Difference between revisions of "Diagonal Mirroring"
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'''[[Main Page|Home]] * [[Chess]] * [[Chess Position|Position]] * Diagonal Mirroring''' | '''[[Main Page|Home]] * [[Chess]] * [[Chess Position|Position]] * Diagonal Mirroring''' | ||
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| + | [[FILE:Hilma af Klint - Group IX SUW, The Swan No. 7 (13945).jpg|border|right|thumb| [[:Category:Hilma af Klint|Hilma af Klint]] - Group IX SUW, The Swan No. 7 | ||
| + | <ref>[[:Category:Hilma af Klint|Hilma af Klint]] - [https://commons.wikimedia.org/wiki/File:Hilma_af_Klint_-_Group_IX_SUW,_The_Swan_No._7_(13945).jpg Group IX SUW, The Swan No. 7], 1915, [https://en.wikipedia.org/wiki/Wikimedia_Commons Wikimedia Commons]</ref> ]] | ||
'''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. | '''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. | ||
Revision as of 16:23, 6 March 2020
Home * Chess * Position * Diagonal Mirroring
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Diagonal mirroring mirrors all pieces along the main diagonal or main anti-diagonal. It is applicable in pawn-less endgames with castling no longer possible. Along with horizontal and/or vertical flipping, diagonal mirroring is used in pawn-less 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 Mirror | |||
|---|---|---|---|---|---|
|
|
| |||
| 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 rank-file mapping needs to swap rank and file. A pure 8x8 Board may be mirrored along the main diagonal that way in C:
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;
}
See also
External Links
- Mirror from Wikipedia
- Mirroring (psychology) from Wikipedia
- Reflection (mathematics) from Wikipedia
- Reflection (physics) from Wikipedia
- Reflection symmetry from Wikipedia
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