No, unfortunately the exponential map actually has neither the short route or the long route. They take an erroneous (not torque-minimal) path when interpolating, and thus aren't generally suitable for arbitrary interpolation. This is another reason why you don't want to use them. Quaternions allow you to have both the short route and the long route (you want both - I can't emphasize this enough - it is a fallacy to suggest that not having the long route would be a good thing!), your choice. Quaternions also offer your choice of interpolator, since you can't have both for spherical interpolation: slerp gives you constant speed, but only 2 endpoints, whereas lerp doesn't give you constant speed but supports an arbitrary number of endpoints.
I guess I should make this clear that everything you guys say about quaternions is true
, no one should have a single doubt about how good quaternions for rotations are. I use them everywhere the day I realized matrices are retarded, and will keep using them because of all the things they can do.
But this thread is simply not about quaternions! :)
No, unfortunately the exponential map actually has neither the short route or the long route.
Wait, maybe I don't know what the short route means, because I thought it's when an angle exceeds 180° it inverses the axis and rotates 360° - angle, i.e. in other direction, to take the minimal path? This is what I see from numbers Gibbs vector shows, it's what direction example shows in the code from the first page, I can make a 3D example, but a proper fix should be found first to make interpolation work for >90° angle difference without big error accumulation.
They take an erroneous (not torque-minimal) path when interpolating
Not sure what you mean by "erroneous path", any path they take in any direction looks applicable for instant and <90° rotations so far, maybe I miss something.
EDIT: If it's about torque for >90° rotations (<90° rotations have torque too, but at max the error is 8°, I consider it not big, opinions may vary), I can repeat myself the third time: yes, it's a real deal breaker
right now, I think maybe it has a fix I currently miss.