# Recognizing Visibility Graphs of Triangulated Irregular Networks

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.

## Authors

• 1 publication
• ### Recognizing Visibility Graphs of Polygons with Holes and Internal-External Visibility Graphs of Polygons

Visibility graph of a polygon corresponds to its internal diagonals and ...
04/13/2018 ∙ by Hossein Boomari, et al. ∙ 0

• ### Computational Complexity Aspects of Point Visibility Graphs

A point visibility graph is a graph induced by a set of points in the pl...
11/06/2017 ∙ by Anne-Sophie Himmel, et al. ∙ 0

• ### Computing Boundary Cycle of a Pseudo-Triangle Polygon from its Visibility Graph

Visibility graph of a simple polygon is a graph with the same vertex set...
02/16/2020 ∙ by Hossein Boomari Soheila Farokhi, et al. ∙ 0

• ### Pseudo-Triangle Visibility Graph: Characterization and Reconstruction

The visibility graph of a simple polygon represents visibility relations...
05/02/2019 ∙ by Sahar Mehrpour, et al. ∙ 0

• ### Bounded-Degree Spanners in the Presence of Polygonal Obstacles

Let V be a finite set of vertices in the plane and S be a finite set of ...
09/15/2020 ∙ by André van Renssen, et al. ∙ 0

• ### Shortest Watchman Tours in Simple Polygons under Rotated Monotone Visibility

We present an O(nrG) time algorithm for computing and maintaining a mini...
07/16/2020 ∙ by Bengt J. Nilsson, et al. ∙ 0

• ### Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Unit square (grid) visibility graphs (USV and USGV, resp.) are described...
06/19/2017 ∙ by Katrin Casel, et al. ∙ 0

##### This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.