Transformation matrix

2D

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

${\begin{pmatrix}1&0&0&x\\0&1&0&y\\0&0&1&z\\0&0&0&1\end{pmatrix}}$

${\begin{pmatrix}x&0&0&0\\0&y&0&0\\0&0&z&0\\0&0&0&1\end{pmatrix}}$

${\begin{pmatrix}x^{2}c'+c&xyc'-zs&xzc'+ys&0\\yxc'+zs&y^{2}c'+c&yzc'-xs&0\\xzc'-ys&yzc'+xs&z^{2}c'+c&0\\0&0&0&1\end{pmatrix}}$

with

${\begin{aligned}c&=\cos({\mathit {angle}})\\c'&=1-c\\s&=\sin({\mathit {angle}})\end{aligned}}$