From Gortler's Foundations of Computer Graphics (i.e., self-study):Let $\mathbf{\vec{e}}^t = \mathbf{\vec{w}}^t E$ and let $P$ be a camera matrix that is just some arbitrary $4$ by $4$ matrix with dashes in its 3rd row. Given the world coordinates of 6 points in space as well as their normalized device coordinates, how would one compute the 12 unknown entries in the matrix $PE^{-1}$? (Note: this can only be solved up to an unknown scale factor) (Hint: set up an appropriate homogeneous linear system with a right hand side of zero).Here the dashes matrix the author refers to takes form$$\begin{bmatrix}n_1 & 0 & a & 0 \\0 & n_2 & b & 0 \\- & - & - & - \\0 & 0 & -1 & 0 \\\end{bmatrix}$$where we do not care what the values with dashes are. How does one use the hint to solve this problem? I think we can infer that $a$ and $b$ (the scale factors) are undetermined, but that we can infer what the $n_1$ and $n_2$ are.
Solving a problem from *Foundations of Computer Graphics*:
projections;matrices