module Shape
        ( Shape
        , area
        , square
        , circle
        )
where

data Shape = Rectangle Side Side
           | Ellipse Radius Radius
           | RtTriangle Side Side
           | Polygon [Vertex]
  deriving Show

type Radius = Float
type Side = Float
type Vertex = (Float, Float)

area :: Shape -> Float
area (Rectangle  s1 s2) = s1 * s2
area (RtTriangle s1 s2) = s1 * s2 / 2

square :: Side -> Shape
square s = Rectangle s s

circle :: Radius -> Shape
circle r = Ellipse r r

rectangle :: Side -> Side -> Shape
rectangle s1 s2 = Polygon [(x, y), (-x, y), (-x, -y), (x, -y)]
    where
        x = s1 / 2
        y = s2 / 2

rtTriangle :: Side -> Side -> Shape
rtTriangle s1 s2 = Polygon [(0, 0), (s1, 0), (0, s2)]

regularPolygon :: Int -> Side -> Shape
regularPolygon n s =
        let
                angleinc = (pi * 2) / fromIntegral n
                radius   = (s * sin ((pi - angleinc) / 2)) / (sin angleinc)
                regularVerts 0 _ = []
                regularVerts n angle =
                        (radius * cos angle, radius * sin angle) : regularVerts
                                (n - 1)
                                (angle + angleinc)
        in
                Polygon (regularVerts n 0)