A compact differential formula for the first derivative of a unit quaternion curve

Journal of Visualization and Computer Animation

Volumn 7, Issue 1, 1996, Pages 43-57

  Kim, Myoung Jun ^a   Kim, Myung Soo ^b   Shin, Sung Yong ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b Pohang University of Science and Technology (POSTECH)   (South Korea)

Author keywords

Differential; Exponential; Logarithm; Quaternion; Rotation; SO(3)

Indexed keywords

EID: 0003042792     PISSN: 10498907     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1778(199601)7:1<43::AID-VIS136>3.0.CO;2-T     Document Type: Article

References (12)

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2. M.-S. Kim and K.-W. Nam, 'Interpolating solid orientations with circular blending quaternion curves', to appear in Computer-Aided Design.
3. A preliminary version appeared in N.M. Thalmann and D. Thalmann (eds), Communicating with Virtual Worlds (Proc. CG International '93), Springer-Verlag, Tokyo, 1993, pp. 258-269.
4. M.-S. Kim and K.-W. Nam, 'Hermite interpolation of solid orientations with circular blending quaternion curves', to appear in Proc. CG International '94.
5. K. Shoemake, 'Animating rotation with quaternion curves', Computer Graphics (Proc. SIGGRAPH '85), 19, (3), pp. 245-254 (1985).
6. K. Shoemake, 'Quaternion calculus for animation', Math for SIGGRAPH (ACM SIGGRAPH '91 Course Notes #2), 1991.
7. M. Curtis, Matrix Groups, Springer-Verlag, New York, 1979.
8. W. Boehm, 'On cubics: a survey', Computer Vision, Graphics, and Image Processing, 19, 201-226 (1982).
9. Sir William Hamilton, Elements of Quaternions, Vol. I, 3rd Ed., Chelsea Pub., New York, 1969.
10. K. Shoemake, private communication, February 1994.
11. G. Spivak, Calculus on Manifolds, Addison-Wesley, Reading, Mass., 1965.
12. G. Strang, Linear Algebra and its Applications, 3rd edn, HBJ Pub., Orlando, 1988.