# A Study of Model Iterations of Fitts' Law and Its Application to Human-Computer Interactions
## 5 Conclusions
### Discuss
[PERSON]'s formula considered more factors than [PERSON] and [PERSON]'s, and his research provided inspiration for subsequent formulations for various situations. Yet, the formula itself is not widely used. With the progression of research, the original formulation of [PERSON] law needs to be appropriately adapted to different interaction scenarios. In touchscreen interactions, most target acquisition tasks are two-dimensional, making the two-dimensional formula well-suited for addressing these tasks. [PERSON]'s formula has been validated by researchers in the context of touchscreen interaction [104]. [PERSON] et al. tested the validity of [PERSON]'s adaptation of [PERSON] law for smartphone and tablet touchscreen interactions, establishing a linear relationship between the index of difficulty and movement time [105]. Currently, for the interactive aspects of touchscreens, [PERSON]'s formula is considered appropriate. When dealing with small touchscreens, [PERSON] et al. 's Fitts' law is recommended for small target acquisition tasks. This new adjustment addresses the inaccuracies of the original formula under extreme conditions and serves as a model for small target acquisition on touchscreens [89]. Touchscreen human-machine interfaces (HMIs) are often used as the primary control interface in vehicles. Touchscreens for in-vehicle deployment often necessitate time-consuming and costly experiential testing and user trials. [PERSON] et al. proposed a model combining [PERSON] law with [PERSON]'s law. This model provides an effective design and evaluation tool capable of making valuable predictions about visual requirements and performance limitations associated with in-vehicle HMIs much earlier in the design cycle than traditional design evaluation techniques. This model holds significant reference value for the design of touchscreen interfaces under driving tasks [65]. The interaction of handheld devices such as mice also occurs on a two-dimensional plane, and such interaction behavior can be explained by Fitts' law. [PERSON] et al. modified the original [PERSON] law to present a formula applicable to mouse devices, offering guidance for the design of these devices [72]. For the application of [PERSON] law in pedaling, the effects of leg movement and footwear should be considered. [PERSON] et al. summarize the use of the original formula of Fitts' law in foot motion and propose a modification that accounts for both visually controlled and non-visually controlled motion. Their research provides important guidance for the application of [PERSON] law in pedal equipment [79]. In the two-dimensional context, several formulas are primarily used for developing touchscreen interfaces. Among the more well-known formulas, [PERSON]'s formula hasgained significant recognition and is widely used in the design of touchscreen interactive interfaces. For other applications, modifications of the formula by later researchers can better meet specific needs. In contrast to 2D formulas, several formulas within the 3D context do not have widely recognized, appropriate counterparts and must rely on those proposed for specific experimental scenarios. Due to the different use situations, it is impossible to compare the formulas. Several of the three-dimensional formulas in Table 2 are presented in different contexts and have different scopes of application. The definitions for both movement time (MT) and index of difficulty (ID) in these three-dimensional variants differ significantly. Formulas that consider the three dimensions of length, width, and height are more effective in guiding in-space motion than the original Fitts formulas. For target acquisition in 3D space, [PERSON]'s formulation is particularly noteworthy [23]. The extended model in the spherical coordinate system proposed by [PERSON] can be utilized during the design and evaluation phases of development, aiding designers and developers [7].