Bar charts are one of the most common visualization types. In a classic graphical perception paper, Cleveland & McGill studied how different bar chart designs impact the accuracy with which viewers can complete simple perceptual tasks. They found that people perform substantially worse on stacked bar charts than on aligned bar charts, and that comparisons between adjacent bars are more accurate than between widely separated bars. However, the study did not explore why these differences occur. In this paper, we describe a series of follow-up experiments to further explore and explain their results. While our results generally confirm Cleveland & McGill's ranking of various bar chart configurations, we provide additional insight into the bar chart reading task and the sources of participants' errors. We use our results to propose new hypotheses on the perception of bar charts.
We present Energy Redistribution (ER) sampling as an unbiased method to solve correlated integral problems. ER sampling is a hybrid algorithm that uses Metropolis sampling-like mutation strategies in a standard Monte Carlo integration setting, rather than resorting to an intermediate probability distribution step. In the context of global illumination, we present Energy Redistribution Path Tracing (ERPT). Beginning with an inital set of light samples taken from a path tracer, ERPT uses path mutations to redistribute the energy of the samples over the image plane to reduce variance. The result is a global illumination algorithm that is conceptually simpler than Metropolis Light Transport (MLT) while retaining its most powerful feature, path mutation. We compare images generated with the new technique to standard path tracing and MLT.
Comparing slopes is a fundamental graph reading task and the aspect ratio chosen for a plot influences how easy these comparisons are to make. According to Banking to 45°, a classic design guideline first proposed and studied by Cleveland et al., aspect ratios that center slopes around 45° minimize errors in visual judgments of slope ratios. This paper revisits this earlier work. Through exploratory pilot studies that expand Cleveland et al.'s experimental design, we develop an empirical model of slope ratio estimation that fits more extreme slope ratio judgments and two common slope ratio estimation strategies. We then run two experiments to validate our model. In the first, we show that our model fits more generally than the one proposed by Cleveland et al. and we find that, in general, slope ratio errors are not minimized around 45°. In the second experiment, we explore a novel hypothesis raised by our model: that visible baselines can substantially mitigate errors made in slope judgments. We conclude with an application of our model to aspect ratio selection.
We present Energy Redistribution (ER) sampling as an unbiased method to solve correlated integral problems. ER sampling is a hybrid algorithm that uses Metropolis sampling-like mutation strategies in a standard Monte Carlo integration setting, rather than resorting to an intermediate probability distribution step. In the context of global illumination, we present Energy Redistribution Path Tracing (ERPT). Beginning with an inital set of light samples taken from a path tracer, ERPT uses path mutations to redistribute the energy of the samples over the image plane to reduce variance. The result is a global illumination algorithm that is conceptually simpler than Metropolis Light Transport (MLT) while retaining its most powerful feature, path mutation. We compare images generated with the new technique to standard path tracing and MLT.
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