Slight variations on what other have done. This dies if your polygon is not closed.
#!/usr/bin/perl
use strict;
my @seg = (
[ 1, 1, 2, 1 ],
[ 5, 5, 1, 5 ],
[ 2, 3, 5, 3 ],
[ 5, 3, 5, 5 ],
[ 2, 1, 2, 3 ],
[ 1, 5, 1, 1 ]);
my %starts=map{"@$_[0,1]",$_} @seg;
my @sorted_segs = my $cur = $seg[0];
while (1) {
my $next = $starts{"@$cur[2,3]"};
die "your polygon is broken\n" if !$next;
$next==$seg[0] ? last : push @sorted_segs,$next;
$cur = $next;
}
print "@$_\n" for @sorted_segs;
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