this method calculates the density based on Voronoi diagrams, which are a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space.
At any time the positions of the pedestrians can be represented as a set of points, from which the Voronoi diagram can be generated.
The Voronoi cell area, , for each person can be obtained.
Then, the density and velocity distribution of the space and can be defined as
where is the instantaneous velocity of each person.
The Voronoi density for the measurement area is defined as:
Similarly, the Voronoi velocity is defined as: