Math.Geometry.Grid.Square

A regular arrangement of square tiles. The userguide, with illustrations, is available at https://github.com/mhwombat/grid/wiki. Also see Math.Geometry.Grid for examples of how to use this class.

Unbounded grid with square tiles

data UnboundedSquareGrid

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

Constructors

UnboundedSquareGrid

Instances

Eq UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

(==) :: UnboundedSquareGrid -> UnboundedSquareGrid -> Bool

(/=) :: UnboundedSquareGrid -> UnboundedSquareGrid -> Bool

Show UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

showsPrec :: Int -> UnboundedSquareGrid -> ShowS

show :: UnboundedSquareGrid -> String

showList :: [UnboundedSquareGrid] -> ShowS

Generic UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Rep UnboundedSquareGrid :: Type -> Type

Methods

from :: UnboundedSquareGrid -> Rep UnboundedSquareGrid x

to :: Rep UnboundedSquareGrid x -> UnboundedSquareGrid

Grid UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Index UnboundedSquareGrid :: Type

type Direction UnboundedSquareGrid :: Type

Methods

indices :: UnboundedSquareGrid -> [Index UnboundedSquareGrid]

distance :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> Int

minDistance :: UnboundedSquareGrid -> [Index UnboundedSquareGrid] -> Index UnboundedSquareGrid -> Int

neighbours :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> [Index UnboundedSquareGrid]

neighboursOfSet :: UnboundedSquareGrid -> [Index UnboundedSquareGrid] -> [Index UnboundedSquareGrid]

neighbour :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Direction UnboundedSquareGrid -> Maybe (Index UnboundedSquareGrid)

numNeighbours :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Int

contains :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Bool

tileCount :: UnboundedSquareGrid -> Int

null :: UnboundedSquareGrid -> Bool

nonNull :: UnboundedSquareGrid -> Bool

edges :: UnboundedSquareGrid -> [(Index UnboundedSquareGrid, Index UnboundedSquareGrid)]

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

isAdjacent :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> Bool

adjacentTilesToward :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> [Index UnboundedSquareGrid]

minimalPaths :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> [[Index UnboundedSquareGrid]]

directionTo :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> [Direction UnboundedSquareGrid]

defaultMinDistance :: UnboundedSquareGrid -> [Index UnboundedSquareGrid] -> Index UnboundedSquareGrid -> Int

defaultNeighbours :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> [Index UnboundedSquareGrid]

defaultNeighboursOfSet :: UnboundedSquareGrid -> [Index UnboundedSquareGrid] -> [Index UnboundedSquareGrid]

defaultNeighbour :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Direction UnboundedSquareGrid -> Maybe (Index UnboundedSquareGrid)

defaultTileCount :: UnboundedSquareGrid -> Int

defaultEdges :: UnboundedSquareGrid -> [(Index UnboundedSquareGrid, Index UnboundedSquareGrid)]

defaultIsAdjacent :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> Bool

defaultAdjacentTilesToward :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> [Index UnboundedSquareGrid]

defaultMinimalPaths :: UnboundedSquareGrid -> Index UnboundedSquareGrid -> Index UnboundedSquareGrid -> [[Index UnboundedSquareGrid]]

type Rep UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Rep UnboundedSquareGrid = D1 (MetaData "UnboundedSquareGrid" "Math.Geometry.Grid.SquareInternal" "grid-7.8.12-1ADrZUlWO0vHdPyzqP6MYM" False) (C1 (MetaCons "UnboundedSquareGrid" PrefixI False) (U1 :: Type -> Type))

type Index UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Index UnboundedSquareGrid = (Int, Int)

type Direction UnboundedSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Direction UnboundedSquareGrid = SquareDirection

Rectangular grid with square tiles

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

Defined in Math.Geometry.Grid.SquareInternal

Methods

(==) :: RectSquareGrid -> RectSquareGrid -> Bool

(/=) :: RectSquareGrid -> RectSquareGrid -> Bool

Show RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

showsPrec :: Int -> RectSquareGrid -> ShowS

show :: RectSquareGrid -> String

showList :: [RectSquareGrid] -> ShowS

Generic RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Rep RectSquareGrid :: Type -> Type

Methods

from :: RectSquareGrid -> Rep RectSquareGrid x

to :: Rep RectSquareGrid x -> RectSquareGrid

BoundedGrid RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

tileSideCount :: RectSquareGrid -> Int

boundary :: RectSquareGrid -> [Index RectSquareGrid]

isBoundary :: RectSquareGrid -> Index RectSquareGrid -> Bool

centre :: RectSquareGrid -> [Index RectSquareGrid]

isCentre :: RectSquareGrid -> Index RectSquareGrid -> Bool

defaultBoundary :: RectSquareGrid -> [Index RectSquareGrid]

defaultIsBoundary :: RectSquareGrid -> Index RectSquareGrid -> Bool

defaultCentre :: RectSquareGrid -> [Index RectSquareGrid]

defaultIsCentre :: RectSquareGrid -> Index RectSquareGrid -> Bool

FiniteGrid RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Size RectSquareGrid :: Type

Methods

size :: RectSquareGrid -> Size RectSquareGrid

maxPossibleDistance :: RectSquareGrid -> Int

Grid RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Index RectSquareGrid :: Type

type Direction RectSquareGrid :: Type

Methods

indices :: RectSquareGrid -> [Index RectSquareGrid]

distance :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> Int

minDistance :: RectSquareGrid -> [Index RectSquareGrid] -> Index RectSquareGrid -> Int

neighbours :: RectSquareGrid -> Index RectSquareGrid -> [Index RectSquareGrid]

neighboursOfSet :: RectSquareGrid -> [Index RectSquareGrid] -> [Index RectSquareGrid]

neighbour :: RectSquareGrid -> Index RectSquareGrid -> Direction RectSquareGrid -> Maybe (Index RectSquareGrid)

numNeighbours :: RectSquareGrid -> Index RectSquareGrid -> Int

contains :: RectSquareGrid -> Index RectSquareGrid -> Bool

tileCount :: RectSquareGrid -> Int

null :: RectSquareGrid -> Bool

nonNull :: RectSquareGrid -> Bool

edges :: RectSquareGrid -> [(Index RectSquareGrid, Index RectSquareGrid)]

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

isAdjacent :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> Bool

adjacentTilesToward :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> [Index RectSquareGrid]

minimalPaths :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> [[Index RectSquareGrid]]

directionTo :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> [Direction RectSquareGrid]

defaultMinDistance :: RectSquareGrid -> [Index RectSquareGrid] -> Index RectSquareGrid -> Int

defaultNeighbours :: RectSquareGrid -> Index RectSquareGrid -> [Index RectSquareGrid]

defaultNeighboursOfSet :: RectSquareGrid -> [Index RectSquareGrid] -> [Index RectSquareGrid]

defaultNeighbour :: RectSquareGrid -> Index RectSquareGrid -> Direction RectSquareGrid -> Maybe (Index RectSquareGrid)

defaultTileCount :: RectSquareGrid -> Int

defaultEdges :: RectSquareGrid -> [(Index RectSquareGrid, Index RectSquareGrid)]

defaultIsAdjacent :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> Bool

defaultAdjacentTilesToward :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> [Index RectSquareGrid]

defaultMinimalPaths :: RectSquareGrid -> Index RectSquareGrid -> Index RectSquareGrid -> [[Index RectSquareGrid]]

type Rep RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Rep RectSquareGrid = D1 (MetaData "RectSquareGrid" "Math.Geometry.Grid.SquareInternal" "grid-7.8.12-1ADrZUlWO0vHdPyzqP6MYM" False) (C1 (MetaCons "RectSquareGrid" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Int, Int)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [(Int, Int)])))

type Size RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Size RectSquareGrid = (Int, Int)

type Index RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Index RectSquareGrid = (Int, Int)

type Direction RectSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Direction RectSquareGrid = SquareDirection

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.

Toroidal grid with square tiles

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

Defined in Math.Geometry.Grid.SquareInternal

Methods

(==) :: TorSquareGrid -> TorSquareGrid -> Bool

(/=) :: TorSquareGrid -> TorSquareGrid -> Bool

Show TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

showsPrec :: Int -> TorSquareGrid -> ShowS

show :: TorSquareGrid -> String

showList :: [TorSquareGrid] -> ShowS

Generic TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Rep TorSquareGrid :: Type -> Type

Methods

from :: TorSquareGrid -> Rep TorSquareGrid x

to :: Rep TorSquareGrid x -> TorSquareGrid

WrappedGrid TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Methods

normalise :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid

denormalise :: TorSquareGrid -> Index TorSquareGrid -> [Index TorSquareGrid]

FiniteGrid TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Size TorSquareGrid :: Type

Methods

size :: TorSquareGrid -> Size TorSquareGrid

maxPossibleDistance :: TorSquareGrid -> Int

Grid TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

Associated Types

type Index TorSquareGrid :: Type

type Direction TorSquareGrid :: Type

Methods

indices :: TorSquareGrid -> [Index TorSquareGrid]

distance :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> Int

minDistance :: TorSquareGrid -> [Index TorSquareGrid] -> Index TorSquareGrid -> Int

neighbours :: TorSquareGrid -> Index TorSquareGrid -> [Index TorSquareGrid]

neighboursOfSet :: TorSquareGrid -> [Index TorSquareGrid] -> [Index TorSquareGrid]

neighbour :: TorSquareGrid -> Index TorSquareGrid -> Direction TorSquareGrid -> Maybe (Index TorSquareGrid)

numNeighbours :: TorSquareGrid -> Index TorSquareGrid -> Int

contains :: TorSquareGrid -> Index TorSquareGrid -> Bool

tileCount :: TorSquareGrid -> Int

null :: TorSquareGrid -> Bool

nonNull :: TorSquareGrid -> Bool

edges :: TorSquareGrid -> [(Index TorSquareGrid, Index TorSquareGrid)]

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

isAdjacent :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> Bool

adjacentTilesToward :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> [Index TorSquareGrid]

minimalPaths :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> [[Index TorSquareGrid]]

directionTo :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> [Direction TorSquareGrid]

defaultMinDistance :: TorSquareGrid -> [Index TorSquareGrid] -> Index TorSquareGrid -> Int

defaultNeighbours :: TorSquareGrid -> Index TorSquareGrid -> [Index TorSquareGrid]

defaultNeighboursOfSet :: TorSquareGrid -> [Index TorSquareGrid] -> [Index TorSquareGrid]

defaultNeighbour :: TorSquareGrid -> Index TorSquareGrid -> Direction TorSquareGrid -> Maybe (Index TorSquareGrid)

defaultTileCount :: TorSquareGrid -> Int

defaultEdges :: TorSquareGrid -> [(Index TorSquareGrid, Index TorSquareGrid)]

defaultIsAdjacent :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> Bool

defaultAdjacentTilesToward :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> [Index TorSquareGrid]

defaultMinimalPaths :: TorSquareGrid -> Index TorSquareGrid -> Index TorSquareGrid -> [[Index TorSquareGrid]]

type Rep TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Rep TorSquareGrid = D1 (MetaData "TorSquareGrid" "Math.Geometry.Grid.SquareInternal" "grid-7.8.12-1ADrZUlWO0vHdPyzqP6MYM" False) (C1 (MetaCons "TorSquareGrid" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Int, Int)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [(Int, Int)])))

type Size TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Size TorSquareGrid = (Int, Int)

type Index TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Index TorSquareGrid = (Int, Int)

type Direction TorSquareGrid

Defined in Math.Geometry.Grid.SquareInternal

type Direction TorSquareGrid = SquareDirection

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.