TERRAIN VISIBILITY WITH MULTIPLE VIEWPOINTS-Reference-Cited by-同舟云学术

TERRAIN VISIBILITY WITH MULTIPLE VIEWPOINTS

Published:2014-12 Issue:04 Volume:24 Page:275-306
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

HURTADO FERRAN¹,LÖFFLER MAARTEN²,MATOS INÊS³⁴,SACRISTÁN VERA¹,SAUMELL MARIA⁵,SILVEIRA RODRIGO I.³⁴,STAALS FRANK⁶

Affiliation:

1. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, Spain

2. Department of Information and Computing Sciences, Universiteit Utrecht, Buys Ballot Lab., office 485, Princetonplein 5, De Uithof, 3584 CC Utrecht, The Netherlands

3. Departamento de Matemática & CIDMA, Universidade de Aveiro, Portugal

4. Dept. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain

5. Department of Mathematics and European Centre of Excellence NTIS (New Technologies for the Information Society), University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

6. Department of Information and Computing Sciences, Universiteit Utrecht, Buys Ballot Lab., office 415, Princetonplein 5, De Uithof, 3584 CC Utrecht, The Netherlands

Abstract

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 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. To the best of our knowledge, the other structures have not been studied before.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195914600085

Reference21 articles.

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