Adaptation of Fitts’ law in three-dimensional interfaces

Abstract

The lack of a consensus choice of the calculation model for adapting Fitts’ law in the development of threedimensional interfaces, and the heterogeneity of the research methodology on the relevant topic, makes it difficult to compare their results. The purpose of the study was to determine the most effective computational model of user experience in the development of spatial interfaces in virtual and reality in two-dimensional and three-dimensional environments. For this purpose, a meta-analysis of a representative sample of scientific papers was carried out, distributed according to measurement criteria (one-dimensional, two-dimensional, three-dimensional) and research areas, and ordered by the percentage of citations. According to the results of formalised distribution criteria, the Shannon equation proposed by Mackenzie (77.8%) and the Machuka angular equation (28.7%) had the highest citation rate in three-dimensional works. The original Fitts equation in this context, even as a primary source, had 4% relevance, and the most effective solution in a two-dimensional plane under Mackenzie’s authorship – only 2%. It was revealed that the most relevant are threedimensional models with the involvement of additional parameters, including trigonometric angular coefficients and sets of coordinates for determining the depth or complex trajectories of achieving goals, which was confirmed by high citation rates of the corresponding approaches. It was established that the effectiveness of each of the demonstrated adaptations of Fitts’ law was not determined only by the type and number of ed parameters, since no less important role is played by the process of comparing theoretical calculations with empirical data obtained as a result of user interaction with hardware complexes, the dynamics of availability of which for a wide range of researchers radically changed during a short period of time (10-20 years), considering the general chronological range of the considered papers (1954-2025). The practical significance of the research lies in the fact that the results obtained can be used to develop user interfaces in virtual and augmented reality tools, form standards, and methodological recommendations when working with spatial interfaces, and improve feedback when analysing user experience.