I find a great article elaborating this.
It's known that the algorithm described in that paper was actually how NVIDIA GPUs performed rasterization (without clipping) for a number of years. (Although modern GPUs have reverted back to a more traditional approach based on clipping.)
To which surface are we projecting the point P? And why that surface?
So is w just z here?
I'm a little confused why w isn't always 1.