Realization of transformations
From Robotics
← Back: Composition of rotations | Overview: Quaternions | Next: ??? → |
Quaternion notation for general transformations
Up to now transformations have been defined by homogeneous matrices combining a rotation matrix and a translation vector
. Now a new notation is introduced to represent a transformation using two quaternions
and
:
The quaternion is equivalent to
and describes the rotation while
is defined as
and so equivalent to the translation.
Applying such a transformation to a quaternion is done by first rotating
with
corresponding to the rotation equation and then adding
:
Combination of transformations
It is known that a combination of transformations is defined as: