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Let's say we have two rotated objects, there Euler-Angles are:

Object | x    |  y   |  z 
1      |  180 |  360 |  180 
2      | -360 | -720 |  360

Both use rotate order XYZ. When rotation is zero the local Y-axis is pointing up.

I'm trying to get the difference in Spins around their local Y-axis. As if there would be a string between the bottoms of Object 1 and Object 2 connected when all orientations were 0,0,0. How many times would the string have spun around / twisted?

Some examples:

#1 | 0, 360, 0
#2 | 0, 0,   0

1 full twist

#1 | 0, 180, 0
#2 | 0, 0,   0

1/2 twist

#1 | 360, 0, 0
#2 | 0,   0, 0

1 twist. (think about the string that was attached to it, this would also count as a twist in the string)

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I've been looking into orientation/rotation and it's different ways of using them, like Quaternions, Euler-Angles and Axis-Angle. I feel like I know how each work in general yet miss the skills for solving this.

Any ideas on how to solve this?

Beta
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Roy Nieterau
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  • What about X(180) followed by Y(180)? Would that be 1 twist or 0? Your question is not well-defined. – Beta Nov 20 '12 at 14:41
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    I agree with Beta. But let me clarify. Twists outside of 0 <= twist < 360 degrees don't really exist. Why? Well simply put there's no such thing when the rotation is slanted towards your axis. See the channels are not independent and all other rotation wobble. SO in reality there's no such data. Quaternions, matrices and axis angles work better because they recognize this fact. Using any of these methods normalizes the answer to the partial range. You can do a guess that doesn't really work in general. Maya know how to do one of these guesses by parenting the objects, no general solution tough – joojaa Nov 21 '12 at 06:35
  • Oh by the way even if you can define X(180) Y(180) What is a contamination where they counter rotate eg X(180) Y(-180)? And what if theres a Z rotation – joojaa Nov 21 '12 at 06:55
  • Those are exactly the issues I haven't been able to wrap my head around. On the other side it's possible to SLERP with Quaternions with a maximum rotation difference of 720 degrees (Michael Isner) yet I've just been unable to understand how that works, especially when thinking about the stuff you guys mentioned. Any thoughts/tips? – Roy Nieterau Dec 11 '12 at 23:14

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