Modeling Two Dimensional Touch Pointing

Abstract

Modeling touch pointing is essential to touchscreen interface development and research, as pointing is one of the most basic and common touch actions users perform on touchscreen devices. Finger-Fitts Law [4] revised the conventional Fitts' law into a 1D (one-dimensional) pointing model for finger touch by explicitly accounting for the fat finger ambiguity (absolute error) problem which was unaccounted for in the original Fitts' law. We generalize Finger-Fitts law to 2D touch pointing by solving two critical problems. First, we extend two of the most successful 2D Fitts law forms to accommodate finger ambiguity. Second, we discovered that using nominal target width and height is a conceptually simple yet effective approach for defining amplitude and directional constraints for 2D touch pointing across different movement directions. The evaluation shows our derived 2D Finger-Fitts law models can be both principled and powerful. Specifically, they outperformed the existing 2D Fitts' laws, as measured by the regression coefficient and model selection information criteria (e.g., Akaike Information Criterion) considering the number of parameters. Finally, 2D Finger-Fitts laws also advance our understanding of touch pointing and thereby serve as the basis for touch interface designs.

Keywords: Fitts’ law; finger input; pointing models.

Figure 1:

A illustration of option 1: using nominal width (x-length) and height (y-length) to define amplitude (W) and directional (H) constraints. (a): in vertical movement direction, y-length is W and x-length is H. (b): in horizontal movement direction, x-length is W and y-length is H. (c): in angled movement direction, if the direction falls within the grey area, x-length is W and y-length is H; if the direction is within the white area, y-length is W and x-length is H.

Figure 2:

A illustration of option 2: using apparent width (in blue) and height (in green) to define amplitude (W) and directional (H) constraints.

Figure 3:

An illustration of experimental setting. The dotted circles show 3 possible movement distances (A). θ is the angle between movement direction and the x-axis of the screen coordinate system. The blue rectangle is the starting rectangle and the red rectangle is the target.

Figure 4:

Left: a participant in the study. Right: a screenshot of the task.

Figure 5:

MT vs. ID regressions for 5 model candidates. As shown, the Finger-Fitts Euclidean Simplified model (d) performed the best, and all the 2D Finger-Fitts models (b, d, and e) outperform their counterparts 2D Fitts’ models (a [26] and c [1]).