231 lines
14 KiB
Java
231 lines
14 KiB
Java
/**
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* Copyright (c) 2011-2015, SpaceToad and the BuildCraft Team
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* http://www.mod-buildcraft.com
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*
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* BuildCraft is distributed under the terms of the Minecraft Mod Public
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* License 1.0, or MMPL. Please check the contents of the license located in
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* http://www.mod-buildcraft.com/MMPL-1.0.txt
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*/
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package buildcraft.core.lib.utils;
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/**
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* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
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*
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* Based on example code by Stefan Gustavson (stegu@itn.liu.se).
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* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
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* Better rank ordering method by Stefan Gustavson in 2012.
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*
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* This could be speeded up even further, but it's useful as it is.
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*
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* Version 2012-03-09
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*
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* This code was placed in the public domain by its original author,
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* Stefan Gustavson. You may use it as you see fit, but
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* attribution is appreciated.
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*
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*/
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public final class SimplexNoise { // Simplex noise in 2D, 3D and 4D
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private static Grad[] grad3 = {new Grad(1, 1, 0), new Grad(-1, 1, 0), new Grad(1, -1, 0), new Grad(-1, -1, 0),
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new Grad(1, 0, 1), new Grad(-1, 0, 1),
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new Grad(1, 0, -1), new Grad(-1, 0, -1), new Grad(0, 1, 1), new Grad(0, -1, 1), new Grad(0, 1, -1), new Grad(0, -1, -1)};
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// private static Grad grad4[]= {new Grad(0,1,1,1),new Grad(0,1,1,-1),new Grad(0,1,-1,1),new Grad(0,1,-1,-1),
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// new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
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// new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
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// new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
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// new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
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// new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
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// new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
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// new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};
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private static short[] p = {151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103,
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30, 69, 142, 8, 99, 37, 240, 21, 10, 23,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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61, 156, 180};
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// To remove the need for index wrapping, double the permutation table length
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private static short[] perm = new short[512];
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private static short[] permMod12 = new short[512];
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static {
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for (int i = 0; i < 512; i++) {
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perm[i] = p[i & 255];
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permMod12[i] = (short) (perm[i] % 12);
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}
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}
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// Skewing and unskewing factors for 2, 3, and 4 dimensions
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private static final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
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private static final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
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// private static final double F3 = 1.0/3.0;
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// private static final double G3 = 1.0/6.0;
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// private static final double F4 = (Math.sqrt(5.0)-1.0)/4.0;
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// private static final double G4 = (5.0-Math.sqrt(5.0))/20.0;
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/**
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* Deactivate constructor
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*/
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private SimplexNoise() {
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}
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// This method is a *lot* faster than using (int)Math.floor(x)
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private static int fastfloor(double x) {
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int xi = (int) x;
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return x < xi ? xi - 1 : xi;
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}
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private static double dot(Grad g, double x, double y) {
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return g.x * x + g.y * y;
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}
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// private static double dot(Grad g, double x, double y, double z) {
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// return g.x*x + g.y*y + g.z*z; }
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//
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// private static double dot(Grad g, double x, double y, double z, double w) {
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// return g.x*x + g.y*y + g.z*z + g.w*w; }
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// 2D simplex noise
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public static double noise(double xin, double yin) {
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double n0, n1, n2; // Noise contributions from the three corners
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// Skew the input space to determine which simplex cell we're in
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double s = (xin + yin) * F2; // Hairy factor for 2D
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int i = fastfloor(xin + s);
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int j = fastfloor(yin + s);
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double t = (i + j) * G2;
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double originX0 = i - t; // Unskew the cell origin back to (x,y) space
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double originY0 = j - t;
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double x0 = xin - originX0; // The x,y distances from the cell origin
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double y0 = yin - originY0;
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// For the 2D case, the simplex shape is an equilateral triangle.
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// Determine which simplex we are in.
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int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
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if (x0 > y0) {
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i1 = 1;
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j1 = 0;
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} else {
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// lower triangle, XY order: (0,0)->(1,0)->(1,1)
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i1 = 0;
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j1 = 1;
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} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
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// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
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// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
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// c = (3-sqrt(3))/6
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double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
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double y1 = y0 - j1 + G2;
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double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
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double y2 = y0 - 1.0 + 2.0 * G2;
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// Work out the hashed gradient indices of the three simplex corners
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int ii = i & 255;
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int jj = j & 255;
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int gi0 = permMod12[ii + perm[jj]];
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int gi1 = permMod12[ii + i1 + perm[jj + j1]];
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int gi2 = permMod12[ii + 1 + perm[jj + 1]];
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// Calculate the contribution from the three corners
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double t0 = 0.5 - x0 * x0 - y0 * y0;
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if (t0 < 0) {
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n0 = 0.0;
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} else {
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t0 *= t0;
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n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
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}
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double t1 = 0.5 - x1 * x1 - y1 * y1;
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if (t1 < 0) {
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n1 = 0.0;
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} else {
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t1 *= t1;
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n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
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}
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double t2 = 0.5 - x2 * x2 - y2 * y2;
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if (t2 < 0) {
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n2 = 0.0;
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} else {
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t2 *= t2;
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n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
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}
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// Add contributions from each corner to get the final noise value.
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// The result is scaled to return values in the interval [-1,1].
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return 70.0 * (n0 + n1 + n2);
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}
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/*
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*
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* // 3D simplex noise public static double noise(double xin, double yin, double zin) { double n0, n1, n2, n3; // Noise contributions from the four corners
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* // 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 =
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* fastfloor(xin+s); int j = fastfloor(yin+s); int k = fastfloor(zin+s); double t = (i+j+k)*G3; double X0 = i-t; // Unskew the cell origin back to (x,y,z)
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* 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
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* 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
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* 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;
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* 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
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* 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
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* 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
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* (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.
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* 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 +
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* 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; //
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* 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
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* four simplex corners int ii = i & 255; int jj = j & 255; int kk = k & 255; int gi0 = permMod12[ii+perm[jj+perm[kk]]]; int gi1 =
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* permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]]; int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]]; int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]]; //
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* 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 *
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* 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); }
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* 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 -
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* 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
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* noise value. // The result is scaled to stay just inside [-1,1] return 32.0*(n0 + n1 + n2 + n3); }
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*
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*
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* // 4D simplex noise, better simplex rank ordering method 2012-03-09 public static double noise(double x, double y, double z, double w) {
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*
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* 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
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* double s = (x + y + z + w) * F4; // Factor for 4D skewing int i = fastfloor(x + s); int j = fastfloor(y + s); int k = fastfloor(z + s); int l =
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* fastfloor(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
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* 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 -
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* 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
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* we're in, we need to // determine the magnitude ordering of x0, y0, z0 and w0. // Six pair-wise comparisons are performed between each possible pair //
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* of the four coordinates, and the results are used to rank the numbers. int rankx = 0; int ranky = 0; int rankz = 0; int rankw = 0; if(x0 > y0) rankx++;
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* else ranky++; if(x0 > z0) rankx++; else rankz++; if(x0 > w0) rankx++; else rankw++; if(y0 > z0) ranky++; else rankz++; if(y0 > w0) ranky++; else rankw++;
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* if(z0 > w0) rankz++; else rankw++; int i1, j1, k1, l1; // The integer offsets for the second simplex corner int i2, j2, k2, l2; // The integer offsets
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* 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,
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* 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
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* non-zero entries make any sense. // We use a thresholding to set the coordinates in turn from the largest magnitude. // Rank 3 denotes the largest
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* coordinate. i1 = rankx >= 3 ? 1 : 0; j1 = ranky >= 3 ? 1 : 0; k1 = rankz >= 3 ? 1 : 0; l1 = rankw >= 3 ? 1 : 0; // Rank 2 denotes the second largest
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* coordinate. i2 = rankx >= 2 ? 1 : 0; j2 = ranky >= 2 ? 1 : 0; k2 = rankz >= 2 ? 1 : 0; l2 = rankw >= 2 ? 1 : 0; // Rank 1 denotes the second smallest
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* coordinate. i3 = rankx >= 1 ? 1 : 0; j3 = ranky >= 1 ? 1 : 0; k3 = rankz >= 1 ? 1 : 0; l3 = rankw >= 1 ? 1 : 0; // The fifth corner has all coordinate
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* offsets = 1, so no need to compute that. double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords double y1 = y0 - j1 + G4; double z1 =
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* z0 - k1 + G4; double w1 = w0 - l1 + G4; double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords double y2 = y0 - j2 + 2.0*G4;
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* double z2 = z0 - k2 + 2.0*G4; double w2 = w0 - l2 + 2.0*G4; double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords double y3 = y0
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* - j3 + 3.0*G4; double z3 = z0 - k3 + 3.0*G4; double w3 = w0 - l3 + 3.0*G4; double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
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* double y4 = y0 - 1.0 + 4.0*G4; double z4 = z0 - 1.0 + 4.0*G4; double w4 = w0 - 1.0 + 4.0*G4; // Work out the hashed gradient indices of the five simplex
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* 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 =
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* 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 =
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* 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
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* 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); }
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* 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 -
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* 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 -
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* 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;
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* 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
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* 27.0 * (n0 + n1 + n2 + n3 + n4); }
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*/
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// Inner class to speed upp gradient computations
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// (array access is a lot slower than member access)
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private static class Grad {
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double x, y, z, w;
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Grad(double x, double y, double z) {
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this.x = x;
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this.y = y;
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this.z = z;
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}
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Grad(double x, double y, double z, double w) {
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this.x = x;
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this.y = y;
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this.z = z;
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this.w = w;
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}
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}
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}
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