IME the trick to getting an intuitive understanding of quaternion rotations is just to treat them as "basically axis-angle". The vector part of the quaternion is the axis and the scalar part is "basically the angle". 1/2
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I know that's not really true, but it's good enough to get started, and then you can learn all about bivectors and Clifford algebras and whatnot later once you have the basic intuition. 2/2
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