Transform interface

The operations should be largely self-explanatory:

data Transform {- abstract type -}

 {- creators -}
combinedTr :: Translation -> Scaling -> Rotation -> Transform
generalTr  :: Double -> Double -> Double -> Double -> Translation -> Transform
idTr       :: Transform
transTr    :: Translation -> Transform
scaleTr    :: Scaling     -> Transform
rotateTr   :: Rotation    -> Transform

{- setter functions -}
addTranslation :: Transform -> Translation -> Transform
setTranslation :: Transform -> Translation -> Transform

addScaling :: Transform -> Scaling   -> Transform
setScaling :: Transform -> Scaling   -> Transform

addRotation :: Transform -> Rotation  -> Transform
setRotation :: Transform -> Rotation  -> Transform

combineTransforms :: Transform -> Transform -> Transform

 {- querying/getter functions -}
getScaling     :: Transform -> Scaling
getRotation    :: Transform -> Rotation
getTranslation :: Transform -> Translation
getUpperLeft   :: Transform -> (Double,Double,Double,Double)

detTransform    :: Transform -> Int
invertTransform :: Transform -> Transform

 {- predicates -}
hasRotation :: Transform -> Bool (see comments)
isIdentity  :: Transform -> Bool
isDetZero   :: Transform -> Bool