Determine if a polygon is complex.

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I want to determine if a polygon is complex not using inbuilt functions.
This is my rough idea.
for edge = 1:n
for otheredge = 1:n
if edge crosses otheredge
disp ('complex polygon')
disp ('non complex polygon')
I doubt anyone could help me as I have searched high and low with no luck. I don't know how to come up with a value for the edges to determine if they cross or not. I guess maybe you could make all the edges into linear equations ? Also that loop is just a quick brainstorm. Attached is some examples of where the polygon is complex and not.
Shapes c and d are complex. I have no idea how I would figure out d. Maybe calculate the points which are within other points.
Any slight bit of help or input would be appreciated.
NOTE: I am using shoelace formula to calculate area and if some how someone knows how to determine if polygon is complex or not how could I use this information to calculate maybe the area of d.

Accepted Answer

Sean de Wolski
Sean de Wolski on 26 Mar 2014
Edited: Sean de Wolski on 26 Mar 2014
If you have the Mapping Toolbox, you can use polyxpoly to test if to line segments intersect. I'm sure there's a utility to do this on the FEX as well.
Actually, geom2d looks like it has an intersection function for this.

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