Perspective projection

Projection from a fixed centre onto an image plane. With centre at the origin and plane $z=f$, a point $(x,y,z)$ with $z\ne 0$ maps to $(fx/z,fy/z,f)$. The image-plane convention may put the plane in front of the centre, giving a virtual upright image, or behind it, giving an inverted physical image.

Conversion of a transformed column of homogeneous coordinates $(X,Y,Z,W)$ with $W\ne 0$ to $(X/W,Y/W,Z/W)$. This is the nonlinear step in an otherwise matrix-based perspective projection pipeline.