```module Utils.Rectangle where
import Test.LazySmallCheck

import Utils.Point
import Control.DeepSeq

newtype Rectangle a = Rectangle ((a,a),(a,a)) deriving (Eq,Show)

a `s` b = rnf a `seq` b

instance (NFData a) => NFData (Rectangle a) where
rnf (Rectangle ((a,b),(c,d))) = (a `s` b `s` c `s` d) `seq` ()

left   (Rectangle ((x,y),(w,h))) = x
right  (Rectangle ((x,y),(w,h))) = x+w
top    (Rectangle ((x,y),(w,h))) = y
bottom (Rectangle ((x,y),(w,h))) = y+h
topLeft  (Rectangle ((x,y),(w,h))) = (x,y)
topRight (Rectangle ((x,y),(w,h))) = (x+w,y)
bottomLeft (Rectangle ((x,y),(w,h))) = (x,y+h)
bottomRight (Rectangle ((x,y),(w,h))) = (x+w,y+h)
vertices r = [topLeft r, topRight r, bottomLeft r, bottomRight r]
rSize (Rectangle ((x,y),(w,h))) = (w,h)
rArea r = let (w,h) = rSize r in (w*h)

instance (Num a, Ord a , Serial a) => Serial (Rectangle a) where
series = cons4 \$ \a b c d -> mkRectangle (a,b) (c,d)

-- | Create rectangle around point (x,y)
around (x,y) (w,h) = mkRectangle (x', y') (w,h)
where (x',y') = (x-(w/2),y-(h/2))

mkRectangle (x,y) (w,h) = Rectangle ((x-negW,y-negH),(abs w,abs h))
where
negH | h<0  = abs h
| h>=0 = 0
negW | w<0  = abs w
| w>=0 = 0

mkRectCorners (x1,y1) (x2,y2) = Rectangle ((x,y),(w,h))
where
x = min x1 x2
y = min y1 y2
w = abs (x1-x2)
h = abs (y1-y2)

prop_Corners :: (Int,Int) -> (Int,Int) -> Bool
prop_Corners p w = mkRectCorners p (p+w) == mkRectangle p w

mkRec = uncurry mkRectangle

-- | Return rectangle r2 in coordinate system defined by r1
inCoords r1 r2@(Rectangle (pos,size)) = Rectangle (pos-topLeft r1,size )

-- | Return a point in coordinates of given rectangle
inCoords' r1 pt = pt - topLeft r1

-- | Adjust the size of the rectangle to be divisible by 2^n.
enlargeToNthPower n (Rectangle ((x,y),(w,h))) = Rectangle ((x,y),(w2,h2))
where
pad x = x + (np - x `mod` np)
np = 2^n

intersection r1 r2
= mkRectCorners (max (left r1)   (left r2)
,max (top r1)    (top r2))
(min (right r1)  (right r2)
,min (bottom r1) (bottom r2))

propIntersectionArea r1 r2
= (intersects r1 r2)
==> rArea (intersection r1 r2) <= rArea r1 &&
rArea (intersection r1 r2) <= rArea r2

propIntersectionCommutes r1 r2
= (intersects r1 r2)
==> (intersection r1 r2) == (intersection r2 r1)

intersects rect1 rect2
= intersect1D (left rect1, right rect1) (left rect2, right rect2) &&
intersect1D (top rect1, bottom rect1) (top rect2, bottom rect2)

contains a b = left a <= left b
&& top a <= top b
&& bottom a >= bottom b
&& right a >= right b

intersect1D (x,y) (u,w) =
not \$ (x < min u w && y < min u w) || (x > max u w && y > max u w)

prop_intersect1DCommutes a b
= intersect1D  a b == intersect1D b a

prop_intersectsCommutes sa@(_,(s1,s2)) sb@(b,(s3,s4))
= intersects (mkRec sa) (mkRec sb) == intersects (mkRec sb) (mkRec sa)

-- | Create a tiling of a rectangles.
tile tilesize overlap r = [mkRectangle ((x,y)-overlap) tilesize
| x <- [startx,startx+fst tilesize..endx]
, y <- [starty,starty+fst tilesize..endy]]
where
startx = left r-fst overlap
starty = top  r-snd overlap
endx = right  r+fst overlap
endy = bottom r+snd overlap

-- | Scale a rectangle
scale (a,b) (Rectangle ((x,y),(s1,s2)))
= mkRectangle (round (a*fromIntegral x),round (b*fromIntegral y))
(round (a*fromIntegral s1),round (b*fromIntegral s2))

toInt (Rectangle (p, s))
= Rectangle (both round p
,both round s)
where both f (a,b) = (f a , f b)

```