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TERRAIN VISIBILITY WITH MULTIPLE VIEWPOINTS

Ferrán HurtadoDepartament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, SpainMaarten LöfflerDepartment of Information and Computing Sciences, Universiteit Utrecht, Buys Ballot Lab., office 485, Princetonplein 5, De Uithof, 3584 CC Utrecht, The NetherlandsInês MatosDepartamento de Matemática & CIDMA, Universidade de Aveiro, PortugalVera SacristánDepartament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, SpainMaria SaumellDepartment of Mathematics and European Centre of Excellence NTIS (New Technologies for the Information Society), University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech RepublicRodrigo I. SilveiraDepartamento de Matemática & CIDMA, Universidade de Aveiro, PortugalFrank StaalsDepartment of Information and Computing Sciences, Universiteit Utrecht, Buys Ballot Lab., office 415, Princetonplein 5, De Uithof, 3584 CC Utrecht, The Netherlands

2014en

ABI

Annotatsiya

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.

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Identifikatorlar

DOI: 10.1142/s0218195914600085

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