[MUD-Dev] Re: Hex-grid mapping

[James Wilson]

On Tue, 01 Dec 1998, Jon Leonard wrote:
>On Tue, Dec 01, 1998 at 02:42:18AM -0500, Matthew R. Sheahan wrote:
>> i'm in the design phase for a project where i want to use hex-grid
>> mapping, and this has led me to realize that i don't know any decent
>> methodology at all for tracking coordinates on a hex-grid.  ideally
>> i'd like something not very different from Cartesian coordinates, and
>> which permits easy determination of what locations are adjacent to
>> a given coordinate.  this seems like the kind of thing which has
>> probably been solved to death, so i thought i'd ask around instead of
>> reinventing the wheel.   does anyone have any suggestions, or resources
>> to point me to?
>
>Treat it just like cartesian coordinates, except that instead of using
>sqrt(x*x + y*y) for distance, use sqrt(x*x - x*y + y*y).
>
>That gives a coordinate grid that looks like this:
>
>                      /   \   /   \   /   \   /   \   /   \   /   \   
>                    |  0,5  |  1,5  |  2,5  |  3,5  |  4,5  |  5,5  |
>                  /   \   /   \   /   \   /   \   /   \   /   \   /
>                |  0,4  |  1,4  |  2,4  |  3,4  |  4,4  |  5,4  |
>              /   \   /   \   /   \   /   \   /   \   /   \   /
>            |  0,3  |  1,3  |  2,3  |  3,3  |  4,3  |  5,3  |
>          /   \   /   \   /   \   /   \   /   \   /   \   /
>        |  0,2  |  1,2  |  2,2  |  3,2  |  4,2  |  5,2  |
>      /   \   /   \   /   \   /   \   /   \   /   \   /
>    |  0,1  |  1,1  |  2,1  |  3,1  |  4,1  |  5,1  |
>  /   \   /   \   /   \   /   \   /   \   /   \   /
>|  0,0  |  1,0  |  2,0  |  3,0  |  4,0  |  5,0  |
>  \   /   \   /   \   /   \   /   \   /   \   /
>

this isn't a hex grid. It's a warped square grid. A hex grid has the useful
property that any cell has six neighbors, which is often a better fit for
tactical simulations than the square grid's four-with-four-diagonals neigbors.
For instance, diagonal motion makes a lot more sense in hexes than in squares
(assuming one move equals the traversal of one border). 

You can't tweak your equation to give them six neigbors, so don't try. (The
number of neighbors of each cell is a topological invariant, i.e. you can warp
space in any smooth way and each square will still have
four-with-four-diagonals neighbors.)

James