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A Manual Approach to Cartogram Construction using Triangular Lattice Transformation

A Manual Approach to Cartogram Construction using Triangular Lattice Transformation

Barry Kronenfeld, Eastern Illinois University

Automated algorithms are limited in their ability to produce aesthetically pleasing cartograms, while currently available methods for manual cartogram construction (i.e. block cartograms) do not define a continuous spatial transformation. I propose an alternative framework for cartogram construction using triangular lattice transformation. In the proposed framework, a regular lattice is transformed by repositioning vertices until vertex density approximates population density, forming a dot-density map. The original and transformed lattices define a continuous transformation from geographic space to cartogram space. The transformation is reusable and can be applied to any geographic dataset, acting as a type of map projection. Sample tools for constructing and applying cartograms are demonstrated, and the approach is illustrated with a population cartogram of Illinois, USA. By separating the task of defining a cartogram from the map design process, the proposed framework aims to facilitate more widespread application of cartograms to the analysis of population-dependent variables.

NACIS 2014


Nathaniel V. KELSO

October 10, 2014


  1. Barry  J.  Kronenfeld,  Eastern  Illinois  University   NACIS  2014  

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  4. Carto-SOM – Cartogram creation using self-organizing maps Roberto HENRIQUES1, Fernando

    BAÇÃO1 and Victor LOBO1,2   Dominique  Andrieu,   Christian  Kaiser,   André  Ourednik  
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  10. ¡  blocky   ¡  not  a  continuous   transformation  

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  12. SOURCE   TRIANGLE   TARGET   TRIANGLE   Tobler  1973/2005

      Inoue  et  al.  2007   Henriques  et  al.  2009  
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  22. Diffusion   Cartogram   Manual     Cartogram  

  23. ¡  Cartograms  can  be  constructed  manually  by   defining  a

       piecewise  linear  transformation   between  triangular  lattices.   ¡  An  infinite  variety  of  cartograms  are  possible.   ¡  Construction  is  time-­‐consuming.   ¡  However,  techniques  to  facilitate  faster   construction  are  being  developed   §  transformation  patterns   §  hierarchical  work  flow    
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  28. Mapping  Project   Final  Map   Symbology ,  Labels,  

    etc.   Density   Surface   Definition   Geographic   Data   Cartogram   Construction  
  29. Mapping  Project   Final  Map   Symbology,   Labels,  etc.

      Cartogram  Definition   Density   Surface   Definition   Cartogram   Construction   Geographic   Data   Map   Transformation  
  30. ¡  Looks    (Sun  &  Li  2010)   ¡  Variety

     (Sui  &  Holt  2008)   ¡  Fun  (Dent  1976)  
  31. 1.  Build  a  tool  for  manual  cartogram   construction  

    2.  Allow  for  continuous  transformation   3.  Identify  GUI  characteristics  to  facilitate  ease-­‐ of-­‐use   4.  Provide  flexibility  to  integrate  algorithms  or   algorithmic  components   5.  Make  it  look/feel  cool  
  32. ¡  Dot-­‐density  framework   ¡  Size  and  shape  feedback  

    ¡  Linking  &  brushing   ¡  Transformation  patterns   ¡  Hierarchical  construction  process