Shapes_FP_Vlad

data Square = Square { squareSide :: Double }
  deriving (Show, Eq)

data Rectangle = Rect { rectWidth :: Double , rectHeight :: Double }
  deriving (Show, Eq)

data Circle = Circle { circleRadius :: Double }
  deriving (Show, Eq)

data Triangle = Triangle { triangleSide1 :: Double, triangleSide2 :: Double, triangleSide3 :: Double }
  deriving (Show, Eq)

data RegularPolygon = Poly { polySides :: Int , polySideLength :: Double }
  deriving (Show, Eq)


--typeclass
class Shape a where
  corners :: a -> Int
  circumference :: a -> Double
  surface :: a -> Double
  rescale :: Double -> a -> a

instance Shape Square where
  corners (Square squareSide) = 4
  circumference (Square squareSide) = 4 * squareSide
  surface (Square squareSide) = squareSide * squareSide
  rescale factor (Square squareSide) = Square (factor * squareSide)

instance Shape Rectangle where
  corners (Rect w h) = 4
  circumference (Rect w h) = 2 * (w + h)
  surface (Rect w h) = w * h
  rescale factor (Rect w h) = Rect (factor * w) (factor * h)

instance Shape Circle where
  corners _ = 0
  circumference (Circle r) = 2 * pi * r
  surface (Circle r) = pi * r * r
  rescale factor (Circle r) = Circle (factor * r)

-- Bonus
instance Shape Triangle where
  corners _ = 3
  circumference (Triangle l1 l2 l3) = l1 + l2 + l3
  surface (Triangle l1 l2 l3) = sqrt (s * (s - l1) * (s - l2) * (s - l3))
    where
      s = (l1 + l2 + l3) / 2
  rescale factor (Triangle l1 l2 l3) = Triangle (factor * l1) (factor * l2) (factor * l3)

-- NOTE: 'instance' takes a TYPE ctor (RegularPolygon) , whereas for the methods we pattern match of DATA (Poly) ctors


doubleSides :: Int -> Double
doubleSides sides = fromIntegral sides

instance Shape RegularPolygon where
  corners (Poly sides _) = sides
  circumference (Poly sides sideLength) = doubleSides sides * sideLength
  surface (Poly sides sideLength) = (doubleSides sides * sideLength * apothem) / 2
    where
      apothem = sideLength / (2 * tan (pi / doubleSides sides))
  rescale factor (Poly sides sideLength) = Poly sides (factor * sideLength)