Sometimes, it's hard to tell wether a certain object or figure blocks line of sight (LoS). To solve this problem, you can use a thread, diagrams, or the following simple mathematical approach:
- Draw a line between attacker and target (both center of the space), and calculate its slope
- Draw a line between attacker (center) and the corner of the space that might block LoS, and calculate its slope
- Compare the slopes from both lines to determine where the corner lies compared to the attacker-target line.
The slope is just the y-difference divided by the x-difference. Since we're only interested in how steep the slope is, we can ignore negative distances. Here are a few examples:
(A = attacker, T = target, B = blocking obstacle)
(1)
XXXT
AXBB
The y-difference between A and T is 1, the x-difference is 3, so the slope is 1/3. The y-difference between A and the upper left corner from the left B is 0.5 (a half space - we start at the center of A), the x-difference is 1.5, which yields 0.5/1.5 = 1/3. Since both slopes are identical, the upper left corner from the blocking obstacle lies exactly on the line between A and T, so A sees T.
(2a)
XXT
ABB
Slope from A-T-line is 1/2, slope from A-C-line is 0.5/0.5 = 1 (C = upper left corner). Since 1 is steeper than 1/2, C lies above the A-T-line, and A doesn't see B.
(2b)
AX
BX
BT
... the same situation as (2a), just from another angle of view. Slope A-T is 2 (we don't care about negative slope), slope A-C is 1 (C = upper right corner). Here, A-T is steeper than A-C, but since it leads downwards, C lies again above A-T.
You may like this approach, or you don't, and I understand people who prefer other ways. I prefer this one because it's exact, universal, and you don't need any utilities, but that's just personal taste.
