How wide is a "line", i.e. Lightning Bolt?

[Jens]

I only have the SRD. It says:

A line-shaped spell shoots away from you in a line in the direction you designate. It starts from any corner of your square and extends to the limit of its range or until it strikes a barrier that blocks line of effect. A line-shaped spell affects all creatures in squares that the line passes through.

Now, that sounds simple to me. It sounds like the PHB has some more text that makes things complicated, but let's see what the SRD text implies. I especially note the last sentence since it invalidates a lot of what has been written above.

A line (which is one-dimensional) may touch an object without passing through it. This has a couple of implications:

- It is possible to cast a line-spell so that it doesn't affect any squares at all. Just cast it *exactly* along the lines separating the squares. Then it touches a lot of squares but doesn't pass through any at all. Alternatively, the line spell may be cast at a 'just about but not exactly' right angle, giving a row/column of affected squares.

- If a line-spell is cast at an angle *exactly* 45 degrees, it will touch (and thereby affect) only about half as many squares as it would had it been cast at an angle of 'just about but not exactly' 45 degrees.

Now, some may say that this makes the number for affected squares vary wildly, but they would be wrong. It would be *possible* to place the line in such a way that it would affect very few squares, but unless that is what is desired, the number of affected squares will be fairly constant.

Btw, how do you make those neat drawings/diagrams?

Of the diagrams above, only (all of) Tabarnak Smokeblower's (with the red squares unaffected) and Caliban's #5 and #7 are correct, the rest are not because they allow squares to be affected without being passed through.

Note: Aiming a spell in such a way that it touches a square without passing through is difficult. Out of a continuum of direction, it has to be cast in one specific direction. It's like picking a rational number from the set of real numbers, if you know what I mean (and if you don't nevermind )

 

[Jhyrryl]

In geometry, a point is infinitely small, therefore it takes up no space. The point defined by an intersection of two lines (and for that matter, the lines themselves), act only as a reference for seperating two areas, but they do *not* fall outside those areas. By extension, the point defined by an intersection must "belong" in one or more squares.

The PHB has another set of rules that deals with lines drawn on the battle mat -- cover. If you're drawing lines between combatants and the line exactly crosses an intersection, if any of the squares adjacent to that intersection are occupied, there is going to be cover.

As for making the diagrams, I'm using Excel and taking screenshots. I suspect Caliban is too.

 

[Jhyrryl]

Had to go to work and couldn't continue...

Anyway, so a point at an intersection *must* belong in one or more of the squares bounded by the lines defining that point. In geometry, which we really don't have any choice but to use, the point actually belongs to *all* of the squares. When defining a bounded region, the points that define the line or curve of the boundary are included in the region. Equations that evaluate whether an intersection will occur between a given intersection and some other geometric "object" will always evaluate as "true", even if the only such intersection is a point that makes up the boundary -- in this case, a corner.

The PHB has another set of rules that deals with lines drawn on the battle mat -- cover. If you're drawing lines between combatants and the line exactly crosses an intersection, if any of the squares adjacent to that intersection are occupied, there is going to be cover.

Actually, I guess this isn't exactly correct, as it would result in a 5 ft. (or even a 10 ft.) corridor always generating cover. The rules for cover are a little more complicated.

 

[Caliban]

I only have the SRD. It says:Now, that sounds simple to me. It sounds like the PHB has some more text that makes things complicated, but let's see what the SRD text implies. I especially note the last sentence since it invalidates a lot of what has been written above.

A line (which is one-dimensional) may touch an object without passing through it. This has a couple of implications:

- It is possible to cast a line-spell so that it doesn't affect any squares at all. Just cast it *exactly* along the lines separating the squares. Then it touches a lot of squares but doesn't pass through any at all. Alternatively, the line spell may be cast at a 'just about but not exactly' right angle, giving a row/column of affected squares.

- If a line-spell is cast at an angle *exactly* 45 degrees, it will touch (and thereby affect) only about half as many squares as it would had it been cast at an angle of 'just about but not exactly' 45 degrees.

Now, some may say that this makes the number for affected squares vary wildly, but they would be wrong. It would be *possible* to place the line in such a way that it would affect very few squares, but unless that is what is desired, the number of affected squares will be fairly constant.

Btw, how do you make those neat drawings/diagrams?

Of the diagrams above, only (all of) Tabarnak Smokeblower's (with the red squares unaffected) and Caliban's #5 and #7 are correct, the rest are not because they allow squares to be affected without being passed through.

Note: Aiming a spell in such a way that it touches a square without passing through is difficult. Out of a continuum of direction, it has to be cast in one specific direction. It's like picking a rational number from the set of real numbers, if you know what I mean (and if you don't nevermind )

*shrug* Sorry, but you are the one who is incorrect. It affects every square it touches, not just the ones it passes through. This is illustrated in the diagrams in the PHB, and in the text included with the diagram.

The SRD may be missing that bit of text, but the PHB trumps the SRD.

Besides, it's the only way that really makes sense.

 

[jgsugden]

I went through this thread pretty quickly, but I didn't see one thing mentioned: The 3.5 PHB has an inconsistency related to this situation.

The text on page 176 of the PHB specifies that the line must 'pass through' the square for it to be affected. The illustraion has text which says the line must 'pass through or touch a square' to affect it.

The illustration then goes on to show the line damaging all 4 squares around an intersection where the line connects. If you note in that diagram that the line goes through only that intersection (3 over and 5 up fromt he origen) you'll see why it is the only set of four sqaures being damaged.

The illustration text must be correct to prevent the 'no squares being damaged by a bolt fired along a grid line' problem.

 

[Jens]

In my previous post, I should probably have made it clearer that I was only referring to the SRD all along to see what its rule would mean. Instead of writing that only a few illustrations were 'corrct', I should probably have specified that they are 'correct by the rules in the SRD' or something like that. I guess I should also find a new PHB and read the rule for myself, even though I believe jgsugden has describe it very well (thanks). How much of a difference is there between the rule and the illustration?

By working out the implications of the SRD rule (and apparantly the rule on page 176 of the PHB), I figured that it could better be compared to the PHB illustrations. Contrary to Caliban, I think the SRD/PHB176 rule makes a lot of sense, more than the illustrations and the accompanying text (please correct me if I have misunderstood how it is set up.) But I guess we don't have to agree on what makes sense

The reason I think the illustrations make less sense than the SRD/PHB176 rule is that they seem to give a 'bonus' or windfall area of effect by placing the line so that it follows boundaries or crosses intersections. Imo, it is better to avoid giving an extra benefit in special cases.

Jhyrryl,

Thanks for a good reply. It made me wonder: Are the squares bounded? I mean, are all edges and corners included? If they are, the squares overlap, and that sounds weird to me. It seems to me that you assume all edges and corners to be included, and that your conclusion would be different without that assumption?
[I think that for the squares to be non-overlapping, each can only be 'bounded' on two sides and include two corners. But if a game rule relies on something like that, I don't think it belongs in the game in the first place .]

jgsugden,
Thanks for the explanation. You talk about a 'no squares being damaged by a bolt fired along a grid line' problem. Couldn't that just be considered a quirky disadvantage that is *really* easy for the caster to avoid? Afterall, instead of casting *exactly* along the grid line, he can just cast at a slightly different angle, resulting in a row or column of squares being affected.

 

[SnowDog]

IMO the "pass through or touch" (i.e. what it says in the text accompanying the diagram in the PH) is the only way that makes sense.

To do otherwise, to assume that a line spell has zero width and as such can straddle the boundary between two squares perfectly and hit nobody, just raises his huge flag of disbelief.

You could then aim a lightning bolt between two 5' creatures and solidly hit the 10' creature standing in front of them. "Great," you say, "more power to the mages."

No, not great. Contrast that with a situation where you can aim one millimeter to the left of the spot aimed at in the above example and you've managed to fry the poor halfling standing in front of the giant with XD6 damage. And every single spellcaster is capable of making that one-millimeter targeting decision in combat every single time, with no attack roll, no skill, nothing.

The fact that this zero-width spell can hit everything in a 5' square if it so much as touches one millimeter within that square and yet hit nothing within either square if it "floats" on the boundary creates a really messy situation.

I'd much rather just deal with the situation that depending on how you fire it, it impacts a varying number of squares. Much cleaner and nicer, and follows the rules of the PH explicitly (even if the SRD leaves room for discussion).

That's how I'll be playing it next session in my game. I've already pointed my players at the great diagrams provided earlier. Others are, of course, free to disagree .

 

[Jhyrryl]

It made me wonder: Are the squares bounded? I mean, are all edges and corners included? If they are, the squares overlap, and that sounds weird to me. It seems to me that you assume all edges and corners to be included, and that your conclusion would be different without that assumption?

Yes, they're all bounded. A non-bounded region has no shape.

Whether they overlap is philosophically subjective, I suppose, but if you're of the opinion that they do overlap, it's only by an infintely small amount: the width of a geometric line. A geometric line is 1 point "wide" and since points have no width by definition (they are infinitely small), the line has no width. In my mind that's sharing a boundary, not overlapping, because the width of the shared space actually takes up no space at all. But it's all just semantics.

The end result is the same either way though: if a spell's line effect runs along the boundary of squares A and B, it affects them both, because both squares include the points of the line in their geometric definition.

 

[Jens]

SnowDog,

If you don't like that a mage can cast a line spell so precisely that he can straddle the boundary between two squares perfectly and hit nobody (when casting it at a *slightly* different angle would hit one of the squares), how can you like it any better that a mage can cast a line spell so precisely that he can straddle the boundary between two squares perfectly and hit both (when casting it at a *slightly* different angle would miss one of the squares)?

I think both are problematic, but I think the latter is worse than the first. An in-game reason for this is that creatures don't typically take up *all* of a 5'x5' square; two characters in adjacent squares do not touch each other, there is space between them.

Imo, the best solution is to rule that a mage simply *cannot* aim the line spell that accurately (after all, it would have to be 'infinitely' accurate, which is pretty difficult), meaning that he must affect one of the squares and cannot affect both. The practical implication is that a line spell cannot be aimed through an intersection. However, this will probably lead to arguments so it wouldn't be practical.

Imo, the second best (but probably more practical) solution is to rule that line spells only affect squares which are entered; to affect the most squares, a mage should avoid hitting intersections (and we know this is really easy) but if he wants to hit fewer squares it's no big deal (even though we know this is really difficult). The only problem would be casting straight N/S/E/W, in which case I wouldn't hesitate to require the caster to deside which of the two possible columns/rows he wants to affect.

Jherryl,

I'm not sure what you mean by saying that something 'has no shape'. I distinctly remember several of my professors teaching about 'open balls' and 'open half-planes' as opposed to closed dittos. I'm not trying to twist your argument; I just don't really know how to respond. I don't think it's a matter of semantics but of geometric definitions, which should be precise. But I don't remember any definition of a square resembling those of points and lines etc., so even though I don't think you're right, I can't really argue with your assertion that a square must be bounded.
Anyway, I stand by what I said earlier: A rule that relies on the (un)boundedness of grid squares does not belong in the game. Therefore, (un)boundedness should not matter for the interpretation.

 

[Jhyrryl]

Jherryl,

I'm not sure what you mean by saying that something 'has no shape'. I distinctly remember several of my professors teaching about 'open balls' and 'open half-planes' as opposed to closed dittos. I'm not trying to twist your argument; I just don't really know how to respond. I don't think it's a matter of semantics but of geometric definitions, which should be precise. But I don't remember any definition of a square resembling those of points and lines etc., so even though I don't think you're right, I can't really argue with your assertion that a square must be bounded.
Anyway, I stand by what I said earlier: A rule that relies on the (un)boundedness of grid squares does not belong in the game. Therefore, (un)boundedness should not matter for the interpretation.

I'm trying to keep this in the realm of a basic geometry that's available to the masses, namely, Euclidean plane geometry. I highly doubt that the designers of D&D ever ventured outside their knowledge of that geometry in trying to come up with rules for a battlemat. Discussions of abstract constructs like half-planes (by which I assume you mean projective planes) just doesn't make sense at the gaming table.

From that perspective, the set of points that define the area of a polygon, like a square, include the points that define the shape and position of that polygon. In the diagram below, all four squares are adjacent to each other. Square 1's area and position is defined by the points A, B, D, and E. Square 2's area and position is defined by the points B, C, E, and F.

The definitions of squares 1 and 2 share a common line segment that runs between points B and E. Because all the points along that segment exist in the set of points that define the area of both squares 1 and 2, a spell's line effect that is designated to run along such a segment, must affect both squares.

Likewise, the definitions of all four squares in the diagram share a common point, E. That point is within the set of points that define the area of all four squares, and as such, a spell's line effect that is designated to pass through that point, must affect all four adjacent squares.

That all said, I almost agree with you when you state that a rule that relies on the boundedness definition of shape shouldn't be in the rules. On the other hand, I completely understand where WotC was coming from in make their definition of a line effect work this way. With this definition, it's very clear what happens at an intersection between squares, because it's the same thing that happens when the line effect runs entirely between rows of squares: it affects the squares on either side.

Had they defined the effect to run from the center of your square, there would have been much more ambiguity about what happens at an intersection. Not only that, but by defining the line effect to originate at the center of a square (and presumable ignoring that starting square), the effect becomes much more weak than other spell areas. Generally speaking, increasing the length of a line has nowhere near the power increase of increasing the radius of a sphere when you are talking about damage dealing spells.

I think the decision that was made was well thought out from a game mechanics perspective. It's going to be extremely easy to use, and it brings the usefulness of lightning bolt back up to that of a 3rd level spell when compared to fireball. In 3.0, the only use for lightning bolt was to have something you could use to damage creatures that are immune to fire. Now it's going to have enough significant tactical value on the battlefield for spellcasters to seriously consider keeping their 3rd level loadouts mixed.

But, I do think WotC dropped the ball in with regard to describing the effect. They should have anticipated from their own play-testing that some clarification would be desired by people with regard to what constitutes "going through" a square. This is the real problem: WotC has its own definitions for the battlemat. Those definitions and the implications hidden in them, should have been spelled out (and likely will be in the miniatures rulebook). Explicit knowledge of geometry (in whatever format), should not have been assumed on the part of the designers, just like in story writing, where the author should never assume anything about a reader's knowledge of an environment, history, or other critical aspect of the story's setting.