Hexes, real world measurements, and GURPS reality

[Anaraxes]

Originally Posted by maximara

But when you look at the area per hex "lost" you quickly see the problem:

The "problem" is that you're using total area, regardless of distance from the center point covered by the circle. The former is useful only if imagine an area being freely reshaped by the caster to catch all the nooks and crannies, and want to be sure to get every square inch possible out of your FP expenditure. The latter (just round down) is more useful if you want to approximate the notional circular area on a hex map.

Pull out your compass and just draw a circle of various radii on a sheet of hex paper. Then look at where the boundary line falls. You'll see it cuts about halfway through a ring of hexes. You can include those partial hexes, or exclude them. GURPS rounds down (toward the center of the circle, excluding those partial hexes). Simple, and doesn't require any equations.

[maximara]

Originally Posted by Varyon

GURPS rounding is pretty consistently one way - either all fractions round up, or all fractions round down, depending on what we're dealing with.

Except when dealing with the Speed/Range and Size formulas:

Speed/Range formula: 2 - 6*log(Distance in Yards)

Size formula: 6*log(length in yards) - 2

Round to nearest integer.

But to keep everything consistent spell area should have been rounded up.

Originally Posted by Varyon

I thought there was something wrong with your methodology for determining how much area is missing, so I printed out some hex paper and grabbed a compass. Rounding up does indeed appear to give a better approximation - in each case, there are six hexes that are ~half filled, and the rest (if applicable) are more than half filled (with a 4-yard radius, there were another six that were very nearly completely filled, with only a tiny sliver empty) - also for 3 and 4-yard radii, the area starts to peek into the next row over. I suspect with larger radii, you may well have it be the case that it would be more accurate to be +2 relative to the RAW, then +3, and so forth, but I'm not certain.

Another way to do this is to take the compass and get the distance from the hexagons (assume each hexagon is a yard across). Now take the compass and use the point where three hexagons meet as your center. Now it is far easier to find the number of hexes for a certain radius.

[Varyon]

Originally Posted by maximara

Except when dealing with the Speed/Range and Size formulas:

Speed/Range formula: 2 - 6*log(Distance in Yards)

Size formula: 6*log(length in yards) - 2

Round to nearest integer.

Errr... no? SSR roughly follows that equation, but just sets things somewhere close where the numbers aren't a mess, and then when you actually use the table, you round up to the nearest SSR - 32 yards is -8 Range, while the equation put it at around -7.03 (which would round to -7).

Originally Posted by maximara

But to keep everything consistent spell area should have been rounded up.

Consistent with what? Some things round up (point cost), some things round down (damage). What thing that rounds up are you comparing area of effect to?

Originally Posted by maximara

Another way to do this is to take the compass and get the distance from the hexagons (assume each hexagon is a yard across). Now take the compass and use the point where three hexagons meet as your center. Now it is far easier to find the number of hexes for a certain radius.

Not really. At 1 yard, this is most of three hexes (the three meeting in the middle) and a tiny bit of some others. At 2 yards, it's those three, most of some of those adjacent to them and half of the others, and a sliver of some more. I suspect you'd rapidly end up with a discombobulated mess. It's a given you're going to lose some resolution mapping a circular area onto a hex map, but that's just the way things go. Of course, personally I'm somewhat-inclined to just have many GURPS area effects literally affect hexes - when someone is creating a magical wall of flame ex nihilo, is it really that much stranger when it looks honeycombed?

[hal]

Originally Posted by malloyd

Edit: In the case of that Rain spell, what the conflicting results are telling you is the spell description isn't intended to give you a total volume of water. If you are calculating it for some reason, you're exceeding the intent of the spell and it's perfectly reasonable for the GM to rule that if you attempt to concentrate all the water into a smaller area that it falls on, some (or all) of it mysteriously evaporates and you can get whatever amount he says, inconsistent with *either* calculated volume. The point of the spell isn't to provide a fixed volume of water, the 1" is color text more than anything, telling you it's pretty heavy rain. Note that other water creation spells do stuff completely out of proportion to the volume of water produced (most notably the fire extinguishing effect of Create Water), so it's even harder to take these numbers too seriously in a broader context

Hmmm. If I am calculating something as a GM or as "Alaconius" analyzing spell structures in GURPS MAGIC, I think we can dispense with the idea that I'm somehow perverting the rules for any given benefit. If I'm analyzing a spell for its real world implications, then it is for the purpose of determining what the implications are using real world data, concepts, and formulas.

I have to respectfully disagree with much of what people have said in this thread, but mostly with what you yourself wrote above.

To wit:

The math of Hexagonal grid is pretty simple. If you use the actual templates provided for in GURPS MAGIC pg 15, or GURPS BASIC SET page 239, you can count from edge to edge, knowing that from side to side of each hex, is 3 feet. A 4 hex radius spell when measured from end to end, is precisely 7 hexes wide. This makes the diameter of said "circle" to be equal to exactly 21 feet.

As for any other problems with GURPS MAGIC that arises with trying to match the implications of the spell with real world effects...

If people don't much care about it, then having something drop a given number of gallons of water over a given area of ground for 1 hour doesn't much matter. Why? They do not CARE. If on the other hand, someone wants to know how much water descends over that same surface space in the span of an hour, the spell description spells it out. 1 Inch for one hour over a diameter of 10 Hex Radius. Using GURPS rules from the pages of not one source book, but two (which are in perfect agreement with each other), measuring from end to end still ends up being only 57 feet. So, pick the center of a hex for a single point, and we'll call it the Center.

A geometrical shape that has a length of 57 feet, and forms a perfect circle, will have a diameter that runs through that one point, measuring 57 feet. This means that the Radius is equal to 1/2 of 57 feet, or 28.5 feet.

So, either a spell cast using GURPS MAGIC that is an area spell, appears as a perfect circle to the senses of the characters in a GURPS Game universe, or it appears as a hexagonal like shape that matches Identically, the illustrations given on pages 15 of GURPS MAGIC or 239 of GURPS BASIC SET: Characters.

As best as I can see, that's the only real issue here.

How people want to play it in their game worlds is fine. How people want to debate the meaning of "IS" is - that's fine. Me? I work with math to figure out the implications of the spells as if I were really there in such a game universe applying analysis of geometry or what have you.

If the formulas for describing the real world exist and can be applied to analysis of GURPS MAGIC, all the better in my opinion.

By the by, I think I've been using 6 tons as the figure for how much Iron is produced by Stone to Metal in GURPS MAGIC.

Doing the math:

Diameter of Cylinder is equal to Pi * R^2 * Height. The height of a hex is defined to be 6' in height. The distance from side to side of a hex is 3 feet. Thus, the volume in cubic feet of a "pure circle area spell" would be 42.4115. Multiplied by 491.5 lbs/ft^3 = gives us 20845.25265 lbs or 10.422 short tons. All that for a mere 10 energy.

So, yes, I'm actual geometry and other mathematical formulas to the world in a GURPS MAGIC game - as if the world that GURPS MAGIC exists within is essentially the same as a non-magic world (such as ours).

GURPS MAGIC doesn't say how the water is made to arrive. It doesn't say that a rain cloud is instantly formed at the end of the spell casting and then starts to rain. It does't say how much water was actually falling that MISSED the area of effect. It doesn't say how high the rain starts from before it falls. All of these things will have to be adjudicated by the GM as they see fit.

But frankly? There are OTHER issues that have to be addressed by a GM who has either the resources or the inclination or even both. If you need to know how much rain falls on plants for farming needs, and having THAT information helps? Great. If you don't have a need for that information? No problem. If I have a set of rules that determines how much crops are produced in a growing season, and it depends on how much or how little rain comes into play - then it matters.

Rain in real life can force ripe grain seeds to fall to the ground before it can be harvested (and thus lowers the yield per acre value of harvest in real life). You can be certain that if magic really did exist, that during harvest, there may well be people who'd pay the Mage 1/10th of their harvest to the Mage for keeping the rain away during harvest time. The mage need not earn any more money than 1/10th the harvest of a village and then sell the proceeds of that grain on the market. Keep some of it for his own consumption, sell the rest and he is standing pretty pat.

Shhhhh. Don't mention this to those who are participating in the Mages are Coins thread, or they'll start figuring out ways for mage born to earn their income from the less wealthy serfs in the villages being set up for discussion...

[hal]

Originally Posted by Varyon

Not really. At 1 yard, this is most of three hexes (the three meeting in the middle) and a tiny bit of some others. At 2 yards, it's those three, most of some of those adjacent to them and half of the others, and a sliver of some more. I suspect you'd rapidly end up with a discombobulated mess. It's a given you're going to lose some resolution mapping a circular area onto a hex map, but that's just the way things go. Of course, personally I'm somewhat-inclined to just have many GURPS area effects literally affect hexes - when someone is creating a magical wall of flame ex nihilo, is it really that much stranger when it looks honeycombed?

Implications...

IN GURPS, it is possible to have more than one person in a hex - correct? If a circle were such that part of it were inside of a hex, but not more than 1/2 of the hex, why could there not be a person who gets within 1/2 inch of a "effect boundary" without actively entering said effect?

Just playing devil's advocate here. Me? A perfect circle would be inscribed within the edges of the hexes furtherest from the Center of Effect. The real problem here that I see is this...

The distance between side to side of a hex measures precisely 3 feet in GURPS. Question now is: What is the LENGTH of a diagonal of a single hex plus the length of a BASE of a hex (ie a side itself)? In a 4 hex diameter spell area as depicted on page 15 of GURPS MAGIC, you have 1/2 of a diagonal in the hex of origin, plus a hex side length. Then a FULL diagonal, plus one more hex side length.

One has to wonder what that "length" is from center to the very edge of the hex in that case?

[Varyon]

Originally Posted by hal

Just playing devil's advocate here. Me? A perfect circle would be inscribed within the edges of the hexes furtherest from the Center of Effect.

An option between "perfect circle" and "honeycomb spells" would be to say the spell conforms roughly to the diagrams from the books, resulting in a shape somewhere between a hexagon and a circle. It doesn't even need to be regular/even - perhaps the edges are fuzzy/wavy, chaotically varying a bit in distance, but ultimately approximating a hexagon.

[hal]

Originally Posted by Varyon

An option between "perfect circle" and "honeycomb spells" would be to say the spell conforms roughly to the diagrams from the books, resulting in a shape somewhere between a hexagon and a circle. It doesn't even need to be regular/even - perhaps the edges are fuzzy/wavy, chaotically varying a bit in distance, but ultimately approximating a hexagon.

So, in your game universe, your "area spells" are not perfect circles, they're honeycomb shaped. I can respect that.

[Celjabba]

You could also say that any casting of an area spell split reality into 2 parallel universe.

In one, the spell cover a perfect geometric circle.
In the other, the spell cover an hex-based tiling.

At times, an Outside-Context entity switch the characters between the 2 universes, a perception filter making them unable to notice the transition or the difference between the 2 realities.

[Varyon]

Originally Posted by hal

So, in your game universe, your "area spells" are not perfect circles, they're honeycomb shaped. I can respect that.

I'm thinking very roughly honeycomb-shaped, with fuzzy, chaotic edges. Indeed, those that last more than a brief moment may well shift around a bit, making it difficult to determine the actual center of the area of effect (but for purposes of combat, there's always enough in each nominally-included hex to fully affect the occupants, and not enough in the adjacent hexes to affect their occupants).

[Anaraxes]

Originally Posted by maximara

But to keep everything consistent spell area should have been rounded up.

Easy enough to houserule if you want it to round the other way.

But it does create the problem that you can't cast an area spell covering 1 hex. (Since the first area increment, 1 yard radius, base FP cost, results in the 7-hex megahex, projecting that sequence the other way to get a 1 hex area, you'd have to cast a 0-yard radius spell at 0 increments for 0 * base FP cost. That results in an infinite increase in actual error over calculated area, which is of course a vastly larger error from mapping to hexes than the error you get by rounding down. If you're concerned about the math and unfairly losing area, that is.) Better arbitrarily plug that hole by also houseruling that a 1 hex area costs, oh, 0.5 * base FP cost for a 0.5 yard radius to fit inside that hex. Not longer a smooth progression, but there we are.