I am reading Introduction to Algebraic Geometry by Justin R. Smith, and Exercise 2 of section 1.6 (p.33) states the following:
In computer graphics, after a scene in $\mathbb R P^3$ has been constructed, it is viewed — i.e., there is a “camera” that photographs the scene with proper perspective. Suppose this camera lies at the origin and is pointed in the positive $z$ direction. Describe the mapping that shows how the scene looks. How do we handle the situation where the camera is not at the origin and pointed in the $z$-direction?
The answer for the first part (camera at origin) says it is given by (from $\mathbb R^3\subset\def\R{\mathbb R}\R P^3$ to $\R P^2$)
$$\begin{bmatrix}x\\y\\z\\1\end{bmatrix}\mapsto\begin{bmatrix}x\\y\\z\end{bmatrix}$$
I'm very confused by where this comes from, especially because this answer seems totally independent of the fact that the camera is facing $z$-axis.
OK, I realize that the point is we are making the plane $z=0$ become points at infinity, and this is achieved by making $z$ (implicitly) the last coordinate in $\mathbb R P^2$.