Usually affine transform matrix (in 2D) is represented like
A is responsible for linear transformation (no translation) and block
B is responsible for translation.
D is always zero and block
C is always one.
What if I put some values into blocks
C I will affect only third (bottom) component of 2D vector, which should be always 1 and usually plays no role.
But can it? Are there some generalizations, where third component plays some role and consequently, bottom row of transform matrix also does?
And one more question: does this decomposition is actual only for 2D? Is it the same for 2D and xD?