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=== Quaternions as Motors === First, the quaternions are exactly the subset of [[motors]] that perform pure rotations about the origin without any translation. In ...

...and the functionality is properly generalized in rigid geometric algebra. Motors cannot perform improper isometries that include an odd number of [[reflecti Motors are capable of representing any general screw motion consisting of a rotati ...

...tion of both the product and antiproduct allows us to calculate a complete dual of any element using only the multiplication and reversion operations of th ...ct into 3D space. This nicely consistent rule means that purely rotational motors are the unit quaternions that we would expect. ...