The De Casteljau algorithm on SE(3)
Claudio Altafini
In A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek (eds.)
Nonlinear Control in Year 2000, Springer-Verlag, 2000.
Smooth closed-form curves on the Lie group of
rigid body motions are constructed via the De Casteljau algorithm.
Due to the lack of a bi-invariant metric on $SE(3) $, the resulting
curve depends on the choice of the metric tensor.
The two most common cases are analyzed
postscript file (g-zipped)