Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings

TL;DR

This paper investigates how users choose viewpoints in 3D graph drawings using a VR study with 23 participants across 36 graphs. It evaluates a broad set of 21 aesthetic measures, including a new 3D metric called Isometric Viewpoint Deviation, and analyzes how these measures align with user preferences and combinations thereof. The findings show that both traditional 2D metrics like Stress and Crossings and 3D specifics such as Edge-Node Overlap and the ISO score predict user preferences, with combined measures offering stronger explanatory power. An open-access dataset of graphs and computed aesthetics is released to enable further research on viewpoint evaluation and optimization in immersive graph analysis.

Abstract

The visual analysis of graphs in 3D has become increasingly popular, accelerated by the rise of immersive technology, such as augmented and virtual reality. Unlike 2D drawings, 3D graph layouts are highly viewpoint-dependent, making perspective selection critical for revealing structural and relational patterns. Despite its importance, there is limited empirical evidence guiding what constitutes an effective or preferred viewpoint from the user's perspective. In this paper, we present a systematic investigation into user-preferred viewpoints in 3D graph visualisations. We conducted a controlled study with 23 participants in a virtual reality environment, where users selected their most and least preferred viewpoints for 36 different graphs varying in size and layout. From this data, enriched by qualitative feedback, we distil common strategies underlying viewpoint choice. We further analyse the alignment of user preferences with classical 2D aesthetic criteria (e.g., Crossings), 3D-specific measures (e.g., Node-Node Occlusion), and introduce a novel measure capturing the perceivability of a graph's principal axes (Isometric Viewpoint Deviation). Our data-driven analysis indicates that Stress, Crossings, Gabriel Ratio, Edge-Node Overlap, and Isometric Viewpoint Deviation are key indicators of viewpoint preference. Beyond our findings, we contribute a publicly available dataset consisting of the graphs and computed aesthetic measures, supporting further research and the development of viewpoint evaluation measures for 3D graph drawing.

Figures (40)

• Figure 1: The VR study application, perceived and controlled using the Apple Vision Pro. The 3D graph drawing (A) can be rotated by a gaze and pinch interaction, or sliders (B). Users can store up to three preferred or disregarded perspectives (C).
• Figure 2: Example of eight graphs (of 36, reflecting the different types) showing the distribution of selected perspectives (sphere surface) along with three perspective projections (either best (green) or worst (red)), discussed in \ref{['sec:results-chosen-perspectives']}. The complete set of perspectives is shown in \ref{['sec:appendix-chosen-perspectives-spheres-all']}.
• Figure 3: The first two components of a PCA of the best (green) and worst (red) user-chosen perspectives (left), in total $2 \times 36 \times 23 = 1.656$ samples with 21 measures each. The projection on the first component (left, below) already shows a good separation of the data points. A correlation analysis indicates that some aesthetic measures are highly correlated (especially the overlap measures NN*, EN*, and NE*), while others are not (right).
• Figure 4: The distributions of values (best: green, worst: red) for 21 aesthetic measures (top seven rows) and combinations of these (LR and SQP) with 21, 5, or 3 measures each (last two rows).
• Figure A1: The distribution of all perspectives selected by users as best (green) and worst (red) mapped on a sphere surface for graph S-0 (sem_0_20_16) with $|V| = 20, \; |E| = 16$.