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 = qw²+qx²+qy²+qz² = 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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