Merging a set of polygons

The paper presents a new algorithm for merging a set of polygons based on a sweep-line technique. The algorithm operates on simple polygons and a limited set of non-simple polygons considered as legal polygons. At first, the algorithm separates loops and rings of the polygons located at the odd levels of hierarchy. The sweeping process is then started separately for the loops and the rings. During sweeping the loops, the inner polygons are identified. They participate at filling the holes what is done in the second step. The main task of the sweeping process is to determine common vertices and overlapping edges. After that, merging of the polygons is realized by a walk-about of the edges. The expected time complexity of the algorithm is O(k log k), k=m+I where m represents the total number of vertices of all polygons in the input set, and I is the number of touching edges among polygons. At the end the efficiency of the algorithm is illustrated using data from geodesy.