Some (untested) pseudo-code that may help (assuming from your description that you have separate arrays for each of X, Y, and Z):

• calculate distance from origin (or some other point) for each point in your set

  @dist = map sqrt($x[$_]**2+$y[$_]**2+$z[$_]**2), 0..$#x; or, for some $x0, $y0, $z0, @dist = map sqrt(($x[$_]-$x0)**2+($y[$_]-$y0)**2+($z[$_]-$z0)**2), 0..$#x;

• sort points by that distance

  @indices = sort {$dist[$a]<=>$dist[$b]} 0..$#dist;
  @dist = @dist[@indices];
  @x = @x[@indices];
  @y = @y[@indices];
  @z = @z[@indices];
  @name = @name[@incides];
  [download]

• loop through your points, for each point checking distance of the following points only until the distance from origin has increased by your cutoff

  for my $one (0..$#@dist-1) {
      my $two = $one;
      while (++$two < @dist && $dist[$two]-$dist[$one] <= $cutoff) {
          print "found pair: ($x[$one],$y[$one],$z[$one]) and
  ($x[$two],$y[$two],$z[$two])\n"
              if sqrt(($x[$one]-$x[$two])**2+($y[$one]-$y[$two])**2+($z[
  +$one]-$z[$two])**2) <= $cutoff;
      }
  }
  [download]

This limits how much work the interior loop has to do for each iteration of the exterior loop (unless you have points mosty lying within cutoff distance from the surface of a sphere around your chosen origin, so some knowlege of your data will help choose a good origin).

Update: added code fragments
Update: sort the names with the points :)

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