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

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Book cover Modeling, Simulation and Visual Analysis of Crowds

Part of the book series: The International Series in Video Computing ((VICO,volume 11))

Abstract

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.

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Notes

  1. 1.

    The velocity term is the inspiration for the name. The original SF model considered only agent positions [11].

  2. 2.

    While the formula doesn’t preclude using an implicit integration scheme, the common practice has been to use a low-order explicit integrator such as forward Euler.

  3. 3.

    If the agent were perfectly capable of maintaining its position, it would travel no distance at all.

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Acknowledgements

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

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Authors and Affiliations

  1. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Sean Curtis, Stephen J. Guy & Dinesh Manocha

  2. Hajj Research Institute, Umm al-Qura University, Makkah, Saudi Arabia

    Basim Zafar

Authors
  1. Sean Curtis
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  2. Stephen J. Guy
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  3. Basim Zafar
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  4. Dinesh Manocha
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Corresponding author

Correspondence to Sean Curtis .

Editor information

Editors and Affiliations

  1. Center for Vision Technologies, SRI International, Princeton, New Jersey, USA

    Saad Ali

  2. Department of Computer Science, Drexel University, Philadelphia, Pennsylvania, USA

    Ko Nishino

  3. Department of Computer Science, University of North Carolina, Chapel Hill, North Carolina, USA

    Dinesh Manocha

  4. Center for Research in Computer Vision, University of Central Florida, Orlando, Florida, USA

    Mubarak Shah

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Curtis, S., Guy, S.J., Zafar, B., Manocha, D. (2013). Virtual Tawaf: A Velocity-Space-Based Solution for Simulating Heterogeneous Behavior in Dense Crowds. In: Ali, S., Nishino, K., Manocha, D., Shah, M. (eds) Modeling, Simulation and Visual Analysis of Crowds. The International Series in Video Computing, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8483-7_8

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  • DOI: https://doi.org/10.1007/978-1-4614-8483-7_8

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