Although VERY beautiful, it is incorrect: 
#!/cadappl/bin/perl -w -Ilib

use strict;

my @r = ( 
  [ 5, 3, 5, 5 ],
  [ 1, 1, 2, 1 ],
  [ 2, 3, 5, 3 ],
  [ 5, 5, 1, 5 ],
  [ 2, 1, 2, 3 ],
  [ 1, 5, 1, 1 ],
);
my @x = sort { $a->[2] <=> $b->[0] || $a->[3] <=> $b->[1] || -1 } @r;
foreach (@x)
{
        print "$_->[0],$_->[1],$_->[2],$_->[3]\n";
}

[download]
Output: 
1,5,1,1
1,1,2,1
2,1,2,3
5,5,1,5
2,3,5,3
5,3,5,5

[download]
I changed the order of @r to show the error.

In reply to Re^2: reordering segments to form a polygon by Jaap
in thread reordering segments to form a polygon by dada

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