diff --git a/src/Data/NumIdr/Homogeneous.idr b/src/Data/NumIdr/Homogeneous.idr
index 87f5a39..a40fe7f 100644
--- a/src/Data/NumIdr/Homogeneous.idr
+++ b/src/Data/NumIdr/Homogeneous.idr
@@ -27,7 +27,7 @@ public export
 HMatrix' : Nat -> Type -> Type
 HMatrix' n = HMatrix n n
 
-||| An `n`-dimensional homogeneous vector type.
+||| An homogeneous vector type.
 |||
 ||| Homogeneous vectors are vectors intended to be multiplied with homogeneous
 ||| matrices (see `HMatrix`). They have an extra dimension compared to regular
@@ -129,6 +129,7 @@ translationH : Num a => Vector n a -> HMatrix' n a
 translationH {n} v with (viewShape v)
   _ | Shape [n] = hmatrix identity v
 
+
 ||| Construct a 2D homogeneous matrix that rotates by the given angle (in radians).
 export
 rotate2DH : Double -> HMatrix' 2 Double
@@ -148,3 +149,20 @@ rotate3DYH = matrixToH . rotate3DY
 export
 rotate3DZH : Double -> HMatrix' 3 Double
 rotate3DZH = matrixToH . rotate3DZ
+
+
+export
+reflectH : {n : _} -> Neg a => Fin n -> HMatrix' n a
+reflectH i = indexSet [weaken i,weaken i] (-1) identity
+
+export
+reflectXH : {n : _} -> Neg a => HMatrix' (1 + n) a
+reflectXH = reflectH 0
+
+export
+reflectYH : {n : _} -> Neg a => HMatrix' (2 + n) a
+reflectYH = reflectH 0
+
+export
+reflectZH : {n : _} -> Neg a => HMatrix' (3 + n) a
+reflectZH = reflectH 0
diff --git a/src/Data/NumIdr/Interfaces.idr b/src/Data/NumIdr/Interfaces.idr
index f6a3fc1..37c12e8 100644
--- a/src/Data/NumIdr/Interfaces.idr
+++ b/src/Data/NumIdr/Interfaces.idr
@@ -31,7 +31,6 @@ export
 FieldCmp Double where
   abslt = (<) `on` abs
 
-
 -- Alternative implementations of `Eq` and `FieldCmp` that compare floating
 -- point numbers approximately, useful when working with transforms
 namespace Eq
diff --git a/src/Data/NumIdr/Matrix.idr b/src/Data/NumIdr/Matrix.idr
index 7cace16..1f5753f 100644
--- a/src/Data/NumIdr/Matrix.idr
+++ b/src/Data/NumIdr/Matrix.idr
@@ -96,6 +96,23 @@ rotate3DZ : Double -> Matrix' 3 Double
 rotate3DZ a = matrix [[cos a, - sin a, 0], [sin a, cos a, 0], [0,0,1]]
 
 
+export
+reflect : {n : _} -> Neg a => Fin n -> Matrix' n a
+reflect i = indexSet [i, i] (-1) (repeatDiag 1 0)
+
+export
+reflectX : {n : _} -> Neg a => Matrix' (1 + n) a
+reflectX = reflect 0
+
+export
+reflectY : {n : _} -> Neg a => Matrix' (2 + n) a
+reflectY = reflect 1
+
+export
+reflectZ : {n : _} -> Neg a => Matrix' (3 + n) a
+reflectZ = reflect 2
+
+
 --------------------------------------------------------------------------------
 -- Indexing
 --------------------------------------------------------------------------------
@@ -225,6 +242,14 @@ trace : Num a => Matrix m n a -> a
 trace = sum . diagonal'
 
 
+||| Construct a matrix that reflects a vector along a hyperplane of the
+||| given normal vector. The input does not have to be a unit vector.
+export
+reflectNormal : (Neg a, Fractional a) => Vector n a -> Matrix' n a
+reflectNormal {n} v with (viewShape v)
+  _ | Shape [n] = repeatDiag 1 0 - (2 / normSq v) *. outer v v
+
+
 --------------------------------------------------------------------------------
 -- Matrix multiplication
 --------------------------------------------------------------------------------
diff --git a/src/Data/NumIdr/Transform/Orthonormal.idr b/src/Data/NumIdr/Transform/Orthonormal.idr
index 9209dca..263e04b 100644
--- a/src/Data/NumIdr/Transform/Orthonormal.idr
+++ b/src/Data/NumIdr/Transform/Orthonormal.idr
@@ -40,7 +40,7 @@ fromMatrix mat = if isOrthonormal' mat then Just (unsafeMkTrans (matrixToH mat))
 ||| Construct an orthonormal transform that reflects a particular coordinate.
 export
 reflect : {n : _} -> Neg a => Fin n -> Orthonormal n a
-reflect i = unsafeMkTrans $ indexSet [weaken i,weaken i] (-1) identity
+reflect = unsafeMkTrans . reflectH
 
 ||| The orthonormal transform that reflects on the x-coordinate (first coordinate).
 export
diff --git a/src/Data/NumIdr/Transform/Rotation.idr b/src/Data/NumIdr/Transform/Rotation.idr
index 7ed18be..34b8fe2 100644
--- a/src/Data/NumIdr/Transform/Rotation.idr
+++ b/src/Data/NumIdr/Transform/Rotation.idr
@@ -25,6 +25,7 @@ isRotation' : FieldCmp a => Matrix' n a -> Bool
 isRotation' mat = isOrthonormal' mat && det mat == 1
 
 ||| Try to constuct a rotation from a matrix.
+export
 fromMatrix : FieldCmp a => Matrix' n a -> Maybe (Rotation n a)
 fromMatrix mat = if isRotation' mat then Just (unsafeMkTrans $ matrixToH mat)
                                     else Nothing
@@ -35,6 +36,11 @@ isRotation : FieldCmp a => HMatrix' n a -> Bool
 isRotation {n} mat with (viewShape mat)
   _ | Shape [S n, S n] = isHMatrix mat && all (==0) (mat !!.. [EndBound last, One last])
 
+export
+fromHMatrix : FieldCmp a => HMatrix' n a -> Maybe (Rotation n a)
+fromHMatrix mat = if isRotation mat then Just (unsafeMkTrans mat)
+                                    else Nothing
+
 ||| Construct a 2D rotation that rotates by the given angle (in radians).
 export
 rotate2D : Num a => Double -> Rotation 2 Double