6.1 Description

$\mathrm{Aff}(2)$ is the group of affine transformations on the 2D plane. It has six degrees of freedom: two for translation, one for rotation, one for scale, one for stretch and one for shear. Subgroups include $\mathrm{Sim}(2)$ .

$\displaystyle X=\left(\begin{array}{c\vert c} \mathbf{A} & \mathbf{t}\\ \hline \mathbf{0} & 1 \end{array}\right)$	$\displaystyle \in$	$\displaystyle \mathrm{Aff}(2)\subset\mathbb{R}^{3\times3}$	(71)
$\displaystyle X^{-1}$	$\displaystyle =$	$\displaystyle \left(\begin{array}{c\vert c} \mathbf{A}^{-1} & -\mathbf{A}^{-1}\mathbf{t}\\ \hline \mathbf{0} & 1 \end{array}\right)$	(72)