1.5维地形多视点Voronoi视度图研究
On Voronoi visibility maps of 1.5D terrains with multiple viewpoints
摘要：
给定$n$ -顶点1.5D地形$\T$和$m<n$视点的集合$\A$，Voronoi可见性图$\vorvis(\T,\A)$是将$\T$划分成区域，使得每个区域被分配给最近的（在欧几里德距离中）可见视点。彩色可见性图$\colvis(\T,\A)$是将$\T$划分为具有相同可见视点集合的区域。在本文中，我们提出了一个算法来计算$\vorvis(\T,\A)$，运行在$O(n+(m^2+k_c)\log n)$时间，其中$k_c$和$k_v$表示$\colvis(\T,\A)$和$\vorvis(\T,\A)$，分别总的复杂性。这改进了以前的算法这个问题。我们还将我们的算法推广到高阶Voronoi可见性映射，以及其他距离的Voronoi可见性映射。最后，我们证明了有关$k_v$的界限$k_c$，我们展示了我们的算法的应用，有限的视线范围的问题。
英文摘要：
Given an $n$-vertex 1.5D terrain $\T$ and a set $\A$ of $m<n$ viewpoints, the Voronoi visibility map $\vorvis(\T,\A)$ is a partitioning of $\T$ into regions such that each region is assigned to the closest (in Euclidean distance) visible viewpoint. The colored visibility map $\colvis(\T,\A)$ is a partitioning of $\T$ into regions that have the same set of visible viewpoints. In this paper, we propose an algorithm to compute $\vorvis(\T,\A)$ that runs in $O(n+(m^2+k_c)\log n)$ time, where $k_c$ and $k_v$ denote the total complexity of $\colvis(\T,\A)$ and $\vorvis(\T,\A)$, respectively. This improves upon a previous algorithm for this problem. We also generalize our algorithm to higher order Voronoi visibility maps, and to Voronoi visibility maps with respect to other distances. Finally, we prove bounds relating $k_v$ to $k_c$, and we show an application of our algorithm to a problem on limited range of sight.
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