An Algorithm for Computing the Overlay of k-Dimensional Spaces

The overlay operation, as supported by geographic information systems, is often limited to 2-dimensional spaces and polygonal regions. The problem can be generalized to k-dimensional spaces, k ≥ 1, and to arbitrary kinds of spatial objects. A z-order-based algorithm for this general form of overlay is given. The algorithm produces an approximate answer, which is then refined. As with other z-order algorithms, a spatial object is represented by a set of intervals in 1-dimensional space. "Redundancy" — the number of these intervals — can be selected. The performance of the overlay algorithm is determined by redundancy. The performance of the overlay algorithm, and its dependence on redundancy is studied experimentally. Minimal redundancy should be avoided as it leads to poor performance.