diff --git a/src/Diagrams/TwoD/Compile.hs b/src/Diagrams/TwoD/Compile.hs
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+++ b/src/Diagrams/TwoD/Compile.hs
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+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.TwoD.Compile
+-- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Functions to rewrite the RTree form of diagrams during backend rendering.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.TwoD.Compile
+       ( toOutput
+
+       ) where
+
+import Diagrams.Core
+import Diagrams.Core.Compile    (mapRTreeStyle)
+import Diagrams.Core.Types      (RTree)
+import Diagrams.TwoD.Arrow
+import Diagrams.TwoD.Attributes
+import Diagrams.TwoD.Size       (SizeSpec2D, sizePair)
+import Diagrams.TwoD.Types      (R2)
+
+-- | Take a getter, a setter, and two scaling terms, return a function
+-- that rewrites the given Measure-containing Attribute into Output
+-- units.  The scaling terms are from Normalized to Output and from
+-- Global to Output.
+modifyStyle :: AttributeClass a =>
+                 (a -> Measure Double) ->
+                 (Measure Double -> Style R2 -> Style R2) ->
+                 SizeSpec2D -> Double ->
+                 Style R2 -> Style R2
+modifyStyle get set outputSize gs sty = case getAttr sty of
+    Nothing -> sty
+    Just a  -> case get a of
+        Output _     -> sty
+        Normalized t -> set (Output $ sqrt (w*h) * t) sty where
+          (w,h) = sizePair outputSize
+        Local _      -> sty
+        Global t     -> set (Output $ gs * t) sty
+
+-- | Convert all of the @LineWidth@ attributes in an @RTree@ to output
+--   units. 'w' and 'h' are the width and height of the final diagram.
+--   The scaling factor is the geometric mean of 'h' and 'w'.
+toOutput :: SizeSpec2D -> Double -> RTree b R2 () -> RTree b R2 ()
+toOutput ns gs = mapRTreeStyle f
+  where
+    f = modifyStyle getLineWidth lineWidth ns gs .
+        modifyStyle getHeadSize headSize ns gs .
+        modifyStyle getTailSize tailSize ns gs