Relevant quotes to start:
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).
Big Creatures and Cover: 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.
Suppose a situation with a large creature A fighting two medium creatures B and C, arranged as follows (with B adjacent and flanked by A and C):
A3 A4 B C
Conveniently, the vertical layout is identical - the large creature inhabits 8 total cubes.
For determining cover, it's clear that A does not have cover from C, as C can determine the cover against A2 using the most advantageous corner. The question, though, is whether C has cover from A, which becomes a big question because it depends on how you define corners. There are, of course, more options than outlined in the CRB:
A corner is...
- the point at which 3 vertices of the cube meet and there are 8 of them.
- the point at which 3 vertices of the cube meet but only on a single face, meaning there are 4 of them.
- The corner-edge of any 2 faces of the cube and there are 12 of them (4 top, 4 bottom, 4 vertical).
In option 1, C has cover as A does not have a clear line to 2 of the bottom corners, but can clearly hit the top corners from either of its upper cubes and 2 of the bottom corners on the north side of the initial diagram.
In option 2, if A is able to select the face, C does not have cover as it will clearly select the upper 4 corners or the north face corners
In option 3, C has cover from A as 6 of the 12 edges do not have clear lines (clear lines to the top 4 + 2 verticals on the north side).
So how does one determine corners?
the rules are written based on a 2D perspective, where you seem to try to evaluate them in a 3D pattern (unless I misunderstood your point). If you look at the example on page 194 of the CRB, you will see that.
As for your large creature, since it has reach against creature C, you have to use the rules ranged attacks:
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.
in this case, the north-East corner of A2 (the best square for the big creature), does not have a clear line to all 4 corners of creature C.
Therefore C has cover...