I am looking for an algorithm to identify all of the rectangles bounded by two parallel edges of a polygon. The rectangle must remain inside of the polygon at all times. My polygon is simple and will never have an acute angle. I have looked for algorithms already, but they seem to only work for convex or orthogonal polygons. Is there a good approach to this. At this point, I am thinking I should group all edges by parallelity and inspect those sets to find rectangular regions. It sounds bad.
This post is related to another post: Cover a Concave Polygon with a minimum number of rectangles
I am hoping to split up the questions so I can attract better answers.