Pythagoras in the game... 3D Combat

[Fieari]

My players have reached a level where they're doing a lot of aerial manuevers. When encountering danger, one of the first things the sorcerer does is cast fly on himself and if there's time, some of the others. I don't actually have a problem with this... most of their enemies have been able to fly for some time now and it's only fair that the players can now reach this level.

Except for the bookkeeping.

Now, I've played D&D without any battlemap or even graph paper before, everything simply described. Things like attacks of opportunity and area effects and line of sight and how far you can go in a turn are REALLY hard to adjucate. When one of my players brought in that battlemap plus minis, the improvement of the game was tremendous. Quite frankly, the rules were more fun.

But now that another dimension has been added to the battlefield... ack! I feel like I'm back in the days without any tangible minis and such. So the dragon is here, but a hundred and thirty feet up, while you are HERE, but only twenty feet off the ground. We can see that there's 70 feet lateral difference between the two, but can the dragon reach you to snatch you up, or won't he reach you with a single move? If so, will he be in range for a breath attack? Where exactly will he be?

We've only had this problem for two sessions now. We're handling it by giving one of the players the job of "Pythagoras Boy" whose job is to use the pythagorian theroem to determine hypotenueses every round. As enjoyable as that is, I was wondering if anyone else had any better ideas?

 

[reanjr]

Yeah. Ignore the grid. It only gets in the way.

Other than that, you could use a computer to keep track of character locations.

 

[shilsen]

We have a number of little columns of varying sizes which we use for 3D combat. It's obvious to everyone that they're not to scale, but just having a figure two inches above another makes it easier for the players to visualize what's going on.

 

[Cor Azer]

I hasn't come up as often in my game yet (which is somewhat surprising, considering the average level is 15), but when there is a combattant flying, we tend to use a dice beside each model to indicate how many 10ft "squares" the model is in the air.

For going up and down at an angle, we just use the same idea as moving at an angle on a regular 2D map - first angle is 5ft, second is 10ft. Hasn't yet seemed to be a problem.

 

[Pinotage]

Since I run a lot of underwater combat in my game, this comes up quite a lot. I've resorted to generating two battlemaps - one is a side on view indicating elevation and the other is a top down view. My players got the hang of it really quickly, and now can adjudicate distance reasonably quickly. For flying I've generally just given one battlemap as most creatures that fly in my games don't tend to go for hand in hand - the rest of the stuff is easy to adjudicate on the fly.

Pinotage

 

[Fieari]

Hmm... I like that last idea. A pair of mats. That could work. That could work.

 

[Squire James]

A decent "quick and dirty" Pythagoran: Take the longer dimension and add half the shorter dimension. It is less accurate if one distance is a lot more than the other (where the true answer is a negligible amount above the longer dimension), but it is accurate enough for gameplay IMO.

 

[RandomPrecision]

For the visual, having two planes to put minis on will work (as previously suggested by others), probably one for the x-y plane and one for the x-z plane. For actually computing distance for the range of flying creatures and other uses, you might consider making a table of possible lengths and heights (if you have a grid with 10x10 foot squares, you'll probably just want to make your tables axes in increments of 10), where following the row for x to the column for y gives sqrt(x^2+y^2).

Edit: And remember your Pythagorean Triples. 3^2+4^2=5^2, and multiples of the 3-4-5 triangle exist proportionally (6-8-10 is a Triple too). 5-12-13 is another and 7-24-25 or 9-40-41.

I actually found a formula for those back in high school geometry - ([X^2-1]/2), where X is any number gives Y, and Y+1 gives Z, the hypoteneuse, and AX, AY, AZ are dimensions for a right triangle, where A is any constant. Maybe this could be useful in some way, I don't know.