Here's a little tip to get you going:

my @directions = ('w', 'sw', 's', 'se', 'e', 'ne', 'n', 'nw');
my $anchor = $directions[int($real_angle/45 + 0.5)];
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this piece of untested code would save you 40 lines of code. Not bad eh? Before thinking of speed, try to see if you can make your code more compact.