= Principal point
In an ideal <camera> model, the <principal point> is the intersection of the <optical axis> with the image plane, expressed in image <pixel> coordinates $(c_x,c_y)$. It supplies the coordinate offset in <perspective projection>. For a scene point $(X,Y,Z)$ expressed relative to the <camera>, the model is
$$
u=f_x\frac{X}{Z}+c_x,\qquad v=f_y\frac{Y}{Z}+c_y,
$$
where $f_x,f_y$ are <focal lengths> in <pixel> units. Thus the <principal point> belongs to the camera's internal geometry; the <camera>'s position and orientation in the world are separate parameters.<Camera Calibration and 3D Reconstruction by OpenCV>[Detailed Description, intrinsic matrix and pinhole projection equations]{ref}
For $f_x=800$, $c_x=320$, $X=0.1$ metres and $Z=2$ metres, the horizontal coordinate is $u=360$ pixels. A point on the <optical axis> instead has $X=Y=0$ and projects to $(c_x,c_y)$. The <principal point> is often near the image center, but <camera calibration> estimates it rather than establishing that it must be exactly centered. Cropping an image also changes the <principal point>'s coordinate values: removing 20 columns from the left changes $c_x=320$ to $300$, without physically moving the <optical axis>.
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