Fitts’s Law: Towards a Geometric Explanation

In designing human-computer interfaces, designers use an empirical Fitts’s Law, according to which the average time T of accessing an icon of size w at a distance d from the center of the screen is proportional to the logarithm of the ratio w/d. There exist explanations for this law, but these explanations have gaps. In this paper, we show that these gaps can be explained if we analyze this problem from the geometric viewpoint. Thus, we get a geometric explanation of the Fitts’s Law. What is Fitts’s Law. The efficiency of computer-based systems for education, information, commerce, etc., strongly depends on the user-friendliness of the corresponding interfaces, in particular, on the location and size of the appropriate icones. When deciding the location and size of different icons on a computer screen, designers use the Fitts’s Law [3, 4]. This law describe how the average time T of accessing an icon depends on the distance d from the center of the screen to the icon and on the linear size w of this icon: T = a+ b · ln ( d w ) , for some constants a and b. How Fitts’s Law is used in interface design. The use of Fitts’s Law started with the very first mouse-accessible interfaces; see, e.g., [1]. It is based on the following idea. Each icon corresponds to a specific task or group of tasks. Some tasks are more frequent, some are rarer: for example, editing is a frequent task, while logging off is a rarer task. For each task, we can empirically determine the frequency fi with which this task is performed. We can therefore gauge the