David Ebert, James Kukla, and Christopher Shaw
CSEE Department
University of Maryland Baltimore County
Baltimore, MD 21250 USA
{ebert, jkukla1}@cs.umbc.edu, cdshaw@acm.org
Introduction
The goal of our work is the comprehensible display of multi-dimensional information. We have developed a system, the Stereoscopic Field Analyzer (SFA), that allows the incorporation of perceptual cues to increase the clarity and quantity of information conveyed from the visualization system [4]. The SFA system combined glyph-based visualization [5], two-handed interaction, and stereo viewing to increase the perceptualization of the data. Glyph, or iconic, visualization allows multiple information attributes to be included in the parameters of the glyph: shape, color, transparency, orientation. SFA combined glyph-based volume rendering with the two-handed minimally-immersive interaction metaphor to provide interactive visualization, manipulation, and exploration of multivariate, volumetric information spaces. SFA uses a glyph' s location, 3D sizes, color and opacity to encode up to 8 attributes of scalar data per glyph. To aid in the design of useful information visualizations, we have developed a new technique for the procedural generation of glyph shapes based on mathematical functions. The system uses superquadric functions for the generation of glyph shapes, providing intuitive, smoothly varying shapes.
Perceptually-motivated Shapes for Visualization
Shape variation has a high priority in human perception. Cleveland [3] sites experimental evidence that shows the most accurate method to visually decoded quantitative variable in 2D is to display position along the scale. This is followed in decreasing order of accuracy by interval length, slope angle, area, volume, and color. Bertin offers a similar hierarchy in his treatise on thematic cartography [2]. SFA employs glyph position in 3D, 3D scale (corresponding to Cleveland's length, area and volume) and color.
The design of glyph shape is a difficult problems because glyph shape variation must be able to convey changes in associated data values in a comprehensible manner [5]. This paper describes our new system for the procedural generation of glyph shapes for glyph-based in volumetric visualization using superquadrics [1]. Our goal for glyph design was to allow the automatic mapping of data to shape in a comprehensible, easily controllable manner. Superquadrics are a natural choice to satisfy this goal. Superquadrics [1], are extensions of quadric surfaces where the trigonometric terms are each raised to exponents. For our initial implementation, we have chosen superellipses due to their familiarity, but the system can be easily extended to use other types of superquadrics as well as combinations of types. For example, supertoroids could be used for negative values and superellipsoids for positive values. The superellipsoid exponents allow continuous control over the characteristics (in some sense the "roundness" or "pointiness") of the shape in the two major planes which intersect to form the shape, allowing a very simple, intuitive, abstract schema of shape specification. Varying the exponents achieves smooth, understandable transitions in shape. Therefore, mapping data values to the exponents proves not only a continuous, automatic control over the shape's overall flavor, but a comprehensible shape mapping as well.
Results
We have applied this shape mapping mechanism of the visualization of document similarities in a corpus. Figure 1 shows the visualization of the similarity of the 1833 documents from the Wall Street Journal to five themes: Gold prices (x axis), foreign exchange rates of the U.S. dollar (y axis), the Federal Reserve Bank (z access), stock prices (conversely mapped to the superellipsoid exponents), and Manuel Noriega (conversely mapped to color). The star shaped glyphs (least volume) have the lowest similarity, with similarity increasing through spherical shapes to cuboidal shapes.
Conclusions
We have developed a new technique for the intuitive, perceptually meaningful creation of glyph shapes. This is been combined with results of the SFA system to provide a powerful, minimally-immersive, perceptually-motivated information visualization system.
References
[1] A. Barr. Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 1(1):11-23, 1981.
[2] J. Bertin. Semiology of Graphics. University of Wisconsin Press, 1983.
[3] William S. Cleveland. The Elements of Graphics Data. Wadsworth Advanced Books and Software, Monterey, CA., 1985.
[4] David Ebert, Chris Shaw, Amen Zwa, and Cindy Starr. Two-handed interactive stereoscopic visualization. Proceedings IEEE Visualization '96, October, 1996.
[5] Frank Post, Theo van Walsum, Frits Post, and Deborah Silver. Iconic techniques for feature visualization. In Proceedings Visualization '96, October, 1995.