Simplifying Massive Contour Maps

  • Lars Arge
  • Lasse Deleuran
  • Thomas Mølhave
  • Morten Revsbæk
  • Jakob Truelsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)


We present a simple, efficient and practical algorithm for constructing and subsequently simplifying contour maps from massive high-resolution DEMs, under some practically realistic assumptions on the DEM and contours.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    TPIE - Templated Portable I/O-Environment,
  2. 2.
    Agarwal, P., Arge, L., Mølhave, T., Sadri, B.: I/O-efficient algorithms for computing contours on a terrain. In: Proc. Symposium on Computational Geometry, pp. 129–138 (2008)Google Scholar
  3. 3.
    Agarwal, P.K., Arge, L., Murali, T.M., Varadarajan, K., Vitter, J.S.: I/O-efficient algorithms for contour line extraction and planar graph blocking. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, pp. 117–126 (1998)Google Scholar
  4. 4.
    Agarwal, P.K., Arge, L., Yi, K.: I/O-efficient batched union-find and its applications to terrain analysis. ACM Trans. Algorithms 7(1), 11:1–11:21 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Aggarwal, A., Vitter, S., Jeffrey: The input/output complexity of sorting and related problems. Commun. ACM 31(9), 1116–1127 (1988)CrossRefGoogle Scholar
  6. 6.
    Arge, L.: External memory data structures. In: Abello, J., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Massive Data Sets, pp. 313–358 (2002)Google Scholar
  7. 7.
    Arge, L., Larsen, K., Mølhave, T., van Walderveen, F.: Cleaning massive sonar point clouds. In: Proc ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems, pp. 152–161 (2010)Google Scholar
  8. 8.
    Cabello, S., Liu, Y., Mantler, A., Snoeyink, J.: Testing homotopy for paths in the plane. In: Proc. Symposium on Computational Geometry, pp. 160–169 (2002)Google Scholar
  9. 9.
    Carr, H., Snoeyink, J., van de Panne, M.: Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree. In: Computational Geometry, pp. 42–58 (2010) (Special Issue on the 14th Annual Fall Workshop)Google Scholar
  10. 10.
    Danner, A., Mølhave, T., Yi, K., Agarwal, P., Arge, L., Mitasova, H.: TerraStream: From elevation data to watershed hierarchies. In: Proc. ACM International Symposium on Advances in Geographic Information Systems, pp. 28:1–28:8 (2007)Google Scholar
  11. 11.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry – Algorithms and Applications (1997)Google Scholar
  12. 12.
    de Berg, M., van Kreveld, M., Schirra, S.: A new approach to subdivision simplification. In: Proc. 12th Internat. Sympos. Comput.-Assist. Cartog., pp. 79–88 (1995)Google Scholar
  13. 13.
    Douglas, D., Peucker, T.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature (1973)Google Scholar
  14. 14.
    Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. In: Proc. IEEE Symposium on Foundations of Computer Science, pp. 454–463 (2000)Google Scholar
  15. 15.
    Garland, M., Heckbert, P.: Surface simplification using quadric error metrics. In: Proc. Computer Graphics and Interactive Techniques, pp. 209–216 (1997)Google Scholar
  16. 16.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. SIGMOD International Conference on Management of Data, pp. 47–57 (1984)Google Scholar
  17. 17.
    Heckbert, P.S., Garland, M.: Survey of polygonal surface simplification algorithms. Technical report, CS Dept., Carnegie Mellon U (to appear)Google Scholar
  18. 18.
    Hershberger, J., Snoeyink, J.: Computing minimum length paths of a given homotopy class. Comput. Geom. Theory Appl, 63–97 (1994)Google Scholar
  19. 19.
    Saalfeld, A.: Topologically consistent line simplification with the douglas peucker algorithm. In: Geographic Information Science (1999)Google Scholar
  20. 20.
    Vitter, J.: External memory algorithms and data structures: Dealing with MASSIVE data. ACM Computing Surveys, 209–271 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lars Arge
    • 1
  • Lasse Deleuran
    • 1
  • Thomas Mølhave
    • 2
  • Morten Revsbæk
    • 1
  • Jakob Truelsen
    • 3
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityDenmark
  2. 2.Department of Computer ScienceDuke UniversityUSA
  3. 3.SCALGO, Scalable AlgorithmicsDenmark

Personalised recommendations