Math.Geometry.Grid.Octagonal

A regular arrangement of octagonal tiles. Octagons won't tile a regular plane (there will be diamond-shaped gaps between the tiles), but they will tile a hyperbolic plane. (Alternatively, you can think of these as squares on a board game where diagonal moves are allowed.) 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 octagonal tiles

data UnboundedOctGrid

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

Constructors

UnboundedOctGrid

Instances

Eq UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

(==) :: UnboundedOctGrid -> UnboundedOctGrid -> Bool

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

Show UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

showsPrec :: Int -> UnboundedOctGrid -> ShowS

show :: UnboundedOctGrid -> String

showList :: [UnboundedOctGrid] -> ShowS

Generic UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Rep UnboundedOctGrid :: Type -> Type

Methods

from :: UnboundedOctGrid -> Rep UnboundedOctGrid x

to :: Rep UnboundedOctGrid x -> UnboundedOctGrid

Grid UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Index UnboundedOctGrid :: Type

type Direction UnboundedOctGrid :: Type

Methods

indices :: UnboundedOctGrid -> [Index UnboundedOctGrid]

distance :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Int

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

neighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid]

neighboursOfSet :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> [Index UnboundedOctGrid]

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

numNeighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> Int

contains :: UnboundedOctGrid -> Index UnboundedOctGrid -> Bool

tileCount :: UnboundedOctGrid -> Int

null :: UnboundedOctGrid -> Bool

nonNull :: UnboundedOctGrid -> Bool

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

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

isAdjacent :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Bool

adjacentTilesToward :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid]

minimalPaths :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [[Index UnboundedOctGrid]]

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

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

defaultNeighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid]

defaultNeighboursOfSet :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> [Index UnboundedOctGrid]

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

defaultTileCount :: UnboundedOctGrid -> Int

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

defaultIsAdjacent :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Bool

defaultAdjacentTilesToward :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid]

defaultMinimalPaths :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [[Index UnboundedOctGrid]]

type Rep UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

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

type Index UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Index UnboundedOctGrid = (Int, Int)

type Direction UnboundedOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Direction UnboundedOctGrid = OctDirection

Rectangular grid with octagonal tiles

data RectOctGrid

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

Instances

Eq RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

(==) :: RectOctGrid -> RectOctGrid -> Bool

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

Show RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

showsPrec :: Int -> RectOctGrid -> ShowS

show :: RectOctGrid -> String

showList :: [RectOctGrid] -> ShowS

Generic RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Rep RectOctGrid :: Type -> Type

Methods

from :: RectOctGrid -> Rep RectOctGrid x

to :: Rep RectOctGrid x -> RectOctGrid

BoundedGrid RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

tileSideCount :: RectOctGrid -> Int

boundary :: RectOctGrid -> [Index RectOctGrid]

isBoundary :: RectOctGrid -> Index RectOctGrid -> Bool

centre :: RectOctGrid -> [Index RectOctGrid]

isCentre :: RectOctGrid -> Index RectOctGrid -> Bool

defaultBoundary :: RectOctGrid -> [Index RectOctGrid]

defaultIsBoundary :: RectOctGrid -> Index RectOctGrid -> Bool

defaultCentre :: RectOctGrid -> [Index RectOctGrid]

defaultIsCentre :: RectOctGrid -> Index RectOctGrid -> Bool

FiniteGrid RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Size RectOctGrid :: Type

Methods

size :: RectOctGrid -> Size RectOctGrid

maxPossibleDistance :: RectOctGrid -> Int

Grid RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Index RectOctGrid :: Type

type Direction RectOctGrid :: Type

Methods

indices :: RectOctGrid -> [Index RectOctGrid]

distance :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Int

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

neighbours :: RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid]

neighboursOfSet :: RectOctGrid -> [Index RectOctGrid] -> [Index RectOctGrid]

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

numNeighbours :: RectOctGrid -> Index RectOctGrid -> Int

contains :: RectOctGrid -> Index RectOctGrid -> Bool

tileCount :: RectOctGrid -> Int

null :: RectOctGrid -> Bool

nonNull :: RectOctGrid -> Bool

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

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

isAdjacent :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Bool

adjacentTilesToward :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid]

minimalPaths :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [[Index RectOctGrid]]

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

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

defaultNeighbours :: RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid]

defaultNeighboursOfSet :: RectOctGrid -> [Index RectOctGrid] -> [Index RectOctGrid]

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

defaultTileCount :: RectOctGrid -> Int

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

defaultIsAdjacent :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Bool

defaultAdjacentTilesToward :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid]

defaultMinimalPaths :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [[Index RectOctGrid]]

type Rep RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Rep RectOctGrid = D1 (MetaData "RectOctGrid" "Math.Geometry.Grid.OctagonalInternal" "grid-7.8.12-1ADrZUlWO0vHdPyzqP6MYM" False) (C1 (MetaCons "RectOctGrid" 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 RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Size RectOctGrid = (Int, Int)

type Index RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Index RectOctGrid = (Int, Int)

type Direction RectOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Direction RectOctGrid = OctDirection

rectOctGrid :: Int -> Int -> RectOctGrid

rectOctGrid r c produces a rectangular grid with r rows and c columns, using octagonal 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 octagonal tiles

data TorOctGrid

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

Instances

Eq TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

(==) :: TorOctGrid -> TorOctGrid -> Bool

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

Show TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

showsPrec :: Int -> TorOctGrid -> ShowS

show :: TorOctGrid -> String

showList :: [TorOctGrid] -> ShowS

Generic TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Rep TorOctGrid :: Type -> Type

Methods

from :: TorOctGrid -> Rep TorOctGrid x

to :: Rep TorOctGrid x -> TorOctGrid

WrappedGrid TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Methods

normalise :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid

denormalise :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid]

FiniteGrid TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Size TorOctGrid :: Type

Methods

size :: TorOctGrid -> Size TorOctGrid

maxPossibleDistance :: TorOctGrid -> Int

Grid TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

Associated Types

type Index TorOctGrid :: Type

type Direction TorOctGrid :: Type

Methods

indices :: TorOctGrid -> [Index TorOctGrid]

distance :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Int

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

neighbours :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid]

neighboursOfSet :: TorOctGrid -> [Index TorOctGrid] -> [Index TorOctGrid]

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

numNeighbours :: TorOctGrid -> Index TorOctGrid -> Int

contains :: TorOctGrid -> Index TorOctGrid -> Bool

tileCount :: TorOctGrid -> Int

null :: TorOctGrid -> Bool

nonNull :: TorOctGrid -> Bool

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

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

isAdjacent :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Bool

adjacentTilesToward :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid]

minimalPaths :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [[Index TorOctGrid]]

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

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

defaultNeighbours :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid]

defaultNeighboursOfSet :: TorOctGrid -> [Index TorOctGrid] -> [Index TorOctGrid]

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

defaultTileCount :: TorOctGrid -> Int

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

defaultIsAdjacent :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Bool

defaultAdjacentTilesToward :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid]

defaultMinimalPaths :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [[Index TorOctGrid]]

type Rep TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Rep TorOctGrid = D1 (MetaData "TorOctGrid" "Math.Geometry.Grid.OctagonalInternal" "grid-7.8.12-1ADrZUlWO0vHdPyzqP6MYM" False) (C1 (MetaCons "TorOctGrid" 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 TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Size TorOctGrid = (Int, Int)

type Index TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Index TorOctGrid = (Int, Int)

type Direction TorOctGrid

Defined in Math.Geometry.Grid.OctagonalInternal

type Direction TorOctGrid = OctDirection

torOctGrid :: Int -> Int -> TorOctGrid

torOctGrid r c returns a toroidal grid with r rows and c columns, using octagonal 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.