mach1.9pants: I agree that in this situation, it would make sense for the corner to not count. From my reading of the rules, however, it seems otherwise. Pg 280 of the PHB states:
"If one or two of those lines are blocked by an obstacle or an enemy, the target has cover. (A line isn't blocked if it runs along the edge of an obstacle's or an enemy's square.)"
I understand that the above does NOT mention corners specifically, and it is my interpretation that is making me believe what I believe. But I don't see how running along an edge of a wall is any different from running past a corner. I see no way of interpreting that they are different without saying that the two situations below are different from eachother in some way:
(the right situation is meant to be a corridor along a diagonal)
If running along an edge is fine but running along a corner is not, that would seem to mean that the visibility for the above two situations from the Hero to the Troll are slightly different. Of course it's no cover for both situations because of the upper right corner of the hero, but the point remains. I would be perfectly open to a rules clarification on the subject, but even the fact that we have differing opinions means that the RAW is at least slightly ambiguous. This is also how many I have spoken to believe the case to be.
Perhaps it would make for a better ruleset to claim that the corner doesn't count, but then you get into vision angles and whether or not the corner should count in one situation but not in another. If the angle is particularly shallow then it makes no sense for the corner to block visibility. But if it's a sharp angle, then it makes sense for it to do so. That is the ambiguity that my proposed rules hope to eliminate.
Edit: I would like to say however that I have corrected myself twice now, the elf situation is different from what I originally posted. Line of Sight and Line of Effect do NOT travel along an object's edge or corner, they get stopped, so our Hero in my original diagram does not have line of sight or effect to either elf, and so can not interact with them in any way at all. Cover seems to work slightly differently once line of sight/effect are established. The troll situation remains as stated.