Approve this tow Equations in photogrammetry $($a$)$

$($b$)$

FIGURE $10-5($a$)$ Auxiliary $x^{\text{'}}{y}^{\text{'}}$ image coordinate system for a tilted

photograph. $($b$)$ Principal plane of a tilted photo.

For any point in a tilted photo, the conversion from the $xy$ fiducial

system to the $x^{\text{'}}{y}^{\text{'}}-$tilted system requires $(1)$ a rotation about the principal

point through the angle $$ and $(2)$ a translation of origin from $o$ to $n.$ The

rotation angle $$ is defined as

$=-180$

The coordinates of image point a after rotation are $x_a^{\text{'}\text{'}}$ and $y_a^{\text{'}\text{'}},$ as shown

in Eig$\_10-5$a$.$ These coordinates, calculated in the same fashion as the $\frac{?}{\text{b}\text{a}\text{r}}(E{)}_C^{\text{'}}$

and $N^{\text{'}}$ coordinates of Eqs. $($C$-2),$ are specified by

$x_a^{\text{'}\text{'}}=x_{a}cos-y_{a}sin$

$y_a^n=x_{a}sin+y_{a}cos$