Portability | portable |
---|---|
Stability | experimental |
Maintainer | amy@nualeargais.ie |
Safe Haskell | Safe-Inferred |
A regular arrangement of tiles. Grids have a variety of uses, including games and self-organising maps. The userguide is available at https://github.com/mhwombat/grid/wiki.
In this package, tiles are called "triangular", "square", etc., based on the number of neighbours they have. For example, a square tile has four neighbours, and a hexagonal tile has six. There are only three regular polygons that can tile a plane: triangles, squares, and hexagons. Of course, other plane tilings are possible if you use irregular polygons, or curved shapes, or if you combine tiles of different shapes.
When you tile other surfaces, things get very interesting. Octagons will tile a hyperbolic plane. (Alternatively, you can think of these as squares on a board game where diagonal moves are allowed.)
For a board game, you probably want to choose the grid type based on the number of directions a player can move, rather than the number of sides the tile will have when you display it. For example, for a game that uses square tiles and allows the user to move diagonally as well as horizontally and vertically, consider using one of the grids with octagonal tiles to model the board. You can still display the tiles as squares, but for internal calculations they are octagons.
NOTE: Version 4.0 uses associated (type) synonyms instead of multi-parameter type classes.
NOTE: Version 3.0 changed the order of parameters for many functions. This makes it easier for the user to write mapping and folding operations.
- class Grid g where
- type Index g
- indices :: g -> [Index g]
- distance :: g -> Index g -> Index g -> Int
- minDistance :: g -> [Index g] -> Index g -> Int
- neighbours :: g -> Index g -> [Index g]
- numNeighbours :: g -> Index g -> Int
- contains :: Eq (Index g) => g -> Index g -> Bool
- viewpoint :: g -> Index g -> [(Index g, Int)]
- tileCount :: g -> Int
- null :: g -> Bool
- nonNull :: g -> Bool
- edges :: Eq (Index g) => g -> [(Index g, Index g)]
- isAdjacent :: Eq (Index g) => g -> Index g -> Index g -> Bool
- adjacentTilesToward :: g -> Index g -> Index g -> [Index g]
- minimalPaths :: Eq (Index g) => g -> Index g -> Index g -> [[Index g]]
- class Grid g => FiniteGrid g where
- class Grid g => BoundedGrid g where
- data UnboundedTriGrid
- data TriTriGrid
- triTriGrid :: Int -> TriTriGrid
- data ParaTriGrid
- paraTriGrid :: Int -> Int -> ParaTriGrid
- data RectTriGrid
- rectTriGrid :: Int -> Int -> RectTriGrid
- data TorTriGrid
- torTriGrid :: Int -> Int -> TorTriGrid
- data UnboundedSquareGrid
- data RectSquareGrid
- rectSquareGrid :: Int -> Int -> RectSquareGrid
- data TorSquareGrid
- torSquareGrid :: Int -> Int -> TorSquareGrid
- data UnboundedHexGrid
- data HexHexGrid
- hexHexGrid :: Int -> HexHexGrid
- data ParaHexGrid
- paraHexGrid :: Int -> Int -> ParaHexGrid
- data UnboundedOctGrid
- data RectOctGrid
- rectOctGrid :: Int -> Int -> RectOctGrid
- data TorOctGrid
- torOctGrid :: Int -> Int -> TorOctGrid
Example
Create a grid.
ghci> let g = hexHexGrid 3 ghci> indices g [(-2,0),(-2,1),(-2,2),(-1,-1),(-1,0),(-1,1),(-1,2),(0,-2),(0,-1),(0,0),(0,1),(0,2),(1,-2),(1,-1),(1,0),(1,1),(2,-2),(2,-1),(2,0)]
Find out if the specified index is contained within the grid.
ghci> g `contains` (0,-2) True ghci> g `contains` (99,99) False
Find out the minimum number of moves to go from one tile in a grid to another tile, moving between adjacent tiles at each step.
ghci> distance g (0,-2) (0,2) 4
Find out the minimum number of moves to go from one tile in a grid to any other tile, moving between adjacent tiles at each step.
ghci> viewpoint g (1,-2) [((-2,0),3),((-2,1),3),((-2,2),4),((-1,-1),2),((-1,0),2),((-1,1),3),((-1,2),4),((0,-2),1),((0,-1),1),((0,0),2),((0,1),3),((0,2),4),((1,-2),0),((1,-1),1),((1,0),2),((1,1),3),((2,-2),1),((2,-1),2),((2,0),3)]
Find out which tiles are adjacent to a particular tile.
ghci> neighbours g (-1,1) [(-2,1),(-2,2),(-1,2),(0,1),(0,0),(-1,0)]
Find how many tiles are adjacent to a particular tile. (Note that the result is consistent with the result from the previous step.)
ghci> numNeighbours g (-1,1) 6
Find out if an index is valid for the grid.
ghci> g `contains` (0,0) True ghci> g `contains` (0,12) False
Find out the physical dimensions of the grid.
ghci> size g 3
Get the list of boundary tiles for a grid.
ghci> boundary g [(-2,2),(-1,2),(0,2),(1,1),(2,0),(2,-1),(2,-2),(1,-2),(0,-2),(-1,-1),(-2,0),(-2,1)]
Find out the number of tiles in the grid.
ghci> tileCount g 19
Check if a grid is null (contains no tiles).
ghci> null g False ghci> nonNull g True
Find the central tile(s) (the tile(s) furthest from the boundary).
ghci> centre g [(0,0)]
Find all of the minimal paths between two points.
ghci> let g = hexHexGrid 3 ghci> minimalPaths g (0,0) (2,-1) [[(0,0),(1,0),(2,-1)],[(0,0),(1,-1),(2,-1)]]
Find all of the pairs of tiles that are adjacent.
ghci> edges g [((-2,0),(-2,1)),((-2,0),(-1,0)),((-2,0),(-1,-1)),((-2,1),(-2,2)),((-2,1),(-1,1)),((-2,1),(-1,0)),((-2,2),(-1,2)),((-2,2),(-1,1)),((-1,-1),(-1,0)),((-1,-1),(0,-1)),((-1,-1),(0,-2)),((-1,0),(-1,1)),((-1,0),(0,0)),((-1,0),(0,-1)),((-1,1),(-1,2)),((-1,1),(0,1)),((-1,1),(0,0)),((-1,2),(0,2)),((-1,2),(0,1)),((0,-2),(0,-1)),((0,-2),(1,-2)),((0,-1),(0,0)),((0,-1),(1,-1)),((0,-1),(1,-2)),((0,0),(0,1)),((0,0),(1,0)),((0,0),(1,-1)),((0,1),(0,2)),((0,1),(1,1)),((0,1),(1,0)),((0,2),(1,1)),((1,-2),(1,-1)),((1,-2),(2,-2)),((1,-1),(1,0)),((1,-1),(2,-1)),((1,-1),(2,-2)),((1,0),(1,1)),((1,0),(2,0)),((1,0),(2,-1)),((1,1),(2,0)),((2,-2),(2,-1)),((2,-1),(2,0))]
Find out if two tiles are adjacent.
ghci> isAdjacent g (-2,0) (-2,1) True ghci> isAdjacent g (-2,0) (0,1) False
A regular arrangement of tiles.
Minimal complete definition: Index
, indices
and distance
.
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 ba
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 abs
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 :: g -> Index g -> [Index g]Source
returns the indices of the tiles in the grid
neighbours
g xg
which are adjacent to the tile with index x
.
numNeighbours :: g -> Index g -> IntSource
returns the number of tiles in the grid
numNeighbours
g xg
which are adjacent to the tile with index x
.
contains :: Eq (Index g) => g -> Index g -> BoolSource
g `'contains'` x
returns True
if the index x
is contained
within the grid g
, otherwise it returns false.
viewpoint :: g -> Index g -> [(Index g, Int)]Source
returns a list of pairs associating the index
of each tile in viewpoint
g xg
with its distance to the tile with index x
.
If x
is not contained within g
, the result is undefined.
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.
isAdjacent :: Eq (Index g) => g -> Index g -> Index g -> BoolSource
returns isAdjacent
g a bTrue
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 :: 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 ba
, 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 ba
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
class Grid g => FiniteGrid g whereSource
A regular arrangement of tiles where the number of tiles is finite.
Minimal complete definition: size
.
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 :: 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 xTrue
if the tile with index x
is
on a boundary of g
, False
otherwise. (Corner tiles are also
boundary tiles.)
centre :: 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 xTrue
if the tile with index x
is
a centre tile of g
, False
otherwise.
Grids with triangular tiles
Unbounded grid with triangular tiles
data UnboundedTriGrid Source
An unbounded grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
Triangular grid with triangular tiles
data TriTriGrid Source
A triangular grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
triTriGrid :: Int -> TriTriGridSource
returns a triangular grid with sides of
length triTriGrid
ss
, using triangular tiles. If s
is nonnegative, the
resulting grid will have s^2
tiles. Otherwise, the resulting grid
will be null and the list of indices will be null.
Parallelogram-shaped grid with triangular tiles
data ParaTriGrid Source
A Parallelogrammatical grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
paraTriGrid :: Int -> Int -> ParaTriGridSource
returns a grid in the shape of a
parallelogram with paraTriGrid
r cr
rows and c
columns, using triangular
tiles. If r
and c
are both nonnegative, the resulting grid will
have 2*r*c
tiles. Otherwise, the resulting grid will be null and
the list of indices will be null.
Rectangular grid with triangular tiles
data RectTriGrid Source
A rectangular grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
rectTriGrid :: Int -> Int -> RectTriGridSource
returns a grid in the shape of a
rectangle (with jagged edges) that has rectTriGrid
r cr
rows and c
columns,
using triangular tiles. If r
and c
are both nonnegative, the
resulting grid will have 2*r*c
tiles. Otherwise, the resulting grid will be null and
the list of indices will be null.
Toroidal grid with triangular tiles
data TorTriGrid Source
A toroidal grid with triangular tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
torTriGrid :: Int -> Int -> TorTriGridSource
returns a toroidal grid with torTriGrid
r cr
rows and c
columns, using triangular tiles. If r
is odd, the result is
undefined because the grid edges would overlap. If r
and c
are both nonnegative, the resulting grid will have 2*r*c
tiles.
Otherwise, the resulting grid will be null and the list of indices
will be null.
Grids with square tiles
Unbounded grid with square tiles
data UnboundedSquareGrid Source
An unbounde grid with square tiles. The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
Rectangular grid with square tiles
data RectSquareGrid Source
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.
rectSquareGrid :: Int -> Int -> RectSquareGridSource
produces a rectangular grid with rectSquareGrid
r cr
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 Source
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.
torSquareGrid :: Int -> Int -> TorSquareGridSource
returns a toroidal grid with torSquareGrid
r cr
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.
Grids with hexagonal tiles
Unbounded grid with hexagonal tiles
data UnboundedHexGrid Source
An unbounded grid with hexagonal tiles The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
Hexagonal grid with hexagonal tiles
data HexHexGrid Source
A hexagonal grid with hexagonal tiles The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
hexHexGrid :: Int -> HexHexGridSource
returns a grid of hexagonal shape, with
sides of length hexHexGrid
ss
, using hexagonal tiles. If s
is nonnegative, the
resulting grid will have 3*s*(s-1) + 1
tiles. Otherwise, the resulting
grid will be null and the list of indices will be null.
Parallelogram-shaped grid with hexagonal tiles
data ParaHexGrid Source
A parallelogramatical grid with hexagonal tiles The grid and its indexing scheme are illustrated in the user guide, available at https://github.com/mhwombat/grid/wiki.
paraHexGrid :: Int -> Int -> ParaHexGridSource
returns a grid in the shape of a
parallelogram with paraHexGrid
r cr
rows and c
columns, using hexagonal 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.
Grids with octagonal tiles
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.
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.
rectOctGrid :: Int -> Int -> RectOctGridSource
produces a rectangular grid with rectOctGrid
r cr
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.
torOctGrid :: Int -> Int -> TorOctGridSource
returns a toroidal grid with torOctGrid
r cr
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.