This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
ν-Quaternion Splines for the Smooth Interpolation of Orientations
March/April 2004 (vol. 10 no. 2)
pp. 224-229

Abstract—We present a new method for smoothly interpolating orientation matrices. It is based upon quaternions and a particular construction of ν-spline curves. The new method has tension parameters and variable knot (time) spacing which both prove to be effective in designing and controlling key frame animations.

[1] G. Brunnett, P.E. Crouch, and F.E. Silva Leite, Spline Elements on Spheres Math. Methods for Curves and Surfaces, M. Daehlen, T. Lyche, and L. Schumaker, eds., pp. 49-54, Vanderbilt Press, 1995.
[2] G. Farin, Curves and Surfaces for CAGD: A Practical Guide. New York: Academic Press, 1997.
[3] T. Foley and G. Nielson, Knot Selection for Parametric Spline Interpolation Math. Methods in Computer Aided Geometric Design, T. Lyche and L. Schumaker, eds., pp. 261-271, Academic Press, 1989.
[4] M.-J. Kim, M.-S. Kim, and S. Shin, A General Construction Scheme for Unit Quaternion Curves with Simple Higher Order Derivatives Proc. SIGGRAPH '95, pp. 369-376, 1995.
[5] M.-J. Kim, M.-S. Kim, and S. Shin, A C2-Continuous B-Spline Quaternion Curve Interpolating a Given Sequence of Solid Orientations Proc. Computer Animation '95, pp. 72-81, Apr. 1995.
[6] G.M. Nielson, Some Piecewise Polynomial Alternatives to Splines under Tension Computer Aided Geometric Design, R.E. Barnhill and R.F. Riesenfeld, eds., pp. 209-235, New York: Academic Press, 1974.
[7] G.M. Nielson and R.W. Heiland, Animated Rotations Using Quaternions and Splines on a 4D Sphere (Russian) Programmirovanie, no. 4, pp. 17-27, July-Aug. 1992.
[8] G.M. Nielson, Smooth Interpolation of Orientations Models and Techniques in Computer Animation, pp. 75-93, Springer, 1993.
[9] F. Park and B. Ravani, Smooth Invariant Interpolation of Rotations ACM Trans. Graphics, vol. 16, no. 3, pp. 277-295, 1997.
[10] R. Ramamoorthi and A.H. Barr, Fast Construction of Accurate Quaternion Splines Proc. ACM SIGGRAPH Conf. Computer Graphics, pp. 287-292, 1997.
[11] J. Schlag, Using Geometric Constructions to Interpolate Orientation with Quaternions Graphics Gems II, pp. 377-380, New York: Academic Press, 1992.
[12] K. Shoemake, Animating Rotations with Quaternion Curves Computer Graphics, vol. 19, no. 3, pp. 245-254, 1985.

Index Terms:
Animation, key frame, inbetweening, quaternion, splines.
Citation:
Gregory M. Nielson, "ν-Quaternion Splines for the Smooth Interpolation of Orientations," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 2, pp. 224-229, March-April 2004, doi:10.1109/TVCG.2004.1260774
Usage of this product signifies your acceptance of the Terms of Use.