Very very simple way to show a correct 60 degree cone on a square grid:
Put down 1 edge of your cone along a cardinal direction from the caster.
Go 3 squares along this line (away from the caster) then 5 squares in a perpendicular direction. (towards the targets)
From this new point, make a diagonal line back to the caster. This is the 2nd edge of your cone.
Congrats! You have constructed a 60 degree angle (well, 59.04) at the caster's location. Now just extend both of those lines to match the spell's dimension.
That seems like an excessive amount of math at the table, unless you already have all that information worked out for all of the common cone sizes.
The math is simple and there are only about 10 or so cone spells total. Better, they ALL fall into 3 different ranges used: 15 ft, 30 and 60 ft. 15 ft and 30 are simple, 60 ft takes only a bit of thought. Just remember to start with 1 square, end with about 3/6/12, always go up or stay the same, and do not exceed the max (5/18/72)
15 ft: 5 squares: 1,1,3 or 1,2,2
30 ft: 18 squares: 1,2,2,3,4,6, is the most common, but 1,2,3,3,4,5 or 1,2,2,3,5,5 are also seen
60 ft: 72 squares: Typically done as follows: 1,2,2,3,4,5,6,7,9,10,11,12. But I have also seen: 1,2,3,3,4,5,6,7,8,10,11,12 Once you know the standard sets, it's is fairly easy to move them around.
It's actually a LOT easier to draw than to describe what you are drawing. Triangles are not hard shapes to do, it is damn square grid that makes it wierd, deciding which partial sqaures are 'in and which are out'. Remember one of the standard settups and fiddle with it by adding and subtracting one square at a time.
That seems like an excessive amount of math at the table, unless you already have all that information worked out for all of the common cone sizes.
The math is simple and there are only about 10 or so cone spells total. Better, they ALL fall into 3 different ranges used: 15 ft, 30 and 60 ft. 15 ft and 30 are simple, 60 ft takes only a bit of thought. Just remember to start with 1 square, end with about 3/6/12, always go up or stay the same, and do not exceed the max (5/18/72)
15 ft: 5 squares: 1,1,3 or 1,2,2
30 ft: 18 squares: 1,2,2,3,4,6, is the most common, but 1,2,3,3,4,5 or 1,2,2,3,5,5 are also seen
60 ft: 72 squares: Typically done as follows: 1,2,2,3,4,5,6,7,9,10,11,12. But I have also seen: 1,2,3,3,4,5,6,7,8,10,11,12 Once you know the standard sets, it's is fairly easy to move them around.
It's actually a LOT easier to draw than to describe what you are drawing. Triangles are not hard shapes to do, it is damn square grid that makes it wierd, deciding which partial sqaures are 'in and which are out'. Remember one of the standard settups and fiddle with it by adding and subtracting one square at a time.
Since a cone is as wide as it is long, the number of squares that should be hit at a given distance from the caster is easily calculated, it's the distance from the caster. This means 15 ft cone hits 6 squares, 30ft hits 21, 60ft hits 78. In all cases the progression from the caster should be 1,2,3,4,5,6,7,8,9,10,11,12.
That seems like an excessive amount of math at the table, unless you already have all that information worked out for all of the common cone sizes.
The math is simple and there are only about 10 or so cone spells total. Better, they ALL fall into 3 different ranges used: 15 ft, 30 and 60 ft. 15 ft and 30 are simple, 60 ft takes only a bit of thought. Just remember to start with 1 square, end with about 3/6/12, always go up or stay the same, and do not exceed the max (5/18/72)
15 ft: 5 squares: 1,1,3 or 1,2,2
30 ft: 18 squares: 1,2,2,3,4,6, is the most common, but 1,2,3,3,4,5 or 1,2,2,3,5,5 are also seen
60 ft: 72 squares: Typically done as follows: 1,2,2,3,4,5,6,7,9,10,11,12. But I have also seen: 1,2,3,3,4,5,6,7,8,10,11,12 Once you know the standard sets, it's is fairly easy to move them around.
It's actually a LOT easier to draw than to describe what you are drawing. Triangles are not hard shapes to do, it is damn square grid that makes it wierd, deciding which partial sqaures are 'in and which are out'. Remember one of the standard settups and fiddle with it by adding and subtracting one square at a time.
The problem isn't really the math to get the number of squares to use, it is the list of widths you give. They use only one rule to generate that doesn't help you at all make sure you know you're doing it right; you could get to the end of a 60' cone and easily find you've used 75 squares. There is no algorithm to construct a roughly triangular shape with a non-triangular number. You can say that it is "easy" but that is only because you've memorized the list already. There are much simpler ways to do it already given in the rules.
Very very simple way to show a correct 60 degree cone on a square grid:
Put down 1 edge of your cone along a cardinal direction from the caster.
Go 3 squares along this line (away from the caster) then 5 squares in a perpendicular direction. (towards the targets)
From this new point, make a diagonal line back to the caster. This is the 2nd edge of your cone.
Congrats! You have constructed a 60 degree angle (well, 59.04) at the caster's location. Now just extend both of those lines to match the spell's dimension.
A cone that is 5 squares wide 3 squares from the caster is definitely not the shape described by the PHB. (I was wrong in my earlier post, it should be about 53 degree cones, I think.)
A cone that is 5 squares wide 3 squares from the caster is definitely not the shape described by the PHB. (I was wrong in my earlier post, it should be about 53 degree cones, I think.)
It's not 5 squares wide 3 steps from the caster. Just try following the directions.
Edit: Made a picture illustrating how to do it. C = caster, then follow the instructions to draw the red, orange, green, blue and purple lines. The resulting cone is ~60 degrees, and so it is as wide as it is long at every point.
I did. one edge is 5 squares from the other 3 squares from the caster.
They are 5 squares apart =/= the cone is 5 squares wide! Just look at the picture - the width of the cone is any line parallel to the purple one, not the orange one.
I mean you could make a template that way (though if you are going to go to all that trouble, I'd probably just build a correct template) but that seems like a disaster to do at the table unless you already know how to do it for each size of cone again.
That seems like an excessive amount of math at the table, unless you already have all that information worked out for all of the common cone sizes.
The math is simple and there are only about 10 or so cone spells total. Better, they ALL fall into 3 different ranges used: 15 ft, 30 and 60 ft. 15 ft and 30 are simple, 60 ft takes only a bit of thought. Just remember to start with 1 square, end with about 3/6/12, always go up or stay the same, and do not exceed the max (5/18/72)
15 ft: 5 squares: 1,1,3 or 1,2,2
30 ft: 18 squares: 1,2,2,3,4,6, is the most common, but 1,2,3,3,4,5 or 1,2,2,3,5,5 are also seen
60 ft: 72 squares: Typically done as follows: 1,2,2,3,4,5,6,7,9,10,11,12. But I have also seen: 1,2,3,3,4,5,6,7,8,10,11,12 Once you know the standard sets, it's is fairly easy to move them around.
It's actually a LOT easier to draw than to describe what you are drawing. Triangles are not hard shapes to do, it is damn square grid that makes it wierd, deciding which partial sqaures are 'in and which are out'. Remember one of the standard settups and fiddle with it by adding and subtracting one square at a time.
Since a cone is as wide as it is long, the number of squares that should be hit at a given distance from the caster is easily calculated, it's the distance from the caster. This means 15 ft cone hits 6 squares, 30ft hits 21, 60ft hits 78. In all cases the progression from the caster should be 1,2,3,4,5,6,7,8,9,10,11,12.
The problem with square grids is that it does not accurately represent reality. It's why I prefer Hexs. They are not perfect, but at least people instinctively recognize that a partial hex is possible and accept it. All rooms can not divided up into a 5ft squares and spells do not accurately map to the grid. You either end up adding extra square feet or cutting it. You choose to increase it dramatically.
Your progression has an area that is too large. Specifically, is is an extra 150 SF (6 extra 5ft squares). That is why I did the 1,2,2,3,4,5,6,7,9,10,11,12 progression.
Similarly, a 15 ft cone is NOT 123, because that is a square foot of of 150 sq ft, and it should be 125 sq ft. The 30 ft is not 123456 because that is a square footage of 525 sq ft and it should be 425.
Yes, you can say screw it and just give the players much bigger areas because you choose a grid rather than a hex. Or you can play by the actual rules and accept the fact that it takes a little bit more work to make things come out right
As per the directions, you very simply extend (or reduce) the length of the blue and green lines to match the dimension of the cone you're casting and then join them with a purple line. The whole process should take you about 10-20 seconds, and will generate you an accurate 60 degree cone of any length.
Your progression has an area that is WAY too large. Specifically, is is an ex extra 150 SF. That is why I did the 1,2,2,3,4,5,6,7,9,10,11,12 progression.
As per the directions, you very simply extend (or reduce) the length of the blue and green lines to match the dimension of the cone you're casting and then join them with a purple line. The whole process should take you about 10-20 seconds, and will generate you an accurate 60 degree cone of any length.
My point (I won't speak for Lunali) is that these methods are probably fine for your table, but the two accepted methods (templates and "token counting") produce much quicker results (you don't actually need to physically place tokens for "token counting"), the correct shapes and don't require memorizing arbitrary patterns or making essentially a template that isn't the correct angle anyway and must have one side fixed to a cardinal direction.
I guarantee you that I (or anyone still familiar with even basic secondary-school level geometry) could make the required cone before you can fish out your template or count your tokens. And calling a 59.04 degree angle inaccurate for representing the correct 60 when you were talking about a 53 degree angle earlier and not understanding what the width of a cone refers to speaks for itself.
I guarantee you that I (or anyone still familiar with even basic secondary-school level geometry) could make the required cone before you can fish out your template or count your tokens. And calling a 59.04 degree angle inaccurate for representing the correct 60 when you were talking about a 53 degree angle earlier and not understanding what the width of a cone refers to speaks for itself.
Stop with the ad hominem. You can invent ways to do it all you like.
I don't see the point in harassing me about my understanding of geometry when I can figure out what the double of an angle that has a tangent is 0.5 is (which results in a triangle that has a width of 1 unit at a distance of 1 unit from the origin).
I guarantee you that I (or anyone still familiar with even basic secondary-school level geometry) could make the required cone before you can fish out your template or count your tokens. And calling a 59.04 degree angle inaccurate for representing the correct 60 when you were talking about a 53 degree angle earlier and not understanding what the width of a cone refers to speaks for itself.
60° isn’t correct. That will give you an equilateral triangle, which doesn’t satisfy the PHB-defined property that the base be equal to the height. Your middle-school insults aren’t doing you any favors.
Again, you are misunderstanding what the width of a cone is. From the picture, the cone's width is the purple line, not the orange one. Are you able to draw me a cone generated using your method so I can try to see what you're actually doing?
I guarantee you that I (or anyone still familiar with even basic secondary-school level geometry) could make the required cone before you can fish out your template or count your tokens. And calling a 59.04 degree angle inaccurate for representing the correct 60 when you were talking about a 53 degree angle earlier and not understanding what the width of a cone refers to speaks for itself.
60° isn’t correct. That will give you an equilateral triangle, which doesn’t satisfy the PHB-defined property that the base be equal to the height. Your middle-school insults aren’t doing you any favors.
The wording is 'A cone's width at a given point along its length (purple line on my picture) is equal to that point's distance from the point of origin (green line on my picture).' The book says width, not height, so it is the textbook definition of an equilateral triangle when looked at in 2 dimensions.
The distance to the purple line is not the length of the green line. I am on mobile and cannot draw a diagram. The distance between a point and a line is the shortest path, which is at a right angle to the line.
That seems like an excessive amount of math at the table, unless you already have all that information worked out for all of the common cone sizes.
Very very simple way to show a correct 60 degree cone on a square grid:
The math is simple and there are only about 10 or so cone spells total. Better, they ALL fall into 3 different ranges used: 15 ft, 30 and 60 ft. 15 ft and 30 are simple, 60 ft takes only a bit of thought. Just remember to start with 1 square, end with about 3/6/12, always go up or stay the same, and do not exceed the max (5/18/72)
15 ft: 5 squares: 1,1,3 or 1,2,2
30 ft: 18 squares: 1,2,2,3,4,6, is the most common, but 1,2,3,3,4,5 or 1,2,2,3,5,5 are also seen
60 ft: 72 squares: Typically done as follows: 1,2,2,3,4,5,6,7,9,10,11,12. But I have also seen: 1,2,3,3,4,5,6,7,8,10,11,12 Once you know the standard sets, it's is fairly easy to move them around.
It's actually a LOT easier to draw than to describe what you are drawing. Triangles are not hard shapes to do, it is damn square grid that makes it wierd, deciding which partial sqaures are 'in and which are out'. Remember one of the standard settups and fiddle with it by adding and subtracting one square at a time.
Since a cone is as wide as it is long, the number of squares that should be hit at a given distance from the caster is easily calculated, it's the distance from the caster. This means 15 ft cone hits 6 squares, 30ft hits 21, 60ft hits 78. In all cases the progression from the caster should be 1,2,3,4,5,6,7,8,9,10,11,12.
The problem isn't really the math to get the number of squares to use, it is the list of widths you give. They use only one rule to generate that doesn't help you at all make sure you know you're doing it right; you could get to the end of a 60' cone and easily find you've used 75 squares. There is no algorithm to construct a roughly triangular shape with a non-triangular number. You can say that it is "easy" but that is only because you've memorized the list already. There are much simpler ways to do it already given in the rules.
A cone that is 5 squares wide 3 squares from the caster is definitely not the shape described by the PHB. (I was wrong in my earlier post, it should be about 53 degree cones, I think.)
It's not 5 squares wide 3 steps from the caster. Just try following the directions.
Edit: Made a picture illustrating how to do it. C = caster, then follow the instructions to draw the red, orange, green, blue and purple lines. The resulting cone is ~60 degrees, and so it is as wide as it is long at every point.
I did. one edge is 5 squares from the other 3 squares from the caster.
They are 5 squares apart =/= the cone is 5 squares wide! Just look at the picture - the width of the cone is any line parallel to the purple one, not the orange one.
I mean you could make a template that way (though if you are going to go to all that trouble, I'd probably just build a correct template) but that seems like a disaster to do at the table unless you already know how to do it for each size of cone again.
The problem with square grids is that it does not accurately represent reality. It's why I prefer Hexs. They are not perfect, but at least people instinctively recognize that a partial hex is possible and accept it. All rooms can not divided up into a 5ft squares and spells do not accurately map to the grid. You either end up adding extra square feet or cutting it. You choose to increase it dramatically.
Your progression has an area that is too large. Specifically, is is an extra 150 SF (6 extra 5ft squares). That is why I did the 1,2,2,3,4,5,6,7,9,10,11,12 progression.
Similarly, a 15 ft cone is NOT 123, because that is a square foot of of 150 sq ft, and it should be 125 sq ft. The 30 ft is not 123456 because that is a square footage of 525 sq ft and it should be 425.
Yes, you can say screw it and just give the players much bigger areas because you choose a grid rather than a hex. Or you can play by the actual rules and accept the fact that it takes a little bit more work to make things come out right
As per the directions, you very simply extend (or reduce) the length of the blue and green lines to match the dimension of the cone you're casting and then join them with a purple line. The whole process should take you about 10-20 seconds, and will generate you an accurate 60 degree cone of any length.
My point (I won't speak for Lunali) is that these methods are probably fine for your table, but the two accepted methods (templates and "token counting") produce much quicker results (you don't actually need to physically place tokens for "token counting"), the correct shapes and don't require memorizing arbitrary patterns or making essentially a template that isn't the correct angle anyway and must have one side fixed to a cardinal direction.
I guarantee you that I (or anyone still familiar with even basic secondary-school level geometry) could make the required cone before you can fish out your template or count your tokens. And calling a 59.04 degree angle inaccurate for representing the correct 60 when you were talking about a 53 degree angle earlier and not understanding what the width of a cone refers to speaks for itself.
Stop with the ad hominem. You can invent ways to do it all you like.
I don't see the point in harassing me about my understanding of geometry when I can figure out what the double of an angle that has a tangent is 0.5 is (which results in a triangle that has a width of 1 unit at a distance of 1 unit from the origin).
You didn't understand what I said this time. Talk about misunderstanding geometry.
60° isn’t correct. That will give you an equilateral triangle, which doesn’t satisfy the PHB-defined property that the base be equal to the height. Your middle-school insults aren’t doing you any favors.
Again, you are misunderstanding what the width of a cone is. From the picture, the cone's width is the purple line, not the orange one. Are you able to draw me a cone generated using your method so I can try to see what you're actually doing?
The wording is 'A cone's width at a given point along its length (purple line on my picture) is equal to that point's distance from the point of origin (green line on my picture).' The book says width, not height, so it is the textbook definition of an equilateral triangle when looked at in 2 dimensions.
The distance to the purple line is not the length of the green line. I am on mobile and cannot draw a diagram. The distance between a point and a line is the shortest path, which is at a right angle to the line.