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Computer Animation 1995
A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations
Geneva, Switzerland
April 19-April 21
ISBN: 0-8186-7062-2
Myoung-Jun Kim, 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
Sung Yong Shin, Dept. of Comput. Sci., Korea Adv. Inst. of Sci. & Technol., Tajeon, South Korea
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, Myung-Soo Kim, Sung Yong Shin, "A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations," ca, pp.72, Computer Animation 1995, 1995
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