rotate90

rotate90 is a transform filter corresponding to the following 4 basic transforms.

• id, the identity
• rotate₉₀: counterclockwise rotation about the board center by 90°
• rotate₁₈₀: rotation by 180° about the board center
• rotate₂₇₀: clockwise rotation about the board center by 90°

rotate90 is normally called with a single argument filter, F:

      rotate90 F

rotate90 also accepts an optional count parameter. rotate90 F matches the current position if any transformation of F by one of the 4 basic transforms above matches the current position. These 4 transforms are examples of dihedral transforms.

For example, suppose F is the filter {Ka1 kh8}, matching a position in which the white king is on a1 and the black king is on h8. If we transform this filter by rotate₉₀ we get the new filter {Kh1 ka8}. That is, if spin the chessboard 90° counterclockwise about the center of the board, the a1 square will wind up on h1 and the h8 square will wind up on a8. The filters that results from transforming {Ka1 kh8} by all the elements of rotate90, which is to say the identity and the three rotations, are:

  {Ka1 kh8}      
  {Kh1 ka8}    
  {Ka8 kh1}      
  {Kh8 ka1}

The filter rotate90 {Ka1 kh8} will thus match a position if any of these 4 filters match the position, that is, if the white and black king are on opposite corners. (This can also be done, more efficiently, via k==diagonal 7 K[a1,h1] )

If F is a set filter then so is

rotate90 F

in which case its value is the union of the values of each of the sets represented by each transformed version of F.

For example,

rotate90 a1 is the set [a1,h1,a8,h8].

If F is a numeric filter then so is rotate90 F in which case its value is the maximum of the values of the 4 rotations of F which match the position.

rotate90 count F

is a numeric filter whose value is the number of distinct matching transformed versions of F. For example, if the current position is the initial position, then

rotate90 count find {Qa1 qh8}

is equal to 0 if neither {Qa1 qh8} nor {Qh1 qa8} occur in the game; is equal to 1 if exactly one of these configurations does; and is equal to 2 if both of them do.

The rotate90 filter also modifies directions parameters and filters. Thus,

rotate90 ray right (R K)

will match if and only if

ray orthogonal (R K)

matches.