Maps help people to make decisions and come to an agreement in, for example, navigation, spatial planning, or politics. Effective maps are as simple as possible so that immediately convey their message. This can be achieved by schematization: shapes on the map are simplified according to some design rules, so that complicated shapes do not clutter the map and the user can focus on the relevant spatial relations between objects on the map.
It is not only structures of geographic structures that can be conveyed with schematic maps. Schematic maps can also be used to show the structure of other types of networks. Doing so brings its own challenges:
Traditionally schematized maps often represent complex linear features (roads, rivers etc.) and region boundaries by just a few curved strokes. However, current automated methods for schematization are mostly restricted to straight lines, so that features on the map often become jagged sequences of short strokes. This makes maps visually more complex and more difficult to read than necessary. Therefore, together with colleagues in geography, cartography and cognitive psychology, we are now researching automated methods to draw schematized maps with curves.
Results on schematization of region outlines can be found in:
Initial experiments with curved metro maps are described in:
Maps with curved metro lines may also benefit from curved labels:
On schematic maps of public transport systems, distances on the map are typically not proportional to actual travel times, which may cause surprises for the map user. The following is a report of a study in which I explore several possible solutions:
One of the solutions requires dividing the map into zones, such that zone boundary crossings are indicative of travel time. In effect, we want to “round” the travel times on the links of the networks to integral multiples of some standard zone diameter: the rounded numbers then indicate how many zone boundaries are crossed by each edge. The following paper explores the complexity of this problem:
Ideally, the route between a pair of metro stations that appears to be the shortest on the map, should also be the shortest route (or the fastest connection) between these stations in reality. The following abstract reports on a little experiment with straight-line metro map drawing based on this principle:
On a map of small scale, polygons must often be aggregated, for examples: shapes representing individual buildings are aggregated into shapes representing entire built-up areas, villages or cities. Here is our latest approach:
Some older papers of mine are about how to put symbols and labels on a map:
Figures in books, on screen etc. often contain points that need to be labelled. It is not always possible to place the labels close to the points. A reasonable alternative is to place the labels next to the actual illustration and connect each point to its label by a curve. To do this, we have to decide where exactly to place each point's label and how to draw the curves such that the connections between points and labels are clear and the curves do not clutter the figure. The following paper presents algorithms for doing so: