D&D 4E Non-Euclidean Geometry in 4E?

[nem z]

I think ideal solution for everyone would have been to have orthogonal movement cost 2, diagonal movement cost 3, and for humans to have a speed of 12, not 6.

That's probably the best solution for a square grid, especially if terrain modifiers like slope or ice are priced as +X to the cost.

I still think I'm going to convert to hexes with facing and half-hex rules, though... or maybe go for the gusto with "any six mutually adjacent equilateral triangles = one hex".

 

[HeinorNY]

I think ideal solution for everyone would have been to have orthogonal movement cost 2, diagonal movement cost 3, and for humans to have a speed of 12, not 6.

It's interesting.
How would this rule work with ranged attacks? Just double the numbers? What about area attacks?

This rule poped up a few times on this thread. I think I know it from somewhere...

 

[Lackhand]

It's interesting.
How would this rule work with ranged attacks? Just double the numbers? What about area attacks?

This rule poped up a few times on this thread. I think I know it from somewhere...

The rule is mathematically identical to 1-2-1-2 but with slightly easier math because nothing in the math ever changes for going on a diagonal (ie, having to maintain the bit of state between whether this was a cheap or an expensive diagonal -- all diagonals are equally expensive).

Someone upthread mentioned it's a 1st edition inherited idea. While it's true that everyone had 12" moves in 1st edition, I'm having a hard time locating anything about diagonals

 

[nem z]

Actually, a little messing around has shown that that my 6 triangles idea earlier has some real potential. Just define the distance between any two vertexes (including the center of a hex) as 2.5 feet and the math works out rather cleanly for any measurement task.

It allows for much more sensible base sizes, such as medium = hex, large = hex + the next ring of triangles around it, small = 2 adjacent triangles, etc.

Reach or radius is calculated in terms of steps from a vertex to the next, so that makes it possible not only to half hex-and-a-half weapons for reach, but also half-hex reach weapons for fists, daggers, etc.

It also gets rid of the "drift" evasion problem as well since now you can end a turn on any properly-shaped arrangement of triangles, including with your base centered on the intersection of 3 hexes rather than centered in one. (Incidentally, that means that moving along a spline into the next 'diagonal' hex is exactly 1.5 times as far as moving fully into an adjacent one.)

Heck, setting it up this way even allows a much easier time of drawing rectangular rooms, leaving only a few half-triangles of questionable space rather than half hexes (and I'd advise just letting the players overlap that little bit into the wall so long as at least 4 full triangles are in unquestioned open space).

 

[Benimoto]

The rule is mathematically identical to 1-2-1-2 but with slightly easier math because nothing in the math ever changes for going on a diagonal (ie, having to maintain the bit of state between whether this was a cheap or an expensive diagonal -- all diagonals are equally expensive).

The problem is that it's not mathematically identical to 1-2-1-2. It's mathematically identical to 1.5-1.5-1.5-1.5. A lot of assumptions on measuring range using the 1-2-1-2 system hinge on the fact that the first diagonal is cheap.

If you measure ranges using the 1-2-1-2 system, all adjacent squares are 1 square away from you. If you use the 2 straight/3 diagonal system, some adjacent squares are 2 movement points away, and some are 3. This means that you have to do some weird adjusting to allow for things like 5-foot steps, 5-foot reach, 10-foot reach, etc.

 

[Puggins]

Could we at least ask the designers to include a sidebar with the option for more "accurate" measurements? I know that sounds like a bit of a cop-out, but it's pretty clear that this is a pretty divisive issue. A bit of official acknowledgment would go a long, long way.

 

[Lackhand]

The problem is that it's not mathematically identical to 1-2-1-2. It's mathematically identical to 1.5-1.5-1.5-1.5. A lot of assumptions on measuring range using the 1-2-1-2 system hinge on the fact that the first diagonal is cheap.

If you measure ranges using the 1-2-1-2 system, all adjacent squares are 1 square away from you. If you use the 2 straight/3 diagonal system, some adjacent squares are 2 movement points away, and some are 3. This means that you have to do some weird adjusting to allow for things like 5-foot steps, 5-foot reach, 10-foot reach, etc.

Lies and calumny! 5 foot steps are an explicit exception to every rule; so they remain here.
10 foot reach, similarly has the corner-filling hack in both systems.

All this solves is the counting aspect

 

[HeinorNY]

Could we at least ask the designers to include a sidebar with the option for more "accurate" measurements? I know that sounds like a bit of a cop-out, but it's pretty clear that this is a pretty divisive issue. A bit of official acknowledgment would go a long, long way.

I think a sidebar for simple movement would fit better. The better rule should be core, not optional.

 

[Arkhandus]

Better is subjective.

1-1 diagonals is more intuitive to folks that aren't extremely nerdy toward math (I'm not nerdy enough! .....so I like 1-1 diagonals).

It's more intuitive to newbies.

If we want to reinforce the nerdity of our hobby, we should reinstate THAC0, confusing roll high/roll low subsystems, and such. It was good and nerdy back in the day, and utterly confusing for newbies.

Edit: OH! And tables/charts! Lots of 'em! Like even further back in the day!

 

[Lackhand]

I think a sidebar for simple movement would fit better. The better rule should be core, not optional.

Hey! Put down that can opener! Worms are not tasty (or nootrishus).

Or, put another way: The rule that should be core is the one that maximizes some arbitrary function of fun, realistic, simple, and <mystery requirement>.

It is completely unclear which of 1-2-1-2 and 1-1-1-1 maximizes all of those, and for my money, the whole thing should be scrapped and there should be some more abstract 'zones' system that doesn't require exact miniature placement.

C'est la vie. I'm foiled, it's 1-1-1-1 motion... and so if it must be so, then I'm going to at least ignore the grid (since I play on a white board, no marks ). Or do whatever the DM wants.