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

Abstract

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.

Vadere: An Open-Source Simulation Framework to Promote Interdisciplinary Understanding

“…The results are so-called velocity-based models [14,73]. At the same time several more model types emerged: velocityobstacle-based models [22,4,13] for collision avoidance inspired by robotics, rule-based models such as [65,84] and models which combine different approaches like the optimal steps model (OSM) [68]. Most models have been adjusted and extended to fit the findings from interdisciplinary experiments and studies.…”

“…Several approaches for modeling microscopic pedestrian dynamics have been developed in the last decades [88]. Among these are models based on cellular automata (CA) [25,5,45,79,18,87], models based on ordinary differential equations (ODE) [34,9,8,14,73], models based on cognitive heuristics [65,84] and models based on optimizing a utility, such as the quasicontinuous optimal steps model [68,75,76,77].…”

Can a Good Break Shot Determine the Game Outcome in 9-Ball?

“…One possible approach is to adopt the Voronoi diagrams which is a partitioning of a 2-D plane based on the “nearest-neighbor” rules ( Aurenhammer, 1991 ) assigning each dot to a corresponding cell. As a computational geometry method, Voronoi diagrams have been widely applied in various disciplines ( Fonseca et al, 2012 ; Lopes et al, 2017 ; Sun et al, 2018 ; Xiao et al, 2018 ). In civics and planning, Xiao et al (2018) used Voronoi diagrams to describe the pedestrian motion patterns wherein each pedestrian was represented by a point in a Voronoi cell.…”

A route navigation algorithm for pedestrian simulation based on grid potential field

“…As to the spatial map representation modeling, the visibility graph, [12][13][14] the Voronoi diagram, [15][16][17][18][19][20] and the navigation mesh [21][22][23][24] serve as the widely used map generation modeling method. In the visibility graph, the initial position, the goal position, and the vertices of obstacles in the simulation scenario are represented by the nodes.…”

“…And the walking direction of pedestrian in Voronoi cell can be divided into destination direction, potential detour direction, and potential following direction. 18 The three elementary walking directions are calculated inspired by the characteristics of the shapes of Voronoi cell. Sˇeda and Pich 19 have shown that generalized Voronoi diagrams can be used for fast generation of smooth paths sufficiently distant from obstacles.…”