Spiderman graph: Visibility in urban regions

Motivated by the inaccuracy of GPS devices in urban regions, we study the problem of computing the visibility graph of an urban region. Given a scene of buildings, where a building is represented by the set of its walls, the vertices of the graph correspond to the buildings' walls, and there is an edge between two walls if and only if they are weakly visible to each other. We present efficient algorithms for several scenes, including a sophisticated O(n2log2⁡n)O(n2log2⁡n)-time algorithm for a scene consisting of n walls of varying heights parallel to the yz-plane, where visibility is restricted to directions whose projections on the xy-plane are horizontal. This algorithm uses persistent search trees.