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Re: Averaging quaternions [message #38703 is a reply to message #38643]

Mon, 22 March 2004 00:54

Arnold Neumaier
Messages: 5
Registered: March 2004

Junior Member

jelansberry wrote:

> I'm not following what you mean by a "normalization" interval (or
> "normalization bounds" below). Euler angles do not require "normalization."
> I still maintain that any "discontinuity" in the Euler angles usually is the
> result of passing through the singularity that exists in any three-parameter
> representation of the direction cosine matrix, and it is generally easy to
> avoid this situation.

No. One has this phenomenon alreasy in 2D rotations. The rotation angle is determined
only up to a multiple of 2 pi, and one has to normalize the angle by, say,
forcing it into the interval ]-pi,pi]. Then you get problems in averaging
two very close rotation angles, one just below pi, one just abouve -pi.
The result will be close to zero instead of close to +-pi.

If you choose as normalization interval [0,2 pi[, the same problem happens
when averaging a tiny rotation to the right (angle=eps) and to the left
(angle=2 pi-eps).

There is no way to avoid such discontinuities, and one has the same
problems in 3 dimensions, and with quaternions.

But the quaternion recipe I gave a few days ago works perfectly
if the rotations to be averaged are not too much scattered.

Arnold Neumaier

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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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