Arc Length-Based Aspect Ratio Selection

Abstract

The aspect ratio of a plot has a dramatic impact on our ability to perceive trends and patterns in the data. Previous approaches for automatically selecting the aspect ratio have been based on adjusting the orientations or angles of the line segments in the plot. In contrast, we recommend a simple, effective method for selecting the aspect ratio: minimize the arc length of the data curve while keeping the area of the plot constant. The approach is parameterization invariant, robust to a wide range of inputs, preserves visual symmetries in the data, and is a compromise between previously proposed techniques. Further, we demonstrate that it can be effectively used to select the aspect ratio of contour plots. We believe arc length should become the default aspect ratio selection method.

Mathematical foundations of arc length-based aspect ratio selection

“…We establish the connection between AL and the principle of banking to 45 • and derive the upper and lower bounds of its produced averaged absolute slopes. Finally, we conduct a comprehensive quantitative comparison between the five methods AL, AWO, RV, MS, MLC, with similar experimental setting of Talbot et al [15]. Our results contribute to the understanding of aspect ratio selection methods in three aspects: first, we show that AWO always performs similarly to AL, while MS is not.…”

“…They also found that the orientation resolution is maximized when the average orientation between them is 45 • . Based on these two observations, Cleveland et al [1,2,3] and the following Heer and Agrawala [6] as well as Talbot et al [15] proposed a few methods for aspect ratio selection with different properties, see Table 1.…”

“…Motivated from the geometric observation, Guha and Cleveland [13] suggested the resultant vector (RV) that uses the ratio of the total variation of line segments in the y and x directions as the aspect ratio. Likewise, Talbot et al [15] proposed an alternative method, arc length based aspect ratio selection (AL), which determines the aspect ratio by minimizing the arc length while keeping the area of the plot constant. As shown in Table 1, this method has demonstrated many empirical advantages over previous methods, such as parameterization invariance, symmetry preservation and robustness.…”

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.…”

Evaluation of alternative glyph designs for time series data in a small multiple setting

“…Even today these line charts are among the most popular time series visualization techniques and their details are actively discussed in the visualization community, as for example the arc length-based aspect ratio selection [31]. Furthermore, visualization techniques such as stacked graphs (e.g.…”