Stevens also distinguished ratio from interval (his term from quantitative).

The findings on the lack of benefit of many animations run counter to the assumptions of many people.

Or in a three-dimensional display, to rotate, translate, and zoom.

The Nonlinear Magnification Homepage maintained by Keahey links to downloadable versions of many of these papers: http://www.cs.indiana.edu/hyplan/tkeahey/research/nlm/nlm.html.


This system is known to many outside the field because of its appearance in the feature film Jurassic Park.


Personal communication, Graham Wills, April 2000.

There are five additional three-dimensional geometries that are homogeneous but nonisotropic, which together with the three isotropic geometries (spherical, Euclidean, and hyperbolic) form Thurston's Eight Model Geometries [Thu97, Section 3.8,] [Wee85, Chapter 18,].

An equivalent statement is that hyperbolic objects have negative Gaussian curvature.

Technically, a hyperboloid embedded in a space one dimension higher than itself is the Minkowski model, and our projection is the standard mapping from the Minkowski to the Klein-Beltrami model.

The word ``hyperbolic'' should not be confused with the word ``hyperspace'', which is sometimes used in popular literature to mean 4-space.

The Shape of Space, by Jeff Weeks, contains an eminently readable exposition of dimensionality and embedding [Wee85].

The typographical error of having r instead of 22#22 in both the Euclidean and hyperbolic equations in [Mun97] is corrected here.


Intersections could theoretically occur, since we do not explicitly check for them, but our layout algorithm is designed to make them highly unlikely. We have never observed non-tree link intersection in practice.

Two studies have found beneficial effects from 3D kinetic depth cues for both trees [SM93] and general graphs [WF96], where larger structures could be understood with kinetic 3D than with flat 2D layouts.

We use the term ``color'' advisedly: although we explicitly distinguish between hue, saturation, and brightness in the Constellation system (Section 5.3), in H3 colors are assigned as RGB triplets. Although sophisticated developers could of course choose to distinguish between hue, saturation, and brightness at the application layer, it would be misleading to imply that H3 supports those three perceptual channels instead of a single channel of color.


The library API also allows the trivial solution of nonsquare windows with a distorted aspect ratio so that the sphere at infinity is drawn as an ellipsoid.

All standard libraries support the additional projection step from 3D Euclidean space to 2D screen space.



If we relaxed that requirement, spanning tree creation would instead require the 84#84 time of Kruskal's algorithm.

The most recent version of the software has a somewhat smaller memory footprint, but the fundamental point remains.







Although this resource was available at the time of the project in 1996, in 1998 Brooks stopped keeping this list because of an upstream provider charging policy change.

In 1996 hardware texturing support in low-end machines was less common than it is in 2000.

Parts of this pipeline were implemented by Eric Hoffman.

We used previously existing spherical geodesic code extracted from the spherescribble interactive software by Millie Niss, available from http://www.geom.umn.edu/software/download/spherescribble.html.


This particular backbone segmentation was suggested by collaborators who were familiar with the multicast community.




``Greeking'' is a term from the publishing world for this type of placeholder.

Interestingly, this assumption is much stronger for visible graphical scenes than for textual descriptions of scenes.

The three accompanying videos are available in online digitized form from

Another difficulty with large-scale web visualization is that more and more of the web is being converted to dynamically programmed content instead of indexable static HTML pages.


On a personal note, in the 1980's I was personally horrified at the idea of wasting expensive supercomputer CPU cycles by running a Unix shell instead of using a job control language for batch processing. I have, of course, expanded my world view since then.

Videos demonstrating the systems in action are available at http://graphics.stanford.edu/~munzner/videos.html.

Tamara Munzner