5e Arcs should be 60 degrees not 90 degrees?

[wheelmanforhire]

Hello, have been using Fantasy Grounds for several months and just realized the cones/arcs in FG (90 degrees) are too wide for 5e spell cones!

Spell effect arcs in 5e are defined as "A cone's width at a given point along its length is equal to that point's distance from the point of origin" (pg 204 PHB).

Pretty sure that is mathematically an angle of 60 degrees (slightly less if you're drawing the arc from the perimeter of the casters square vs from the center).

Could we get one of the following (in order of flexibility - and preference)
a) an arc control adjuster on the arc... right now you can drag to adjust radius (good)... but we need another control to adjust arc's degrees - this allows for arcs of any degree and radius.
b) A pref for setting the fixed arc degrees
c) A patch that changes the arc degrees in 5e to 60 degrees.

Thanks!

[Moon Wizard]

My trig is really rusty, but I believe it works out to ~53 degrees. I'm sure Dulux-Oz will be able to give more exact figures.

There are ways to have extensions provide custom pointers such as a 45/60 degree cones through Lua code, but there is no built-in way to do that with the current engine. We'll probably wait until Unity rebuild to look at something like this.

Regards,
JPG

[dulux-oz]

Since I was asked: :)

Yeah, it's 53.13 degrees. You end up with a triangle with the short side x, the long side 2x (not the hypotenuse), and therefore the acute angle is (1/2)*tan^(-1), (opposite on adjacent) which is half the full angle, so double it - and you get 53.13 degrees.

I did some work on using different shaped Pointers a while back and put it up on the FG Wiki under "Pointer Toolkit"- it won't work "out of the box" but it allows someone to write code to have Pointers of all sorts of shapes and sizes.

Edit: I originally said 60 degrees, but then my sub-conscious went to work and kept nagging at me. :)

[wheelmanforhire]

I almost TPK'd a party with Extra Wide (tm) spell arcs :D

I had dine some looking before posting... And saw Delux-Oz's shaped pointers stuff... And read most of it! I was worried that each new FG update would wipe out the customization (or prevent the upgrade)?

Also I struggled with finding and opening the pak files to even try to find where to insert the custom code. It was easier to make a token spell template. I'm s programmer but not familiar with FG customization, so I didn't take that road.

[gandhi39]

20318

20319

Based on page 204 of the PHB, I believe the side length ("l" on the first picture) should be equal to twice the radius (width = 2x the radius), resulting on an equilaterus triangle, with 60º angles (as on the second picture).

[Nylanfs]

Don't be bringing no mathz and geometry into our game! :-)

[Griogre]

The side legs of the 5E cone are the same length of an equilateral triangle, yes, but the part opposite the origin should be an arc so that "at a given point along its length is equal to that point's distance is equal to that's points distance from the point of origin."

Basically, one leg "sweeps" around to the other one so you have a piece of pie shaped cone that is one sixth of a circle.

[lordjeb]

You had me at pie. ;)

[Griogre]

LOL, you know - now that I look at the book illustration and read that thing again... you've converted me. The base of a 3D cone is flat so from the perspective of someone being shot the area would be a triangle. Years of other editions have clouded my mind - most recently 4E which mostly ignored the 3rd dimension on areas.

[Andraax]

20318

20319

Based on page 204 of the PHB, I believe the side length ("l" on the first picture) should be equal to twice the radius (width = 2x the radius), resulting on an equilaterus triangle, with 60º angles (as on the second picture).

Dulux-Oz is correct. It's not quite an equilateral triangle. You're not measuring the side of the cone, but a line through the center. It looks more like this:

https://s3.silent-tower.org/images/Cone.jpg

The upper triangle is a right triangle (angle A is 90 degrees). Therefore, the tangent of angle B is 1/2 X divided by X, or 1/2. My calculator says the arctan of .5 is ~26.565 degrees. Double this for ~53.13 degrees.

[Griogre]

Damn, I should of paid more attention in that self paced trig class. :p It was the last class I took at UCSB and all I really remember about it was that trig was real practical math - and that calculators and computers where made to eat up this stuff. :)

[Andraax]

And, the triangle solver app on my calculator concurs...

https://s3.silent-tower.org/images/Cone2.jpg

https://s3.silent-tower.org/images/Cone3.jpg

Or, using the top half of my previous diagram (again, you have to double angle B):

https://s3.silent-tower.org/images/Cone1.jpg

[Griogre]

This is the type of thing where I really like to know what the designer was thinking - clearly simplification of some sort but why a 63.5 63.5 53 degree triangle would be considered simpler than a 60 60 60 one? Seems like one of those things that happened due to a "translation" from designer notes to a rulebook manual.

[gandhi39]

Let's say I cast my cone straight forward. The top point of the cone comes out of my hand. It then goes foreward drawing a line paralel to the ground ending at the center of a circle perpendicular to that line. The line is the height of the cone.

Now let's say a bird is flying above the battleground. In 2D it sees an equilaterus triangle. Of course there is half of the cone above and half of it below that triangle. But ideally the bird does not actually see the 3D cone.

I think the best way to draw a cone on the battlegrid is an equilaterus triangle, not a slice of a circle (not an arc). Otherwise the area of effect of certain spells would be defined as an arc, not a cone. I mean: it's not a cone with part of a sphere coming out of it's circle base. It ends on the circle.

The trick is: you wouldn't choose the height of this triangle, but the length of a side.

Someone mentioned an extension to make custom pointers. Could I make equilaterus triangles defined by the length of their sides with this extension?

[Moon Wizard]

The settings in the client support setting the default cone angle to 30,45, 60, 90, 120 and 180 as well as "5E" (which is the result of this discussion).

You can override the default cone angle setting using an extension with the imagesettings tag.
https://www.fantasygrounds.com/refdoc/imagesettings.xcp

Regards,
JPG

[gandhi39]

Thank you, Moon Wizard.

I don't know much but I'll try to make an extension. A 60º arc should be enough for me.

[Andraax]

Here is the differences, graphically. The grey figure is an equilateral triangle. The green figure is a cone with 60 degrees. The red figure is a cone with ~53.13 degrees. You'll note that they are *very* similar. Also, the reason cones are drawn as arcs is because the range of the far end is equal distance from a point, which yields an arc. If it was drawn as a triangle, then you would need to explain why the sides of the cone are further from the spell caster than the center is (the sides of the triangle are ~1.12 x the distance from the point to the center of the far end)...

https://s3.silent-tower.org/images/Cone-Triangle.png

[Nickademus]

Honestly, I don't see anything in the 5e PHB that says that the end of the cone is "equal distance from a point". It just says:

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.
That would mean that the cone has to be a triangle since any kind of arc would have a smaller width where the curve of the arc is; i.e. the widest part of the cone should be the farthest point, which would be the edge of the triangle.

[Andraax]

It then goes foreward drawing a line paralel to the ground ending at the center of a circle perpendicular to that line. The line is the height of the cone.

Now let's say a bird is flying above the battleground. In 2D it sees an equilaterus triangle. Of course there is half of the cone above and half of it below that triangle. But ideally the bird does not actually see the 3D cone.

I think the best way to draw a cone on the battlegrid is an equilaterus triangle, not a slice of a circle (not an arc). Otherwise the area of effect of certain spells would be defined as an arc, not a cone. I mean: it's not a cone with part of a sphere coming out of it's circle base. It ends on the circle.

The trick is: you wouldn't choose the height of this triangle, but the length of a side.


Honestly, I don't see anything in the 5e PHB that says that the end of the cone is "equal distance from a point". It just says:

That would mean that the cone has to be a triangle since any kind of arc would have a smaller width where the curve of the arc is; i.e. the widest part of the cone should be the farthest point, which would be the edge of the triangle.

Why is the edge of the cone farther from the spell caster than the center of the cone? Does magic travel faster / farther on the edges of the spell effect than it does in the center?

https://s3.silent-tower.org/images/Triangle.png

[gandhi39]

The ranges from the tip of the cone to any point in the circunference of the base is equal. But on a 2D sideview (as you would see the battlegrid) this base is but a line; one of the sides of a triangle on a plane paralel to the ground. You don't see the circular base the cone.

In 3D the cone fills further above and below that triangle plane as you get closer to the base of the cone. But yes, in 2D the sides of the triangle go further horizontally than its height for exemple, since its not an arc.

[gandhi39]

Why is the edge of the cone farther from the spell caster than the center of the cone? Does magic travel faster / farther on the edges of the spell effect than it does in the center?

https://s3.silent-tower.org/images/Triangle.png

The question is not the travel speed of magic, but "what area does it occupy when the spell is in effect?". Actually "what area on 2D?" and "what space on 3D?". If that was the question, we would only have spheric areas of effect.

[Nickademus]

Why is the edge of the cone farther from the spell caster than the center of the cone?

Because the PHB said so. I imagine it's a matter of keeping things simple. If a cone is three squares long, it will be three squares wide at the end. If the cone is five squares long, it will be five squares wide at the end. Players and GMs can quickly figure out the dimensions of a cone without having to use any math.

[gandhi39]

Because the PHB said so. I imagine it's a matter of keeping things simple. If a cone is three squares long, it will be three squares wide at the end. If the cone is five squares long, it will be five squares wide at the end. Players and GMs can quickly figure out the dimensions of a cone without having to use any math.

The question is: how long is the cone? Should we measure its height? Or the length from the tip to a point in the circunference of the base?

20330

[LordEntrails]

Damn, I should of paid more attention in that self paced trig class. :p It was the last class I took at UCSB and all I really remember about it was that trig was real practical math - and that calculators and computers where made to eat up this stuff. :)
Years ago I visited the UCSB campus (when my older sister was in school nearby). A college that has it's own beach... yeah, I can imagine academics weren't foremost on your mind!

Maybe they have wifi and power outlets on the beach now? *G*

[Andraax]

The magic radiates from the spell caster. Assuming it radiates at the same speed / intensity at the edges as it does in the center, it forms the conical section of a sphere in 3D:

https://s3.silent-tower.org/images/Spherical_sector.png

When you view a cross section of this conical section in 2D, it appears as an arc:

https://s3.silent-tower.org/images/Geometries_img_1.jpg

[gandhi39]

The magic radiates from the spell caster. Assuming it radiates at the same speed / intensity at the edges as it does in the center, it forms the conical section of a sphere in 3D:

https://s3.silent-tower.org/images/Spherical_sector.png

When you view a cross section of this conical section in 2D, it appears as an arc:

https://s3.silent-tower.org/images/Geometries_img_1.jpg

That is true. If we are talking about a conical section of a sphere, than the 2D projection is an arc.

If we are talking about a regular cone, than the 2D projection is a triangle.

[Andraax]

That is true. If we are talking about a conical section of a sphere, than the 2D projection is an arc.

If we are talking about a regular cone, than the 2D projection is a triangle.

So, you believe it travels faster on the edges than in the center? Because that would be the only way it would have a flat bottom...

[Nickademus]

The question is: how long is the cone? Should we measure its height? Or the length from the tip to a point in the circunference of the base?
You measure it from the point of origin of the spell, which is usually the caster, out to its maximum length, as stated in the spell/source description. I'm not sure what the confusion is.

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.


So, you believe it travels faster on the edges than in the center? Because that would be the only way it would have a flat bottom...
Yes. Because that is what would happen to achieve the effect described in the PHB.

[gandhi39]

You measure it from the point of origin of the spell, which is usually the caster, out to its maximum length, as stated in the spell/source description. I'm not sure what the confusion is.


The maximum length would be from the caster to a point in the circunference of the cone's base. But one can argue the intended length is from the caster to the center of that circunference.

[gandhi39]

So, you believe it travels faster on the edges than in the center? Because that would be the only way it would have a flat bottom...

The book says "cone", not "conical section of a sphere".

[Andraax]

You measure it from the point of origin of the spell, which is usually the caster, out to its maximum length, as stated in the spell/source description. I'm not sure what the confusion is.

Because if you measure out to it's maximum distance in the center, then the sides would be longer than the maximum distance if it's a flat bottomed cone. And if you measure out to the maximum distance along the sides of the cone, then the distance to the center of the cone is shorter than the maximum distance.

So, the maximum distance for magic is variable based on the angle the target is from the spell caster? If you measure to the center, I'll always aim 30 degrees away from my target, because my maximum distance will automatically be increased for a cone type spell; if you measure along the edge, then again I'll aim 30 degrees off because that's the only way to achieve maximum distance...

[gandhi39]

Because if you measure out to it's maximum distance in the center, then the sides would be longer than the maximum distance if it's a flat bottomed cone. And if you measure out to the maximum distance along the sides of the cone, then the distance to the center of the cone is shorter than the maximum distance.

So, the maximum distance for magic is variable based on the angle the target is from the spell caster? If you measure to the center, I'll always aim 30 degrees away from my target, because my maximum distance will automatically be increased for a cone type spell; if you measure along the edge, then again I'll aim 30 degrees off because that's the only way to achieve maximum distance...

Yes. If it's a cone you will reach greater distances on the edges of the base.

[Nickademus]

Because if you measure out to it's maximum distance in the center, then the sides would be longer than the maximum distance if it's a flat bottomed cone. And if you measure out to the maximum distance along the sides of the cone, then the distance to the center of the cone is shorter than the maximum distance.The PHB doesn't technically say which ray of the cone you are using as the primary targeting. I'm sure it is assumed that the middle is, but your GM may allow you to shift the cone's area so that some other ray is the one that is 'extending in a direction you choose'.


So, the maximum distance for magic is variable based on the angle the target is from the spell caster? If you measure to the center, I'll always aim 30 degrees away from my target, because my maximum distance will automatically be increased for a cone type spell; if you measure along the edge, then again I'll aim 30 degrees off because that's the only way to achieve maximum distance...
Again, your GM may allow you to shift your cone so that you get more distance than the spell/source states (and I wouldn't blame you for good use of a spell), but most GMs I've seen use gridded battlemaps and round partial areas up or down. So you may need a big cone to get any significant gain from this.

In my personal opinion based on my observations, I don't see where any of this matters since it seems to be for targeting a single enemy and getting the most reach out of the cone. I've never seen anyone use a cone on just one enemy. The cone is always positioned to get as many enemies as possible, not to reach the farthest enemy. So I don't see a player caring about this except in rare situations where the cone just happens to line up with the most enemies and the side reaching the farthest enemy. But then you would still be positioning the cone there for max targets regardless of it you get an extra square or two on the side.

[Bidmaron]

A cone set on its base is stable and does not rock like a spherical arc-slice would do.