Analytic determination of gradients of intervisibility over continuous randomly-generated topography

Determination of the existence of intervisibility between pairs of points a bove realistically undulating terrain is a fundamental operation within lan d-based military simulations. However, transitions between regions where an intelligently piloted vehicle is respectively exposed and concealed are of particular importance, yet are often very difficult to identify a priori. Tn this paper we show how a meaningful gradient of intervisibility can be d irectly calculated, and we argue that this provides a valuable indication o f the direction to the nearest point of opposite visibility. Moreover, dire ct methods for evaluating such gradients are also relevant to some classes of behavioural models for vehicles moving over such terrain. Numerical simu lation results are presented in support of the theoretical analyses. We will also outline how. simple randomized, yet differentiable topography, exhibiting realistic undulations, can be conveniently generated as a therm alized elastic manifold. The availability of such an ensemble of different topographies provides a powerful test of the adaptability of any terrain-de pendent algorithm, and forms an integral part of the validation of our anal ysis.