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...the FGED series. However, I knew at the time that I didn’t want to present dual quaternions in the usual ways that they have always been introduced in the ...thbf b(\mathbf a x \mathbf a)\mathbf b = \mathbf{ba} x \mathbf {ab}$$. Two reflections produce a rotation that we represent by the quaternion $$\mathbf q = \mathb ...

...ich is a line when $$n = 3$$. Geometrically, these two interpretations are dual to each other, and their distances to the origin are reciprocals of each ot ...responds to the one-dimensional space of the point that it represents. The dual of a point materializes when we consider all of the directions of space tha ...

...Plücker coordinates, [[quaternions]], and screw theory (which makes use of dual quaternions). This makes rigid geometric algebra a natural fit for areas of ...de of its inputs and outputs, we can make the same statement about how the dual operation relates to the antigrade of its inputs and outputs. ...

...Motors cannot perform improper isometries that include an odd number of [[reflections]]; those are instead performed by operators called [[flectors]]. ...