Comparison of Various Methods for the Calculation of the Distance Potential Field

  • Tobias Kretz
  • Cornelia Bönisch
  • Peter Vortisch
Conference paper


The distance from a given position toward one or more destinations, exits, and way points is an important input variable in most models of pedestrian dynamics. Except for special cases without obstacles in a concave scenario—i.e. each position is visible from any other—the calculation of these distances is a non-trivial task. This is not a big problem as long as the model only demands the distances to be stored in a Static Floor Field (or Potential Field), which never changes throughout the whole simulation. Then a pre-calculation once before the simulation starts is sufficient. But if one wants to allow changes of the geometry during a simulation run—imagine doors or the blocking of a corridor due to some hazard—in the Distance Potential Field, calculation time matters strongly. We give an overview over existing and new exact and approximate methods to calculate a potential field, analytical investigations for their exactness, and tests of their computation speed. The advantages and drawbacks of the methods are discussed.


Grid Cell Cellular Automaton Visibility Graph Speed Error Diagonal Motion 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Burstedde, K. Klauck, A. Schadschneider, and J. Zittarz. Simulation of pedestrian dynamics using a 2-dimensional cellular automaton. Physica A, 295:507, 2001. zbMATHCrossRefGoogle Scholar
  2. 2.
    A. Schadschneider, Bionics-inspired cellular automaton model for pedestrian dynamics. In M. Fukui, Y. Sugiyama, M. Schreckenberg, and D.E. Wolf (eds), Traffic and Granular Flow ’01, page 499. Springer, Berlin, 2003. Google Scholar
  3. 3.
    A. Kirchner and A. Schadschneider. Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics. Physica A, 312(1–2):260–276, 2002. zbMATHCrossRefGoogle Scholar
  4. 4.
    A. Kirchner. Modellierung und statistische Physik biologischer und sozialer Systeme. PhD thesis, Universität zu Köln, 2002. Google Scholar
  5. 5.
    K. Nishinari, A. Kirchner, A. Namazi, and A. Schadschneider. Extended floor field CA model for evacuation dynamics. IEICE Transactions on Information and Systems, E87-D:726–732, 2004. Google Scholar
  6. 6.
    T. Kretz and M. Schreckenberg. The F.A.S.T.-model. In S. El Yacoubi, B. Chopard, and S. Bandini (eds), Cellular Automata—7th International Conference on Cellular Automata for Research and Industry, ACRI 2006, Proceedings, page 712. Springer, Berlin, 2006. Google Scholar
  7. 7.
    A. Schadschneider, W. Klingsch, H. Klüpfel, T. Kretz, C. Rogsch, and A. Seyfried. Evacuation dynamics: empirical results, modeling and applications. In R.A. Meyers (ed), Encyclopedia of Complexity and System Science. Springer, Berlin, 2009. Google Scholar
  8. 8.
    O. Khatib. The potential field approach and operational space formulation in robot control. In K.S. Narendra (ed), Adaptive and Learning Systems—Theory and Application, page 367. Plenum, New York, 1986. Google Scholar
  9. 9.
    J.-C. Latombe. Robot Motion Planning. Kluwer Academic, Dordrecht, 1991. Google Scholar
  10. 10.
    J. Meister. Simulation of crowd dynamics with special focus on building evacuations. Master’s thesis, Fachhochschule Wedel, 2007. Google Scholar
  11. 11.
    M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry. Springer, Berlin, 1997. zbMATHGoogle Scholar
  12. 12.
    H. Klüpfel. A Cellular Automaton Model for Crowd Movement and Egress Simulation. PhD thesis, Universität Duisburg-Essen, 2003. Google Scholar
  13. 13.
    T. Kretz. Pedestrian Traffic—Simulation and Experiments. PhD thesis, Universität Duisburg-Essen, 2007. Google Scholar
  14. 14.
    E.W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269–271, 1959. zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    J.E. Bresenham. Algorithm for computer control of a digital plotter. IBM Systems Journal, 4:25–30, 1965. CrossRefGoogle Scholar
  16. 16.
    M. Schultz, S. Lehmann, and H. Fricks. A discrete microscopic model for pedestrian dynamics to manage emergency situations in airport terminals. In N. Waldau, P. Gattermann, H. Knoflacher, and M. Schreckenberg (eds), Pedestrian and Evacuation Dynamics 2005, page 369. Springer, Berlin, 2006. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tobias Kretz
    • 1
  • Cornelia Bönisch
    • 1
  • Peter Vortisch
    • 1
  1. 1.PTV AGKarlsruheGermany

Personalised recommendations