Chapter 9

Visualizing Time and Space

Synopsis

The recent history of data visualization is much harder to characterize because innovations have been so varied, and have occurred at an accelerated pace and have appeared across a wider range of disciplines. Among the many threads that could be traced, two general categories stand out; these have made data graphics far more powerful and accessible than ever before. First, graphical methods have become increasingly dynamic and interactive, capable of showing changes over time by animation and changing the nature of a graph from a static image to one that a viewer can directly manipulate, zoom or query. Second, the escape from flatland has been continued, with a variety of new approaches to understanding data in ever higher dimensions.

Chapter contents

• The Laws of Motion
• The Horse in Motion
  • A Trick of the Eye
• Étienne-Jules Marey and a Science of Visualizing Time and Motion
  • La Méthode Graphique
  • Chronophotography
  • Falling cats
• Computer Graphics Animation
• Animated Algorithms
  • The MDS movie
  • Color similarity
  • The Monte Carlo Method
  • RANDU
• Travels in High-D Space
  • Diabetes classification
• Hardware and Software
  • Software
• Telling Stories with Animated Graphics

Selected Figures

Figure 9.1: The Horse in Motion Photographs of the horse “Sally Gardner”running at a gallop, June 19, 1878. Source: Library of Congress, Prints and Photographs Division, LC-DIG-ppmsca-06607.

Figure 9.2: Seeing motion Zoopraxiscope disk showing thirteen images of a kicking horse. The frames at the bottom show the sequence of extension of the hind legs together with the support of the fore legs. Source: Wikimedia Commons.

Figure 9.3: Recording flight A harness, designed to register the trajectory, force and speed of a bird’s wing in flight. Source: Étienne-Jules Marey, La machine animale, locomotion terestre et aérienne. Paris: Librairie Germer Baillière, 1873, fig. 104.

Figure 9.4: Photographic gun One of Marey’s photographic guns. The cylinder at the top holds the film roll, recording twenty-four images over a two-second period. Source: Wikimedia Commons.

Figure 9.5: Starting a sprint Chronophotograph of a runner beginning a sprint. Source: Étienne-Jules Marey, Flight/WordPress.com.

Figure 9.6: Falling cat Successive images of a falling cat, captured at twelve frames per second on a chronophotographic device. The sequence starts at the upper left, and is continued at the left of the lower panel. Source: “Photographs of a Tumbling Cat,” Nature, 51:1308 (1894), pp. 80–81, fig. 1.

Figure 9.7: Visual proof Computer-drawn images of rotation according to the mathematical model, overlaid on photographs of a falling cat. Source: T. R. Kane and M. P. Sher, “A Dynamical Explanation of the Falling Cat Phenomenon,” International Journal Solids Struc- tures, 5 (1969), pp. 663–670, fig. 6. Reprinted with permission from Elsevier.

Figure 9.8: Parametric apple Computer-generated image of an apple using parametric equations for the 3D solid surface. Rendering of the surface uses methods to simulate illumination from a light source in front of the viewer. Source: © The Authors.

Figure 9.9: 3D graphics model of a cat Left: the form of the cat is defined by a wire frame consisting of points and connecting lines; right: the model of the cat has had fur applied and is then animated, twisting as it falls. Source: nonecg.com.

Figure 9.10: Early examples of CRT displays CRT displays from 1950 to 1965. Source: (top) National Institute of Standards and Technology/Wikimedia Commons; (bottom) Todd Dailey / Wikimedia Commons / CC BY-SA 2.0.

Figure 9.11: Dimensions of color similarity Ekman’s five-factor solution for the similarities among colors. Source: Gosta Ekman, “Dimensions of color vision,” Journal of Psychology, 38:2 (1954), pp. 467–474, fig. 3. Reprinted with permission of Taylor & Francis Ltd.

Figure 9.12: The first statistical movie Four frames from the multidimensional scaling movie, the first animation of a statistical algorithm. Left: initial configuration for fourteen colors; right: final configuration, making the order of interpoint distances most closely agree with the order of the similarity judgments. Source: J. B. Kruskal, Multidimensional Scaling, AT&T Bell Laboratories, 1962.

Figure 9.13: RANDU Plot of successive pairs of 800 random numbers generated by the RANDU algorithm. Nothing unusual stands out: the points appear to be randomly and uniformly distributed in the unit square. Source: © The Authors. Rcode: 09_13-randu1.R

Figure 9.14: RANDU in 3D Three-dimensional plots of successive triples of 400 sets of random numbers generated by RANDU. The left panel shows the positions of the points in a standard unit cube, with axes x[i], x[i+1], x[i+2]. The right figure shows the same plot rotated slightly. The points now appear on 15 parallel planes in 3-space, indicating their systematic (non-random) pattern. Source: © The Authors. Rcode: 09_14-randu2.R

Figure 9.15: Diabetes data Reproduction of a graph similar to that from Reaven and Miller (1968) on the relationship between glucose and insulin response to being given an oral dose of glucose. Source: © The Authors. Rcode: 09_15-diabetes.R

Figure 9.16: PRIM9 view Artist’s rendition of the data from Reaven and Miller (1979) as seen in three dimensions using the PRIM-9 system. Labels have been added by the author, identifying the three groups of patients. Source: G. M. Reaven and R. G. Miller, “An attempt to define the nature of chemical diabetes using a multidimensional analysis,” Diabetologia, 16 (1979), pp. 17–24, fig. 1. Reprinted by permission from Springer Nature.

Figure 9.17: DataDesk A multiwindow graphics system for the Apple Macintosh, providing dynamic graphics, linked plots and brushing. The plot windows show a scatterplot, a 3D plot that can be rotated around any axis, a histogram, a boxplot and a parallel-coordinates plot. A collection of plot control buttons is shown at the right. Source: DataDesk / YouTube.

Figure 9.18: Moving bubble chart Three frames of an animated sequence, plotting life expectancy against income per person for 142 nations from 1809 to 2015. Income is plotted on a log scale. The bubble area is proportional to total population and is colored by geographic region in the original. China has been selected to track its position over time. Source: Gapminder.

Plate P.16: MDS solution Re-creation of the MDS solution for Ekman’s color similarities data. This figure represents the final configuration of the points shown in the right-most panel of the MDS movie, Figure 9.12. The dashed circle is at the average distance of the points from the origin. Source: © The Authors.