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Computer Animation 1995
A C/sup 2/continuous Bspline quaternion curve interpolating a given sequence of solid orientations
Geneva, Switzerland
April 19April 21
ISBN: 0818670622
ASCII Text  x  
MyoungJun Kim, MyungSoo Kim, Sung Yong Shin, "A C/sup 2/continuous Bspline quaternion curve interpolating a given sequence of solid orientations," Computer Animation, pp. 72, Computer Animation 1995, 1995.  
BibTex  x  
@article{ 10.1109/CA.1995.393545, author = {MyoungJun Kim and MyungSoo Kim and Sung Yong Shin}, title = {A C/sup 2/continuous Bspline quaternion curve interpolating a given sequence of solid orientations}, journal ={Computer Animation}, volume = {0}, year = {1995}, isbn = {0818670622}, pages = {72}, doi = {http://doi.ieeecomputersociety.org/10.1109/CA.1995.393545}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  Computer Animation TI  A C/sup 2/continuous Bspline quaternion curve interpolating a given sequence of solid orientations SN  0818670622 SP EP A1  MyoungJun Kim, A1  MyungSoo Kim, A1  Sung Yong Shin, PY  1995 KW  interpolation; computer animation; solid modelling; splines (mathematics); C/sup 2/continuous Bspline quaternion curve; solid orientations; interpolation; rotation group; de Casteljau type construction method; iterative refinement solution VL  0 JA  Computer Animation ER   
An algorithm is presented that constructs a C/sup 2/continuous Bspline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of Bspline curves can be extended to generate Bspline quaternion curves; however, the Bspline quaternion curves do not have C/sup 2/continuity in SO(3). The authors recently suggested a new construction method that can extend a Bspline curve to a similar one in SO(3) while preserving the C/sup k/continuity of the Bspline curve. We adapt this method for the construction of a Bspline quaternion interpolation curve. Thus, the problem essentially reduces to the problem of finding the control points for the Bspline interpolation curve. However, due to the nonlinearity of the associated constraint equations, it is nontrivial to compute the Bspline 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 Bspline quaternion curve; solid orientations; interpolation; rotation group; de Casteljau type construction method; iterative refinement solution
Citation:
MyoungJun Kim, MyungSoo Kim, Sung Yong Shin, "A C/sup 2/continuous Bspline quaternion curve interpolating a given sequence of solid orientations," ca, pp.72, Computer Animation 1995, 1995
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