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Issue No.06 - November/December (2010 vol.16)
pp: 881-889
ABSTRACT
Statistical data associated with geographic regions is nowadays globally available in large amounts and hence automated methods to visually display these data are in high demand. There are several well-established thematic map types for quantitative data on the ratio-scale associated with regions: choropleth maps, cartograms, and proportional symbol maps. However, all these maps suffer from limitations, especially if large data values are associated with small regions. To overcome these limitations, we propose a novel type of quantitative thematic map, the necklace map. In a necklace map, the regions of the underlying two-dimensional map are projected onto intervals on a one-dimensional curve (the necklace) that surrounds the map regions. Symbols are scaled such that their area corresponds to the data of their region and placed without overlap inside the corresponding interval on the necklace. Necklace maps appear clear and uncluttered and allow for comparatively large symbol sizes. They visualize data sets well which are not proportional to region sizes. The linear ordering of the symbols along the necklace facilitates an easy comparison of symbol sizes. One map can contain several nested or disjoint necklaces to visualize clustered data. The advantages of necklace maps come at a price: the association between a symbol and its region is weaker than with other types of maps. Interactivity can help to strengthen this association if necessary. We present an automated approach to generate necklace maps which allows the user to interactively control the final symbol placement. We validate our approach with experiments using various data sets and maps.
INDEX TERMS
Geographic Visualization, Automated Cartography, Proportional Symbol Maps, Necklace Maps
CITATION
Bettina Speckmann, Kevin Verbeek, "Necklace Maps", IEEE Transactions on Visualization & Computer Graphics, vol.16, no. 6, pp. 881-889, November/December 2010, doi:10.1109/TVCG.2010.180
REFERENCES
[1] M. A. Bekos, M. Kaufmann, A. Symvonis, and A. Wolff, Boundary labeling: Models and efficient algorithms for rectangular maps. Computational Geometry: Theory and Applications, 36 (3): 215–236, 2007.
[2] S. Cabello, H. Haverkort, M. van Kreveld, and B. Speckmann, Algorithmic aspects of proportional symbol maps. Algorithmica, 2010. to appear.
[3] B. Dent, Cartography - thematic map design. McGraw-Hill, 5th edition, 1999.
[4] D. Dorling, Area Cartograms: their Use and Creation, volume 59 of Concepts and Techniques in Modern Geography. University of East An-glia, Environmental Publications, Norwich, 1996.
[5] J. A. Dougenik, N. R. Chrisman, and D. R. Niemeyer, An algorithm to construct continous area cartograms. Professional Geographer, 3: 75–81, 1985.
[6] H. Edelsbrunner and E. Waupotitsch, A combinatorial approach to cartograms. Computational Geometry: Theory and Applications, 7: 343–360, 1997.
[7] M. Gastner and M. Newman, Diffusion-based method for producing density-equalizing maps. Proc. National Academy of Sciences of the United States of America (PNAS), 101 (20): 7499–7504, 2004.
[8] R. Heilmann, D. A. Keim, C. Panse, and M. Sips, Recmap: Rectangular map approximations. In Proc. IEEE Symposium on Information Visualization (INFOVIS), pages 33–40, 2004.
[9] D. Keim, S. North, and C. Panse, Cartodraw: A fast algorithm for generating contiguous cartograms. IEEE Transactions on Visualization and Computer Graphics, 10: 95–110, 2004.
[10] C. Kocmoud and D. House, A constraint-based approach to constructing continuous cartograms. In Proc. Intern. Symposium on Spatial Data Handling (SDH), pages 236–246, 1998.
[11] M. v. Kreveld and B. Speckmann, On rectangular cartograms. Computational Geometry: Theory and Applications, 37 (3): 175187, 2007.
[12] E. Raisz, The rectangular statistical cartogram. Geographical Review, 24: 292–296, 1934.
[13] T. A. Slocum, R. B. McMaster, F. C. Kessler, and H. H. Howard, Thematic Cartography and Geographic Visualization. Prentice Hall, 2nd edition, 2003.
[14] B. Speckmann, M. van Kreveld, and S. Florisson, A linear programming approach to rectangular cartograms. In Proc. 12th Intern. Symposium on Spatial Data Handling (SDH), pages 527–546, 2006.
[15] B. Speckmann and K. Verbeek, Algorithms for necklace maps. In preparation, 2010.
[16] W. Tobler, Pseudo-cartograms. The American Cartographer, 13: 43–50, 1986.
[17] M. van Kreveld, E. Schramm, and A. Wolff, Algorithms for the placement of diagrams on maps. In Proc. 12th Intern. Symposium on Advances in Geographic Information Systems (ACM GIS), pages 222–231, 2004.
[18] J. Wood and J. Dykes, Spatially ordered treemaps. IEEE Transactions on Visualization and Computer Graphics, 14: 1348–1355, 2008.
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