I have some equations I would like to convert to an homographic matrix in order to help me to apply some transformations to my images. In the first case I have these two linear equations: $$ x' = A + Bx + Cy $$ $$ y' = D + Ex + Fy $$ The homographic matrix must be an affine homographic matrix and I thought it was something like that $$ H=\begin{pmatrix}B&C&A\\E&F&D\\0&0&1\end{pmatrix}$$ but when I try to have a scale different of 1 it does not work.
My other equations are of the forms: $$ x' = A + Bx + Cy + Dxx + Exy + Fyy $$ $$ y' = G + Hx + Iy + Jxx + Kxy + Lyy $$
This time I would expect something like that $$ H=\begin{pmatrix}B&C&A\\H&I&G\\..&..&1\end{pmatrix}$$ but I don't really know. If someone can help me with this.
Thank you.