Arcane Wonders Forum
Mage Wars => Rules Discussion => Topic started by: Santar on March 12, 2017, 12:59:47 PM
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Hi,
The situation is as follows: there is a mage adjacent to a zone with a Steep Hill. He wants to cast a Wall on one of the borders of Steep Hill zone. What are his options? Will the Steep Hill prevent him from casting a wall on the opposite border, for example?
(https://pp.userapi.com/c637317/v637317767/3d8b0/WbYrRax_e_E.jpg) (https://pp.userapi.com/c637317/v637317767/3d8b7/P5GyvlCIDe8.jpg)
(https://pp.userapi.com/c636522/v636522313/52ae4/TXn9qwFDKIg.jpg)
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this is a good question. i believe that since los did not pass through two sides, you can see all three walls. though it seems like the wall directly across should be blocked. since you can see into each zone at an angle above and below the hill you should be able to see those walls via those zones.
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Strictly speaking, it depends upon how do we interpret "passes through" in the Steep Hill text.
Literal interpretation ("touches" <> "passes through") implies that all three borders are visible. However an official opinion will be greatly appreciated.
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I believe you cannot place a wall directly across from the hill. only above it and below it. But you should be able to place one above or below and extend it to the far side across from your mage...i think
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The paladin can cast all 3 walls from his current position.
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(http://skrinshoter.ru/s/120317/5ss7at0c.png)
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The key concept is that the Paladin has LoS to the zone that Steep Hill is attached to. Thus, he can build walls on any side of that zone.
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The key concept is that the Paladin has LoS to the zone that Steep Hill is attached to. Thus, he can build walls on any side of that zone.
Ahh. Makes sekse! Thanks for clarifying.
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Similarly, if the Paladin wanted to target any of these walls with a ranged attack that includes Range 1, he is able to, because he has LoS to the zone with the Steep Hill.
Interestingly, and correct me if I'm wrong, but I think if his ranged attack was, say, Range 2-3 (or if we swap the Paladin for an [mwcard=FWJ01]Akiro's Hammer[/mwcard]), he would still be able to target the wall across from the Hill because, even though the Hill blocks LoS to the zone at Range 2, the rules for targeting walls say that as long as you have Range to a zone on either side of the wall, and as long as you have LoS to the Wall itself, you can target the wall (even if you don't have LoS to the zone that you have Range to). This is why, for example, a Skeleton Archer can use his Ranged attack against a Wall on the border of his zone (e.g. he has LoS to the Wall, and one of the zones that the wall borders is at Range 1, even though the Archer can't see that zone).
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The key concept is that the Paladin has LoS to the zone that Steep Hill is attached to. Thus, he can build walls on any side of that zone.
Exactly what I said when discussing the problem with TS in a local chat. However it seems things have changed.
Rulebook (recent version available for download): "At least one of the two zones adjacent to the target zone border must be in range, and the zone border in LoS when you cast the wall spell"
Old rulebook I've downloaded previously: "At least one of the two zones adjacent to the wall must be in range and LoS when you cast the wall spell"
So strictly speaking, building a wall requires a LoS to the zone border, not the zone.
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an adjacent zone must be in LOS to target the wall, the zone with the steep hill is, so you can target the three walls (even if it is not realistic).
about range, targetting a wall is range 0 and 1 from an adjacent zone.
so it should be range 1-2 in this situation, and Akiro's hammer should be able to target the three walls.
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When targeting a zone border, one of the two zones adjacent to the border must be within range of the spell, and the border itself needs to be in Line of Sight. So, it doesn't matter that you have Line of Sight to the zone containing the Steep Hill, what matters is if you have Line of Sight to the zone border. Line of Sight and Range are checked separately. Hagen is completely right on this.
So, Steep Hill blocks Line of Sight if it passes through two "sides" of the zone, meaning the question is whether or not it passes through a second "side" of the zone before reaching the Zone Border. Now, the "side" of a zone isn't a game term, so we just have to trust common English a bit with this, but I think it's fairly clear that the "side" of the zone is synonymous with Zone Border. They are in actuality the same thing.
This would mean that when you trace Line of Sight, you are getting to and touching the second side of the zone, BUT you are not passing through it. So you would be able to target any of the zone borders adjacent to the Steep Hill. Which are, as iNano and exid pointed out, vulnerable to range 2 attacks in the example setup, like those from Akiro's Hammer, because again Range and Line of Sight are checked separately.
Edit: Just to remind people of the rules, for those saying that two of the borders would be visible but the far one wouldn't be, Line of Sight is traced from the center of the zone to the center of the zone border. So all three questioned borders are identical in the presented problem, with Line of Sight having to first pass through one border and then touch the middle of the border in question. Whatever answer applies to one, applies to all three. You can't skew the origin or the destination to try and circumvent obstacles.
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argl!
I allways forget that LOS is to the wall...
but then it would seem logical that the steep hill cuts LOS to the three walls.
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When targeting a zone border, one of the two zones adjacent to the border must be within range of the spell, and the border itself needs to be in Line of Sight. So, it doesn't matter that you have Line of Sight to the zone containing the Steep Hill, what matters is if you have Line of Sight to the zone border. Line of Sight and Range are checked separately. Hagen is completely right on this.
So, Steep Hill blocks Line of Sight if it passes through two "sides" of the zone, meaning the question is whether or not it passes through a second "side" of the zone before reaching the Zone Border. Now, the "side" of a zone isn't a game term, so we just have to trust common English a bit with this, but I think it's fairly clear that the "side" of the zone is synonymous with Zone Border. They are in actuality the same thing.
This would mean that when you trace Line of Sight, you are getting to and touching the second side of the zone, BUT you are not passing through it. So you would be able to target any of the zone borders adjacent to the Steep Hill. Which are, as iNano and exid pointed out, vulnerable to range 2 attacks in the example setup, like those from Akiro's Hammer, because again Range and Line of Sight are checked separately.
Edit: Just to remind people of the rules, for those saying that two of the borders would be visible but the far one wouldn't be, Line of Sight is traced from the center of the zone to the center of the zone border. So all three questioned borders are identical in the presented problem, with Line of Sight having to first pass through one border and then touch the middle of the border in question. Whatever answer applies to one, applies to all three. You can't skew the origin or the destination to try and circumvent obstacles.
Apologies for raising this thread from the dead, but this situation came up in a game tonight, and we fell to arguing.
The result we came up with opposes Zuberi's reasoning here.
The problem is that the rules for LoS as written have not taken into account any possibility that something other than a wall can block LoS:
"Some walls block LoS. You cannot cast a spell or make a ranged attack through a wall that blocks LoS. . . Draw an imaginary straight line from the centre of the attacker's or caster's zone to the centre of the target's zone. LoS is blocked if the line crosses through a zone border that has a wall on it with the blocks LoS trait. . . When drawing LoS to a wall, draw it to the centre of the zone border."
That's what we've got to go on.
The Steep Hill is a different beast. It sits within the zone, not on a zone border the way a wall does. It says:
"LoS that passes through two sides of this zone is blocked."
The language on the Steep Hill card is loose and imprecise. However, it is clear that because Steep Hill sits within the zone and not on its border it does something different to a wall and the rules as written on LoS (which talk strictly about conjurations on zone borders) cannot completely apply.
Because "LoS that passes through two sides of this zone is blocked" the Steep Hill needs to be envisaged as a raised platform with straight up and down sides. Since LoS goes from centre to centre there isn't any virtual 'gentle slope' you can peek over to look into a diagonally adjacent zone.
Simply put, if you are standing in a zone adjacent to a Steep Hill you do not have LoS to any zone border other than the one directly in front of you, because there is a large mass of earth sitting in the middle of the zone.
It has been argued that walls, sitting on a zone border, do not "cross" a border, but clearly the rules on range show that walls belong to, and affect, both bordering zones and thus casting a wall must necessitate "passing" the zone border in some way. (You might also say that since you can't have two walls back-to-back against each on either side of a zone border a wall must have a foot in both camps, as it were.)
If you think of it like that, then you need to cross two zone borders to cast a wall along the far or side zone borders of an adjacent zone (even if only by a little bit).
I am usually all in favour of taking rules-as-written, but in this case I do not think the rule has been written. LoS as it refers to seeing through walls is certainly there and is very clear, but there is nothing other than a fairly vague one line for a LoS blocker that sits within a zone. Rules-as-intended need to have the casting vote.
tl/dr: You can't build a wall on the other side of a Steep Hill, because you can't see the zone border as there is a Steep Hill in the way.
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RAW works as Zuberi previously explained. You can imagine that the Zone Borders rise WITH the effect of the Steep Hill so that all 3 Zone Borders are still visible from the Paladin's position. i.e. The difference in tracing LOS between a Wall and a Steep Hill is that a Wall along a single Zone Border blocks LOS, while it takes crossing two Zone Borders of a Steep Hill to block LOS.
It seems several interpretations posted here consider the Steep Hill to act as a Wall in the middle of the Zone, which is not supported by the RAW.
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Strictly speaking, it depends upon how do we interpret "passes through" in the Steep Hill text.
Literal interpretation ("touches" <> "passes through") implies that all three borders are visible. However an official opinion will be greatly appreciated.
The critical wording is in the new LOS rule for the border where the wall is being cast, and the wording of Steep Hill.
The zone border is not the same as the far side of the zone. The SH prevents sight to the zone border directly across from the adjacent creature.
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Let me try to phrase my previous explanation a little differently with an example:
A normal wall doesn't block line of sight to itself. I think we can all agree on that. Thus, it doesn't block line of sight TO the zone border that it occupies. It just blocks any attempts to trace line of sight ACROSS the zone border it occupies.
Similarly, a Steep Hill doesn't block line of sight TO the second border of the zone it sits in. It only blocks line of sight ACROSS the second border. Ergo, you can target a wall on the opposite side of a steep hill.
It has been argued that walls, sitting on a zone border, do not "cross" a border, but clearly the rules on range show that walls belong to, and affect, both bordering zones and thus casting a wall must necessitate "passing" the zone border in some way. (You might also say that since you can't have two walls back-to-back against each on either side of a zone border a wall must have a foot in both camps, as it were.)
Draw two squares on a sheet of paper that share one side. Can you draw a line to the shared side without crossing it? Yes. I don't know how you came to your assumptions, but casting a wall doesn't necessitate passing the zone border. It's on the border. It's not in both camps. It's on their shared border. It is literally the line between two squares.
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Strictly speaking, it depends upon how do we interpret "passes through" in the Steep Hill text.
Literal interpretation ("touches" <> "passes through") implies that all three borders are visible. However an official opinion will be greatly appreciated.
The critical wording is in the new LOS rule for the border where the wall is being cast, and the wording of Steep Hill.
The zone border is not the same as the far side of the zone. The SH prevents sight to the zone border directly across from the adjacent creature.
What rule are you referencing?
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I have seen on these forums that it is dangerous to go against Zuberi in a rules argument, but because I am still grumpy that my newly-summoned phalanx of goblin legionnaires was shredded by a wall of pikes + force wave combo last night, here goes.
A normal wall doesn't block line of sight to itself. I think we can all agree on that. Thus, it doesn't block line of sight TO the zone border that it occupies. It just blocks any attempts to trace line of sight ACROSS the zone border it occupies.
Agreed.
Similarly, a Steep Hill doesn't block line of sight TO the second border of the zone it sits in. It only blocks line of sight ACROSS the second border. Ergo, you can target a wall on the opposite side of a steep hill.
This is where we differ. Let me start off by reflecting your first paragraph to indicate what I think is going on, and then I'll try to explain why.
A Steep Hill doesn't block line of sight to itself. I think we can all agree on that. Thus, it doesn't block line of sight TO the zone that it occupies. It just blocks any attempts to trace line of sight ACROSS the zone it occupies.
The key is the language used on the Steep Hill card: "LoS which passes through two sides of this zone is blocked."
Various posts on this thread, including Zuberi's, have equated 'sides' here to mean 'zone borders'. I don't think it does. Arcane Wonders has been in this business for a long time, and I give them the benefit of the doubt when it comes to the language they use. If they meant 'side' to mean 'zone border', they would surely have written 'zone border.' They must have been thinking of a different concept with 'side'. (In passing, I note that the codex definition for Zone Border does not use the word 'side' anywhere.)
I would argue that the intent is to differentiate the Hill's effect from the rulebook's section on Line of Sight, which is explicitly and only discussing LoS as it relates to walls and zone borders, and is silent on LoS as it relates to conjurations inside a zone.
I'd like to see an official ruling, but before such a thing shows up, I present my theory:
The Steep Hill's wording introduces a second meaning for line of sight, one that is used in wargaming - a virtual line between the active creature and its target, where 'Zone borders' are not a relevant consideration but the 'sides' of the zone are.
With the Steep Hill what we have is some terrain that sits above the 'floor level' of the arena. Functionally it is like a building in a war game, one that effectively has the same ground dimensions as the zone it sits in. If you're standing in front of the 'SH building' you can only see and target its front wall and what is on its roof. if the line of sight passes through the 'SH building' you can't see through it to what is beyond, and you can't see or target its three far side walls (which would be the zone borders, so you couldn't build a wall on them).
A tidier way of putting it on the card might have been "LoS that passes beyond the centre of this zone is blocked."
As I say, that's my view. I appreciate that there are others and would love a ruling on it.
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Strictly speaking, it depends upon how do we interpret "passes through" in the Steep Hill text.
Literal interpretation ("touches" <> "passes through") implies that all three borders are visible. However an official opinion will be greatly appreciated.
The critical wording is in the new LOS rule for the border where the wall is being cast, and the wording of Steep Hill.
The zone border is not the same as the far side of the zone. The SH prevents sight to the zone border directly across from the adjacent creature.
What rule are you referencing?
I am referencing Hagen’s quote of the rule change on walls ... “and the zone border in LoS when you cast the wall spell" ... and I am suggesting that the zone border on the far side of the zone is not in LOS by the wording on the Steep Hill spell card. The zone border is not part of the zone... even the farthest reaches of the zone.
That is ... it passes through two sides of the zone before reaching the zone border. The side of the zone is the farthest point within the zone, just before the zone stops existing and the zone border is reached. At least that is my interpretation of the terms zone border and side of the zone.
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I am referencing Hagen’s quote of the rule change on walls ... “and the zone border in LoS when you cast the wall spell" ... and I am suggesting that the zone border on the far side of the zone is not in LOS by the wording on the Steep Hill spell card. The zone border is not part of the zone... even the farthest reaches of the zone.
That is ... it passes through two sides of the zone before reaching the zone border. The side of the zone is the farthest point within the zone, just before the zone stops existing and the zone border is reached. At least that is my interpretation of the terms zone border and side of the zone.
I like this idea. More elegantly put than my earlier screed.
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I am referencing Hagen’s quote of the rule change on walls ... “and the zone border in LoS when you cast the wall spell" ... and I am suggesting that the zone border on the far side of the zone is not in LOS by the wording on the Steep Hill spell card. The zone border is not part of the zone... even the farthest reaches of the zone.
That is ... it passes through two sides of the zone before reaching the zone border. The side of the zone is the farthest point within the zone, just before the zone stops existing and the zone border is reached. At least that is my interpretation of the terms zone border and side of the zone.
I like this idea. More elegantly put than my earlier screed.
Me too. The idea that a "zone side" and a "zone border" are distinct concepts makes the effect of Steep Hill as written feel more 'realistic' to me. This changes my earlier thinking where I was equating a zone side with a zone border.
An official ruling would be nice and if "zone side" is different, then the definition should be added to the Codex.
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I think the key thing people are forgetting here is that zone borders are one dimensional. They're literally the line between two squares. They have no depth. Or as the codex puts it, they are the "Intersection between two zones." They are where the zones touch.
You are correct that they aren't considered to be in either zone, but they're also not occupying space outside of them. They exist as the intersection of the two zones. They're a line, not a box. Once you cross out of one zone, you're in another. There's no space between. You cross zone borders, you don't enter them.
Walls are the only thing that are able to exist on a border. ON it, not in it. There is no "in".
I will agree that the rules don't explicitly say that this is synonymous with the "side" of a zone, but I honestly can't fathom another interpretation. There are no other edges involved to possibly count as the side of a zone. You never pass a line before reaching the zone border because the border is the ONLY line there.
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I think the key thing people are forgetting here is that zone borders are one dimensional. They're literally the line between two squares. They have no depth. Or as the codex puts it, they are the "Intersection between two zones." They are where the zones touch.
You are correct that they aren't considered to be in either zone, but they're also not occupying space outside of them. They exist as the intersection of the two zones. They're a line, not a box. Once you cross out of one zone, you're in another. There's no space between. You cross zone borders, you don't enter them.
Walls are the only thing that are able to exist on a border. ON it, not in it. There is no "in".
I will agree that the rules don't explicitly say that this is synonymous with the "side" of a zone, but I honestly can't fathom another interpretation. There are no other edges involved to possibly count as the side of a zone. You never pass a line before reaching the zone border because the border is the ONLY line there.
The RAW version 4.0 added a "Step 3: Leaving the Zone Effects" to the Move Action that may give us insight to AW intent. This step allows effects to happen BEFORE encountering a Wall during Creature movement. This suggest some timing 'space' happens when leaving a zone and before entering the zone border where the wall exists. This 'space' could be seen as the 'zone side' mentioned in the Steep Hill spell effect. Since we already have effects that trigger when leaving a zone, but before entering a wall we might extend this logic to include LOS. i.e. we trace line of sight into and out of a zone and LOS can now be blocked by effects as the LOS leaves the zone but before it reaches a wall or zone border.
A ruling from AW would be nice here.
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You might want to reread the movement rules. You don't leave your zone of origin until step 5, the Move step, which happens after encountering walls. They are very clear that until then you are still within your zone of origin. While resolving the wall step, you are still inside your starting zone and if any effects happen during that step that halt your movement you will remain in your starting zone. You never ENTER the zone border at all. You merely cross it, which happens after encountering walls.
You talk about drawing a line out of a zone before it reaches a zone border. Please show me on the game board exactly where this is at? Where are you drawing the line to that is both outside of the zone and has not yet hit a zone border? Let's actually look at the geometry involved here, because I really can't picture what you're talking about.
If you guys want to talk about Rules as Intended, they were intended to be functional. You are supposed to be able to ACTUALLY trace a line on the board from point A to point B and see whether or not it meets the necessary requirements for Line of Sight. Please show me where the point is at on the board that is outside of the zone but hasn't yet encountered a zone border?
In both RAW and RAI the card is using plain english. The sides of the zone means THE SIDES of the ZONE. Look on the game board, and the lines marking its sides, i.e. the zone borders, are what's being referenced. It's not some great enigma. It's normal english. As long as you haven't crossed two of those lines, steep hill isn't blocking your line of sight. Tracing to a line is not the same as crossing it. This is a really simple problem that you guys are trying to make into something else by imagining there are additional invisible boundaries at play that the rules just neglected to ever mention.
I'm sorry. I know this has started to come off somewhat mean. But I'm not sure how else to be nice about this. You guys don't like how it works thematically, I get that and can agree with where you're coming from. But because of this, you're making up a problem where there is none.
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Since we are talking about Steep Hills, I have a second question.
How high is a Steep Hill?
On the one hand we know that flying creatures have their line of sight blocked by it, but not by walls. So it is clearly higher than a wall.
But on the other hand we also know that it does not provide the Indirect trait, so standing on it does not let a ground creature see over an adjacent wall. So it is clearly lower than a wall.
I know that the magic-infused mage wars arena is a place where physics often seems to work differently to the real world, but just how high is the Steep Hill?
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You talk about drawing a line out of a zone before it reaches a zone border. Please show me on the game board exactly where this is at? Where are you drawing the line to that is both outside of the zone and has not yet hit a zone border? Let's actually look at the geometry involved here, because I really can't picture what you're talking about.
The zone border is not within the zone, therefore it must follow that the zone does not extend into the zone border. The edge of the zone abuts the zone border at its farthest reach, but does not extend into it.
Geometrically, I am thinking of the sum of 1/2 raised to "n" where "n" goes from 1 to infinity... in theory this equals one... however at no time does the sum ever come to one. => You can walk half-way to a point, then half that distance again, then half again and again... but you will never reach that point. As you say, it is a two-dimensional line... having no width you never reach it.
In my mind, it makes sense both geometrically and thematically.
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On the one hand we know that flying creatures have their line of sight blocked by it, but not by walls. So it is clearly higher than a wall.
You still see flying creatures behind steep hill.
A flying creature has line of sight to all creatures and all creatures have line of sight to a flying creature.
Only obscured breaks what i just said.
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And obscured doesnt really break it. It just does so you cannot target it 2 or more zones away, you actually still have line of sight to the object.
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Is your argument really that zones extend infitesimally without ever touching the border? And you think this is not only sensible, but somehow functional? Cause I don’t see it. I think you need to get out of the theoretical and look at the board. Zones have an edge. It’s not theoretical, it’s marked with lines. Those lines are the zone borders. If you reach one, you’ve reached the other. Postulating that another secret invisible edge exists that has just never been mentioned before is really sounding like a conspiracy theory.
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On the one hand we know that flying creatures have their line of sight blocked by it, but not by walls. So it is clearly higher than a wall.
You still see flying creatures behind steep hill.
A flying creature has line of sight to all creatures and all creatures have line of sight to a flying creature.
Only obscured breaks what i just said.
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And obscured doesnt really break it. It just does so you cannot target it 2 or more zones away, you actually still have line of sight to the object.
Ah.
I was focussed on the rulebook's section on Walls and LoS that I neglected to read the final sentence of the section on Flying.
So I guess the answer to my initial question is that the Hill is lower than a Wall (small hill, then!) This would also explain why a Wall on the other side of a Hill can be targeted by ranged attacks and spells.
I am still not convinced that you should be able to see the ground immediately on the dead side of the hill in order to cast a Wall. That just seems silly to me.
But I guess I have played games with silly rules before.
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Is your argument really that zones extend infitesimally without ever touching the border? And you think this is not only sensible, but somehow functional? Cause I don’t see it. I think you need to get out of the theoretical and look at the board. Zones have an edge. It’s not theoretical, it’s marked with lines. Those lines are the zone borders. If you reach one, you’ve reached the other. Postulating that another secret invisible edge exists that has just never been mentioned before is really sounding like a conspiracy theory.
If we want to start talking down theory and suggest we start looking at the physical board I would have to say that the concept of the zone border being a one dimensional line is also non-sensical.
You can see the mark on the board. Therefore it has two dimensions. A two-dimensional object by definition has two edges on either side. If you reach one edge you have to cross a little bit of space to get to the other. So there is 'something', on the board, between two adjacent zones. Whether that 'something' is a Zone Border could be argued, but it is there.
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Is your argument really that zones extend infitesimally without ever touching the border? And you think this is not only sensible, but somehow functional? Cause I don’t see it. I think you need to get out of the theoretical and look at the board. Zones have an edge. It’s not theoretical, it’s marked with lines. Those lines are the zone borders. If you reach one, you’ve reached the other. Postulating that another secret invisible edge exists that has just never been mentioned before is really sounding like a conspiracy theory.
If we want to start talking down theory and suggest we start looking at the physical board I would have to say that the concept of the zone border being a one dimensional line is also non-sensical.
You can see the mark on the board. Therefore it has two dimensions. A two-dimensional object by definition has two edges on either side. If you reach one edge you have to cross a little bit of space to get to the other. So there is 'something', on the board, between two adjacent zones. Whether that 'something' is a Zone Border could be argued, but it is there.
I want you to know that I really appreciate this response. It reminds me of myself being a smart ass in geometry class way back in high school. I also appreciate the entire discourse. I don't think there are ever any stupid questions, and you and others have been quite creative in your arguments.
That said, I think I am done with this thread. My argument basically just appeals to a common sense approach of plain english. Not every word in the language needs to be made into a game term, when it is just being used according to its normal definition, in my opinion. The sides of the zones are clearly labeled. We know those lines also mark the zone borders. Ergo, they're synonymous. I really can't say anything else on the subject. If you guys are going to reject this explanation and substitute in theories of invisible sides that are infinitely close to the border without touching it, then I don't think there's really anything I can do to convince you otherwise.
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I just want to point out that Zub was an active playtester at the time Steep Hill was introduced and has worked on supplement directly with AW. Generally I trust his rulings as rarely (if ever) I have seen him be incorrect. While I do not want to put words into Aaron mouth, I did work closely on the project and can say that Steep Hill is supposed to work in the way the Zuberi describes. That being said I am giving a banana sticker to Zub for going in depth on the question presented, and one for Jacksmack for clarifying the interaction with flying and Steep Hill. It is an easy thing to overlook. Thanks everyone for keeping things civil.
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You're welcome.
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What you guys are doing here is essentially Topology 1.
Look at the Arena as a subset of R². (R = real numbers, missing the right symbol.)
Lets say, for simplicity, Arena = (0,3)x(0,4). Please not that those are open intervalls, meaning the Arena Walls do not count towards the arena. (0,0), the lower left corner of the Arena is not inside the Arena.
Each Zone is an open subset of Arena. Each zone may definied as (i,1+1)x(j,j+1) for i=0,1,2; j=0,1,2,3.
(You cant define a topology this way, because the sets we call zone borders are in none of this open subsets.)
If an object is inside a zone, it occupies a interior point of given Zone. That is a point for which a neigbourhood exists which is in the Zone as well. Take a small circle, put it around the point and stay in the zone.
Similary to the sum of 1/2+1/4+1/8+1/16+... you will find such a small circle, unless you are on the zone border. your circle will always contain points of another zone (or points outside the arena) if you're on the zone border.
Zone borders are the boundaries of the open subsets zone. They are defined by closed subsets, ix[j,j+1] or [i,i+1]xj. This is where Walls are. Please note that they are excactly 1 point wide. Or high, depending on which one you look.
Objects other than walls can only exist in Zones. They have coordinates inside the zones. In our example a creature can never have a whole number as a coordinate.
That is ... it passes through two sides of the zone before reaching the zone border. The side of the zone is the farthest point within the zone, just before the zone stops existing and the zone border is reached. At least that is my interpretation of the terms zone border and side of the zone.
(I kinda lost myself here, but I guess the quote is what I want to prove wrong. Probably. It's fun anyway.)
To me, being on one side of of a zone border is being inside a zone.
There is no closest point to the wall, as you can always find another point. (Add 1/(2^(n+1)) and get closer to 1.)
Zone borders do not contain interior points of Zones, therefore Zone borders are not inside zones.
If you draw a line from zone A to zone B, thats a set of points. You can track every single point you use on this way. If we want to see if LoS crosses two sides of a zone, we need to look at the set of points marking the way we took. We start inside a Zone and use a straight line, because that is how you check LoS.
Crossing a zone border is the same as adding a point to our way-set. Remember, zone borders are excactly one point wide. The point we add isn't inside any zone, it has a whole number as one coordinate. If you cross another zone border, you add another of those points.
Now we need to ask ourselves, does steep hill block our LoS?
Say Steep Hill is in the zone (i,i+1)x(j,j+1). And we start tracking LoS outside this zone.
If we cross 2 zone borders, steep hill blocks our LoS. We now check our way-set and look for points that meet at least one of 4 criterias:
-its coordinates are (i,x)
-its coordinates are (i+1,x)
-its coordinates are (x,j)
-its coordinates are (x,j+1),
where x doesn't matter.
We find 0, 1 or 2 of those points.
This is how many Zone borders we cross.
0 Zone Borders: LoS doesn't cross Steep hill. Stee Hill doesn't block LoS.
1: LoS goes into the zone with Steep Hill. Steep Hill doesn't block LoS.
OR 1: LoS crosses a corner of the Steep Hill zone. WIll come to this in a second.
2: LoS crosses the Steep Hill zone and Steep Hill blocks LoS.
The corner case (see what I did here?) is the most interesting. This is what we want to know.
Let us take a close look at our way-set now. We know it contains one point on Steep Hill zone's borders. It is (i,j); (i+1,j); (i,j+1) or (i+1,j+1).
Do you know what our way-set doesn't contain? Any point from our Steep Hill zone. Not a single one.
And this why I am saying:
Steep Hill doesn't block LoS if LoS crosses one of his zone's borders.
His effect can't be used because his zone doesn't matter in that scenario.
q.e.d.
Anyone understood that? Not sure I did.
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To me, being on one side of of a zone border is being inside a zone.
...
Zone borders do not contain interior points of Zones, therefore Zone borders are not inside zones.
Thank you for agreeing with me. My point is dependant on this interpretation.
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If we cross 2 zone borders, steep hill blocks our LoS. We now check our way-set and look for points that meet at least one of 4 criterias:
-its coordinates are (i,x)
-its coordinates are (i+1,x)
-its coordinates are (x,j)
-its coordinates are (x,j+1),
where x doesn't matter.
We find 0, 1 or 2 of those points.
This is how many Zone borders we cross.
0 Zone Borders: LoS doesn't cross Steep hill. Stee Hill doesn't block LoS.
1: LoS goes into the zone with Steep Hill. Steep Hill doesn't block LoS.
OR 1: LoS crosses a corner of the Steep Hill zone. WIll come to this in a second.
2: LoS crosses the Steep Hill zone and Steep Hill blocks LoS.
So, this is where I messed things up.
I totally forgot what the original question was. We want to track LoS to the Zone border itself.
The above number of points does not show hw many Zone borders we cross, it shows how many zone borders we meet. If we stop drawing the line once we meet a zone border, we stilll add one of the above points to our way-set. We do not add any points to our way-set that do belong to another zone.
What does it mean if LoS crosses passes through (that's what steep hill actually uses, sorry) a side of a zone? It means it doesn't end there. That means or way-set needs to contain points of the other zone as well.
Let's count the points again from my quote again, shall we?
0: Stays at it is. No steep hill involved.
1: Stays at it is. Both cases. While the second one still is interesting, it does not answer the original post's question.
(Steep Hill doesn' block LoS to a wall between itself and you either. )
2: Now things get a little more complicated. Finding 2 of those points does for itself not mean passing through two sides of steep hill's zone. To accomplish this you need to find points of at least three zones: Steep hill's zone and two adjacent zones.
If you pass through something, you start at one side of it and end up on the other side.
If you start or end tracking LoS at a zone border, LoS does not pass through it.
To finally answer the question:
Our way-set does not contain points from the zone "behind the wall", therefore LoS does not pass through two sides of Steep Hill's zone. This means the paladin does have LoS to all three walls.
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I thought of another example that may work. Get yourself a giant cardboard box. Are the walls of the box inside of it? No, they surround it making up its edges. They're part of the infrastructure of the box. However, if you sit inside of this box, can you touch the walls or do you have to leave the box before you can touch them? Clearly, you can touch them without leaving.
Zone borders are the walls/edges/sides of the zone, just like the sides of a cardboard box. They're a part of the zone even though they're not in the zone. Neither can exist without the other. Just like you can't have a cardboard box without sides.
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A lot of meme materiel in this thread.
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A lot of meme materiel in this thread.
8)