Aren't the objects in a different coordinate system (world coordinate) than the camera coordinate? Don't we need a coordinate transformation from the world to the camera before perspective projection?
Can perspective projections be used to reduce the number of dimensions by more than 1 (such as going from 3d to 1d or from 4d to 2d)? What do objects in more than 3 dimensions look like?
On an unrelated note, in animated movies and videogames do we rely on one base "pinhole camera" point in 4d or 3d in order to render every frame's scene objects relative to the "camera"'s rotation and position?
What would it look like if we projected onto the x or y plane instead?