Quaternion, why divide angle by 2?

Finn The Human · 2018-09-22T10:31:01

I'm trying to understand why the formula for creating a quaternion from an axis angle representation divides theta by 2: \(cos(\theta / 2), \hat{v}sin(\theta/2)\) As far as i understand this is because quaternions do double cover? IE a quat represents 720 degrees of rotation, not just 360? But that doesn't make much sense to me, since cos(45) = cos(45+360) = cos(405). Like any input to cos is going to yield the same output. So yeah, i don't get this, why is the angle divided by 2?

Math and Physics Programming

Started by mathematical September 18, 2018 06:03 AM

10 comments, last by mathematical 6 years, 4 months ago

mathematical

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September 22, 2018 10:31 AM

Thanks everyone for helping, i think this post is resolved

@Maciej Mizerski between your two posts i gained a lot of insight into how quaternions work, tough it's much less visual than i'd hoped ? Your insight was very helpful and much appreciated.