From which squares does a Tower Shield provide Total Cover?

When a character uses a tower shield for total cover, which squares does that protect against? Obviously the square on the other side of the shield, but what about the diagonals?

Total Cover: If you don't have line of effect to your target (that is, you cannot draw any line from your square to your target's square without crossing a solid barrier), he is considered to have total cover from you. You can't make an attack against a target that has total cover.

From the definition of total cover, you can draw lines from the diagonals that don't pass through the covered edge so it would seem to me to be partial cover if anything.

A tower shield typically grants a Medium wielder total cover against melee attacks launched by Medium foes from the square opposite the shield and from similar foes' melee attacks launched from the squares to the left and right of the square opposite the shield…

The tower shield says

As a standard action, however, you can use a tower shield to grant you total cover until the beginning of your next turn. When using a tower shield in this way, you must choose one edge of your space. That edge is treated as a solid wall for attacks targeting you only. You gain total cover for attacks that pass through this edge and no cover for attacks that do not pass through this edge.

Then Cover says

When making a melee attack against an adjacent target, your target has cover if any line from any corner of your square to the target's square goes through a wall (including a low wall). When making a melee attack against a target that isn't adjacent to you (such as with a reach weapon), use the rules for determining cover from ranged attacks.

So to determine if the defender has cover from them, the Medium foes armed with longswords occupying the left and right squares opposite the tower shield must draw a line from the least advantageous corners of their squares to the most advantageous corner of the defender's square, and such a line will go through the tower shield, giving the defender total cover.

…But for foes making ranged attacks and using reach, it's a little different

Cover also says

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target's square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC).

Thus, if attackers are employing ranged weapons or attacking with reach, to determine if the defender has cover from their attacks, the attackers, instead, pick the line to be drawn from their most advantageous corners to the defender's most advantageous corner.

While this still leaves the defender with total cover from attacks by the typical Medium attacker on the shield's opposite side, it's unclear if adjacent foes to the left and right of that attacker that are armed with ranged weapons are likewise impaired. The typical Medium creatures to the left and right of the shield opposite side can pick a corner that causes the traced line to skirt the tower shield's border, which would normally be sufficient to grant the defender cover (therefore total cover via the tower shield), but it's only from attacks that pass through the tower shield's edge against which the defender gains total cover, and whether this is through enough is a question for the GM. Ask the GM if it's possible for a dude with a crossbow to run up to the diagonal edge of your tower shield and cap you with a crossbow by, essentially, shooting around the tower shield. If the GM rules it is possible, admire such a foe's bravery before gutting him.

• Thanks for the explanation. One of the sticking points we had was whether you could use any corner or the least/most advantageous. I'll be the GM for this and it's my first time running a campaign, so trying to get through these kinds of questions that come up. Commented Oct 7, 2016 at 13:15
• @Capellan You're welcome. It's an extraordinarily poorly phrased and organized section of the rules. Seriously, a publisher could probably make some quick cash on a book consisting solely of diagrams illustrating, detailing, and addressing questions about grid management. Commented Oct 7, 2016 at 13:29
• This answer actually helped me to clarify the rules on my head. Thanks. Commented Oct 7, 2016 at 17:36
• Please, 2023 downvoter, tell me how to improve this answer! Commented Mar 3, 2023 at 7:38
• Not my downvote, but I may guess. The claim about a cover from central attacker's left and right squeres being total is questionable to a degree. Shield may provide cover against them - "attack" here in context being "a line, by which an attack possibility is determined" (raised shield being like a regular wall). Not saying, it can't be interpreted your way. Also, touching a corner or a border does't block abovementioned lines (at least from diagrams from both PF 1 and D&D 3.5). Commented Sep 18, 2023 at 6:48