SOE ex.8.1
import Shape
fiveCircles' = circlesRegion `Intersect` rectangleRegion
where
ps = [0, 2 ..] ++ [-2, -4 ..]
circleShape = Shape (circle 1)
circleShapes = map (flip Translate circleShape) [(x,y) | x <- ps, y <- ps]
circlesRegion = foldl Union Empty circleShapes
rectangleRegion = Translate (4, 0) (Shape $ rectangle 10 2)
circlesRegion' = foldl Union Empty (map circleR1At circleCenters)
where
spiral = concat $ map (replicate 2) [1..]
directions = cycle [(2, 0), (0, 2), (-2, 0), (0, -2)]
circleCenters = scanl (\(x,y) (dx,dy) -> (x+dx, y+dy)) (0,0) $
concat $ zipWith replicate spiral directions
circleR1At v = Translate v (Shape (circle 1))
{-
fiveCircles' is theory correct but practically impossible to achieve.
All cycles in 2D plan (for axe negative infinite to positive infinite)
are almost impossible to test "Intersect".
(Especially the way we implement the "intersect")
circlesRegion' is just for fun, it defines all cycles from origin and spiral to infinite.
-}
data Region
= Shape Shape
| Translate Vector Region
| Scale Vector Region
| Complement Region
| Region `Union` Region
| Region `Intersect` Region
| Empty
deriving Show
type Vector = (Float, Float)
infixr 5 `Union`
infixr 6 `Intersect`
