  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 \emph{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.
