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Re: [pbmserv-dev] Re: [pbmserv] Palago notation?

Hi,

There's no randomness in the Palago space labelling scheme. For a given turn, the M move positions are labelled in anticlockwise order by angle relative to the tile group's centre of mass, starting with the upper leftmost tile as move 1. The idea was to keep similar move numbers close together. This isn't an ideal scheme as the numbers need to be recomputed each turn - not much use if you want to replay a game with actual tiles from a written move list, for example.

Another option would be to use the actual [row,col] grid coordinates of each tile, but this would make the notation very clumsy and get confusing due to the hexagonal nature of the grid. It's much more elegant to specify moves as say "9b" than "[-12,17]b".

Yet another option would be to use a fixed cell labelling scheme such as the spiral honeycomb mosaic (SHM): http://ozviz.wasp.uwa.edu.au/~pbourke/texture_colour/shm/
I've devised a similar spiral labelling scheme for recent implementations of hexagonal tiling games which seems to work well, a bit like SHM but without the discontinuities:

8 9 10

7 1 2 11

18 6 0 3 12

17 5 4 13

16 15 14

The benefit is that each number refers to exactly one grid position for the entire game (and indeed for all games) rather than the move position numbers appearing to jump around each turn. I'd probably use this scheme in future.

Cameron


At 11:53 PM 9/18/2009, David J Bush wrote: 
| > Could someone please define for me the space numbering
| > scheme used in Palago here on Gamerz? Thanks.
|
| Essentially random.  The possible spaces are renumbered each turn.
|  You can't tell anything by looking at the notation.
|  It's the saem with all of Cameron's boardless games.
|  Would you like to suggest a better system?

Well I doubt Cameron made use of any random value generator in
his program. Renumbering the spaces is fine, as long as this is
done in a consistent manner, otherwise, as you point out, the
whole purpose of a notation system is defeated. Cameron's
algorithm is deterministic, but it's not easy for the user to
determine what it is. So, I would suggest a scheme which IS easy
to understand. For example, label the vacant spaces in the
leftmost column top to bottom, then the next column to the right
top to bottom, etc. until you reach the bottom space of the
rightmost column.


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