Aerial combat and higher ground: how to measure distances in 3D on grid maps.

[GallupsMirror]

The Pickle in 3D The Trouble with Tribbles 3D Combat Sooner or later, it happens. The party... ...stands atop a 100-foot tower. Somebody shoots an arrow at a distant monster on the ground. ...is flying on a magic carpet. An anti-paladin on a winged horse dive-bombs them from above with a lance. ...is jumping across a 30-foot chasm. One side is 15 feet higher than the other. Welcome to 3D combat. How far apart is creature A from creature B in situations like these? The answer is what decides player movement costs, weapon range increments, the results of flying or leaping, and various associated bonuses, penalties, and limitations. It's easy to measure distances on a flat grid, but how do you count off distances on a grid in three dimensions? This comes up regularly in the games I play or DM. If it happens to you too, read on, and I will tell you my delicious recipe for...

The Cleaning Solution in 3D GallupsMirror's 3D-Grid Fudge - Serve Hot! Step One: Measure (Count off the three distances (X,Y,Z).) 1. Altitude: How many squares higher/lower is point A than point B? Example Answer: 27 2. Longitude: How many squares farther east/west is point A than point B? Example Answer: 75 3. Latitude: How many squares farther north/south is point A than point B? Example Answer: 1 Step Two: Mix (Square each measurement. Add the three results together.) 1. 27 x 27 = 729 2. 75 x 75 = 5625 3. 1 x 1 = 1 4. 729 + 5625 + 1 = 6355 Step Three: Bake (Find the square root.) The square root of 6355 = 79.718254 Step Four: Serve (Round off. Serve on a doily.) Answer: Point A and point B are 79 squares apart. In 5E, 1 square = 5 feet, so 79 squares = 395 feet.   A formulaic plot?   All your maths are belong to us! This works fine for 5E. Pathfinder, or, as I like to call it, Mathgrinder, has that wacky rule where every other single diagonal square you travel counts as two squares. Pathfinder math won't work with real math, in part because the diagonals of a square are 1.4142..., not 1.5 times the length of the sides, so, to be compatible mechanically with Pathfinder, the formula would have to be modified to give the wrong answer. This bugs me a little. It can be done but I'd rather not. Like my delicious 3D fudge? Try one of my brownies. Hit my tip jar too.

[ArBee]

Its also perfectly reasonable to take which ever is largest, the number of squares between the targets on the board, or the targets height.
In the above example this would be 75. Only 4 squares off and no maths involved!

[GallupsMirror]

Originally Posted by ArBee

Its also perfectly reasonable to take which ever is largest, the number of squares between the targets on the board, or the targets height.
In the above example this would be 75. Only 4 squares off and no maths involved!

I like maths. The 'longest distance' method is situationally in/accurate and exploitable. For instance, position yourself on an axial diagonal like this...

100 x 100 = 10000
100 x 100 = 10000
100 x 100 = 10000
√30000 = 173

...and your ranged weapon counts as 100 squares away from a target that has to move 173 squares to engage you in melee. I could think of more exploits but I'll shut up now, because nobody ever finds this stuff as fun and interesting as I do.

Anyway, I hope this helps your gaming in some way. Thanks for posting ArBee.

[Hextor]

Ah, trigonometry... I thought I left you in high school where you belonged.



To answer this question, I have more of an option A/B situation.

Ranged weapon/spell is Option A.
Movement is Option B.

Option A (which actually came up in my very first campaign ever as a Fireball spell) should be simple enough. Figure out the hypotenuse. Don't make yourself crazy if everything else fits (line of sight, concealment, etc). Any other variable would make the effect or weapon have the same effect on a flat plane.

Option B depends on slope. You should calculate it as difficult terrain if its a steep incline. There are rules in the 3.5 PHB for such movement. I would recommend this as it keeps it easier. IF they are moving by air, break up the vertical in to a similar grid as you would for ground combat. Allow them to move vertical, horizontal or diagonal like a Queen in Chess, but add the Y axis. This would mean there would be a movement to the left, to the right, up, and down. IF you would like the diagonal option, I would suggest allowing them to move to any adjacent box for five feet of movement.

These will keep you the most sane and have worked for me since that very first game back in 2005. No, I haven't been playing very long at all compared to many here, but I've found it works well.