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Re: Averaging quaternions [message #38628 is a reply to message #38627]

Fri, 19 March 2004 07:14

John Lansberry
Messages: 3
Registered: March 2004

Junior Member

"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

Hi Graham,

It might help a lot to explain a little more about what you mean by
"regularly sampled" and "averaging."

Do you mean that you have time samples of quaternions over time? In other
words, you have q(t1), q(t2), q(t3), etc., where t1, t2, t3, etc. are evenly
spaced time points (not that even spacing is all that important).

Is each sample a valid quaternion?

By "averaging," what do you really want?

SLERP (as suggested by OUP) is generally used to interpolate between two
(valid) quaternions. The result is always a valid quaternion. SLERP is in
fact valid for any two unit vectors of equal dimension (not just
quaternions). So, you can use SLERP to find the quaternion at the midpoint
of your time interval and call that an "average".

My guess is that you need something more complex - try Googling on
"averaging quaternions".

John

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[Message index]

		Re: Averaging quaternions By: Arnold Neumaier on Fri, 19 March 2004 08:24
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 07:22
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 07:14
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 06:53
		Re: Averaging quaternions By: One Usenet Poster on Thu, 18 March 2004 20:17
		Re: Averaging quaternions By: Craig Markwardt on Thu, 18 March 2004 15:39
		Re: Averaging quaternions By: GrahamWilsonCA on Mon, 29 March 2004 12:45

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