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Representing Rotations and Orientations in Geometric Computing
March/April 2008 (vol. 28 no. 2)
pp. 75-83
Jehee Lee, Seoul National University
In 3D space, orientations and rotations are not interchangeable. Therefore, we should represent them differently and appropriately.

1. R. Goldman, "Illicit Expressions in Vector Algebra," ACM Trans. Graphics, vol. 4, no.3, 1985, pp. 223–243.
2. R. Goldman, "Vector Geometry: A Coordinate-Free Approach," ACM Siggraph, tutorial notes, course no. 16, ACM Press, 1985.
3. T. DeRose, "Geometric Programming: A Coordinate-Free Approach," ACM Siggraph, tutorial notes, course no. 25, ACM Press, 1988.
4. L. Dorst and S. Mann, "Geometric Algebra: A Computational Framework for Geometrical Applications, Part 1," IEEE Computer Graphics and Applications, vol. 22, no. 3, 2002, pp. 24–31.
5. L. Dorst and S. Mann, "Geometric Algebra: A Computational Framework for Geometrical Applications, Part 2," IEEE Computer Graphics and Applications, vol. 23, no. 4, 2003, pp. 58–67.
6. M. Alexa, "Linear Combination of Transformations," Proc. Siggraph, ACM Press, 2002, pp. 380–387.
7. K. Shoemake, "Animating Rotation with Quaternion Curves," Proc. Siggraph, ACM Press, 1985, pp. 245–254.
8. S. Buss and J. Fillmore, "Spherical Averages and Applications to Spherical Splines and Interpolation," ACM Trans. Graphics, vol. 20, no. 2, 2001, pp. 95–126.
1. K. Shoemake, "Animating Rotation with Quaternion Curves," Proc. Siggraph, ACM Press, 1985, pp. 245–254.
2. T. Igarashi, T. Moscovich, and J. Hughes, "Spatial Keyframing for Performance-Driven Animation," ACM Siggraph/Eurographics Symp. Computer Animation, ACM Press, 2005, pp. 107–115.
3. G. Hanotaux and B. Peroche, "Interactive Control of Interpolations for Animation and Modeling," Proc. Graphics Interface, AK Peters, 1993, pp. 33–42.
4. J. Johnstone and J. Williams, "Rational Control of Orientation for Animation," Proc. Graphics Interface, AK Peters, 1995, pp. 179–186.
5. D. Pletinckx, "Quaternion Calculus as a Basic Tool in Computer Graphics," The Visual Computer, vol. 5, Springer, 1989, pp. 2–13.
6. S. Buss and J. Fillmore, "Spherical Averages and Applications to Spherical Splines and Interpolation," ACM Trans. Graphics, vol. 20, no. 2, ACM Press, 2001, pp. 95–126.
7. J. Lee and S. Shin, "Motion Fairing," Proc. Computer Animation, IEEE Press, 1996, pp. 136–143.
8. M.J. Kim, M.S. Kim, and S. Shin, "A General Construction Scheme for Unit Quaternion Curves with Simple High Order Derivatives," Proc. Siggraph, vol. 29, ACM Press, 1995, pp. 369–376.
9. J. Lee and S. Shin, "General Construction of Time-Domain Filters for Orientation Data," IEEE Trans. Visualization and Computer Graphics, vol. 8, no. 2, 2002, pp. 119–128.
10. F. Park and B. Ravani, "Smooth Invariant Interpolation of Rotations," ACM Trans. Graphics, vol. 16, no. 3, 1997, pp. 277–295.

Index Terms:
rotation and orientation, coordinate-free geometric programming, unit quaternion, rotation vector, axis-angle representation
Citation:
Jehee Lee, "Representing Rotations and Orientations in Geometric Computing," IEEE Computer Graphics and Applications, vol. 28, no. 2, pp. 75-83, March-April 2008, doi:10.1109/MCG.2008.37
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