if working with it as a polygon, the most you'll be able to determine is "inside" or "outside", since it's an enclosed ring -- there's no difference to the polygon (from a computational geometry standpoint) whether it's "outside above" or "outside below".

 

what you'll need to do is treat the top 4 segments and bottom 4 segments as oriented line segments (you won't need to use the two vertical side segments).  your point can then be tested against these sets of segments to determine what side they're on.

 

the test goes something like this:  say your polygon winds counter-clockwise, if the point is on right side of all four bottom segments then it's "below", if it's on the right side of all four top segments then it's "above".

 

determining which side of a line a point falls on is just a cross product, and you can find that code all over the 'net, BUT... you need to be a bit smart about it, because you're working with line *segments*, and most "simple" code out there will assume an infinite line.  (and you can easily craft a failure case where your point is on the correct side of the segment, but the wrong side of that segment if extended to an infinite line - just put the point in a concave "valley", for example)

 

here are a few snippets of comp. geom. to get you started, google for the rest:

http://paulbourke.net/geometry/pointline/

http://wiki.processing.org/w/Find_which_side_of_a_line_a_point_is_on

 

hth

 

[[or, a completely different approach would be to create two more polygons, invisibly modelling the remaining "white space" above and below your visible polygon, then use point-in-polygon against THOSE to determine above/below -- conceptually simpler, and probably less code to write, but more computationally expensive overall behind the scenes]]

 

I went with your second suggestion and it works perfect!