Cubic spline algorithms for orientation interpolation

International Journal for Numerical Methods in Engineering

Volumn 46, Issue 1, 1999, Pages 45-64

  Kang, I G ^a   Park, F C ^a  

^a Seoul National University   (South Korea)

Author keywords

Cubic spline; Interpolation; Orientation; Rotation; SO(3)

Indexed keywords

ALGORITHMS; DIFFERENTIATION (CALCULUS); INTERPOLATION; MATRIX ALGEBRA;

CUBIC SPLINE ALGORITHMS; ORIENTATION INTERPOLATION;

COMPUTATIONAL GEOMETRY;

EID: 0033327791     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990910)46:1<45::AID-NME662>3.0.CO;2-K     Document Type: Article

References (22)

1. Shoemake K. Animating rotation with quaternion curves. ACM Siggraph 1985; 19(3):245-254.
2. Kim MS, Nam KW. Hermite interpolation of solid orientations with circular blending quaternion curves. Journal of Visualization and Computer Animation 1996; 7:95-110.
3. Ge QJ, Ravani B. Geometric construction of Bézier motions. ASME Journal of Mechanical Design 1994; 116: 749-755.
4. Ge QJ, Ravani B. Computer-aided design of motion interpolants. ASME Journal of Mechanical Design 1994; 116: 756-762.
5. Park FC, Ravani B. Bézier curves on Riemannian manifolds and Lie groups with kinematics applications. ASME Journal of Mechanical Design 1995, 117(1):36-40.
6. Barr AH, Currin B, Gabriel S, Hughes JF. Smooth interpolation of orientations with angular velocity constraints using quaternions. Computer Graphics 1992; 25(2):313-320.
7. Hart JC, Francis GK, Kaufman LH. Visualizing quaternion rotation. ACM Transactions on Graphics 1994; 13: 256-276.
8. Juttler B. Visualization of moving objects using dual quaternion curves. Computers and Graphics 1994; 18(3): 315-326.
9. Park FC, Ravani B. Smooth invariant interpolation of rotations. ACM Transactions on Computer Graphics 1997; 16(3):277-295.
10. McCarthy JM. Introduction to Theoretical Kinematics. MIT Press: Cambridge, MA, 1990.
11. Gantmacher R. Matrix Theory, Vols. I-II. Chelsea Publishing Company: New York, 1960.
12. Mladenova C. A contribution to the modelling and control of manipulators. Journal of Intelligent and Robotic Systems 1990; 3:349-363.
13. Tsiotras P, Junkins JL, Schaub H. Higher-order Cayley transforms with applications to attitude representations. AIAA Journal of Guidance, Control and Dynamics 1997; 20(3):528-534.
14. Shuster MD. A survey of attitude representations. AIAA Journal of Guidance, Control and Dynamics 1993; 41(4):439-517.
15. Marandi SR, Modi V. A preferred co-ordinated system and the associated orientation representation in attitude dynamics. Acta Astronautica 1987; 15(11):833-843.
16. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical Recipes in C. Cambridge University Press: Cambridge, 1988.
17. Park FC, Kang IG. Cubic interpolation on the rotation group using Cayley parameters. Proceedings of the ASME Design Automation Conference, Irvine, CA, 1996.
18. Noakes L, Heinzinger G, Paden B. Cubic splines on curved spaces. IMA Journal of Mathematical Control and Applications 1989; 6:465-473.
19. Zefran M, Kumar V, Croke C. On the generation of smooth three-dimensional rigid body motions. IEEE Transactions on Robotics and Automation, (1999), to appear.
20. Park FC. Distance metrics on the rigid-body motions with applications to mechanism design. ASME Special 50th Anniversary Design Issue 1995; 117(B):87-92.
21. Wagner M, Ravani B. Computer aided design of robot trajectories using rational motions. In Recent Advances in Robot Kinematics, Lenarcic J, Parenti-Castelli V (eds). Kluwer: Dordrecht, 1996.
22. Juttler B, Wagner M. Computer-aided design with rational B-spline motions. ASME Journal of Mechanical Design 1996; 118(2):193-201.