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I know what you're thinking, "It's half a sphere." Bear with me, because in terms of Pathfinder spell effects, that definition requires a bit more precision. Unfortunately, I'm having trouble coming up with a precise definition that doesn't do wonky weird things with one spell or another.
I'll start with the three definitions I see as plausible, though all have their issues.
1) A hemisphere is shaped like a dome, and has no flat-plane surface. This is as if you cut a hollow sphere in half.
2) A hemisphere is shaped like a dome with a flat surface, typically beneath the caster's feet. This is as if you cut a solid sphere in half. In other words, the spell effect fills the entire volume described as its area of effect rather than act as a 2D lens.
3) Because Pathfinder has no facing rules, a hemisphere faces all directions simultaneously, and is therefore equivalent to a sphere. I reject this definition because there are spherical spells and abilities, and as a distinction has been made by calling certain effects hemispherical, I must assume that this distinction corresponds to some real meaning.
Most GMs I have encountered expect that the first definition is true, but there are too many contexts where it makes no sense. I'll begin with the biggest example.
School abjuration; Level cleric 4, shaman 4, witch 4
Casting Time 1 round
Components V, S, DF
Range 10 ft.
Area 10-ft.-radius emanation centered on you
Duration 1 minute/level (D)
Saving Throw none; Spell Resistance yes
You bring into being a mobile, hemispherical energy field that incorporeal creatures cannot enter.
This spell can be used only defensively, not aggressively. Forcing an abjuration barrier against creatures that the spell keeps at bay collapses the barrier.
If we use the former definition, this spell accomplishes nothing. Any incorporeal creature can simply burrow under the dome, and pop up from the unprotected ground plane. As I can't imagine the author's intent was to make a 4th level slot-waster, the first definition is nonsensical. Another corner case would be a caster standing upwards from the ghost on a steep staircase or ramp. In this situation, part of the dome would end in open air, allowing the ghost to duck under it and enter the forbidden area. Of course, the dome could re-orient such that its radius is orthogonal to the normal plane, but that still doesn't solve the burrowing ghost problem.
The same issues arise with Antilife shell. However, as only a small subset of living creatures have burrowing ability, it seems less absurd that this vulnerability of the spell exists. Every type of creature that anti-incorporeal shell should hedge out could bypass the spell entirely if it does not fill a volume.
However, this volumetric definition runs into a problem when we talk about Wall of Ice.
School evocation [cold]; Level bloodrager 4, magus 4, sorcerer/wizard 4, summoner 3, unchained summoner 4; Bloodline boreal 4; Elemental School water 4
CASTING
Casting Time 1 standard action
Components V, S, M (a piece of quartz or rock crystal)
EFFECT
Range medium (100 ft. + 10 ft./level)
Effect anchored plane of ice, up to one 10-ft. square/level, or hemisphere of ice with a radius of up to 3 ft. + 1 ft./level
Duration 1 min./level
Saving Throw Reflex negates; see text; Spell Resistance yes
DESCRIPTION
This spell creates an anchored plane of ice or a hemisphere of ice, depending on the version selected. A wall of ice cannot form in an area occupied by physical objects or creatures. Its surface must be smooth and unbroken when created. Any creature adjacent to the wall when it is created may attempt a Reflex save to disrupt the wall as it is being formed. A successful save indicates that the spell automatically fails. Fire can melt a wall of ice, and it deals full damage to the wall (instead of the normal half damage taken by objects). Suddenly melting a wall of ice creates a great cloud of steamy fog that lasts for 10 minutes.
Ice Plane: A sheet of strong, hard ice appears. The wall is 1 inch thick per caster level. It covers up to a 10-foot-square area per caster level (so a 10th-level wizard can create a wall of ice 100 feet long and 10 feet high, a wall 50 feet long and 20 feet high, or any other combination of length and height that does not exceed 1,000 square feet). The plane can be oriented in any fashion as long as it is anchored. A vertical wall need only be anchored on the floor, while a horizontal or slanting wall must be anchored on two opposite sides.
Each 10-foot square of wall has 3 hit points per inch of thickness. Creatures can hit the wall automatically. A section of wall whose hit points drop to 0 is breached. If a creature tries to break through the wall with a single attack, the DC for the Strength check is 15 + caster level.
Even when the ice has been broken through, a sheet of frigid air remains. Any creature stepping through it (including the one who broke through the wall) takes 1d6 points of cold damage + 1 point per caster level (no save).
Hemisphere: The wall takes the form of a hemisphere whose maximum radius is 3 feet + 1 foot per caster level. The hemisphere is as hard to break through as the ice plane form, but it does not deal damage to those who go through a breach.
As we see, if the hemisphere creates a volume of ice, we succeed only in entombing ourselves like a woolly mammoth. Just as obviously as Anti-incorporeal could not have been intended to be useless, the hemisphere version of Wall of Ice couldn't be made as a suicide trap for unwary evokers. Even if we allow it to be a hollow hemisphere, it seems odd that there is no mention of the slippery floor those inside the sphere will have to navigate. One would assume that is because Wall of Ice acts as a simple dome, according to our first definition.
I can think of only one method of reconciling these definitions, and I would like input. Hopefully I can get a dev to chime in (so hit the FAQ button!)
- By default, a hemisphere is a two-dimensional dome oriented such that the bottom of the caster's feet would be the 'sphere's' center, and the radius is parallel to the caster's vertical axis. The caster may alter this orientation, but must specify that they are doing so when the effect is created. (In other words, it's like an igloo all around you, but you can flip it upside down or make it like a shield if you mention that's what you're doing when you cast.)
- However, if the effect is an emanation, the hemispherical effect occupies the entire volume within its radius. The effect otherwise works as before. (In other words, while the 'shell' spells are described as 'barriers' and evoke images of 2D surfaces, they are in fact volumes that the hedged creature-type can't enter. This prevents burrowing baddies and the like, and even teleportation effects from working (potentially).
I think this has to be how things work. I can't make sense of it otherwise. Thoughts?
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Basic principles: Spells (as well as feats, class abilities, etc.) are generally intended to do something. If there are two possible interpretations of the text of a spell (feat, ability, etc.) and one of them allows it to function and the other makes it utterly nonfunctional and useless, the first should be assumed to be correct until proven otherwise.
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I'm gonna go out on a limb and suggest Pathfinder wasn't written by rigorously-defining mathematicians. Some user-side educated guessing is often required.
For hemispheres I think it falls into three possible cases:
1) A hemispheric volume. Such as the area threatened by Black Tentacles. Everything in the area gets violated.
2) A proper, fully-enclosed hemispheric surface; including the flat bottom. Shell spells for example; the name suggests we're talking about surfaces, not volumes. But clearly Anti-Incorporeal Shell isn't meant to allow entry from below.
3) A partially-enclosed hemispheric surface or dome. Wall of Ice is an example; it doesn't make the ground slick and you could burrow into it from below.
For each spell you need to interpret which case makes the most sense. Using the principle the Paladin mentioned: spells do something useful.
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...Pathfinder wasn't written by rigorously-defining mathematicians...
No kidding.
Shell spells for example; the name suggests we're talking about surfaces, not volumes. But clearly Anti-Incorporeal Shell isn't meant to allow entry from below.
I dunno about this one. The description of emanations in the Magic section of the CRB is fairly clear. That said, it really doesn't jibe well with the textual description of those spells, as you mention.
By the rules, an emanation is volumetric but doesn't pass through barriers; thus, the example anti-incorporeal shell would fill a hemisphere centered on the caster stopping at any barriers which provide total cover, like the ground. So an incorporeal entity could burrow under the caster, but would hit the shell when attempting to "pop up" from underneath the spell effect.
Most spells that affect an area function as a burst, an emanation, or a spread. In each case, you select the spell’s point of origin and measure its effect from that point.
A burst spell affects whatever it catches in its area, including creatures that you can’t see. It can’t affect creatures with total cover from its point of origin (in other words, its effects don’t extend around corners). The default shape for a burst effect is a sphere, but some burst spells are specifically described as cone-shaped. a burst’s area defines how far from the point of origin the spell’s effect extends.
An emanation spell functions like a burst spell, except that the effect continues to radiate from the point of origin for the duration of the spell. Most emanations are cones or spheres.
I don't know why the spell dictates a hemispehere; perhaps the author just had it stuck in their head that the caster would be standing on the ground. In any case, I think it's safe to assume that the hemisphere emanating from the caster's square ends just below her feet (or her front, or back, if you choose to allow them to orient the hemisphere).
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RPG Superstar 2011 Top 32
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I think you missed one possibility, which is that the hemisphere acts as in case one but includes the plane that nominally divides the sphere in two, but not the interior volume. That solves your anti-X issue, and you can rationalize wall of ice in that most situations the ground (or creatures thereupon) would block the "floor" from forming.
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I think you missed one possibility, which is that the hemisphere acts as in case one but includes the plane that nominally divides the sphere in two, but not the interior volume. That solves your anti-X issue, and you can rationalize wall of ice in that most situations the ground (or creatures thereupon) would block the "floor" from forming.
I did consider that, but Wall of Ice has the stipulation that if attempted to form intersecting solid objects, the spell auto-fails. So if we imagine it as trying to make a floor but running into the ground, the spell can't be cast as a hemisphere.
Originally I had thought of hemispheres as you describe, and that is an acceptable definition of a hemisphere. In fact, mathematicians often define the surface area of a hemisphere as 3*pi*r^2, which takes that surface into account.
But hemispheres can also be defined without that surface, so I thought it was too much of a 'mileage may vary' definition.
As for the wall of ice example, I see no reason the effect would be volumetric. My reading is that it creates a sheet of ice 1 inch thick per caster level in the shape of a hemisphere with a maximium radius of 3 feet + 1 foot per caster level; as it does not indicate that the hemisphere is enclosed, I would assume it is an open-ended dome. My thought process is:
It's a hemisphere, not a hemishell, this means it covers all volume to the edges of the hemisphere
Interesting; I believe that in common use a sphere is not implied to be solid - globes, basketballs, beach balls, etc. are all commonly referred to as spheres. I point this out as support of hemisphere and sphere spells being shells RAI, on acceptance of the prior theory regarding the number of mathematicians writing for Pathfinder.
Is the volumetric/solid argument based on the wording of hemisphere (vs shell being in the title) also your reasoning for sphere spells, such as resilient sphere and telekinetic sphere?
A sphere is determined by the outside shape of the object. Sphere itself does not stipulate solid or hollow in and of itself.
Sphere has a specific definition in Pathfinder, and is definitely not hollow:
A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads.
Edit: yes, this makes some spells not work the way they probably should (resilient sphere springs to mind), but as long as you apply "well, it's supposed to work" and fudge around the odd edge cases, it'll all be okay.
Edit of Edit: Thought exercise - what if the centre of the 10' hemisphere is 5' in from the edge of a cliff?
Anti-Whatever Shell is specifically described as an emanation. Emanations fill a volume. Thus, it's a volume hemispherical in shape, forbidding, for example, burrowing under and through it.
The Pathfinder definition of "sphere" as volumetric only applies to bursts, emanations or spreads. Wall of Ice is none of those, so we needn't use that definition (which, as you've pointed out, would just entomb us) in this case. So, we're left with nothing but intuition which would tell us that it's a hollow hemisphere.
As for orientation, I would definitely say that you could flip it whichever way you want, both for emanations and whatever Wall of Ice is. There's nothing that states that the plane of the hemisphere has to align with any ground whatsoever. This wouldn't even make sense in a place where there is no objective "ground".
As an aside, I'm guessing that a hemispherical shape was chosen to clarify that it does not extend below the ground, but emanations already don't extend through total cover, so it's a bit odd.
Sphere has a specific definition in Pathfinder, and is definitely not hollow:
A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads.
I had always read the quoted sphere definition as applying specifically for defining a spell Area (such as for fireball), and not for defining aspects of a conjuration spell Effect (such as the mentioned resilient sphere) as such spells don't specify a burst, emanation, or spread area or effect. I understand how one could read them from your perspective as well.
At my own table I've always ruled summoned spheres and hemispheres as being hollow, as I think that's the RAI. I think that if the effects of resilient sphere and the hemisphere option of wall of ice were meant to be solid, the spell descriptions would include some mention of those trapped inside being unable to take actions requiring movement, break DCs to escape, etc. I realize that resilient sphere specifies that those inside can breathe, but I believe that's to clarify that trapping them in the sphere isn't going to cause them to run out of air and suffocate, not to imply that they're trapped in solid force.
Le Petite Mort, has this issue come up in PFS play or is it more for your own peace of mind?
Sphere has a specific definition in Pathfinder, and is definitely not hollow:
A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads.Edit: yes, this makes some spells not work the way they probably should (resilient sphere springs to mind), but as long as you apply "well, it's supposed to work" and fudge around the odd edge cases, it'll all be okay.
Edit of Edit: Thought exercise - what if the centre of the 10' hemisphere is 5' in from the edge of a cliff?
A definition cannot reference itself and still be a definition. This is a description of an effect, not a definition.
A Sphere is a 3 dimensional shape whose outer edges are equal distant from a single point in space.
Whether the effect his hollow or solid is extraneous to the definition of a sphere.
There isn't a difference between the "pathfinder definition" of a sphere and a real-world definition of a sphere.
Obviously Hemisphere means sphere, otherwise emergency force sphere would be misnamed.
Sphere has a specific definition in Pathfinder, and is definitely not hollow:
A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads.Edit: yes, this makes some spells not work the way they probably should (resilient sphere springs to mind), but as long as you apply "well, it's supposed to work" and fudge around the odd edge cases, it'll all be okay.
Edit of Edit: Thought exercise - what if the centre of the 10' hemisphere is 5' in from the edge of a cliff?
A definition cannot reference itself and still be a definition. This is a description of an effect, not a definition.
A Sphere is a 3 dimensional shape whose outer edges are equal distant from a single point in space.
Whether the effect his hollow or solid is extraneous to the definition of a sphere.
There isn't a difference between the "pathfinder definition" of a sphere and a real-world definition of a sphere.
Just want to get this straight... you just said that the part of the rules which says that spells with an area described as a sphere "fill a spherical area" somehow doesn't indicate that the area is filled?
Because in Pathfinder a "sphere-shaped spell expands from its point of origin to fill a spherical area". That's the rule.
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...Pathfinder wasn't written by rigorously-defining mathematicians...
No kidding.
Shell spells for example; the name suggests we're talking about surfaces, not volumes. But clearly Anti-Incorporeal Shell isn't meant to allow entry from below.
We mathematicians define a sphere as the points in 3-dimensional space equidistant from the center. Thus, a sphere is just the shell. If the object is supposed to be solid all the way to center, we call it a ball. A similar definition is that a box is just the surface, but a brick is solid. As a shortcut, we can talk about the volume of a sphere or a box and really mean the volume of the ball or brick enclosed by the sphere or box.
But I doubt Pathfinder uses the mathematical definitions rigorously.
The Anti-Incoporeal Shell spell said, "You bring into being a mobile, hemispherical energy field that incorporeal creatures cannot enter." The hemisphere is just a shell, but the interior of the hemisphere, the part that an incorporeal creature cannot enter, would be a half-ball. A solid object can never enter a surface, though it can overlap a surface, so that sentence is talking about the interior rather than the shell.
Wall of Ice forms a shell. The spell neglected to mention the thickness of the hemispherical shell--the perfect zero thickness of a true hemisphere would be useless--just like it does not mention the strength of the ice in the hemisphere, either. Thus, we copy the thickness from the wall description: 1 inch thick per caster level. For brevity, Pathfinder rules often explain details only in the first case when those details apply to all cases.
As for the bottom of these hemispheres, I doubt the spells intended a perfect planar slice. I believe they form a shell that reaches to the ground, even if the ground is not flat and smooth. For example, if the spellcaster is standing next to a ditch, the shell would extend the bottom of the ditch. A levitating caster could get a full sphere, though for a wall of ice, the "anchored" description of the spell would require a height at which bottom of the sphere rests on the ground.
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Le Petite Mort, has this issue come up in PFS play or is it more for your own peace of mind?
Peace of mind. Someone on reddit said something to the effect of, "Be aware that a clever GM can have ghosts burrow up from underneath the shell," and several /r/Pathfinder_RPG regulars concurring. I found that odd. Why would a spell be designed to be useless? I argued that hemispheres have flat bottoms, as I found a number of mathematical definitions of the surface area of a hemisphere indicating that.
But it felt like an insubstantial argument, as Pathfinder doesn't use strict mathematical definitions for things. I wanted clarity in Pathfinder jargon and logic.
So I worked it out in my OP here, and came, I think, to the correct reasoning behind the burrowing-ghost's impossibility. I considered just deleting the post, but I felt that I might get good counter-arguments, clarification from developers (or at least fellow players), and because when this question is asked by others they might find this thread through Google and settle the argument in their own games.
I am satisfied that my logic was correct. A sphere or hemisphere occupies all points within its radius if it is a burst, emanation, or spread. If its effect is none of those, it occupies only the points equidistant from its center (though it may have some thickness defined by the spell).
Just want to get this straight... you just said that the part of the rules which says that spells with an area described as a sphere "fill a spherical area" somehow doesn't indicate that the area is filled?
Because in Pathfinder a "sphere-shaped spell expands from its point of origin to fill a spherical area". That's the rule.
I said that the part of the rules that reference a sphere creates a spell effect that is a shape whose outer surface is equal distant to a point in space. Whether the interior of the spell effect fills the point between the origin and the outer surface is immaterial to the definition of a sphere.
It could be solid -- in which case you have a solid sphere. or it could be empty, in which case you have a shell.
Both are spheres.
Peace of mind. Someone on reddit said something to the effect of, "Be aware that a clever GM can have ghosts burrow up from underneath the shell," and several /r/Pathfinder_RPG regulars concurring. I found that odd. Why would a spell be designed to be useless? I argued that hemispheres have flat bottoms, as I found a number of mathematical definitions of the surface area of a hemisphere indicating that.
I'm sorry, but no. A hemisphere is half a sphere, or a dome with a bottom surface -- they can't burrow up from underneath. The spell's effect is in between you and the incorporeal undead.