Virtual Tawaf: A Velocity-Space-Based Solution for Simulating Heterogeneous Behavior in Dense Crowds

  • Sean CurtisEmail author
  • Stephen J. Guy
  • Basim Zafar
  • Dinesh Manocha
Part of the The International Series in Video Computing book series (VICO, volume 11)


We present a system to simulate the movement of individual agents in large-scale crowds performing the Tawaf. The Tawaf serves as a unique test case; the large crowd consists of a heterogeneous set of pilgrims, varying in both physical capacity and activity. Furthermore, the density of the crowd reaches extremely high levels (up to 8 people/m2). This extreme density can place impractical constraints on simulation parameters. We use a velocity-space-based pedestrian model which exhibits consistent results even under extreme density: reciprocal velocity obstacles (RVO). Furthermore, we extend RVO to include priority and right of way—agents respond to potential collisions asymmetrically depending on context; one agent may yield, to varying degrees, to another. Our system uses a finite state machine to specify the behavior of the agents at each time step, to model the varied behaviors seen during the Tawaf. The finite-state machine, used in conjunction with RVO, generates collision-free trajectories for tens of thousands of agents in the performance of the Tawaf. The overall system can model agents with varying age, gender and behaviors, supporting the heterogeneity observed in the performance of the Tawaf, even at high densities.


Subject Agent Repulsive Force Cellular Automaton Finite State Machine Crowd Behavior 
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.



This research is supported in part by ARO Contract W911NF-10-1-0506, NSF awards 0917040, 0904990 and 1000579.


  1. 1.
    Al-Haboubi, M., Selim, S.: A design to minimize congestion around the ka’aba. Comput. Ind. Eng. 32(2), 419–428 (1997)CrossRefGoogle Scholar
  2. 2.
    Algadhi, S., Mahmassani, H.: Modelling crowd behavior and movement: application to makkah pilgrimage. Transp. Traffic Theory 1990, 59–78 (1990)Google Scholar
  3. 3.
    Bandini, S., Federici, M., Manzoni, S., Vizzari, G.: Towards a methodology for situated cellular agent based crowd simulations. Engineering societies in the agents world VI, pp. 203–220. Springer, Berlin/Heidelberg (2006)Google Scholar
  4. 4.
    Chraibi, M., Seyfried, A., Schadschneider, A.: Generalized centrifugal-force model for pedestrian dynamics. Phys. Rev. E 82(4), 046,111 (2010)Google Scholar
  5. 5.
  6. 6.
    Curtis, S., Snape, J., Manocha, D.: Way portals: Efficient multi-agent navigation with line-segment goals. In: Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D), Costa Mesa, CA, USA (2012)Google Scholar
  7. 7.
    Durupinar, F., Pelechano, N., Allbeck, J., Gudukbay, U., Badler, N.: How the ocean personality model on the perception of crowds. Comput. Graph. Appl. IEEE 31(3), 22–31 (2010)Google Scholar
  8. 8.
    Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. Int. J. Robot. Res. 17(7), 760–762 (1998)CrossRefGoogle Scholar
  9. 9.
    Funge, J., Tu, X., Terzopoulos, D.: Cognitive modeling: knowledge, reasoning and planning for intelligent characters. In: SIGGRAPH, pp. 29–38. ACM, Los Angeles, CA, USA (1999)Google Scholar
  10. 10.
    Guy, S.J., Chhugani, J., Curtis, S., Lin, M.C., Dubey, P., Manocha, D.: Pledestrians: A least-effort approach to crowd simulation. In: Symposium on Computer Animation. ACM, Madrid, Spain (2010)Google Scholar
  11. 11.
    Helbing, D., Molnar, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51(5), 4282–4286 (1995)CrossRefGoogle Scholar
  12. 12.
    Johansson, A., Helbing, D., Al-Abideen, H., Al-Bosta, S.: From crowd dynamics to crowd safety: A video-based analysis. Advances in Complex Systems 11(04), 497–527 (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Ju, E., Choi, M.G., Park, M., Lee, J., Lee, K.H., Takahashi, S.: Morphable crowds. ACM Trans. Graph. 29(6), 140 (2010)Google Scholar
  14. 14.
    Koshak, N., Fouda, A.: Analyzing pedestrian movement in mataf using gps and gis to support space redesign. In: The 9th International Conference on Design and Decision Support Systems in Architecture and Urban Planning, The Netherlands/Holland (2008)Google Scholar
  15. 15.
    Lee, K.H., Choi, M.G., Hong, Q., Lee, J.: Group behavior from video: a data-driven approach to crowd simulation. In: Symposium on Computer Animation, San Diego, CA, USA pp. 109–118 (2007)Google Scholar
  16. 16.
    Mehran, R., Oyama, A., Shah, M.: Abnormal crowd behavior detection using social force model. CVPR, Miami Beach, FL, USA (2009)Google Scholar
  17. 17.
    Moussaïd, M., Perozo, N., Garnier, S., Helbing, D., Theraulaz, G.: The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PLoS ONE 5(4), e10,047 (2010). doi:10.1371/journal.pone.0010047.
  18. 18.
    Mulyana, W., Gunawan, T.: Hajj crowd simulation based on intelligent agent. In: 2010 International Conference on Computer and Communication Engineering (ICCCE), pp. 1–4. IEEE, Kuala Lumpur, Malyasia (2010)Google Scholar
  19. 19.
    Narain, R., Golas, A., Curtis, S., Lin, M.C.: Aggregate dynamics for dense crowd simulation. ACM Trans. Graph. 28, 122:1–122:8 (2009). doi: Google Scholar
  20. 20.
    Ondřej, J., Pettré, J., Olivier, A.H., Donikian, S.: A synthetic-vision based steering approach for crowd simulation. In: Proceedings of the SIGGRAPH, Los Angeles, CA pp. 123:1–123:9 (2010)Google Scholar
  21. 21.
    Patil, S., van den Berg, J., Curtis, S., Lin, M., Manocha, D.: Directing crowd simulations using navigation fields. IEEE TVCG, pp. 244–254 (2010)Google Scholar
  22. 22.
    Pelechano, N., Allbeck, J., Badler, N.: Controlling individual agents in high-density crowd simulation. In: SCA07, San Diego, CA, USA (2007)Google Scholar
  23. 23.
    Reynolds, C.: Flocks, herds and schools: A distributed behavioral model. In: SIGGRAPH, Anaheim, CA, USA (1987)Google Scholar
  24. 24.
    Sarmady, S., Haron, F., Talib, A.: A cellular automata model for circular movements of pedestrians during tawaf. Simul. Model. Pract. Theory 19(3), 969–985 (2010)CrossRefGoogle Scholar
  25. 25.
    Schadschneider, A.: Cellular automaton approach to pedestrian dynamics – theory. Pedestr. Evacuation Dyn. (2001)Google Scholar
  26. 26.
    Treuille, A., Cooper, S., Popović, Z.: Continuum crowds. In: ACM SIGGRAPH 2006, pp. 1160–1168. ACM, Boston, MA, USA (2006)Google Scholar
  27. 27.
    Ulicny, B., Thalmann, D.: Towards interactive real-time crowd behavior simulation. In: Computer Graphics Forum, vol. 21, pp. 767–775. Wiley Online Library (2002)Google Scholar
  28. 28.
    van den Berg, J., Guy, S.J., Lin, M., Manocha, D.: Reciprocal n-body collision avoidance. In: International Symposium on Robotics Research, Lucerne, Switzerland (2009)Google Scholar
  29. 29.
    Yeh, H., Curtis, S., Patil, S., van den Berg, J., Manocha, D., Lin, M.: Composite agents. Proceedings of SCA, Dublin, Ireland pp. 39–47 (2008)Google Scholar
  30. 30.
    Yersin, B., Maim, J., Pettré, J., Thalmann, D.: Crowd patches: populating large-scale virtual environments for real-time applications. In: I3D09, pp. 207–214. ACM, Boston, MA, USA (2009)Google Scholar
  31. 31.
    Yu, Q., Terzopoulos, D.: A decision network framework for the behavioral animation of virtual humans. In: Symposium on Computer Animation, San Diego, CA, USA pp. 119–128 (2007)Google Scholar
  32. 32.
    Zafar, B.: Analysis of the Mataf – Ramadan 1432 AH. Tech. rep., Hajj Research Institute, Umm al-Qura University, Saudi Arabia (2011)Google Scholar
  33. 33.
    Zainuddin, Z., Thinakaran, K., Abu-Sulyman, I.: Simulating the circumambulation of the ka’aba using simwalk. Eur. J. Sci. Res. 38(3), 454–464 (2009)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sean Curtis
    • 1
    Email author
  • Stephen J. Guy
    • 1
  • Basim Zafar
    • 2
  • Dinesh Manocha
    • 1
  1. 1.University of North Carolina at Chapel HillChapel HillUSA
  2. 2.Hajj Research InstituteUmm al-Qura UniversityMakkahSaudi Arabia

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