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Re:Visualizing quaternions: An explorable video series by erichocean on Friday October 26, 2018 @06:47PM (#18313254)
They're basically the ratio of two vectors, if that helps.

Check out Geometric Algebra for more info, specifically the 5D Conformal model [0]. It's way easier to use than linear algebra and that acres of sin()/cos()/tan() scattered everywhere in your code.

[0] http://versor.mat.ucsb.edu/

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