Here we have some axial hints. They create three leafs, A B and C. You’ll notice that area B has a non-axial side. Big whoop-dee-doo, this doesn’t affect things one bit.
The blue tinted area is a raytrace of player1’s line of sight. He can see directly see everything that is shaded.
The gray area is the Potentially Visible Set (I wrote “Viewable”, sue me). Everything in this area is drawn by the graphics card regardless of the fact that the player can’t physically see most of the stuff in area C. You will notice that everything is shaded gray. That is because in this situation, axial hints are in a least efficient possible position.
Because player1’s line of sight includes just a small part of area C, all of area C and beyond is drawn. Not very efficient silly mapper!
Here, we see Player2’s line of sight. He can’t directly see into area C at all but it is still included in his PVS. Why? Because he has the potential of moving over to Player1’s position where area C is part of his line of sight. Imagine that there are actually large rooms beyond the doorways of this hallway on either end. Standing anywhere in one of those rooms, everything in the entire map will still be completely drawn because of badly placed hints. Yuck.
To fix, we have here a single diagonal hint. It now has 4 leaf nodes. The number of leaf nodes doesn’t exactly co-relate to efficiency. What is important is reducing the amount of geometry being drawn in the game world. That’s the whole point of the PVS and leaf nodes in the first place.
You can see that Player1’s LOS includes areas A B C, but no part of area D is not part of his LOS. He can move anywhere in area B and his LOS will never include area D. So we can drop area D from his PVS. Nothing in area D or beyond will be drawn. Yay.
Let’s say Player1 moves to Player2’s position in this newly hinted area. Player2 can move anywhere in area A and his LOS will only include areas A and B. As long as he stays in area A, C and D will never become part of his LOS so areas C and D are dropped from his PVS and are not drawn.
As you can see, in this situation, diagonal hint brushes are more useful than axial hint brushes. Keep in mind, this does not mean that diagonal hint brushes are always better, just better in situations like this. There are plenty of other cases where axial hints will do a better job. It all depends on the situation.