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Created page with "'''Home * Chess * Position * Vertical Flipping''' FILE:FrontAerial.gif|border|right|thumb|Acrobatic Flip <ref>A [https://en.wikipedia.o..."
'''[[Main Page|Home]] * [[Chess]] * [[Chess Position|Position]] * Vertical Flipping'''
[[FILE:FrontAerial.gif|border|right|thumb|Acrobatic Flip <ref>A [https://en.wikipedia.org/wiki/Front_aerial front aerial] performed as part of an [https://en.wikipedia.org/wiki/Acro_dance acro dance] routine, image by [https://en.wikipedia.org/wiki/User:Lambtron User: Lambtron], April 29, 2008, [https://en.wikipedia.org/wiki/Flip_%28acrobatic%29 Flip (acrobatic) from Wikipedia]</ref>]]
'''Vertical Flipping''' mirrors all [[Pieces|pieces]] along the horizontal axis between the 4th and 5th [[Ranks|rank]]. Opposed to [[Color Flipping|color flipping]] it does not swap the piece colors and [[Side to move|side to move]], and therefor with respect to the [[Pawn Spans|front span]] of [[Pawn|pawns]], is only applicable in pawn-less [[Endgame|endgames]] with [[Castling|castling]] no longer possible, and results in an equivalent position with identical [[Evaluation|evaluation]] and same number of attacks and moves. Along with [[Horizontal Mirroring|horizontal]] and/or [[Diagonal Mirroring|diagonal mirroring]], vertical flipping 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
! Vertical Flip
! Color Flip
|-
| <fentt border="double" style="font-size:24pt">k7/8/NK2B3/8/8/8/8/8</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/NK2B3/8/k7</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/nk2b3/8/K7</fentt>
|-
| k7/8/NK2B3/8/8/8/8/8 w - -
| 8/8/8/8/8/NK2B3/8/k7 w - -
| 8/8/8/8/8/nk2b3/8/K7 b - -
|}
=Flipping an 8x8 Board=
An [[8x8 Board]] with a [[Squares|rank-file mapping]], needs to perform an [[General Setwise Operations#ExclusiveOr|exclusive or]] with 56 (A8 in [[Square Mapping Considerations#LittleEndianRankFileMapping|LERF]]) to vertically flip square coordinates. A pure 8x8 Board may be vertically flipped that way in [[C]]:
<pre>
int board[64], sq, s, f;
for (sq = 0; sq < 32; ++sq) {
s = board[sq];
board[sq] = board[sq^56];
board[sq^56] = s;
}
</pre>
=See also=
* [[Color Flipping]]
* [[Diagonal Mirroring]]
* [[Flipping Mirroring and Rotating|Flipping, Mirroring and Rotating]] of [[Bitboards]]
* [[Horizontal Mirroring]]
=External Links=
* [http://en.wiktionary.org/wiki/flip flip - Wiktionary]
: [http://en.wiktionary.org/wiki/ausflippen ausflippen - Wiktionary]
* [https://en.wikipedia.org/wiki/Flip Flip from Wikipedia]
* [https://en.wikipedia.org/wiki/Flip_%28mathematics%29 Flip (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_%28mathematics%29 Reflection (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_%28physics%29 Reflection (physics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_symmetry Reflection symmetry from Wikipedia]
=References=
<references />
'''[[Chess Position|Up one Level]]'''
[[FILE:FrontAerial.gif|border|right|thumb|Acrobatic Flip <ref>A [https://en.wikipedia.org/wiki/Front_aerial front aerial] performed as part of an [https://en.wikipedia.org/wiki/Acro_dance acro dance] routine, image by [https://en.wikipedia.org/wiki/User:Lambtron User: Lambtron], April 29, 2008, [https://en.wikipedia.org/wiki/Flip_%28acrobatic%29 Flip (acrobatic) from Wikipedia]</ref>]]
'''Vertical Flipping''' mirrors all [[Pieces|pieces]] along the horizontal axis between the 4th and 5th [[Ranks|rank]]. Opposed to [[Color Flipping|color flipping]] it does not swap the piece colors and [[Side to move|side to move]], and therefor with respect to the [[Pawn Spans|front span]] of [[Pawn|pawns]], is only applicable in pawn-less [[Endgame|endgames]] with [[Castling|castling]] no longer possible, and results in an equivalent position with identical [[Evaluation|evaluation]] and same number of attacks and moves. Along with [[Horizontal Mirroring|horizontal]] and/or [[Diagonal Mirroring|diagonal mirroring]], vertical flipping 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
! Vertical Flip
! Color Flip
|-
| <fentt border="double" style="font-size:24pt">k7/8/NK2B3/8/8/8/8/8</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/NK2B3/8/k7</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/nk2b3/8/K7</fentt>
|-
| k7/8/NK2B3/8/8/8/8/8 w - -
| 8/8/8/8/8/NK2B3/8/k7 w - -
| 8/8/8/8/8/nk2b3/8/K7 b - -
|}
=Flipping an 8x8 Board=
An [[8x8 Board]] with a [[Squares|rank-file mapping]], needs to perform an [[General Setwise Operations#ExclusiveOr|exclusive or]] with 56 (A8 in [[Square Mapping Considerations#LittleEndianRankFileMapping|LERF]]) to vertically flip square coordinates. A pure 8x8 Board may be vertically flipped that way in [[C]]:
<pre>
int board[64], sq, s, f;
for (sq = 0; sq < 32; ++sq) {
s = board[sq];
board[sq] = board[sq^56];
board[sq^56] = s;
}
</pre>
=See also=
* [[Color Flipping]]
* [[Diagonal Mirroring]]
* [[Flipping Mirroring and Rotating|Flipping, Mirroring and Rotating]] of [[Bitboards]]
* [[Horizontal Mirroring]]
=External Links=
* [http://en.wiktionary.org/wiki/flip flip - Wiktionary]
: [http://en.wiktionary.org/wiki/ausflippen ausflippen - Wiktionary]
* [https://en.wikipedia.org/wiki/Flip Flip from Wikipedia]
* [https://en.wikipedia.org/wiki/Flip_%28mathematics%29 Flip (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_%28mathematics%29 Reflection (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_%28physics%29 Reflection (physics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Reflection_symmetry Reflection symmetry from Wikipedia]
=References=
<references />
'''[[Chess Position|Up one Level]]'''
