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LOS Comparisons

I stated my opinion on the Line of Sight Calculator page that the Level 3 Dead Zone Rule presented on page 21 of Maximum Tech was in error. If the distance from the intervening object to each of the units is the same, then the calculation is fine. But if they are different, especially if they are much different, the formula can give some unexpected results.

I'll give an example, albeit an extreme one, that illustrates the problem. Let's use two units, 20 hexes apart, the lower one on Level 1 terrain, and the higher one on Level 3 terrain, and calculate how high an intervening hex can be and not block line of sight. The intervening hex can be anywhere in between, very close to one or the other unit, or closer to the center. If you calculate the maximum height (the graphs show partial levels, but you get the idea), and graph it across those 20 hexes, you get the following graphs:

First, I'll show the graph obtained by diagramming the heights, because that makes the most sense. Notice I'm showing the lower unit at Level 2 (one level higher than it is resting on) and the higher unit at Level 4 (also one level higher than it is resting on):

Notice that the maximum height of the intervening hexes forms a basically straight line, between one unit and the other, as you might expect. (I didn't bother showing a straight line on this diagram, as it would run right over the tops of the shaded areas.)

Using the Dead Zone Rule formula, however, all heck breaks loose. While the maximum terrain height near the center between the two units is about right, the closer it gets to either unit, the more out of whack it gets:

As the diagram above shows, according to the formula, at a distance of 2 hexes from the higher unit, the intervening hex can be as high as seven (count 'em, 7) levels high! Obviously, that can't be the case; it's 3 levels higher than the firing line of the unit. And when closer to the lower unit, it's off just as much, only in the other direction: at 2 levels from the lower unit, the formula indicates that the intervening hex can be no higher than -1 (negative 1) level in height. That's 3 levels below the unit's firing line. The blue line represents what a logical maximum height would be, and shows how far off from that the calculation really is.

Anyhow, I hope that this illustration shows why, if you decide you want to use the Dead Zone formula from Maximum Tech, you should take great care in doing so. I highly recommend the Diagram method, instead, as it gives accurate and logical results.

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