  This paper revisits the little-known Gibbs-Rodrigues representation of
rotations in a three-dimensional space and demonstrates a set of algorithms for
handling it. In this representation the rotation is itself represented as a
three-dimensional vector. The vector is parallel to the axis of rotation and
its three components transform covariantly on change of coordinates. The
mapping from rotations to vectors is 1:1 apart from computation error. The
discontinuities of the representation require special handling but are not
problematic. The rotation matrix can be generated efficiently from the vector
without the use of transcendental functions, and vice-versa. The representation
is more efficient than Euler angles, has affinities with Hassenpflug's Argyris
angles and is very closely related to the quaternion representation. While the
quaternion representation avoids the discontinuities inherent in any
3-component representation, this problem is readily overcome. The present paper
gives efficient algorithms for computing the set of rotations which map a given
vector to another of the same length and the rotation which maps a given pair
of vectors to another pair of the same length and subtended angle.
