# D&D 4ENon-Euclidean Geometry in 4E?

#### Benimoto

##### First Post
ainatan said:
Benimoto said:
Those corner squares are less than 50% covered, and a 10-foot line doesn't even quite touch the center of the corner squares.
That 50% rule is just for area effects, not reach.
Well the whole reach thing breaks down in the fact that creatures with larger than 10 foot reach don't get the extra squares that creatures with 10-foot reach get.

And, on a separate point, for those advocating the 2 movement, 3 diagonal system, you'll notice that for any movement with an even number of movement points, you're really going with something similar to a 2-1-2-1 diagonal system instead of the present 1-2-1-2 system. This creates some weird problems when you try to use the system for things like reach or spell radius.

In fact, using the 2 straight, 3 diagonal system, or any system that penalizes the first diagonal, you'll notice the first weird effect with creatures that have 5 foot reach, like basically everybody. If you consider 5 feet equal to two distance points, a creature with 5 foot reach can't even attack diagonally, since that's three distance points away. You also lose the ability to take a 5-foot step diagonally. I would consider that a weird effect.

And for all the people still complaining about the "diagonal dodge", notice what Shoe said earlier:
DMShoe said:
Besides -- the defender who is trying to "defend" by standing in the middle of an open room isn't doing his job very well. Even with 1-2-1, the monster could move out to the side and then charge the wizard. The defender should either be back near the wizard, or basing the monster. Just sayin'.
He's pretty much confirming that moving and charging in 4th edition works similarly or the same as it works in the DDM rules. That is:

Move up to your speed = move action
Shift (5 foot step) = move action
Any kind of attack = attack action
Charge (move up to your speed and standard melee attack) = attack action

You can, of course, use your attack action to take a second move action. Charging no longer has to be in a straight line, and isn't stopped by difficult terrain or allies anymore.

So, most of the examples where the creature can only move 30 feet and then attack just don't apply to 4th edition. The range that creatures can attack from dramatically increases, and defenders have to be way more active, engaging threats and pinning them down, than passive. Just standing in the way won't work no matter what movement system you use.

#### Rel

##### Liquid Awesome
heirodule said:
Will fireballs be firecubes now?

No, I would assume that they emanate from the caster's crotch just like they always have.

That's one sacred cow that we just can't afford to lose.

What?

#### Sir Sebastian Hardin

##### First Post
I don't know if I'm totally on board with counting diagonals as 1, but I'm not against it either. I can definitely see the possibility of movement anomalies. However, given that the advantage in movement would apply to both PCs and their enemies, and that 4e is based around making movement easier and combat more dynamic, then it may work fine.

The problem is not "who wins" with this system. It is about believability. The fights scene would look pretty wierd with all PCs and monsters moving in zig-zag diagonal paths, avoiding AoO's and dodging Firecubes.

#### Sir Sebastian Hardin

##### First Post
Benimoto said:
In fact, using the 2 straight, 3 diagonal system, or any system that penalizes the first diagonal, you'll notice the first weird effect with creatures that have 5 foot reach, like basically everybody. If you consider 5 feet equal to two distance points, a creature with 5 foot reach can't even attack diagonally, since that's three distance points away. You also lose the ability to take a 5-foot step diagonally. I would consider that a weird effect.

The guy that propposed this rule already stated that a 5' step ia always posible in any direction.
AND when you attack diagonaly, the other guy is noy 5ft away. He is not 3 distance points away he is about 2.5' away from you (he is on the center of the square, not at farthest corner)

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#### Benimoto

##### First Post
Sir Sebastian Hardin said:
The problem is not "who wins" with this system. It is about believability. The fights scene would look pretty wierd with all PCs and monsters moving in zig-zag diagonal paths, avoiding AoO's and dodging Firecubes.
I agree. Hopefully, another of the 4th edition promises comes through, and they manage to make interesting, varied terrain the default.

In other words, hopefully battles will have a dozen participants moving organically around interesting obstacles, enemies, and other impediments instead of just three people facing off in an empty 50x50 room.

If that were the case, I could pretty easily ignore the slight weirdness of the 1-1 movement system.

#### WhatGravitas

##### Explorer
Puggins said:
All movement into a clear square costs 1.

The first diagonal movement of any move action costs an extra 1. All other subsequent diagonals in that move action cost 1.
That's actually great. It avoids the shown problem and is easy. Like it - it's going to be in my games now.

By the way: The 1-1-1-1 method hasn't many problems: All problems shown in this thread are basically the same example. If that's the only problem... then I consider it a minor problem, after all, all critics could only produce that situation, which is pretty special and if you're down to a 2 man party, you're already on the losing side.

Cheers, LT.

##### 5ever, or until 2024
1 diagonal equals 2 is Taxicab geometry (or actually, it is manhatten distance, which is part of taxicab geometry).

1 diagonal equals 1 is Chebyshev distance. Also called chessboard distance for the way the king moves on a chessboard.

Chebyshev may appear the simpler abstraction, but I really think that Taxicab, which means there is no real shortcut to diagonals, is simpler in practice, especially when the quirkier elements of "fast" diagonals start to come into play. And I think I played with Taxicab back in the day, maybe from Combat and Tactics?

##### First Post
Rel said:
No, I would assume that they emanate from the caster's crotch just like they always have.

That's one sacred cow that we just can't afford to lose.

What?

No, no... don't you remember the lessons of William Wallace? Lightning Bolts from your eyes, Fireballs from your arse...

#### delericho

##### Legend
Benimoto said:
I agree. Hopefully, another of the 4th edition promises comes through, and they manage to make interesting, varied terrain the default.

I think it's absolutely fantastic that they're going to all the trouble of adding lots of fun and exciting terrain effects into the game... while simultaneously making it much easier to go around them.

#### Benimoto

##### First Post
Sir Sebastian Hardin said:
The guy that propposed this rule already stated that a 5' step ia always posible in any direction.
AND when you attack diagonaly, the other guy is noy 5ft away. He is not 3 distance points away he is about 2.5' away from you (he is on the center of the square, not at farthest corner)
But the thing is, then you've already made one exception to the rule for 5 foot steps, and you're saying that you can't count reach the same way as movement. Besides, why is the enemy 2.5 feet away? Is he standing frozen in the center of his square while you're moving to the very edge of yours? What if you have two attacks and you want to split them and attack opponents on either side of you?

The problem with the 2=straight, 3=diagonal system is that you can't measure spell radius and reach using the same system as movement without things getting really weird. If you try to measure 10 foot reach the same way you do movement, you end up with this:

That's weird looking. You certainly can't expect that a creature with a reach weapon will be able to defend himself with attacks of opportunity. You can attack only 4 more squares than if you had a non-reach weapon. And radius spells are even weirder looking. Fireball is almost completely diamond shaped.

So basically, with the 2=straight, 3=diagonal system is until you move 15 feet, it's not any different that a 1=straight, 2=diagonal system. It's really just a system for measuring longer distances, and you have to use exceptions to handle much close-in fighting.

So I believe my position stands. Using any system to model distances on a square (or hex-based) grid, the more "realism" you try to build in, the more you'll end up with weird glitches and a rule system full of exceptions and special cases. I prefer a system with as few glitches as possible. The 3.5 system was pretty good, but it had a certain amount of problems. The 1 square=1 square system has as many negative points as the rest of them, but at least its simple, and so I don't really mind the switch.

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#### rkanodia

##### First Post
heirodule said:
Will fireballs be firecubes now?
Eh, to a first order approximation, a sphere is a cube anyway.

#### Imban

##### First Post
Benimoto said:
Using any system to model distances on a square (or hex-based) grid, the more "realism" you try to build in

Actually, this isn't true of hex-based grids as long as we're constrained to 2D movement. With hexes, any hex Y hexes away is equidistant and you don't have to worry about diagonals. Granted, as soon as flight enters the picture, this stops working quite so well.

#### delericho

##### Legend
Benimoto said:
The problem with the 2=straight, 3=diagonal system is that you can't measure spell radius and reach using the same system as movement without things getting really weird. If you try to measure 10 foot reach the same way you do movement, you end up with this:

Unless you declare a 10 ft. reach to be 5 points, not 4. In which case the result you get is the closest approximation to the circle that is possible on a square grid (attached).

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#### delericho

##### Legend
Oops, duplicate post.

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#### Nine Hands

##### Explorer
Greenfaun said:
I'm glad to see there are other fans of the hexmap out there.

Does anyone have experience playing with a hex grid and three-dimensional combat? I.e. flying or underwater? It seems like that's one place where a three-vertex coordinate system might be more useful than hexes' sexy tesselation.

I've played and run Mekton which uses hexes exclusively and we usually mix it up in air-to-air combat with fighters at all different altitudes. We just mark the altitude with a die and use the greater of the two distances (height or hex distance), no need to heavy math in a fast paced battle.

#### HeinorNY

##### First Post
Wormwood said:
I'd imagine that sticking closer to the defendee or attacking the antagonist would be a better solution.

Actually the better solution would be to arrange the miniatures on the grid this way:

The distances between characters would remain the same, but the Wizard would be much safer.

The best defensive tactic is not the formation of the party, their powers, actions, etc, It's the alignment of the grid! Players can use the inconsistence of the rule to create these bizarre situations. It's GOING to happen. A new branch of combat tactics will surge in 4E.

Players will say: "Could we just put the grid this way instead of that way, so I can reach the opponent in 1 round instead of 2?"

It just can't get into my mind, it's just wrong, it's a thing the should not be. They are at the same distance but they are not. H.P.Lovecraft came with this new rule, it gotta be!

#### Aexalon

##### Explorer
delericho said:
Unless you declare a 10 ft. reach to be 5 points, not 4. In which case the result you get is the closest approximation to the circle that is possible on a square grid (attached).

Of course, that in itself is a quirk that needs introduced to make the system work.
Not necessarely. The area of effect you're describing looks a bit more like a 12.5' radius circle anyway. Which would indeed be 5pts in a 5' = 2pts metric.

Hex circles "suffer" from the same problem. An actual 10' radius circle looks horrible (see Unearthed Arcana's version of the gargantuan size critter); A 12.5' radius circle looks pretty nice (same link, the area labelled as the 10' radius circle).

#### Christian

##### Explorer
Greenfaun said:
I'm generally a fan of hex-grids, but it's been a long time since I've gamed with someone who didn't hate hex-grid playmaps with a fiery passion. My sample isn't scientific, I know, but I kind of assume that everyone hates hex-maps now.

My group uses a hex grid in 3.5, and I have no doubt we'll continue to use it if and when we convert to D&D v4.

Imban said:
Actually, this isn't true of hex-based grids as long as we're constrained to 2D movement. With hexes, any hex Y hexes away is equidistant and you don't have to worry about diagonals. Granted, as soon as flight enters the picture, this stops working quite so well.

I hadn't noticed a problem with Champions Hex Flight.

With regard to distance itself, a simple rule of thumb is: max distance = longer length + 1/3 shorter length for a fair approximation. So, if a target is 100 feet away horizontally and 30 feet up vertically, an approximation is that he is 110 feet away (it's actually 104.4). This is typically good enough, even for Close range calculations.

This "rule of thumb" also works well with hexes if using numbers of hexes instead of feet (for that example, 20 hexes horizontal and 20 hexes vertical is considered 27 hexes away, but is actually closer to 28).

The number comes up a little bit high if the longer distance is much greater than the shorter, a little bit low if the two distances are close to the same. But, it's a good general rule of thumb without doing square and square root calculations in a DM's head.

This rule gets a bit squishy with using number of squares for a square system in any direction except real close to a grid line because the DM cannot just count out the distance in squares unless the target is close to a grid line. Course, for a square system, a DM could change the equation to: longest + 1/3 (x + y) where x and y are the other two dimension distances, but that's more of a pain calculation.

But it works fine for hexes.

#### danzig138

##### Explorer
Mouseferatu said:
As someone who's played both ways--the "1, 2, 1, 2" method, and the "a square is a square is a square" method--I cannot disagree with you more strongly. Even in a group of very intelligent people, the boost in speed and ease of play far outweighs any initial cognitive dissonance.
Word. My map guy, who is not stupid by any means, had a much easier time of things once I said "Screw it. Don't worry about the odd diagonal thing, just count the damn squares". Sped things up a bit for everyone.

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