ON SOME UNION AND INTERSECTION PROBLEMS FOR POLYGONS WITH FIXED ORIENTATIONS.

We describe how to perform a general decomposition of a set of polygons with fixed orientations, in order to solve various computational geometry problems which are important in VLSI design. The decomposition is very simple and efficiently computable, and it allows the subsequent application of algorithms for the rectilinear case, leading to some very efficient and some optimal solutions. We illustrate the technique in detail at the problem of finding the connected components of a set of polygons, for which we derive an optimal solution. The wide applicability of the method is then demonstrated at the problem of findings all pairs of intersecting polygons, yielding an optimal solution.