Investigation of Voronoi diagram based direction choices using uni- and bi-directional trajectory data

In a crowd, individuals make different motion choices such as "moving to destination," "following another pedestrian," and "making a detour." For the sake of convenience, the three direction choices are respectively called destination direction, following direction, and detour direction in this paper. Here, it is found that the featured direction choices could be inspired by the shape characteristics of the Voronoi diagram. To be specific, in the Voronoi cell of a pedestrian, the direction to a Voronoi node is regarded as a potential "detour" direction and the direction perpendicular to a Voronoi link is regarded as a potential "following" direction. A pedestrian generally owns several alternative Voronoi nodes and Voronoi links in a Voronoi cell, and the optimal detour and following direction are determined by considering related factors such as deviation. Plus the destination direction which is directly pointing to the destination, the three basic direction choices are defined in a Voronoi cell. In order to evaluate the Voronoi diagram based basic directions, the empirical trajectory data in both uni- and bi-directional flow experiments are extracted. A time series method considering the step frequency is used to reduce the original trajectories' swaying phenomena which might disturb the recognition of actual forward direction. The deviations between the empirical velocity direction and the basic directions are investigated, and each velocity direction is classified into a basic direction or regarded as an inexplicable direction according to the deviations. The analysis results show that each basic direction could be a potential direction choice for a pedestrian. The combination of the three basic directions could cover most empirical velocity direction choices in both uni- and bi-directional flow experiments.