Copyright	(c) Amy de Buitléir 2012-2019
License	BSD-style
Maintainer	amy@nualeargais.ie
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Geometry.Grid.Octagonal

Contents

Unbounded grid with octagonal tiles
Rectangular grid with octagonal tiles
Toroidal grid with octagonal tiles

Description

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.

Synopsis

data UnboundedOctGrid = UnboundedOctGrid
data RectOctGrid
rectOctGrid :: Int -> Int -> RectOctGrid
data TorOctGrid
torOctGrid :: Int -> Int -> TorOctGrid

Unbounded grid with octagonal tiles

data UnboundedOctGrid Source #

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

Instances details

Eq UnboundedOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods (==) :: UnboundedOctGrid -> UnboundedOctGrid -> Bool # (/=) :: UnboundedOctGrid -> UnboundedOctGrid -> Bool #
Show UnboundedOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods showsPrec :: Int -> UnboundedOctGrid -> ShowS # show :: UnboundedOctGrid -> String # showList :: [UnboundedOctGrid] -> ShowS #
Generic UnboundedOctGrid Source #
Instance details 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 Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Associated Types type Index UnboundedOctGrid Source # type Direction UnboundedOctGrid Source # Methods indices :: UnboundedOctGrid -> [Index UnboundedOctGrid] Source # distance :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Int Source # minDistance :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> Index UnboundedOctGrid -> Int Source # neighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid] Source # neighboursOfSet :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> [Index UnboundedOctGrid] Source # neighbour :: UnboundedOctGrid -> Index UnboundedOctGrid -> Direction UnboundedOctGrid -> Maybe (Index UnboundedOctGrid) Source # numNeighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> Int Source # contains :: UnboundedOctGrid -> Index UnboundedOctGrid -> Bool Source # tileCount :: UnboundedOctGrid -> Int Source # null :: UnboundedOctGrid -> Bool Source # nonNull :: UnboundedOctGrid -> Bool Source # edges :: UnboundedOctGrid -> [(Index UnboundedOctGrid, Index UnboundedOctGrid)] Source # viewpoint :: UnboundedOctGrid -> Index UnboundedOctGrid -> [(Index UnboundedOctGrid, Int)] Source # isAdjacent :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Bool Source # adjacentTilesToward :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid] Source # minimalPaths :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [[Index UnboundedOctGrid]] Source # directionTo :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [Direction UnboundedOctGrid] Source # defaultMinDistance :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> Index UnboundedOctGrid -> Int Source # defaultNeighbours :: UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid] Source # defaultNeighboursOfSet :: UnboundedOctGrid -> [Index UnboundedOctGrid] -> [Index UnboundedOctGrid] Source # defaultNeighbour :: UnboundedOctGrid -> Index UnboundedOctGrid -> Direction UnboundedOctGrid -> Maybe (Index UnboundedOctGrid) Source # defaultTileCount :: UnboundedOctGrid -> Int Source # defaultEdges :: UnboundedOctGrid -> [(Index UnboundedOctGrid, Index UnboundedOctGrid)] Source # defaultIsAdjacent :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> Bool Source # defaultAdjacentTilesToward :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [Index UnboundedOctGrid] Source # defaultMinimalPaths :: UnboundedOctGrid -> Index UnboundedOctGrid -> Index UnboundedOctGrid -> [[Index UnboundedOctGrid]] Source #
type Rep UnboundedOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Rep UnboundedOctGrid = D1 ('MetaData "UnboundedOctGrid" "Math.Geometry.Grid.OctagonalInternal" "grid-7.8.15-inplace" 'False) (C1 ('MetaCons "UnboundedOctGrid" 'PrefixI 'False) (U1 :: Type -> Type))
type Index UnboundedOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Index UnboundedOctGrid = (Int, Int)
type Direction UnboundedOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Direction UnboundedOctGrid = OctDirection

Rectangular grid with octagonal tiles

data RectOctGrid Source #

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

Instances details

Eq RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods (==) :: RectOctGrid -> RectOctGrid -> Bool # (/=) :: RectOctGrid -> RectOctGrid -> Bool #
Show RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods showsPrec :: Int -> RectOctGrid -> ShowS # show :: RectOctGrid -> String # showList :: [RectOctGrid] -> ShowS #
Generic RectOctGrid Source #
Instance details 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 Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods tileSideCount :: RectOctGrid -> Int Source # boundary :: RectOctGrid -> [Index RectOctGrid] Source # isBoundary :: RectOctGrid -> Index RectOctGrid -> Bool Source # centre :: RectOctGrid -> [Index RectOctGrid] Source # isCentre :: RectOctGrid -> Index RectOctGrid -> Bool Source # defaultBoundary :: RectOctGrid -> [Index RectOctGrid] Source # defaultIsBoundary :: RectOctGrid -> Index RectOctGrid -> Bool Source # defaultCentre :: RectOctGrid -> [Index RectOctGrid] Source # defaultIsCentre :: RectOctGrid -> Index RectOctGrid -> Bool Source #
FiniteGrid RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Associated Types type Size RectOctGrid Source # Methods size :: RectOctGrid -> Size RectOctGrid Source # maxPossibleDistance :: RectOctGrid -> Int Source #
Grid RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Associated Types type Index RectOctGrid Source # type Direction RectOctGrid Source # Methods indices :: RectOctGrid -> [Index RectOctGrid] Source # distance :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Int Source # minDistance :: RectOctGrid -> [Index RectOctGrid] -> Index RectOctGrid -> Int Source # neighbours :: RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid] Source # neighboursOfSet :: RectOctGrid -> [Index RectOctGrid] -> [Index RectOctGrid] Source # neighbour :: RectOctGrid -> Index RectOctGrid -> Direction RectOctGrid -> Maybe (Index RectOctGrid) Source # numNeighbours :: RectOctGrid -> Index RectOctGrid -> Int Source # contains :: RectOctGrid -> Index RectOctGrid -> Bool Source # tileCount :: RectOctGrid -> Int Source # null :: RectOctGrid -> Bool Source # nonNull :: RectOctGrid -> Bool Source # edges :: RectOctGrid -> [(Index RectOctGrid, Index RectOctGrid)] Source # viewpoint :: RectOctGrid -> Index RectOctGrid -> [(Index RectOctGrid, Int)] Source # isAdjacent :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Bool Source # adjacentTilesToward :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid] Source # minimalPaths :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [[Index RectOctGrid]] Source # directionTo :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [Direction RectOctGrid] Source # defaultMinDistance :: RectOctGrid -> [Index RectOctGrid] -> Index RectOctGrid -> Int Source # defaultNeighbours :: RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid] Source # defaultNeighboursOfSet :: RectOctGrid -> [Index RectOctGrid] -> [Index RectOctGrid] Source # defaultNeighbour :: RectOctGrid -> Index RectOctGrid -> Direction RectOctGrid -> Maybe (Index RectOctGrid) Source # defaultTileCount :: RectOctGrid -> Int Source # defaultEdges :: RectOctGrid -> [(Index RectOctGrid, Index RectOctGrid)] Source # defaultIsAdjacent :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> Bool Source # defaultAdjacentTilesToward :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [Index RectOctGrid] Source # defaultMinimalPaths :: RectOctGrid -> Index RectOctGrid -> Index RectOctGrid -> [[Index RectOctGrid]] Source #
type Rep RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Rep RectOctGrid = D1 ('MetaData "RectOctGrid" "Math.Geometry.Grid.OctagonalInternal" "grid-7.8.15-inplace" '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 Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Size RectOctGrid = (Int, Int)
type Index RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Index RectOctGrid = (Int, Int)
type Direction RectOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Direction RectOctGrid = OctDirection

rectOctGrid :: Int -> Int -> RectOctGrid Source #

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 Source #

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

Instances details

Eq TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods (==) :: TorOctGrid -> TorOctGrid -> Bool # (/=) :: TorOctGrid -> TorOctGrid -> Bool #
Show TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods showsPrec :: Int -> TorOctGrid -> ShowS # show :: TorOctGrid -> String # showList :: [TorOctGrid] -> ShowS #
Generic TorOctGrid Source #
Instance details 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 Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Methods normalise :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid Source # denormalise :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid] Source #
FiniteGrid TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Associated Types type Size TorOctGrid Source # Methods size :: TorOctGrid -> Size TorOctGrid Source # maxPossibleDistance :: TorOctGrid -> Int Source #
Grid TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal Associated Types type Index TorOctGrid Source # type Direction TorOctGrid Source # Methods indices :: TorOctGrid -> [Index TorOctGrid] Source # distance :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Int Source # minDistance :: TorOctGrid -> [Index TorOctGrid] -> Index TorOctGrid -> Int Source # neighbours :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid] Source # neighboursOfSet :: TorOctGrid -> [Index TorOctGrid] -> [Index TorOctGrid] Source # neighbour :: TorOctGrid -> Index TorOctGrid -> Direction TorOctGrid -> Maybe (Index TorOctGrid) Source # numNeighbours :: TorOctGrid -> Index TorOctGrid -> Int Source # contains :: TorOctGrid -> Index TorOctGrid -> Bool Source # tileCount :: TorOctGrid -> Int Source # null :: TorOctGrid -> Bool Source # nonNull :: TorOctGrid -> Bool Source # edges :: TorOctGrid -> [(Index TorOctGrid, Index TorOctGrid)] Source # viewpoint :: TorOctGrid -> Index TorOctGrid -> [(Index TorOctGrid, Int)] Source # isAdjacent :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Bool Source # adjacentTilesToward :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid] Source # minimalPaths :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [[Index TorOctGrid]] Source # directionTo :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [Direction TorOctGrid] Source # defaultMinDistance :: TorOctGrid -> [Index TorOctGrid] -> Index TorOctGrid -> Int Source # defaultNeighbours :: TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid] Source # defaultNeighboursOfSet :: TorOctGrid -> [Index TorOctGrid] -> [Index TorOctGrid] Source # defaultNeighbour :: TorOctGrid -> Index TorOctGrid -> Direction TorOctGrid -> Maybe (Index TorOctGrid) Source # defaultTileCount :: TorOctGrid -> Int Source # defaultEdges :: TorOctGrid -> [(Index TorOctGrid, Index TorOctGrid)] Source # defaultIsAdjacent :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> Bool Source # defaultAdjacentTilesToward :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [Index TorOctGrid] Source # defaultMinimalPaths :: TorOctGrid -> Index TorOctGrid -> Index TorOctGrid -> [[Index TorOctGrid]] Source #
type Rep TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Rep TorOctGrid = D1 ('MetaData "TorOctGrid" "Math.Geometry.Grid.OctagonalInternal" "grid-7.8.15-inplace" '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 Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Size TorOctGrid = (Int, Int)
type Index TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Index TorOctGrid = (Int, Int)
type Direction TorOctGrid Source #
Instance details Defined in Math.Geometry.Grid.OctagonalInternal type Direction TorOctGrid = OctDirection

torOctGrid :: Int -> Int -> TorOctGrid Source #

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.