| 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.GridInternal
Description
A module containing private Grid internals. Most developers should
use Grid instead. This module is subject to change without notice.
Synopsis
- class Grid g where
- type Index g
- type Direction g
- 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]
- neighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
- neighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)
- numNeighbours :: Eq (Index g) => g -> Index g -> Int
- 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]
- defaultMinDistance :: g -> [Index g] -> Index g -> Int
- defaultNeighbours :: g -> Index g -> [Index g]
- defaultNeighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g]
- defaultNeighbour :: (Eq (Index g), Eq (Direction g)) => g -> Index g -> Direction g -> Maybe (Index g)
- defaultTileCount :: g -> Int
- defaultEdges :: Eq (Index g) => g -> [(Index g, Index g)]
- defaultIsAdjacent :: g -> Index g -> Index g -> Bool
- defaultAdjacentTilesToward :: Eq (Index g) => g -> Index g -> Index g -> [Index g]
- defaultMinimalPaths :: Eq (Index g) => g -> Index g -> Index g -> [[Index 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
- class Grid g => WrappedGrid g where
- neighboursBasedOn :: (Eq (Index u), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]
- distanceBasedOn :: (Eq (Index g), Grid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> Int
- 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]
- neighboursWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> [Index g]
- 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)
- distanceWrappedBasedOn :: (Eq (Index g), WrappedGrid g, Grid u, Index g ~ Index u) => u -> g -> Index g -> Index g -> Int
- 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]
- sameEdge :: Eq t => (t, t) -> (t, t) -> Bool
- adjacentEdges :: (Grid g, Eq (Index g)) => Index g -> g -> [(Index g, Index g)]
- cartesianIndices :: (Enum r, Enum c, Num r, Num c, Ord r, Ord c) => (r, c) -> [(c, r)]
- cartesianCentre :: (Int, Int) -> [(Int, Int)]
- cartesianMidpoints :: Int -> [Int]
Documentation
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.
neighboursOfSet :: Eq (Index g) => g -> [Index g] -> [Index g] Source #
neighboursOfSet g asg 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 ag which is adjacent to the tile with index a, in the
direction d.
numNeighbours :: Eq (Index g) => g -> Index g -> Int Source #
numNeighbours g ag which are adjacent to the tile with index a.
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.
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 #
Instances
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
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 #
Instances
class Grid g => WrappedGrid g where Source #
A regular arrangement of tiles where the boundaries are joined.
Minimal complete definition: normalisedenormalise
Methods
normalise :: g -> Index g -> Index g Source #
normalise g aa.
TODO: need a clearer description and an illustration.
denormalise :: g -> Index g -> [Index g] Source #
denormalise g aa'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
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 #
cartesianMidpoints :: Int -> [Int] Source #