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)
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 ((xnegW,ynegH),(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 (x1x2)
h = abs (y1y2)
prop_Corners :: (Int,Int) -> (Int,Int) -> Bool
prop_Corners p w = mkRectCorners p (p+w) == mkRectangle p w
mkRec = uncurry mkRectangle
inCoords r1 r2@(Rectangle (pos,size)) = Rectangle (postopLeft r1,size )
inCoords' r1 pt = pt topLeft r1
enlargeToNthPower n (Rectangle ((x,y),(w,h))) = Rectangle ((x,y),(w2,h2))
where
(w2,h2) = (pad w, pad h)
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)
tile tilesize overlap r = [mkRectangle ((x,y)overlap) tilesize
| x <- [startx,startx+fst tilesize..endx]
, y <- [starty,starty+fst tilesize..endy]]
where
startx = left rfst overlap
starty = top rsnd overlap
endx = right r+fst overlap
endy = bottom r+snd overlap
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)