- 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
- 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
- This system is known to
many outside the field because of its appearance in the feature film
- Personal communication, Graham Wills,
- 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
- 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
- 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
- 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.
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
- 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
- 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.
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
- 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
- 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.
demonstrating the systems in action are available at