I am attempting to rotate a vector3 by a given quaternion.

I know that this is true

v' = q * v * (q^-1)


I know that q^(-1) is the inverse which just -q/magnitude(q), but how do I map the multiplication of the vector to the quaternion to get back a vector?

I have found that you can treat v as a matrix, and convert q, and q' to matrices, and then convert v' from a matrix to a vector, but this seems a little over the top just to get a vector. Is there a cleaner implementation that I could use?


Question: Looking for a word with a more positive connotation than "infectious"
Answer: "Contagious smile" and "infectious smiles" are very strong collocations which have a positive connotation. I don't think we really have much choice but to use these expressions when describing an amazing smile that makes others smile, too.