Mosaic Drawings and Cartograms
Cartograms visualize quantitative data about a set of regions such as countries or states. There are several different types of cartograms and – for some – algorithms to automatically construct them exist. We focus on mosaic cartograms: cartograms that use multiples of simple tiles – usually squares...
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| Vydáno v: | Computer graphics forum Ročník 34; číslo 3; s. 361 - 370 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Blackwell Publishing Ltd
01.06.2015
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Cartograms visualize quantitative data about a set of regions such as countries or states. There are several different types of cartograms and – for some – algorithms to automatically construct them exist. We focus on mosaic cartograms: cartograms that use multiples of simple tiles – usually squares or hexagons – to represent regions. Mosaic cartograms communicate well data that consist of, or can be cast into, small integer units (for example, electorial college votes). In addition, they allow users to accurately compare regions and can often maintain a (schematized) version of the input regions’ shapes. We propose the first fully automated method to construct mosaic cartograms. To do so, we first introduce mosaic drawings of triangulated planar graphs. We then show how to modify mosaic drawings into mosaic cartograms with low cartographic error while maintaining correct adjacencies between regions. We validate our approach experimentally and compare to other cartogram methods. |
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| AbstractList | Cartograms visualize quantitative data about a set of regions such as countries or states. There are several different types of cartograms and – for some – algorithms to automatically construct them exist. We focus on mosaic cartograms: cartograms that use multiples of simple tiles – usually squares or hexagons – to represent regions. Mosaic cartograms communicate well data that consist of, or can be cast into, small integer units (for example, electorial college votes). In addition, they allow users to accurately compare regions and can often maintain a (schematized) version of the input regions’ shapes. We propose the first fully automated method to construct mosaic cartograms. To do so, we first introduce mosaic drawings of triangulated planar graphs. We then show how to modify mosaic drawings into mosaic cartograms with low cartographic error while maintaining correct adjacencies between regions. We validate our approach experimentally and compare to other cartogram methods. |
| Author | Pieterse, A. Buchin, K. Sonke, W. Castermans, T. Cano, R. G. Speckmann, B. |
| Author_xml | – sequence: 1 givenname: R. G. surname: Cano fullname: Cano, R. G. email: rgcano@ic.unicamp.br organization: Institute of Computing, University of Campinas, Brazil – sequence: 2 givenname: K. surname: Buchin fullname: Buchin, K. email: k.a.buchin@tue.nl organization: TU Eindhoven, The Netherlands – sequence: 3 givenname: T. surname: Castermans fullname: Castermans, T. email: t.h.a.castermans@student.tue.nl organization: TU Eindhoven, The Netherlands – sequence: 4 givenname: A. surname: Pieterse fullname: Pieterse, A. email: a.pieterse@student.tue.nl organization: TU Eindhoven, The Netherlands – sequence: 5 givenname: W. surname: Sonke fullname: Sonke, W. email: w.m.sonke@student.tue.nl organization: TU Eindhoven, The Netherlands – sequence: 6 givenname: B. surname: Speckmann fullname: Speckmann, B. email: b.speckmann@tue.nl organization: TU Eindhoven, The Netherlands |
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| Cites_doi | 10.1109/INFVIS.2004.57 10.1142/S0129054105002905 10.1111/j.0033-0124.1985.00075.x 10.1142/S0218195910003268 10.1109/TVCG.2008.165 10.1016/j.disc.2007.12.087 10.1016/S0925-7721(96)00006-5 10.1016/j.comgeo.2006.06.002 10.1559/152304086783900194 10.1007/3-540-35589-8_34 10.1007/s00454-013-9521-1 10.2307/208794 10.1109/TVCG.2004.1260761 10.1559/152304092783721231 10.1179/000870404X21121 10.1073/pnas.0400280101 10.1137/S0097539702411381 |
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| References_xml | – reference: de Berg M., Mumford E., Speckmann B.: On rectilinear duals for vertex-weighted plane graphs. Discrete Mathematics 309, 7 (2009), 1794-1812. 2 – reference: Gastner M., Newman M.: Diffusion-based method for producing density-equalizing maps. Proceedings of the National Academy of Sciences of the United States of America (PNAS) 101, 20 (2004), 7499-7504. 2, 7, 9 – reference: Edelsbrunner H., Waupotitsch E.: A combinatorial approach to cartograms. Computational Geometry: Theory and Applications 7 (1997), 343-360. 2 – reference: Kreveld M. v., Speckmann B.: On rectangular cartograms. Computational Geometry: Theory and Applications 37, 3 (2007), 175-187. 2 – reference: Chiang Y.-T., Lin C.-C., Lu H.-I.: Orderly spanning trees with applications. SIAM Journal on Computing 34, 4 (2005), 924-945. 3, 4 – reference: de Berg M., Mumford E., Speckmann B.: Optimal BSPs and rectilinear cartograms. International Journal of Computational Geometry and Applications 20, 2 (2010), 203-222. 3, 9 – reference: Thomas B., Dorling D.: Advances in the human cartography of the uk. The Cartographic Journal 41, 2 (2004), 109-115. 2 – reference: Tobler W.: Pseudo-cartograms. The American Cartographer 13 (1986), 43-50. 2 – reference: Miura K., Azuma M., Nishizeki T.: Canonical decomposition, realizer, Schnyder labeling and orderly spanning trees of plane graphs. International Journal of Foundations of Computer Science 16, 1 (2005), 117-141. 4 – reference: Raisz E.: The rectangular statistical cartogram. Geographical Review 24 (1934), 292-296. 2 – reference: Wood J., Dykes J.: Spatially ordered treemaps. IEEE Transactions on Visualization and Computer Graphics 14 (2008), 1348-1355. 2 – reference: Carr D.B., Olsen A.R., White D.: Hexagon mosaic maps for display of univariate and bivariate geographical data. Cartography and Geographic Information Systems 19, 4 (1992), 228-236. 3 – reference: Alam M.J., Biedl T.C., Felsner S., Kaufmann M., Kobourov S.G., Ueckerdt T.: Computing cartograms with optimal complexity. Discrete & Computational Geometry 50, 3 (2013), 784-810. 2 – reference: Dougenik J.A., Chrisman N.R., Niemeyer D.R.: An algorithm to construct continous area cartograms. Professional Geographer 3 (1985), 75-81. 2 – reference: Keim D., North S., Panse C.: Cartodraw: A fast algorithm for generating contiguous cartograms. IEEE Transactions on Visualization and Computer Graphics 10 (2004), 95-110. 2 – volume: 10 start-page: 95 year: 2004 end-page: 110 article-title: Cartodraw: A fast algorithm for generating contiguous cartograms publication-title: IEEE Transactions on Visualization and Computer Graphics – start-page: 527 year: 2006 end-page: 546 – volume: 3 start-page: 75 year: 1985 end-page: 81 article-title: An algorithm to construct continous area cartograms publication-title: Professional Geographer – volume: 24 start-page: 292 year: 1934 end-page: 296 article-title: The rectangular statistical cartogram publication-title: Geographical Review – volume: 101 start-page: 7499 issue: 20 year: 2004 end-page: 7504 article-title: Diffusion‐based method for producing density‐equalizing maps publication-title: Proceedings of the National Academy of Sciences of the United States of America (PNAS) – volume: 16 start-page: 117 issue: 1 year: 2005 end-page: 141 article-title: Canonical decomposition, realizer, Schnyder labeling and orderly spanning trees of plane graphs publication-title: International Journal of Foundations of Computer Science – volume: 59 year: 1996 – volume: 309 start-page: 1794 issue: 7 year: 2009 end-page: 1812 article-title: On rectilinear duals for vertex‐weighted plane graphs publication-title: Discrete Mathematics – start-page: 33 year: 2004 end-page: 40 – volume: 20 start-page: 203 issue: 2 year: 2010 end-page: 222 article-title: Optimal BSPs and rectilinear cartograms publication-title: International Journal of Computational Geometry and Applications – volume: 7 start-page: 343 year: 1997 end-page: 360 article-title: A combinatorial approach to cartograms publication-title: Computational Geometry: Theory and Applications – volume: 50 start-page: 784 issue: 3 year: 2013 end-page: 810 article-title: Computing cartograms with optimal complexity publication-title: Discrete & Computational Geometry – volume: 37 start-page: 175 issue: 3 year: 2007 end-page: 187 article-title: On rectangular cartograms publication-title: Computational Geometry: Theory and Applications – volume: 14 start-page: 1348 year: 2008 end-page: 1355 article-title: Spatially ordered treemaps publication-title: IEEE Transactions on Visualization and Computer Graphics – start-page: 117 year: 2011 end-page: 128 – volume: 34 start-page: 924 issue: 4 year: 2005 end-page: 945 article-title: Orderly spanning trees with applications publication-title: SIAM Journal on Computing – volume: 41 start-page: 109 issue: 2 year: 2004 end-page: 115 article-title: Advances in the human cartography of the uk publication-title: The Cartographic Journal – volume: 13 start-page: 43 year: 1986 end-page: 50 article-title: Pseudo‐cartograms publication-title: The American Cartographer – volume: 7478 start-page: 29 year: 2012 end-page: 42 – volume: 19 start-page: 228 issue: 4 year: 1992 end-page: 236 article-title: Hexagon mosaic maps for display of univariate and bivariate geographical data publication-title: Cartography and Geographic Information Systems – start-page: 236 year: 1998 end-page: 246 – ident: e_1_2_8_14_2 doi: 10.1109/INFVIS.2004.57 – ident: e_1_2_8_5_2 – ident: e_1_2_8_21_2 – ident: e_1_2_8_19_2 doi: 10.1142/S0129054105002905 – ident: e_1_2_8_10_2 doi: 10.1111/j.0033-0124.1985.00075.x – volume-title: Concepts and Techniques in Modern Geography year: 1996 ident: e_1_2_8_11_2 – ident: e_1_2_8_9_2 doi: 10.1142/S0218195910003268 – ident: e_1_2_8_15_2 – ident: e_1_2_8_27_2 doi: 10.1109/TVCG.2008.165 – ident: e_1_2_8_8_2 doi: 10.1016/j.disc.2007.12.087 – ident: e_1_2_8_18_2 – ident: e_1_2_8_26_2 – ident: e_1_2_8_12_2 doi: 10.1016/S0925-7721(96)00006-5 – start-page: 117 volume-title: Proc. 18th International Symposium on Graph Drawing (GD 10) year: 2011 ident: e_1_2_8_3_2 – ident: e_1_2_8_17_2 doi: 10.1016/j.comgeo.2006.06.002 – ident: e_1_2_8_20_2 – ident: e_1_2_8_25_2 doi: 10.1559/152304086783900194 – ident: e_1_2_8_23_2 doi: 10.1007/3-540-35589-8_34 – ident: e_1_2_8_2_2 doi: 10.1007/s00454-013-9521-1 – ident: e_1_2_8_22_2 doi: 10.2307/208794 – start-page: 29 volume-title: Lecture Notes in Computer Science year: 2012 ident: e_1_2_8_4_2 – ident: e_1_2_8_16_2 doi: 10.1109/TVCG.2004.1260761 – ident: e_1_2_8_7_2 doi: 10.1559/152304092783721231 – ident: e_1_2_8_24_2 doi: 10.1179/000870404X21121 – ident: e_1_2_8_13_2 doi: 10.1073/pnas.0400280101 – ident: e_1_2_8_6_2 doi: 10.1137/S0097539702411381 |
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| SubjectTerms | Algorithms Analysis Cartography Categories and Subject Descriptors (according to ACM CCS) Computer graphics Construction Data analysis Graphs Hexagons I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Image processing systems Mosaics Studies Tiles |
| Title | Mosaic Drawings and Cartograms |
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