# Maths - Rotations using quaternions - mail from zit0un

From: Zeiht'Oon
To: Martin Baker
Date: 14:38 17-11-04 GMT
Subject: Re: Quaternoins

Hello Martin !

I didn't give any news since I left my quaternion manipulation for a while, but now I'm back !
And I think I noticed a little mistake in your page on "rotations using quaternion"
<https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/index.htm>

```When you develop the product P2 = q * P1 * q' you get P2.w not null, but my    computations give me such a value.
Maybe you forgot one sign. My computations give
P2 =
(w)
0(x)
2 2
qx x + 2 qx qy y + 2 qx qz z + qw x + 2 qw qy z - 2 qw qz y 2 2
- qz x - qy x(y)
2 2 2
2 qy qx x + qy y + 2 qy qz z + 2 qz qw x - qz y + qw y 2
- 2 qw qx z - qx y(z)
2 2
2 qz qx x + 2 qz qy y + qz z - 2 qy qw x - qy z + 2 qx qw y 2 2
- qx z + qw z```

Have a nice day !

zit0un

---------------------------
From: Zeiht'Oon
To: Martin Baker
Date: 14:54 17-11-04 GMT
Subject: Quaternions : next episode...

Hi Martin, it's me again !

I forgot to tell you that I think it would be better to do the following on the "Rotations using quaternion" page :
when you want to develop P2 = q * P1 * q', you should take P1=(1,x,y,z), I think.
This is more consistent with a 3D representation of the points where P1 = (x/1,y/1,z/1)...

so the result is P2.w = qwÂ²+qxÂ²+qyÂ²+qzÂ² = 1 (as q is normalized) and nothing change for the other coordinates.

If you have Maple, the attached file could be useful...

Have a nice day !

zit0un

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 metadata block see also: Correspondence about this page Book Shop - Further reading. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them. Quaternions and Rotation Sequences. Specific to this page here:

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