不规则三角网可见性图的识别
Recognizing Visibility Graphs of Triangulated Irregular Networks
摘要：
不规则三角网（TIN）是一种通常用于近似表示和存储单调地理表面的数据结构。在这种表示中，表面近似于一组三角形面，其在XY平面上的投影是三角剖分。TIN的可见性图是其顶点对应于TIN的顶点的图，并且如果两个顶点在TIN上的对应顶点彼此看到，则两个顶点之间存在边，即连接这些顶点的线段完全位于TIN之上。文献中已经彻底考虑了计算TIN的可见性图及其属性。在本文中，我们考虑这个问题反过来：给定一个图G，是否有一个TIN与G相同的可见性图？我们证明了这个问题对于实数的势理论是完全的。
英文摘要：
A Triangulated Irregular Network (TIN) is a data structure that is usually used for representing and storing monotone geographic surfaces, approximately. In this representation, the surface is approximated by a set of triangular faces whose projection on the XY-plane is a triangulation. The visibility graph of a TIN is a graph whose vertices correspond to the vertices of the TIN and there is an edge between two vertices if their corresponding vertices on TIN see each other, i.e. the segment that connects these vertices completely lies above the TIN. Computing the visibility graph of a TIN and its properties have been considered thoroughly in the literature. In this paper, we consider this problem in reverse: Given a graph G, is there a TIN with the same visibility graph as G? We show that this problem is Complete for Existential Theory of The Reals.
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