{-# LANGUAGE QuantifiedConstraints #-}
{-# LANGUAGE AllowAmbiguousTypes #-}
--------------------------------------------------------------------------------
module Xanthous.Generators.Util
( MCells
, Cells
, CellM
, randInitialize
, initializeEmpty
, numAliveNeighborsM
, numAliveNeighbors
, fillOuterEdgesM
, cloneMArray
, floodFill
, regions
, fillAll
, fillAllM
, fromPoints
, fromPointsM
) where
--------------------------------------------------------------------------------
import Xanthous.Prelude hiding (Foldable, toList, for_)
import Data.Array.ST
import Data.Array.Unboxed
import Control.Monad.ST
import Control.Monad.Random
import Data.Monoid
import Data.Foldable (Foldable, toList, for_)
import qualified Data.Set as Set
import Data.Semigroup.Foldable
--------------------------------------------------------------------------------
import Xanthous.Util (foldlMapM', maximum1, minimum1)
import Xanthous.Data (Dimensions, width, height)
--------------------------------------------------------------------------------
type MCells s = STUArray s (Word, Word) Bool
type Cells = UArray (Word, Word) Bool
type CellM g s a = RandT g (ST s) a
randInitialize :: RandomGen g => Dimensions -> Double -> CellM g s (MCells s)
randInitialize dims aliveChance = do
res <- initializeEmpty dims
for_ [0..dims ^. width] $ \i ->
for_ [0..dims ^. height] $ \j -> do
val <- (>= aliveChance) <$> getRandomR (0, 1)
lift $ writeArray res (i, j) val
pure res
initializeEmpty :: RandomGen g => Dimensions -> CellM g s (MCells s)
initializeEmpty dims =
lift $ newArray ((0, 0), (dims ^. width, dims ^. height)) False
numAliveNeighborsM
:: forall a i j m
. (MArray a Bool m, Ix (i, j), Integral i, Integral j)
=> a (i, j) Bool
-> (i, j)
-> m Word
numAliveNeighborsM cells (x, y) = do
cellBounds <- getBounds cells
getSum <$> foldlMapM'
(fmap (Sum . fromIntegral . fromEnum) . boundedGet cellBounds)
neighborPositions
where
boundedGet :: ((i, j), (i, j)) -> (Int, Int) -> m Bool
boundedGet ((minX, minY), (maxX, maxY)) (i, j)
| x <= minX
|| y <= minY
|| x >= maxX
|| y >= maxY
= pure True
| otherwise =
let nx = fromIntegral $ fromIntegral x + i
ny = fromIntegral $ fromIntegral y + j
in readArray cells (nx, ny)
neighborPositions :: [(Int, Int)]
neighborPositions = [(i, j) | i <- [-1..1], j <- [-1..1], (i, j) /= (0, 0)]
numAliveNeighbors
:: forall a i j
. (IArray a Bool, Ix (i, j), Integral i, Integral j)
=> a (i, j) Bool
-> (i, j)
-> Word
numAliveNeighbors cells (x, y) =
let cellBounds = bounds cells
in getSum $ foldMap
(Sum . fromIntegral . fromEnum . boundedGet cellBounds)
neighborPositions
where
boundedGet :: ((i, j), (i, j)) -> (Int, Int) -> Bool
boundedGet ((minX, minY), (maxX, maxY)) (i, j)
| x <= minX
|| y <= minY
|| x >= maxX
|| y >= maxY
= True
| otherwise =
let nx = fromIntegral $ fromIntegral x + i
ny = fromIntegral $ fromIntegral y + j
in cells ! (nx, ny)
neighborPositions :: [(Int, Int)]
neighborPositions = [(i, j) | i <- [-1..1], j <- [-1..1], (i, j) /= (0, 0)]
fillOuterEdgesM :: (MArray a Bool m, Ix i, Ix j) => a (i, j) Bool -> m ()
fillOuterEdgesM arr = do
((minX, minY), (maxX, maxY)) <- getBounds arr
for_ (range (minX, maxX)) $ \x -> do
writeArray arr (x, minY) True
writeArray arr (x, maxY) True
for_ (range (minY, maxY)) $ \y -> do
writeArray arr (minX, y) True
writeArray arr (maxX, y) True
cloneMArray
:: forall a a' i e m.
( Ix i
, MArray a e m
, MArray a' e m
, IArray UArray e
)
=> a i e
-> m (a' i e)
cloneMArray = thaw @_ @UArray <=< freeze
--------------------------------------------------------------------------------
-- | Flood fill a cell array starting at a point, returning a list of all the
-- (true) cell locations reachable from that point
floodFill :: forall a i j.
( IArray a Bool
, Ix (i, j)
, Enum i , Enum j
, Bounded i , Bounded j
, Eq i , Eq j
, Show i, Show j
)
=> a (i, j) Bool -- ^ array
-> (i, j) -- ^ position
-> Set (i, j)
floodFill = go mempty
where
go :: Set (i, j) -> a (i, j) Bool -> (i, j) -> Set (i, j)
-- TODO pass result in rather than passing seen in, return result
go res arr@(bounds -> arrBounds) idx@(x, y)
| not (inRange arrBounds idx) = res
| not (arr ! idx) = res
| otherwise =
let neighbors
= filter (inRange arrBounds)
. filter (/= idx)
. filter (`notMember` res)
$ (,)
<$> [(if x == minBound then x else pred x)
..
(if x == maxBound then x else succ x)]
<*> [(if y == minBound then y else pred y)
..
(if y == maxBound then y else succ y)]
in foldl' (\r idx' ->
if arr ! idx'
then r <> go (r & contains idx' .~ True) arr idx'
else r)
(res & contains idx .~ True) neighbors
-- | Gives a list of all the disconnected regions in a cell array, represented
-- each as lists of points
regions :: forall a i j.
( IArray a Bool
, Ix (i, j)
, Enum i , Enum j
, Bounded i , Bounded j
, Eq i , Eq j
, Show i, Show j
)
=> a (i, j) Bool
-> [Set (i, j)]
regions arr
| Just firstPoint <- findFirstPoint arr =
let region = floodFill arr firstPoint
arr' = fillAll region arr
in region : regions arr'
| otherwise = []
where
findFirstPoint :: a (i, j) Bool -> Maybe (i, j)
findFirstPoint = fmap fst . headMay . filter snd . assocs
fillAll :: (IArray a Bool, Ix i, Foldable f) => f i -> a i Bool -> a i Bool
fillAll ixes a = accum (const fst) a $ (, (False, ())) <$> toList ixes
fillAllM :: (MArray a Bool m, Ix i, Foldable f) => f i -> a i Bool -> m ()
fillAllM ixes a = for_ ixes $ \i -> writeArray a i False
fromPoints
:: forall a f i.
( IArray a Bool
, Ix i
, Functor f
, Foldable1 f
)
=> f (i, i)
-> a (i, i) Bool
fromPoints points =
let pts = Set.fromList $ toList points
dims = ( (minimum1 $ fst <$> points, minimum1 $ snd <$> points)
, (maximum1 $ fst <$> points, maximum1 $ snd <$> points)
)
in array dims $ range dims <&> \i -> (i, i `member` pts)
fromPointsM
:: (MArray a Bool m, Ix i, Element f ~ i, MonoFoldable f)
=> NonNull f
-> m (a i Bool)
fromPointsM points = do
arr <- newArray (minimum points, maximum points) False
fillAllM (otoList points) arr
pure arr
