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Topological Terrain Map Resolution: Intervisibility, Crest, and Military Crest 1 2 Donald R. Barr , Bard Mansager , William P. Fox, Thomas Riddle Introduction The depiction of terrain in computerized combat simulation models generally takes the form of a discrete approximation. The modeled terrain surface is often represented by a step function over a two-dimensional domain covered by a tessellation of squares or hexagons. Military field testing applications use such digitized terrain maps in connection with target tracking enhancements. Such uses include improvements in accuracy of tracking in the elevation dimension (“z-axis”) using Global Positioning System (GPS--satellite) information. Digital maps are used in many modeling applications in connection with computer displays of units on or above the terrain. In the case where the domain of the approximating terrain surface is covered by squares, it is common to designate the terrain resolution in terms of the length of a side of such a square. Thus, “100-meter terrain”, refers to an approximating function with domain partitioned into squares 100 meters on a side. As the resolution is increased (25-meter and 3-meter terrain data bases are common), the size of the terrain data base increases exponentially. This drives up the cost of development of the database for a given size area, as well as the cost of storing the database and using it in a modeling application. An important determinant of interaction of opposing combat forces is their intervisibility. Intervisibility calculations made between two points on the ground using a given digital terrain database can provide approximations of how much of a given unit (such as an Abrams tank or an infantry squad) located at one point is exposed to visual contact by an opposing unit an another point. Such calculations are computationally expensive, generally involving algorithms that step along a vector (ra