Terrain visibility with multiple viewpoints
Abstract
We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider a triangulated terrain with viewpoints (or guards) located on the terrain surface. A point on the terrain is considered \emph{visible} if it has an unobstructed line of sight to at least one viewpoint. We study several natural and fundamental visibility structures: (1) the visibility map, which is a partition of the terrain into visible and invisible regions; (2) the \emph{colored} visibility map, which is a partition of the terrain into regions whose points have exactly the same visible viewpoints; and (3) the Voronoi visibility map, which is a partition of the terrain into regions whose points have the same closest visible viewpoint. We study the complexity of each structure for both 1.5D and 2.5D terrains, and provide efficient algorithms to construct them. Our algorithm for the visibility map in 2.5D terrains improves on the only existing algorithm in this setting. To the best of our knowledge, the other structures have not been studied before.
Keywords
Cite
@article{arxiv.1309.4323,
title = {Terrain visibility with multiple viewpoints},
author = {Ferran Hurtado and Maarten Löffler and Inês Matos and Vera Sacristán and Maria Saumell and Rodrigo I. Silveira and Frank Staals},
journal= {arXiv preprint arXiv:1309.4323},
year = {2014}
}
Comments
Manuscript accompanying shorter version in ISAAC 2013; some algorithms and bounds have improved with respect to the ISAAC version. The journal version will appear in IJCGA (without Section 4)