I have a following optical system: 3 cams (left and top, which is orthogonal to the left, and right, which is parallel to the left and orthogonal to the top) and the 2 cubes in the 3D-space with following coordinate system:
Each of the points $P_t$, $P_l$, $P_r$ lies in the middle point of the appropriated side on the cube. The length of the each cube's side (left and right) is $c$ (in mm). The cubes are parallel to each other. The distance between the points $P_lP_r = w$
From the optical recognition (matching) I know the 2D-coordinates of these points on the projections in px: $P'_l = (P'_lx, P'_ly)$, $P'_t = (P'_tx, P'_ty)$, $P'_r = (P'_rx, P'_ry)$. The distances from the origin to the projection are also defined: $OO_l = d_l$, $OO_l = d_l$, $OO_r = d_r$ in mm.
The focal lengths $f_l$, $f_t$ and $f_r$ can be also defined and used if needed.
In order to calculate the 3D-coordinates of the cube I need to calculate the scale factor that allows to covert the projections 2D-coordinate in px to the real coordinate in mm.
So how is can I calculate the $P_lx$, $P_lz$ in mm (from the left projection), $P_tx$, $P_ty$ in mm (from the top projection), $P_rx$, $P_rz$ in mm (from the left projection)?
Can someone please help me to solve this problem?