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Automated cartography

Schematization of geographic(?) objects

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:

  • Metaphorical metro maps: design challenges.
    By Herman Haverkort.
    To be presented at the Schematic Mapping Workshop 2022.

Improving the shape of schematizations

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:

  • Topologically safe curved schematization.
    By Arthur van Goethem, Herman Haverkort, Wouter Meulemans, Andreas Reimer, and Bettina Speckmann.
    The Cartographic Journal, 50(3):276–285, 2013.
    text (or contact me for free access)

Initial experiments with curved metro maps are described in:

  • A purely force-directed approach to drawing metro maps with curves.
    By Herman Haverkort and Mathijs Miermans.
    Presented at the Schematic Mapping Workshop 2014.
    Contact me if you would like to receive a two-page description of our work.
  • Drawing metro maps using Bézier curves.
    By Martin Fink, Herman Haverkort, Martin Nöllenburg, Maxwell Roberts, Julian Schuhmann, and Alexander Wolff.
    In Proc. 20th Int. Symp. on Graph Drawing (GD), number 7704 in Lecture Notes in Computer Science (LNCS), pages 463–474, 2013.
    text (or contact me for free access)

Maps with curved metro lines may also benefit from curved labels:

  • Labeling curves with curved labels.
    By Jan-Henrik Haunert, Herman Haverkort, Benjamin Niedermann, Arlind Nocaj, Aidan Slingsby, and Jo Wood.
    Presented at the Schematic Mapping Workshop 2014.
    Contact me if you would like to receive a two-page description of our work.

Improving information in schematizations

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:

  • Embedding cues about travel time in schematic maps.
    By Herman Haverkort.
    Presented at the Schematic Mapping Workshop 2014.
    text (draft of full report).

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:

  • Shortest-path-preserving rounding.
    By Herman Haverkort, David Kübel, and Elmar Langetepe.
    Proc. Int. Workshop on Combinatorial Algorithms (IWOCA), LNCS 11638:265-277, 2019.
    abstract full report

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:

  • Shortest-paths preserving metro maps.
    By Kevin Buchin, Herman Haverkort, Tal Milea, and Okke Schrijvers.
    In Proc. 19th Int. Symp. on Graph Drawing (GD), number 7034 in Lecture Notes in Computer Science (LNCS), pages 445–446, 2012 (abstract accompanying poster).
    abstract (or contact me for free access)

Aggregation of polygonal objects

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:

  • Bicriteria aggregation of polygons via graph cuts.
    By Peter Rottmann, Anne Driemel, Herman Haverkort, Heiko Röglin, and Jan-Henrik Haunert.
    Proc. 11th GIScience, Part II, LIPIcs 208:6:1-16, 2021.

Putting symbols on the map

Some older papers of mine are about how to put symbols and labels on a map:

  • Algorithmic aspects of proportional symbol maps.
    By Sergio Cabello, Herman Haverkort, Marc van Kreveld, and Bettina Speckmann.
    Algorithmica, 58(3):543–565, 2010.
    text (or contact me for free access)

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:

  • Algorithms for multi-criteria one-sided boundary labeling.
    By Marc Benkert, Herman Haverkort, Moritz Kroll, and Martin Nöllenburg.
    Journal on Graph Algorithms and Applications, 13(3):289–317, 2009.
automated_cartography.txt · Last modified: 2022/02/20 17:28 by administrator