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 and (under standard assumptions) near-optimal algorithms to compute it for 1.5D and 2.5D TIN terrains, respectively, 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\emph{视域}。视域是指从给定视点或一组视点可见的所有地形区域的并集。视域的复杂度根据地形的拓扑结构和视点位置的不同可能存在显著差异。本研究探讨了一种新的地形属性——\emph{刺度}，该属性用于度量从所有可能视角观察时地形中局部最高点的数量。我们证明，刺度能有效刻画2.5D TIN地形具有高复杂度视域的潜力。我们分别针对1.5D和2.5D TIN地形提出了最优及（在标准假设下）近似最优的计算算法，并为栅格DEM提供了高效的近似算法。我们通过在大量真实地形数据集上的实验验证了刺度属性的实用性。