grid-3.1: Tools for working with regular grids (graphs, lattices).

Portabilityportable
Stabilityexperimental
Maintaineramy@nualeargais.ie
Safe HaskellNone

Math.Geometry.GridInternal

Contents

Description

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

Synopsis

Generic

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

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

Methods

indices :: g -> [x]Source

Returns the indices of all tiles in a grid.

distance :: g -> x -> x -> IntSource

distance g a b returns the minimum number of moves required to get from the tile at index a to the tile at index b in grid g, 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.

minDistance :: g -> [x] -> x -> IntSource

minDistance g bs a returns the minimum number of moves required to get from any of the tiles at indices bs to the tile at index a in grid g, moving between adjacent tiles at each step. (Two tiles are adjacent if they share an edge.) If a or any of bs are not contained within g, the result is undefined.

size :: g -> sSource

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 :: g -> x -> [x]Source

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

numNeighbours :: g -> x -> IntSource

numNeighbours g x returns the number of tiles in the grid g which are adjacent to the tile with index x.

contains :: g -> x -> BoolSource

g `'contains'` x returns True if the index x is contained within the grid g, otherwise it returns false.

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

viewpoint g x 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 :: g -> IntSource

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

empty :: g -> BoolSource

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

nonEmpty :: g -> BoolSource

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

edges :: g -> [(x, x)]Source

A list of all edges in a grid, where the edges are represented by a pair of indices of adjacent tiles.

isAdjacent :: Grid g s x => g -> x -> x -> BoolSource

isAdjacent g a b returns True if the tile at index a is adjacent to the tile at index b in g. (Two tiles are adjacent if they share an edge.) If a or b are not contained within g, the result is undefined.

adjacentTilesToward :: g -> x -> x -> [x]Source

adjacentTilesToward g a b returns the indices of all tiles which are neighbours of the tile at index a, and which are closer to the tile at b than a is. In other words, it returns the possible next steps on a minimal path from a to b. If a or b are not contained within g, or if there is no path from a to b (e.g., a disconnected grid), the result is undefined.

minimalPaths :: g -> x -> x -> [[x]]Source

minimalPaths g a b returns a list of all minimal paths from the tile at index a to the tile at index b in grid g. A path is a sequence of tiles where each tile in the sequence is adjacent to the previous one. (Two tiles are adjacent if they share an edge.) If a or b are not contained within g, the result is undefined.

Tip: The default implementation of this function calls adjacentTilesToward. If you want to use a custom algorithm, consider modifying adjacentTilesToward instead of minimalPaths.

Instances

class Grid g s x => BoundedGrid g s x whereSource

A regular arrangement of tiles with an edge. Minimal complete definition: boundary.

Methods

boundary :: g -> [x]Source

Returns a the indices of all the tiles at the boundary of a grid, including corner tiles.

isBoundary :: g -> x -> BoolSource

isBoundary g x' returns True if the tile with index x is on a boundary of g, False otherwise. (Corner tiles are also boundary tiles.)

centre :: g -> [x]Source

Returns the index of the tile(s) that require the maximum number of moves to reach the nearest boundary tile. A grid may have more than one central tile (e.g., a rectangular grid with an even number of rows and columns will have four central tiles).

isCentre :: g -> x -> BoolSource

isCentre g x' returns True if the tile with index x is a centre tile of g, False otherwise.

Instances

Grids with triangular tiles

data TriTriGrid Source

A triangular grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

triTriGrid :: Int -> TriTriGridSource

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 Source

A Parallelogrammatical grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

paraTriGrid :: Int -> Int -> ParaTriGridSource

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 Source

A rectangular grid with square tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

rectSquareGrid :: Int -> Int -> RectSquareGridSource

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 Source

A toroidal grid with square tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

torSquareGrid :: Int -> Int -> TorSquareGridSource

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 Source

A hexagonal grid with hexagonal tiles The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

hexHexGrid :: Int -> HexHexGridSource

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 Source

A parallelogramatical grid with hexagonal tiles The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.

Instances

paraHexGrid :: Int -> Int -> ParaHexGridSource

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.