S'far as I've been reading, it applies a 4-parameter adjustment to a 3 dimensional vector. It is not, in and of itself, a 'point'.
It is arguably a way of representing a function taking a (3-d)vector and producing a new (3-d) vector with a new orientation and scale.
The best description I've seen so far is that, whereas a vector could be said to be an operation that, applied to a point, gives another point, a quaternion can be said to be an operation that, applied to a vector, gives another vector.
And I have no trouble believing that it _does_. I just want to know (derive) precisely _how_.
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