module Region(Region(Shape,Translate,Scale,Complement,
 Union,Intersect,Empty),
 Vector,
 containsS,containsR,
 module Shape
 ) where
 
import Shape
-- A Region is either:
data Region = 
 Shape Shape -- primitive shape
 | Translate Vector Region -- translated region
 | Scale Vector Region -- scaled region
 | Complement Region -- inverse of region
 | Region `Union` Region -- union of regions
 | Region `Intersect` Region -- intersection of regions
 | Empty
 deriving Show
type Vector = (Float, Float) 
type Ray = (Vector,Vector)
isLeftOf :: Vertex -> Ray -> Bool
(px,py) `isLeftOf` ((ax,ay),(bx,by))
 = let (s,t) = (px-ax, py-ay)
 (u,v) = (px-bx, py-by)
 in s*v>= t*u
containsS :: Shape -> Vertex -> Bool
(Rectangle s1 s2) `containsS` (x,y)
 = let t1 = s1/2
 t2 = s2/2
 in -t1<=x && x<=t1 && -t2<=y && y<=t2 (Ellipse r1 r2) `containsS` (x,y) = (x/r1)^2 + (y/r2)^2 <= 1 (Polygon pts) `containsS` p = let shiftpts = tail pts ++ [head pts] leftOfList = map isLeftOfp(zip pts shiftpts) isLeftOfp p' = isLeftOf p p' in foldr (&&) True leftOfList (RtTriangle s1 s2) `containsS` p = (Polygon [(0,0),(s1,0),(0,s2)]) `containsS` p containsR :: Region -> Vertex -> Bool
(Shape s) `containsR` p = 
 s `containsS` p
(Translate (u,v) r) `containsR` (x,y) = 
 r `containsR` (x-u,y-v)
(Scale (u,v) r) `containsR` (x,y) = 
 r `containsR` (x/u,y/v)
(Complement r) `containsR` p = 
 not (r `containsR` p)
(r1 `Union` r2) `containsR` p =
 r1 `containsR` p &#124;&#124; r2 `containsR` p
(r1 `Intersect` r2) `containsR` p =
 r1 `containsR` p && r2 `containsR` p
Empty `containsR` p = False 
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