## A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations

Computer Animation (1995)

Geneva, Switzerland

Apr. 19, 1995 to Apr. 21, 1995

ISBN: 0-8186-7062-2

pp: 72

Myoung-Jun Kim , Dept. of Comput. Sci., Korea Adv. Inst. of Sci. & Technol., Tajeon, South Korea

Sung Yong Shin , Dept. of Comput. Sci., Korea Adv. Inst. of Sci. & Technol., Tajeon, South Korea

Myung-Soo Kim , Dept. of Comput. Sci., Korea Adv. Inst. of Sci. & Technol., Tajeon, South Korea

ABSTRACT

An algorithm is presented that constructs a C/sup 2/-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves; however, the B-spline quaternion curves do not have C/sup 2/-continuity in SO(3). The authors recently suggested a new construction method that can extend a B-spline curve to a similar one in SO(3) while preserving the C/sup k/-continuity of the B-spline curve. We adapt this method for the construction of a B-spline quaternion interpolation curve. Thus, the problem essentially reduces to the problem of finding the control points for the B-spline interpolation curve. However, due to the non-linearity of the associated constraint equations, it is non-trivial to compute the B-spline control points. We provide an efficient iterative refinement solution which can approximate the control points very precisely.

INDEX TERMS

interpolation; computer animation; solid modelling; splines (mathematics); C/sup 2/-continuous B-spline quaternion curve; solid orientations; interpolation; rotation group; de Casteljau type construction method; iterative refinement solution

CITATION

Myoung-Jun Kim,
Sung Yong Shin,
Myung-Soo Kim,
"A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations",

*Computer Animation*, vol. 00, no. , pp. 72, 1995, doi:10.1109/CA.1995.393545