Clarity and Computational Efficiency of Orbital Boundary Labeling

TL;DR

This work contributes algorithms to compute two leader styles, orbital-radial and straight-line, for uniform and non-uniform label sizes, optimizing for crossing-free shortest leaders, and reveals that both leader types exhibit similar accuracy, but straight-line leaders yield faster response times.

Abstract

Circular interfaces such as those found on smartwatches, automotive dashboards, cockpit instruments, or in radial visualizations pose unique challenges for placing readable labels. Traditional rectangular labeling methods waste screen space and create visual clutter on these constrained displays. In orbital boundary labeling, the labels (e.g., the features' names) are placed in an annulus-shaped orbit outside of the figure, and each label is connected to its feature using a short, crossing-free leader line. We contribute algorithms to compute two leader styles, orbital-radial and straight-line, for uniform and non-uniform label sizes, optimizing for crossing-free shortest leaders. We evaluate the model and the algorithms with computational experiments and a controlled user experiment. The user experiment reveals that both leader types exhibit similar accuracy, but straight-line leaders yield faster response times.

Figures (16)

• Figure 1: (a)-(c) illustrates challenges on circular displays for labeling a map (background map obtained from maputnik.github.io with © 2015 Lukas Martinelli © 2024 MapLibre contributors under MIT license) while (d) shows a sketch of orbital boundary labeling for thematic maps (background map obtained from commons.wikimedia.org with © 2010 Uwe Dedering under CC BY-SA 3.0 license).
• Figure 2: Illustration of the notation used in this paper. Note that both OR-leaders (red) and SL-leaders (blue) are illustrated, while any labeling we consider will exclusively contain one or the other.
• Figure 3: Relative total leader length $\ell_r$ of OR- and SL-leaders plotted against the number $n$ of features. Black bars indicate the mean.
• Figure 4: Stimuli of three instances with SL-leaders and uniform label length. (a) shows an uniform distribution ($D_u$) of 10 features where a target label ($T_L$) is given in red. (b) shows a uniform and off-center distribution ($D_{u+o}$) of 15 features where a target feature (task $T_\mathcal{F}$) given in red. Lastly, (c) shows an off-center distribution ($D_u$) of 20 features where a target label (task $T_L$) is given in red.
• Figure 5: Participants' response time for each stimulus partition and both leader types with uniform (U) and non-uniform (N) label length. Inside the violin plots a dot plot indicates the mean and 95% confidence interval. All instances are partitioned into their characteristics such as number of labels ($D_{10}$, $D_{15}$, $D_{20}$), feature distribution (uniform $D_{u}$, uniform and non-uniform $D_{u+o}$, non-uniform $D_{o}$), and wether label ($D_{L}$) or feature ($D_{F}$) was the target.