I'm still trying to get my head around the rules for line of effect vs. cover vs. superior cover.
Line of effect is on page 273, and reads thusly:
If every imaginary line you trace to the target passes through or touches a solid obstacle, you don't have line of effect to the target.
Which I think means that
(a) You're able to see some part of the target square from some piece of your square.
(b) Corners and edges block line of effect.
So if you're on opposite sides of a five foot pillar, for example, you don't have line of effect.
Cover, on the other hand, is on page 280, and uses different rules. The relevant bit is at the bottom of the page:
To determine if a target has cover, choose a corner of a square you occupy (or a corner of your attack's origin square) and trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle or enemy, the target has cover. (A line isn't blocked if it runs along the edge of an obstacle's or enemy's square.) If three or four of those lines are blocked but you have line of effect, the target has superior cover.
That's a little convoluted, but the key things to realize are . . .
(a) If the attacker can see one corner, it's superior cover; if he can see two or three, it's normal cover.
(b) Cover is asymmetric. The
attacker picks a corner to "see" from and cover is determined from there.
(c) Lines and corners
don't block the effect.
This means that it's very hard to get superior cover while retaining line of sight. The easiest way to get superior cover is to have one corner of your square barely visible around an obstacle--but then you fail the line of sight rules. It's actually pretty hard to show one corner without showing two.
It also means that asymmetric cover is possible, though it's difficult. I've attached a picture of what I think is the smallest case. Grey is an obstacle. Blue has superior cover against red, but red has no cover against blue.