The rules say you can draw a line of fire through an exact diagonal between blocking terrain and hindering terrain, but can you make close combats if the opposing character is on an exact diagonal, one square away, but around the corner of blocking terrain.

X = blocking
C = character


C
XC

can C fight C close combat, and if not can they range if they are both grounded since you can draw line of fire?

they can do close combat

Here's another issue, which involves ranged combat behind a corner:

A character has a wall or another corner next to him, and tries to shoot diagonally another character that is also next to a corner. 3x3 piece of map: C (character) tries to shoot another character (also C). X is a piece of wall, or the edge of elevated terrain.

C_X
X_X
X_C

Both highlighted corners are on opposite sides, so if both are placed in the LoF, then you can't shoot. But can the shooter lean over the other corner, so that there's only one highlighted corner hurting the LoF, thus making the shooting possible?

This would work on the same manner as residing in the "final" square of hindering terrain, protected by hindering, but so that it doesn't obstruct the LoF.

If the angle is more than a diagonal, then a shooting wouldn't be possible, if it's less than diagonal, then it would be possible. But there are at exact diagonal. I you can't lean over the corner when shooting, then the LoF is blocked, but if you can lean over, then you can shoot the other half that is still visible of the opposing character.

I've added colour for the purposes of distinguishing the squares:

C__X
X__X
X__C

It is possible to draw an unblocked line from the centre of C to the centre of C. Line of fire is not blocked; those two characters can make ranged attacks against each other.

If I was you I wouldn't think of this in terms of characters "leaning" or whatever, because you're just inventing new terms for things that don't really exist. Just check to see if the centre-to-centre line has been blocked at any point.

That's just it. I draw a line from the center of the figure towards the other figure. First it hits the corner of the wall that the figure is next to. Every line of fire drawn from that figure is blocked by the wall, if the line of fire is diagonal, or anything more southern than that. Next the line of fire will hit the corner of the other wall, that is next to the opposing figure. Any line of fire, either drawn diagonally or northern, will hit the wall. The straightest shot drawn would still hit two corners of two walls.

Imagine like this: You're standing next to a wall, and try to look at someone else who is diagonally to you. That someone is also next to a wall. So at first you see the other person completely. Then you add the wall next to you. That wall makes it impossible for you to see the other half of the person. Now you only see the left side of the person. Then you add the wall next to the other person. That wall blocks the line of sight to the other side of the figure. So now you can't see the other figure, unless you lean forward so that the wall you're next to stops blocking your view.

If the situation would be this:

C___
X___
X___
XXXC

There wouldn't be a problem, since even though there are two corners of a wall blocking your view, you still see atleast half of the other figure.

And I know "leaning" is an unknown term to the game, but it's what I use to explain the situation, so that it's similar to being in hindering: protected by it, but not harmed by it. The wall protects you from line of fires drawn to you, but stil lets you "lean" for a better look. But this would only work if you're next to a wall. If you're not adjacent to a wall, then you can't "lean" to find a good LoF.

The corners are clear.

Since there is no continous blocking terrain across the corners, they are clear. See the LoSH rules on LoF and terrain, if you like (pages 25-33).

Don't try and bring real life into this; it'll just make your head hurt Instead, just use a string or simple geometry and take it for what it is: a game played on grid, and that grid sometimes does funky things.

Yeah, line of sight drives my friends nuts. Especially when it looks like there is no way you can have line of sight and you do.

AOBO
COOD

ABCD = Figures
O = Empty square

Figure D is attacking figure A. This situation comes up all the time but it always ends up going right through the middle of the empty squares. Boy I love geometry!

It doesn't actually "hit" the wall in the corner of that square. The wall stops at the exact edge of the square, so that corner is clear.

Old maps are sometimes confusing because they were badly drawn, and a wall would appear to extend partly into the next square (even just a couple of millimetres). But officially, a wall either fills an entire square or it doesn't. You can shoot past the edge of a wall just fine.

It's all just simple geometry. It doesn't have to be confusing (although string often helps).