Editing WoW:SetTexCoord Transformations (section)

===Affine transformations as matrices===
You'll note my matrix example was a 3 dimensional coordinate, and a 3 by 3 matrix, this is because a 2 dimensional matrix isn't enough to represent an affine transformation by itself, because it cannot represent translation. The trick is to add a 'dummy' z coordinate, which ALWAYS has the value 1, and then use the following matrices:

<math>
\begin{pmatrix}
X\\
Y\\
1
\end{pmatrix}
=
\begin{pmatrix}
A&B&C\\
D&E&F\\
0&0&1
\end{pmatrix}
\times
\begin{pmatrix}
x\\
y\\
1
\end{pmatrix}
</math>

Which then yields:
 X = Ax + By + C
 Y = Dx + Ey + F
 1 = 1

In this case, A,B,D,E represent scaling, shearing, and rotation, and C,F represent translation. Matrices of this form also multiply together properly, preserving the last row in the correct format.