A more general answer. Grab a pen or pencil near you. Hold it so it is facing up. We will then define the three axis used.
First degree of freedom is rotating the pen so it still faces up.
Second tilt the pen down either towards, or away from you but not side to side
Last rotate the pen on the same axis as the first time, but because the pen is tilted down this time it will change where it is pointed.
this is a z-x-z euler angle configuration.
In the filter it appears to allow the pen to rotate toward and away from you in the second rotation whereas before it only was allowed to tilt towards you.
So lets get to the same orientation one with the restriction, one without.
Go to the starting position, rotate the pen 180 degrees along the first axis. Then tilt the pen toward you 45 degrees. Lastly rotate the pen around the first axis again 180 degrees. At this point the pen should be pointed away from you 45 degrees.
So after you apply the filter the angles change to no rotation on the first, tilt back 45 degrees on the second, and no rotation on the last. While I would have to play with my pen more to verify this it appears to keep the same orientation with the new y rotation you simply add 180 degrees to the first rotation, negate the second rotation, and subtract 180 degrees from the third rotation.
Go ahead and play around with your pen to make sure this works.
Edited by HappyCoder, 25 June 2013 - 02:05 PM.
In order to give you a concrete answer I would have to know the three axis that are used for the euler angles. Look on Wikipedia if you need clarification on what I mean. The angle system could be z-x-z, z-y-z, ect..