Metro Maps on Octilinear Grid Graphs

Abstract

Schematic transit maps (often called “metro maps” in the literature) are important to produce comprehensible visualizations of complex public transit networks. In this work, we investigate the problem of automatically drawing such maps on an octilinear grid with an arbitrary (but optimal) number of edge bends. Our approach can naturally deal with obstacles that should be respected in the final drawing (points of interest, rivers, coastlines) and can prefer grid edges near the real‐world course of a line. This allows our drawings to be combined with existing maps, for example as overlays in map services. We formulate an integer linear program which can be used to solve the problem exactly. We also provide a fast approximation algorithm which greedily calculates shortest paths between node candidates on the underlying octilinear grid graph. Previous work used local search techniques to update node positions until a local optimum was found, but without guaranteeing octilinearity. We can thus calculate nearly optimal metro maps in a fraction of a second even for complex networks, enabling the interactive use of our method in map editors.

Shape‐Guided Mixed Metro Map Layout

“…Typically, the octolinear layout is mandatory since edge orientation is formulated using a set of binary variables in the model, whereas other aesthetic requirements can be relaxed if they conflict with others. Finally a recent result computes shortest paths between candidate positions of stations on a predefined grid [ BBS20 , BBS21 ]. This was formulated as an ILP, but heuristical solutions through repeated applications of shortest path algorithms can be obtained very quickly.…”

“…This issue can not easily be resolved by simply snapping every edge to the closest octolinear direction. However we can adapt an existing layout algorithm developed by Bast et al [ BBS20 ], which computes octolinear layouts of metro maps given as geographical inputs on predefined grids, and renders edges as piece‐wise octolinear curves.…”

“…In their Octi framework for metro map layout, Bast et al [ BBS20 , BBS21 ] consider a geographic network N as input. Let x min , y min , x max and y max be the minimal maximal x and y coordinate over all stations in N respectively.…”

MetroSets: Visualizing Sets as Metro Maps

“…The area of schematic metro map generation is well researched and several papers have been published on this subject the last few years [9,17,61,83,86,88,89]. An overview of different algorithms up to 2014 is given in Nöllenburg's survey paper [60].…”

Family metro maps

“…Next, we would like to refer to the literature on automatically drawing metro line maps (Hong et al (2004); Stott and Rodgers (2004); No ¨llenberg and Wolff (2011); Bast and Brosi (2020)) for geometric point sets and specified connections. Wolff (2007) gives an extensive list of rules that a map should adhere to, where some of these rules are treated as hard constraints and others as soft constraints.…”