“Fast construction of accurate quaternion splines” by Ramamoorthi and Barr
Conference:
Type(s):
Title:
- Fast construction of accurate quaternion splines
Presenter(s)/Author(s):
Abstract:
In 1992, Barr et al. proposed a method for interpolating orientations with unit quaternion curves by minimizing covariant acceleration. This paper presents a simple improved method which uses cubic basis functions to achieve a speedup of up to three orders of magnitude. A new criterion for automatic refinement based on the Euler-Lagrange error functional is also introduced.
References:
1. A.H. BARR, B. CURRIN, S. GABRIEL, and J.E HUGHES. Smooth interpolation of orientations with angular velocity constraints using quaternions. In SIGGRAPH 92 proceedings, pages 313-320,1992.
2. R. BARTELS, J. BEATTY, and B. BARSKY. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufman, Palo Alto, 1987.
3. M.E COHEN. Interactive spacetime control for animation. In SIG- GRAPH 92 proceedings, pages 293-302,1992.
4. S. GABRIEL and J. KAJIYA. Spline interpolation in curved space. In SIGGRAPH 85 course notes for State of the Art in Image Synthesis(#11), 1985.
5. H.-J. HA. A new camera control method preserving view-up vectors. Master’s thesis, KAIST, Taejon 305-701, Korea, 1996.
6. W.R. HAMILTON. Elements of Quaternions (Volume I, II). Chelsea Publishing Company, 1969.
7. B. JUTTLER. Visualization of moving objects using dual quaternion curves. Computer & Graphics, 18(3):315-326,1994.
8. B. JUTTLER and M.G. WAGNER. Computer-aided design with spatial rational B-spline motions. Journal of Mechanical Design, 118(2):193-201, June 1996.
9. M.-J. KIM, M.-S. KIM, and S. SHIN. A C2-continuous B-spline quaternion curve interpolating a given sequence of solid orientations. In Computer Animation 95 Proceedings, pages 72-81,1995.
10. M.-J. KIM, M.-S. KIM, and S. SHIN. A general construction scheme for unit quaternion curves with simple high order derivatives. In SIGGRAPH 95 proceedings, pages 369-376,1995.
11. M.-S. KIM and K.-W. NAM. Interpolating solid orientations with circular blending quaternion curves. Computer Aided Design, 27(5):385-398,1995.
12. Z. LIU and M.E COHEN. Keyframe motion optimization by relaxing speed and timing. In 6th Eurographics Workshop on Animation and Simulation (Maastricht 1995), pages 144-153,1995.
13. Numerical Algorithms Group, Ltd. NAG Fortran Library Document, 1988.
14. R. RAMAMOORTHI, C. BALL, and A.H. BARR. Dynamic splines with constraints for animation. Technical Report CS-TR-97-03, California Institute of Technology, Included on CD-ROM, January 1997. ftp://ftp.cs.caltech.edu/tr/cs-tr-97-03.ps.Z.
15. B. RAVANI and E PARK. Bezier curves on riemannian manifolds and lie groups with kinematic applications. Journal of Mechanical Design, 117(1):36-40,March 1995.
16. K. SHOEMAKE. Animating rotation with quaternion curves. In SIGGRAPH 85 proceedings, pages 245-254,1985.
17. K. SHOEMAKE. Quaternion calculus for animation. In SIGGRAPH 91 course notes for Math for Siggraph(#2), 1991.
18. D. TERZOPOULOS and H. QIN. Dynamic Nurbs with geometric constraints for interactive sculpting. ACM Transactions on Graphics, 13(2):103-136, April 1994.
19. W. WANG and B. JOE. Orientation interpolation in quaternion space using spherical biarcs. In Graphics Interface 93, pages 24-32,1993.
20. W. WELCH and A. WITKIN. Variational surface modeling. In SIGGRAPH 92 proceedings, pages 157-166,1992.
21. D. ZWILLINGER. Handbook of Differential Equations. Academic Press, San Diego, 1989.
