Diagonal Mirroring

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**[[Home]] * [[Chess]] * [[Chess Position|Position]] * Diagonal Mirroring**

**Diagonal mirroring** mirrors all [[Pieces|pieces]] along the [[Diagonals|main diagonal]] or [[Anti-Diagonals|main anti-diagonal]]. It is applicable in pawn-less [[Endgame|endgames]] with [[Castling|castling]] no longer possible. Along with [[Horizontal Mirroring|horizontal]] and/or [[Vertical Flipping|vertical flipping]], diagonal mirroring is used in pawn-less [[Endgame Tablebases|endgame tablebases]] to restrict a white king to the 10 squares of the a1-d4-d1 triangle of the board.

=Sample Position=
||~ Original  ||~ ||~ Diagonal Mirror ||~ ||~ Anti-Diagonal ||
|| [[image:http://webchess.freehostia.com/diag/chessdiag.php?fen=k7/8/NK2B3/8/8/8/8/8%20w%20-%20-&size=small&coord=yes&cap=no&stm=yes&fb=no&theme=classic&color1=E3CEAA&color2=635147&color3=000000]] ||~ || [[image:http://webchess.freehostia.com/diag/chessdiag.php?fen=8/8/8/5B2/8/8/5K2/5N1k%20w%20-%20-&size=small&coord=yes&cap=no&stm=yes&fb=no&theme=classic&color1=E3CEAA&color2=635147&color3=000000]] ||~ || [[image:http://webchess.freehostia.com/diag/chessdiag.php?fen=k1N5/2K5/8/8/2B5/8/8/8%20w%20-%20-&size=small&coord=yes&cap=no&stm=yes&fb=no&theme=classic&color1=E3CEAA&color2=635147&color3=000000]] ||
|| k7/8/NK2B3/8/8/8/8/8 w - - ||~ || 8/8/8/5B2/8/8/5K2/5N1k w - - ||~ || k1N5/2K5/8/8/2B5/8/8/8 w - - ||

=Mirroring an 8x8 Board= 
An [[8x8 Board]] with a [[Squares|rank-file mapping]] needs to swap [[Ranks|rank]] and [[Files|file]]. A pure 8x8 Board may be mirrored along the main diagonal that way in [[C]]:
[[code format="cpp"]]
int board[64], f, r, sm, sq, s;

for (f = 1; f < 8; ++f)
for (r = 0; r < f; ++r)
{
  sq = 8*r + f;
  sm = 8*f + r;
  s = board[sq];
  board[sq] = board[sm];
  board[sm] = s;
}
[[code]]

=See also=
* [[Color Flipping]]
* [[Flipping Mirroring and Rotating|Flipping, Mirroring and Rotating]] of [[Bitboards]]
* [[Horizontal Mirroring]]
* [[Vertical Flipping]]

=External Links=
* [[http://en.wikipedia.org/wiki/Mirror|Mirror from Wikipedia]]
* [[http://en.wikipedia.org/wiki/Mirroring_%28psychology%29|Mirroring (psychology) from Wikipedia]]
* [[http://en.wikipedia.org/wiki/Reflection_%28mathematics%29|Reflection (mathematics) from Wikipedia]]
* [[http://en.wikipedia.org/wiki/Reflection_%28physics%29|Reflection (physics) from Wikipedia]]
* [[http://en.wikipedia.org/wiki/Reflection_symmetry|Reflection symmetry from Wikipedia]]

=What links here?= 
[[include page="Diagonal Mirroring" component="backlinks" limit="40" ]]
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