[corysama]

It's fun that there have been many approaches to interpolating rotations (geometric algebra, quaternions, even full-matrix interpolation [1]). But, after hand-optimizing the code, the final code ends up mostly the same for all approaches. The difference is in your understanding of the rules and capabilities.

From what little I know, GA seems like the most consistent and capable approach. It's unfamiliar. It's a bit much to take in getting started. But, people who clear that hurdle love it.

Alternatively, everybody uses quaternions while complaining they don't understand them and need a whole book to visualize them. (Visualizing Quaternions by Andrew J. Hanson, Steve Cunningham)

[1]https://www.gamedev.net/tutorials/programming/math-and-physi...

[epistasis]

I'm not a mathematician, and don't have a ton of use for geometry in my work, but was learning GA for fun, and have similarly tried to learn quaternions in the past. GA is fun, quarternions are not fun. I think I understand GA, but I knew I did not understand quaternions after working through lectures and problems. Now that I know some GA, I kind of feel like a I know quaternions, finally.

[segfaultbuserr]

> I think I understand GA, but I knew I did not understand quaternions after working through lectures and problems.

Most physicists stopped using them at the end of 19th century for the same reason...

> More than a third part of a century ago, in the library of an ancient town, a youth might have been seen tasting the sweets of knowledge to see how he liked them. He was of somewhat unprepossessing appearance, carrying on his brow the heavy scowl that the "mostly-fools" consider to mark a scoundrel. In his father's house were not many books, so it was like a journey into strange lands to go book-tasting. Some books were poison; theology and metaphysics in particular they were shut up with a bang. But scientific works were better; there was some sense in seeking the laws of God by observation and experiment, and by reasoning founded thereon. Some very big books bearing stupendous names, such as Newton, Laplace, and so on, attracted his attention. On examination, he concluded that he could understand them if he tried, though the limited capacity of his head made their study undesirable.

> But what was Quaternions? An extraordinary name! Three books; two very big volumes called Elements, and a smaller fat one called Lectures. What could quaternions be? He took those books home and tried to find out. He succeeded after some trouble, but found some of the properties of vectors professedly proved were wholly incomprehensible. How could the square of a vector be negative? And Hamilton was so positive about it. After the deepest research, the youth gave it up, and returned the books. He then died, and was never seen again. He had begun the study of Quaternions too soon.

- Oliver Heaviside, Electromagnetic Theory

[lupire]

Naive Lie Theory is a great book, and the first chapter teaches quaternions.

https://www.goodreads.com/en/book/show/4419538

[dustingetz]

also Physics from Symmetry spends 1/3 the book on lie theory passing through quaternions

https://www.amazon.com/Physics-Symmetry-Undergraduate-Lectur...