I am writing a bilinear interpolation method.
This method can be abstract by solve the equation $Ax = b$, $A$ is a $4\times 4$ matrix below: $$A=\begin{pmatrix} 1 &x_1 &y_1 &x_1y_1\\ 1 & x_2 & y_2 & x_2y_2\\ 1 & x_3 & y_3 & x_3y_3\\ 1 & x_4 & y_4 & x_4y_4\end{pmatrix}$$
Here, $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ and $(x_4, y_4)$ are four points containing the dst interpolation point.
My problem is when $\det(A) = 0$ (then $x \neq A^{-1}b$), what is the quadrangle looks like?