How many 5' cubes are in a 3D cone AoE?

[Coidzor]

Specifically 15' and 30' cones. It seems like this would be 2 different numbers of cubes for each size of cone based upon which of the two shapes/angles is used.

Any links to people modeling it out or going through how to arrive at that step by step would be greatly appreciated, too.

[Exocist]

Should just be:

- Let N equal the length of the cone divided by 5 (I.e. length of cone in 5-ft cubes)

The cone's total cubes are equal to n+4(n-1)+8(n-2) etc (Keep increasing the constant by 4). until n-x is equal to 1, after which the equation ends.

By this formula, a 15 ft cone should have 3+8+8 cubes = 19 cubes.

A 30ft cone should have 6+20+32+36+32+20 cubes = 146 cubes.

I'm not sure if there's a better mathematical way to express this.

[Larrx]

I get something different. A 15' cone (according to the template in the back of my book) is two squares adjacent, 4 squares further out, and 2 squares furthest (which doesn't look like a cone to me, but whatever). To get the 3D volume you just square each of those numbers for 4 + 16 + 4 = 24 for a cone fired sideways.

Diagonal is 1 + 4 + 9 + 4 = 18

30' sideways is 4 + 16 + 36 + 64 + 36 + 4 = 160

diagonal is 1 + 4 + 9 + 16 + 25 + 36 + 25 + 4 = 120

this all assumes that you're firing the cone in mid-air or something and none of it is getting cut-off by the ground. Also, if you are firing it in a 3D space there should be another shape for if you're shooting diagonally to all three axes, but you're on own there.

Also also, what game designer looked at that picture and thought to themselves, "Yep, that's a cone alright." Freaks.

edit: fixed a silly error

[weckar]

What IS the prescribed standard angle for a cone anyway? :smallconfused:
If I could remember that I could write a quick app to figure out this very thing!

I mean, I'm sure that like lines they do not NEED to be fired along one of the cardinal 8 angles (but it is probably most efficient to do so).

[Exocist]

I get something different. A 15' cone (according to the template in the back of my book) is two squares adjacent, 4 squares further out, and 2 squares furthest (which doesn't look like a cone to me, but whatever). To get the 3D volume you just square each of those numbers for 4 + 16 + 4 = 24 for a cone fired sideways.

Diagonal is 1 + 4 + 9 + 4 = 18

30' sideways is 4 + 16 + 36 + 64 + 36 + 4 = 160

diagonal is 1 + 4 + 9 + 16 + 25 + 36 + 25 + 4 = 120

this all assumes that you're firing the cone in mid-air or something and none of it is getting cut-off by the ground. Also, if you are firing it in a 3D space there should be another shape for if you're shooting diagonally to all three axes, but you're on own there.

Also also, what game designer looked at that picture and thought to themselves, "Yep, that's a cone alright." Freaks.

edit: fixed a silly error

That isn't a cone is it? That sounds like a 3D Ellipse to me...

When you said 3D cone, I just assumed it would follow standard cone logic but also build up and down. So 1 cube directly in front, then 5 cubes in a cross shape in front of that, then 9 cubes in front of that, etc.

But I guess game design trumps all :smalltongue:

[Larrx]

That isn't a cone is it? That sounds like a 3D Ellipse to me...

When you said 3D cone, I just assumed it would follow standard cone logic but also build up and down. So 1 cube directly in front, then 5 cubes in a cross shape in front of that, then 9 cubes in front of that, etc.

But I guess game design trumps all :smalltongue:

I didn't say cone, the OP did :) And the people who wrote the silly thing apparently. If you look at the templates they provide it's clearly a circular sector, not a cone, which makes sense physically . . . but . . . totally not a cone so why call it that?

You are forgiven for not realizing that the developer's where wrong-name-using weirdos who didn't trust that we would understand what '90 degree sector of a circle' meant.

[Larrx]

What IS the prescribed standard angle for a cone anyway? :smallconfused:
If I could remember that I could write a quick app to figure out this very thing!

I mean, I'm sure that like lines they do not NEED to be fired along one of the cardinal 8 angles (but it is probably most efficient to do so).

90 degrees (but it's not a cone).

[weckar]

Wouldn't a 2D projection of a cone BE a circle section?

No, I suppose it'd be a triangle...

[Barstro]

If you look at the templates they provide it's clearly a circular sector, not a cone, which makes sense physically . . . but . . . totally not a cone so why call it that?

You are forgiven for not realizing that the developer's where wrong-name-using weirdos who didn't trust that we would understand what '90 degree sector of a circle' meant.

Given the age that many people start playing, they probably didn't expect "sector" to mean anything. But a breath weapon of cold blasting out like an ice-cream cone at least makes a bit of sense (wrong though it may be, mechanically).

Just be glad they simplified things like cones. If I recall my red box correctly, fire-type breaths were lollipop in shape (horizontal nuclear explosion)

[Ualaa]

Referring to page 215 of the Pathfinder core book...

For 15 ft. cones, we have:
A cone launched along the diagonal (NE, NW, SE, or SW, where true north is directly above your square) hits 6 squares.
A cone launched along the non-diagonal (N, S, W, or E, where true north is directly above your square) hits 7 squares.

For 30 ft. cones, we have:
A cone launched along the diagonal (NE, NW, SE, or SW, where true north is directly above your square) hits 24 squares.
A cone launched along the non-diagonal (N, S, W, or E, where true north is directly above your square) hits 28 squares.




NW..N..NE
W....X....E
SW..S...SE

[Calthropstu]

Referring to page 215 of the Pathfinder core book...

For 15 ft. cones, we have:
A cone launched along the diagonal (NE, NW, SE, or SW, where true north is directly above your square) hits 6 squares.
A cone launched along the non-diagonal (N, S, W, or E, where true north is directly above your square) hits 7 squares.

For 30 ft. cones, we have:
A cone launched along the diagonal (NE, NW, SE, or SW, where true north is directly above your square) hits 24 squares.
A cone launched along the non-diagonal (N, S, W, or E, where true north is directly above your square) hits 28 squares.




NW..N..NE
W....X....E
SW..S...SE

This is 2 dimensional, not 3. You're not accounting for up and down. Why might this need to be figured out? Because flying hordes of demons are a thing.

[Ualaa]

The game is simpler on a 2d axis, as long as that is possible.
However if that is not possible, because of flying, then you need to calculate the 'z' axis in addition to the 'x' and 'y'.

If your cone was aimed straight up, you'd get the entire possible cone area.
If the cone was aimed horizontal to the ground, then you're only adding half as many squares.
because the cone isn't going to extend through the ground.


A cross section of the 'Z' axis, with a cone aimed straight up:
...............................................X.X .X...................................
.................................................. X......................................
.................................................M E.....................................
__________Ground Level_______________________________


The cross section of the 'Z' axis, with a cone aimed primarily horizontally:

.................................................. ......X..X..X..............................
.................................................. ..X..X..X..X..............................
..........................................ME..X..X ..X..X..X...............................
_______Ground Level______________________________________


I'm not really sure of a great way to calculate the area in a 3d view.

It's fairly easy to approximate, by using the 2d area, and determine if something is low enough to be within that area by being within that distance... basically pretending the 'X' axis is up/down (elevation) as opposed to horizontal.

[OldTrees1]

A standard D&D cone takes the shape of 1/8th of a D&D sphere (space divided into 5ft cubes & diagonals alternate between +5ft & +10ft).

So you can just use path counting to see the limits 15ft or 30ft of movement would take you:
Aligned to all 3 grids
15ft

321
22
1

30ft

655431
55543
55543
4444
333
1

Rotated 45 degrees on only 1 axis
15ft

33
2222
11

30ft

66
5555
555555
44444444
333333
11

Rotated 45 degrees on 2 axes(each number is now the number +/- from the plane) I think?
Nvm, rotating 45 degrees on 2 axes is a bit hard for me to keep track of.

[Calthropstu]

A standard D&D cone takes the shape of 1/8th of a D&D sphere (space divided into 5ft cubes & diagonals alternate between +5ft & +10ft).

So you can just use path counting to see the limits 15ft or 30ft of movement would take you:
Aligned to all 3 grids
15ft

321
22
1

30ft

655431
55543
55543
4444
333
1

Rotated 45 degrees on only 1 axis
15ft

33
2222
11

30ft

66
5555
555555
44444444
333333
11

Rotated 45 degrees on 2 axes(each number is now the number +/- from the plane) I think?
Nvm, rotating 45 degrees on 2 axes is a bit hard for me to keep track of.
You guys are actually making a lot more of this than you need to. The cone comes out in the shape of a sphere that widens out as it travels. So take a sphere, calculate it coming from the caster at 5 feet. Then calculate a sphere at 10 feet. Then 15. Add each set of spheres together to get the total area.

This is NOT rocket science. Please don't start bringing big math formulas into this... think of the 7 year olds that play. Break their poor little minds.

[Larrx]

You guys are actually making a lot more of this than you need to. The cone comes out in the shape of a sphere that widens out as it travels. So take a sphere, calculate it coming from the caster at 5 feet. Then calculate a sphere at 10 feet. Then 15. Add each set of spheres together to get the total area.

This is NOT rocket science. Please don't start bringing big math formulas into this... think of the 7 year olds that play. Break their poor little minds.

You mean disks, not spheres, and I considered using that, but ultimate decided to go with 5' deep square prisms. Circles are more accurate, but squares make the math easier and I didn't feel the added complexity was really worth it for this sort of niche situation.

So, I was thinking of the children? I used less big scary math than you did :)

Also, not for nothing, but playing D&D as a child instilled in me a love of math (for me it was specifically probability) that is still fun even now that I'm old and used up.

Younguns can in fact handle and have fun with 'big math formulas'.

Also also, sometimes people want 'big math formulas', one easy way to tell is if the OP specifically asks for them. As was the case in this thread. :amused:

[Calthropstu]

You mean disks, not spheres, and I considered using that, but ultimate decided to go with 5' deep square prisms. Circles are more accurate, but squares make the math easier and I didn't feel the added complexity was really worth it for this sort of niche situation.

So, I was thinking of the children? I used less big scary math than you did :)

Also, not for nothing, but playing D&D as a child instilled in me a love of math (for me it was specifically probability) that is still fun even now that I'm old and used up.

Younguns can in fact handle and have fun with 'big math formulas'.

Also also, sometimes people want 'big math formulas', one easy way to tell is if the OP specifically asks for them. As was the case in this thread. :amused:
I meant circles. Basically I was saying use the 5 foot blast, 10 foot blast, 15 foot blast etc rules and add them all together to get the number of cubes affected. At 60 foot (the range of cone of cold) that area gets pretty big with a 60 foot wide burst size.

And yes, some of the older kids (particularly teenagers) can handle the bigger and badder formulae, but the average 7 year old can't even SAY Pythagorean let alone use it. And yes, I see kids as young as 7 at D&D tables on a regular basis.

[Fizban]

Just be glad they simplified things like cones. If I recall my red box correctly, fire-type breaths were lollipop in shape (horizontal nuclear explosion)
In 3.0 cones were actually cones, with height and diameter of equal length because they were defined with only one length. Since figuring out which edge squares were affected required actually drawing the cone to check the edges of each square, they changed it to 90* arcs for sanity. Means you get some mean air space by shooting it across the ground instead of into it though, the "cone" being able to hit straight across the ground and straight up at the same time.

[OldTrees1]

You guys are actually making a lot more of this than you need to. The cone comes out in the shape of a sphere that widens out as it travels. So take a sphere, calculate it coming from the caster at 5 feet. Then calculate a sphere at 10 feet. Then 15. Add each set of spheres together to get the total area.

This is NOT rocket science. Please don't start bringing big math formulas into this... think of the 7 year olds that play. Break their poor little minds.


I meant circles. Basically I was saying use the 5 foot blast, 10 foot blast, 15 foot blast etc rules and add them all together to get the number of cubes affected. At 60 foot (the range of cone of cold) that area gets pretty big with a 60 foot wide burst size.

And yes, some of the older kids (particularly teenagers) can handle the bigger and badder formulae, but the average 7 year old can't even SAY Pythagorean let alone use it. And yes, I see kids as young as 7 at D&D tables on a regular basis.

I summed the shells instead of summing discs/circles. Adding together the disc/circles is not exactly accurate due to 2D & 3D diagonals being the same distance in D&D but it is still a great approximation. Especially if you do it correctly.

A 30ft sphere via summing discs is:
2 30ft circles, 4 25ft circles, 2 20ft circles, 2 15ft circles, and 2 5ft circles. (rotate a 30ft circle for proof)
So an 1/8th of a 30ft sphere is:
0.25 a 30ft circle(24) + 0.50 a 25ft circle(34) + 0.25 a 20ft circle(11) + 0.25 a 15ft circle(6) + 0.25 a 5ft circle(1)
As an approximation it is fairly accurate it only misses about 6 cubes

Of course the even rougher and inaccurate "cone of Xft ~ the sum of circles from 5ft to Xft" approximation works for especially young players.