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Rotation matrix

From Biocrawler, the free encyclopedia.

A rotation matrix is a matrix that generalizes the concept of a rotation of a set of points around a certain axis, about some arbitrary angle (or consequently rotating the axes about another axis).

For the former, in R³, the rotation about the x-axis is given by:

$\begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos{\theta} & \sin{\theta} \\ 0 & - \sin{\theta} & \cos{\theta} \end{pmatrix}$

The rotation about the y-axis is given by:

$\begin{pmatrix} \cos{\theta} & 0 & - \sin{\theta} \\ 0 & 1 & 0 \\ \sin{\theta} & 0 & \cos{\theta} \end{pmatrix}$

The rotation about the z-axis is given by:

$\begin{pmatrix} \cos{\theta} & -\sin{\theta} & 0 \\ \sin{\theta} & \cos{\theta} & 0 \\ 0 & 0 & 1 \end{pmatrix}$

with the equivalent clockwise rotation in R² can be given from the minor M_3,3 of the rotation about the z-axis.

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Rotation matrix

From Biocrawler, the free encyclopedia.

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