This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Virtual Trackballs Revisited
March/April 2004 (vol. 10 no. 2)
pp. 206-216

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. [CHECK END OF SENTENCE]. 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 [CHECK END OF SENTENCE], 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 [CHECK END OF SENTENCE] and discuss studies of the usability of virtual trackballs.

[1] M. Chen, S.J. Mountford, and A. Sellen, A Study in Interactive 3-D Rotation Using 2-D Control Devices Computer Graphics, vol. 22, no. 4, pp. 121-129, Aug. 1988.
[2] K. Shoemake, Arcball: A User Interface for Specifying Three-Dimensional Orientation Using a Mouse Proc. Graphics Interface '92, pp. 151-156, 1992.
[3] G. Bell, Bell's Trackball http://members.tripod.com/professor _tom index.html, 1988.
[4] 3D Studio Max http:/www.3dmax.com, 2003.
[5] S. Card, J. Mackinlay, and B. Shneiderman, Readings in Information Visualization: Using Vision to Think. San Francisco: Morgan Kaufmann, 1999.
[6] Maya from Alias/Wavefront http:/www.aliaswavefront. com, 2003.
[7] K.B. Evans, P.P. Tanner, and M. Wein, Tablet Based Valuators that Provide One, Two or Three Degrees of Freedom Proc. SIGGRAPH '81, Computer Graphics, vol. 15, no. 3, pp. 91-97, 1981.
[8] J. Raskin, The Humane Interface: New Directions for Designing Interactive Systems. Reading, Mass.: Addison Wesley, 2000.
[9] B. Shneiderman, Direct Manipulation: A Step Beyond Programming Languages Computer, vol. 16, no. 8, pp. 57-68, Aug. 1983.
[10] T.G. Zimmerman, J. Lanier, C. Blanchard, S. Bryson, and Y. Harvill, A Hand Gesture Interface Proc. CHI+GI 1987, pp. 189-192, 1987.
[11] Cyberglove http:/www.immersion.com, 2003.
[12] S. Zhai, P. Milgram, and W. Buxton, The Influence of Muscle Groups on Performance of Multiple Degree-of-Freedom Input Proc. Computer Human Interaction Conf. '96, pp. 308-315, 1996.
[13] Logitech http:/www.logicad3d.com, 2003.
[14] K. Hinckley, R. Pausch, J.C. Goble, and N.F. Kassell, Passive Real-World Interface Props for Neurosurgical Visualization Proc. ACM Computer Human Interaction Conf. '94, pp. 452-458, 1994.
[15] C. Ware and J. Rose, Rotating Virtual Objects with Real Handles ACM Trans. Computer-Human Interactions, vol. 6, no. 2, pp. 162-180, 1999.
[16] Spacestick http:/www.vrweb.com, 2003.
[17] L. Bretzner and T. Lindeberg, Use Your Hand as a 3-D Mouse or Relative Orientation from Extended Sequences of Sparse Point and Line Correspondences Using the Affine Trifocal Tensor Proc. European Conf. Computer Vision, pp. 141-157, June 1998.
[18] K. Hinckley, J. Tullio, R. Pausch, D. Proffitt, and N. Kassell, Usability Analysis of 3D Rotation Techniques Proc. User Interface Software and Techonology Symp. '97, pp. 1-10, 1997.
[19] W. Buxton and B. Myers, A Study in Two-Handed Input Proc. Computer Human Interaction, pp. 321-326, 1986.
[20] L.D. Cutler, B. Frölich, and P. Hanrahan, Two-Handed Direct Manipulation on the Responsive Workbench Proc. Symp. Interactive 3D Techniques, 1997.
[21] M.W. Gribnau, I.M. Verstijnen, and J.M. Hennessey, Three Dimensional Object Orientation Using the Non-Dominant Hand Proc. Fourth Int'l Conf. Design and Decision Support Systems in Architecture and Urban Planning, 1998.
[22] Matlab http:/www.mathworks.com, 2003.
[23] H. Flanders, Differential Forms with Applications to the Physical Sciences. Dover, 1989.
[24] F.W. Warner, Foundations of Differential Manifolds and Lie Groups. Springer, 1983.
[25] J.D. Foley, A. van Dam, S.K. Feiner, and J.F. Hughes, Computer Graphics: Principles and Practice, second ed. Addison-Wesley, 1996.
[26] K. Shoemake, Arcball Rotation Control Graphics Gems, P.S. Heckbert, ed., vol. IV, pp. 175-192, Academic Press, 1994.
[27] J. Hultquist, A Virtual Trackball Graphics Gems, A.S. Glassner, ed. , vol. I, chapter 9, pp. 462-463, Academic Press, 1990.
[28] E.B. Dam, M. Koch, and M. Lilholm, Quaternions, Interpolation and Animation Technical Report DIKU-98-5, Dept. of Computer Science, Univ. of Copenhagen, Denmark, July 1998.
[29] E. Pervin and J.A. Webb, Quaternions in Computer Vision and Robotics Technical Report CMU-CS-82-150, Dept. of Computer Science, Carnegie-Mellon Univ., 1982.
[30] I. Jacob and J. Oliver, Evaluation of Techniques for Specifying 3D Rotations with a 2D Input Device Proc. Human Computer Interaction Symp. '95, pp. 63-76, 1995.
[31] T. Partala, Controlling a Single 3D Object: Viewpoint Metaphors, Speed and Subjective satisfaction Proc. Human-Computer Interaction INTERACT '99, pp. 536-543, 1999.
[32] G. Kurtenbach and R. Balakrishnan, Exploring Bimanual Camera Control and Object Manipulation in 3D Graphics Interfaces Proc. Computer Human Interaction '99, pp. 56-63, 1999.
[33] C. Plaisant, D. Carr, and B. Shneiderman, "Image-Browser Taxonomy and Guidelines for Designers," IEEE Software, vol. 12, no. 2, pp. 21-32, Mar. 1995.
[34] E. Frøkjær, M. Hertzum, and K. Hornbæk, Measuring Usability: Are Effectiveness, Efficiency, and Satisfaction Really Correlated? Proc. Computer Human Interaction 2000, pp. 345-352, 2000.
[35] C. Ware, Using Hand Position for Virtual Object Placement Visual Computer, vol. 6, pp. 245-253, 1990.
[36] I. Poupyrev, S. Weghoast, and S. Fels, Non-Isomorphic 3D Rotational Techniques Proc. Computer Human Interaction 2000, pp. 540-547, 2000.

Index Terms:
Virtual trackball, arcball, 3D rotation, 2D mouse, mathematical foundation, usability review.
Citation:
Knud Henriksen, Jon Sporring, Kasper Hornb?, "Virtual Trackballs Revisited," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 2, pp. 206-216, March-April 2004, doi:10.1109/TVCG.2004.1260772
Usage of this product signifies your acceptance of the Terms of Use.