Please use this identifier to cite or link to this item: https://doi.org/10.1073/pnas.1712674115
Title: Fast flow-based algorithm for creating density-equalizing map projections
Authors: Gastner, Michael T 
Seguy, Vivien
More, Pratyush
Keywords: Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
cartography
data visualization
statistical analysis
computer graphics
AREA CARTOGRAMS
EQUATION
Issue Date: 6-Mar-2018
Publisher: NATL ACAD SCIENCES
Citation: Gastner, Michael T, Seguy, Vivien, More, Pratyush (2018-03-06). Fast flow-based algorithm for creating density-equalizing map projections. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 115 (10) : E2156-E2164. ScholarBank@NUS Repository. https://doi.org/10.1073/pnas.1712674115
Abstract: © 2018 National Academy of Sciences. All Rights Reserved. Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts, cartograms can represent correctly which regions share common borders, resulting in insightful visualizations that can be the basis for further spatial statistical analysis. Computer programs can assist data scientists in preparing cartograms, but developing an algorithm that can quickly transform every coordinate on the map (including points that are not exactly on a border) while generating recognizable images has remained a challenge. Methods that translate the cartographic deformations into physics-inspired equations of motion have become popular, but solving these equations with sufficient accuracy can still take several minutes on current hardware. Here we introduce a flow-based algorithm whose equations of motion are numerically easier to solve compared with previous methods. The equations allow straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input. Despite the speedup, the proposed algorithm still keeps the advantages of previous techniques: With comparable quantitative measures of shape distortion, it accurately scales all areas, correctly fits the regions together, and generates a map projection for every point. We demonstrate the use of our algorithm with applications to the 2016 US election results, the gross domestic products of Indian states and Chinese provinces, and the spatial distribution of deaths in the London borough of Kensington and Chelsea between 2011 and 2014.
Source Title: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
URI: https://scholarbank.nus.edu.sg/handle/10635/169012
ISSN: 00278424
10916490
DOI: 10.1073/pnas.1712674115
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