diff --git a/src/Diagrams/Backend/Show.hs b/src/Diagrams/Backend/Show.hs
index 52b0429f..51b605f1 100644
--- a/src/Diagrams/Backend/Show.hs
+++ b/src/Diagrams/Backend/Show.hs
@@ -19,6 +19,7 @@
 module Diagrams.Backend.Show where
 
 import Diagrams.Prelude
+import Diagrams.Core.Transform (onBasis)
 
 import Data.Basis
 
@@ -46,14 +47,8 @@ instance Monoid (Render ShowBackend v) where
 renderTransf :: forall v. (Num (Scalar v), HasLinearMap v, Show (Scalar v))
              => Transformation v -> Doc
 renderTransf t = renderMat mat
-  where tr :: v
-        tr    = transl t
-        basis :: [Basis v]
-        basis = map fst (decompose tr)
-        es :: [v]
-        es    = map basisValue basis
-        vmat :: [v]
-        vmat = map (apply t) es
+  where vmat :: [v]
+        (vmat, _) = onBasis t
         mat :: [[Scalar v]]
         mat = map decompV vmat
 --        mat' :: [[Scalar v]]
diff --git a/src/Diagrams/TwoD/Transform.hs b/src/Diagrams/TwoD/Transform.hs
index f61ab8f8..b4ee3d77 100644
--- a/src/Diagrams/TwoD/Transform.hs
+++ b/src/Diagrams/TwoD/Transform.hs
@@ -48,9 +48,12 @@ module Diagrams.TwoD.Transform
          -- * Scale invariance
        , ScaleInv(..), scaleInv
 
+         -- * component-wise
+       , onBasis
        ) where
 
 import Diagrams.Core
+import qualified Diagrams.Core.Transform as T
 
 import Control.Newtype (over)
 
@@ -308,3 +311,10 @@ instance (V t ~ R2, Transformable t) => Transformable (ScaleInv t) where
       rot = rotateAbout l angle
       l'  = transform tr l
       trans = translate (l' .-. l)
+
+-- | Get the matrix equivalent of the linear transform,
+--   (as a pair of columns) and the translation vector.  This
+--   is mostly useful for implementing backends.
+onBasis :: Transformation R2 -> ((R2, R2), R2)
+onBasis t = ((x, y), v)
+  where ((x:y:[]), v) = T.onBasis t