Data-Spatial Layouts for Grid Maps

Authors Nathan van Beusekom , Wouter Meulemans , Bettina Speckmann , Jo Wood

Thumbnail PDF


  • Filesize: 7.03 MB
  • 17 pages

Document Identifiers

Author Details

Nathan van Beusekom
  • TU Eindhoven, The Netherlands
Wouter Meulemans
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands
Jo Wood
  • City, University of London, UK


We want to thank Kevin Verbeek for useful discussions on the computational aspects of this paper.

Cite AsGet BibTex

Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann, and Jo Wood. Data-Spatial Layouts for Grid Maps. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Grid maps are a well-known technique to visualize data associated with spatial regions. A grid map assigns each region to a tile in a grid (often orthogonal or hexagonal) and then represents the associated data values within this tile. Good grid maps represent the underlying geographic space well: regions that are geographically close are close in the grid map and vice versa. Though Tobler’s law suggests that spatial proximity relates to data similarity, local variations may obscure clusters and patterns in the data. For example, there are often clear differences between urban centers and adjacent rural areas with respect to socio-economic indicators. To get a better view of the data distribution, we propose grid-map layouts that take data values into account and place regions with similar data into close proximity. In the limit, such a data layout is essentially a chart and loses all spatial meaning. We present an algorithm to create hybrid layouts, allowing for trade-offs between data values and geographic space when assigning regions to tiles. Our algorithm also handles hierarchical grid maps and allows us to focus either on data or on geographic space on different levels of the hierarchy. Leveraging our algorithm we explore the design space of (hierarchical) grid maps with a hybrid layout and their semantics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Grid map
  • algorithms
  • trade-offs


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Bonnie Berkowitz and Lazaro Gamio. What you need to know about the measles outbreak, February 2015. Accessed January 2023. URL:
  2. Paul Blickle and Sascha Venohr. Dürfen wir vorstellen: Deutschlands Muslime, January 2015. Accessed January 2023. URL:
  3. Mark Bruls, Kees Huizing, and Jarke J. van Wijk. Squarified treemaps. In Proceedings of the Joint EUROGRAPHICS and IEEE TCVG Symposium on Visualization, pages 33-42, 2000. URL:
  4. Kevin Buchin, Bettina Speckmann, and Sander Verdonschot. Evolution strategies for optimizing rectangular cartograms. In Proceedings of the 7th International Conference on Geographic Information Science, LNCS 7478, pages 29-42, 2012. URL:
  5. Rafael G. Cano, Kevin Buchin, Thom Castermans, Astrid Pieterse, Willem Sonke, and Bettina Speckmann. Mosaic drawings and cartograms. Computer Graphics Forum, 34(3):361-370, 2015. URL:
  6. Ben Casselman and Allison McCann. Where your state gets its money, April 2015. Accessed January 2023. URL:
  7. Mark de Berg, Elena Mumford, and Bettina Speckmann. Optimal BSPs and rectilinear cartograms. International Journal of Computational Geometry & Applications, 20(2):203-222, 2010. URL:
  8. Danny DeBelius. Let’s tesselate: Hexagons for tile grid maps, May 2015. Accessed January 2023. URL:
  9. David Eppstein, Marc van Kreveld, Bettina Speckmann, and Frank Staals. Improved grid map layout by point set matching. International Journal of Computational Geometry & Applications, 25(02):101-122, 2015. URL:
  10. Diansheng Guo, Jin Chen, Alan M. MacEachren, and Ke Liao. A visualization system for space-time and multivariate patterns (vis-stamp). IEEE Transactions on Visualization and Computer Graphics, 12(6):1461-1474, 2006. URL:
  11. Wouter Meulemans, Jason Dykes, Aidan Slingsby, Cagatay Turkay, and Jo Wood. Small multiples with gaps. IEEE Transactions on Visualization and Computer Graphics, 23(1):381-390, 2016. URL:
  12. Wouter Meulemans, Max Sondag, and Bettina Speckmann. A simple pipeline for coherent grid maps. IEEE Transactions on Visualization and Computer Graphics, 27(2):1236-1246, 2020. URL:
  13. Patrick A.P. Moran. Notes on continuous stochastic phenomena. Biometrika, 37(1/2):17-23, 1950. URL:
  14. New York Times. How the rulings affect gay couples, June 2013. Accessed January 2023. URL:
  15. Kenton Powell, Rich Harris, and Feilding Cage. How voter-friendly is your state?, October 2014. Accessed January 2023. URL:
  16. Ben Shneiderman and Martin Wattenberg. Ordered treemap layouts. In Proceedings of the IEEE Symposium on Information Visualization, pages 73-78, 2001. URL:
  17. Aidan Slingsby. Tilemaps for summarising multivariate geographical variation. In Proceedings of the Workshop on Visual Summarization and Report Generation, 2018. Google Scholar
  18. Aidan Slingsby, Mary Kelly, and Jason Dykes. OD maps for showing changes in Irish female migration between 1851 and 1911. Environment and Planning A, 46(12):2795-2797, 2014. URL:
  19. Aidan Slingsby, Jo Wood, and Jason Dykes. Treemap cartography for showing spatial and temporal traffic patterns. Journal of Maps, 6(1):135-146, 2010. URL:
  20. Waldo R. Tobler. A computer movie simulating urban growth in the Detroit region. Economic geography, 46(sup1):234-240, 1970. URL:
  21. Alex Tribou and Keith Collins. This is how fast America changes its mind, June 2015. Accessed January 2023. URL:
  22. Edward R. Tufte. The Visual Display of Quantitative Information, volume 2. Graphics Press Cheshire, CT, 1983. URL:
  23. Hamidreza Validi, Austin Buchanan, and Eugene Lykhovyd. Imposing contiguity constraints in political districting models. Operations Research, 70(2):867-892, 2022. URL:
  24. Marc J. van Kreveld and Bettina Speckmann. On rectangular cartograms. Computational Geometry: Theory and Applications, 37(3):175-187, 2007. URL:
  25. Jo Wood, Donia Badawood, Jason Dykes, and Aidan Slingsby. BallotMaps: Detecting name bias in alphabetically ordered ballot papers. IEEE Transactions on Visualization and Computer Graphics, 17(12):2384-2391, 2011. URL:
  26. Jo Wood and Jason Dykes. Spatially ordered treemaps. IEEE Transactions on Visualization and Computer Graphics, 14(6):1348-1355, 2008. URL:
  27. Jo Wood, Jason Dykes, and Aidan Slingsby. Visualisation of origins, destinations and flows with OD maps. The Cartographic Journal, 47(2):117-129, 2010. URL:
  28. Jo Wood, Aidan Slingsby, and Jason Dykes. Visualizing the dynamics of London’s bicycle-hire scheme. Cartographica: The International Journal for Geographic Information and Geovisualization, 46(4):239-251, 2011. URL: