```{-# LANGUAGE BangPatterns   #-}
{-# LANGUAGE PackageImports #-}
module Reanimate.Transform
( identity
, transformPoint
, mkMatrix
, toTransformation
) where

-- XXX: Use Linear.Matrix instead of Data.Matrix to drop the 'matrix' dependency.
import           Data.List
import           "matrix" Data.Matrix (Matrix)
import qualified "matrix" Data.Matrix as M
import           Data.Maybe
import           Graphics.SvgTree
import           Linear.V2

type TMatrix = Matrix Coord

identity :: TMatrix
identity = M.identity 3

fromList :: [Coord] -> TMatrix
fromList [a,b,c,d,e,f] = M.fromList 3 3 [a,c,e,b,d,f,0,0,1]
fromList _             = error "Reanimate.Transform.fromList: bad input"

transformPoint :: TMatrix -> RPoint -> RPoint
transformPoint m (V2 x y) = V2 (a*x +c*y + e) (b*x + d*y +f)
where
!a = M.unsafeGet 1 1 m
!c = M.unsafeGet 1 2 m
!e = M.unsafeGet 1 3 m
!b = M.unsafeGet 2 1 m
!d = M.unsafeGet 2 2 m
!f = M.unsafeGet 2 3 m
-- (a:c:e:b:d:f:_) = M.toList m

mkMatrix :: Maybe [Transformation] -> TMatrix
mkMatrix Nothing   = identity
mkMatrix (Just ts) = foldl' (*) identity (map transformationMatrix ts)

transformationMatrix :: Transformation -> TMatrix
transformationMatrix transformation =
case transformation of
TransformMatrix a b c d e f -> fromList [a,b,c,d,e,f]
Translate x y               -> translate x y
Scale sx mbSy               -> fromList [sx,0,0,fromMaybe sx mbSy,0,0]
Rotate a Nothing            -> rotate a
Rotate a (Just (x,y))       -> translate x y * rotate a * translate (-x) (-y)
SkewX a                     -> fromList [1,0,tan (a*pi/180),1,0,0]
SkewY a                     -> fromList [1,tan (a*pi/180),0,1,0,0]
TransformUnknown            -> identity
where
translate x y = fromList [1,0,0,1,x,y]
rotate a = fromList [cos r,sin r,-sin r,cos r,0,0]
where r = a * pi / 180

toTransformation :: TMatrix -> Transformation
toTransformation m = TransformMatrix a b c d e f
where
[a,c,e,b,d,f,_,_,_] = M.toList m
```