A new algorithm for continuous area cartogram construction with triangulation of regions and restriction on bearing changes of edges

Ryo Inoue, Eihan Shimizu

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

A continuous area cartogram is a transformed map in which regions are resized relative to their data. It is considered an effective visualization tool for statistical data, and many solutions have been proposed. However, most of these solutions are not mathematically clear or user friendly; further, they do not provide visually elegant area cartograms. An essential condition for the construction of a visually elegant area cartogram is that the resultant region shape should resemble the corresponding regions on geographical maps. Since it is impossible to determine the shape of a region based only on the information of size, area cartogram construction is an ill-posed problem that requires regularization. In this study, we propose a construction algorithm that involves triangulation of regions and regularization through restrictions on the bearing changes of the edges in order to obtain visually clear results. First, we formulate a construction using nonlinear least squares. Then, by linearizing, we derive a simple formula to create area cartograms. The application of our algorithm to the USA population datasets reveals that our algorithm has mathematical clarity and is user friendly.

Original languageEnglish
Pages (from-to)115-125
Number of pages11
JournalCartography and Geographic Information Science
Volume33
Issue number2
DOIs
Publication statusPublished - 2006 Apr 1
Externally publishedYes

Keywords

  • Continuous area cartogram
  • Map transformation
  • Triangulation
  • Visualization

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geography, Planning and Development
  • Management of Technology and Innovation

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