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1) ... after a direct hit on a medium creature?
X = Empty square
0 = Square filled by Fog Cloud
C = Creature
A) 21 squares
XXXXXXX
XX000XX
X00000X
X00C00X
X00000X
XX000XX
XXXXXXX
or
B) 25 squares
XXXXXXX
X00000X
X00000X
X00C00X
X00000X
X00000X
XXXXXXX
2) ... after a hit on a square intersection?
A) 12 squares
XXXXXX
XX00XX
X0000X
X0000X
XX00XX
XXXXXX
or
B) 16 squares
XXXXXX
X0000X
X0000X
X0000X
X0000X
XXXXXX
I assume you mean the alchemist discovery Smoke Bomb? The answer should be A in both cases because all blast areas create the circular approximation, not the square. This is because diagonals are 1.5 (rounded down). So if you have a radius of 2, you only get one square diagonally out from the center.
Yup, I meant the Alchemist's Smoke Bomb* discovery. This is what I thought but I was not sure that "splash radius" followed the same rule than "AoE spells" for the purpose of... well... the AoE. Also, with a typical AoE spell, you can only target a square intersection, not a creature on a square, unlike bombs. It is strange because the AoE of a bomb is much bigger when you perform a direct hit than when you target a square intersection.
This would be interesting to know for sure with a smoke stick and the ninja smoke bomb trick.
1) ... after a direct hit on a medium creature?
Smoke bomb*: "When the alchemist creates a bomb, he can choose to have it create a cloud of thick smoke when it detonates. The cloud functions as fog cloud, filling an area equal to twice the bomb's splash radius for 1 round per level."
Bomb (Su): "Thrown bombs have a range of 20 feet and use the Throw Splash Weapon special attack."
Throw Splash Weapon: "A hit deals direct hit damage to the target, and splash damage to all creatures within 5 feet of the target."
The splash radius is 5'. Double that is 10'. The fog could cover all creatures(/squares) within 10 feet of the target.
2) ... after a hit on a square intersection?
Throw Splash Weapon: "if you target a grid intersection, creatures in all adjacent squares are dealt the splash damage, and the direct hit damage is not dealt to any creature."
"Adjacent squares" is not really something that can be doubled. I would assume it would mean 5' from the intersection (four squares) which would double to be the same as option 1). One could argue that doubling adjacent squares would mean adjacent squares plus all squares adjacent to all of those squares, but I think that's not the intent.
In both cases I think A) is correct.
Yeah, the trouble is that on a direct hit, the bomb is actually a 1.5 square radius. Radius based spells normally hit on the intersection of squares, thus a 5 foot radius spell is actually a 10'x10' cube and a 10' radius is like the picture for 2A. The diagonal corners are not hit because they are 3 squares from the center intersection.
Technically, you could argue that the direct hit is a 3 square radius centered on the target's square. This would create a diamond pattern like 2A but with points. But then you're getting a bit crazy.