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'''[[Main Page|Home]] * [[Chess]] * [[Chess Position|Position]] * Horizontal Mirroring'''
[[FILE:cheating-cheat-chess-mirror-best-demotivational-posters.jpg|border|right|thumb|link=http://bestdemotivationalposters.com/delusion/|Mirroring <ref>[http://bestdemotivationalposters.com/tag/chess/ Chess Demotivational Posters & Images]</ref>]]
'''Horizontal Mirroring''' mirrors all [[Pieces|pieces]] along the vertical axis between the D- and E-[[Files|File]]. Applicable if both sides have lost their [[Castling rights|castling rights]], horizontal mirroring should result in equal static [[Evaluation|evaluation]] [[Score|score]], but not necessarily equal [[Search|search]] result if [[Pieces|pieces]] and [[Squares|squares]] are traversed in different order. Along with [[Vertical Flipping|vertical flipping]] and/or [[Diagonal Mirroring|diagonal mirroring]], horizontal 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=
==Horizontal Mirroring==
{|
|-
! Original
! Horizontal Mirroring
|-
| <fentt border="double" style="font-size:24pt">k7/8/NK2B3/8/8/8/8/8</fentt>
| <fentt border="double" style="font-size:24pt">7k/8/3B2KN/8/8/8/8/8</fentt>
|-
| k7/8/NK2B3/8/8/8/8/8 w - -
| 7k/8/3B2KN/8/8/8/8/8 w - -
|}
==Flipping & Rotation==
[[Vertical Flipping|Vertical flipping]] and horizontal mirroring (or vice versa) results in [https://en.wikipedia.org/wiki/Rotation_%28mathematics%29 rotation] by 180 degrees.
{|
|-
! Vertical Flipping
! 180° Rotation
|-
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/NK2B3/8/k7</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/3B2KN/8/7k</fentt>
|-
| 8/8/8/8/8/NK2B3/8/k7 w - -
| 8/8/8/8/8/3B2KN/8/7k w - -
|}
=Mirroring an 8x8 Board=
An [[8x8 Board]] with a [[Squares|rank-file mapping]] needs to perform an [[General Setwise Operations#ExclusiveOr|exclusive or]] with 7 (h1 in [[Square Mapping Considerations#LittleEndianRankFileMapping|LERF]]) to horizontally mirror square coordinates. A pure 8x8 Board may be mirrored that way in [[C]]:
<pre>
int board[64], sq, s;
for (sq = 0; sq < 64; sq += ++sq & 4) {
s = board[sq];
board[sq] = board[sq^7];
board[sq^7] = s;
}
</pre>
=See also=
* [[Color Flipping]]
* [[Diagonal Mirroring]]
* [[Flipping Mirroring and Rotating|Flipping, Mirroring and Rotating]] of [[Bitboards]]
* [[Vertical Flipping]]
=External Links=
* [https://en.wikipedia.org/wiki/Mirror Mirror from Wikipedia]
* [https://en.wikipedia.org/wiki/Mirroring_%28psychology%29 Mirroring (psychology) 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]
* [https://en.wikipedia.org/wiki/Venus_effect Venus effect from Wikipedia]
* [http://math.ucr.edu/home/baez/physics/General/mirrors.html Why do Mirrors Reverse Left and Right?]
=References=
<references />
'''[[Chess Position|Up one Level]]'''
[[FILE:cheating-cheat-chess-mirror-best-demotivational-posters.jpg|border|right|thumb|link=http://bestdemotivationalposters.com/delusion/|Mirroring <ref>[http://bestdemotivationalposters.com/tag/chess/ Chess Demotivational Posters & Images]</ref>]]
'''Horizontal Mirroring''' mirrors all [[Pieces|pieces]] along the vertical axis between the D- and E-[[Files|File]]. Applicable if both sides have lost their [[Castling rights|castling rights]], horizontal mirroring should result in equal static [[Evaluation|evaluation]] [[Score|score]], but not necessarily equal [[Search|search]] result if [[Pieces|pieces]] and [[Squares|squares]] are traversed in different order. Along with [[Vertical Flipping|vertical flipping]] and/or [[Diagonal Mirroring|diagonal mirroring]], horizontal 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=
==Horizontal Mirroring==
{|
|-
! Original
! Horizontal Mirroring
|-
| <fentt border="double" style="font-size:24pt">k7/8/NK2B3/8/8/8/8/8</fentt>
| <fentt border="double" style="font-size:24pt">7k/8/3B2KN/8/8/8/8/8</fentt>
|-
| k7/8/NK2B3/8/8/8/8/8 w - -
| 7k/8/3B2KN/8/8/8/8/8 w - -
|}
==Flipping & Rotation==
[[Vertical Flipping|Vertical flipping]] and horizontal mirroring (or vice versa) results in [https://en.wikipedia.org/wiki/Rotation_%28mathematics%29 rotation] by 180 degrees.
{|
|-
! Vertical Flipping
! 180° Rotation
|-
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/NK2B3/8/k7</fentt>
| <fentt border="double" style="font-size:24pt">8/8/8/8/8/3B2KN/8/7k</fentt>
|-
| 8/8/8/8/8/NK2B3/8/k7 w - -
| 8/8/8/8/8/3B2KN/8/7k w - -
|}
=Mirroring an 8x8 Board=
An [[8x8 Board]] with a [[Squares|rank-file mapping]] needs to perform an [[General Setwise Operations#ExclusiveOr|exclusive or]] with 7 (h1 in [[Square Mapping Considerations#LittleEndianRankFileMapping|LERF]]) to horizontally mirror square coordinates. A pure 8x8 Board may be mirrored that way in [[C]]:
<pre>
int board[64], sq, s;
for (sq = 0; sq < 64; sq += ++sq & 4) {
s = board[sq];
board[sq] = board[sq^7];
board[sq^7] = s;
}
</pre>
=See also=
* [[Color Flipping]]
* [[Diagonal Mirroring]]
* [[Flipping Mirroring and Rotating|Flipping, Mirroring and Rotating]] of [[Bitboards]]
* [[Vertical Flipping]]
=External Links=
* [https://en.wikipedia.org/wiki/Mirror Mirror from Wikipedia]
* [https://en.wikipedia.org/wiki/Mirroring_%28psychology%29 Mirroring (psychology) 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]
* [https://en.wikipedia.org/wiki/Venus_effect Venus effect from Wikipedia]
* [http://math.ucr.edu/home/baez/physics/General/mirrors.html Why do Mirrors Reverse Left and Right?]
=References=
<references />
'''[[Chess Position|Up one Level]]'''
