Landscape

Landscape is a 6-directional matrix. Coordinates are written as X-Y. Here is example of 4-3 landscape matrix:

Landscape is presented by a coded string containing the chars from base64 notation.

“A” means 0
“a” means 26
“0” means 52
“+” means 62
“/” means 63

Symbols 0-62 are used to identify province indexes, symbol 63 (“/”) is used to identify sea area.

Example landscape:

Legend:
blue region is sea,
yellow is province 0,
purple is province 1,
green is province 2

This can be presented by the next code: “//CCAACCABBB”. By rows:

//CC
AACC
ABBB

Trigonometry summary

We have 6 directions. Let’s code them the next way:

0 – Right
1 – Up-Right
2 – Up-Left
3 – Left
4 – Down-Left
5 – Down-Right

Let’s define arrays of direction sinuses/cosines:

cos = [1, 1 – D, -D, -1, -D, 1 – D];
sin = [0, -1, -1, 0, 1, 1];

where D = Y mod 2.

Verify formulas

For even rows, let’s check the neighbours of 2-1 cell:

D = 1 mod 2 = 1

Direction	Formula	Result
0 – Right	(2 + 1)-(1 + 0)	3-1
1 – Up-Right	(2 + 1 – D)-(1 – 1)	2-0
2 – Up-Left	(2 – D)-(1 – 1)	1-0
3 – Left	(2 – 1)-(1 + 0)	1-1
4 – Down-Left	(2 – D)-(1 + 1)	1-2
5 – Down-Right	(2 + 1 – D)-(1 + 1)	2-2

Success!

For odd rows, let’s check the neighbours of 1-2 cell

D = 2 mod 2 = 0

Direction	Formula	Result
0 – Right	(1 + 1)-(2 + 0)	2-2
1 – Up-Right	(1 + 1 – D)-(2 – 1)	2-1
2 – Up-Left	(1 – D)-(2 – 1)	1-1
3 – Left	(1 – 1)-(2 + 0)	0-2
4 – Down-Left	(1 – D)-(2 + 1)	1-3
5 – Down-Right	(1 + 1 – D)-(2 + 1)	2-3

Success!

Implementation

	public class Dir6
	{
		private static const COS	:Array = [ 1,  1,  0, -1,  0,  1];
		private static const SIN	:Array = [ 0, -1, -1,  0,  1,  1];
		private static const COS_D	:Array = [ 0, -1, -1,  0, -1, -1];
		
		public static function getTargetX(x:int, y:int, d:int):int
		{
			return x + COS[d] + COS_D[d] * (y % 2);
		}
		
		public static function getTargetY(x:int, y:int, d:int):int
		{
			return y + SIN[d];
		}
	}