Virtual Reality in Brazil 2011Simulating crowds based on a space colonization algorithm
Graphical abstract
Highlights
► Biologically inspired crowd simulation algorithm. ► Generates free of collision motion. ► Presents several behaviors encountered in real life (arc formations, least-effort motion, etc.).
Introduction
Animation of crowds finds applications in many areas, including entertainment (e.g., animation of great numbers of persons in movies and games), creation of immersive virtual environments, and evaluation of crowd management techniques (for instance, simulation of the flow of people leaving a football stadium after a match). Several techniques for modeling crowd dynamics already exist, but important aspects of crowd simulation have remained open for further research. Specifically, (i) the existing approaches are often focused on panic situations rather than usual (normal) behavior, in which people in the crowd have goals to seek; (ii) not integrated techniques are usually needed to calibrate the movement of people in low or high density crowds, and to affect local and global motion planning; (iii) existing crowd-modeling methods are often complex, and they require careful parameter tuning to obtain visually convincing results [1], [2]; and (iv) collision-free motion, particularly in high densities is still a problem [3].
In this paper, we propose a novel crowd simulation algorithm that addresses some of the shortcomings of previous methods. Our model is based on the idea that individual agents affect each other by competing for the space where they move, which is represented explicitly by a set of marker points. In contrast to most methods proposed so far, the motion of each agent is thus affected directly not by the presence of neighboring agents, but by their absence, indicated by available markers. This change of perspective leads to a crowd model that is simple and robust, and it recreates emergently several aspects of real crowd behavior. These include collision avoidance (mathematically guaranteed by our algorithm), goal seeking, the dependency of the agents' speed and the smoothness of their trajectories on the density of crowds, and the tendency of people with similar goals in dense crowds to follow each other (form lanes). Furthermore, users can control crowd motion by interactively “spraying” or erasing free-point markers in selected areas of the scene.
In contrast to previous techniques for modeling crowd dynamics, which drew inspiration from psychology (behavioral models) or physics (e.g. models based on particle systems, force fields, or fluid dynamics), our method is inspired by a model of biological patterning. Specifically, it is derived from the space colonization algorithm introduced by Runions et al. [4], [5] to simulate the development of leaf veins and trees. The simulated veins compete for access to sources of the plant hormone auxin, assumed to be distributed throughout the leaf blade. In the case of trees, individual branches compete for access to abstract markers of unoccupied space, which are distributed in the space of future tree crowns. In our work, each agent exploits the local availability of space in order to create an efficient path toward its goal while avoiding other agents. Thus, the simulated motion of human-like agents in crowds is governed by competition for marker points similar to that used to model veins and trees. As such, this work demonstrates a surprising connection between methods used previously to generate biological patterns and crowd dynamics, since human beings also search for available space in order to move.
The remainder of the paper is organized as follows. Previous work on crowd dynamics, crowd simulation, and the space colonization algorithm are reviewed in Section 2. The proposed method for crowd simulation is described in Section 3, with mathematical details left to the appendices. Results of simulated experiments are presented and evaluated in Section 4. Finally, in Section 5, we present conclusions and suggest directions for future work.
Section snippets
Crowd dynamics
The behavior of real crowds was analyzed in the late 1970s and 1990s [6], [7], [8], [9]; results of their analysis provide a useful reference for simulation and animation of crowds. Two important aspects that guide the motion of real people are: goal seeking, reflecting the target destination of each individual; and the least-effort strategy, reflecting the tendency of people to reach the goal along a path requiring the least effort [9]. According to these strategies, people travel along smooth
Modeling crowds with the space colonization algorithm
The proposed method for crowd modeling is based on the space colonization algorithm. In its original applications to biological patterning, veins or tree branches could be regarded as paths created by vein or branch tips as they penetrated free space. In crowd simulation, these growing tips are identified with moving agents. Interestingly, an analogous relation between paths and motions can be observed in the development and applications of ideas related to particle systems. While some
Experimental results
In this section we present several examples that illustrate various features of the proposed crowd simulation method. In particular, we show that different aspects of the crowd dynamics outlined in Section 2.1 are emergent properties of our model. It is important to mention that, unless otherwise indicated, all results were obtained using the same set of parameters, regardless of the density of simulated crowds. The density of markers was set to 15 markers/m2, and the personal space R
Final considerations
In this work, we proposed a new model for crowd simulation. Important aspects of people's motion in a crowd (collision avoidance, goal seeking, relationship between density/speed and smoothness of trajectories on the local density of the crowd, and lane formation) are some of emergent properties of the model. The model also provides a convenient method for interactively controlling the movements of crowds.
Methodologically, the key innovation is the simple way in which the agents monitor their
Acknowledgment
Authors Claudio Jung and Soraia Musse would like to thank Brazilian Agency CNPq for partially funding this work. Authors Alessandro Bicho and Léo Pini Magalhães would like to thank the Brazilian Agency CAPES for partially funding this work. Authors would like to thank Prof. Przemyslaw Prusinkiewicz and M.Sc. Adam Runions for discussions about biological model that inspired the proposal of this work.
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