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2D object-aligned bounding-box intersection test

I have two object-aligned bounding boxes (i.e. not axis aligned, they rotate with the object). I'd like to know if two object-aligned boxes overlap.

My boxes are stored as four x,y points. I've searched around for answers, but I can't make sense of the variable names and algorithms in examples to apply them to my particular case.

Can someone help show me how this would be done, in a clear and simple way? Thanks. (The particular language isn't important, C-style pseudo code is OK.)