# CSASC 2013

9-13 June 2013
Koper, Slovenia
UTC timezone
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# TERRAIN VISIBILITY WITH MULTIPLE VIEWPOINTS

Presented by Dr. Maria SAUMELL
Type: Oral presentation
Track: Discrete and Computational Geometry

## Content

We study the problem of visibility in polyhedral terrains, in the presence of multiple viewpoints. We consider a triangulated terrain with $m>1$ 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 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.

## Place

Location: Koper, Slovenia

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