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Territory Tiles -- Topology

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As we know, planets will have their territories split up into tiles. These tiles will take the form of a 1km hexagon. There's an issue with this though. Using purely hexagons would violate Euler's characteristic for spheres. If you don't know what this means, watch this video

 

Using a similar form of logic, you will be able to see that it's impossible to subdivide a sphere into just hexagons. What the video didn't point out was that there are other combinations of pentagons and hexagons.

 

Using something like subdividing icosahedrons, you could get a lot of tiles. With a large number of tiles, you would have a lot of hexagons, but you still need at least 12 pentagons, one for each vertex of the original icosahedron.

 

Example of subdividing icosahedron

image020.gif

 

I would have to guess that the devs already know this, but if they don't, they should take note.

 

What does this mean? Time to hunt for the 12 rare pentagonal territory tiles. :) Who will be the first to claim one?

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What is a 1km hexagon? Is it 1km from vertex to vertex (along an edge) or is it 1km from one edge through the middle to the other edge? One is much larger than the other.

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NQ already addressed this in the devblog on territory control (https://devblog.dualthegame.com/2015/07/24/territory-control/)

 

 

To simplify the process of planetary territory creation and definition, we have adopted the usual way of partitioning the surface of the planet with a large number of hexagonal tiles (note that you’ll also marginally have 12 pentagons in the lot: there is no way to have an isotropic uniform tiling of a sphere). Tiles are about 1km large

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Devs said "Tiles are about 1km large..." and anytime I've heard JC talk about it, the specifics weren't really mentioned (area vs short dia vs long dia). But your question makes me think of the process of subdividing the icosahedrons. Given a sphere with a certain radius and either a circumscribed or inscribed icosahedron, is it even possible to divide one up such that you always get 1 km (whatever it means) hexagons for any reasonable (50-100km, you know, DU planet sized) radius? We're going to have moons of planets of varying sizes. I'm not knowledgeable about topology, so maybe someone can answer my question. My intuition is that, no, you can't have hexagons of a specified size, but you could have the same number of tiles on each planet object.

 

Also, I did miss the small statement about the 12 pentagons in the devblog post, but this thread was intended more to explain why that's the case as well as make it obvious for everyone.

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The planet in the image they said has a radius of 30 km, which is a circumference of 188.5 KM. By taking the picture supplied I was able to determine that there are approximately 124 hexes around the circumference. If we take it that the tiles have a side length of 1 km, this would equal 108 tiles around the circumference (kinda close). Where as if we assume that it is 1 square km, this would equal a short diameter of 1.07 km. This would work out to about 176 tiles which is a fair bit more than the 124 in the image. So my guess would be the former (side length).

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Didn't they also say that planets will be much larger in full release? I thought I remembered reading that somewhere.

 

Another interesting thing to note: since the tiles will be based on a smooth sphere template, the mountain and valley tiles will actually contain more surface area. (Think of trying to get to the other side of a mountain with a 1km base, a tunnel through the mountain will be 1km long, while going over the mountain could be 4km.) Not sure if this will be an advantage, given the obvious challenges of utilizing an angled surface like a mountainside, but it could make those tiles more valuable too, depending on who is looking to buy it!

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The planet in the image they said has a radius of 30 km, which is a circumference of 188.5 KM. By taking the picture supplied I was able to determine that there are approximately 124 hexes around the circumference. If we take it that the tiles have a side length of 1 km, this would equal 108 tiles around the circumference (kinda close). Where as if we assume that it is 1 square km, this would equal a short diameter of 1.07 km. This would work out to about 176 tiles which is a fair bit more than the 124 in the image. So my guess would be the former (side length).

No, those planets are the Pre-Alpha test planets they have going. The actual Alpha Test will be in 100 Km radius planets, beyond that, is yet to be confirmed, but they have said that the planets are smaller, because the star they orbit is smaller in the starting system and they did confirm that they intend to mix biomes together to create more interesting worlds, so, for all we know, they might be intdeed goin gfor bigger planets after they have players going for planet-hunting, but that's my theory at least, as with the way the built the game, how big a planet was would not really affect performance (because of occlusion), but the horizon could be playing a role in immersion, as we would be able to larger bigger cities.

 

 

 

 

As we know, planets will have their territories split up into tiles. These tiles will take the form of a 1km hexagon. There's an issue with this though. Using purely hexagons would violate Euler's characteristic for spheres. If you don't know what this means, watch this video

 

Using a similar form of logic, you will be able to see that it's impossible to subdivide a sphere into just hexagons. What the video didn't point out was that there are other combinations of pentagons and hexagons.

 

Using something like subdividing icosahedrons, you could get a lot of tiles. With a large number of tiles, you would have a lot of hexagons, but you still need at least 12 pentagons, one for each vertex of the original icosahedron.

 

Example of subdividing icosahedron

image020.gif

 

I would have to guess that the devs already know this, but if they don't, they should take note.

 

What does this mean? Time to hunt for the 12 rare pentagonal territory tiles. :) Who will be the first to claim one?

 

Chances are you won't be seeing pentagonal claims, because the claiming system is not free-form, the hexes are there to be claimed, you simply have to put down a claim unit inside them to claim them.

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I think what people are saying is that, since a territory unit claims a specific "tile", and since there will be a few pentagonal tiles on any given planet, you could claim one by placing a territory unit on it, just like the hexagonal tiles.

Those may be more valuable simply because they are rare.

 

Maybe I missed it, but I don't believe anyone was suggesting that claiming would be freeform. And, unless they make those pentagonal tiles un-claimable, we will see people claim them.

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I don't think they would stop them from being claimed, what's the point. They will be just like any other. May be a little different size, but I don't think it matters that much. If you claim next to one, eventually you would probably grow into it, so to speak. If one was on a nice location, why wouldn't you, unless your a min-maxer, then no one can help you anyways :)

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CaptainTwerkmotor, on 20 Nov 2016 - 09:48 AM, said:

No, those planets are the Pre-Alpha test planets they have going. The actual Alpha Test will be in 100 Km radius planets, beyond that, is yet to be confirmed, but they have said that the planets are smaller, because the star they orbit is smaller in the starting system and they did confirm that they intend to mix biomes together to create more interesting worlds, so, for all we know, they might be intdeed goin gfor bigger planets after they have players going for planet-hunting, but that's my theory at least, as with the way the built the game, how big a planet was would not really affect performance (because of occlusion), but the horizon could be playing a role in immersion, as we would be able to larger bigger cities.

 

My comment was not about planet size, but speculation on how exactly they are measuring a 1 km tile. Is it the length (short or long) or surface area.

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