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.

翻译：地形分析中的一项重要任务是计算视域（viewsheds）。视域是从给定视点或视点集合可见的所有地形区域的并集。视域的复杂度可能因地形地貌和视点位置的不同而显著变化。本研究提出一种新的地形属性——"刺度"（prickliness），用于衡量从所有可能视角观察地形时局部极大值的数量。我们证明，刺度能够有效刻画2.5D TIN地形具有高复杂度视域的潜力。针对TIN地形，我们提出了最优（针对1.5D地形）和近最优（针对2.5D地形）的计算算法，并为栅格DEM开发了高效近似算法。通过在大规模真实地形数据集上的实验，验证了刺度属性的实用价值。