[Bf-funboard] Euler for animator, Quaternions for Blender

[Bob Wenzlaff (AB8TD)]

At 12:13 AM 5/11/2007, you wrote:

>Hi all.
> From the current discussion, it seems to me that there are really interesting
>and highly professional people using Blender.
>I am really intrigued as to what Quaternions, Eulers are.

They are two systems for recording rotations.

Euler angles are your typical Roll/Pitch/Yaw angles.  The problem is 
the three values are not independent and have some singularities 
(gimbal-lock problem at 90 degrees pitch, roll has no effect 
independent from yaw).  A singularity is a spot where there is no 
precise mathematical solution.  Another way to think of the 
gimbal-lock problem is to ask yourself:  "What's my longitude if I'm 
at the north pole".

To solve this problem, a set of rotations can be broken into 4 parts 
called Quaternations.  Quaternations are independent and there are no 
singularities, but they don't represent rotations that can are 
conveniently visualized like Eulers are because they are a pure 
mathematical construct.

Thus internally we want to store animations rotations (at least) in 
Quats, but allow the user to edit in Eulers so he can visualize 
what's going on.  You need to smooth over the singularities, but 
since you have the object on the screen, and the user is providing 
feedback, you can make very good guesses as what to do at these 
singularities (ie; if you are heading towards the Northpole, your 
longitude is the direction you were heading from.)

Robert Wenzlaff



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