[marctenbosch]

I think matrices are easier for people to visualize because they can think about them as a vector frame and coordinate transformations.

Quaternions are seen as this abstract 4D space somehow containing 3D space transformations, and people have a much harder time visualizing 4D space. I do not think spending a lot of time trying to visualize this 4D space, like this video does, is the right way to go. Rotors make that method obsolete.

[jacobolus]

To be honest the hardest part is not understanding single rotations, but understanding how rotations compose.

Thinking about a scalar + bivector as the quotient of two vectors or as the composition of two reflections is easy enough. But that still doesn’t yield a solid understanding of how rotation works – 3D rotation is subtle and tricky, even for people who have pretty good spatial reasoning and a lot of experience working with solid geometry / 3D design.

I have been thinking about the best interactive diagram(s) for giving people a good intuition about that for a long time, and I have some ideas but I still haven’t implemented anything and I’m not sure how well it will work.