An Acrophobic Guard Watchtower Problem on Terrains.

In the acrophobic guard watchtower problem for a polyhedral terrain, a square axis-aligned platform is placed on the top of a tower whose bottom end-point lies on the surface of the terrain. As in the standard watchtower problem, the objective is to minimize the height (i.e., the length) of the watchtower such that every point on the surface of the terrain is weakly visible from the platform placed on the top of the tower. In this paper, we show that in R2 the problem can be solved in O(n) time, and in R3 it takes O(nlog⁡n) time, where n is the total number of vertices of the terrain.