Even with all the new techniques for Euclidean geometry in the previous three chapters, the possibilities of the conformal model are not exhausted. There are more versors in it, and they represent other useful transformations. Euclidean motions were just a special case of doing conformal transformations, which preserve angles. These also include reflection in a sphere and uniform scaling.

All conformal transformations are generated by versor products using the elementary vectors of the conformal model. Whereas the Euclidean motions of the previous chapter involved using the vectors representing dual planes, we now use the dual spheres. An important operation we can then put into rotor form is uniform scaling, and that ...

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