The problem Fitts’ law is a good mathematical model for HCI study, but only fit for one specific movement: pointing. What about other tasks performed in the interaction of human and computers?

The solution extend Fitts’ law to cover the performance evaluation of trajectory-based tasks. The authors give mathematical equations derived from Fitts’ law to characterize the task under four different conditions. The process is in form of four different experiments.

What is Fitts’ law

Fitts’ law is a mathematical model to describe human movement. In particular, for a human pointing task, it is to represent the time needed to perform the task by two variables

MT = a + b * log2((A/W) + c)
  • MT is movement time
  • A is the distance from the starting point to the center of the target
  • W is the width of the target along the axiom of motion
  • a and b are empiracally determined constant and c is 0, 0.5 or 1

In fact, people always treat log2((A/W) + c) part as a whole, and call it index of difficulty (ID); ID represents the difficulty of the task given the design (A and W). Fitts’ law forms the model of speed/accuracy in pointing task.

What is a human pointing task in the Fitts’ law model

The pointing task could be explained by the follwing figure I found from this blog; it also has a great explanation about Fitts’ law and its caveats.

Pointing task

All in all, Fitts’ law tells/matches one intuition:

the wider the target/the closer to the target, the faster the task could be performed

Note though, their relationship is log function, therefore it is not always bigger the better. Increasing the target width from 1cm to 10cm might significantly reduce the MT, increasing it from 1m to 10m might not get the same propotion of reduction in MT.

Aside from this, the famous blog CodingHorror has two blogs (1,2) telling a few very interesting observations from Fitts’ law.

Trajectory-based task: steering

The main task this paper studies is called “steering”: move the object (e.g. mouse, finger) through bounded tunnel. It is illustrated in figure below.

Steering task

The paper uses four experiments to derive a common model for such type of task. The four experiments are:

  1. goal passing: like a steering but only start and end of the tunnel is bounded, which is called 2 “goal”s
  2. constraint-added goal passing: when we add infinite “goal”s to the tunnel
  3. narrowing tunnel: 2 ends have different width
  4. spiral tunnel: curve paths

All experiments are fully-crossed, within-subjects factorial design. Every participant went through all experiments in random order.

With the modeling of results from four experiments, the authors derived a global law for a generic steering task,

MT = a + b * (A/W)

Basically, the authors concluded that, instead of a log relationship like the pointing task has, for steering tasks, the difficulty/time and the design (being A and W) is linear. They also derived a local law, which is similar to the global law. The main take-home message of local law is that instantaneous speed of steering at any point is proportional to the variability permitted.

Linear relationship seems odd, because in real design MT cannot possibly increase unlimited as long we widen the path. Therefore, the authors stated that there existed an upper bound for the path width in steering task. Also, in discussion they talked about the possibility of taking path curvature and path beginning into account.