Minding the Gap: A Quantitative Comparison of Distance Perception on Open vs. Closed Circles

Radial visualizations encode one dimension of a data set with the visual variable angle or arc length. The radial axis conveys a similarity between the positions of the data points, due to the law of proximity. In the literature, two different types of axes are employed in visualizations: open and closed circular axes. Open axes are linear axes bent to form an open circle. A gap between the right and left poles indicates dissimilarity of data points at both poles. Contrarily, closed axes form a full circle. While the choice of the appropriate axis type in the visualization should align with the similarity space, a question arises: Which axis type supports the human perception of proximity better? To answer this question, we conducted a quantitative task-driven experiment (N=28) to evaluate human distance perception on open and closed circular axes. Within four low-level tasks of three types (identify, compare, and summarize), we evaluate accuracy and response time. Based on our results, we provide an empirically grounded guideline for selecting the appropriate axis type. In our extensive post-hoc analysis, we gain preliminary, but valuable insights to inform further research.