Editing 2D computer graphics (section)

===In two dimensions===
[[File:Counterclockwise rotation SVG.svg|thumb|A counterclockwise rotation of a vector through angle ''θ''. The vector is initially aligned with the x-axis.]]
In two dimensions every rotation matrix has the following form:

:<math>
R(\theta) = \begin{bmatrix}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta \\
\end{bmatrix}</math>.

This rotates [[column vector]]s by means of the following [[matrix multiplication]]:

:<math>
\begin{bmatrix}
x' \\
y' \\
\end{bmatrix} = \begin{bmatrix}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta \\
\end{bmatrix}\begin{bmatrix}
x \\
y \\
\end{bmatrix}</math>.

So the coordinates (x',y') of the point (x,y) after rotation are:

:<math>x' = x \cos \theta - y \sin \theta\,</math>,
:<math>y' = x \sin \theta + y \cos \theta\,</math>.

The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. -90°).

:<math>
R(-\theta) = \begin{bmatrix}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta \\
\end{bmatrix}\,</math>.