Math.Geometry.GridInternal

A module containing private Grid internals. Most developers should use Grid instead. This module is subject to change without notice.

Generic

class Eq x => Grid g s x | g -> s, g -> x where

A regular arrangement of tiles. Minimal complete definition: indices, distance, and size.

Methods

indices :: g -> [x]

Returns the indices of all tiles in a grid.

distance :: x -> x -> g -> Int

distance a b returns the minimum number of moves required to get from a to b, moving between adjacent tiles at each step. (Two tiles are adjacent if they share an edge.) If a or b are not contained within g, the result is undefined.

size :: g -> s

Returns the dimensions of the grid. For example, if g is a 4x3 rectangular grid, size g would return (4, 3), while tileCount g would return 12.

neighbours :: x -> g -> [x]

neighbours x g returns the indices of the tiles in the grid g which are adjacent to the tile at x.

inGrid :: x -> g -> Bool

x `'inGrid'` g returns true if the index x is contained within g, otherwise it returns false.

viewpoint :: x -> g -> [(x, Int)]

viewpoint x g returns a list of pairs associating the index of each tile in g with its distance to the tile with index x. If x is not contained within g, the result is undefined.

tileCount :: Grid g s x => g -> Int

Returns the number of tiles in a grid. Compare with size.

empty :: Grid g s x => g -> Bool

Returns True if the number of tiles in a grid is zero, False otherwise.

nonEmpty :: Grid g s x => g -> Bool

Returns False if the number of tiles in a grid is zero, True otherwise.

Instances

Grid HexHexGrid Int (Int, Int)

Grid TriTriGrid Int (Int, Int)

Grid ParaHexGrid (Int, Int) (Int, Int)

Grid TorSquareGrid (Int, Int) (Int, Int)

Grid RectSquareGrid (Int, Int) (Int, Int)

Grid ParaTriGrid (Int, Int) (Int, Int)

Grids with triangular tiles

data TriTriGrid

A triangular grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available from

Instances

Show TriTriGrid

Grid TriTriGrid Int (Int, Int)

triTriGrid :: Int -> TriTriGrid

triTriGrid s returns a triangular grid with sides of length s, using triangular tiles. If s is nonnegative, the resulting grid will have s^2 tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.

data ParaTriGrid

A Parallelogrammatical grid with triangular tiles.

Instances

Show ParaTriGrid

Grid ParaTriGrid (Int, Int) (Int, Int)

paraTriGrid :: Int -> Int -> ParaTriGrid

paraTriGrid r c returns a grid in the shape of a parallelogram with r rows and c columns, using triangular tiles. If r and c are both nonnegative, the resulting grid will have 2*r*c tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.

Grids with square tiles

data RectSquareGrid

A rectangular grid with square tiles.

Instances

Show RectSquareGrid

Grid RectSquareGrid (Int, Int) (Int, Int)

rectSquareGrid :: Int -> Int -> RectSquareGrid

rectSquareGrid r c produces a rectangular grid with r rows and c columns, using square tiles. If r and c are both nonnegative, the resulting grid will have r*c tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.

data TorSquareGrid

A toroidal grid with square tiles.

Instances

Show TorSquareGrid

Grid TorSquareGrid (Int, Int) (Int, Int)

torSquareGrid :: Int -> Int -> TorSquareGrid

torSquareGrid r c returns a toroidal grid with r rows and c columns, using square tiles. If r and c are both nonnegative, the resulting grid will have r*c tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.

Grids with hexagonal tiles

data HexHexGrid

A hexagonal grid with hexagonal tiles

Instances

Show HexHexGrid

Grid HexHexGrid Int (Int, Int)

hexHexGrid :: Int -> HexHexGrid

hexHexGrid s returns a grid of hexagonal shape, with -- sides of length s, using hexagonal tiles. If s is nonnegative, the resulting grid will have 3*s*(s-1) + 1 tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.

data ParaHexGrid

A parallelogramatical grid with hexagonal tiles

Instances

Show ParaHexGrid

Grid ParaHexGrid (Int, Int) (Int, Int)

paraHexGrid :: Int -> Int -> ParaHexGrid

paraHexGrid r c returns a grid in the shape of a parallelogram with r rows and c columns, using hexagonal tiles. If r and c are both nonnegative, the resulting grid will have r*c tiles. Otherwise, the resulting grid will be empty and the list of indices will be null.