Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint called unilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at nearinteractive rates on desktop computers.

Figure 1: An explosion goes off inside a sand pile, sending freely splashing sand and rigid bodies flying in the air (running at less than 20 seconds per frame on a single-processor PC). In such a scenario, sand needs to be modeled as a cohesionless granular material. AbstractWe present a novel continuum-based model that enables efficient simulation of granular materials. Our approach fully solves the internal pressure and frictional stresses in a granular material, thereby allows visually noticeable behaviors of granular materials to be reproduced, including freely dispersing splashes without cohesion, and a global coupling between friction and pressure. The full treatment of internal forces in the material also enables two-way interaction with solid bodies. Our method achieves these results at only a very small fraction of computational costs of the comparable particle-based models for granular flows.

Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint called unilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at nearinteractive rates on desktop computers.

Abstract-Local collision avoidance algorithms in crowd simulation often ignore agents beyond a neighborhood of a certain size. This cutoff can result in sharp changes in trajectory when large groups of agents enter or exit these neighborhoods. In this work, we exploit the insight that exact collision avoidance is not necessary between agents at such large distances, and propose a novel algorithm for extending existing collision avoidance algorithms to perform approximate, long-range collision avoidance. Our formulation performs long-range collision avoidance for distant agent groups to efficiently compute trajectories that are smoother than those obtained with state-of-the-art techniques and at faster rates. Comparison to real-world data demonstrates that crowds simulated with our algorithm exhibit an improved speed sensitivity to density similar to human crowds. Another issue often sidestepped in existing work is that discrete and continuum collision avoidance algorithms have different regions of applicability. For example, low-density crowds cannot be modeled as a continuum, while high-density crowds can be expensive to model using discrete methods. We formulate a hybrid technique for crowd simulation which can accurately and efficiently simulate crowds at any density with seamless transitions between continuum and discrete representations. Our approach blends results from continuum and discrete algorithms, based on local density and velocity variance. In addition to being robust across a variety of group scenarios, it is also highly efficient, running at interactive rates for thousands of agents on portable systems.

(a) (b) (c) Figure 1: Examples of fluids simulated with our technique: (a) a city block hit by a tsunami (vortex domain in yellow) (b) seagulls flying through smoke (c) smoke flow around a sphere. We achieve up to three orders of magnitude of performance over standard grid-only techniques. AbstractSimulating fluids in large-scale scenes with appreciable quality using state-of-the-art methods can lead to high memory and compute requirements. Since memory requirements are proportional to the product of domain dimensions, simulation performance is limited by memory access, as solvers for elliptic problems are not computebound on modern systems. This is a significant concern for largescale scenes. To reduce the memory footprint and memory/compute ratio, vortex singularity bases can be used. Though they form a compact bases for incompressible vector fields, robust and efficient modeling of nonrigid obstacles and free-surfaces can be challenging with these methods.We propose a hybrid domain decomposition approach that couples Eulerian velocity-based simulations with vortex singularity simulations. Our formulation reduces memory footprint by using smaller Eulerian domains with compact vortex bases, thereby improving the memory/compute ratio, and simulation performance by more than 1000x for single phase flows as well as significant improvements for free-surface scenes. Coupling these two heterogeneous methods also affords flexibility in using the most appropriate method for modeling different scene features, as well as allowing robust interaction of vortex methods with free-surfaces and nonrigid obstacles.

Abstract-Local collision avoidance algorithms in crowd simulation often ignore agents beyond a neighborhood of a certain size. This cutoff can result in sharp changes in trajectory when large groups of agents enter or exit these neighborhoods. In this work, we exploit the insight that exact collision avoidance is not necessary between agents at such large distances, and propose a novel algorithm for extending existing collision avoidance algorithms to perform approximate, long-range collision avoidance. Our formulation performs long-range collision avoidance for distant agent groups to efficiently compute trajectories that are smoother than those obtained with state-of-the-art techniques and at faster rates. Comparison to real-world data demonstrates that crowds simulated with our algorithm exhibit an improved speed sensitivity to density similar to human crowds. Another issue often sidestepped in existing work is that discrete and continuum collision avoidance algorithms have different regions of applicability. For example, low-density crowds cannot be modeled as a continuum, while high-density crowds can be expensive to model using discrete methods. We formulate a hybrid technique for crowd simulation which can accurately and efficiently simulate crowds at any density with seamless transitions between continuum and discrete representations. Our approach blends results from continuum and discrete algorithms, based on local density and velocity variance. In addition to being robust across a variety of group scenarios, it is also highly efficient, running at interactive rates for thousands of agents on portable systems.

With the growth in world population, the density of crowds in public places has been increasing steadily, leading to a higher incidence of crowd disasters at high densities. Recent research suggests that emergent chaotic behavior at high densities-known collectively as crowd turbulence-is to blame. Thus, a deeper understanding of crowd turbulence is needed to facilitate efforts to prevent and plan for chaotic conditions in high-density crowds. However, it has been noted that existing algorithms modeling collision avoidance cannot faithfully simulate crowd turbulence. We hypothesize that simulation of crowd turbulence requires modeling of both collision avoidance and frictional forces arising from pedestrian interactions. Accordingly, we propose a model for turbulent crowd simulation, which incorporates a model for interpersonal stress and acceleration constraints similar to real-world pedestrians. Our simulated results demonstrate a close correspondence with observed metrics for crowd turbulence as measured in known crowd disasters.

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