| Copyright | (c) Amy de Buitléir 2012-2019 |
|---|---|
| License | BSD-style |
| Maintainer | amy@nualeargais.ie |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Math.Geometry.Grid
Description
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 6.0 moved the various grid flavours to sub-modules.
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.
Synopsis
- class Grid g where
- indices :: g -> [Index g]
- distance :: g -> Index g -> Index g -> Int
- minDistance :: g -> [Index g] -> Index g -> Int
- neighbours :: Eq (Index g) => g -> Index g -> [Index g]
- neighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)
- contains :: Eq (Index g) => g -> Index g -> Bool
- tileCount :: g -> Int
- null :: g -> Bool
- nonNull :: g -> Bool
- edges :: Eq (Index g) => g -> [(Index g, Index g)]
- viewpoint :: g -> Index g -> [(Index g, Int)]
- isAdjacent :: g -> Index g -> Index g -> Bool
- adjacentTilesToward :: Eq (Index g) => g -> Index g -> Index g -> [Index g]
- minimalPaths :: Eq (Index g) => g -> Index g -> Index g -> [[Index g]]
- directionTo :: g -> Index g -> Index g -> [Direction g]
- type family Index g
- type family Direction g
- class Grid g => FiniteGrid g where
- type Size g
- size :: g -> Size g
- maxPossibleDistance :: g -> Int
- class Grid g => BoundedGrid g where
- tileSideCount :: g -> Int
- boundary :: Eq (Index g) => g -> [Index g]
- isBoundary :: Eq (Index g) => g -> Index g -> Bool
- centre :: Eq (Index g) => g -> [Index g]
- isCentre :: Eq (Index g) => g -> Index g -> Bool
- defaultBoundary :: Eq (Index g) => g -> [Index g]
- defaultIsBoundary :: Eq (Index g) => g -> Index g -> Bool
- defaultCentre :: Eq (Index g) => g -> [Index g]
- defaultIsCentre :: Eq (Index g) => g -> Index g -> Bool
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
Grids
A regular arrangement of tiles.
Minimal complete definition: IndexDirectionindicesdistancedirectionTo
Minimal complete definition
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 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 -> Int Source #
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 :: Eq (Index g) => g -> Index g -> [Index g] Source #
neighbours g ag which are adjacent to the tile with index a.
neighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g) Source #
neighbour g d ag which is adjacent to the tile with index a, in the
direction d.
contains :: Eq (Index g) => g -> Index g -> Bool Source #
g ` returns contains' aTrue 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
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.
viewpoint :: g -> Index g -> [(Index g, Int)] Source #
viewpoint g ag 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 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 :: Eq (Index g) => g -> Index g -> Index g -> [Index g] Source #
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 #
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
adjacentTilesTowardadjacentTilesTowardminimalPaths
directionTo :: g -> Index g -> Index g -> [Direction g] Source #
directionTo g a ba to the
tile at index b in grid g.
Instances
Instances
type family Direction g Source #
Instances
Finite grids
class Grid g => FiniteGrid g where Source #
A regular arrangement of tiles where the number of tiles is finite.
Minimal complete definition: sizemaxPossibleDistance
Methods
Returns the dimensions of the grid.
For example, if g is a 4x3 rectangular grid, size g(4, 3), while tileCount g12.
maxPossibleDistance :: g -> Int Source #
Returns the largest possible distance between two tiles in the grid.
Instances
Bounded grids
class Grid g => BoundedGrid g where Source #
A regular arrangement of tiles with an edge.
Minimal complete definition: tileSideCount
Minimal complete definition
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 aTrue 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 aTrue 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 #