Diagonal wonkiness scenarios

[LowSpine]

The enemies move diagonally as well so it doesn't matter. You can't move diagonally past the corner of a wall, column or any other similar obstruction so it will not help you there either.

You will never get it completely accuate so it is best just to do what is reasonable and easy.

Unless you use a tape measure and even that will not take into account slowing to turn corners, acceleration, etc. So lighten up on pedantry. It isn't worth it.

(What is it with this forum post box dropping letters? It's driving me nuts.)

 

[Rystil Arden]

This is what I meant by you thinking that there is a triangle inequality: the inequality appears when you don't draw the gameworld in battlemat terms. Since it would be unreasonable to expect people to translate square rooms, straight bridges, etc. into the battlemat geometry, the result is a triangle inequality.

Ehhhh, not quite. The way you describe this makes me think you don't know what the triangle inequality is. Just in case, the triangle inequality is not some bad thing that can 'appear'--it's a good guy and we want to have it (4E violates it):

In mathematics, the triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than or equal to the sum of the other two sides but greater than or equal to the difference between the two sides. (In both the less than or equal to and greater than or equal to statements, equality only occurs in the case of a triangle that has a 180° angle and two 0° angles, as shown in the bottom example in the image to the right.) The inequality can be viewed intuitively in either R2 or R3. The figure at the right shows two examples.

The triangle inequality is a theorem in spaces such as the real numbers, all Euclidean spaces, the Lp spaces (p ≥ 1), and any inner product space. It also appears as an axiom in the definition of many structures in mathematical analysis and functional analysis, such as normed vector spaces and metric spaces.

 

[Storminator]

This is a problem with the "occupation" rules, not the movement rules. IMO, moving diagonally between two diagonally occupied squares should carry the same penalties as moving through an occupied square. You choose which occupied diagonal square you're taking the penalties from and just go from there. This also solves the problem of enemies not being able to form a defensive line on a diagonal.

At it's heart, both are problems with mapping the world onto a battlemat, and playing on the battlemat.

According to 3e, and presumably 4e, you don't occupy either diagonal square. If you (the editorial you, not you specifically ) have no problem with one world-to-battlemat distortion, why should another be a problem?

PS

 

[Sir Sebastian Hardin]

Many of you "11:1 guys" act like zealots defending this wonky rule.
What kind of argument is "stop thinking in feet" or "the NPCs know the rules about squares", I COULD think in squares, but the characters don't know anything about squares or diagonals being equal to the sides, or anything like that.
"The grid is not the actual place, it's an abstraction" Come on! I can draw an actual place in Autocad, scale it to 1inch=five feet, plot it, and place a grid on it. It is an actual place (scaled down) and those squares we all see should represent the actual distances we SEE WITH OUR OWN EYES.

One of the most graphic examples is the one that the evil caster uses a burst cenetered on him and he strikes a guy in the diagonal and not a guy in an orthogonal line, eventhough OUR EYES tell us the diagonal guy is FARTHER. The rules say this guy is closer... but our eyes say he is farther!!!! Now that's wonky! (and it's not a weird or uncommon scenario)

The correct argument is not "stop thinking in feet"
it's just "stop thinking"

(this is one of the very few things I dislike about 4e, but it doesn't help when tryng to say the game is not actually being "dumbed down")

 

[SlagMortar]

Rystil, can you point out a case where 3 points in 4E violate the triangle inequality? I ask because I was trying and I can't. I'll requote wikipedia to add emphasis:

In mathematics, the triangle inequality is the theorem stating that for any triangle, the measure of a given side must be less than or equal to the sum of the other two sides but greater than or equal to the difference between the two sides.

I'm not convinced that 4E movement violates the triangle inequality, nor am I convinced that 4E movement does not violate the triangle inequality.

Note that in the examples you gave, the sides of the triangle add up to be at worst equal to the longest side.

 

[SlagMortar]

Got it. 4E movement actually uses Chebyshev distance instead of Euclidean distance. The distance is the maximum of the distance in the x direction or the distance in the y direction.

Chebyshev distance does, in fact, follow the triangle inequality.

I still find it wonky, but at least it is not so wonky as to violate the triangle inequality.

Edit: Now back to your regularly scheduled discussion.

 

[Rystil Arden]

Rystil, can you point out a case where 3 points in 4E violate the triangle inequality? I ask because I was trying and I can't. I'll requote wikipedia to add emphasis:

I'm not convinced that 4E movement violates the triangle inequality, nor am I convinced that 4E movement does not violate the triangle inequality.

Note that in the examples you gave, the sides of the triangle add up to be at worst equal to the longest side.

Equal is insufficient. Go down a bit further:

(In both the less than or equal to and greater than or equal to statements, equality only occurs in the case of a triangle that has a 180° angle and two 0° angles, as shown in the bottom example in the image to the right.)

I'll translate that from mathspeak--the only way you can have a situation where it is equal (and not strictly less than), you have to have a straight line--in other words, you have a flat triangle where two sides are just segments of the third side.

 

[SlagMortar]

I'll translate that from mathspeak--the only way you can have a situation where it is equal (and not strictly less than), you have to have a straight line--in other words, you have a flat triangle where two sides are just segments of the third side.

Don't worry, I speak math.

Care to explain what a 180 degree angle looks like in a non-Euclidean space?

To requote for emphasis:

The triangle inequality is a theorem in spaces such as the real numbers, all Euclidean spaces, the Lp spaces (p ≥ 1), and any inner product space. It also appears as an axiom in the definition of many structures in mathematical analysis and functional analysis, such as normed vector spaces and metric spaces.

Chebyshev space is the L-infinity space.

Would you agree that Manhattan distance does not violate the triangle inequality? Manhattan distance is the L-1 space. The points (0,0), (0,1), (1,0) form a triangle. The lengths of these sides in Manhattan distance are 1, 1, and 2. This gives equality for the condition "the measure of a given side must be greater than or equal to the difference between the other two sides". These points are clearly not on a "straight line" when viewed in Euclidean space.

 

[Geron Raveneye]

It's funny to note that there's at least two sides to the folks speaking for the 1-1-1-1 rule. One side that claims "You need to stop thinking in feet, think in squares, 4E will measure out EVERYTHING in squares", and another side that claims "Stop putting real-world importance on the battlemap, it doesn't map out the whole world, it's just an abstraction for combat."

Oh, right...and then there's people who go "Stop thinking too much about this".

I think 4E will go down in D&D history as one of the editions with the most differing explanations and interpretations for some of its rules.

 

[Sir Sebastian Hardin]

"Stop putting real-world importance on the battlemap, it doesn't map out the whole world, it's just an abstraction for combat."

For those who wield this claim: It is valid if we used a feature-less grid, to know roughly the relative distances between characters, not when using a drawn map, or tiles and stuff that should represent roughly "real" and "acurate" things (that huge 30 ft wide gateway is straight, not curved... etc). Even in the grid-only case, your eyes tells you one thing and the game says another (see my previous post)