module Shape where

triangleArea :: Point -> Point -> Point -> Double
triangleArea p1 p2 p3
    | firstSide + secondSide >= thirdSide && firstSide + thirdSide >= secondSide && secondSide + thirdSide >= firstSide = ((x p1) * ((y p2) - (y p3)) + (x p2) * ((y p3) - (y p1)) + (x p3) * ((y p1) - (y p2))) / 2
    | otherwise = 0
    where
        firstSide = sqrt(((x p2) - (x p1))^2 + ((y p2) - (y p1))^2)
        secondSide = sqrt(((x p3) - (x p2))^2 + ((y p3) - (y p2))^2)
        thirdSide = sqrt(((x p3) - (x p1))^2 + ((y p3) - (y p1))^2)

minx :: Point -> Point -> Point -> Double
minx a b c = min (min (x a) (x b)) (x c)

maxx :: Point -> Point -> Point -> Double
maxx a b c = max (max (x a) (x b)) (x c)

miny :: Point -> Point -> Point -> Double
miny a b c = min (min (y a) (y b)) (y c)

maxy :: Point -> Point -> Point -> Double
maxy a b c = max (max (y a) (y b)) (y c)

data Point = Point { x :: Double, y :: Double } deriving (Show)

-- Rectangles

data Rectangle = Rectangle { p1 :: Point, p2 :: Point } deriving (Show)

-- Circles

data Circle = Circle { m :: Point, r :: Double } deriving (Show)

-- Triangles

data Triangle = Triangle { a :: Point, b :: Point, c :: Point } deriving (Show)

class Area a where
    area :: a -> Double

instance Area Rectangle where
    area (Rectangle p1 p2) = ((x p2) - (x p1)) * ((y p2) - (y p1))

instance Area Circle where
    area (Circle m r) = pi * r * r

instance Area Triangle where
    area (Triangle a b c) = triangleArea a b c

class (Area a) => BoundingBox a where
    bbox :: a -> Rectangle

instance BoundingBox Rectangle where
    bbox (Rectangle p1 p2) = Rectangle { p1 = p1 , p2 = p2 }

instance BoundingBox Circle where
    bbox (Circle m r) = Rectangle { p1 = Point {x = ((x m) - r) , y = ((y m) - r)} , p2 = Point {x = ((x m) + r) , y = ((y m) + r)}}

instance BoundingBox Triangle where
    bbox (Triangle a b c) = Rectangle { p1 = Point {x = (minx a b c) , y = (miny a b c)} , p2 = Point {x = (maxx a b c) , y = (maxy a b c)}}

pa = Point { x = 20, y = 10 }
pb = Point { x = 30, y = 30 }
pc = Point { x = 50, y = 15 }
box = Rectangle { p1 = pa, p2 = pb }
circle = Circle { m = pa, r = 10 }
triangle = Triangle { a = pa, b = pb, c = pc }

main = do
    print(area box)
    print(area circle)
    print(area triangle)
    print(bbox box)
    print(bbox circle)
    print(bbox triangle)