Translating simplex noise code from java to perl

[grondilu]

Hi monks,

I've been growing an interest for computer graphics lately, and most especially for proceduraly generated landscapes (the kind of stuff we can see in open-world or sandbox games). So while educating myself on this subject I learnt a few things about noise, and I learnt about the so-called Perlin noise, which was invented in the eighties or something. In 2002, Perlin improved his algorithm by using a better tesselation of space. It's called the Simplex noise and it's discussed and explained by Stefan Gustavson in this document, while providing a java implementation in public domain.

Well, I don't like java so I wanted to translate it into Perl. I've done it for the 2D dimension, and I thought it was worth sharing with you monks. I'll certainly translate the rest (3D and 4D) later. I will almost certainly write a Perl 6 version as well.

I also added a few lines to create a noise image in PGM format. Here is the result:

http://imgur.com/ArVvBvN

And here is the code (the original java code is in the __END__)

package SimplexNoise;
# see __END__ for credits
use strict;
use warnings;

my @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], 
);

my @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], 
);

use constant p => qw(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 2
+6 197 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 21
+1 133 230
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 1
+86 3 64
52 217 226 250 124 123 5 202 38 147 118 126 255 82 85 212 207 206 59 2
+27 47 16
58 17 182 189 28 42 223 183 170 213 119 248 152 2 44 154 163 70 221 15
+3 101 155
167 43 172 9 129 22 39 253 19 98 108 110 79 113 224 232 178 185 112 10
+4 218 246
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 1
+50 254
138 236 205 93 222 114 67 29 24 72 243 141 128 195 78 66 215 61 156 18
+0);

use constant perm => (p, p);
use constant permMod12 => map { $_ % 12 } perm;

# Skewing and unskewing factors for 2, 3, and 4 dimensions
use constant {
    F2 => 0.5 * (sqrt(3.0) - 1.0),
    G2 => (3.0 - sqrt(3.0)) / 6.0,
    F3 => 1.0 / 3.0,
    G3 => 1.0 / 6.0,
    F4 => (sqrt(5.0) - 1.0) / 4.0,
    G4 => (5.0 - sqrt(5.0)) / 20.0,
};

sub floor {
    my $x = shift;
    my $xi = int($x);
    return $x < $xi ? $xi - 1 : $xi;
}

sub dot {
    my @grad = @{shift()};
    my $sum = 0;
    $sum += $_ * shift @grad for @_;
    $sum;
}

sub noise {
    if (@_ == 2) {
    # 2D noise
    my ($n0, $n1, $n2);
    my ($xin, $yin) = @_;
    my $s = ($xin + $yin) * F2;
    my ($i, $j) = map { floor($_) } $xin + $s, $yin + $s;
    my $t = ($i + $j) * G2;
    my ($X0, $Y0) = ($i - $t, $j - $t);
    my ($x0, $y0) = ($xin - $X0, $yin - $Y0);
    my ($i1, $j1) = $x0 > $y0 ? (1, 0) : (0, 1);
    my ($x1, $y1) = ($x0 - $i1 + G2, $y0 - $j1 + G2);
    my ($x2, $y2) = ($x0 - 1 + 2 * G2, $y0 - 1 + 2 * G2);
    my ($ii, $jj) = ($i & 255, $j & 255);
    my ($gi0, $gi1, $gi2) = (permMod12)[
    $ii + (perm)[$jj],
    $ii + $i1 + (perm)[$jj + $j1],
    $ii + 1 + (perm)[$jj + 1]
    ];
    my $t0 = 0.5 - $x0 * $x0 - $y0 * $y0;
    if ($t0 < 0) { $n0 = 0 }
    else {
        $t0 *= $t0;
        $n0 = $t0 * $t0 * dot($grad3[$gi0], $x0, $y0);
    }
    my $t1 = 0.5 - $x1 * $x1 - $y1 * $y1;
    if ($t1 < 0) { $n1 = 0 }
    else {
        $t1 *= $t1;
        $n1 = $t1 * $t1 * dot($grad3[$gi1], $x1, $y1);
    }
    my $t2 = 0.5 - $x2 * $x2 - $y2 * $y2;
    if ($t2 < 0) { $n2 = 0 }
    else {
        $t2 *= $t2;
        $n2 = $t2 * $t2 * dot($grad3[$gi2], $x2, $y2);
    }
    return 70 * ($n0 + $n1 + $n2);
    } elsif (@_ == 3) {
    # 3D noise
    ...
    } elsif (@_ == 4) {
    # 4D noise
    ...
    } else {...}
}

my $N = 256;

print "P2\n";
print "$N $N\n";
print "255\n";
for my $i (1 .. $N) {
    my $x = $i / 10;
    for my $j (1 .. $N) {
    my $y = $j / 10;
    my $noise =  noise $x, $y;
    print int(($noise + 1) / 2 * 256);
    print $j == $N ? "\n" : ' ';
    }
}

__END__

=pod
=begin java
    /*
     * A speed-improved simplex noise algorithm for 2D, 3D and 4D in J
+ava.
     *
     * Based on example code by Stefan Gustavson ([e-mail]).
     * Optimisations by Peter Eastman ([e-mail]).
     * 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 autho
+r,
     * Stefan Gustavson. You may use it as you see fit, but
     * attribution is appreciated.
     *
     */

    public class SimplexNoise {  // 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,
      131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,2
+40,21,10,23,
      190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,3
+2,57,177,33,
      88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,13
+9,48,27,166,
      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,
      5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,18
+2,189,28,42,
      223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,16
+7, 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), whe
+re
    // c = (3-sqrt(3))/6
    double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) un
+skewed 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 corne
+rs
    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 corner
+s
    // Skew the input space to determine which simplex cell we're in
    double s = (xin+yin+zin)*F3; // Very nice and simple skew factor f
+or 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 tetr
+ahedron.
    // 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 corner
+s
    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 co
+rners
    // Skew the (x,y,z,w) space to determine which cell of 24 simplice
+s 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) spa
+ce
    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 nee
+d to
    // determine the magnitude ordering of x0, y0, z0 and w0.
    // Six pair-wise comparisons are performed between each possible p
+air
    // of the four coordinates, and the results are used to rank the n
+umbers.
    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 c
+orner
    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 mak
+e any sense.
    // We use a thresholding to set the coordinates in turn from the l
+argest 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 corner
+s
    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;
    }
      }
    }
=end java

=cut