Suppose that a Medium creature stands 10 ft. away from a Large one (e.g., after taking a 5 ft. step back), and uses a Tower shield to grant itself total cover towards the direction of the Large creature.
The Large creature then uses a 5 ft. step to approach. It would attempt to approach diagonally, to attack around the shield (using a melee weapon, with 10 ft. reach, as normal for a Large, tall creature). The creature uses the rule for Big Creatures and Cover to select the most advantageous square:
Any creature with a space larger than 5 feet (1 square) determines cover against melee attacks slightly differently than smaller creatures do. Such a creature can choose any square that it occupies to determine if an opponent has cover against its melee attacks. Similarly, when making a melee attack against such a creature, you can pick any of the squares it occupies to determine if it has cover against you.
As far as I can tell, for any movement other than down-left, the Tower shield will grant total cover without further clarification.
In this situation, does the Medium creature have cover from the attack?
The relevant cover rule for cover is the following one:
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.
I see two possible interpretations of how the reach and big creatures rules might interact:
- The Large creature is adjacent to the Medium creature and making a melee attack, so it must take the least advantageous corner of its chosen square (top right), which crosses the Tower shield edge and grants total cover.
- The chosen square of the Large creature is not adjacent to the Medium creature, so it may take the most advantageous corner of its square (bottom right), which does not cross the Tower shield edge.
Note: This question is similar to this one, but specifically addresses Large creatures and larger.
The cover rules, specifically regarding the difference between melee and ranged attacks, for reference:
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).
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.