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Re: Did you know....

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xXIcanthinkofanameXx is not online. xXIcanthinkofanameXx
Joined: 05 May 2012
Total Posts: 857
10 Jul 2016 12:59 AM
You can actually take the natural logarithm of a quaternion. And you can raise e to the power of a quaternion. Math is weird.
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ElectroTM is not online. ElectroTM
Joined: 23 Nov 2012
Total Posts: 1135
10 Jul 2016 01:01 AM
tracked because I'm not going to remember that, but it seems interesting. :P


y-you too...
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xXIcanthinkofanameXx is not online. xXIcanthinkofanameXx
Joined: 05 May 2012
Total Posts: 857
10 Jul 2016 01:05 AM
It's because of Eulers formula. e^(ia)=cos(a)+isin(a) but since quaternions are 4 dimensional it would be more like e^(na)=cos(a)+nsin(a) where n is the axis of rotation. So if you take ln(e^(na)) you just get na. And then taking e to the quaternion power is a bit trickier, but it's just the inverse.
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wfvj014 is not online. wfvj014
Joined: 30 Apr 2012
Total Posts: 145
10 Jul 2016 01:07 AM
:o
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xXIcanthinkofanameXx is not online. xXIcanthinkofanameXx
Joined: 05 May 2012
Total Posts: 857
10 Jul 2016 01:14 AM
That also means there's a one-to-one map from the set of unit quaternions to R3. So, there are as many unit quaternions as there are vectors in R3.
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