Goal: display interconnections among thousands of points, with little to no hierarchical structure inherent the data
Approach 1 : randomly distribute points on the surface of a sphere, interconnecting them through the interior. Using as the domain the set of interconnections among Internet Autonomous System identifiers, we have a fairly messy result:

Even a subset is hard to decipher:
>An advantage to the 3D sphere projection method is a reduction in crossing lines, especially with VRML or MPEG animation tools to support display.
Projecting even a few interconnections is a challenge. Depicting paths from several BGP peers to a single destination network (in this case Sun Microsystems), as seen by a routing observation point in Oregon:

While relatively simple, it quickly becomes difficult to scale up in terms of visualization, and we have found it easier to use 3D graphics for similar data:

Once the 3D model of this data is available, one can use interactive tools to manipulate it (1.8MB VRML model). One can also create MPEG animations, viewable with the MTV player from www.mpeg.org or the UCB mpeg_play utility. This example is only one of many that suggests that 3D visualization is not always the optimal choice. It is typically a complexity tradeoff between scene and data complexity and data complexity, and influenced by the degree of need to manipulate scenes and objects. Time series, perhaps as animations, can be useful for both 2D and 3D visualizations.
updated 26 dec 1997
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