Invariant representations of finite rotation matrices and some applications

Invariant representations of finite rotation matrices and some applications

Invariant spinor representations of finite rotation matrices

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Some Computational Properties of Rotation Representations

There are four main parameterizations of the rotation group SO(3). Two of them (rotation angle and axis, and the closely related quaternion components) as well as the matrix form of rotation representation are particularly of interest in computer vision, graphics, and robotics. Some of their computational properties are explored here. Operation counts are given for primitive operations of norma...

Principal Rotation Representations of Proper NxN Orthogonal Matrices

Three and four parameter representations of 3x3 orthogonal matrices are extended to the general case of proper NxN orthogonal matrices. These developments generalize the classical Rodrigues parameter, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensions. The developments presented generalize and extend the classical result known as the Cayley tran...