module Matrix (Matrix (..), Point, Vector, scale, invert, apply) where

type Point = (Float, Float)

type Vector = Point

data Matrix = Matrix (Float, Float) (Float, Float)
  deriving (Show)

scale :: Float -> Matrix -> Matrix
scale r (Matrix (a, b) (c, d)) = Matrix (r * a, r * b) (r * c, r * d)

invert :: Matrix -> Matrix
invert (Matrix (a, b) (c, d)) =
  scale
    (1 / (a * d - b * c))
    (Matrix (d, -b) (-c, a))

apply :: Matrix -> Vector -> Vector
apply (Matrix (a, b) (c, d)) (x, y) =
  ( a * x + b * y,
    c * x + d * y
  )