content: /*****************************************************************************
   *                        Shapeways, Inc Copyright (c) 2011
   *                               Java Source
   *
   * This source is licensed under the GNU LGPL v2.1
   * Please read http://www.gnu.org/copyleft/lgpl.html for more information
   *
   * This software comes with the standard NO WARRANTY disclaimer for any
   * purpose. Use it at your own risk. If there's a problem you get to fix it.
   *
   ****************************************************************************/
  package abfab3d.util;
  
  
  /**
   * A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
   *
   * Based on example code by Stefan Gustavson (stegu@itn.liu.se).
   * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
   * 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.
   *
   *
   *
   *
   */
  public class SimplexNoise {  // Simplex noise in 2D, 3D and 4D
  
      // seed for random numbers generator 
      protected double m_seed = 1;
  
      public SimplexNoise(int seed){
          m_seed = seed;
      }
  
    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 static short perm[] = new short[512];
    private static short permMod12[] = new short[512];
    static {
      for(int i=0; i<512; i++)
      {
        perm[i]=p[i & 255];
        permMod12[i] = (short)(perm[i] % 12);
      }
    }
  
    // 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 static double noise(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 static double noise(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
      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 static double noise(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;
      }
    }
  }
  