Copyright	(c) Amy de Buitléir 2012-2015
License	BSD-style
Maintainer	amy@nualeargais.ie
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Math.Geometry.GridInternal

Description

A module containing private Grid internals. Most developers should use Grid instead. This module is subject to change without notice.

Synopsis

Documentation

class Grid g where Source

A regular arrangement of tiles. Minimal complete definition: Index, Direction, indices, distance, directionTo.

Minimal complete definition

indices, distance, directionTo

Associated Types

type Index g Source

type Direction g Source

Methods

indices :: g -> [Index g] Source

Returns the indices of all tiles in a grid.

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

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 Source

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

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

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

neighboursOfSet g as returns the indices of the tiles in the grid 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

neighbour g d a returns the indices of the tile in the grid g which is adjacent to the tile with index a, in the direction d.

numNeighbours :: Eq (Index g) => g -> Index g -> Int Source

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

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

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

tileCount :: g -> Int Source

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

null :: g -> Bool Source

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

nonNull :: g -> Bool Source

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

viewpoint g a returns a list of pairs associating the index of each tile in 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 -> Bool Source

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

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]] Source

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.

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

directionTo g a b returns the direction(s) of the next tile(s) in a minimal path from the tile at index a to the tile at index b in grid g.

defaultMinDistance :: g -> [Index g] -> Index g -> Int Source

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 -> Int Source

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

defaultIsAdjacent :: g -> Index g -> Index g -> Bool Source

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 where Source

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

Associated Types

type Size g Source

Methods

size :: g -> Size g Source

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.

maxPossibleDistance :: g -> Int Source

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

class Grid g => BoundedGrid g where Source

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

Minimal complete definition

tileSideCount

Methods

tileSideCount :: g -> Int Source

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 -> Bool Source

isBoundary g a' returns 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 -> Bool Source

isCentre g a' returns 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 -> Bool Source

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

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

class Grid g => WrappedGrid g where Source

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

Methods

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

normalise g a returns the "normal" indices for a. TODO: need a clearer description and an illustration.

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

denormalise g a returns all of the indices in 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.

Instances

WrappedGrid XCylTriGrid Source
WrappedGrid YCylTriGrid Source
WrappedGrid TorTriGrid Source
WrappedGrid TorSquareGrid Source
WrappedGrid TorOctGrid Source

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 -> Int Source

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 -> Int Source

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

sameEdge :: Eq t => (t, t) -> (t, t) -> Bool Source

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

cartesianIndices :: (Enum r, Enum c, Num r, Num c, Ord r, Ord c) => (r, c) -> [(c, r)] Source

cartesianCentre :: (Int, Int) -> [(Int, Int)] Source

cartesianMidpoints :: Int -> [Int] Source

Grid XCylTriGrid Source
Grid YCylTriGrid Source
Grid TorTriGrid Source
Grid RectTriGrid Source
Grid ParaTriGrid Source
Grid TriTriGrid Source
Grid UnboundedTriGrid Source
Grid TorSquareGrid Source
Grid RectSquareGrid Source
Grid UnboundedSquareGrid Source
Grid ParaHexGrid Source
Grid HexHexGrid Source
Grid UnboundedHexGrid Source
Grid RectHexGrid Source
Grid HexHexGrid Source
Grid UnboundedHexGrid Source
Grid TorOctGrid Source
Grid RectOctGrid Source
Grid UnboundedOctGrid Source
Grid g => Grid (LGridMap g v) Source

FiniteGrid XCylTriGrid Source
FiniteGrid YCylTriGrid Source
FiniteGrid TorTriGrid Source
FiniteGrid RectTriGrid Source
FiniteGrid ParaTriGrid Source
FiniteGrid TriTriGrid Source
FiniteGrid TorSquareGrid Source
FiniteGrid RectSquareGrid Source
FiniteGrid ParaHexGrid Source
FiniteGrid HexHexGrid Source
FiniteGrid RectHexGrid Source
FiniteGrid HexHexGrid Source
FiniteGrid TorOctGrid Source
FiniteGrid RectOctGrid Source
FiniteGrid g => FiniteGrid (LGridMap g v) Source

BoundedGrid RectTriGrid Source
BoundedGrid ParaTriGrid Source
BoundedGrid TriTriGrid Source
BoundedGrid RectSquareGrid Source
BoundedGrid ParaHexGrid Source
BoundedGrid HexHexGrid Source
BoundedGrid RectHexGrid Source
BoundedGrid HexHexGrid Source
BoundedGrid RectOctGrid Source