The plane is a choice
A projection has a centre and a surface, and they move independently. Keep the eye and turn the picture plane and every point of any scene lands where one 3×3 matrix says, to 2.5e-13 px. Move the eye instead and the matrix fitted to four points is exact at those four and out by 32.0 px everywhere else. The first is a homography of the picture; the second is parallax, and nothing about the picture can undo it.
part 3 · construction