Research Output

Visualizing Sets with Linear Diagrams.

  This paper presents the first design principles that optimize the visualization of sets using linear diagrams.
These principles are justified through empirical studies that evaluate the impact of graphical features on task
performance. Linear diagrams represent sets using straight line segments, with line overlaps corresponding
to set intersections. This study builds on recent empirical research, which establishes that linear diagrams
can be superior to prominent set visualization techniques, namely Euler and Venn diagrams. We address
the problem of how to best visualize overlapping sets using linear diagrams. To solve the problem, we
investigate which graphical features of linear diagrams significantly impact user task performance. To
this end, we conducted seven crowdsourced empirical studies involving a total of 1,760 participants. These
studies allowed us to identify the following design principles, which significantly aid task performance: use
a minimal number of line segments, use guidelines where overlaps start and end, and draw lines that are
thin as opposed to thick bars. We also evaluated the following graphical properties that did not significantly
impact task performance: color, orientation, and set order. The results are brought to life through a freely
available software implementation that automatically draws linear diagrams with user-controlled graphical
choices. An important consequence of our research is that users are now able to create effective visualizations
of sets automatically, thus improving human–computer interaction.

  • Type:


  • Date:

    14 December 2015

  • Publication Status:


  • Publisher


  • DOI:


  • ISSN:


  • Library of Congress:

    QA75 Electronic computers. Computer science

  • Dewey Decimal Classification:

    004 Data processing & computer science

  • Funders:

    Engineering and Physical Sciences Research Council


Rodgers, P., Stapleton, G., & Chapman, P. (2015). Visualizing Sets with Linear Diagrams. ACM transactions on computer-human interaction : a publication of the Association for Computing Machinery, 22(6), 1-39.



Sets; visualization; linear diagrams;

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    Visualizing sets with linear diagrams

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    © ACM, 2015. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Computer-Human Interaction, 22/6 Dec.2015

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