Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given multiple quaternions representing orientations, and I want to average them. Each one has a different weight, and they all sum up to one.

How can I get the average of them? Simple multiplication by weights and addition won't work, since it doesn't take into account that (qw, qx, qy, qz) = (-qw, -qx, -qy, -qz)..

share|improve this question
Google gives en.wikipedia.org/wiki/Generalized_quaternion_interpolation Someone who knows more may be able to expand. –  Peter Taylor Sep 1 '11 at 9:50

1 Answer 1

up vote 1 down vote accepted

I assume you are thinking of unit quaternions and you are using them to represent rotations? If that is the case then here is a paper on the related subject of means and averages in the rotation group. It might not be a very easy read though if you don't understand the notation.

Barring that, Here's what I might try: Pick a canonical form for your quaternions. Then convert each to the canonical form and finally perform your weighted linear combination.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.