title: Virtual trackballs revisited.
abstract: Rotation of three-dimensional objects by a two-dimensional mouse is a typical task in computer-aided design, operation simulations, and desktop virtual reality. The most commonly used rotation technique is a virtual trackball surrounding the object and operated by the mouse pointer. This article reviews and provides a mathematical foundation for virtual trackballs. The first, but still popular, virtual trackball was described by Chen et al. We show that the virtual trackball by Chen et al. does not rotate the object along the intended great circular arc on the virtual trackball and we give a correction. Another popular virtual trackball is Shoemake's quaternion implementation, which we show to be a special case of the virtual trackball by Chen et al.. Shoemake extends the scope of the virtual trackball to the full screen. Unfortunately, Shoemake's virtual trackball is inhomogeneous and discontinuous with consequences for usability. Finally, we review Bell's virtual trackball and discuss studies of the usability of virtual trackballs.
authors.affiliation: Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark. kaiip@diku.dk
authors.forename: Knud
authors.initials: K
authors.lastname: Henriksen
authors.forename: Jon
authors.initials: J
authors.lastname: Sporring
authors.forename: Kasper
authors.initials: K
authors.lastname: Hornbaek
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D016287:Computer Peripherals; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012399:Rotation; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014584:User-Computer Interface