On the X-Y Convex Hull of a Set of X-Y Polygons

We study the class of rectilinear polygons, called X Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the.~class of X Y polygons and present efficient algorithms for computing the X Y convex hulls of an X Y polygon and of a set of X Y polygons under various conditions. Unlike convex hulls in the Euclidean plane, the X Y convex hull of a set of X Y polygons may not exist. The condition under which the X Y convex hull exists is given and an algorithm for testing if the given set of X Y polygons satisfies the condition is also presented.