Difference between revisions of "Realization of transformations"
From Robotics
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</math> | </math> | ||
The quaternion <math>e</math> is equivalent to <math>\mathbf{R}</math> and describes the rotation while <math>p</math> is defined as <math>0 \oplus \vec{\mathbf{p}}</math> and so equivalent to the translation. | The quaternion <math>e</math> is equivalent to <math>\mathbf{R}</math> and describes the rotation while <math>p</math> is defined as <math>0 \oplus \vec{\mathbf{p}}</math> and so equivalent to the translation. | ||
+ | :<math> | ||
+ | e \equiv \mathbf{R} \qquad \quad p = 0 \oplus \vec{\mathbf{p}} | ||
+ | </math> |
Revision as of 10:55, 15 October 2015
← Back: Composition of rotations | Overview: Quaternions | Next: ??? → |
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.