Fig. 2: Population mobility vector (PMV).
From: Unravelling the spatial directionality of urban mobility
a Schematic diagram showing the method to vectorise the mobility flow on a Cartesian plane with the y-axis along the geographical meridian and pointing towards true north. The direction of the unit outflow vector (black arrow) is defined from the origin (i, green) to the destination (j, blue), and the magnitude is defined as the relative flow (i.e., the flow from i to j normalised by the outflow Oi). b Definition of PMV. The origin i has three destinations, and each flow from i to j can be represented as a vector using the method shown in (a). Taking a vector sum of these vectors, we obtain the PMV \(\vec{{T}_{i}}\) (red arrow) on this Cartesian plane. c Definition of the relative direction. The relative direction (θi) of the PMV is defined as the direction referenced to the city centre (white dot, Methods), which can be calculated as the angle between the direction of the PMV (red arrow) and the direction to the city centre (black line). d–f Maps of PMVs for d Beijing, e Tianjin, and f Foshan. The length and colour of the arrow are proportional to the magnitude of the PMV. The white dot represents the city centre. Vector basemap and map tiles were provided by CartoDB under a Creative Commons licence CC BY 4.0. Source data are provided as a Source Data file.
