@lisyarus

> it is just matrix multiplication (or is it called AI these days?)

LOL

@lisyarus
Very thorough. I'll have to book mark it. It makes my old brain hurt.

I've always used transformation matrices derived from Euler angles. However I work with the perl PDL a lot, and internally their 3d graphics routines use quaternions. It might be useful for me to understand how to use them someday.

@lisyarus Under "Quaternions in Clifford (aka geometric) algebra" near the end, there's a problem with your definition of i, j, and k. Notice that ij ≠ k, but instead ij = −k, so these are not actually isomorphic to the quaternions. You need to negate all three bivectors so that i = −e₂₃, j = −e₃₁, and k = −e₁₂.

@lisyarus There's also a typo in the "Quaternions in Clifford (aka geometric) algebra" section where you accidentally say e₁e₃ = −e₃e₂. There's another typo in the first line of the "Dot product via conjugation" section where the closing parenthesis is missing for (w,x,y,z).

@lisyarus I am not a statistically significant sample, but I really enjoyed this! 😃

It is (obviously) the kind of topic one could write a book on, so in a blog post choices need to be made on what to include and what to skip. But overall it feels like a nice stepping stone for anyone who would like to learn about quaternions!