Hermite interpolation of solid orientations with circular blending quaternion curves

Journal of Visualization and Computer Animation

Volumn 7, Issue 2, 1996, Pages 95-110

  Kim, Myung Soo ^a   Nam, Kee Won ^a  

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

Author keywords

Angular velocity; Animation; Hermite interpolation; Orientation; Quaternion; Rotation

Indexed keywords

EID: 0038320324     PISSN: 10498907     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1778(199604)7:2<95::AID-VIS138>3.0.CO;2-8     Document Type: Article

References (14)

1. J. Schlag, 'Using geometric constructions to interpolate orientation with quaternions', in J. Arvo (ed.), Graphics Gems II, Academic Press, Boston, 1991, pp. 377-380.
2. K. Shoemake, 'Animating rotation with quaternion curves', Computer Graphics (Proc. SIGGRAPH '85), 19, (3), 245-254 (1985).
3. 2-continuous B-spline quaternion curve interpolating a given sequence of solid orientations', Proc. Computer Animation '95, Geneva, Switzerland, 19-21, April 1995, pp. 72-81.
4. M.-J. Kim, M.-S. Kim and S. Y. Shin, 'A general construction scheme for unit quaternion curves with simple high order derivatives', Computer Graphics (Proc. SIGGRAPH'95), 1995, pp. 369-376.
5. M. Curtis, Matrix Groups, Springer-Verlag, New York, 1979.
6. M.-S. Kim and K.-W. Nam, 'Interpolating solid orientations with circular blending quaternion curves', Computer-Aided Design, 27, (5), 385-398 (1995).
7. G. Nielson, 'Smooth interpolation of orientations', in N.M. Thalmann and D. Thalmann (eds), Models and Techniques in Computer Animation (Proc. Computer Animation '93), Springer-Verlag, 1993, pp. 75-93.
8. W. Wang and B. Joe, 'Orientation interpolation in quaternion space using spherical biarcs', Proc. Graphics Interface '93, 1993, pp. 24-32.
9. A. Barr, B. Currin, S. Gabriel and J. Hughes, 'Smooth interpolation of orientations with angular velocity constraints using quaternions', Computer Graphics (Proc. SIGGRAPH '92), 26, (2), 313-320 (1992).
10. G. Hanotaux and B. Peroche, 'Interactive control of interpolations for animation and modeling', Proc. Graphics Interface '93, 1993, pp. 201-208.
11. M.-J. Kim, M.-S. Kim and S. Y. Shin, 'A compact differential formula for the first derivative of a unit quaternion curve', The Journal of Visualization and Computer Animation, 7, 43-57 (1996).
12. K.-W. Nam and M.-S. Kim, 'Hermite interpolation of solid orientations based on a smooth blending of two great circular arcs on SO(3)', in R. Earnshaw and J. Vince (eds), Computer Graphics: Development in Virtual Environments, Academic Press, 1995, pp. 171-183.
13. K. Shoemake, 'Quaternion calculus for animation', Math for SIGGRAPH (ACM SIGGRAPH '91 Course Notes #2), 1991.
14. M. Spivak, Calculus on Manifolds, Addison-Wesley, Reading, Mass., 1965.