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Re: Averaging quaternions [message #38712 is a reply to message #38643]

Sat, 20 March 2004 07:23

jelansberry
Messages: 3
Registered: March 2004

Junior Member

I've finally realized that all I contributed was questions and complaints
and no alternative solutions.

If I were doing this, I would probably convert the quaternions to Euler (or
Bryant) angles first (convert the quaternion to a direction cosine matrix,
then extract the Euler angles). Then, I would compute the average of the
Euler angles, and then convert the resulting average Euler angles back to a
quaternion (convert the Euler angles to a direction cosine matrix, then
extract the quaternion).

The only thing you have to worry about with Euler (or Bryant) angles is that
there will always be a singularity for any chosen sequence. For example, if
you choose a 3-2-1 Bryant sequence (i.e., first rotation about the 3-axis,
second rotation about the subsequent 2-axis, third rotation about the
subsequent 1-axis) then there will be a singularity whenever the second
rotation angle is an odd multiple of 90 degrees (in that case, there is no
unique solution for the first and third rotation angles). However, you can
always look at the data and select an Euler (or Bryant) sequence that has no
singularity.

John

"Graham" <GrahamWilsonCA@yahoo.ca> wrote in message
news:eda30d78.0403181434.229b3b53@posting.google.com...
> Does anyone know if it is possible to take an average of regularly
> sampled quaternions to get a mean orientation (i.e. a mean rotation
> matrix)? I seem to recall there being a trick involved but beyond
> re-normalizing the resuling (averaged) quaternion, I cannot remember
> what it is.
>
> Cheers,
> Graham

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[Message index]

		Averaging quaternions By: GrahamWilsonCA on Thu, 18 March 2004 14:34
		Re: Averaging quaternions By: Arnold Neumaier on Mon, 22 March 2004 00:54
		Re: Averaging quaternions By: jelansberry on Sun, 21 March 2004 15:26
		Re: Averaging quaternions By: Arnold Neumaier on Sun, 21 March 2004 09:48
		Re: Averaging quaternions By: jelansberry on Sun, 21 March 2004 09:15
		Re: Averaging quaternions By: Arnold Neumaier on Sun, 21 March 2004 00:47
		Re: Averaging quaternions By: jelansberry on Sat, 20 March 2004 07:23
		Re: Averaging quaternions By: Arnold Neumaier on Tue, 30 March 2004 02:53

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