November 23, 2017, 04:17:43 PM

Author Topic: Steep Hill + wall and LoS  (Read 1067 times)

Arkdeniz

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Re: Steep Hill + wall and LoS
« Reply #30 on: November 14, 2017, 12:57:47 AM »
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 donít see it. I think you need to get out of the theoretical and look at the board. Zones have an edge. Itís not theoretical, itís marked with lines. Those lines are the zone borders. If you reach one, youíve 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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Zuberi

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Re: Steep Hill + wall and LoS
« Reply #31 on: November 14, 2017, 08:16:00 AM »
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 donít see it. I think you need to get out of the theoretical and look at the board. Zones have an edge. Itís not theoretical, itís marked with lines. Those lines are the zone borders. If you reach one, youíve 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.

Coshade

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Re: Steep Hill + wall and LoS
« Reply #32 on: November 14, 2017, 11:21:14 AM »
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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Arkdeniz

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Re: Steep Hill + wall and LoS
« Reply #33 on: November 14, 2017, 02:03:55 PM »
You're welcome.
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aridigas

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Re: Steep Hill + wall and LoS
« Reply #34 on: November 15, 2017, 04:19:12 PM »
What you guys are doing here is essentially Topology 1.

Look at the Arena as a subset of R≤. (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.

DaveW

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Re: Steep Hill + wall and LoS
« Reply #35 on: November 15, 2017, 07:08:30 PM »
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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aridigas

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Re: Steep Hill + wall and LoS
« Reply #36 on: November 16, 2017, 12:09:26 AM »
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.

Zuberi

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Re: Steep Hill + wall and LoS
« Reply #37 on: November 16, 2017, 07:03:36 AM »
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.

jacksmack

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Re: Steep Hill + wall and LoS
« Reply #38 on: November 16, 2017, 03:53:53 PM »
A lot of meme materiel in this thread.

drmambo23

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Re: Steep Hill + wall and LoS
« Reply #39 on: November 16, 2017, 04:36:30 PM »
A lot of meme materiel in this thread.

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