Talk:Quaternions and spatial rotation: Difference between revisions

Revision as of 15:46, 5 July 2016

Revision as of 16:09, 5 July 2016

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::::The responding editor is correct; we do not allow external links in the body of an article and this is typically associated with spam and linkbait. On the other items, we would probably want independent secondary sources about the results if they were to be included, such as press articles, review articles in academic journals, etc. rather than getting the information directly from a paper publishing original research. [[User:CorporateM|CorporateM]] ([[User_talk:CorporateM|Talk]]) 19:53, 18 January 2015 (UTC)

Can someone please give a reference and/or rewrite the section [[Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix]] to actually give a derivation of athe rotation matrixmatrices from a quaternion transformation. In other words, the section needs more mathematical elaboration / a concrete proof / a reference that the sandwich product in the quaternion transformation <math>q * v * q^{-1}</math> is equal to the end result 3D rotation matrixmatrices described in the section.:

: <math> \mathbf{R}=

\begin{bmatrix}

c + a_x^2 (1-c) &

a_x a_y (1-c) - a_z s &

a_x a_z (1-c) + a_y s \\

a_y a_x (1-c) + a_z s &

c + a_y^2 (1-c) &

a_y a_z (1-c) - a_x s \\

a_z a_x (1-c) - a_y s &

a_z a_y (1-c) + a_x s &

c + a_z^2 (1-c)

\end{bmatrix}

</math>

where <math>s</math> and <math>c</math> are {{math|sin ''&theta;''}} and {{math|cos ''&theta;''}}, respectively; as well as the rotation matrix:

: <math> \mathbf{R} = \begin{bmatrix}

1 - 2 q_j^2 - 2 q_k^2 &