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Diffstat (limited to 'src/libnoiseforjava/module/Simplex.java')
| -rw-r--r-- | src/libnoiseforjava/module/Simplex.java | 395 |
1 files changed, 395 insertions, 0 deletions
diff --git a/src/libnoiseforjava/module/Simplex.java b/src/libnoiseforjava/module/Simplex.java new file mode 100644 index 0000000..82d58c6 --- /dev/null +++ b/src/libnoiseforjava/module/Simplex.java @@ -0,0 +1,395 @@ +package libnoiseforjava.module;
+
+/**
+ * Michael Nugent
+ * Date: 3/9/12
+ * Time: 6:12 PM
+ * URL: https://github.com/michaelnugent/libnoiseforjava
+ * Package: libnoiseforjava.module
+ */
+
+
+/*
+* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
+*
+* Based on example code by Stefan Gustavson ([email protected]).
+* Optimisations by Peter Eastman ([email protected]).
+* Better rank ordering method by Stefan Gustavson in 2012.
+*
+* This could be speeded up even further, but it's useful as it is.
+*
+* Version 2012-03-09
+*
+* This code was placed in the public domain by its original author,
+* Stefan Gustavson. You may use it as you see fit, but
+* attribution is appreciated.
+*
+* Modified by Michael Nugent ([email protected]) for the
+* libnoise framework 20120309
+* All libnoise expects 3d, but I've left the 2d and 4d functions in for
+* reference.
+*
+*/
+
+public class Simplex extends ModuleBase { // Simplex noise in 2D, 3D and 4D
+ private static Grad grad3[] = {new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
+ new Grad(1,0,1),new Grad(-1,0,1),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)};
+
+ 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),
+ new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
+ new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
+ new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
+ new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
+ new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
+ new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
+ new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};
+
+ private static short 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};
+ // To remove the need for index wrapping, double the permutation table length
+ private short perm[] = new short[512];
+ private short permMod12[] = new short[512];
+
+ private double seed = 0;
+
+ public Simplex() {
+ super(0);
+ for(int i=0; i<512; i++) {
+ perm[i]=p[i & 255];
+ permMod12[i] = (short)(perm[i] % 12);
+ }
+ }
+
+ public double getSeed() {
+ return seed;
+ }
+
+ public void setSeed(double seed) {
+ this.seed = seed;
+ }
+
+ public void setSeed(int seed) {
+ this.seed = (double)seed;
+ }
+
+ // Skewing and unskewing factors for 2, 3, and 4 dimensions
+ private static final double F2 = 0.5*(Math.sqrt(3.0)-1.0);
+ private static final double G2 = (3.0-Math.sqrt(3.0))/6.0;
+ private static final double F3 = 1.0/3.0;
+ private static final double G3 = 1.0/6.0;
+ private static final double F4 = (Math.sqrt(5.0)-1.0)/4.0;
+ private static final double G4 = (5.0-Math.sqrt(5.0))/20.0;
+
+ // This method is a *lot* faster than using (int)Math.floor(x)
+ private static int fastfloor(double x) {
+ int xi = (int)x;
+ return x<xi ? xi-1 : xi;
+ }
+
+ private static double dot(Grad g, double x, double y) {
+ return g.x*x + g.y*y;
+ }
+
+ private static double dot(Grad g, double x, double y, double z) {
+ return g.x*x + g.y*y + g.z*z;
+ }
+
+ private static double dot(Grad g, double x, double y, double z, double w) {
+ return g.x*x + g.y*y + g.z*z + g.w*w;
+ }
+
+
+ // 2D simplex noise
+ public double getValue2d(double xin, double yin) {
+ 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 = fastfloor(xin+s);
+ int j = fastfloor(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 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
+ double y2 = y0 - 1.0 + 2.0 * G2;
+ // Work out the hashed gradient indices of the three simplex corners
+ int ii = i & 255;
+ int jj = j & 255;
+
+ int gi0 = permMod12[ii+perm[jj]];
+ int gi1 = permMod12[ii+i1+perm[jj+j1]];
+ int gi2 = permMod12[ii+1+perm[jj+1]];
+ // 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);
+ }
+
+
+ // 3D simplex noise
+ public double getValue(double xin, double yin, double zin) {
+ double n0, n1, n2, n3; // Noise contributions from the four corners
+ // Skew the input space to determine which simplex cell we're in
+ xin+=(seed + (seed * 7)) % Double.MAX_VALUE;
+ xin+=(seed + (seed * 13)) % Double.MAX_VALUE;
+ xin+=(seed + (seed * 17)) % Double.MAX_VALUE;
+ double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
+ int i = 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) 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 = permMod12[ii+perm[jj+perm[kk]]];
+ int gi1 = 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]]];
+ // 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);
+ }
+
+
+ // 4D simplex noise, better simplex rank ordering method 2012-03-09
+ public double getValue4d(double x, double y, double z, double w) {
+
+ 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 = fastfloor(x + s);
+ int j = fastfloor(y + s);
+ int k = fastfloor(z + s);
+ int l = 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 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.
+ // Six pair-wise comparisons are performed between each possible pair
+ // 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++; 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++;
+ 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 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.
+ // Rank 3 denotes the largest 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 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 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 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 = 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;
+ 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 - 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
+ 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 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);
+ }
+
+ // Inner class to speed upp gradient computations
+ // (array access is a lot slower than member access)
+ private static class Grad
+ {
+ double x, y, z, w;
+
+ Grad(double x, double y, double z)
+ {
+ this.x = x;
+ this.y = y;
+ this.z = z;
+ }
+
+ Grad(double x, double y, double z, double w)
+ {
+ this.x = x;
+ this.y = y;
+ this.z = z;
+ this.w = w;
+ }
+ }
+}
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