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Quaternions and their exponential form

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I've just started working with quaternions and have already managed to get it working to perform various kinds of rotations. The main operation that I use both for calculating rotations and for their combining is, of course, the standard quaternion multiplication which takes 16 scalar multiplications and 12 scalar additions.

I've also heard, that a lot operations with quaternions may be optimized by using their exponential form (here, for example) and some "substitute" for the Euler's formula which is working for quaternions (here). It turned out for me, however, to be a problem to find concrete examples of how to use it in code. I've only found that the formula is mostly used for performing interpolations (but no examples of it either).

So, my questions are: can anyone tell if there is a real use of such things in 3D-programming, and, if yes, are there any ways for me to use it if there are no interpolations in my game (I'm rotating moons around the planets of the solar system, so that is just useless)?

Thanks a lot!

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