3_2_-1 => -44.368_23.583_-218.345_0.983_-0.012_0.005_-0.382_0.041_0.20
+5_-0.538_-0.876_0.100      -56.368_2.583_-28.745_0.883_-0.012_0.005_-
+0.382_0.041_0.205_-0.538_-0.876_0.100 ...
[download]

my $input = $ARGV[0];
open(INFILE,"$input") or die "cannot open file $input!\n";
my $output = $ARGV[1];
my %total_hash_keys=();
my %tri_hash = ();
#set bin width
my $grid = 2;
my $step = 0;
my $block_size = 10000;
my $block_no = 0;

my @points;
while(<INFILE>){my @array = split(/\t/,$_); push @points, [@array];} 
close(INFILE);

#construct hash table
for(my $i=0;$i<@points;$i++){
  for(my $j=$i+1;$j<@points;$j++){
    for(my $k=$j+1;$k<@points;$k++){
      $step++;
      my @pt1 = (${$points[$i]}[0],${$points[$i]}[1],${$points[$i]}[2]
+);
      my @pt2 = (${$points[$j]}[0],${$points[$j]}[1],${$points[$j]}[2]
+);
      my @pt3 = (${$points[$k]}[0],${$points[$k]}[1],${$points[$k]}[2]
+; 
 
      #simplified calculation for the value of the hash;
      my @matrix = (@pt1,@pt2,@pt3);
      for(my $res=0;$res<@points;$res++){
        #transform coor, and bin the new coor as a generated key
        my @old_xyz = @{$points[$res]};
        my @new_xyz = transform(@old_xyz,@matrix);
        foreach(@new_xyz){$_ = int($_/$grid); }
        my $key = $new_xyz[0]."_".$new_xyz[1]."_".$new_xyz[2];
        foreach(@matrix){$_ = sprintf "%.3f",$_;}
        my $value = "";
        for(my $temp=0;$temp<@matrix;$temp++){$value .= $matrix[$temp]
+."_"; } 
        $total_hash_keys{$key}=0;
        push @{$tri_hash{$key}},$value;
      }
      if(($step % $block_size) == 0){#write to disk file
        $block_no = int($step/$block_size);
        my $tmp_hash_file = "tmp_hash".$block_no;
        open(OUTFILE,">$tmp_hash_file") or die "cannot write to file $
+tmp_hash_file!\n";
        foreach(keys %tri_hash){
          print OUTFILE "$_\t";
          print OUTFILE "@{$tri_hash{$_}}\n";
        }
        %tri_hash = ();#free memory
      }
    }#for k
  }#for j
}#for i

my $total_file_no = int($step/$block_size);

open(OUTFILE,">$output") or die "cannot write to file $output!\n";
while(($my_key,$my_value)=each %total_hash_keys){
  print OUTFILE $my_key."=>";
  for(my $i=1;$i<$total_file_no + 1;$i++){
    my $hash_file = "tmp_hash".$i; open(INFILE,"$hash_file") or die;
    while(<INFILE>){
      my @array = split(/\t/,$_);
      if($array[0] eq $my_key){
        chomp ($array[1]);
        print OUTFILE $array[1];
        last;
       }
     }
     close(INFILE);
   }
   print OUTFILE "\n";
}

sub transform{
        my ($x,$y,$z,@t) = @_;
        my $new_x=$x*$t[0]+$y*$t[3]+$z*$t[6];
        my $new_y=$x*$t[1]+$y*$t[4]+$z*$t[7];
        my $new_z=$x*$t[2]+$y*$t[5]+$z*$t[8];
        return ($new_x,$new_y,$new_z);
}
[download]

We are about 5% closer to understanding the bigger picture so at this point I'll give up trying to figure out how best to help you and simply toss a little database code in your direction instead:

#!/usr/bin/env perl
use strict;
use warnings;
use DBI;

my $dbh = DBI->connect('dbi:SQLite:dbname=delme.sqlite', '');

$dbh->do('CREATE TABLE Bins (Xk INTEGER, Yk INTEGER, Zk INTEGER, Data 
+TEXT)');

my $sql = 'INSERT INTO Bins (Xk, Yk, Zk, Data) VALUES (?, ?, ?, ?)';
my $sth = $dbh->prepare ($sql);

while (defined (my $data = <DATA>)) {
    my ($xKey, $yKey, $zKey) = split ' ', $data;
    
    chomp $data;
    $sth->execute((map {int} $xKey, $yKey, $zKey), $data);
}

$sql = 'SELECT * FROM Bins ORDER BY Xk, Yk, Zk';
$sth = $dbh->prepare($sql);
$sth->execute();

while (my $row = $sth->fetchrow_hashref()) {
    print "$row->{Xk}, $row->{Yk}, $row->{Zk} => $row->{Data}\n";
}


__DATA__
4.941 32.586 -1.772 -44.368_23.583_-218.345_0.983_-0.012_0.005_-0.382_
+0.041_0.205
15.354 22.823 10.556 -56.368_2.583_-28.745_0.883_-0.012_0.005_-0.382_0
+.041_0.205
-0.495 12.345 98.234 -0.382_0.041_0.205_-28.745_0.883_-0.012_0.005_-0.
+382_0.041
[download]

Prints:

0, 12, 98 => -0.495 12.345 98.234 -0.382_0.041_0.205_-28.745_0.883_-0.
+012_0.005_-0.382_0.041
4, 32, -1 => 4.941 32.586 -1.772 -44.368_23.583_-218.345_0.983_-0.012_
+0.005_-0.382_0.041_0.205
15, 22, 10 => 15.354 22.823 10.556 -56.368_2.583_-28.745_0.883_-0.012_
+0.005_-0.382_0.041_0.205
[download]

True laziness is hard work

Thank you very much for your help, GrandFather. I apologize for missing the point of your question. indeed building a database seems a plausible thing to do given the large quantity of data i have.
i have about 10,000 such input files, each consisting of a point cloud. i am constructing a hash table for each input file, so in the end i have about 10,000 hashes. (not all hash tables are huge, as most files only have about 20 points as opposed to the 100 points that cause the problem i mentioned here)
eventually what i'd like to do with these hashes is that i will do pairwise comparison and look for common keys between each pair. that information will be used to compute a distance/dissimilarity measure between the pair of point clouds from which the pair of hash tables being compared come from. in the very end i hope to perform clustering on the 10,000 sets of point clouds.