Is there an easy way of detecting the intersection of two concave polygons that have all of their sides either parallel or orthogonal to one another?
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So all sides of both polygons run north/south or east/west? I don't think you'll get anything easy. By making the sides very small, you can fake a diagonal line, and make the polygons do whatever you want. So now you've eliminated the only thing that could have helped you out. The answer might change if there is a minimum side length and maximum polygon diameter, however. – Teepeemm Sep 23 '13 at 14:20
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A lot of problems with rectilinear (isothetic) polygons was studied by Preparata and Shamos (for example - in the book Computational Geometry: An Introduction).
I think, you have to look at the sweep line algorithm

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