An Empirical Model of Slope Ratio Comparisons

Talbot, Justin; Gerth, John; Hanrahan, Pat

doi:10.1109/tvcg.2012.196

Cited by 45 publications

(36 citation statements)

References 12 publications

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“…Table 1: Comparison between various aspect ratio selection methods, where AO and AWO, AS and RV, LOR and MLC are three paired parameterization variant and invariant forms, "?" represents that we differ in our observation to Talbot et al [16]. 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.…”

Section: Introductioncontrasting

confidence: 54%

“…MS selects smaller aspect ratios for most of data, while it produces overly taller aspect ratios in some cases (In(x) and 9-13). In contrast, MLC produces slightly larger aspect ratios for most of data, whereas it selects smaller ones for the gamma (2,16) and 9-13. es. This indicates that MS is not always similar to AL, even though Figure 8(b) and (c) have a similar distribution of the sorted slopes.…”

Section: Al Vs Msmentioning

confidence: 91%

“…We explore its mathematical foundation, and conduct an experiment to compare AL with another methods. Talbot et al [16] expand the experimental design of Cleveland et al [4] and show that banking to 45 • is not necessarily the best choice. Inspired by this result, Fink et al [5] recently proposed to select the aspect ratio for 2D scatter plots based on Delaunay triangulation.…”

Section: Related Workmentioning

confidence: 99%

“…However, it is not obvious whether the aspect ratio produced by Equation 16 really converges to 1. Now we show that AL has a tendency to satisfy banking to 45 • by computing the bounds of the average absolute slopes generated by AL.…”

Section: The Bounds Of Al's Average Absolute Slopementioning

confidence: 99%

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Mathematical foundations of arc length-based aspect ratio selection

Han

Wang

Zhang³

et al. 2016

2016 IEEE Pacific Visualization Symposium (PacificVis)

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The aspect ratio of a plot can strongly influence the perception of trends in the data. Arc length based aspect ratio selection (AL) has demonstrated many empirical advantages over previous methods. However, it is still not clear why and when this method works. In this paper, we attempt to unravel its mystery by exploring its mathematical foundation. First, we explain the rationale why this method is parameterization invariant and follow the same rationale to extend previous methods which are not parameterization invariant. As such, we propose maximizing weighted local curvature (MLC), a parameterization invariant form of local orientation resolution (LOR) and reveal the theoretical connection between average slope (AS) and resultant vector (RV). Furthermore, we establish a mathematical connection between AL and banking to 45 degrees and derive the upper and lower bounds of its average absolute slopes. Finally, we conduct a quantitative comparison that revises the understanding of aspect ratio selection methods in three aspects: (1) showing that AL, AWO and RV always perform very similarly while MS is not; (2) demonstrating the advantages in the robustness of RV over AL; (3) providing a counterexample where all previous methods produce poor results while MLC works well.

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Section: Introductioncontrasting

confidence: 54%

Section: Al Vs Msmentioning

confidence: 91%

Section: Related Workmentioning

confidence: 99%

Section: The Bounds Of Al's Average Absolute Slopementioning

confidence: 99%

See 2 more Smart Citations

Mathematical foundations of arc length-based aspect ratio selection

Han

Wang

Zhang³

et al. 2016

2016 IEEE Pacific Visualization Symposium (PacificVis)

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“…This paper is part of a broader effort to quantify how visual encoding (how data is represented in visual features) can improve or detract from user performance [2,5,18,24,25,33,44,46,51]. Previous studies have looked at topics as diverse as adjusting chart height to improve slope comparison [43] and adjusting aspect ratios of treemap components to facilitate area comparison [30]. By understanding the effect of specific visual encodings on user performance, researchers can help programmers improve default design options in visualization software.…”

Section: Introductionmentioning

confidence: 99%

The relation between visualization size, grouping, and user performance

Gramazio¹,

Schloss

Laidlaw³

2014

IEEE Trans. Visual. Comput. Graphics

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In this paper we make the following contributions: (1) we describe how the grouping, quantity, and size of visual marks affects search time based on the results from two experiments; (2) we report how search performance relates to self-reported difficulty in finding the target for different display types; and (3) we present design guidelines based on our findings to facilitate the design of effective visualizations. Both Experiment 1 and 2 asked participants to search for a unique target in colored visualizations to test how the grouping, quantity, and size of marks affects user performance. In Experiment 1, the target square was embedded in a grid of squares and in Experiment 2 the target was a point in a scatterplot. Search performance was faster when colors were spatially grouped than when they were randomly arranged. The quantity of marks had little effect on search time for grouped displays ("pop-out"), but increasing the quantity of marks slowed reaction time for random displays. Regardless of color layout (grouped vs. random), response times were slowest for the smallest mark size and decreased as mark size increased to a point, after which response times plateaued. In addition to these two experiments we also include potential application areas, as well as results from a small case study where we report preliminary findings that size may affect how users infer how visualizations should be used. We conclude with a list of design guidelines that focus on how to best create visualizations based on grouping, quantity, and size of visual marks.

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Crafting Visualizations of Time-Oriented Data

Aigner,

Miksch,

Schumann

et al. 2023

Human–Computer Interaction Series

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Many different types of data are related to time. Meteorological data, financial data, census data, medical data, simulation data, news articles, photo collections, or project plans, to name only a few examples, all contain temporal information. In theory, because all these data are time-oriented, they should be representable with one and the same visualization approach. In practice, however, the data exhibit specific characteristics and hence each of the above examples requires a dedicated visualization.

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An Empirical Model of Slope Ratio Comparisons

Cited by 45 publications

References 12 publications

Mathematical foundations of arc length-based aspect ratio selection

Mathematical foundations of arc length-based aspect ratio selection

The relation between visualization size, grouping, and user performance

Crafting Visualizations of Time-Oriented Data

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