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GeoInformatica

, Volume 15, Issue 2, pp 381–397 | Cite as

Efficient viewshed computation on terrain in external memory

  • Marcus V. A. Andrade
  • Salles V. G. Magalhães
  • Mirella A. Magalhães
  • W. Randolph Franklin
  • Barbara M. Cutler
Article

Abstract

The recent availability of detailed geographic data permits terrain applications to process large areas at high resolution. However the required massive data processing presents significant challenges, demanding algorithms optimized for both data movement and computation. One such application is viewshed computation, that is, to determine all the points visible from a given point p. In this paper, we present an efficient algorithm to compute viewsheds on terrain stored in external memory. In the usual case where the observer’s radius of interest is smaller than the terrain size, the algorithm complexity is θ(scan(n 2)) where n 2 is the number of points in an n × n DEM and scan(n 2) is the minimum number of I/O operations required to read n 2 contiguous items from external memory. This is much faster than existing published algorithms.

Keywords

GIS External memory processing Viewshed Visibility maps 

Notes

Acknowledgements

This work was partially supported by CNPq—the Brazilian Council of Technological and Scientific Development, FAPEMIG—the Research Support Foundation of the State of Minas Gerais (Brazil) and by NSF grants CCR-0306502 and DMS-0327634 and by DARPA/DSO/GeoStar.

References

  1. 1.
    Aggarwal A, Vitter JS (1988) The input/output complexity of sorting and related problems. Commun ACM 31(9):1116–1127CrossRefGoogle Scholar
  2. 2.
    Andrade MVA (2007) EMViewshed project. http://www.dpi.ufv.br/~marcus/projects/EMViewshed.htm
  3. 3.
    Arge L, Chase JS, Halpin P, Toma L, Vitter JS, Urban D, Wickremesinghe R (2003) Efficient flow computation on massive grid terrains. GeoInformatica 7:283–313CrossRefGoogle Scholar
  4. 4.
    Arge L, Vengroff DE, Vitter JS (2007) External-memory algorithms for processing line segments in geographic information systems. Algorithmica 47(1):1–25CrossRefGoogle Scholar
  5. 5.
    Ben-Moshe B, Ben-Shimol Y, Segal M, Ben-Yehezkel Y, Dvir A (2007) Automated antenna positioning algorithms for wireless fixed-access networks. Journal of Heuristics 13(3):243–263CrossRefGoogle Scholar
  6. 6.
    Ben-Moshe B, Carmi P, Katz MJ (2004) Approximating the visible region of a point on a terrain. In: Proc. algorithm engineering and experiments (ALENEX’04), pp 120–128Google Scholar
  7. 7.
    Ben-Moshe B, Katz MJ, Mitchell JSB (2007) A constant-factor approximation algorithm for optimal 1.5d terrain guarding. SIAM J Comput 36(6):1631–1647CrossRefGoogle Scholar
  8. 8.
    Ben-Moshe B, Katz MJ, Mitchell JSB, Nir Y (2004) Visibility preserving terrain simplification—an experimental study. Comp Geom Theor App 28(2–3):175–190Google Scholar
  9. 9.
    Bespamyatnikh S, Chen Z, Wang K, Zhu B (2001) On the planar two-watchtower problem. In: In 7th international computing and combinatorics conference. Springer, London, pp 121–130Google Scholar
  10. 10.
    Bresenham J (1965) An incremental algorithm for digital plotting. IBM Syst J 4:25–30CrossRefGoogle Scholar
  11. 11.
    Camp RJ, Sinton DT, Knight RL (1997) Viewsheds: A complementary management approach to buffer zones. Wildl Soc Bull 25:612–615Google Scholar
  12. 12.
    Creative Commons (2007) http://creativecommons.org/license/cc-gpl. Accessed Feb 2008
  13. 13.
    Dementiev R, Kettner L, Sanders P (2005) Stxxl: standard template library for xxl data sets. Technical report, Fakultat fur Informatik, Universitat Karlsruhe. http://stxxl.sourceforge.net/. Accessed July 2007
  14. 14.
    Eidenbenz S (2002) Approximation algorithms for terrain guarding. Inf Process Lett 82(2):99–105CrossRefGoogle Scholar
  15. 15.
    De Floriani L, Magillo P (2003) Algorithms for visibility computation on terrains: a survey. Environ Plann, B Plann Des 30:709–728CrossRefGoogle Scholar
  16. 16.
    De Floriani L, Puppo E, Magillo P (1999) Applications of computational geometry to geographic information systems. In: Urrutia J, Sack JR, (eds) Handbook of computational geometry. Elsevier Science, Amsterdam, pp 333–388Google Scholar
  17. 17.
    Franklin WR (1973) Triangulated irregular network program. http://www.ecse.rpi.edu/~wrf/wiki/Research/tin73.tgz. Accessed 30 Oct 2008
  18. 18.
    Franklin WR (2002) Siting observers on terrain. In: Springer-Verlag (ed) In: Richardson D, van Oosterom P (eds) Advances in spatial data handling: 10th international symposium on spatial data handling, pp 109–120Google Scholar
  19. 19.
    Franklin WR, Ray C (1994) Higher isn’t necessarily better—visibility algorithms and experiments. In: 6th symposium on spatial data handling. Taylor & Francis, Edinburgh, pp 751–770Google Scholar
  20. 20.
    Franklin WR, Vogt C (2006) Tradeoffs when multiple observer siting on large terrain cells. In: 12th international symposium on spatial data handling. Springer, New York, pp 845–861CrossRefGoogle Scholar
  21. 21.
    Goodrich MT, Tsay JJ, Vangroff DE, Vitter JS (1993) External-memory computational geometry. In: IEEE symp. on foundations of computer science, vol 714, pp 714–723Google Scholar
  22. 22.
    Haverkort H, Toma L, Zhuang Y (2007) Computing visibility on terrains in external memory. In: Proceedings of the ninth workshop on algorithm engineering and experiments / workshop on analytic algorithms and combinatorics (ALENEX/ANALCO)Google Scholar
  23. 23.
    Hein JL (2002) Discrete mathematics. Jones & Bartlett, Boston. ISBN 0763722103, 9780763722104.Google Scholar
  24. 24.
    Kumler MP (1994) An intensive comparison of triangulated irregular network (tins) and digital elevation models (dems). Cartographica 31(2)Google Scholar
  25. 25.
    Lake IR, Lovett AA, Bateman IJ, Langford IH (1998) Modelling environmental influences on property prices in an urban environment. Comput Environ Urban Syst 22:121–136CrossRefGoogle Scholar
  26. 26.
    Lee J, Stucky D (1998) On applying viewshed analysis for determining least-cost paths on digital elevation models. Int J Geogr Inf Sci 12:891–905CrossRefGoogle Scholar
  27. 27.
    Li Z, Zhu Q, Gold C (2005) Digital terrain modeling—principles and methodology. CRC, Boca RatonGoogle Scholar
  28. 28.
    Line-of-Sight Technical Working Group (LOS TWG) (2004) Line-of-sight (LOS) compendium. Technical report, U.S. Army Corps of Engineers, Engineer Research and Development Center/ Topographic Engineering Center (ERDC/TEC). http://www.tec.army.mil/operations/programs/LOS/LOS. Accessed 30 Oct 2008
  29. 29.
    The Shuttle Radar Topography Mission (SRTM) (2007) http://www2.jpl.nasa.gov/srtm/. Accessed Feb 2008
  30. 30.
    Stewart AJ (1998) Fast horizon computation at all points of a terrain with visibility and shading applications. In: IEEE Trans. visualization computer graphics, vol 4. IEEE Educational Activities Department, Piscataway, pp 82–93Google Scholar
  31. 31.
    US Geological Survey (2007) The USGS center for LIDAR information coordination and knowledge. http://lidar.cr.usgs.gov/. Accessed Feb 2008
  32. 32.
    van Kreveld M (1996) Variations on sweep algorithms: efficient computation of extended viewsheds and class intervals. In: Symposium on spatial data handling, pp 15–27Google Scholar
  33. 33.
    Young-Hoon K, Rana S, Wise S (2004) Exploring multiple viewshed analysis using terrain features and optimization techniques. Comput Geotech 30:1019–10323Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Marcus V. A. Andrade
    • 1
    • 2
  • Salles V. G. Magalhães
    • 1
  • Mirella A. Magalhães
    • 1
  • W. Randolph Franklin
    • 2
  • Barbara M. Cutler
    • 3
  1. 1.DPIUniversidade Federal de ViçosaViçosaBrasil
  2. 2.ECSE Dept.Rensselaer Polytechnic InstituteTroyUSA
  3. 3.CS Dept.Rensselaer Polytechnic InstituteTroyUSA

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