Intervisibility

The Basic Algorithm

To determine intervisibility, it is essential to have a digital representation of terrain as either a gridded digital elevation model (DEM) or a triangulated irregular network (TIN) and to define two point locations, a viewpoint and a target. At both locations, a height above the terrain should also be defined. It is possible to identify the line of sight as the straight line that would run between the two points. The target and the viewpoint are said to be intervisible if the land surface between them does not rise above the line of sight. If it does, then they are not intervisible; the target is not visible from the viewpoint. Usually, 1 will be returned by an intervisibility operation when the target is in view, and 0 when it is not. Other values can result, but they can always be reformulated to the 0/1 outcome. For example, some software returns either the angle between the line of sight and the horizontal for locations that are visible, or 0 for those that are not (see Figure 1).

Figure 1 To an observer at a specific height above the ground, some parts of the surrounding landscape are visible (indicated by the solid profile lines), but others are not (indicated by dashed lines)

The extension of intervisibility is to make the determination exhaustively for every potential target in the terrain. The result is known as the viewshed (echoing the watershed) and is typically a binary mapping of the landscape, with locations in view indicated as 1, and those out of view as 0. Determination of a viewshed typically requires additional parameters, including specifying the planimetric extent of the view specified as starting from one compass direction and extending to another. For example, the extent of view may represent the human visual field, which is approximately 120°.

Extensions

Because the elevations at each end of the line of sight should be specified as heights above the ground, it [Page 242]does not follow that two intervisible locations are necessarily intervisible at ground level, nor does it ever follow that because one location at one height is visible from another location at another height, the reverse will be true if the heights are reversed.

In addition to one point being visible from another, it is possible to determine whether a feature of a particular height viewed from one location would be backed by sky or by terrain. This is essential information for applications in landscape planning and in some military applications.

Furthermore, light and other electromagnetic radiation does not travel through the atmosphere in a straight line, but is bent by refraction and longer wavelengths, such as radio, are diffracted around obstacles. This can be accommodated in the line-of-sight determination by using a curved line, as opposed to a straight line, and by modeling refraction and diffraction.

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