150 lines
4.2 KiB
Haskell
150 lines
4.2 KiB
Haskell
{-# LANGUAGE TupleSections #-}
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module Geometry.Zone
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( ddaExt
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)
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where
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import Geometry.Data
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import Data.Foldable
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import qualified Data.IntMap.Strict as IM
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import qualified Data.IntSet as IS
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foldl2'
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:: (b -> a -> a -> b)
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-> b
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-> [a]
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-> b
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foldl2' f s (t:ts) = fst $ foldl' g (s, t) ts
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where
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g (r,x) y = (f r x y,y)
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foldl2' _ s _ = s
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sortArguments
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:: Ord a
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=> (a -> a -> b)
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-> a -> a -> b
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sortArguments f x y
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| x < y = f x y
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| otherwise = f y x
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sortArgumentsReverse
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:: Ord a
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=> (a -> a -> [b])
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-> a -> a -> [b]
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sortArgumentsReverse f x y
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| x < y = f x y
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| otherwise = reverse $ f y x
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intervalBounds
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:: Float -- ^ interval threshold
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-> Float -- ^ First endpoint
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-> Float -- ^ Second endpoint
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-> [Float]
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intervalBounds = sortArgumentsReverse . f
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where
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f r a b
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| x > b = [a]
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| otherwise = (a : [x,x+r..b])
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where
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x = floorTo r a + r
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floorTo :: Float -> Float -> Float
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floorTo r x = r * (fromIntegral ((floor $ x / r) :: Int))
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ceilingTo :: Float -> Float -> Float
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ceilingTo r x = r * (fromIntegral ((ceiling $ x / r) :: Int))
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divTo :: Float -> Float -> Int
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{-# INLINE divTo #-}
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divTo s = floor . (/s)
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flipV :: Point2 -> Point2
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{-# INLINE flipV #-}
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flipV (V2 a b) = V2 b a
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applyInverted
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:: (Point2 -> Point2 -> [Point2])
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-> Point2 -> Point2 -> [Point2]
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applyInverted f sp@(V2 sx sy) ep@(V2 ex ey)
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| abs (sx-ex) > abs (sy-ey) = f sp ep
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| otherwise = map flipV $ f (flipV sp) (flipV ep)
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sizeZoneOfPoint' :: Float -> Point2 -> V2 Int
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sizeZoneOfPoint' s = fmap (divTo s)
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increasingInterval :: Int -> Int -> [Int]
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increasingInterval x y
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| y > x = [x .. y]
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| otherwise = [y .. x]
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-- | Determines which horizontal and vertical lines on a grid are crossed by a
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-- line. For each adds the x-y index of the square to the right or above the
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-- crossed grid line. Also adds the index of the square containing the start
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-- point.
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ddaExt :: Float -> V2 Float -> V2 Float -> IM.IntMap IS.IntSet
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ddaExt s sp@(V2 sx sy) ep@(V2 ex ey)
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| x1 <= x2 = addys . IM.fromDistinctAscList $ zip [x1 .. x2]
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$ map (IS.singleton . divTo s) [x1y,x1y+ydx..]
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| otherwise = addys . IM.fromDistinctAscList $ zip [x2-1 .. x1-1]
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$ map (IS.singleton . divTo s) [x2y,x2y+ydx..]
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where
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x1 = divTo s sx
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x2 = divTo s ex
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x1y = fx' sp ep $ s * (fromIntegral x1)
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x2y = fx' sp ep $ s * (fromIntegral x2)
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ydx = s * ydx' sp ep
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addys m = add2s m ypairs
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y1 = divTo s sy
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y2 = divTo s ey
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y1x = fy' sp ep $ s * (fromIntegral y1)
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y2x = fy' sp ep $ s * (fromIntegral y2)
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xdy = s * xdy' sp ep
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ypairs
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| y1 <= y2 = zip (map (divTo s) [y1x,y1x+xdy..])
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[y1 .. y2]
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| otherwise = zip (map (divTo s) [y2x,y2x+xdy..])
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[y2-1 .. y1-1]
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ydx' :: Point2 -> Point2 -> Float
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{-# INLINE ydx' #-}
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ydx' (V2 sx sy) (V2 ex ey)
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| sx == ex = 0
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| otherwise = (ey - sy) / (ex - sx)
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xInt' :: Float -> Point2 -> Point2 -> Float
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xInt' s (V2 sx _) (V2 ex _)
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| ex > sx = ceilingTo s sx
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| otherwise = floorTo s sx
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fx' :: Point2 -> Point2 -> Float -> Float
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fx' sp@(V2 sx sy) ep@(V2 _ ey) x
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| sy == ey = sy
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| otherwise = sy + ydx' sp ep * (x - sx)
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xdy' :: Point2 -> Point2 -> Float
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xdy' (V2 sx sy) (V2 ex ey)
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| sy == ey = 0
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| otherwise = (ex - sx) / (ey - sy)
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yInt' :: Float -> Point2 -> Point2 -> Float
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yInt' s (V2 _ sy) (V2 _ ey)
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| ey > sy = ceilingTo s sy
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| otherwise = floorTo s sy
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fy' :: Point2 -> Point2 -> Float -> Float
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fy' sp@(V2 sx sy) ep@(V2 ex _) y
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| sx == ex = sx
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| otherwise = sx + xdy' sp ep * (y - sy)
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add2s :: IM.IntMap IS.IntSet -> [(Int,Int)] -> IM.IntMap IS.IntSet
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{-# INLINE add2s #-}
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add2s imis = foldl'
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(\m (k,x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)
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imis
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addV2s :: IM.IntMap IS.IntSet -> [V2 Int] -> IM.IntMap IS.IntSet
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{-# INLINE addV2s #-}
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addV2s imis = foldl'
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(\m (V2 k x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)
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imis
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pairsToIntMapSet :: [V2 Int] -> IM.IntMap IS.IntSet
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pairsToIntMapSet = foldl'
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(\m (V2 k x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)
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IM.empty
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