perspective divide

Dividing a homogeneous point's first coordinates by its last one to recover its true image-plane position.

The perspective divide converts a homogeneous coordinate $(x, y, w)$ back into an ordinary image-plane point $(x/w, y/w)$ . It is the step that makes projective geometry actually projective -- without it, homogeneous coordinates would just be an unnecessarily padded way of writing an affine transform.

Examples

The homogeneous point $(8,4,2)$ becomes the true pixel location $(4,2)$ once both coordinates are divided by $2$ .