An Extension of Wilkinson’s Algorithm for Positioning Tick Labels on Axes

Abstract

The non-data components of a visualization, such as axes and legends, can often be just as important as the data itself. They provide contextual information essential to interpreting the data. In this paper, we describe an automated system for choosing positions and labels for axis tick marks. Our system extends Wilkinson’s optimization-based labeling approach to create a more robust, full-featured axis labeler. We define an expanded space of axis labelings by automatically generating additional nice numbers as needed and by permitting the extreme labels to occur inside the data range. These changes provide flexibility in problematic cases, without degrading quality elsewhere. We also propose an additional optimization criterion, legibility, which allows us to simultaneously optimize over label formatting, font size, and orientation. To solve this revised optimization problem, we describe the optimization function and an efficient search algorithm. Finally, we compare our method to previous work using both quantitative and qualitative metrics. This paper is a good example of how ideas from automated graphic design can be applied to information visualization.

Evaluating the efficiency of physical visualizations

“…As color coding is common in 3D bar charts, bars from each country were assigned a separate color using a categorical scale from ColorBrewer2.org. Axis labellings were automatically computed using the algorithm by Talbot et al [35]. In order to facilitate the reading of values and as recommended by Tufte [37, p. 126], tick lines were also displayed on bars.…”

Learning Perceptual Kernels for Visualization Design

“…Following Bertin, researchers in multiple disciplines have conducted human subjects experiments [6,14,21,24,37,38,46] and proposed perceptuallymotivated rankings of visual variables for nominal, ordinal or quantitative data [6,24,25,27,36]. Researchers have also investigated how different choices of design parameters such as aspect ratio [5,13,42], chart size [16,23], axis labeling [43] and animation design [17,29] influence the effectiveness of graphs. This work typically compares the effectiveness of alternative visual variables.…”

Order of Magnitude Markers: An Empirical Study on Large Magnitude Number Detection

“…Talbot et al [22] address that problem by demonstrating an improved solution for generating and labeling axes. Our user study is designed to test more functional aspects of the representations such as whether numbers can be perceived and compared correctly, rather than whether aesthetically pleasing representations perform better or worse.…”