{-# LANGUAGE TypeOperators, TypeSynonymInstances #-}

module Transformable ( Coord
                     , Vector3
                     , Transform
                     , Transformable(..)
                     , translate
                     , rotate
                     , scale
                     ) where

import Data.LinearMap

type Coord = Double

type Vector3 = (Coord, Coord, Coord)
type Transform = Vector3 :-* Vector3

class Transformable a where
  (><) :: Transform -> a -> a

instance Transformable Transform where
  t1 >< t2 = t1 *.* t2

instance Transformable Vector3 where
  t >< v = t `lapply` v

translate :: Coord -> Coord -> Transform
translate dx dy = linear $ \(x, y, w) -> (x + w*dx, y + w*dy, w)

rotate :: Coord -> Transform
rotate a = linear $ \(x, y, w) -> (c*x - s*y, s*x + c*y, w) where
  c = cos a
  s = sin a

scale :: Coord -> Transform
scale s = linear $ \(x, y, w) -> (s*y, s*y, w)