Automatic Generation of Diagrammatic Subway Maps for Any Date with Maple

Abstract

The second author was one of the authors of a computer package written in Maple that could automatically generate railway maps of a network for any date. This package was presented at ACA’2008 and its design and implementation is described in a previous article. Each section of the network was colored accordingly to its characteristics. The position of the nodes (stations, junctions, $$\ldots $$) was obtained from a list of geographical coordinates. The work presented here deals with a similar although not identical case: now subway networks are treated as graphs with the help of a computer algebra system in order to obtain the diagrammatic map for any date. Most subway network maps follow more or less closely the ideas introduced by Harry Beck in his diagrammatic design of London subway map (the distances between stations and geographic orientation of the lines don’t have to be respected, as the clarity and the number of stations between two stations is the key information to be visualized). Therefore allocating nodes is far simpler, and we have decided to manually allocate the stations on a predefined grid and to automatize the drawing of the network. The situation is also simpler because all lines are double track and electrified. For instance in Madrid subway there are minor differences between lines, such as the kind of catenary (classic or rigid), the loading gauge (narrow/broad), $$\ldots $$ that will not be considered here. Each node and edge of the graph has dates associated: inauguration date/closure date–the latter if applies. The package takes advantage of the simplifications w.r.t. the previous article mentioned above and the features of Maple’sGraphTheory package. This way the approach, although general, can be implemented in relatively few lines of code. We know of no other similar works. The work is illustrated with the case of Madrid subway network, one of the biggest ones in the world.