Y. Jin, T. J. A. de Jong, M. Tennekes, and M. Chen. Radial Icicle Tree (RIT): Node separation and area constancy. To appear in IEEE Transactions on Visualization and Computer Graphics, 30(1), 2024. (To be presented at IEEE VIS 2023.) (Early version: arXiv: 2307.10481, 2023.)
Icicle Tree Plots and Sunburst Tree Plots are two commonlyused visual representations for tree visualization. As illustrated in Fig. 1 (below), some visual patterns depicted by these plots may exhibit undesirable qualities. As illustrated on the left of Fig. 1, in an icicle tree, some thin nodes may be difficult to notice (marked as (a) in the figure), and two nodes that belong to different subtrees but are encoded using the same color (e.g., because of same categorical label or semantic type) may visually appear as a single node (marked as (b) in the figure). As illustrated in the middle of Fig. 1, a sunburst tree may feature nodes that are of the same data values but mapped to visual objects of different sizes (marked as (c) in the figure). Meanwhile, a sunburst tree may also exhibit issues (a) and (b).
In this work, the IVAS methodology was adopted systematically in the process for designing a new visual representation, referred to as Radial Icicle Tree (RIT) as shown on the right of Fig. 1 (above). We used the icicle tree design as the starting point for analyzing symptoms, causes, remedies, and side effects about a visual representation. In Fig. 2 (below), we illustrate the design process starting from Design 1 on the top-left to Design 3.3 on the bottom-right.
Design 1: Icicle Tree Plot
Symptom: (a) Hard-to-see thin nodes and (b) visually-merged nodes as illustrated in Fig. 1.
Cause: The width of the display space is limited, causing thin nodes and a lack of gaps between subtrees and nodes.
Remedy: Transform it to polar coordinates (i.e., sunburst) to gain more space as the circumference is longer than the width. It can alleviate (a) as some thin nodes become more noticeable.
Side-effect: It does not address (b) while introducing issue (c) of inconsistent size encoding.
We then considered the design of the sunburst tree as Design 2.1 in Fig. 2. The side-effect in Design 1 became the symptom in Design 2.1.
Design 2.1 ∼ 2.5 Sunburst Tree Plot and its Variants
Symptoms: Aforementioned issues (b) and (c). Issue (a) is not fully addressed.
Cause: The size encoding based on rectangles is now distorted. The gaps between subtrees and nodes have been abstracted away.
Remedy: One remedy may be to add larger gaps proportionally to ensure area constancy, resulting in Design 2.2 in Fig. 2.
Side-effect: A new issue, (d) arises, i.e., the interpretation of these gaps is inconsistent with the conventional interpretation about a portion of the outer edge that is not connected to any child node. Conventionally it would mean that a parent node does pass all of its data value to its child nodes. This interpretation cannot be applied to the “new type” of gaps introduced for area constancy.
Remedy: Instead of reducing the angle of each annular sector, another remedy may be to reduce the height of each annular sector to ensure that the corresponding full annulus has the same area as other full annuli (including the root node that may be depicted as a circle or a full annulus). This is shown as Design 2.3 in Fig. 2.
Side-effect: Issue (b) reappears, while the advantage gained by Design 2.1 for addressing the issue (a) starts dissipating because reducing the height of a small annular sector will also make the sector narrower in terms of its arc length.
Remedy: We can add boundary lines between nodes to address (a) and (b) as shown in Design 2.4 in Fig. 2.
Side-effect: Boundary lines may take up some space that would worsen issue (a) for small and thin nodes. They may change the size perception and such changes will affect small and thin nodes more. We consider this as Issue (e).
Remedy: Boundary lines can also be applied to icicle tree plots as shown in Design 2.5 in Fig. 2.
Side-effect: Similar to Design 2.4, issue (a) may become worse for small and thin nodes, and issue (e) may occur as the size perception is also affected.
Design 3.2 and Design 3.3: Radial Icicle Tree
Symptoms: Design 2.3 addressed issue (c), but not an issue (b). Meanwhile, issue (a) is not fully addressed.
Remedy: Similar to Design 3.1 for an icicle tree, we can also cut away a triangle or fan-like shape at each end of each annular sector. Note that only one of such cuts is illustrated in Design 3.2 in Fig. 2, though the cuts are to be applied to every annular sector, except a full circle or a full annulus. The cuts enable the separation of nodes and subtrees.
Side-effect: Naturally, issue (f) arises since the cuts mean size loss, which would undermine our objective of area constancy.
Remedy: Issue (f) can be addressed by adding a thin top-up annular sector to each annular sector that has lost a portion of its area due to the cuts. As long as we can ensure that the top-up sector is of the same size as the lost area, we can maintain area constancy. This is shown as Design 3.3 in Fig. 2.