What assumptions can you make about the collection of vertices? Is the geometric figure always convex? Can edges cross?

The vector cross product of a pair of successive edges in the x-y plane will be negative if the lines break right (clockwise), positive if they break left (counterclockwise). Given vertices at ($x1,$y1), ($x2,$y2), and ($x3,$y3),

my ($dx1, $dy1) = ($x2 - $x1, $y2 - $y1);
my ($dx2, $dy2) = ($x3 - $x2, $y3 - $y2);
my $cross = $dx1*$dy2 - $dy1*$dx2;
print $cross < 0
      ? "clockwise"
      :   $cross == 0
          ? "collinear"
          : "counterclockwise";
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That is not reliable unless the figure is convex. A banana shaped figure will have different sign at different vertices.

The numeric tags on those variables look like a shout for arrays, but they are just labels. The natural place to use arrays here is to group x and y for each vertex.

After Compline,
Zaxo