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

[Imban]

To expand on my last post, you cannot assume that because an orthagonal step and a diagonal step are equivalent in movement cost, that any step, orthagonal or diagonal, is 5' and that the grid is mapped with the traditional coordinate system.

There are two ways around this, that I can see:

1) You can honestly move faster along a diagonal path than an orthagonal path. As a result, you cannot rotate the grid and keep spaces identical - there is actually a great difference in distance between the characters in Figure A and the characters in Figure B, even if they can reach each other in equal time without impediments. As such, the solution is to actually be further from your enemies (duh) and try to not line up on a diagonal.

This forces you to assume a universal grid of reference for your gameworld. This is relatively practical, really.

2) "It's all an abstraction, you really should just relax."

I think you could also probably make a case for the grid not mapping to the traditional coordinate system but conceptualizing that hurts my brain. As such, I will leave how that would work an exercise for future posters.

 

[HeinorNY]

To expand on my last post, you cannot assume that because an orthagonal step and a diagonal step are equivalent in movement cost, that any step, orthagonal or diagonal, is 5' and that the grid is mapped with the traditional coordinate system.

Do you mean 1-1-1-1 may not be 5ft-5ft-5ft-5ft but actually 5ft-15ft-20ft-30ft?

 

[Imban]

Blue = Wizard
Green = Fighter
X = Monster

To borrow your own pictures, my solution requires you to assume that in Figure B, the distance is 6 squares, but its actual distance: approximately 42.4 feet. The real distance is 42.4 feet. It's just that characters are actually notably faster along diagonals, capable of covering 30 feet in 6 seconds with orthagonal movement in Figure A and 42.4 feet in 6 seconds with diagonal movement in Figure B, and somewhere in between if they engage in a mixture of both.

Do you mean 1-1-1-1 may not be 5ft-5ft-5ft-5ft but actually 5ft-15ft-20ft-30ft?

Yeah, 1-1-1-1 can actually be any combination of 5ft orthagonal and 7ft diagonal steps. In order for this to make "sense" - though it posits a very strange world - there has to be an absolute grid of reference, so rotating the grid isn't really an issue.

If you don't know how you line up as regards to the absolute grid (say, you have a random outdoor encounter) you have to determine it based on ranges, which I suppose calls into play the "doesn't map exactly" thing I mentioned earlier. This means you will actually be closer in squares if you choose to lay out the grid diagonally than if you choose to lay it out orthagonally, because if you need to base your battle map on known ranges rather than a premade grid, you need it to obey known ranges.

 

[Nom]

Aside: Bungie actually invented this movement mechanic some time ago. In Marathon, if you sidestepped at the same time as you ran your horizontal vector was added to your forward vector, and thus a character moving at about 20 degrees to the straight-line was faster than one moving straight ahead.

On topic: I was playing with my daughter with counters on one of the D&D maps. Since she's only 3, I naturally just counted the diagonals as 1. And then realised, "This is much simpler than 1.5 and makes almost no difference to the big picture.".

 

[Epic Meepo]

4E world is simply an anisotropic space. The problems stem from transferring geometry tailored to isotropic, euclidean space to it.

Euclidean space tends to stay fairly constant outside of quantum field effects...

Curved spacetime? Quantum fields? And here I thought the calculus for optimizing Power Attack was bad; now power gamers are going to need a complete theory of quantum gravity to get the most bang for their buck.

Well, screw this. I'm replacing my battlemat with a lattice of microscopic strings that take on the properites of either squares or hexes, depending upon their mode of vibration. And they allow all rules from all previous editions to exist in 4.0; you just can't notice their effects because all previous editions are confined to six compactified dimensions that are too small to see.

 

[Imban]

Aside: Bungie actually invented this movement mechanic some time ago. In Marathon, if you sidestepped at the same time as you ran your horizontal vector was added to your forward vector, and thus a character moving at about 20 degrees to the straight-line was faster than one moving straight ahead.

On topic: I was playing with my daughter with counters on one of the D&D maps. Since she's only 3, I naturally just counted the diagonals as 1. And then realised, "This is much simpler than 1.5 and makes almost no difference to the big picture.".

Was Marathon really the first game with it? I thought it was endemic to early first-person shooters, actually - I'm almost sure the same effect existed in Doom, for instance.

I'm waiting for the final rules to see for what I think of the new movement style. As I've said, I use a virtual tabletop, so 1-2-1-2 doesn't lose me any time at all except with very zig-zagging paths, difficult terrain, or both, but unless I notice a real loss in functionality from using 1-1-1-1 movement, I'll probably stick with it. There's not enough information to determine all of its effects on typical combat and tactics in 4e as of yet, anyway.

 

[nem z]

it worked that way in quake as well, if you jump and keep strafing in opposite directions. 'Hopping' was -way- faster than normal running, plus all that extra movement made you a more difficult target.

I'd also note that the idea of being faster in a diagonal line than an axis one is flat-out crazy. If we agree it is the same speed/distance for the hypotenuse I expect that your area problem is in the rounding error of all the bits of squares you ignored when it didn't line up perfectly with the grid.

I'm currently more interested in finding a way to rule for hex maps that disallows the 'drift' evasion pattern.

 

[Amazing Triangle]

I am okay with the 1-1-1-1-1-1-1 diagonals. For years I actually didn't know any different. Guess it all stems from not having a map the first 2 years of playing. So now it feels cumbersome to play with the 1-2-1-2-1-2 rules that seem counter to what you would think. Yeah sure you can use the math to show it but don't we do enough math when we build characters. Why try to do all that counting the squares while trying to keep your attack bonus, damage bonus, AC and skill checks all in check do to conditional modifiers...?

Just my 2 cents

 

[Christian]

I'm currently more interested in finding a way to rule for hex maps that disallows the 'drift' evasion pattern.

The what?

 

[KarinsDad]

I'm currently more interested in finding a way to rule for hex maps that disallows the 'drift' evasion pattern.

If by this, you mean the same distance along multiple paths in the direction of a spline, I was toying with a way, but hadn't had the time to really sit down and think about it.

If one regards each 60 degree turn as an extra unit of movement (i.e. one has to slow up a bit to turn a corner), and also allowed movement through half hexes along a spline, then this might just resolve the issue.

But, I haven't had time to carefully consider it. Thoughts anyone?