Advertisement

Terrain Visibility with Multiple Viewpoints

  • Ferran Hurtado
  • Maarten Löffler
  • Inês Matos
  • Vera Sacristán
  • Maria Saumell
  • Rodrigo I. Silveira
  • Frank Staals
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

Abstract

We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider three fundamental visibility structures: the visibility map, the colored visibility map, and the Voronoi visibility map. 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.

Keywords

Voronoi Region Visibility Structure Multiple Viewpoint Power Diagram Leftmost Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM J. Comput. 16(1), 78–96 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ben-Moshe, B., Katz, M., Mitchell, J.: A constant-factor approximation algorithm for optimal 1.5D terrain guarding. SIAM J. Comput. 36(6), 1631–1647 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bose, P., Shermer, T., Toussaint, G., Zhu, B.: Guarding polyhedral terrains. Comput. Geom. 7(3), 173–185 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Catry, F., Rego, F., Santos, T., Almeida, J., Relvas, P.: Fires prevention in Portugal - using GIS to help improving early fire detection effectiveness. In: 4th Int. Wildland Fire Conf. (2007)Google Scholar
  5. 5.
    Cole, R., Sharir, M.: Visibility problems for polyhedral terrains. J. Symbolic Comput. 7(1), 11–30 (1989)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Coll, N., Madern, N., Sellarès, J.A.: Good-visibility maps visualization. Vis. Comput. 26(2), 109–120 (2010)CrossRefGoogle Scholar
  7. 7.
    Gibson, M., Kanade, G., Krohn, E., Varadarajan, K.: An approximation scheme for terrain guarding. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 140–148. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Hurtado, F., Löffler, M., Matos, I., Sacristán, V., Saumell, M., Silveira, R.I., Staals, F.: Terrain visibility with multiple viewpoints (2013), arXiv:1309.4323 [cs.CG]Google Scholar
  9. 9.
    Katz, M.J., Overmars, M.H., Sharir, M.: Efficient hidden surface removal for objects with small union size. Comput. Geom. 2, 223–234 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    King, J., Krohn, E.: Terrain guarding is NP-hard. SIAM J. Comput. 40(5), 1316–1339 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lv, P., Zhang, J.-F., Lu, M.: An optimal method for multiple observers sitting on terrain based on improved simulated annealing techniques. In: Ali, M., Dapoigny, R. (eds.) IEA/AIE 2006. LNCS (LNAI), vol. 4031, pp. 373–382. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Möller, B.: Changing wind-power landscapes: regional assessment of visual impact on land use and population in Northern Jutland, Denmark. Appl. Energ. 83(5), 477–494 (2006)CrossRefGoogle Scholar
  13. 13.
    Reif, J.H., Sen, S.: An efficient output-sensitive hidden surface removal algorithm and its parallelization. In: Proc. 4th Symp. Computational Geometry, pp. 193–200. ACM (1988)Google Scholar
  14. 14.
    Yick, J., Mukherjee, B., Ghosal, D.: Wireless sensor network survey. Comput. Netw. 52(12), 2292–2330 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ferran Hurtado
    • 1
  • Maarten Löffler
    • 2
  • Inês Matos
    • 1
    • 4
  • Vera Sacristán
    • 1
  • Maria Saumell
    • 5
  • Rodrigo I. Silveira
    • 3
    • 1
  • Frank Staals
    • 2
  1. 1.Dept. Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaSpain
  2. 2.Dept. of Information and Computing SciencesUniversiteit UtrechtThe Netherlands
  3. 3.Dept. de MatemáticaUniversidade de AveiroPortugal
  4. 4.Dept. de Matemática & CIDMAUniversidade de AveiroPortugal
  5. 5.Département d’InformatiqueUniversité Libre de BruxellesBelgium

Personalised recommendations