Hexes, real world measurements, and GURPS reality

[hal]

Hi All,
In a different thread, I posted information regarding a spell where the radius would be based on real world math and the fact that although Hexes are not circles, we use hexes to map things on the table top.

Just listing my "work" to show how I get to that and seeing where I'm going wrong...

For spells that are Area affect, a hex radius of 1 means that the edge to edge aspect of the area spell is essentially 1 hex. A 2 hex radius is the hex the spell caster is standing in, plus all adjacent hexes.

Since the distance from hex side to hex side is 1 yard, a true circle with a diameter of 1 yard has a radius of 1/2 yard. Correct?

Since the distance from hex side to hex side where you have three hexes total or 3 yards, has a radius of half that or 1.5 Yards.

Since the distance from hex side to hex side of 5 hexes (which is in GURPS, a 3 hex radius spell area), the diameter is 5 yards with a radius of 2.5 Yards.

That GURPS uses Hexes for mapping purposes does not equate to a Spell with a Radius effect (effectively a circle) is going to zig-zag to perfectly conform to actual HEX shapes in the reality of GURPS MAGIC.

Am I missing something here if I actively use real world numbers that measures things in lbs per cubic foot, or Inches per square yard, etc?

Just a minor disquieting thought after seeing someone "correct" my presumptions in a manner that had me thinking "Huh?"

So for example, if GURPS describes something as having the attributes of a Hax in volume or in size or what have you, should I be actively using real world values or adjusted values based on hexagons?

Just my thinking here.

[Varyon]

With regard to real-world measurements, you can do it either way; I assume there's a bit of leeway with respect to where things are actually located that doesn't quite match up cleanly with the hex map. Of course, in this case there's also differences in opinion as to what an n-hex-radius would be on the battle map - when n is 1, does that mean it's a 1-hex area (comparable to a 0.5-yard-radius circle) or a 7-hex area (a central hex and all of those adjacent to it, comparable to a 1.5-yard-radius circle)? I think the official rules are the latter; my own leanings would probably be more the former, as you described here.

[Tyneras]

I've only ever viewed hexes as a tactical battle map aid, with area spells being (generally) 12 foot high cylinders with a circular perimeter, not a weird jagged edged shape made of a clump of hexagonal prisms. The description of Area spells doesn't even mention hexes.

[ericthered]

Originally Posted by Tyneras

I've only ever viewed hexes as a tactical battle map aid, with area spells being (generally) 12 foot high cylinders with a circular perimeter, not a weird jagged edged shape made of a clump of hexagonal prisms. The description of Area spells doesn't even mention hexes.

Same here. I view hexes as an optional gurps rule that lots of other people use.

[Stormcrow]

Originally Posted by hal

For spells that are Area affect, a hex radius of 1 means that the edge to edge aspect of the area spell is essentially 1 hex. A 2 hex radius is the hex the spell caster is standing in, plus all adjacent hexes.

Area spells are not measured in hex-radiuses. They are measured in yard-radiuses. When you cast an Area spell, you can (usually) choose to cast it at a 1-yard radius, a 2-yard radius, a 3-yard radius, and so on.

Page 239 of the Basic Set, and page 13 of GURPS Magic, show how to translate Area spell areas into hexes. The spell does not actually follow hexagonal geometry; that's just a convenient way to track it on a battle map.

Since hexes are measured from center to center, and since anything in a hex, whether it's actually in the center, is considered within a spell's area if it affects that hex, you must understand that true multiple-unit-radius circles of spells would, strictly speaking, cut through the center of the hexes. So translating a radius to a hexagonal battle map is necessarily an inexact process.

Am I missing something here if I actively use real world numbers that measures things in lbs per cubic foot, or Inches per square yard, etc?

Use real-world numbers except when you're using a hexagonal battle map. Then use hexes.

So for example, if GURPS describes something as having the attributes of a Hax in volume or in size or what have you, should I be actively using real world values or adjusted values based on hexagons?

If GURPS describes something in terms of hexes, assume it's somewhere between the minimum and maximum possible radiuses. To use hexes is to fudge for convenience.

[maximara]

Originally Posted by Stormcrow

Area spells are not measured in hex-radiuses. They are measured in yard-radiuses. When you cast an Area spell, you can (usually) choose to cast it at a 1-yard radius, a 2-yard radius, a 3-yard radius, and so on.

Page 239 of the Basic Set, and page 13 of GURPS Magic, show how to translate Area spell areas into hexes. The spell does not actually follow hexagonal geometry; that's just a convenient way to track it on a battle map.

Magic 13 and Basic Set 239 are identical but the way they are worded is problematic.

"Represent Area spells on a battle map as follows. The area of effect of a spell cast over a one-yard radius is a single hex. The area of effect of a spell cast over a two-yard radius
is a central hex and all adjacent hexes. The area
of effect of a spell cast over a three-yard radius is a central two-yard area of effect plus the ring of hexes adjacent to that." (sic)

The problem is there is no way that works with how the diagram is set up. You can confirm this with this progression:

0.5 (inradius of hex ie center to a side), 1.5. 2.5. 3.5 ect.

The text is wrong as 1 yard radius spell covers one whole hex and about half of the surrounding six hexes.

If the hex was two yards across than the progression becomes this:
1 (inradius of hex ie center to a side), 3. 5. 7 ect.

which would invalidate the diagram.

[maximara]

I did the math using the text and the diagram and it is telling (a hex 1 yd across is 0.866 yd^2):

Text Radius: Text Area (A=πr2) Hexes covered: Diagram Radius: Area Covered (A=πr2); pictured hexes; actual hexes
1 yd 3.142 yd2 3.628 hexes 0.5 yd 0.866 yd2; 1 hex
2 yd 12.57 yd2 14.52 hexes 1.5 yd 7.813 yd2; 7 hexes; 9 hexes
3 yd 28.64 yd2 32.00 hexes 2.5 yd 19.63 yd2; 19 hexes; 22.67 hexes
4 yd 50.27 yd2 50.05 hexes 3.5 yd 38.48 yd2; 37 hexes; 44.42 hexes

As you can see the text radius result is much higher coverage than the diagram presents (remember they are small parts of hexes), And no matter how you slice it the text and diagram are at odds with each other.

[Stormcrow]

Originally Posted by maximara

"Represent Area spells on a battle map as follows. The area of effect of a spell cast over a one-yard radius is a single hex. The area of effect of a spell cast over a two-yard radius
is a central hex and all adjacent hexes. The area
of effect of a spell cast over a three-yard radius is a central two-yard area of effect plus the ring of hexes adjacent to that." (sic)

The problem is there is no way that works with how the diagram is set up.

Notice that they don't say "A one-yard radius is equal to a single hex." They are giving you a translation, not an accurate measurement. Most Area spells will be cast over an area wider than one yard, so the half-yard around the edge never really matters all that much, especially since GURPS assumes that anything in a partial hex takes up that entire hex.

In other words, it's intentionally simplified for gaming.

[malloyd]

Originally Posted by hal

Am I missing something here if I actively use real world numbers that measures things in lbs per cubic foot, or Inches per square yard, etc?

Yes. You are missing the very basic fact that this text is not about converting hexes to real world measurements. It is about determining whether a spell affects something standing in a particular hex. If the radius of the spell effect does not encompass all (or at least almost all) of a particular hex said something is in, it is assumed to be unaffected.

That is all it means. All distance and area measurements in a game system that are less than the resolution of the grid/hex scale, (and all times less than the turn scale, the other place this sort of thing comes up) are BELOW THE RESOLUTION of the model. Hexes and turns are not precision measuring units, and precision units are largely pointless for resolving anything on the combat scale you would be using hexes and turns for. If you are trying to use both at once, you are doing something they are not intended to do, and will need to resolve the relationship with good judgement on the part of the GM rather than some sort of appeal the the rules. If it makes a difference which you choose, that is a sure sign you are below the resolution of the model of the game engine, and the "actual" result, whatever that means, is indeterminate. That's why games have GMs.

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

[Varyon]

Originally Posted by maximara

"Represent Area spells on a battle map as follows. The area of effect of a spell cast over a one-yard radius is a single hex. The area of effect of a spell cast over a two-yard radius
is a central hex and all adjacent hexes. The area
of effect of a spell cast over a three-yard radius is a central two-yard area of effect plus the ring of hexes adjacent to that." (sic)

The problem is there is no way that works with how the diagram is set up.

Looks like when representing an area spell on a battlemap, you only include the hexes that are entirely within the spell's area (and always center it in the center of a hex, so that you can't get two or three in the area by placing it at an intersection), which is perfectly consistent with the diagram. When discussing effects like in hal's Rain thread, it probably best to just ignore the hexes, using the nominal radius. Sure, an actual 1 yard radius that is centered on the center of a hex would affect that entire hex and a bit below half of the adjacent hexes, and for determining how much water you can collect from that you'll want to use the area of a circle, but for determining if your salt golem gets dissolved, use the diagram. If it really bugs you, either rewrite all references to "n yard radius" with "(n-0.5) yard radius" (so the values are close enough) or have the hexes adjacent to those the diagram indicates be partially affected in some way (such as being able to Dodge without a Retreat/Dodge and Drop, suffering half damage, or whatever would be appropriate for "fills only ~half your hex instead of the whole thing").