The Geometry of Rectangles

The methods developed earlier to intersect planar convex polygons are certainly applicable to a collection of rectangles. Similarly, a collection of segments, each of which is either parallel or orthogonal to any other member of the collection, can be handled by the general segment intersection technique described in the preceding chapter. However, the very special nature of segments having just two orthogonal directions, or of rectangles whose sides are such segments, suggests that perhaps more efficientad hoctechniques can be developed to treat such highly structured cases. And in the process of studying this class of problems one may acquire more insight into the geometric properties possessed by the objects mentioned above—rectangles and orthogonal segments—and may succeed in characterizing the wider class to which the techniques are still applicable.