The Visual Computer

, Volume 26, Issue 2, pp 109–120 | Cite as

Good-visibility maps visualization

  • Narcís Coll
  • Narcís Madern
  • J. Antoni Sellarès
Original Article


Given a set V of viewpoints and a set S of obstacles in an environmental space, the good-visibility depth of a point q in relation to V and S is a measure of how deep or central q is with respect to the points in V that see q while minding the obstacles of S. The good-visibility map determined by V and S is the subdivision of the environmental space in good-visibility regions where all points have the same fixed good-visibility depth. In this paper we present algorithms for computing and efficiently visualizing, using graphics hardware capabilities, good-visibility maps in the plane as well as on triangulated terrains, where the obstacles are the terrain faces. Finally, we present experimental results obtained with the implementation of our algorithms.


Visibility Good-visibility Visualization Graphics hardware 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abellanas, M., Canales, S., Hernández, G.: Buena iluminación. In: Actas de las IV Jornadas de Matemática Discreta y Algorítmica, pp. 239–246 (2004) Google Scholar
  2. 2.
    Abellanas, M., Bajuelos, A., Hernández, G., Matos, I.: Good illumination with limited visibility. In: Proceedings of International Conference of Numerical Analysis and Applied Mathematics, pp. 35–38. Wiley/VCH Verlag, New York (2005) Google Scholar
  3. 3.
    Abellanas, M., Bajuelos, A.L., Matos, I.: Good θ-illumination of points. In: Proceedings of the 23rd European Workshop on Computational Geometry, pp. 61–64 (2007) Google Scholar
  4. 4.
    Abellanas, M., Bajuelos, A.L., Matos, I.: Some problems related to good illumination. In: Proceedings of 7th Annual International Workshop on Computational Geometry and Applications (CGA’07), ICCSA 2007. Lecture Notes in Computer Science, vol. 4705, pp. 1–14. Springer, Berlin (2007) Google Scholar
  5. 5.
    Aichholzer, O., Fabila-Monroy, R., Flores-Peñaloza, D., Hackl, T., Huemer, C., Urrutia, J., Vogtenhuber, B.: Modem illumination of monotone polygons. In: Proceedings of the 25th European Workshop on Computational Geometry EuroCG ’09, pp. 167–170 (2009) Google Scholar
  6. 6.
    Asano, T., Ghosh, S.K., Shermer, T.C.: Visibility in the Plane. Handbook of Computational Geometry. North-Holland, Amsterdam (2000) Google Scholar
  7. 7.
    Balaban, I.J.: An optimal algorithm for finding segments intersections. In: SCG ’95: Proceedings of the Eleventh Annual Symposium on Computational Geometry, pp. 211–219. ACM, New York (1995) CrossRefGoogle Scholar
  8. 8.
    Ben-Moshe, B., Carmi, P., Katz, M.J.: Approximating the visible region of a point on a terrain. GeoInformatica 12(1), 21–36 (2008) CrossRefGoogle Scholar
  9. 9.
    Canales, S.: Métodos heurísticos en problemas geométricos, visibilidad, iluminación y vigilancia, Ph.D. thesis. Universidad Politécnica de Madrid (2004) Google Scholar
  10. 10.
    Coll, N., Fort, M., Madern, N., Sellarès, J.A.: Multi-visibility maps of triangulated terrains. Int. J. Geographic. Inf. Sci. 21(10), 1115–1134 (2007) CrossRefGoogle Scholar
  11. 11.
    Coll, N., Madern, N., Sellares, J.A.: Drawing good-visibility maps with graphics hardware. In: Proceedings of Computer Graphics International Conference (CGI), pp. 286–293 (2008) Google Scholar
  12. 12.
    Fisher, I., Gotsman, C.: Drawing depth contours with graphics hardware. In: Proceedings of the 18th Annual Canadian Conference on Computational Geometry, CCCG 2006, Queen’s University, Ontario, Canada, 14–16 August 2006 Google Scholar
  13. 13.
    General-purpose computation on graphics hardware webpage
  14. 14.
    Ghosh, S.K.: Visibility Algorithms in the Plane. Cambridge University Press, Cambridge (2007) zbMATHCrossRefGoogle Scholar
  15. 15.
    Katz, M.J., Overmars, M.H., Sharir, M.: Efficient hidden surface removal for objects with small union size. Comput. Geom. Theory Appl. 2, 223–234 (1992) zbMATHMathSciNetGoogle Scholar
  16. 16.
    Krishnan, S., Mustafa, N.H., Venkatasubramanian, S.: Hardware-assisted computation of depth contours. In: SODA ’02: Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, pp. 558–567. SIAM, Philadelphia (2002) Google Scholar
  17. 17.
    Miller, K., Ramaswami, S., Rousseeuw, P., Sellarès, J.A., Souvaine, D., Streinu, I., Struyf, A.: Efficient computation of location depth contours by methods of computational geometry. J. Stat. Comput. 13, 153–162 (2003) CrossRefGoogle Scholar
  18. 18.
    Miller, K., Ramaswami, S., Rousseeuw, P., Sellarès, J.A., Souvaine, D., Streinu, I., Struyf, A.: Fast implementation of depth contours using topological sweep. Stat. Comput. 153–162 (2003) Google Scholar
  19. 19.
    Mustafa, N., Krishnan, S., Venkatasubramanian, S.: Statistical data depth and the graphics hardware. In: Liu, R., Serfling, R., Souvaine, D. (eds.) Data Depth: Robust Multivariate Analysis. Computational Geometry and Applications, vol. 72, pp. 223–246. AMS, Providence (2006) Google Scholar
  20. 20.
    Okamoto, Y., Uno, T., Christ, D., Hoffmann, M.: Improved bounds for wireless localization. In: SWAT ’08: Proceedings of the 11th Scandinavian Workshop on Algorithm Theory, pp. 77–89. Springer, Berlin (2008) Google Scholar
  21. 21.
    O’Rourke, J.: Visibility. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, pp. 643–664. CRC Press, Boca Raton (2004) Google Scholar
  22. 22.
    Owens, J.D., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A.E., Purcell, T.J.: A survey of general-purpose computation on graphics hardware. Comput. Graph. Forum 26(1), 80–113 (2007) CrossRefGoogle Scholar
  23. 23.
    Reif, J.H., Sen, S.: An efficient output-sensitive hidden surface removal algorithm and its parallelization. In: SCG ’88: Proceedings of the Fourth Annual Symposium on Computational Geometry, pp. 193–200. ACM, New York (1988) CrossRefGoogle Scholar
  24. 24.
    Tseng, Y., Wang, Y., Hu, C.: Efficient placement and dispatch of sensors in a wireless sensor network. IEEE Trans. Mobile Comput. 7(2), 262–274 (2008) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Narcís Coll
    • 1
  • Narcís Madern
    • 1
  • J. Antoni Sellarès
    • 1
  1. 1.GironaSpain

Personalised recommendations