Hey stu69art, good luck with your search for an alternative algorithm. Here are a few testcases that you can use to verify your results that covers most of the cases you might encounter. Let us know how you get on:)

#! perl -slw
use strict;

sub direction{
    local($_, @_= @_);
    push @_, $_[0];
    $_+= $a->[0]*$b->[1]-$a->[1]*$b->[0] while ($a,$b)=(shift,$_[0]), 
+@_;
    $_ < 0;
}
=pod
|   .
|  /.\
| // \\
|//   -
|\\   _
| \\ //
|  \v/
+---v-----
=cut
my @inflectiveC = ([0,3],[3,6],[5,4],[4,4],[3,5],[1,3],[3,1],[4,2],[5,
+2],[3,0]);
print direction(@inflectiveC) ? 'Clockwise' : 'Not clockwise';

my @inflectiveA = reverse @inflectiveC;
print direction(@inflectiveA) ? 'Clockwise' : 'Not clockwise';

my @mirroredXC = reverse map{ [ 0 - $_->[0], $_->[1]] } @inflectiveC;
print direction(@mirroredXC) ? 'Clockwise' : 'Not clockwise';

my @mirroredXA = map{ [ 0 - $_->[0], $_->[1]] } @inflectiveC;
print direction(@mirroredXA) ? 'Clockwise' : 'Not clockwise';

my @mirroredYC = reverse map{ [$_->[0], 0 - $_->[1]] } @inflectiveC;
print direction(@mirroredXC) ? 'Clockwise' : 'Not clockwise';

my @mirroredYA = map{ [$_->[0], 0 - $_->[1]] } @inflectiveC;
print direction(@mirroredXA) ? 'Clockwise' : 'Not clockwise';
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