Fundamentals of Computer Graphics, 3rd Edition

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2 7

2 7

Tamara Munzner

Visualization

A major application area of computer graphics is visualization, where computer-

generated images are used to help people understand both spatial and non-spatial

data. Visualization is used when the goal is to augment human capabilities in

situations where the problem is not sufficiently well defined for a computer to

handle algorithmically. If a totally automatic solution can completely replace hu-

man judgement, then visualization is not typically required. Visualization can be

used to generate new hypotheses when exploring a completely unfamiliar dataset,

to confirm existing hypotheses in a partially understood dataset, or to present in-

formation about a known dataset to another audience.

Visualization allows people to offload cognition to the perceptual system, us-

ing carefully designed images as a form of external memory. The human visual

system is a very high-bandwidth channel to the brain, with a significant amount

of processing occurring in parallel and at the pre-conscious level. We can thus

use external images as a substitute for keeping track of things inside our own

heads. For an example, let us consider the task of understanding the relationships

between a subset of the topics in the splendid book G

¨

odel, Escher, Bach: The

Eternal Golden Braid (Hofstadter, 1979); see Figure 27.1.

When we see the dataset as a text list, at the low level we must read words

and compare them to memories of previously read words. It is hard to keep track

of just these dozen topics using cognition and memory alone, let alone the hun-

dreds of topics in the full book. The higher-level problem of identifying neigh-

borhoods, for instance finding all the topics two hops away from the target topic

Paradoxes,isverydifficult.

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676 27. Visualization

Infinity - Lewis Carroll

Infinity - Zeno

Infinity - Paradoxes

Infinity - Halting problem

Zeno - Lewis Carroll

Paradoxes - Lewis Carroll

Paradoxes - Epimenides

Paradoxes - Self-ref

Epimenides - Self-ref

Epimenides - Tarski

Tarski - Epimenides

Halting problem - Decision procedures

Halting problem - Turing

Lewis Carroll - Wordplay

Tarski - Truth vs. provability

Tarski - Undecidability

Figure 27.1. Keeping track of relationships between topics is difficult using a text list.

Figure 27.2 shows an external visual representation of the same dataset as a

node-link graph, where each topic is a node and the linkage between two topics

is shown directly with a line. Following the lines by moving our eyes around the

image is a fast low-level operation with minimal cognitive load, so higher-level

neighborhood finding becomes possible. The placement of the nodes and the

routing of the links between them was created automatically by the dot graph

drawing program (Gansner et al., 1993).

We call the mapping of dataset attributes to a visual representation a visual

encoding. One of the central problems in visualization is choosing appropriate

encodings from the enormous space of possibile visual representations, taking

into account the characteristics of the human perceptual system, the dataset in

question, and the task at hand.

Infinity

Halting problemZeno Paradoxes

Lewis Carroll TuringDecision procedures

Self-ref

Epimenides

Wordplay Tarski

Truth vs. provability Undecidability

Figure 27.2. Substituting perception for cognition and memory allows us to understand

relationships between book topics quickly.