16
Figure 15. A typical sequence of action with the pan-and-zoom technique: zooming-out to visualize the
target beacon, panning and zooming-in to reach the target proper, finally cursor-pointing to it.
4. FITTS’ LAW IN MULTISCALE POINTING: A
THEORETICAL ANALYSIS
The navigation techniques introduced in the previous section have been mostly evaluated in
terms of their usability for high-level tasks. For example, I lornbæk and prokjær (2001) have
compared the usability of linear, fish-eye and bi-focal displays for reading documents and
Baudisch et al. (2002) have compared focus-plus-context, fisheye and pan-and-zoom
interfaces for tasks such as verifying connections on a circuit board. Gutwin (2002) conducted
an experiment on target-reaching with a fish-eye display using the ISO 9241-9 point-select
task (Soukoreff and Mackenzie, this issue), although they did not systematically control target
distance and target size. Guiard et al. (1999) conducted an experiment with a bi-focal display
with Fitts’ (1954) reciprocal pointing protocol, but the user controlled the cursor at a single
scale. Assessing Fitts’ law in multiscale electronic worlds is still an open research question.
This section presents the theoretical analysis that structured our experimental work on Fitts’
law in multiscale pointing. As described above, multiscale pointing consists of three phases
and therefore movement time (MT) corresponds to the sum of the durations of these phases.
Phase 2, zooming-in-and-panning, is not only the phase whose completion takes most time, it
is also the most complex of the three. While phase 1 involves just scale and phase 3 just
space, phase 2 demands an intricate coordination of action in both space and scale. This is
why we focus on phase 2 below.
4.1. Multiscale View Pointing
Consider a view-pointing task defined by a view size V, a distance D to the target and a target
size W (D and W are specified in document space, e.g. at scale 1; recall that V is scale
independent). We are interested in the case where target distance is very large compared with
target size—that is, in tasks with a high index of difficulty ID = log2 (D/W + 1).
To start with (Phase 1), one must zoom-out until the target (in fact, the beacon that represents
it) enters the view. Let us call sin the scale at which this happens (Figure 16). Once the target
is within the view, the user can start panning and zooming-in (Phase 2) towards the target.
Navigation ends when the target is big enough within the view so as to be pointed at. Since
we are interested in view pointing rather than the final act of cursor pointing, let us consider
the limiting case where navigation ends when the target completely fills the view, calling sout
the scale at which this happens (Figure 16). On the scale dimension, the user has navigated
from sin to sout (again, we ignore the zoom-out phase to concentrate on zoom-in-and-pan). In