Portability | portable |
---|---|

Stability | experimental |

Maintainer | amy@nualeargais.ie |

Safe Haskell | Safe-Inferred |

A module containing private `Grid`

internals. Most developers should
use `Grid`

instead. This module is subject to change without notice.

- class Grid g where
- type Index g
- type Direction g
- indices :: g -> [Index g]
- distance :: g -> Index g -> Index g -> Int
- minDistance :: g -> [Index g] -> Index g -> Int
- neighbours :: Eq (Index g) => g -> Index g -> [Index g]
- neighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
- neighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)
- numNeighbours :: Eq (Index g) => g -> Index g -> Int
- contains :: Eq (Index g) => g -> Index g -> Bool
- tileCount :: g -> Int
- null :: g -> Bool
- nonNull :: g -> Bool
- edges :: Eq (Index g) => g -> [(Index g, Index g)]
- viewpoint :: g -> Index g -> [(Index g, Int)]
- isAdjacent :: g -> Index g -> Index g -> Bool
- adjacentTilesToward :: Eq (Index g) => g -> Index g -> Index g -> [Index g]
- minimalPaths :: Eq (Index g) => g -> Index g -> Index g -> [[Index g]]
- directionTo :: g -> Index g -> Index g -> [Direction g]
- defaultMinDistance :: g -> [Index g] -> Index g -> Int
- defaultNeighbours :: g -> Index g -> [Index g]
- defaultNeighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
- defaultNeighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)
- defaultTileCount :: g -> Int
- defaultEdges :: Eq (Index g) => g -> [(Index g, Index g)]
- defaultIsAdjacent :: g -> Index g -> Index g -> Bool
- defaultAdjacentTilesToward :: Eq (Index g) => g -> Index g -> Index g -> [Index g]
- defaultMinimalPaths :: Eq (Index g) => g -> Index g -> Index g -> [[Index g]]

- class Grid g => FiniteGrid g where
- type Size s
- size :: g -> Size g
- maxPossibleDistance :: g -> Int

- class Grid g => BoundedGrid g where
- tileSideCount :: g -> Int
- boundary :: Eq (Index g) => g -> [Index g]
- isBoundary :: Eq (Index g) => g -> Index g -> Bool
- centre :: Eq (Index g) => g -> [Index g]
- isCentre :: Eq (Index g) => g -> Index g -> Bool
- defaultBoundary :: Eq (Index g) => g -> [Index g]
- defaultIsBoundary :: Eq (Index g) => g -> Index g -> Bool
- defaultCentre :: Eq (Index g) => g -> [Index g]
- defaultIsCentre :: Eq (Index g) => g -> Index g -> Bool

- class Grid g => WrappedGrid g where
- neighboursBasedOn :: (Eq (Index u), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]
- distanceBasedOn :: (Eq (Index g), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> Int
- directionToBasedOn :: (Eq (Index g), Eq (Direction g), Grid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Index g -> [Direction g]
- neighboursWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]
- neighbourWrappedBasedOn :: (Eq (Index g), Eq (Direction g), WrappedGrid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Direction g -> Maybe (Index g)
- distanceWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> Int
- directionToWrappedBasedOn :: (Eq (Index g), Eq (Direction g), WrappedGrid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Index g -> [Direction g]
- sameEdge :: Eq t => (t, t) -> (t, t) -> Bool
- adjacentEdges :: (Grid g, Eq (Index g)) => Index g -> g -> [(Index g, Index g)]
- cartesianIndices :: (Enum r, Enum c, Num r, Num c, Ord r, Ord c) => (r, c) -> [(c, r)]
- cartesianCentre :: (Int, Int) -> [(Int, Int)]
- cartesianMidpoints :: Int -> [Int]

# Documentation

A regular arrangement of tiles.
Minimal complete definition:

, `Index`

, `Direction`

,
`indices`

, `distance`

.
`directionTo`

indices :: g -> [Index g]Source

Returns the indices of all tiles in a grid.

distance :: g -> Index g -> Index g -> IntSource

returns the minimum number of moves required
to get from the tile at index `distance`

g a b`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 -> IntSource

returns the minimum number of moves
required to get from any of the tiles at indices `minDistance`

g bs a`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 :: Eq (Index g) => g -> Index g -> [Index g]Source

returns the indices of the tiles in the grid
`neighbours`

g a`g`

which are adjacent to the tile with index `a`

.

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

returns the indices of the tiles in the
grid `neighboursOfSet`

g as`g`

which are adjacent to any of the tiles with index in
`as`

.

neighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)Source

returns the indices of the tile in the grid
`neighbour`

g d a`g`

which is adjacent to the tile with index `a`

, in the
direction `d`

.

numNeighbours :: Eq (Index g) => g -> Index g -> IntSource

returns the number of tiles in the grid
`numNeighbours`

g a`g`

which are adjacent to the tile with index `a`

.

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

`g `'contains'` a`

returns `True`

if the index `a`

is contained
within the grid `g`

, otherwise it returns false.

Returns the number of tiles in a grid. Compare with

.
`size`

Returns `True`

if the number of tiles in a grid is zero, `False`

otherwise.

Returns `False`

if the number of tiles in a grid is zero, `True`

otherwise.

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

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

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

returns a list of pairs associating the index
of each tile in `viewpoint`

g a`g`

with its distance to the tile with index `a`

.
If `a`

is not contained within `g`

, the result is undefined.

isAdjacent :: g -> Index g -> Index g -> BoolSource

returns `isAdjacent`

g a b`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 :: Eq (Index g) => g -> Index g -> Index g -> [Index g]Source

returns the indices of all tiles
which are neighbours of the tile at index `adjacentTilesToward`

g a b`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]]Source

returns a list of all minimal paths from
the tile at index `minimalPaths`

g a b`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

. If you want to use a custom algorithm,
consider modifying `adjacentTilesToward`

instead of
`adjacentTilesToward`

.
`minimalPaths`

directionTo :: g -> Index g -> Index g -> [Direction g]Source

returns the direction(s) of the next
tile(s) in a `directionTo`

g a b*minimal* path from the tile at index `a`

to the
tile at index `b`

in grid `g`

.

defaultMinDistance :: g -> [Index g] -> Index g -> IntSource

defaultNeighbours :: g -> Index g -> [Index g]Source

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

defaultNeighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)Source

defaultTileCount :: g -> IntSource

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

defaultIsAdjacent :: g -> Index g -> Index g -> BoolSource

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

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

class Grid g => FiniteGrid g whereSource

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

, `size`

.
`maxPossibleDistance`

Returns the dimensions of the grid.
For example, if `g`

is a 4x3 rectangular grid,

would
return `size`

g`(4, 3)`

, while

would return `tileCount`

g`12`

.

maxPossibleDistance :: g -> IntSource

Returns the largest possible distance between two tiles in the grid.

class Grid g => BoundedGrid g whereSource

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

.
`tileSideCount`

tileSideCount :: g -> IntSource

Returns the number of sides a tile has

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

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

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

' returns `isBoundary`

g a`True`

if the tile with index `a`

is
on a boundary of `g`

, `False`

otherwise. (Corner tiles are also
boundary tiles.)

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

' returns `isCentre`

g a`True`

if the tile with index `a`

is
a centre tile of `g`

, `False`

otherwise.

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

defaultIsBoundary :: Eq (Index g) => g -> Index g -> BoolSource

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

defaultIsCentre :: Eq (Index g) => g -> Index g -> BoolSource

class Grid g => WrappedGrid g whereSource

A regular arrangement of tiles where the boundaries are joined.
Minimal complete definition:

and `normalise`

.
`denormalise`

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

returns the normal indices for `normalise`

g a`a`

.
TODO: need a clearer description and an illustration.

denormalise :: g -> Index g -> [Index g]Source

returns all of the indices in `denormalise`

g a`a`

's
translation group. In other words, it returns `a`

plus the
indices obtained by translating `a`

in each direction by the
extent of the grid along that direction.
TODO: need a clearer description and an illustration.

neighboursBasedOn :: (Eq (Index u), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]Source

distanceBasedOn :: (Eq (Index g), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> IntSource

directionToBasedOn :: (Eq (Index g), Eq (Direction g), Grid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Index g -> [Direction g]Source

neighboursWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]Source

neighbourWrappedBasedOn :: (Eq (Index g), Eq (Direction g), WrappedGrid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Direction g -> Maybe (Index g)Source

distanceWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> IntSource

directionToWrappedBasedOn :: (Eq (Index g), Eq (Direction g), WrappedGrid g, Grid u, Index g ~ Index u, Direction g ~ Direction u) => u -> g -> Index g -> Index g -> [Direction g]Source

cartesianMidpoints :: Int -> [Int]Source