Metrochrones: Schematic Isochrones for Schematic Metro Maps

ABSTRACT

In the context of public transportation, isochrone maps display the area accessible from a starting point within a given travel time. Transit networks are often displayed using a schematic representation, where each edge is restricted to a given set of orientations. In this article, we present an algorithm for generating Metrochrones, which are schematic isochrones enclosing the reachable area of a transit map. The isochrones are restricted to the same set of orientations as the underlying transit map. Our approach guarantees that the isochrones correctly separate the reachable and unreachable stations in the network. Moreover, the result is optimized towards a simple visualization by (a) minimizing the number of bends in the isochrone, (b) forcing the isochrone away from lines in the transit network, and (c) avoiding small crossing angles. We show that our approach can easily be extended to other isolines, such as travel fares.

KEYWORDS:

• Isochrones
• schematic
• metro maps
• isolines
• travel fares

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Brimkov et al. (2011) report a minimum distance of $\sqrt{2}/2$ to guarantee connectivity via the 4-neighbourhood on a unit grid, resulting in a minimum grid spacing of $w^{\ast }=\sqrt{2}{d}^{\ast }$ in the rectilinear case.

Additional information

Notes on contributors

Axel Forsch

Axel Forsch finished his Master of Science in Geodesy and Geoinformation at the University of Bonn in 2019. Currently, he continues his studies at the University of Bonn within the frame of a PhD programme regarding Volunteered Geographic Information. His research is focused on the algorithmic analysis and visualization of movement patterns. A central topic of Axel Forsch's research is to infer routing preferences from trajectories recorded by cyclists.

Jan-Henrik Haunert

Jan-Henrik Haunert holds a diploma and doctoral degree in geodesy and geoinformatics from the University of Hannover, Germany. He has been a postdoctoral researcher at the institute of computer science at the University of Würzburg, and a professor for geoinformatics at the University of Osnabrück. In 2016, he took up a full professorship for geoinformation at the University of Bonn. His research is concerned with the development of efficient algorithms for geovisualization and spatial analysis. In particular, he applies methods from combinatorial optimization and computational geometry to tasks in automated cartography, such as map generalization and cartographic label placement.