Graphics › Coordinate spaces
Projection
Flattening 3D onto a 2D image. Two ways to do it: orthographic keeps everything its true size; perspective shrinks whatever's far away.
what the camera records
Rays converge on the eye, so the far object lands closer to the centre and is recorded smaller — that's the ÷ depth that gives a sense of distance. Widen the FOV and more of the scene crams onto the same image.
From a 3D volume to a 2D picture
The projection matrix takes the chunk of view space the camera can actually see — the view volume — and warps it into the canonical cube [−1, 1]³ (clip space / NDC). Whatever falls outside gets clipped; whatever's inside is squashed flat into the image when you drop the z.
Orthographic
The view volume is a box. Projection lines are parallel, so an object's on-screen size doesn't depend on its distance — near and far draw the same. Perfect for CAD, blueprints, isometric strategy games, UI, shadow maps. Defined by left/right/bottom/top/near/far; the matrix just scales and shifts each axis to land in −1…1.
Perspective
The view volume is a frustum — a pyramid with the tip chopped off. Projection lines converge on the eye, so distant things land nearer the centre and end up smaller: the look of a real photograph. Defined by a field of view, an aspect ratio, and near/far planes — see perspective & the divide for how the ÷w does the shrinking.
Which one?