7.1 Description

$\mathrm{SL}(3)$ is the group of unit-determinant linear transformations, representing among other things homographies on the 2D projective plane. It has eight degrees of freedom: two for translation, one for rotation, one for scale, one for stretch, one for shear, and two for perspective change. Subgroups include $\mathrm{Aff}(2)$ and $\mathrm{SO}(3)$ .

$\displaystyle \mathbf{H}$	$\displaystyle \in$	$\displaystyle \mathrm{SL}(3)\subset\mathbb{R}^{3\times3}$	(83)
$\displaystyle \det\left(\mathbf{H}\right)$	$\displaystyle =$	$\displaystyle 1$	(84)

Ethan Eade 2012-02-16