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Torus board generators - Printable Version

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Torus board generators - dale walton - 07-31-2020

Several of my games can alternatively be played on toruses.  In general, any of your defined grids can be converted to a torus, by defining a unit cell of the tessellation to be the torus (any unit cell,not just the primary unit cell) You can restrict this unit cell to a parallelogram shape without diminishing the possibilities - but if the cells of the torus are only represented once, or only repeated at the edges some games may have a different preferred shap such as a limping board.

The problem is in representation. There are 4 general methods:
1) show each cell once, do not show the edge linking connections (implicit)
2) As in 1, but add connection lines from opposite edges (messy)
3) As in 1, but repeat cells on one of each pair of opposite edges (doubled edges)
4) Continuous tessellation showing a multiple of unit cells worth of duplicated pieces, with a play region within it highlighted (and reference numbered)

Other topological boards such as mobius strips, Kline bottles, polyhedra (gridded spheres) may also be of interest. - But toruses are the most common and easiest to implement.


RE: Torus board generators - cambolbro - 07-31-2020

Hi Dale,

We will eventually support cylindrical, toroidal and projective boards (e.g. Projex).

I'm thinking that a nice way to visualise them might be something along the lines of your option 4), but with the main board shown normally and surrounded by ghosted copies drawn at each board side (and possibly corner) at say 25% opacity. 

Only half of the ghosted boards would be drawn but that should hopefully show the necessary information.

Surakarta already does something similar -- the corner sites project back to themselves in loops -- but that's a specific mechanism for this game.

Regards,
Cameron


RE: Torus board generators - dale walton - 07-31-2020

Good to hear.

I think the need depends on the game. In Throngs, quadrupling the area is OK (don't make it cross-shaped) - a little more e.g. 6x would be better so that one can easily imagine any point as the center. But for placement games or those with limited movement, option 3 can work - or even option 1.

I also found that putting the reference area in a corner allowed edge labelling of the play points. If the center region is highlighted, it should use cell labelling. With cell labelling, perhaps all cells can be redundantly labelled.