Shouldn't your point of origin be a 5ft tile, rather than being on the lines? I feel like since each tile is usually 5ft, then 15ft would be three tiles in front of you, otherwise how could you got someone 5ft away?
By definition, when playing on a grid, you snap AOEs to grid intersections, not grid spaces, but Xanathar's has alternate AOE rules for grids. You might find the token method more intuitive.
To argue the shape of a cone from the diagonal, um, use math. A cone of length 2 diagonals away from you is two diagonals wide. There's a little estimation at the end, but here is what I came up with. It's a nice color coded chart :D
(I don't know why it won't let me attach the image. But here is the link):
I think "use math" works the same whether you are on a diagonal or not or anywhere between. But actually using math at the table would slow down the gameplay so much that it would make cone spells atrocious to use. I'd argue that if you want to "use math" then you do it by making some sort of readable/usable template and just apply that.
Wysperra, I hadn't noticed this until when this topic came back up, but your hex examples all assume points of origin as an entire hex, rather than intersections. It make for some quite wonky circular spells. Your 5' radius spell has a 15' diameter and hits 7 spaces instead of 4, as we'd expect in squares. Shouldn't the points of origin be at vertices (meaning a 5' radius only hits a triangle of 3 spaces in hex land)?
I think you don't need to think so hard even if you are using squares you simply make a triangle, mechanically even if the lines of the cone are drawn through middles of the squares the spell will still effect the entity so in my opinion a 15 feet cone should be like 5, 15, 25 as in increase in width for every 5 feet away from the point of origin.
Pretty sure cones would have to work in one of these ways if you're going for RAW. Bottom line is that a 30 foot cone would cover an area of 21 squares in a vague triangular shape. The problem with the 90deg cone is it really cuts into the forward range but as long as you only cover 21 squares I would rule as legal. So the player has the choice of narrow and long or wide and short. I have seen players try to go 90 degrees and 6 diagonal intersections which is just too much area.
The diagonal cones that look like 90 degree shapes are not in line with RAW. These shapes do not satisfy the requirement of having the same cone width as the distance from the origin point.
A more accurate attempt would be something like this (pointing northeast, affected squares marked by X):
The diagonal cones that look like 90 degree shapes are not in line with RAW.
You're right. According to the cone description from PHB, the triangle should be almost equilateral, so a 60-degree angle is a more accurate representation, as far as I understand.
For me, one of best representation is the one proposed by @Seventhguest on this page.
Based on if the length of how far the cone is out (30ft) i have found that the cone at the end reaches a height of 80ft and the sides equal 57ft (thank trigonometry it actually useful)
Based on if the length of how far the cone is out (30ft) i have found that the cone at the end reaches a height of 80ft and the sides equal 57ft (thank trigonometry it actually useful)
Could you provide me with how you obtained those values?
As far as I understand, a 30 feet cone at the end has a diameter of 30 feet (or a radius of 15 feet), so the height should also be 30 feet, right?
Based on if the length of how far the cone is out (30ft) i have found that the cone at the end reaches a height of 80ft and the sides equal 57ft (thank trigonometry it actually useful)
Could you provide me with how you obtained those values?
As far as I understand, a 30 feet cone at the end has a diameter of 30 feet (or a radius of 15 feet), so the height should also be 30 feet, right?
Sorry to revive an old thread, but sometimes I need to write things out to really grasp them. As amny have already cited:
Cone
A cone extends in a direction you choose from its point of origin. A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise.
The first sentence is not in contention, I think most agree with that. Moreover, the sentence in the second paragraph is moot for this conversation. Thus, the only point of clarification needed is the following:
A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
Historically in this thread, there are two interpretations of length - one that is mathematically correct, and the other which is not technically correct mathematically, but could still be the intent of the designers. I will argue that, in either case, the resulting shape could not be that of the rightmost image in Diagram 2.5 on page 87 of XGtE (the one with the 90-degree angle). Moreover, I will show that some (if not most) of the "spell template" products you buy are incorrectly cut (I have the ones from ArcKnight and, while nice to look at and use for non-cones, they are not correct for cones).
For this brief discussion, let's remove the three-dimensional discussion as any cross-sectional cut of a cone parallel to the caster's extended arm (assuming the spell emanates from the caster's hand) is always a triangle. Moreover, it has already been stated, but for clarification, a three-dimensional cone (think of traffic cones) does not have a rounded base. That is, the farthest edge of a cone is not a sector of a sphere - it is flat.
Hence, the two-dimensional cross-section will always be a triangle (again, not the sector of a circle).
Assumptions
A cone's width is defined to be the length of the line segment connecting two points on the edge of the cone that are equidistant to the cone's origin. That is,
(if you cannot see that image, the direct link is here). This definition of width seems to have been agreed upon and it matches nice with the base diameter definition from mathematics.
The word "point" in the description given by the designers is only vague because we don't all agree on the designers' intent with the word length. Thus, let's consider the only two viable definitions for length.
Mathematical Length of a Cone
As has been mentioned, in mathematics, the length of a cone is the measure of the shortest distance along its edge from the tip of the cone (the caster in our case) to the base of the cone (the edge of the spell in our case). If this is the definition we adhere to, then the cone's width at any point is the same as the edge length of our triangle. That is,
(again, if you cannot see that, please see here). In this case, we have an equilateral triangle and, as such, the angle between the side lengths of the area of effect is 60 degrees.
Pause to check if the designers can do mathematics
Here is the moment you should go to XGtE and discover that the designers think this is a 90-degree angle. This is also the moment you should grade that template you bought, make two copies of it and fan them out. If, when combined edge-to-edge, they form a straight angle (180-degree angle), then the person who designed your template knew what they were doing. If you have anything other than a 180-degree angle, they used the non-math definition.
Alternative Length of a Cone
I only include this for completeness, as this is not how the length of a cone is defined; however, the designers decided to not tell us their version of length, so it is in our hands to figure out what they meant.
The only other conventional definition that could be acceptable for the word length here is the length of the perpendicular bisector from the caster to the far edge of the spell. That is,
(again, here is a link). Based on WotC bad math in the past, and lack of wanting to even think mathematically, I don't believe this is what they meant, but let's play the game. If L is the length then L = W in that image. Therefore, looking at the lower triangle, we have a right triangle with legs L and L/2 and hypotenuse (by the Pythagorean Theorem) of sqrt(5)/2 L (EDIT: I also made a math error there, but it is now fixed... but not in the following image). That is,
(link). Since the sine is opposite over hypotenuse, the angle between the spell's edge and the perpendicular bisector is arcsin(1/sqrt(5)) ~ 26.6 degrees. Double this, and we have the alternative reality angle of roughly 53.1 degrees.
Pause to check the designers again
This still doesn't agree with the designer's 90 degree visual in XGtE. Moreover, if this were the agreed upon convention, then three of your cone templates, edge-to-edge, should from an angle slighlty greater than 180 degrees. My guess is that this is not the case (as it is not with ArcKnight's products nor is it correct in Guilt-Free Gaming's templates).
The moral of the story is this: Reality bends to the lowest common denominator eventually. If we say something is true long enough without ever questioning it, people will eventually defend the incorrectness not out of logic, but out of unwillingness to think or move the needle away from the status quo. This has been the evolution of D&D since its inception but has only been exacerbated in the last decade or so. I call it - the dumbening.
D&D 3.5e had 90-degree cones, but this is not the case in 5e.
@SagaTympana posted the XGtE's diagram here. To me, it doesn’t look like the cone in that book is 90 degrees wide. It's actually quite good!
Cones in 5e are not equilateral triangles because not all the angles are 60 degrees. But it's true they're almost equilateral. If you follow the description from the PHB, you will get something like this, where C is the caster:
D&D 3.5e had 90-degree cones, but this is not the case in 5e.
@SagaTympana posted the XGtE's diagram here. To me, it doesn’t look like the cone in that book is 90 degrees wide. It's actually quite good!
Cones in 5e are not equilateral triangles because not all the angles are 60 degrees. But it's true they're almost equilateral. If you follow the description from the PHB, you will get something like this, where C is the caster:
ACK!
There's goes my cred! Thanks for catching the error.
Also, the only reason the cones in D&D are not equilateral is because of the language they are using. They are defining length to be the altitude (or length of perpendicular bisector) of the triangle - not what the length actually is mathematically. I am fine with that; however, this means that a 60-foot cone (which has a maximum perpendicular bisector length of 60 feet) can damage/affect targets along its edges up to 67 feet away from the caster. This gives an extra 10 feet (since the AoE bleed into those extra squares) along the edges.
In other words:
PLAYER: How far away is the enemy?
DM: 70 feet... sorry, he is outside of the area of your Cone of Cold.
PLAYER: That's fine, I will aim 26 degrees to his left so I hit him.
By definition, when playing on a grid, you snap AOEs to grid intersections, not grid spaces, but Xanathar's has alternate AOE rules for grids. You might find the token method more intuitive.
"Sooner or later, your Players are going to smash your railroad into a sandbox."
-Vedexent
"real life is a super high CR."
-OboeLauren
"............anybody got any potatoes? We could drop a potato in each hole an' see which ones get viciously mauled by horrible monsters?"
-Ilyara Thundertale
To argue the shape of a cone from the diagonal, um, use math. A cone of length 2 diagonals away from you is two diagonals wide. There's a little estimation at the end, but here is what I came up with. It's a nice color coded chart :D
(I don't know why it won't let me attach the image. But here is the link):
Diagonal Cone Spell Area
What about non-diagonal?
"Sooner or later, your Players are going to smash your railroad into a sandbox."
-Vedexent
"real life is a super high CR."
-OboeLauren
"............anybody got any potatoes? We could drop a potato in each hole an' see which ones get viciously mauled by horrible monsters?"
-Ilyara Thundertale
I think "use math" works the same whether you are on a diagonal or not or anywhere between. But actually using math at the table would slow down the gameplay so much that it would make cone spells atrocious to use. I'd argue that if you want to "use math" then you do it by making some sort of readable/usable template and just apply that.
Wysperra, I hadn't noticed this until when this topic came back up, but your hex examples all assume points of origin as an entire hex, rather than intersections. It make for some quite wonky circular spells. Your 5' radius spell has a 15' diameter and hits 7 spaces instead of 4, as we'd expect in squares. Shouldn't the points of origin be at vertices (meaning a 5' radius only hits a triangle of 3 spaces in hex land)?
“Orthogonal”
That or gridless
I think you don't need to think so hard even if you are using squares you simply make a triangle, mechanically even if the lines of the cone are drawn through middles of the squares the spell will still effect the entity so in my opinion a 15 feet cone should be like 5, 15, 25 as in increase in width for every 5 feet away from the point of origin.
https://photos.app.goo.gl/z8qty9FDMFVzxht16
Pretty sure cones would have to work in one of these ways if you're going for RAW. Bottom line is that a 30 foot cone would cover an area of 21 squares in a vague triangular shape. The problem with the 90deg cone is it really cuts into the forward range but as long as you only cover 21 squares I would rule as legal. So the player has the choice of narrow and long or wide and short. I have seen players try to go 90 degrees and 6 diagonal intersections which is just too much area.
The diagonal cones that look like 90 degree shapes are not in line with RAW. These shapes do not satisfy the requirement of having the same cone width as the distance from the origin point.
A more accurate attempt would be something like this (pointing northeast, affected squares marked by X):
OOXOOO
OOXXOO
OXXXXO
XXXXXX
XXXXXX
XXOOOO
You're right. According to the cone description from PHB, the triangle should be almost equilateral, so a 60-degree angle is a more accurate representation, as far as I understand.
For me, one of best representation is the one proposed by @Seventhguest on this page.
Based on if the length of how far the cone is out (30ft) i have found that the cone at the end reaches a height of 80ft and the sides equal 57ft (thank trigonometry it actually useful)
"Sooner or later, your Players are going to smash your railroad into a sandbox."
-Vedexent
"real life is a super high CR."
-OboeLauren
"............anybody got any potatoes? We could drop a potato in each hole an' see which ones get viciously mauled by horrible monsters?"
-Ilyara Thundertale
Cubes are missing from your diagram. What does a 10' cube look like in hexes?
It looks like a rhombus - a tilted square/diamond
Could you provide me with how you obtained those values?
As far as I understand, a 30 feet cone at the end has a diameter of 30 feet (or a radius of 15 feet), so the height should also be 30 feet, right?
I’m guessing trig wasn’t their best subject.
Creating Epic Boons on DDB
DDB Buyers' Guide
Hardcovers, DDB & You
Content Troubleshooting
Sorry to revive an old thread, but sometimes I need to write things out to really grasp them. As amny have already cited:
The first sentence is not in contention, I think most agree with that. Moreover, the sentence in the second paragraph is moot for this conversation. Thus, the only point of clarification needed is the following:
Historically in this thread, there are two interpretations of length - one that is mathematically correct, and the other which is not technically correct mathematically, but could still be the intent of the designers. I will argue that, in either case, the resulting shape could not be that of the rightmost image in Diagram 2.5 on page 87 of XGtE (the one with the 90-degree angle). Moreover, I will show that some (if not most) of the "spell template" products you buy are incorrectly cut (I have the ones from ArcKnight and, while nice to look at and use for non-cones, they are not correct for cones).
For this brief discussion, let's remove the three-dimensional discussion as any cross-sectional cut of a cone parallel to the caster's extended arm (assuming the spell emanates from the caster's hand) is always a triangle. Moreover, it has already been stated, but for clarification, a three-dimensional cone (think of traffic cones) does not have a rounded base. That is, the farthest edge of a cone is not a sector of a sphere - it is flat.
Hence, the two-dimensional cross-section will always be a triangle (again, not the sector of a circle).
Assumptions
A cone's width is defined to be the length of the line segment connecting two points on the edge of the cone that are equidistant to the cone's origin. That is,
(if you cannot see that image, the direct link is here). This definition of width seems to have been agreed upon and it matches nice with the base diameter definition from mathematics.
The word "point" in the description given by the designers is only vague because we don't all agree on the designers' intent with the word length. Thus, let's consider the only two viable definitions for length.
Mathematical Length of a Cone
As has been mentioned, in mathematics, the length of a cone is the measure of the shortest distance along its edge from the tip of the cone (the caster in our case) to the base of the cone (the edge of the spell in our case). If this is the definition we adhere to, then the cone's width at any point is the same as the edge length of our triangle. That is,
(again, if you cannot see that, please see here). In this case, we have an equilateral triangle and, as such, the angle between the side lengths of the area of effect is 60 degrees.
Pause to check if the designers can do mathematics
Here is the moment you should go to XGtE and discover that the designers think this is a 90-degree angle. This is also the moment you should grade that template you bought, make two copies of it and fan them out. If, when combined edge-to-edge, they form a straight angle (180-degree angle), then the person who designed your template knew what they were doing. If you have anything other than a 180-degree angle, they used the non-math definition.
Alternative Length of a Cone
I only include this for completeness, as this is not how the length of a cone is defined; however, the designers decided to not tell us their version of length, so it is in our hands to figure out what they meant.
The only other conventional definition that could be acceptable for the word length here is the length of the perpendicular bisector from the caster to the far edge of the spell. That is,
(again, here is a link). Based on WotC bad math in the past, and lack of wanting to even think mathematically, I don't believe this is what they meant, but let's play the game. If L is the length then L = W in that image. Therefore, looking at the lower triangle, we have a right triangle with legs L and L/2 and hypotenuse (by the Pythagorean Theorem) of sqrt(5)/2 L (EDIT: I also made a math error there, but it is now fixed... but not in the following image). That is,
(link). Since the sine is opposite over hypotenuse, the angle between the spell's edge and the perpendicular bisector is arcsin(1/sqrt(5)) ~ 26.6 degrees. Double this, and we have the alternative reality angle of roughly 53.1 degrees.
Pause to check the designers again
This still doesn't agree with the designer's 90 degree visual in XGtE. Moreover, if this were the agreed upon convention, then three of your cone templates, edge-to-edge, should from an angle slighlty greater than 180 degrees. My guess is that this is not the case (as it is not with ArcKnight's products nor is it correct in Guilt-Free Gaming's templates).
The moral of the story is this: Reality bends to the lowest common denominator eventually. If we say something is true long enough without ever questioning it, people will eventually defend the incorrectness not out of logic, but out of unwillingness to think or move the needle away from the status quo. This has been the evolution of D&D since its inception but has only been exacerbated in the last decade or so. I call it - the dumbening.
D&D 3.5e had 90-degree cones, but this is not the case in 5e.
@SagaTympana posted the XGtE's diagram here. To me, it doesn’t look like the cone in that book is 90 degrees wide. It's actually quite good!
Cones in 5e are not equilateral triangles because not all the angles are 60 degrees. But it's true they're almost equilateral. If you follow the description from the PHB, you will get something like this, where C is the caster:
ACK!
There's goes my cred! Thanks for catching the error.
However, the image that was sent to you is only 1/3 of the images on those two pages concerning cones. Go to Dungeon Master's Tools - Xanathar's Guide to Everything - Dungeons & Dragons - Sources - D&D Beyond (dndbeyond.com) and scroll down to Diagram 2.5. You will see what I am talking about.
Also, the only reason the cones in D&D are not equilateral is because of the language they are using. They are defining length to be the altitude (or length of perpendicular bisector) of the triangle - not what the length actually is mathematically. I am fine with that; however, this means that a 60-foot cone (which has a maximum perpendicular bisector length of 60 feet) can damage/affect targets along its edges up to 67 feet away from the caster. This gives an extra 10 feet (since the AoE bleed into those extra squares) along the edges.
In other words:
PLAYER: How far away is the enemy?
DM: 70 feet... sorry, he is outside of the area of your Cone of Cold.
PLAYER: That's fine, I will aim 26 degrees to his left so I hit him.