Minimizing the distortion of affine spline motions

Graphical Models

Volumn 64, Issue 2, 2002, Pages 128-144

  Hyun, Dae Eun ^a   Jüttler, Bert ^b   Kim, Myung Soo ^a  

^a Seoul National University   (South Korea)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Affine spline motion; Curve; Degree elevation; Energy optimization; Keyframe animation; Knot insertion; Rigidity

Indexed keywords

ALGORITHMS; ANIMATION; CONSTRAINT THEORY; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

AFFINE SPLINE MOTIONS; ENERGY OPTIMIZATION;

COMPUTER GRAPHICS;

GRAPHICAL METHOD;

EID: 0036523622     PISSN: 15240703     EISSN: None     Source Type: Journal    
DOI: 10.1006/gmod.2002.0569     Document Type: Conference Paper

References (17)

1. A. Barr, B. Currin, S. Gabriel, and J. Hughes. Smooth interpolation of orientations with angular velocity constraints using quaternions. Computer Graphics (Proc. of SIGGRAPH '92, Chicago, IL, July 26-31, 1992), 26(2), pp. 313-320.
2. O. Bottema and B. Roth, Theoretical Kinematics (Corrected reprint of the 1979 edition), Dover, New YorK, 1990.
3. T.-I. Chang, J.-H. Lee, M.-S. Kim, and S.J. Hong, Direct manipulation of generalized cylinders based on B-spline motion, Visual Comput. 14(5/6), 1998, 228-239.
4. G. Elber and M.-S. Kim, Geometric constraint solver using multivariate rational spline functions, in Proc. of the Sixth ACM Symposium on Solid Modeling and Applications, Ann Arbor, Michigan, June 6-8, 2001, pp. 1-10.
5. G. Farin, Curves and Surfaces for Computer Aided Geometric Design (4th ed.), Academic Press, Boston, MA, 1997.
6. J. Hoschek and D. Lasser, Computer Aided Geometric Design, AK Peters, Wellesley, MA, 1993.
7. J. Johnstone and J. Williams, A rational model of the surface swept by a curve, Comput. Graphics Forum 14(3), 1995, 77-88.
8. B. Jüttler, Visualization of moving objects using dual quaternion curves, Comput. Graphics 18(3), 1994, 315-326.
9. B. Jüttler, Spatial rational motions and their application in computer aided geometric design, in Mathematical Methods for Curves and Surfaces (M.Dæhlen, T. Lyche, and L.L. Schumaker, Eds.), pp. 271-280, Vanderbilt University Press, La Vergne, TN, 1995.
10. B. Jüttler and M.G. Wagner, Computer-aided design with spatial rational B-spline motions, ASME J. Mech. Design 118, 1996, 193-201.
11. M.-J. Kim, M.-S. Kim, and S.Y. Shin, A general construction scheme for unit quaternion curves with simple high order derivatives, in Proc. of SIGGRAPH '95, Los Angeles, August 6-11, 1995, pp. 369-376.
12. M.-S. Kim and G. Elber, Problem reduction to parameter space, in The Mathematics of Surfaces IX, Proc. of the Ninth IMA Conference (R. Cipolla and R. Martin, Eds.), pp. 82-98, Springer-Verlag, London, 2000.
13. L. Ma, Z. Jiang, and K. Chan, Interpolating and approximating moving frames using B-splines, in Proc. of Pacific Graphics 2000, Hong Kong, October 3-5, 2000, pp. 154-164.
14. R. Ramamoorthi and A. Barr, Fast construction of accurate quaternion splines, in Proc. of SIGGRAPH '97, Los Angeles, August 3-8, 1997, pp. 287-292.
15. K. Shoemake, Animating rotation with quaternion curves, Computer Graphics (Proc. of SIGGRAPH '85) 19, 1985, 245-254.
16. K. Shoemake, Quaternion calculus for animation, in Math for SIGGRAPH (ACM SIGGRAPH '91 Course Notes #2), 1991.
17. K. Shoemake and T. Duff, Matrix animation and polar decomposition, in Proc. of Graphics Interface '92, Toronto, Ontario, Canada, 1992, pp. 258-264.