords + double y1 = y0 - j1 + G3; + double z1 = z0 - k1 + G3; + double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords + double y2 = y0 - j2 + 2.0 * G3; + double z2 = z0 - k2 + 2.0 * G3; + double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords + double y3 = y0 - 1.0 + 3.0 * G3; + double z3 = z0 - 1.0 + 3.0 * G3; + + // Work out the hashed gradient indices of the four simplex corners + int ii = i & 255; + int jj = j & 255; + int kk = k & 255; + int gi0 = perm[ii + perm[jj + perm[kk]]] % 12; + int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12; + int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12; + int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12; + + // Calculate the contribution from the four corners + double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0; + if (t0 < 0) { + n0 = 0.0; + } else { + t0 *= t0; + n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0); + } + + double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1; + if (t1 < 0) { + n1 = 0.0; + } else { + t1 *= t1; + n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1); + } + + double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2; + if (t2 < 0) { + n2 = 0.0; + } else { + t2 *= t2; + n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2); + } + + double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3; + if (t3 < 0) { + n3 = 0.0; + } else { + t3 *= t3; + n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3); + } + + // Add contributions from each corner to get the final noise value. + // The result is scaled to stay just inside [-1,1] + return 32.0 * (n0 + n1 + n2 + n3); + } + + @Override + public double noise(double xin, double yin) { + xin += offsetX; + yin += offsetY; + + double n0, n1, n2; // Noise contributions from the three corners + + // Skew the input space to determine which simplex cell we're in + double s = (xin + yin) * F2; // Hairy factor for 2D + int i = floor(xin + s); + int j = floor(yin + s); + double t = (i + j) * G2; + double X0 = i - t; // Unskew the cell origin back to (x,y) space + double Y0 = j - t; + double x0 = xin - X0; // The x,y distances from the cell origin + double y0 = yin - Y0; + + // For the 2D case, the simplex shape is an equilateral triangle. + + // Determine which simplex we are in. + int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords + if (x0 > y0) { + i1 = 1; + j1 = 0; + } // lower triangle, XY order: (0,0)->(1,0)->(1,1) + else { + i1 = 0; + j1 = 1; + } // upper triangle, YX order: (0,0)->(0,1)->(1,1) + + // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and + // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where + // c = (3-sqrt(3))/6 + + double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords + double y1 = y0 - j1 + G2; + double x2 = x0 + G22; // Offsets for last corner in (x,y) unskewed coords + double y2 = y0 + G22; + + // Work out the hashed gradient indices of the three simplex corners + int ii = i & 255; + int jj = j & 255; + int gi0 = perm[ii + perm[jj]] % 12; + int gi1 = perm[ii + i1 + perm[jj + j1]] % 12; + int gi2 = perm[ii + 1 + perm[jj + 1]] % 12; + + // Calculate the contribution from the three corners + double t0 = 0.5 - x0 * x0 - y0 * y0; + if (t0 < 0) { + n0 = 0.0; + } else { + t0 *= t0; + n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient + } + + double t1 = 0.5 - x1 * x1 - y1 * y1; + if (t1 < 0) { + n1 = 0.0; + } else { + t1 *= t1; + n1 = t1 * t1 * dot(grad3[gi1], x1, y1); + } + + double t2 = 0.5 - x2 * x2 - y2 * y2; + if (t2 < 0) { + n2 = 0.0; + } else { + t2 *= t2; + n2 = t2 * t2 * dot(grad3[gi2], x2, y2); + } + + // Add contributions from each corner to get the final noise value. + // The result is scaled to return values in the interval [-1,1]. + return 70.0 * (n0 + n1 + n2); + } + + /** + * Computes and returns the 4D simplex noise for the given coordinates in 4D space + * + * @param xin X coordinate + * @param yin Y coordinate + * @param zin Z coordinate + * @param win W coordinate + * @return Noise at given location, from range -1 to 1 + */ + public double noise(double x, double y, double z, double w) { + x += offsetX; + y += offsetY; + z += offsetZ; + w += offsetW; + + double n0, n1, n2, n3, n4; // Noise contributions from the five corners + + // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in + double s = (x + y + z + w) * F4; // Factor for 4D skewing + int i = floor(x + s); + int j = floor(y + s); + int k = floor(z + s); + int l = floor(w + s); + + double t = (i + j + k + l) * G4; // Factor for 4D unskewing + double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space + double Y0 = j - t; + double Z0 = k - t; + double W0 = l - t; + double x0 = x - X0; // The x,y,z,w distances from the cell origin + double y0 = y - Y0; + double z0 = z - Z0; + double w0 = w - W0; + + // For the 4D case, the simplex is a 4D shape I won't even try to describe. + // To find out which of the 24 possible simplices we're in, we need to + // determine the magnitude ordering of x0, y0, z0 and w0. + // The method below is a good way of finding the ordering of x,y,z,w and + // then find the correct traversal order for the simplex we’re in. + // First, six pair-wise comparisons are performed between each possible pair + // of the four coordinates, and the results are used to add up binary bits + // for an integer index. + int c1 = (x0 > y0) ? 32 : 0; + int c2 = (x0 > z0) ? 16 : 0; + int c3 = (y0 > z0) ? 8 : 0; + int c4 = (x0 > w0) ? 4 : 0; + int c5 = (y0 > w0) ? 2 : 0; + int c6 = (z0 > w0) ? 1 : 0; + int c = c1 + c2 + c3 + c4 + c5 + c6; + int i1, j1, k1, l1; // The integer offsets for the second simplex corner + int i2, j2, k2, l2; // The integer offsets for the third simplex corner + int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner + + // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. + // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w + // impossible. Only the 24 indices which have non-zero entries make any sense. + // We use a thresholding to set the coordinates in turn from the largest magnitude. + + // The number 3 in the "simplex" array is at the position of the largest coordinate. + i1 = simplex[c][0] >= 3 ? 1 : 0; + j1 = simplex[c][1] >= 3 ? 1 : 0; + k1 = simplex[c][2] >= 3 ? 1 : 0; + l1 = simplex[c][3] >= 3 ? 1 : 0; + + // The number 2 in the "simplex" array is at the second largest coordinate. + i2 = simplex[c][0] >= 2 ? 1 : 0; + j2 = simplex[c][1] >= 2 ? 1 : 0; + k2 = simplex[c][2] >= 2 ? 1 : 0; + l2 = simplex[c][3] >= 2 ? 1 : 0; + + // The number 1 in the "simplex" array is at the second smallest coordinate. + i3 = simplex[c][0] >= 1 ? 1 : 0; + j3 = simplex[c][1] >= 1 ? 1 : 0; + k3 = simplex[c][2] >= 1 ? 1 : 0; + l3 = simplex[c][3] >= 1 ? 1 : 0; + + // The fifth corner has all coordinate offsets = 1, so no need to look that up. + + double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords + double y1 = y0 - j1 + G4; + double z1 = z0 - k1 + G4; + double w1 = w0 - l1 + G4; + + double x2 = x0 - i2 + G42; // Offsets for third corner in (x,y,z,w) coords + double y2 = y0 - j2 + G42; + double z2 = z0 - k2 + G42; + double w2 = w0 - l2 + G42; + + double x3 = x0 - i3 + G43; // Offsets for fourth corner in (x,y,z,w) coords + double y3 = y0 - j3 + G43; + double z3 = z0 - k3 + G43; + double w3 = w0 - l3 + G43; + + double x4 = x0 + G44; // Offsets for last corner in (x,y,z,w) coords + double y4 = y0 + G44; + double z4 = z0 + G44; + double w4 = w0 + G44; + + // Work out the hashed gradient indices of the five simplex corners + int ii = i & 255; + int jj = j & 255; + int kk = k & 255; + int ll = l & 255; + + int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32; + int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32; + int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32; + int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32; + int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32; + + // Calculate the contribution from the five corners + double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0; + if (t0 < 0) { + n0 = 0.0; + } else { + t0 *= t0; + n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0); + } + + double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1; + if (t1 < 0) { + n1 = 0.0; + } else { + t1 *= t1; + n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1); + } + + double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2; + if (t2 < 0) { + n2 = 0.0; + } else { + t2 *= t2; + n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2); + } + + double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3; + if (t3 < 0) { + n3 = 0.0; + } else { + t3 *= t3; + n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3); + } + + double t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4; + if (t4 < 0) { + n4 = 0.0; + } else { + t4 *= t4; + n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4); + } + + // Sum up and scale the result to cover the range [-1,1] + return 27.0 * (n0 + n1 + n2 + n3 + n4); + } + + /** + * Gets the singleton unseeded instance of this generator + * + * @return Singleton + */ + public static SimplexNoiseGenerator getInstance() { + return instance; + } +} |