The problem of analytical assessment of visualization is separated into a problem of information mapping and a problem of cognitive and perceptual support. These problems are analyzed and discussed in this article. It is argued that presentational modalities (i.e., semantic invariants) must be identified to be able to construct a taxonomy of graphical displays and their potential to visualize certain types of information. The problem of assessing displays analytically is illustrated by two new displays developed for a water treatment plant. In these displays, one graphical type is embedded into another. Common graphical modalities are identified from displays used in the process industry in general. © 1999 John Wiley & Sons, Inc.