Extended Fitts' law for 3D pointing tasks using 3D target arrangements

Yeonjoo Cha, Rohae Myung

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


This study explored an extended 3D Fitts' model, which was more appropriate than the original Fitts' model for pointing tasks in 3D environment. The inclination angle and azimuth angle for spherical coordinate system were added to Fitts' original model formulation. Experiments were conducted by manipulating the distance to the target, the size of target, and the 3D target arrangement, which were described using the two angles of inclination (θ1) and azimuth (θ2). Given the starting point as the center of the coordinates, θ1 was the angle between the positive y-axis and the target location, while θ2 was the angle between the positive x-axis and the projected target location on the x-. z plane. All four variables were found to be significant for the movement time (MT) (p<0.0001). After incorporating the two variables, θ1 and θ2, into the original Fitts' model, the extended Fitts' model with 3D target arrangements for spherical coordinate system showed better agreement with the empirical data than previous models in terms of the correlation coefficient and the standard error of the residuals for the measured and predicted MTs. Relevance to industry: This study presents an extended Fitts' model with a higher degree of predictability than previous studies for pointing task in three-dimensional space. In many situations, people implement pointing tasks in a three-dimensional environment, so it is important for designers to predict human performance accurately. Instead of using Euclidean coordinate system, spherical coordinate system can be also used for 3D pointing tasks. The extended model with spherical coordinate system can be used during the design and evaluation stage of the development process to help designers and developers.

Original languageEnglish
Pages (from-to)350-355
Number of pages6
JournalInternational Journal of Industrial Ergonomics
Issue number4
Publication statusPublished - 2013 Jul

Bibliographical note

Funding Information:
I would like to thank Daecheol Park for his efforts to complete this manuscript. Many thanks also go to anonymous reviewers for their thorough and thoughtful comments on the original manuscript. In addition, I'd like to thank for the support by the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2012047330 ).


  • 3D pointing task
  • Fitts' law
  • Movement time
  • Spherical coordinate system

ASJC Scopus subject areas

  • Human Factors and Ergonomics
  • Public Health, Environmental and Occupational Health


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