Window Queries On Planar Subdivisions Arising From Overlapping Polygons

We present efficient algorithms for partitioning 2dimensional space into faces arising from the boundaries of overlapping polygons. In particular, we examine the case where the partitioning arises from overlaying m k-sided simple polygons. A dynamic data structure is presented for storing the partitioning that arises from m polygons with at most k sides each in space O(km) if the polygons are assumed to be convex, and space O(km) for simple polygons. Our structure returns T distinct regions from an axis-aligned orthogonal range search in worst case O(mk + (m + k)(logmk)T ) time, and can be updated in O(km) time.