[blt]

This is a great comment. As someone who is familiar with R^3 geometry but not projection or clipping, I feel like I could almost implement it from your comment alone.

Can you explain more about clipping before/after the divide by w operation? Is this about avoiding coordinates with w = 0? Otherwise all the geometric ideas seem to make sense in both the world/view-space frustum and the ±1 box.

[Sharlin]

Essentially, yes. The points of any edge that crosses the near plane escape to the infinity and if you naively just w-divide the endpoints, the image of the lineseg is not the points between the endpoints, but actually all the other points on the line that "wrap around" through infinity. The projective space not only contains all the points at infinity, it identifies each pair of infinity points "opposite" to each other (and then maps them to the w=0 plane), so lines are actually loops and between any two points there are two distinct line segments, an "internal" and "external" one. This is disconcerting to say the least.

Moreover, all geometry that is fully behind the camera will actually get projected in front of the camera into the distance by the w division because they have z<0, w<0 so the signs cancel out. I think clipping against the back plane would get rid of these, but it's still weird. And now my brain hurts.

Historically, of course, divisions were expensive and culling as much as possible before the perspective division was a performance question as well.