The "fat cross" shape

[Bhruic]

I'm trying to figure out how the "fat cross" figures out how to expand. There are a few obvious parts - the outer boundaries are always 3 squares wide, for example. But I can't figure out how it's working the rest of the squares. It's most apparent at Legendary city size.



As you can see in this picture, the edges are pretty staggered, making it suggest that they are going with a 'round' edge system. But if they are, I can't figure out how they are determining whether a square should or should not be within the city boundaries.

Anyone have an idea? At first I went with a simple 'circle' system, where if your boundary was, say, 4 (that is, your borders extend 4 squares along x, y, -x, -y), then it would only encompass squares that were sqrt(x^2 + y^2) <= 4. Unfortunately, this doesn't seem to be the case. At 4 squares, the border encompasses the square +3, +3 (which is approximately 4.24).

So at this point I can't figure out how they are doing it.

Bh

[Enigma_Nova]

The Cross-shape is static for all cities, with the exception that it won't go more than one tile into the ocean, and the tiles already beloning to another Civ won't convert to your city immediately.

[Bhruic]

Yes, I'm well aware of that. My question had nothing to do with the whether it was static or not, but how the shape itself is determined.

Bh

[Mujadaddy]

It's a circle... you're not taking into account half the radius of the home square.

[xxFlukexx]

Ok, think of it like this:
You can move 6 tiles from the cap
But if you move diagonally twice, you lose a move.

So, left right down and up from the cap you go 6 spaces away.
One diagonal + left/right/up/down 5 times gets you the next square over
If you do diag+diag then you can move 3 more tiles
Diag+diag+diag takes up 3 moves -1 for 2 diags gives you 2 more moves left
Diagx4 = 4 moves -2 for 4 diags leaves you with no more moves left.

See, it's like a fun game. Maybe there's a better formula for it all nice and mathematical like, but my above method works. Now for smaller fat crosses, mm I think it's the same, but maybe diag might lose a move in smaller ones, I dunno. I don't know if this will help much, since the 'fat cross' is not a happy shape, it might not have a happy formula.

I guess you can simply say that it encompasses every square you can reach by moving 8 times without moving diagonally. It is also capped at going no more than 6 tiles away fom the cap(or can't go outside the 13x13 box centered at the cap) Ack, that's wasn't an easy formula either, oh well I tried.

[Axxaer]

Originally posted by xxFlukexx
See, it's like a fun game.

[Aeson]

I think it's something like: (Look for RCP in Civ III for examples)

+1 for any straight "move"
+1.5 for any diagonal "move"
= round down the total

So at radius 6 you have 6 tiles straight away. Then you replace a straight away with diagonal for 6.5, but that gets rounded down to 6 still.

[Sava]

me too

[Tim Nollan]

these posts cheer me up)

[crazysoliprice]

Quite interetsing.....

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