On the comparisons of unit dual quaternion and homogeneous transformation matrix (Q742334)

It is very well known that the group \(\mathrm{SE}(3)\) of direct Euclidean motions of \({\mathbb R}^3\) can be described, on the one hand, in terms of dual unit quaternions and, on the other hand, in terms of particular \(4\times 4\) matrices, which are addressed as `homogeneous transformation matrices' in the present article. The basic facts about these two approaches are recalled in detail, and their computational efficiency is discussed and compared.