Time-Space Maps from Triangulations

  • Sandra Bies
  • Marc van Kreveld
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


Time-space maps show travel time as distances on a map. We discuss the case of time-space maps with a single center; here the travel times from a single source location to a number of destinations are shown by their distances. To accomplish this while maintaining recognizability, the input map must be deformed in a suitable manner. We present three different methods and analyze them experimentally.


  1. 1.
    Ahmed, N., Miller, H.: Time-space transformations of geographic space for exploring, analyzing and visualizing transportation systems. J. of Transport Geography 15, 2–17 (2007)CrossRefGoogle Scholar
  2. 2.
    Albers, G., Guibas, L.J., Mitchell, J.S.B., Roos, T.: Voronoi diagrams of moving points. Int. J. Comput. Geometry Appl. 8(3), 365–380 (1998)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Aronov, B., Seidel, R., Souvaine, D.L.: On compatible triangulations of simple polygons. Comput. Geom. 3, 27–35 (1993)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    de Berg, M., Mumford, E., Speckmann, B.: Optimal BSPs and rectilinear cartograms. Int. J. Comput. Geometry Appl. 20(2), 203–222 (2010)MATHCrossRefGoogle Scholar
  5. 5.
    Cabello, S., Demaine, E.D., Rote, G.: Planar embeddings of graphs with specified edge lengths. J. Graph Algorithms Appl. 11(1), 259–276 (2007)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dorling, D.: Area Cartograms: their Use and Creation. Concepts and Techniques in Modern Geography, vol. 59. Environmental Publications, Norwich (1996)Google Scholar
  7. 7.
    Dougenik, J., Chrisman, N., Niemeyer, D.: An algorithm to construct continuous area cartograms. Prof. Geographer 37, 75–81 (1985)CrossRefGoogle Scholar
  8. 8.
    Kaiser, C., Walsh, F., Farmer, C.J.Q., Pozdnoukhov, A.: User-Centric Time-Distance Representation of Road Networks. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) GIScience 2010. LNCS, vol. 6292, pp. 85–99. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Keim, D., North, S., Panse, C.: CartoDraw: A fast algorithm for generating contiguous cartograms. IEEE Trans. Visu. and Comp. Graphics 10, 95–110 (2004)CrossRefGoogle Scholar
  10. 10.
    van Kreveld, M., Speckmann, B.: On rectangular cartograms. Comput. Geom. 37(3), 175–187 (2007)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Nöllenburg, M., Wolff, A.: A Mixed-Integer Program for Drawing High-Quality Metro Maps. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 321–333. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Olson, J.: Noncontiguous area cartograms. Prof. Geographer 28, 371–380 (1976)CrossRefGoogle Scholar
  13. 13.
    Saalfeld, A.: Joint triangulations and triangulation maps. In: Proc. 3rd ACM Symposium on Computational Geometry, pp. 195–204 (1987)Google Scholar
  14. 14.
    Shimizu, E., Inoue, R.: A new algorithm for distance cartogram construction. International Journal of Geographical Information Science 23(11), 1453–1470 (2009)CrossRefGoogle Scholar
  15. 15.
    Tobler, W.: Thirty-five years of computer cartograms. Annals of the Assoc. American Cartographers 94(1), 58–71 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sandra Bies
    • 1
  • Marc van Kreveld
    • 1
  1. 1.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands

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