diff --git a/light.cabal b/light.cabal
--- a/light.cabal
+++ b/light.cabal
@@ -1,5 +1,5 @@
 name:                light
-version:             0.2.0.0
+version:             0.2.0.1
 synopsis:            a simple physics engine
 description:         A simple physics engine(dynamics only) with collision dection
 homepage:            https://github.com/suzumiyasmith/light#readme
@@ -34,6 +34,7 @@
                      , linear
                      , lens
                      , containers
+                     , QuickCheck
   ghc-options:         -threaded -rtsopts -with-rtsopts=-N
   default-language:    Haskell2010
 
diff --git a/src/Physics/Light.hs b/src/Physics/Light.hs
--- a/src/Physics/Light.hs
+++ b/src/Physics/Light.hs
@@ -5,6 +5,7 @@
 import GJK
 
 import Control.Lens
+import Control.Arrow
 import Control.Monad.Writer.Lazy
 import Data.Fixed
 import Data.Function
@@ -15,14 +16,13 @@
 data Object2D = Object2D
   { _position :: V3 Double
   , _velocity :: V3 Double
-  , _acceleration :: V3 Double
   , _shape :: [Convex]
   }
 
 makeLenses ''Object2D
 
 instance Show Object2D where
-  show o = show (o ^. position, o ^. velocity, o ^. acceleration)
+  show o = show (o ^. position, o ^. velocity)
 
 type PhysicsWorld = (IM.IntMap Object2D, Int)
 
@@ -37,12 +37,11 @@
 addObjects [] w = w
 
 update :: Double -> IM.IntMap Object2D -> IM.IntMap Object2D
-update dt = fmap w
-  where
-    w :: Object2D -> Object2D
-    w o = o
+update dt = fmap $ updateObject2D dt
+
+updateObject2D :: Double -> Object2D -> Object2D
+updateObject2D dt o = o
       & position %~ (+ o ^. velocity ^* dt)
-      & velocity %~ (+ o ^. acceleration ^* dt)
       & position .  _z %~ (`mod'` (2 * pi))
 
 detectCollision :: IM.IntMap Object2D -> [(Int, Int)]
@@ -81,3 +80,9 @@
 
 rotateMatrix2D :: Double -> V2 (V2 Double)
 rotateMatrix2D r = V2 (V2 (cos r) (-sin r)) (V2 (sin r) (cos r))
+
+worldToLocal :: V3 Double -> V3 Double -> V3 Double
+worldToLocal o = (flip (-) o) >>> (_xy %~ (rotateMatrix2D (o ^. _z) !*))
+
+localToWorld :: V3 Double -> V3 Double -> V3 Double
+localToWorld o = (+ o) <<< (_xy %~ (rotateMatrix2D (- o ^. _z) !*))
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -1,24 +1,32 @@
 import Control.Lens
 import Control.Arrow
-import qualified Data.IntMap.Lazy as IM
+import Control.Monad
 import Linear
 import Physics.Light
+import Test.QuickCheck
 
 main :: IO ()
 main = do
   print $ (detectCollision . fst) <$> (updateTest <$> [1 .. 1000] <*> [testWorld1, testWorld2])
+  quickCheck (\(o, w) -> 0.00001 > norm (worldToLocal o (localToWorld o w) - w))
 
+instance Arbitrary a => Arbitrary (V3 a) where
+  arbitrary = liftM3 V3 arbitrary arbitrary arbitrary
+  shrink v = [ v & _x .~ x'  | x' <- shrink $ v ^. _x ]
+    ++ [ v & _y .~ y' | y' <- shrink $ v ^. _y ]
+    ++ [ v & _z .~ z' | z' <- shrink $ v ^. _z ]
+
 testShape1 = [circle 1, ellipse 0.5 3]
 
 testShape2 = polygon $ V2 <$> [-1, 1] <*> [-1, 1]
 
-o1 = Object2D 0 (V3 0 0 1) 0 testShape1
+o1 = Object2D 0 (V3 0 0 1) testShape1
 
-o2 = Object2D (V3 1.5 0 0) (V3 0 0 0) 0 [testShape2]
+o2 = Object2D (V3 1.5 0 0) (V3 0 0 0) [testShape2]
 
-o3 = Object2D (V3 (-1.5) 0 0) (V3 0 0 0) 0 [testShape2]
+o3 = Object2D (V3 (-1.5) 0 0) (V3 0 0 0) [testShape2]
 
-o4 = Object2D (V3 (-1.5) 0 0) (V3 1 0 0) 0 [testShape2]
+o4 = Object2D (V3 (-1.5) 0 0) (V3 1 0 0) [testShape2]
 
 testWorld1 = newPhysicsWorld & addObjects [o1, o2, o3]
 testWorld2 = newPhysicsWorld & addObjects [o1, o3, o4]