In a 8X8 chessboard, I was wondering how to implement the symmetry of the board.
A lot of positions are just mirrors or rotations of one another (with no pawns or castling capabilities left the directions are indistinguishable).
By using a combination of vertical, horizontal and diagonal mirrorings of the board it is always possible to fix the position of a piece within the a1-d1-d4 triangle.
How to implement these symmetries on chess board?
How does implementation depends on choice of board representation chosen(Bit-boards, 0x88, 8×8 array, and so on) ?
Edit 1: The main goal is the implementation of the endgame engine generator and compress its results
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There are several ways to tackle rotation of a chess board. The easiest way to implement it is the same way we think about it. You create a grid of 8×8, and each position on the grid may or may not have a chess piece on top. To mirror that grid, you simply create another chess board, and place each piece in the old chess board in its mirrored location.
This, however, can be simplified by removing the grid altogether. The grid is arbitrary and serves primarily for us to understand better. So you could use a chess board object to emulate all positions on the chess board, but the only information it would actually require are the types and positions of the chess pieces themselves.
The chess piece itself can be abstracted away into type and position information. If you do not need to know how it moves, then the only reason the type would be useful is for you to compare with other chess pieces and ensure that other than position, types are the same in order to say that it is the same.
The chess board can mirror itself simply by returning another chess board instance with the positions altered (i.e. for each chess piece’s x coordinate, piece.x = 9 – piece.x).
At that point, the problem simply becomes iterating the chess pieces of one chess board and another and verifying that all the positions and types are the same (you can optimize by checking the number of pieces first).
Note that if you don’t require comparing mirrored versions of chessboards, you can optimize further by using only one instance and computing where a chess piece, if it were mirrored, would be relative to that current spot and then check for the existence and type of that piece.
Hope that helps. I think it’s important to present an interface that is easy for you to understand and let the underlying implementation optimize how data is represented and/or utilized.