--{-# LANGUAGE TupleSections #-}
module Geometry.Zone
    ( ddaExt
    ) 
    where
import Geometry.Data

import Data.Foldable
import qualified Data.IntMap.Strict as IM
import qualified Data.IntSet as IS

--foldl2'
--    :: (b -> a -> a -> b) 
--    -> b 
--    -> [a]
--    -> b
--foldl2' f s (t:ts) = fst $ foldl' g (s, t) ts
--  where
--    g (r,x) y = (f r x y,y)
--foldl2' _ s _ = s

--sortArguments 
--    :: Ord a 
--    => (a -> a -> b)
--    -> a -> a -> b
--sortArguments f x y
--    | x < y = f x y
--    | otherwise = f y x
--sortArgumentsReverse
--    :: Ord a 
--    => (a -> a -> [b])
--    -> a -> a -> [b]
--sortArgumentsReverse f x y
--    | x < y = f x y
--    | otherwise = reverse $ f y x
--
--intervalBounds
--    :: Float    -- ^ interval threshold
--    -> Float    -- ^ First endpoint
--    -> Float    -- ^ Second endpoint
--    -> [Float]
--intervalBounds = sortArgumentsReverse . f
--  where 
--    f r a b 
--        | x > b = [a]
--        | otherwise = (a : [x,x+r..b])
--      where
--        x = floorTo r a + r

--floorTo :: Float -> Float -> Float
--floorTo r x = r * (fromIntegral ((floor $ x / r) :: Int))

--ceilingTo :: Float -> Float -> Float
--ceilingTo r x = r * (fromIntegral ((ceiling $ x / r) :: Int))

divTo :: Float -> Float -> Int
{-# INLINE divTo #-}
divTo s = floor . (/s)

--flipV :: Point2 -> Point2
--{-# INLINE flipV #-}
--flipV (V2 a b) = V2 b a

--applyInverted 
--    :: (Point2 -> Point2 -> [Point2])
--    -> Point2 -> Point2 -> [Point2]
--applyInverted f sp@(V2 sx sy) ep@(V2 ex ey)
--    | abs (sx-ex) > abs (sy-ey) = f sp ep
--    | otherwise = map flipV $ f (flipV sp) (flipV ep)

sizeZoneOfPoint' :: Float -> Point2 -> V2 Int
{-# INLINE sizeZoneOfPoint' #-}
sizeZoneOfPoint' s = fmap (divTo s)

--increasingInterval :: Int -> Int -> [Int]
--increasingInterval x y
--    | y > x = [x .. y]
--    | otherwise = [y .. x]

-- | Determines which horizontal and vertical lines on a grid are crossed by a
-- line. For each adds the x-y index of the square to the right or above the
-- crossed grid line. Also adds the index of the square containing the start
-- point.
ddaExt :: Float -> V2 Float -> V2 Float -> IM.IntMap IS.IntSet
ddaExt s sp@(V2 sx sy) ep@(V2 ex ey) 
    | x1 <= x2 = addsp . addys . IM.fromDistinctAscList $ zip [x1 .. x2] 
                    $ map (IS.singleton . divTo s) [x1y,x1y+ydx..]
    | otherwise = addsp . addys . IM.fromDistinctAscList $ zip [x2-1 .. x1-1]
                    $ map (IS.singleton . divTo s) [x2y,x2y+ydx..]
  where
    addsp im = let V2 x y = sizeZoneOfPoint' s sp
            in insertXY im (x,y)
    x1 = divTo s sx
    x2 = divTo s ex
    x1y = fx' sp ep $ s * fromIntegral x1
    x2y = fx' sp ep $ s * fromIntegral x2
    ydx = s * ydx' sp ep
    addys m = add2s m ypairs 
    y1 = divTo s sy
    y2 = divTo s ey
    y1x = fy' sp ep $ s * fromIntegral y1
    y2x = fy' sp ep $ s * fromIntegral y2
    xdy = s * xdy' sp ep
    ypairs 
        | y1 <= y2  = zip (map (divTo s) [y1x,y1x+xdy..])
                         [y1 .. y2] 
        | otherwise = zip (map (divTo s) [y2x,y2x+xdy..])
                         [y2-1 .. y1-1] 

ydx' :: Point2 -> Point2 -> Float
{-# INLINE ydx' #-}
ydx' (V2 sx sy) (V2 ex ey)
    | sx == ex = 0
    | otherwise = (ey - sy) / (ex - sx)
fx' :: Point2 -> Point2 -> Float -> Float
{-# INLINE fx' #-}
fx' sp@(V2 sx sy) ep@(V2 _ ey) x
    | sy == ey = sy
    | otherwise = sy + ydx' sp ep * (x - sx)

xdy' :: Point2 -> Point2 -> Float
{-# INLINE xdy' #-}
xdy' (V2 sx sy) (V2 ex ey)
    | sy == ey = 0
    | otherwise = (ex - sx) / (ey - sy)
fy' :: Point2 -> Point2 -> Float -> Float
{-# INLINE fy' #-}
fy' sp@(V2 sx sy) ep@(V2 ex _) y
    | sx == ex = sx
    | otherwise = sx + xdy' sp ep * (y - sy)

add2s :: IM.IntMap IS.IntSet -> [(Int,Int)] -> IM.IntMap IS.IntSet
{-# INLINE add2s #-}
add2s = foldl' 
    (\m (k,x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)

insertXY :: IM.IntMap IS.IntSet -> (Int,Int) -> IM.IntMap IS.IntSet
{-# INLINE insertXY #-}
insertXY m (k,x) = IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m

--addV2s :: IM.IntMap IS.IntSet -> [V2 Int] -> IM.IntMap IS.IntSet
--{-# INLINE addV2s #-}
--addV2s imis = foldl' 
--    (\m (V2 k x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)
--    imis

--pairsToIntMapSet :: [V2 Int] -> IM.IntMap IS.IntSet
--pairsToIntMapSet = foldl' 
--    (\m (V2 k x) -> IM.insertWith (\_ old -> IS.insert x old) k (IS.singleton x) m)
--    IM.empty