I'm having trouble understanding cones because the portrayal of orthogonal cones in the Areas diagram in CRB Chapter 9 is inconsistent. For my own benefit, I drew a diagram here.
On the left side, I drew a 15 foot burst (cyan) and a 30 foot burst (red) originating from a corner of a character's space. I drew imaginary black lines to split the bursts into quarter circles. The filled-in cyan areas are my attempt to create 15 foot cones with this approach (orthogonal and diagonal), and the filled-in red areas are the same cones extended into 30 foot cones. I included the squares that the black lines cut through so that at least the 30 foot cones would match the ones in the Areas diagram.
On the right side, I did much the same, but with emanations from a single space instead. I also excluded the squares that the black lines cut through this time so that at least the 15 foot cones would match the ones in the Area diagram.
In both cases, the diagonal cones appear to be the same shape, so only the orthogonal ones are an issue. More of the orthogonal cones in the diagram seem to be two squares wide at the origin point, so that lends credence to the burst approach. However, I'm leaning towards the emanation approach as the more accurate one for a few reasons.
- Orthogonal cones still have more squares with this approach than diagonals, but to a lesser degree than the other approach.
- The Areas diagram puts no emphasis on the corner of the first square of a cone, unlike the bursts and lines in the same diagram.
- The rule text for orthogonal cones suggests that it comes from a square edge rather than a corner, similar to emanations.
So which cones are correct? The left ones? The right ones? Both?
Just because your cones are better, doesn‘t mean they‘re correct, I‘m afraid to say.
What I can imagine happened here, is that they did the 15‘ diagonal first, using it as a baseline. Then they chose the 7 sq orthogonal over the 8 sq for area similarity.
If one now looks at them separately and try and double the distance, quadrupling the area does seem to be the right solution: It does work perfectly with the diagonal; so you come up with the 28 sq monstrosity for the orthogonal. It‘s a bit like rounding in to steps from 1.49 to 1.5 to 2.
In many cases there are viable solutions, that are able to abstract reality in a better way than the RAW.
You can either stick to the book or houserule.
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You might find my Area Templates helpful in this discussion.
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.
.
Example: 30' diagonal cone.
⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜
Ⓜ️️️️️️️️️️️️️️️️️️️️️️⬜⬜⬜⬜⬜⬜⬜⬜
They are made from emoji that work on this site. You can easily cut and paste them into your posts and then modify them to show people your diagrams.
Just because your cones are better, doesn‘t mean they‘re correct, I‘m afraid to say.
You can either stick to the book or houserule.
Which cones are "my cones" precisely? I drew both sets of cones. I drew the "burst" ones on the left because that was consistent with the 30 foot and 60 foot cones in the Areas diagram. I drew the "emanation" ones on the right because that was consistent with the 15 foot cones in the Areas diagram. So which approach is RAW? Am I really supposed to use the "emanation" based 15 foot cone but the "burst" based 30 foot and 60 foot cones? What about 20 foot cones? 120 foot cones?
So which approach is RAW? Am I really supposed to use the "emanation" based 15 foot cone but the "burst" based 30 foot and 60 foot cones?
RAW is that you use the cone shapes as they are illustrated in the book.
For your convenience, my diagrams show the variations in positioning based on your choice of starting corner.
What about 20 foot cones? 120 foot cones?
Unless they have been added since I made my templates, there are no 20' or 120' cones in the game. They are all 15', 30', or 60'.
Shockwave has variable cone size between 15 and 60, and you can also go up to 70 using Widen Spell.
That's interesting. Thanks.
Shockwave has variable cone size between 15 and 60, and you can also go up to 70 using Widen Spell.That's interesting. Thanks.
Additionally, the Tarrasque has a 120-foot cone effect. We can't rely exclusively on the Areas diagram because it is not an exhaustive demonstration of every possible cone.
You might find my Area Templates helpful in this discussion.
I wish more people did this.
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As a general answer: trying to draw 90 degree cones on a square grid always has rounding errors. The diagonal cones handle these pretty well, the orthogonal cones don't. The larger your cone is, the better you can approximate a good-looking orthogonal cone.
I think there's also an element of history here: many of these templates originate in D&D 3.0 and only some of them have ever changed. That the larger cones start at corners makes sense if you know that in 3.x and PF1 bursts and emanations also started at corners, so it was at least consistent.
Actually it's really just the 15ft orthogonal cone that's not consistent with anything else. Everything else starts at a corner and calculates the distance from there. Just not the 15ft orthogonal cone; that one starts at the edge of a square.
Why? Probably because they didn't want the area between the diagonal and orthogonal to be too different on that one (7 or 8 squares). Also, the 15ft orthogonal code is kinda convenient to fire through just a small gap in your front line, which matters because the range is so short.
Whatever the reason; it's just the rule now. The rule just says "use the diagram", not "calculate it using this formula".
So what about drawing any other cones? Well the 30ft and 60ft cone are drawn in the same way, so if you have a 70 or 120ft cone to draw, you can just do it that way too. That's a pretty safe extrapolation.
The only really tricky question is how to draw a 20ft orthogonal cone, which could happen with Widen Spell and Burning Hands.
The rules don't really help you because they don't give you a geometric instruction; the rule is literally "The cone extends
out for a number of feet, widening as it goes, as shown in
the Areas diagram". Except we have no diagram for a 20ft cone. We don't know if we should use the 15ft or 30ft diagram to extrapolate from. You might get either:
⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜Ⓜ️️️️️️️️️️️️️️️️️️️️️️⬜⬜⬜
⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬜
or
⬜⬜⬜Ⓜ️️️️️️️️️️️️️️️️️️️️️️⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜
I think I'd probably go with the first one, because:
* 20 is closer to 15 than to 30
* The first diagram has an area of 12 squares. The second one has an area of 16 squares. Compare that to the area of the diagonal 20ft cone:
⬜⬜⬜⬜⬜⬜⬜
⬜Ⓜ️️️️️️️️️️️️️️️️️️️️️️⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜
The diagonal cone has only 10 squares. So to avoid the area of the cone being drastically bigger depending on the rotation, the first diagram is best.
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You might find my Area Templates helpful in this discussion.I wish more people did this.
Well it was your brilliant idea to use the emojis this way. :)
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This topic got me intrigued so I did a little thinking about it. I see that Ascalaphus has beaten me to this, but the fact that we independently came to similar conclusions makes me think we are on the right basic path.
-----
I started by coming up with a few design principles:
• The lengths of the cones need to follow the normal rules for distance.
• The cones need to originate from a corner.
• The cones should cover a 90° arc.
• The cones should be symmetrical along their midlines.
• All four diagonal cones should be the same shape as each other.
• All four orthogonal cones should be the same shape as each other.
• The diagonal cones should cover approximately the same area as the orthogonal ones.
—--
Let’s start applying these principle to the 30’ cones. Because the cones are supposed to originate froma corner rather than the center of a square, it makes sense to start with a 30’ burst which originates from a corner at the center of the burst.
30’ Burst
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
If I draw horizontal and vertical lines through the corner at the center, then the burst splits into the four sections shown below.
30’ Diagonal Cones (24 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
These are exactly the same shape as the 30’ cone shown in the CRB so this methd seems to work correctly.
—--
Applying the same process to bursts from 15’ to 70’ produces the following results. (The arrows point to the corner of origin.)
15’ Diagonal Cone (6 squares)
⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜
⬜⬛⬛⬜⬜
⬜⬛⬛⬛⬜
↗️⬜⬜⬜⬜
20’ Diagonal Cone (11 squares)
⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜
25’ Diagonal Cone (17 squares)
⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜
30’ Diagonal Cone (24 squares)
⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜
35’ Diagonal Cone (33 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜
40’ Diagonal Cone (43 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜
45’ Diagonal Cone (54 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
50’ Diagonal Cone (67 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
55’ Diagonal Cone (81 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
60’ Diagonal Cone (96 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
65’ Diagonal Cone (113 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
70’ Diagonal Cone (131 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Other than possibly not matching the size of the orthogonal cones, these all satisfy the design principles that I set.
In addition to producing the CRB version of the 30’ cone, both the 15’ cone and the 60’ cone match those shown in the CRB. That makes me think that I’ve followed the correct process.
—--
Now let’s take a look at the orthogonal cones. Let’s start with a 30’ burst again.
30’ Burst
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Drawing two diagonal lines through the center corner creates a problem that we didn’t have with the diagonal cones. The lines pass through some of the squares rather than between squares. I’m not sure what to do with those, so I’m going to leave them in place to start with.
30’ Orthogonal Cones? (20 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Notice that the separated sections are only 25’ long, so we’ve got a major problem. We have 16 squares unused, so I’ll try reattaching 4 of them to one side of each of the four sections.
30’ Orthogonal Cones? (24 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
The lack of symmetry is a problem, so I’ll try adding four more squares symmetrically to each cone. Essentially I’m duplicating each of the diagonal line of squares when I split the burst into 4 pieces.
30’ Orthogonal Cones? (28 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
This fixes our problems and produces the same shape as that in the CRB, so it seems to be the correct approach. But the area of these cones, 28 squares, doesn’t match the 24 squares of the corresponding diagonal cones. From the diagonal cones to the orthogonal cones there is a ((28–24)/24)•100%=16 ⅔% increase in area. That’s not great, but I can see why the designers were willing to live with it to satisfy all of those other criteria.
—--
Applying the same process to bursts from 15’ to 70’ produces the following results. (The arrows point to the corner of origin.)
15’ Orthogonal Cone? (8 squares)
⬜⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬜⬜
⬜⬜↗️⬜⬜⬜
20’ Orthogonal Cone? (14 squares)
⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬜↗️⬜⬜⬜⬜
25’ Orthogonal Cone (20 squares)
⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬜↗️⬜⬜⬜⬜
30’ Orthogonal Cone (28 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜
35’ Orthogonal Cone (38 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜
40’ Orthogonal Cone (48 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜
45’ Orthogonal Cone (60 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜
50’ Orthogonal Cone (74 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜⬜
55’ Orthogonal Cone (88 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜⬜
60’ Orthogonal Cone (104 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜
65’ Orthogonal Cone (122 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
70’ Orthogonal Cone (140 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜↗️⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
In addition to producing the CRB version of the 30’ cone, this method has produced the CRB version of the 60’ cone. That suggests that this is the method that the designers used.
But importantly it hasn’t produced the CRB version of the 15’ cone. I think I know why that is, but we need to compare the sizes of all the diagonal cones to their orthogonal counterparts in order to see why.
Length (approximate % Increase)
15’ (33%)
20’ (27%)
25’ (18%)
30’ (17%)
35’ (15%)
40’ (12%)
45’ (11%)
50’ (10%)
55’ (9%)
60’ (8%)
65’ (8%)
70’ (7%)
The 30’ diagrams in the CRB indicate that 17% was considered to be within the acceptable range so I think that the 25’ through 70’ versions are fine. I think that they changed the 15’ version because it has a whopping 33 ⅓% increase. So how should it be fixed?
—--
Let’s go back to the basics and start with a 15’ burst.
15’ Burst
⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜
If we split off the non-diagonal squares we get these ‘cones.’
15’ Orthogonal Cones? (4 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜
⬜⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬜
⬜⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬜
⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Obviously, those are too short, so I’ll try the duplicating trick that we used for the 30’ cones. I’ll duplicate each of the 8 diagonal squares and reattach 4 of them to each cone.
15’ Orthogonal Cones? (8 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
That's how I made the cones that were too much larger than the diagonal ones. So what if we try just adding 2 of the diagonal squares to each of the four sections?
15’ Orthogonal Cones? (6 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜
⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
These are exactly the same size as the diagonal cones, but we have the symmetry issue again. We can restore symmetry by adding just a single square to each
15’ Orthogonal Cones? (7 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜
⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜
⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜
⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
It’s a reasonable compromise. The area increase is now ((7–6)/6)•100%=16 ⅔% which is the same as that for the 30’ cones, we haverestored symmetry, and the cone is now 15’ long. This is my best quess as to how they came up with the CRB version of the 15’ orthogonal cone.
15’ Orthogonal Cone (7 squares)
⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜
⬜⬛⬛⬛⬜
⬜⬜⬛⬜⬜
⬜⬜Ⓜ️️️️️️️️️️️️️️️️️️️️️️⬜⬜
I’m unclear whether the same process should be applied to the 20’ orthogonal cone, as well, or if a 27% increase is within the acceptable range. If we were to modify it I think the result would look something like this.
20’ burst
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Split it, leaving the diagonal squares alone.
20’ Orthogonal Cones? (8 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜
⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜
⬜⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬜
⬜⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬜
⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Reattach each of the diagonal squares to the 4 sections.
20’ Orthogonal Cones? (11 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
Correcting the asymmetry by adding one square to each gives us the following.
20’ Orthogonal Cones? (12 squares)
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
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This brings the area increase to ((12–11)/11)•100%=9%. This gets rid of all the cases where the % increase is greater than 18% – right around the value for the 30’ cones which we know is acceptable.
Length (approximate % Increase)
15’ (17%)
20’ (9%)
25’ (18%)
30’ (17%)
35’ (15%)
40’ (12%)
45’ (11%)
50’ (10%)
55’ (9%)
60’ (8%)
65’ (8%)
70’ (7%)
20’ Orthogonal Cone (12 squares)
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This is my best guess for the 20’ orthogonal cone.
This would mean that all of the orthogonal cones are derived using the same process, except for the 15’ and 20’ cones which are slightly modified to have comparable areas with their diagonal counterparts.
It's still weird to use both methods for the orthogonal cones, though. A 15' cone should not suddenly become wider at the start if it extends 15' further than before. The angle at the start hasn't changed.
Even ignoring the terrible example set by the Areas diagram, the one in the text isn't much better.
For instance, when a green dragon uses its breath weapon, it breathes a cone of poisonous gas that originates at the edge of one square of its space and affects a quarter-circle area 30 feet on each edge.
This contradicts the corner-based 30' cone shown in the Areas diagram.
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If there truly is a "first square of the cone" for us to use the edge of as the origin of the cone, then which square are we using? The distance to the leftmost part of the cone and the rightmost part must both be 30 feet, so neither square works. Furthermore, I am only assuming the dragon is Large, since I can't find a green dragon with a cone of only 30 feet.
Maybe the example in the Line rules is better.
For example, the lightning bolt spell’s area is a 60-foot line that’s 5 feet wide.
Area 120-foot line
My disappointment is immeasurable, and my day is ruined.
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The rules for cones say "A cone shoots out from you in a quarter circle on the grid." For every cone over 15 feet, you need to make a Burst of the appropriate range first, and take only a quarter of that burst. You can split is in either a + or X fashion. You should follow the pre-made templates in the Area rules for reference.
Also, I too made a cone shape example, for every range between 15 to 60, seen here.
The rules for cones say "A cone shoots out from you in a quarter circle on the grid." For every cone over 15 feet, you need to make a Burst of the appropriate range first, and take only a quarter of that burst. You can split is in either a + or X fashion. You should follow the pre-made templates in the Area rules for reference.
Also, I too made a cone shape example, for every range between 15 to 60, seen here.
Nice diagrams!
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The programmer part of me was getting strong Conway's Game of Life vibes from some of those, lol.
The rules for cones say "A cone shoots out from you in a quarter circle on the grid." For every cone over 15 feet, you need to make a Burst of the appropriate range first, and take only a quarter of that burst. You can split is in either a + or X fashion. You should follow the pre-made templates in the Area rules for reference.
Also, I too made a cone shape example, for every range between 15 to 60, seen here.
Why conclude from that sentence that the circle to take a quarter of must be a Burst rather than a single-space emanation?
Because all the CRB's examples other than the 15ft orthogonal cone are quarters of a burst.
Alright, then. But the Areas diagram doesn't show any cones greater than 15 feet and less than 30 feet in length. Why use the burst for those?
I wish this stuff was covered in the FAQ. How do questions usually make it into the FAQ?
I wish this stuff was covered in the FAQ. How do questions usually make it into the FAQ?
Obscure Magic.
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Because all the CRB's examples other than the 15ft orthogonal cone are quarters of a burst.Alright, then. But the Areas diagram doesn't show any cones greater than 15 feet and less than 30 feet in length. Why use the burst for those?
Because out of the 6 examples for cones we are given, only a single one uses an emanation for its base.
If you are shown 5 examples on how to something, and 1 example on how to do it differently, how could you not assume the method shown more is the default, while the outlier is an exception?
So stop asking this same question in different ways. I have given my answer, and if you can't accept it then tough luck.
Also, things only get into the Frequently Asked Questions list if they're frequently asked, and as far as I can tell the cone examples we have all given in this thread are widely accepted as correct.
I still have the impression that the 30-foot and 60-foot cones are genuinely a mistake made by an illustrator who was thinking of 1e cones. Have there been any later official drawings of orthogonal cones that could be used to better discern the developers' intent?
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Just read the text on how to draw a cone. That's all you need to do. Forget the templates. The text says it all
Well the text says:
The cone extends out for a number of feet, widening as it goes, as shown in the Areas diagram.
First edition had an actual description for how to draw a cone. (And IIRC, back then the diagram didn't match with the description either.) Second edition tells you to just use the diagram.
The second edition way sidesteps all mathematical ambiguity (because there is no math) as long as you use standard cones. Sadly they didn't put cones in the diagram for areas you can create with Widen Spell.
It does not tell us to just use the diagrams, because the diagrams don't and can't cover all circumstances; like widened spells, as you say. The fact that we also have diagrams is a nice touch, but not necessary for knowing the rules for drawing cones. They are helpful examples
I don't think we would be having this discussion if the provided diagrams were helpful examples, but yes, I do agree that the text probably gives a better indication of what the orthogonal cones should look like.