diff --git a/src/Data/NumIdr/Homogeneous.idr b/src/Data/NumIdr/Homogeneous.idr
index e91f466..16b4708 100644
--- a/src/Data/NumIdr/Homogeneous.idr
+++ b/src/Data/NumIdr/Homogeneous.idr
@@ -103,8 +103,9 @@ scalingH : {n : _} -> Num a => a -> HMatrix' n a
 scalingH x = indexSet [last,last] 1 $ repeatDiag x 0
 
 export
-translationH : {n : _} -> Num a => Vector n a -> HMatrix' n a
-translationH = hmatrix identity
+translationH : Num a => Vector n a -> HMatrix' n a
+translationH {n} v with (viewShape v)
+  _ | Shape [n] = hmatrix identity v
 
 export
 rotation2DH : Double -> HMatrix' 2 Double
diff --git a/src/Data/NumIdr/Transform/Point.idr b/src/Data/NumIdr/Transform/Point.idr
index fdb9f06..b7cdf95 100644
--- a/src/Data/NumIdr/Transform/Point.idr
+++ b/src/Data/NumIdr/Transform/Point.idr
@@ -27,6 +27,10 @@ export
 fromVector : Vector n a -> Point n a
 fromVector = MkPoint
 
+export
+toVector : Point n a -> Vector n a
+toVector = vec
+
 export
 point : Vect n a -> Point n a
 point = fromVector . vector
@@ -83,20 +87,22 @@ export
 
 
 --------------------------------------------------------------------------------
--- Interface implementations
+-- Arithmetic operations
 --------------------------------------------------------------------------------
 
 
-namespace Right
-  export
-  (+) : Num a => Point n a -> Vector n a -> Point n a
-  MkPoint a + b = MkPoint (zipWith (+) a b)
+-- Affine space operations
 
 namespace Left
   export
   (+) : Num a => Vector n a -> Point n a -> Point n a
   a + MkPoint b = MkPoint (zipWith (+) a b)
 
+namespace Right
+  export
+  (+) : Num a => Point n a -> Vector n a -> Point n a
+  MkPoint a + b = MkPoint (zipWith (+) a b)
+
 
 export
 (-) : Neg a => Point n a -> Point n a -> Vector n a
@@ -108,6 +114,39 @@ MkPoint a - MkPoint b = zipWith (-) a b
 --------------------------------------------------------------------------------
 
 
+export
+Zippable (Point n) where
+  zipWith f (MkPoint v1) (MkPoint v2) = MkPoint (zipWith f v1 v2)
+  zipWith3 f (MkPoint v1) (MkPoint v2) (MkPoint v3) = MkPoint (zipWith3 f v1 v2 v3)
+  unzipWith f (MkPoint v) = bimap MkPoint MkPoint (unzipWith f v)
+  unzipWith3 f (MkPoint v) = bimap MkPoint (bimap MkPoint MkPoint) (unzipWith3 f v)
+
+export
+Functor (Point n) where
+  map f (MkPoint v) = MkPoint (map f v)
+
+export
+{n : _} -> Applicative (Point n) where
+  pure = MkPoint . pure
+  MkPoint f <*> MkPoint v = MkPoint (f <*> v)
+
+{n : _} -> Monad (Point n) where
+  join (MkPoint v) = MkPoint $ join $ map unwrap v
+    where
+      unwrap : Point n a -> Vector n a
+      unwrap (MkPoint x) = x
+
+export
+Foldable (Point n) where
+  foldl f z (MkPoint v) = foldl f z v
+  foldr f z (MkPoint v) = foldr f z v
+  null (MkPoint v) = null v
+  toList (MkPoint v) = toList v
+
+export
+Traversable (Point n) where
+  traverse f (MkPoint v) = map MkPoint (traverse f v)
+
 export
 Show a => Show (Point n a) where
   showPrec d (MkPoint v) = showCon d "point " $
@@ -117,7 +156,6 @@ export
 Cast a b => Cast (Point n a) (Point n b) where
   cast (MkPoint v) = MkPoint (cast v)
 
-
 export
 Num a => Mult (Matrix m n a) (Point n a) (Point m a) where
   mat *. MkPoint v = MkPoint (mat *. v)
diff --git a/src/Data/NumIdr/Transform/Transform.idr b/src/Data/NumIdr/Transform/Transform.idr
new file mode 100644
index 0000000..0a0d594
--- /dev/null
+++ b/src/Data/NumIdr/Transform/Transform.idr
@@ -0,0 +1,78 @@
+module Data.NumIdr.Transform.Transform
+
+import Data.Vect
+import Data.NumIdr.Interfaces
+import Data.NumIdr.Array
+import Data.NumIdr.Vector
+import Data.NumIdr.Matrix
+import Data.NumIdr.Homogeneous
+import Data.NumIdr.Transform.Point
+
+public export
+data TransType = TAffine | TIsometry | TRigid | TTranslation
+               | TLinear | TOrthonormal | TRotation | TTrivial
+
+
+-- Lower numbers can be coerced to higher numbers
+toSignature : TransType -> (Fin 4, Bool)
+toSignature TAffine = (3, True)
+toSignature TIsometry = (2, True)
+toSignature TRigid = (1, True)
+toSignature TTranslation = (0, True)
+toSignature TLinear = (3, False)
+toSignature TOrthonormal = (2, False)
+toSignature TRotation = (1, False)
+toSignature TTrivial = (0, False)
+
+public export
+fromSignature : (Fin 4, Bool) -> TransType
+fromSignature (3, True) = TAffine
+fromSignature (2, True) = TIsometry
+fromSignature (1, True) = TRigid
+fromSignature (0, True) = TTranslation
+fromSignature (3, False) = TLinear
+fromSignature (2, False) = TOrthonormal
+fromSignature (1, False) = TRotation
+fromSignature (0, False) = TTrivial
+
+public export
+(:<) : TransType -> TransType -> Bool
+x :< y with (toSignature x, toSignature y)
+  _ | ((xn, xb), (yn, yb)) = (xn <= yn) && (xb >= yb)
+
+public export
+transMult : TransType -> TransType -> TransType
+transMult x y with (toSignature x, toSignature y)
+  _ | ((xn, xb), (yn, yb)) = fromSignature (max xn yn, xb && yb)
+
+public export
+linearize : TransType -> TransType
+linearize = fromSignature . mapSnd (const False) . toSignature
+
+export
+data Transform : TransType -> Nat -> Type -> Type where
+  MkTrans : (type : TransType) -> HMatrix' n a -> Transform type n a
+
+
+mulPoint : Num a => HMatrix' n a -> Point n a -> Point n a
+mulPoint m p = fromVector $ zipWith (+) (getMatrix m *. toVector p)
+                                        (getTranslationVector m)
+
+mulVector : Num a => HMatrix' n a -> Vector n a -> Vector n a
+mulVector m v = getMatrix m *. v
+
+export
+Num a => Mult (Transform type n a) (Point n a) (Point n a) where
+  MkTrans _ m *. p = mulPoint m p
+
+export
+Num a => Mult (Transform type n a) (Vector n a) (Vector n a) where
+  MkTrans _ m *. v = mulVector m v
+
+export
+Num a => Mult (Transform t1 n a) (Transform t2 n a) (Transform (transMult t1 t2) n a) where
+  MkTrans _ m1 *. MkTrans _ m2 = MkTrans _ (m1 *. m2)
+
+export
+{t2 : _} -> So (t1 :< t2) => Cast (Transform t1 n a) (Transform t2 n a) where
+  cast (MkTrans t1 m) = MkTrans t2 m