### Abstract

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 language | English |
---|---|

Pages (from-to) | 350-355 |

Number of pages | 6 |

Journal | International Journal of Industrial Ergonomics |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Jul 1 |

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### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

**Extended Fitts' law for 3D pointing tasks using 3D target arrangements.** / Cha, Yeonjoo; Myung, Rohae.

Research output: Contribution to journal › Article

*International Journal of Industrial Ergonomics*, vol. 43, no. 4, pp. 350-355. https://doi.org/10.1016/j.ergon.2013.05.005

}

TY - JOUR

T1 - Extended Fitts' law for 3D pointing tasks using 3D target arrangements

AU - Cha, Yeonjoo

AU - Myung, Rohae

PY - 2013/7/1

Y1 - 2013/7/1

N2 - 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.

AB - 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.

KW - 3D pointing task

KW - Fitts' law

KW - Movement time

KW - Spherical coordinate system

UR - http://www.scopus.com/inward/record.url?scp=84880621977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880621977&partnerID=8YFLogxK

U2 - 10.1016/j.ergon.2013.05.005

DO - 10.1016/j.ergon.2013.05.005

M3 - Article

AN - SCOPUS:84880621977

VL - 43

SP - 350

EP - 355

JO - International Journal of Industrial Ergonomics

JF - International Journal of Industrial Ergonomics

SN - 0169-8141

IS - 4

ER -