Representing quantities on Venn and Euler diagrams can be achieved through the use of multi-attribute glyphs. These glyphs can also act as an aid to assist in the visual decoding of the membership of segments within the diagrams and convey other data attributes as well. Instead of area-proportional Venn and Euler diagrams to indicate quantities, this approach uses separate overlaid glyphs to decouple the representation of data from logical combinations. It also uses glyph attributes to assist in visual decoding of membership of regions. This approach can scale to higher-order logical diagrams and potentially offer more accurate visual estimation than area-proportional techniques. The depiction of data on set diagrams is useful in various applications (e.g. Boolean queries, genetic informatics). Area-proportional set diagrams have become popular in research (e.g. [1-6]) and software (e.g. see eulerdiagrams.org). However, the area-proportional approach has shortcomings, such as:
1. Visual comparison of irregular areas is difficult. Information visualization
researchers indicate difficulty with visual comparison of areas and/or a preference
for using length instead of area for faster visual comparison (e.g. [
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Instead, a glyph-based approach is considered. The use of glyphs within set
diagrams is not new. Glyphs have been used to represent items in a dataset (first 3 in fig.
1). Spoerri’s approach [
The contribution of this paper explores, in section 2, the use of glyphs (pictographic and scaled glyphs) to indicate quantities and the use of additional visual attributes to indicate set membership or other data. Results are discussed in section 3. 2
Our approach is focused on the use of glyphs to decouple the depiction of logical
relationships (e.g. Venn and Euler diagrams) separate from the depiction of quantities.
By decoupling the quantity from the set diagram, visual attributes more amenable to
fast estimation (e.g. size, origentation and color) can be used [
Sketches and Real-Data Mockups
To quickly iterate through conceptual ideas, loose sketches were followed by
mockups using simple sets of real-data. Loose sketches can reveal limitations of promising
ideas when implemented with real-data, (e.g. occlusion, imperceptible differences,
large dynamic ranges, etc). For rapid mock-ups, we divided the Titanic passenger list
into 4 sets for a Venn diagram and 3 sets for an Euler diagram which resulted in
useful properties such as empty segments, small segments and large segments.
Markers of a fixed size can be repeated to represent quantities ranging from simple
dots to pictographs e.g. Isotype [
However, a pictograph approach has some challenges:
• Some regions of the set diagram are too small to fit the pictographs. The addition
of the leader line could increase the effort to visually decode the relationships.
• The irregular shape of some regions of the set diagram requires an irregular
placement. Pictographs organized linearly can be visually estimated by length, which is
preferred to visual estimation of area (e.g. [
Background Color: Color can be used, but is problematic. It is challenging to
decode the color in intersections as color is not understood as separable [
Background Texture: Textures have been used to aid in identification of set
membership e.g. [
Glyph with Colors: The same coloring used in the set diagram can be reused in glyphs to indicate membership. Rather than blend colors, however, the colors can be kept separate within the glyph. The layout of the color could be organized as stripes, or radially resembling a bullseye or pie.
Glyph with Oriented Whisker: In some set diagrams (e.g. Venn) the placement
of the label is typically around the perimeter which can be leveraged by the glyph,
specifically by modifying the shape with an added whisker [
The glyph-based approach also allows for additional visual attributes to convey additional data values. For example, the whisker-based glyphs can use: • Traditional visualization attributes, such as brightness, hue, texture • Shape-based attributes, such as closure, curvature or edge type • Each whisker-shape can be independently modified to indicate a data attribute with respect to the set membership, for example whisker length or width • The internal area of the glyph can be used, in larger glyphs, for example, as a pie chart or with a pictograph. The whisker-based approach may work well with Venn diagrams, but has may have issues with Euler diagrams and issues where whiskers are potentially occluded. The image below shows a 5-way Venn diagram that has been modified from ellipses to increase the size of the smaller regions to make the technique more workable.
Our contribution shows that glyphs can be used to separate the representation of data
such as quantities from the representation of sets. Glyphs can:
• Indicate data layered over set diagrams, either as scalable glyphs or as pictographs,
and simple size is preferred for fast visual estimation as opposed to irregularly
shaped areas [
Implementation on a wide variety of data sets and testing with users requires further effort. Other work could include 3D and interaction techniques, for example, on interaction, extend whiskers to set labels to aid interpretation of whiskers.