In fact, this group is Spin(3), the 2-fold cover of SO(3), the group of rotations of R. This has been known for quite some time and is perhaps the simplest realization of Hamilton’s expectations about the potential of quaternions for physics. One reason for the renewed interest is the fact that the resulting substitution of matrices by quaternions speeds up considerably the numerical calculatio...

A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points for which corresponding pairs have been determined. In this paper a comparative analysis of four popular and eecient algorithms is given. Each computes the trans-lational and rotational components of the transform in closed-form as the solution to a least squares formulation of the ...

A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points for which corresponding pairs have been determined. In this paper a comparative analysis of four popular and efficient algorithms is given. Each computes the translational and rotational components of the transform in closed-form as the solution to a least squares formulation of the...

Two solutions of the homogeneous matrix equation AX=ZB, that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot wrist coordinate frames, are proposed. The presented methods introduce the Kronecker product and dual quaternions to solve the rotations and translations problem, simultaneously, with no propagation error. The experimen...