18
Since V is fixed for a given navigation, this shows that multiscale view pointing follows Fitts'
law. As the motor control involved in multiscale navigation is quite different from that of a
traditional pointing task, this is a nontrivial finding. Fitts' law is known to hold for movements
in which speed goes up, then down, without a plateau. However in our case, zooming-in
requires continuous control where panning movements correct the error revealed by the
increased scale. When starting the task, the user does not know the size of the target, just its
approximate position, as marked by the scale-invariant beacon that represents the target at
small scales. The user ‘cruises’ through the tunnel at a fairly constant speed determined by
her/his ability to process information, until the real target replaces the beacon and fills the
view.
The above derivation offers a theoretical basis for predicting that multiscale pointing follows
Fitts’ law—in fact a simplified version of the law with a zero intercept. In addition it delivers
a new prediction, namely that navigation time must be inversely proportional to view size.
Inverse proportionality is a highly non-linear relationship. Equation 4 says that gradually
decreasing view size should lengthen MT in an accelerated way, thus suggesting that V is a
critical factor that must be taken into account in modeling multiscale navigation. Equation 4
has a problem, however: it implies that as V rises toward infinity, MT should tend to 0,
obviously an implausible prediction. In the next section we handle this difficulty by enriching
the model with a supplementary assumption.
4.3. Limited Human Capacity for Handling Information Flows
Equation 4 can be recast as
ID/MT (bits/s) = k V, (5)
simply noting 1/k as k , since the inverse of a constant is a constant. This equation states that
the bandwidth of navigation in a zoomable interface is proportional to view size. This
proportionality makes sense for small views. However, as view size is scaled up, we must
obviously assume some ceiling constraint to reflect the limited capacity of humans for
exploiting the information outflow from a computer—for example, in 2D space one cannot
reasonably predict that the navigation bandwidth will be doubled if the view is increased from
1m2 to 2m2.
This human-factor limitation can be construed of in terms of a simple fluid-dynamics model
where some fluid must flow through two pipes mounted in series, with the first pipe modeling
the view offered by computer (Vc) and the second pipe the maximal view a human can exploit
(Vh), assumed here to be constant. In this model the flow of liquid that successfully traverses
the system is proportional to the cross section of the smaller pipe. That is,
for Vc <Vh, ID/MT (bit/s) = k V (6)
for Vc ≥Vh, ID/MT (bit/s) = constant (7)
5. EXPERIMENTAL RESULTS
We conducted two experimental studies on target acquisition in a pan-and-zoom interface to
test the predictions of the above model. Experiment 1 (Guiard et al., 2001) tested the
prediction that multiscale pointing should obey Fitts’ law with a zero intercept (Equation 4).
Experiment 2 (Guiard et al., 2004) tested the predictions that for small view sizes, pointing
time should be inversely proportional to view size (Equation 6) and that for larger view sizes,