  An important task in terrain analysis is computing \emph{viewsheds}. A
viewshed is the union of all the parts of the terrain that are visible from a
given viewpoint or set of viewpoints. The complexity of a viewshed can vary
significantly 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 angles of
view. We show that the prickliness effectively captures the potential of 2.5D
TIN terrains to have high complexity viewsheds. We present optimal (for 1.5D
terrains) and near-optimal (for 2.5D terrains) algorithms to compute it for TIN
terrains, and efficient approximate algorithms for raster DEMs. We validate the
usefulness of the prickliness attribute with experiments in a large set of real
terrains.
