An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms

Literature Cited

• Ahmed , N. and Miller , H. J. 2007 . Time–space transformations of geographic space for exploring, analyzing and visualizing transportation systems . Journal of Transport Geography , 15 ( 1 ) : 2 – 17 .
   Web of Science ®Google Scholar
• Binmore , K. G. 1980 . Topological ideas. Vol. 2. The foundations of analysis: A straightforward introduction. , New York : Cambridge University Press .
   Google Scholar
• Dorling , D. 1994 . “ Cartograms for visualizing human geography ” . In Visualization in geographical information systems , Edited by: Hearnshaw , H. H. and Unwin , D. J. 85 – 102 . Chichester , , UK : Wiley .
   Google Scholar
• Dorling , D. 1996 . Area cartograms: Their use and creation, concepts and techniques in modern geography , Norwich , , UK : School of Environmental Sciences, University of East Anglia .
   Google Scholar
• Dorling , D. 2007 . Worldmapper: The human anatomy of a small planet . PLoS Medicine , 4 ( 1 ) : 13
   Web of Science ®Google Scholar
• Dorling , D. , Barford , A. and Newman , M. 2006 . Worldmapper: The world as you've never seen it before . IEEE Transactions on Visualization and Computer Graphics , 12 ( 5 ) : 757 – 64 .
   PubMed Web of Science ®Google Scholar
• Dougenik , J. A. , Chrisman , N. R. and Niemeyer , D. R. 1985 . An algorithm to construct continuous area cartograms . The Professional Geographer , 37 ( 1 ) : 75 – 81 .
   Web of Science ®Google Scholar
• Du , C. and Liu , L. 1999 . Constructing contiguous area cartogram using Arcview Avenue . Paper presented at the Proceedings of Geoinformatics’ 99 Conference , San Diego, CA
   Google Scholar
• Florisson , S. , van Kreveld , M. and Speckmann , B. 2005 . “ Rectangular cartograms: Construction & animation ” . In Paper presented at the Proceedings of the Twenty-First Annual Symposium on Computational Geometry Pisa , , Italy
   Google Scholar
• Friis , H. R. 1974 . Statistical cartography in the United States prior to 1870 and the role of Joseph C. G. Kennedy and the U.S. Census Office . Cartography and Geographic Information Science , 1 ( 2 ) : 131 – 57 .
   Google Scholar
• Gastner , M. T. and Newman , M. E. J. 2004 . Diffusion-based method for producing density-equalizing maps . Proceedings of the National Academy of Sciences, USA , 101 ( 20 ) : 7499 – 7504 .
   PubMed Web of Science ®Google Scholar
• Gastner , M. T. , Shalizi , C. R. and Newman , M. E. J. 2005 . Maps and cartograms of the 2004 U.S. presidential election results . Advances in Complex Systems , 8 ( 1 ) : 117 – 23 .
   Web of Science ®Google Scholar
• Gusein-Zade , S. M. and Tikunov , V. S. 1993 . A new technique for constructing continuous cartograms . Cartography and Geographic Information Science , 20 ( 3 ) : 167 – 73 .
   Google Scholar
• Heilmann , R. , Keim , D. A. , Panse , C. and Sips , M. Recmap: Rectangular map approximations . Paper presented at the IEEE Symposium on Information Visualization . Austin, TX .
   Google Scholar
• Henriques , R. , BaÇão , F. and Lobo , V. 2009 . Carto-Som: Cartogram creation using self-organizing maps . International Journal of Geographical Information Science , 23 ( 4 ) : 483 – 511 .
   Web of Science ®Google Scholar
• House , D. H. and Kocmoud , C. J. Continuous cartogram construction . Paper presented at IEEE Visualization’98 . Research Triangle Park , NC .
   Google Scholar
• Inoue , R. and Shimizu , E. 2006 . A new algorithm for continuous area cartogram construction with triangulation of regions and restriction on bearing changes of edges . Cartography and Geographic Information Science , 33 ( 2 ) : 115 – 25 .
   Google Scholar
• Johnson , D. A. and Glenn , W. H. 1960 . Topology: The rubber-sheet geometry , Georgetown , CT : Webster House .
   Google Scholar
• Keim , D. A. , North , S. C. and Panse , C. 2004 . Cartodraw: A fast algorithm for generating contiguous cartograms . IEEE Transactions on Visualization and Computer Graphics , 10 ( 1 ) : 95 – 110 .
   PubMed Web of Science ®Google Scholar
• Keim , D. A. , Panse , C. and North , S. C. 2005 . Medial-axis-based cartograms . Computer Graphics and Applications, IEEE , 25 ( 3 ) : 60 – 68 .
   PubMed Web of Science ®Google Scholar
• Kocmoud , C. J. 1997 . Constructing continuous cartograms: A constraint-based approach. Master's thesis , College Station , TX : Texas A&M University .
   Google Scholar
• Lekien , F. and Leonard , N. E. 2009 . Nonuniform coverage and cartograms . SIAM Journal on Control and Optimization , 48 ( 1 ) : 351 – 72 .
   Web of Science ®Google Scholar
• Nijenhuis , A. 1974 . Strong derivatives and inverse mappings . The American Mathematical Monthly , 81 ( 9 ) : 969 – 80 .
   Web of Science ®Google Scholar
• Raisz , E. 1934 . The rectangular statistical cartogram . Geographical Review , 24 ( 2 ) : 292 – 96 .
   Google Scholar
• Raisz , E. 1936 . Rectangular statistical cartograms of the world . Journal of Geography , 35 ( 1 ) : 8 – 10 .
   Google Scholar
• Roth , R. E. , Woodruff , A. W. and Johnson , Z. F. 2002 . Value-by-alpha maps: An alternative technique to the cartogram . The Cartographic Journal , 47 ( 2 ) : 130 – 40 .
   Web of Science ®Google Scholar
• Sauvy , J. and Sauvy , S. 1974 . The child's discovery of space: From hopscotch to mazes: An introduction to intuitive topology. , London : Penguin Education .
   Google Scholar
• Skupin , A. and Fabrikant , S. I. 2003 . Spatialization methods: A cartographic research agenda for non-geographic information visualization . Cartography and Geographic Information Science , 30 ( 2 ) : 99 – 119 .
   Google Scholar
• Sun , H. and Li , Z. H. 2010 . Effectiveness of cartogram for the representation of spatial data . Cartographic Journal , 47 ( 1 ) : 12 – 21 .
   Web of Science ®Google Scholar
• Sun , S. and Manson , S. M. 2007 . “ Distance cartogram: Concept, approximate algorithm, and examples ” . In Paper presented at the 2007 International Workshop on Geographic Information Science Beijing
   Google Scholar
• Tobler , W. R. 1973 . A continuous transformation useful for districting . Annals of the New York Academy of Sciences , 219 ( 1 ) : 215 – 20 .
   PubMedGoogle Scholar
• Tobler , W. R. 1986 . Pseudo-cartograms . Cartography and Geographic Information Science , 13 ( 1 ) : 43 – 50 .
   Web of Science ®Google Scholar
• Tobler , W. R. 2004 . Thirty five years of computer cartograms . Annals of the Association of American Geographers , 94 ( 1 ) : 58 – 73 .
   Web of Science ®Google Scholar
• van Kreveld , M and Speckmann , B. 2007 . On rectangular cartograms . Computational Geometry , 37 ( 3 ) : 175 – 87 .
   Web of Science ®Google Scholar
• Webb , R. 2006 . Cartography: A popular perspective . Nature , 439 ( 7078 ) : 800
   PubMed Web of Science ®Google Scholar