# A Study of Model Iterations of Fitts' Law and Its Application to Human-Computer Interactions
## 5 Conclusions
### Discuss  
Fitts' law provides a robust model for motion in two dimensions and is widely recognized in that context. However, [PERSON]'s modification of the original Fitts formula, proposing a modified version, has gained greater acceptance. On the other hand, motion within three dimensions is more intricate, resulting in a diverse range of proposed formulas. Each formula has its specific conditions of applicability, necessitating a meticulous comparison of the usage conditions for each formula. In general, [PERSON] law should not be mechanically applied in HCIs, but should be considered in practical situations. The formula highlights the importance of target size and distance. However, when different interaction devices are involved, factors such as movement direction, target thickness, position effect, interference, user age, and user psychology combine randomly with the previous factors. Designers must carefully select the original or modified versions of Fitts' law that correspond to the scope of their study when designing related products. Certain aspects warrant special attention when applying [PERSON] law. One such consideration arises when modeling motion for pointing at small targets, particularly on small-screen devices. In these cases, the traditional Fitts' law becomes less accurate. This poses challenges when using [PERSON] law to assess pointing performance on mobile touchscreen devices, as the accuracy of finger input is typically lower compared to mouse pointing (commonly known as the \"fat finger problem\") [89]. In such scenarios, alternative models that deviate from [PERSON] law demonstrate better predictive performance. Furthermore, traditional Fitts' law studies have not adequately addressed the impact of age on movement time and should be given more serious consideration. As individuals age, their motor skills and ability to achieve goals through physical movement change. Consequently, the time required to accomplish a given task may vary with age. Therefore, future experiments related to [PERSON] law must devote more attention to understanding the effects of age differences on users' movement behaviors. Unlike other scientific laws, [PERSON] law was not developed mathematically from the principles of human movement systems but is instead derived from information theory. However, the similarities between information theory and human movement systems are coincidental. This implies that [PERSON] law applies to interactions between humans and various devices and can only be validated experimentally, rather than theoretically [103]. The various variants proposed by different researchers may yield different results under different experimental conditions, making it extremely challenging to compare the validity of the individual formulations. In the two-dimensional context, [PERSON] law is generally recognized through the motion time formula given in Equation (4), where the definition of the index of difficulty (ID) is crucial for the rewriting of variant formulas. The individual intra-two-dimensional formulas in Table 1 are the currently recognized formulas, as well as the original formulas. Among the formulas that consider only target width and distance, [PERSON] original formula and [PERSON]'s formula are the most widely recognized and applied. [PERSON]'s formula is similar to [PERSON]'s; however, using the bullseye as the target endpoint is more reliable than using the edges. Both [PERSON] and [PERSON]'s formulas were developed based on information theory, with [PERSON]'s formula being more aligned with the principles of information theory. In addition, [PERSON] original Formula (1), in which A is multiplied by two to ensure that the ID is positive, differs from [PERSON]'s definition of A. This modification was confirmed by [PERSON]'s experiments as a better fit than the original formula, and the later widely adopted ID was [PERSON]'s formula. [PERSON]'s formula, which incorporates finger widths into the ID, is appropriate for inverse Fitts tasks that take finger widths into account.