Cover MUST be drawn from a corner, despite the fact that line of sight is drawn from any space to any space. This is in the rulebook, and expanded upon in the FAQ:
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Q: Can you clarify how line of sight and cover are determined?
A: There are subtle differences in how to determine line of sight and cover. Though they both require you to trace lines on the battle grid, you can (and often do) use a different line to determine cover from the one you use to establish line of sight. Let's look first at how to determine line of sight and then cover:
Line of sight exists if the attacking player can trace a line from any part of the attacker's space to any part of the defender's space without crossing or touching a wall. This means that a traced line doesn't provide line of sight if it even nicks the corner or runs along the edge of a wall. (Note, a wall square with a beveled corner is treated just like a normal wall that extends to the corner. Tracing line of sight through the small cut off area is not allowed.) Low objects and other characters do not block line of sight. You only need to be able to trace a single line from one character to another; if one traced line nicks the corner of a wall but other clear lines exist between the characters, there is line of sight. You can check as often as you need to. After a few skirmishes, it will become second nature and you won't need to try more than once or twice to handle most situations.
To determine whether the defender has cover, the attacking player chooses a corner of any square in the attacking character's space. (For big attackers, you can even choose the corners of squares along the sides of or within the attacking character's space.) The attacking player can -- and often must -- choose a corner that can't be used to establish line of sight. Next, the attacking player attempts to trace unobstructed lines from that corner to all parts of the defending character's space. (For big defenders, this means all parts of all squares of the defender's space.) A line is unobstructed if it crosses neither walls nor squares containing low objects or characters. Unlike line of sight, just touching one of those things doesn't provide cover; the traced line must actually cross the square containing the character or terrain feature. (Exception: When determining cover, an attacker can ignore low objects in its own space and any adjacent squares.) If the attacking player can trace unobstructed lines to all parts of the defender's space, the defender does not have cover. However, if one or more of the traced lines is obstructed, the defender has cover (+4 bonus to Defense).