A Polyomino is a puzzle piece composed of a number equally sized grid-squares. Depending on the number of squares they can go by different names.
We represent polyominos as a Set of points with an x and y coordinate.
Typically puzzles and games involving polyominos have physical puzzle pieces that can be flipped over and rotated. The pieces can also be placed down on the puzzle board at different locations.
This means that to decide whether two sets of points represent the same Polyomino puzzle piece, we need to consider them equivalent under these transformations:
An unplaced polyomino puzzle piece. It is characterized by a normalized PointSet, making it invariant to any combination 90 degree rotation, mirroring, and translation.
val name : t -> charGets the 'name' of a polyomino. The name is unique for polyomino of a the same order (i.e. if two polyominos have the same order and the same name, it means they are the same polyomino)
Compares two polymoninos to see if they represent the same shape; invariant to rotation, mirroring and translation
val order : t -> intThe number of squares in a polyomino is called its 'order'.
val points : t -> PointSet.tGets the canonical PointSet that characterizes this Polyomino
val variants : t -> PointSet.t List.tGets all variants of a given Polyomino. A variant is simlar shape obtained by applying rotation and mirroring transformations (but no translation). I.e. it is a specific orientation of Polyomino that has not yet been placed on a specific location of the board.
val to_string : t -> stringCreate a 'string-image' of the polyomino
val of_order : int -> t listObtain all unique polymino of order n
val pp_poly : Format.formatter -> t -> unitPrint string image of polyomino to a formatter