Visualization of Subsurface Data Using Three-Dimensional Cartograms

  • Ziqiang Li
  • Saman A. AryanaEmail author
Conference paper
Part of the Advances in Science, Technology & Innovation book series (ASTI)


A three-dimensional cartogram is a thematic 3D map on which the volume of each region is linearly proportional to an extensive property enclosed within. This work formulated a 3D cartogram using a linear diffusion process. The 3D cartogram algorithm may be applied to a uniform Cartesian grid such that the distribution of the property of interest, such as the hydrocarbon pore volume in each cell, is equalized throughout the transformed domain. The spatial distortion of the grid cells serves as the qualitative indicator of this property, and the color may be used to visualize the spatial distribution of another property, such as permeability. Such a 3D cartogram on which a second property is mapped is a two-variable 3D cartogram.


Two-Variable 3D cartograms Diffusion Topology-preserving cartograms 



This work has been made possible through financial support from the Carbon Management Institute at the University of Wyoming. The corresponding author thanks Director Coddington for the lively discussions.


  1. 1.
    Robinson, A.H., Petchenik, B.B.: The Nature of Maps: essays toward Understanding Maps and Mapping. University of Chicago Press, Chicago (1976)Google Scholar
  2. 2.
    Dent, B.D.: Cartography: thematic Map Design, 5th edn. McGraw-Hill Higher Education, New York (1999)Google Scholar
  3. 3.
    Tobler, W.: Thirty five years of computer cartograms. Ann. Assoc. Am. Geogr. 94(1), 58–73 (2004)CrossRefGoogle Scholar
  4. 4.
    Raisz, E.: The rectangular statistical cartogram. Geogr. Rev. 24(2), 292–296 (1934)CrossRefGoogle Scholar
  5. 5.
    Dougenik, J.A., Chrisman, N.R., Niemeyer, D.R.: An algorithm to construct continuous area cartograms. The Professional Geographer 37(1), 75–81 (1985)CrossRefGoogle Scholar
  6. 6.
    Alam, M.J., Kobourov, S.G., Veeramoni, S.: Quantitative measures for cartogram generation techniques. Comput. Graphics Forum 34(3), 351–360 (2015)CrossRefGoogle Scholar
  7. 7.
    Nusrat, S., Kobourov, S.: The state of the art in cartograms. Comput. Graphics Forum 35(3), 619–642 (2016)CrossRefGoogle Scholar
  8. 8.
    Gastner, M.T., Newman, M.E.J.: Diffusion-based method for producing density-equalizing maps. Proc. Natl. Acad. Sci. 101(20), 7499–7504 (2004)CrossRefGoogle Scholar
  9. 9.
    Li, Z., Aryana, S.A.: Diffusion-based cartogram on spheres. Cartography Geog. Inf. Sci. (2017)Google Scholar
  10. 10.
    Gastner, M.T., Seguy, V., More, P.: Fast flow-based algorithm for creating density-equalizing map projections. Proc. Natl. Acad. Sci. 115(10), E2156–E2164 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of WyomingLaramieUSA

Personalised recommendations