In this video, I am going to talk about our work of 2-dimensional touch pointing models.
This work is the collaboration between our lab and Shumin Zhai from Google.
The most widely known touch pointing model is Fitts’ Law.
Here are the most widely known 2D version of Fitts law.
Euclidean model proposed by Accot and Zhai in 2003
and the Smaller-of model proposed by Mackenzie and Buxton in 1992.
They work well in mouse and pen-based pointing but face some problems in touch-based pointing.
For example, both models predicted that if the target width, height, and distance
are proportionally reduced, the pointing time should remain the same.
But for touch pointing, this assumption is violated.
Let’s take typing on the soft keyboard on the smartphone,
and smartwatch as an example.
Typing on the smartphone is much faster than typing on the smartwatch.
However, this is against what Fitts’ law suggests.
Fitts’ law suggests that the typing speed should remain the same
from phone to watch,
because the size of a key and distance between keys are proportionally reduced.
We refer to this phenomenon as the violation of scale independence.
This cannot be explained by the existing 2D Fitts’ law.
Finger-Fitts Law was proposed to account for ambiguity for finger touch for 1D touch pointing.
The basic idea is that it introduces the component presented by sigma a
that caused the ambiguity by finger touch.
And this part of the ambiguity is independent from the task.
So it should be removed from the Fitts law formula
that explains the speed-accuracy trade-off of the motor system.
The Finger Fitts law has been shown better performance in touch pointing,
compared with traditional Fitts Law.
In this paper, we derive the 2D Finger Fitts Law by introducing the idea of
accounting the finger ambiguity to the two most widely used 2D Fitts law,
Euclidean Form and Smaller-of model.
The basic idea of our refinement is that we subtract the component from the target width
that represents the ambiguity of finger touch.
For these two models, we also subtracted the ambiguity from the target width and height.
This leads to 3 possible model candidates of 2D Finger Fitts law.
The first model is that the c square is subtracted from
both W and H square as the same ambiguity.
The second one is that we subtract different ambiguity from W and H,
and for the smaller-of model, we subtract the c square from the minimum of the width and the height.
To evaluate the model candidate, we conduct a rectangular target acquisition experiment
with different combinations of distance, x-, and y-length,
which refers to the nominal width and height of the target.
We recruited 18 participants in total.
63 combinations and 16 pointing directions were considered.
We evaluate 5 model candidates in Euclidean and Smaller Of Form with the observations.
2 Fitt’s Law models and 3 Finger Fitts law.
Our results show that in smaller-of formulations, Smaller-Of Finger-Fitts law has better performance
than the Smaller-Of Fitts law model in three metrics we measured.
R square value, leave one out root mean square, and widely adopted information criteria WAIC.
Our results also show that Euclidean Finger Fitts law outperforms Euclidean Fitts law.
These two Finger Fitts law models perform better in R square value,
leave one out cross-validation, and also in WAIC.
The Euclidean Finger-Fitts law which considers W and H
has the same ambiguity, perform almost identical to the one that
considers ambiguity separately in W and H direction.
We conclude that since the Euclidean Finger Fitts Simplified model
has one less parameter, this is the best model we have.
The 2D finger Fitts law also explains the violation of scale independence.
These two model shows that if we proportionally reduce
the width and the distance in the task,
it will increase the value of the index of the difficulty.
This is because of the c square value is not canceled out
if you reduce A and W proportionally.
In this research, we derive the 2 models for modeling 2D touch pointing.
We called them 2D Finger Fitts Law.
Our research expands the paradigm of Finger Fitts law from 1D to 2D.
They have better model fitting performance than Fitts’ law
and explain the violation of scale independence in touch pointing.