Counting squares for circle AoE

[heavyfuel]

Is there some easy and practical way to see which squares are affected by a circle AoE? It gets incredibly frustrating to count when the AoE is something larger than a 25ft radius

[Zombimode]

Is there some easy and practical way to see which squares are affected by a circle AoE? It gets incredibly frustrating to count when the AoE is something larger than a 25ft radius

Yeah, look at the templates in the DMG.

[heavyfuel]

Yeah, look at the templates in the DMG.

Oh! Thanks for the sarcastic answer!

Not only does the DMG not have a template for every possible radius, but you still need to count the squares to see if a creature is inside the area, especially if he ends up on an edge.

[Extra Anchovies]

1. Figure out which area effects you want to be able to easily measure.
2. Get some paper.
3. Convert the area-effect sizes to inches (5 feet in-game = 1 inch out-of-game)
4. Draw circles of the proper radius for burst effects, and quarter-circles of the appropriate side length for cones
5. Cut out the shapes, and punch out a small circle at the very center of each circle
6. Label each radius-effect and cone-effect template with the size of its area-effect (e.g. "20-foot radius")
7. When placing radius-effects on the battle grid, place the punched center hole over the target corner
8. When placing cone-effects, place the corner that forms a right angle over the corner of origin. Turn it to any angle you want.
9. Everything that is at least 50% underneath (or above, if you slid it under) the templates is in the area of effect.

Not restricting cones to 45º rotation intervals also increases their tactical use by a great deal.

Alternately, if you're feeling up for it, play on a hex map. It doesn't change gameplay at all, it gives cones twelve points and angles of origin rather than the normal eight (increasing their tactical effectiveness), and makes radii super easy to measure (pick a target square, and count 1 square outwards from it for every 5 feet in the radius).

[Jeff the Green]

If you've got access to a computer while you play, you could use this (https://docs.google.com/spreadsheet/pub?key=0AiCd3kHd21VzdGZVcFViaTZsc01teWtsNlUySjdVT 3c&output=html). Copy/paste it into a Google sheet or Excel spreadsheet and put a "=" in front of the formulae. Then just put in the coordinates of each target you think might be in range and it'll tell you the distance.

[Elkad]

Wire templates.
Bunch of companies make them, here is one.
http://paizo.com/companies/steelSqwire

Or make your own out of coat hangers.

[JusticeZero]

Or just houserule that diagonals are 5'. That's what I ended up doing.

[Forrestfire]

Use a ruler. If a square is within x inches of the center, it's hit, assuming a grid of inch-wide squares.

[DM Nate]

Or just houserule that diagonals are 5'. That's what I ended up doing.

I could totally see this being abused. Personally, I use grid paper for combat anyway and just make a template if the issue comes up. A square's in the circle if more than 50% of it is covered by the template.

[Curmudgeon]

Get a few common nails, some string, and stick-on labels. Tie string to a nail, measure out the battle grid inches for a common effect radius, and cut to that length. Wrap a stick-on label over the nail and adhere it to itself, then write the radius (each inch = 5') on that label. Repeat for other common radii. Make one extra, long and unlabeled, so you can grab the string at the actual distance and hold it against a yardstick for your measurement. Hauling out the yardstick is an annoyance, so having the premeasured "templates" that you can stretch out from the originating grid intersection is more convenient.

[Extra Anchovies]

I could totally see this being abused. Personally, I use grid paper for combat anyway and just make a template if the issue comes up. A square's in the circle if more than 50% of it is covered by the template.

The diagonal-movement-cost nonsense is why I prefer hex grids. It's actually a lot easier to find distance on a hex map than on a square grid when you aren't moving like chess pieces.

[nedz]

Yeah, look at the templates in the DMG.Oh! Thanks for the sarcastic answer!

Not only does the DMG not have a template for every possible radius, but you still need to count the squares to see if a creature is inside the area, especially if he ends up on an edge.

It's not even the right answer — see below.

I use floorplans and find that a 10' wide piece of corridor makes for a perfect ruler — of course this is not RAW because π

[Curmudgeon]

The diagonal-movement-cost nonsense is why I prefer hex grids. It's actually a lot easier to find distance on a hex map than on a square grid when you aren't moving like chess pieces.
What exactly is "nonsense" about the diagonal movement rules? The diagonal of a square is √2 times its side, or ~1.41x. The D&D diagonal movement rule is 1x cost for the odd numbered diagonal movement (first, third, & c.) and 2x cost for even numbered diagonal moves. That's a bit under 1.5x on average (exactly 1.5x for an even number of diagonals, but less than that for an odd number of diagonals). It works out mathematically very sensibly: the exact opposite of "nonsense".

Hex grids don't make measuring distance easier if you're not going exactly along any of their 6 simple lines. What they do do is reduce the number of adjacent spaces (a ¼ reduction in enemies makes a huge difference in large group combats), and make positioning Large+ size characters problematic.

[Elkad]

Hex grids don't make measuring distance easier if you're not going exactly along any of their 6 simple lines. What they do do is reduce the number of adjacent spaces (a ¼ reduction in enemies makes a huge difference in large group combats), and make positioning Large+ size characters problematic.

What? Direction or what line the target is on on a hex map makes no difference at all. Count the hexes to the target by a shortest path and that's the range. (or for long ranges, subtract the grid coords from hexA to hexB, since most hex maps are numbered)

Never having to count diagonals=easier in my book.

[Phelix-Mu]

Since I generally play over skype without a battle grid, I just eyeball it and give characters an estimate of how many they can hit.

[Curmudgeon]

What? Direction or what line the target is on on a hex map makes no difference at all. Count the hexes to the target by a shortest path and that's the range.
You've still got to count the hexes or count the squares in either case. With a hex mat you've got to use a straight edge to figure the shortest path unless it happens to be in one of those six easy directions. With the D&D square grid you can count the horizontal and vertical differences separately and don't need to worry about individual squares along the route unless there are obstructions or difficult terrain. Total distance is 1.5 x the shorter of those two (diagonals), plus the difference (non-diagonals). Round down and multiply by 5' (convert from squares to feet). That's it.

[Jeff the Green]

What exactly is "nonsense" about the diagonal movement rules? The diagonal of a square is √2 times its side, or ~1.41x. The D&D diagonal movement rule is 1x cost for the odd numbered diagonal movement (first, third, & c.) and 2x cost for even numbered diagonal moves. That's a bit under 1.5x on average (exactly 1.5x for an even number of diagonals, but less than that for an odd number of diagonals). It works out mathematically very sensibly: the exact opposite of "nonsense".

Taking into acount Benford's law (http://en.wikipedia.org/wiki/Benford's_law)*, it's almost precisely correct on average for speeds greater than 15'. Have a graph (https://www.desmos.com/calculator/l0mykbpnfu). The logfloor(x)(1+1/r) describes how likely you are to move r spaces given a maximum speed of x spaces. The (floor(1.5r))/(sqrt(2r2) is the ratio between D&D distance and Euclidian distance along a diagonal r squares up and r squares down. The sum of the product of the two is the average ratio of D&D distance and Euclidian distance. And the floor(x) means that e.g. any value x such that 2 ≤ x < 3 is considered to be 2. That first line segment is a move speed of 10'.

The green line is the ratio between 1.5 and sqrt(2) (i.e. the ratio of D&D and Euclidian distance without taking Benford's law into account), and the purple one is a perfect 1:1 correspondance.


Total distance is 1.5 x the shorter of those two (diagonals), plus the difference (non-diagonals). Round down and multiply by 5' (convert from squares to feet). That's it.

Can you (or anyone) explain how you'd get the equivalent for three-dimensional movement? I've been trying to figure it out but geometry is not my strong suit.

*Yes, I know Benford's law doesn't strictly apply here. It is a good approximation for these sorts of problems, though.

[Coidzor]

Wire templates.
Bunch of companies make them, here is one.
http://paizo.com/companies/steelSqwire

Or make your own out of coat hangers.

We used some spare pipe cleaners to make a variety of cones and bursts sized up from the templates for our battle grid.

[Divide by Zero]

Get a ruler, measure from the starting point of the effect to the center of the potential target's square. Easiest solution IMO unless you regularly run combats where large numbers of enemies are hit simultaneously.

[Rubik]

https://www.youtube.com/watch?v=SyKwyAWJZcI

[Battleship789]

I extrapolated these 60-ft radius areas from the cone breath weapon diagrams in the Draconomicon a few years ago. The left picture is centered on a square and the right is centered on a corner.

http://oi61.tinypic.com/119osk4.jpg

[OldTrees1]

It is rather simple to deduce how the edge will look.

Centered on center
OOOOXXXOOOO
OOXXOOOXXOO
XXOOOOOOOXX

Centered on corner
OOOOXXOOOO
OOXXOOXXOO
XXOOOOOOXX

From that we can see that every 10ft of X we see a drop of -5ft in Y until we reach the circle's corner at X=Y. By expanding this out from each of the 4 cardinal directions, we can quickly map out a circle of any size(even say a 1305ft radius).

[heavyfuel]

1. Figure out which area effects you want to be able to easily measure.
2. Get some paper.
3. Convert the area-effect sizes to inches (5 feet in-game = 1 inch out-of-game)
4. Draw circles of the proper radius for burst effects, and quarter-circles of the appropriate side length for cones
5. Cut out the shapes, and punch out a small circle at the very center of each circle
6. Label each radius-effect and cone-effect template with the size of its area-effect (e.g. "20-foot radius")
7. When placing radius-effects on the battle grid, place the punched center hole over the target corner
8. When placing cone-effects, place the corner that forms a right angle over the corner of origin. Turn it to any angle you want.
9. Everything that is at least 50% underneath (or above, if you slid it under) the templates is in the area of effect.

Not restricting cones to 45º rotation intervals also increases their tactical use by a great deal.

Alternately, if you're feeling up for it, play on a hex map. It doesn't change gameplay at all, it gives cones twelve points and angles of origin rather than the normal eight (increasing their tactical effectiveness), and makes radii super easy to measure (pick a target square, and count 1 square outwards from it for every 5 feet in the radius).


Wire templates.
Bunch of companies make them, here is one.
http://paizo.com/companies/steelSqwire

Or make your own out of coat hangers.


Use a ruler. If a square is within x inches of the center, it's hit, assuming a grid of inch-wide squares.


Get a few common nails, some string, and stick-on labels. Tie string to a nail, measure out the battle grid inches for a common effect radius, and cut to that length. Wrap a stick-on label over the nail and adhere it to itself, then write the radius (each inch = 5') on that label. Repeat for other common radii. Make one extra, long and unlabeled, so you can grab the string at the actual distance and hold it against a yardstick for your measurement. Hauling out the yardstick is an annoyance, so having the premeasured "templates" that you can stretch out from the originating grid intersection is more convenient.


We used some spare pipe cleaners to make a variety of cones and bursts sized up from the templates for our battle grid.


Get a ruler, measure from the starting point of the effect to the center of the potential target's square. Easiest solution IMO unless you regularly run combats where large numbers of enemies are hit simultaneously.


I might convince the table to buy the templates, although making a DIY mini-project out of it is probably better. Thank you all for the suggestions!


If you've got access to a computer while you play, you could use this (https://docs.google.com/spreadsheet/pub?key=0AiCd3kHd21VzdGZVcFViaTZsc01teWtsNlUySjdVT 3c&output=html). Copy/paste it into a Google sheet or Excel spreadsheet and put a "=" in front of the formulae. Then just put in the coordinates of each target you think might be in range and it'll tell you the distance.

Hmmm, I do use my PC/Onenote to help my DMing, so that'll definitely help. Thanks! (PS: Nice Halloween avatar)


I extrapolated these 60-ft radius areas from the cone breath weapon diagrams in the Draconomicon a few years ago. The left picture is centered on a square and the right is centered on a corner.

http://oi61.tinypic.com/119osk4.jpg

This might work if printed, but even then, is a much better template because it pretty much has every radius that is normally used in a battle.


It is rather simple to deduce how the edge will look.

Centered on center
OOOOXXXOOOO
OOXXOOOXXOO
XXOOOOOOOXX

Centered on corner
OOOOXXOOOO
OOXXOOXXOO
XXOOOOOOXX

From that we can see that every 10ft of X we see a drop of -5ft in Y until we reach the circle's corner at X=Y. By expanding this out from each of the 4 cardinal directions, we can quickly map out a circle of any size(even say a 1305ft radius).

I'm not sure I understand you. Care to elaborate on that? Specifically, how would calculate the 1305ft radius? Wouldn't this make the shape rhombus-like for larger circles?

[OldTrees1]

I'm not sure I understand you. Care to elaborate on that? Specifically, how would calculate the 1305ft radius? Wouldn't this make the shape rhombus-like for larger circles?

Yes, D&D circles are IRL rhombuses.


How to draw a D&D circle with a 1305ft radius centered on a square:

Step 1:
Find the 4 squares that are 1305ft away orthagonally. [The Key Squares]

X
XX
X


Step 2:
Add the squares flanking the Key Squares.

XXX
X
X
XX
X
X
XXX


Step 3:
The next 2 squares in each direction are 1 square further in

OOXXXOO
XXOOOXX
OX
OX
XO
XO
XO
OX
OXXO
XO
OX
OX
OX
XO
XO
XXOOOXX
OOXXXOO


Step 4:
Repeat Step 3 until you close the D&D Circle

OOOOXXXOOOO
OOXXOOOXXOO
XXOOOOOOOXX
OOX
OOX
OXO
OXO
XOO
XOO
XOO
OXO
OXO
OOX
OOXXOO
XOO
OXO
OXO
OOX
OOX
OOX
OXO
OXO
XOO
XOO
XXOOOOOOOXX
OOXXOOOXXOO
OOOOXXXOOOO


I regularly use this for placing 30ft-120ft circular rooms. It takes less time than referencing a chart.

[JusticeZero]

I've yet to see any abuse of it. It isn't clear what "abuse" there would be; I certainly am not problematizing anything about it.

[Jeff the Green]

Hmmm, I do use my PC/Onenote to help my DMing, so that'll definitely help. Thanks! (PS: Nice Halloween avatar)

No problem. (And thanks.)

If you go back to it now (https://docs.google.com/spreadsheet/pub?key=0AiCd3kHd21VzdGZVcFViaTZsc01teWtsNlUySjdVT 3c&output=html), there'll be a new version. Copy of Sheet 2 actually follows RAW as I know it rather than semi-Euclidian distance. Just put the formulae in the pink boxes into a new sheet (copy them one at a time; for some reason when I try to copy the entire table it screws it up) and make sure it's aligned properly; Labels should be row 1, x distance should be A2, Y distance B2, etc.

[Astralia123]

As long as you center a square instead of a point, you can easily calculate the distance from the center to the specific square.

This is somewhat problematic, because in many cases the effective spell area's diameter is 5-feet longer than spell description.

[Astralia123]

Yes, D&D circles are IRL rhombuses.


How to draw a D&D circle with a 1305ft radius centered on a square:

Step 1:
Find the 4 squares that are 1305ft away orthagonally. [The Key Squares]

X
XX
X


Step 2:
Add the squares flanking the Key Squares.

XXX
X
X
XX
X
X
XXX


Step 3:
The next 2 squares in each direction are 1 square further in

OOXXXOO
XXOOOXX
OX
OX
XO
XO
XO
OX
OXXO
XO
OX
OX
OX
XO
XO
XXOOOXX
OOXXXOO


Step 4:
Repeat Step 3 until you close the D&D Circle

OOOOXXXOOOO
OOXXOOOXXOO
XXOOOOOOOXX
OOX
OOX
OXO
OXO
XOO
XOO
XOO
OXO
OXO
OOX
OOXXOO
XOO
OXO
OXO
OOX
OOX
OOX
OXO
OXO
XOO
XOO
XXOOOOOOOXX
OOXXOOOXXOO
OOOOXXXOOOO


I regularly use this for placing 30ft-120ft circular rooms. It takes less time than referencing a chart.

Just what I said, the diameter is 5 feet larger.
But well, who cares if EVERY spell affects an extra square? Let's forget about the stupid-centering-on-crossing-point way of drawing circles.

[Anlashok]

This is why D&D 4e's avant garde "**** it, it's a square" methodology has started to grow on me a bit.

[OldTrees1]

Just what I said, the diameter is 5 feet larger.
But well, who cares if EVERY spell affects an extra square? Let's forget about the stupid-centering-on-crossing-point way of drawing circles.

They are both useful for DMs that design their own rooms. I have had rooms with a 30ft diameter and rooms with a 25ft diameter depending on the size of the corridor they connect to. I have even had 20ft by 45ft oval rooms.

However I agree that spells should use one or the other. My Players use the "center on a square" casting.

[heavyfuel]

This is why D&D 4e's avant garde "**** it, it's a square" methodology has started to grow on me a bit.

As my 4e knowledge is sub-par at best, what exactly is this approach?


No problem. (And thanks.)

If you go back to it now (https://docs.google.com/spreadsheet/pub?key=0AiCd3kHd21VzdGZVcFViaTZsc01teWtsNlUySjdVT 3c&output=html), there'll be a new version. Copy of Sheet 2 actually follows RAW as I know it rather than semi-Euclidian distance. Just put the formulae in the pink boxes into a new sheet (copy them one at a time; for some reason when I try to copy the entire table it screws it up) and make sure it's aligned properly; Labels should be row 1, x distance should be A2, Y distance B2, etc.

Nice one! Thanks again mate

[OldTrees1]

As my 4e knowledge is sub-par at best, what exactly is this approach?


4E fireballs make Squares not RhombusesOctagons*.

Blast 5 would be
XXXXX
XXXXX
XXXXX
XXXXX
XXXXX
A 10ft 3.5 circle would be
OXXXO
XXXXX
XXXXX
XXXXX
OXXXO

The difference increases as the radius increases

*Wow it is late. I should have caught it earlier. 3.5 Circles are Octagons not Rhombuses.

[Divide by Zero]

As my 4e knowledge is sub-par at best, what exactly is this approach?

All area effects in 4E are squares.

[nedz]

Can you (or anyone) explain how you'd get the equivalent for three-dimensional movement? I've been trying to figure it out but geometry is not my strong suit.

It's just another special case of the general metric.
√ ( x2 + y2 + z2 )

for x = y = z = 1; that's √(3) or 1.732
and for x = y = z = 2; that's √(12), or 3.46, for a long diagonal.

for a partial diagonal move though, then it's the same as a 2D diagonal move.

[Curmudgeon]

It's just another special case of the general metric.
√ ( x2 + y2 + z2 )
Sorry, but that's not the way the RAW works. Any D&D diagonal follows the same rules: 5' on odd numbers of squares and 10' on even numbers. That's the case if the diagonal is 7.07' (2D diagonal) or 8.66' (3D diagonal). However, this gets complicated by the aerial maneuverability rules, with (usually) double movement cost when there's an upward component and (always) half movement cost when there's a downward component.

[nedz]

Sorry, but that's not the way the RAW works. Any D&D diagonal follows the same rules: 5' on odd numbers of squares and 10' on even numbers. That's the case if the diagonal is 7.07' (2D diagonal) or 8.66' (3D diagonal). However, this gets complicated by the aerial maneuverability rules, with (usually) double movement cost when there's an upward component and (always) half movement cost when there's a downward component.

Well I'm going to assume that we both know that my answer is mathematically correct — and I interpreted Jeff the Green's question in that light.

As to RAW — that talks about squares, at least in so far as diagonal movement in concerned.

As for the flying rules, well these are poorly defined. Some of the Maneuverability classes quote up angles of 45o or 60o yet you are left to your own devices on interpreting how these work on the battle grid.

[Elkad]

You've still got to count the hexes or count the squares in either case. With a hex mat you've got to use a straight edge to figure the shortest path unless it happens to be in one of those six easy directions.

Straight edge? You can eyeball whether a hex is closer to your destination or not. That is the only thing that matters. Take any path you want (that gets closer each time), you'll get the same answer every time.

For long ranges, it's even faster to just do the subtraction (that's why most hexes come numbered).

[Invader]

Wire templates.
Bunch of companies make them, here is one.
http://paizo.com/companies/steelSqwire

Or make your own out of coat hangers.

I second this.