Methodology

The main criteria to be satisfied in a realistic simulation of the pavement scene described before are

1. No two people should collide with each other.
2. People should not collide with or go through obstacles in the scene, such as the sides of the pavement and the subway in the scene under consideration.
3. Motion of people in the scene should satisfy both the above conditions without being jerky, i.e., no oscillations or sudden shift in position.

Firstly, we started off with the basic model that people enter the pavement at a random position from either end and move towards the other end. To avoid collisions, we employed the social forces model described in [3]. In this, there is a repulsive force between any two people in the scene, with the magnitude of the force being inversely proportional to the square of the distance between them. The extra features we added in addition to the social forces model is that every person experiences forces only with people in front of him, which can be characterized mathematically as people whose relative position with respect to him has a positive dot product with his velocity. Essentially, this means that each person is influenced only by people in the 180 degrees field of view in front of him. Also, we restricted the influence of each person to within some neighborhood region around him. A sample of the crowd behavior produced by this model is shown below.

Figure: Crowd behavior using semi-circular field around each person