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 density distribution of the space $\rho_{xy}$ can be defined as

The Voronoi density for the measurement area is defined as:

For a given trajectory $\vec{x_i}(t)$, the velocity $v_i(t)$ is calculated by use of the displacement of pedestrian $i$ in a small time interval $\Delta t^\prime$ around $t$:

The spatial mean velocity is the average of the instantaneous velocities $v_i(t)$ for all pedestrians $N$ who have an intersection with the measurement area at the time $t$:

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