Analysis of Pedestrian Motion Using Voronoi Diagrams in Complex Geometries

Abstract

Voronoi diagrams are an established method in the analysis of pedestrian motion for constructing a density from two-dimensional positions. It is in turn used to give pointwise values for speed, movement direction, flow etc. The method was first described for high-density situations inside a crowd moving in a simple geometry without considering the influence of walls. However, more complicated distance calculations are needed for more complicated geometries where there are several obstacles or corners. In addition, partially empty spaces also require special treatment to avoid excessively big cells. These problems can lead to estimation errors when not handled correctly in subsequent use. In this work, we give details on how to adapt the calculations of Voronoi diagrams to make them fit for the presence of walls and obstacles in complex geometries. Furthermore, we show how that for persons at the edge of a group the personal space can be reasonably restricted. Based on these modifications, having pointwise values for quantities of interest allows to give average values for arbitrary geometries, not just for lines or rectangles of measurements. However, in order to obtain reasonable measurement values, different quantities may need different kind of averages—arithmetic or harmonic, or weighted with density.