Approximative Terrain Guarding with Given Number of Guards

Guarding a surface is a well known optimization problem of the visibility site analysis and has many applications. The basic problem is searching for the minimum number of guards needed to guard (see) the entire surface. More realistic is the guarding where the number of guards is upward limited and the optimization problem is to search for their locations in order to guard as much surface as possible. In the paper this problem is treated in detail. Several known heuristics (greedy add, greedy add with swap and stingy drop) are revised and a new technique called solution improving technique is proposed. The technique improves the results of the known algorithms and is used in indirect solving of the problem. Tests on 44 DEMs from USGS DEM Repository showed that our technique yields comparative results for smaller number of guards and better results for higher number of guards

Terrain prickliness: theoretical grounds for high complexity viewsheds

An important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union of all the triangle parts that are visible from the viewpoint. The complexity of a viewshed can vary significantly, from constant to quadratic in the number of terrain vertices, depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible perspectives. We show that the prickliness effectively captures the potential of 2.5D terrains to have high complexity viewsheds, and we present near-optimal algorithms to compute the prickliness of 1.5D and 2.5D terrains. We also report on some experiments relating the prickliness of real word 2.5D terrains to the size of the terrains and to their viewshed complexity.Peer ReviewedPostprint (author's final draft