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 Grid g where

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

Associated Types

type Index g

Methods

indices :: g -> [Index g]

Returns the indices of all tiles in a grid.

distance :: g -> Index g -> Index g -> Int

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 -> [Index g] -> Index g -> Int

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.

neighbours :: g -> Index g -> [Index g]

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

numNeighbours :: g -> Index g -> Int

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

contains :: Eq (Index g) => g -> Index g -> Bool

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

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

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 -> Int

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

null :: g -> Bool

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

nonNull :: g -> Bool

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

edges :: Eq (Index g) => g -> [(Index g, Index g)]

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

isAdjacent :: Eq (Index g) => g -> Index g -> Index g -> Bool

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 -> Index g -> Index g -> [Index g]

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 :: Eq (Index g) => g -> Index g -> Index g -> [[Index g]]

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

Grid ParaHexGrid

Grid HexHexGrid

Grid UnboundedHexGrid

Grid TorSquareGrid

Grid RectSquareGrid

Grid UnboundedSquareGrid

Grid TorTriGrid

Grid RectTriGrid

Grid ParaTriGrid

Grid TriTriGrid

Grid UnboundedTriGrid

Grid g => Grid (LGridMap g v)

class Grid g => FiniteGrid g where

A regular arrangement of tiles where the number of tiles is finite. Minimal complete definition: size.

Associated Types

type Size s

Methods

size :: g -> Size g

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.

Instances

FiniteGrid ParaHexGrid

FiniteGrid HexHexGrid

FiniteGrid TorSquareGrid

FiniteGrid RectSquareGrid

FiniteGrid TorTriGrid

FiniteGrid RectTriGrid

FiniteGrid ParaTriGrid

FiniteGrid TriTriGrid

FiniteGrid g => FiniteGrid (LGridMap g v)

class Grid g => BoundedGrid g where

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

Methods

tileSideCount :: g -> Int

Returns the number of sides a tile has

boundary :: g -> [Index g]

Returns a the indices of all the tiles at the boundary of a grid.

isBoundary :: Eq (Index g) => g -> Index g -> Bool

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 -> [Index g]

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 :: Eq (Index g) => g -> Index g -> Bool

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

Instances

BoundedGrid ParaHexGrid

BoundedGrid HexHexGrid

BoundedGrid RectSquareGrid

BoundedGrid RectTriGrid

BoundedGrid ParaTriGrid

BoundedGrid TriTriGrid

class Grid g => WrappedGrid g where

Methods

normalise :: g -> Index g -> Index g

Instances

WrappedGrid TorSquareGrid

WrappedGrid TorTriGrid

Grids with triangular tiles

data UnboundedTriGrid

Instances

Show UnboundedTriGrid

Grid UnboundedTriGrid

data TriTriGrid

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

Eq TriTriGrid

Show TriTriGrid

BoundedGrid TriTriGrid

FiniteGrid TriTriGrid

Grid TriTriGrid

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 null and the list of indices will be null.

data ParaTriGrid

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

Eq ParaTriGrid

Show ParaTriGrid

BoundedGrid ParaTriGrid

FiniteGrid ParaTriGrid

Grid ParaTriGrid

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 null and the list of indices will be null.

data RectTriGrid

A rectangular 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

Eq RectTriGrid

Show RectTriGrid

BoundedGrid RectTriGrid

FiniteGrid RectTriGrid

Grid RectTriGrid

rectTriGrid :: Int -> Int -> RectTriGrid

rectTriGrid r c returns a grid in the shape of a rectangle (with jagged edges) that has 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 null and the list of indices will be null.

data TorTriGrid

A toroidal 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

Eq TorTriGrid

Show TorTriGrid

WrappedGrid TorTriGrid

FiniteGrid TorTriGrid

Grid TorTriGrid

torTriGrid :: Int -> Int -> TorTriGrid

torTriGrid r c returns a toroidal grid with r rows and c columns, using triangular tiles. If r is odd, the result is undefined because the grid edges would overlap. If r and c are both nonnegative, the resulting grid will have 2*r*c tiles. Otherwise, the resulting grid will be null and the list of indices will be null.

Grids with square tiles

data UnboundedSquareGrid

Instances

Show UnboundedSquareGrid

Grid UnboundedSquareGrid

data RectSquareGrid

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

Eq RectSquareGrid

Show RectSquareGrid

BoundedGrid RectSquareGrid

FiniteGrid RectSquareGrid

Grid RectSquareGrid

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 null and the list of indices will be null.

data TorSquareGrid

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

Eq TorSquareGrid

Show TorSquareGrid

WrappedGrid TorSquareGrid

FiniteGrid TorSquareGrid

Grid TorSquareGrid

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 null and the list of indices will be null.

Grids with hexagonal tiles

data UnboundedHexGrid

Instances

Show UnboundedHexGrid

Grid UnboundedHexGrid

data HexHexGrid

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

Eq HexHexGrid

Show HexHexGrid

BoundedGrid HexHexGrid

FiniteGrid HexHexGrid

Grid HexHexGrid

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 null and the list of indices will be null.

data ParaHexGrid

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

Eq ParaHexGrid

Show ParaHexGrid

BoundedGrid ParaHexGrid

FiniteGrid ParaHexGrid

Grid ParaHexGrid

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 null and the list of indices will be null.