diff --git a/src/Data/AffineSpace/Point.hs b/src/Data/AffineSpace/Point.hs
--- a/src/Data/AffineSpace/Point.hs
+++ b/src/Data/AffineSpace/Point.hs
@@ -1,9 +1,8 @@
-{-# LANGUAGE TypeFamilies
-           , MultiParamTypeClasses
-           , FlexibleInstances
-           , DeriveFunctor
-           , DeriveDataTypeable
-  #-}
+{-# LANGUAGE DeriveDataTypeable    #-}
+{-# LANGUAGE DeriveFunctor         #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TypeFamilies          #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.AffineSpace.Point
@@ -18,17 +17,19 @@
 
 module Data.AffineSpace.Point
        ( -- * Points
-
-         Point(..), unPoint, origin, (*.)
+         Point(..), unPoint, origin, (*.), mirror,
 
+         -- * Reflection through a point
+         relative, relative2, relative3,
+         reflectThrough,
        ) where
 
-import Data.VectorSpace
-import Data.AffineSpace
+import           Data.AffineSpace
+import           Data.VectorSpace
 
-import Control.Newtype
-import Data.Data (Data)
-import Data.Typeable (Typeable)
+import           Control.Newtype
+import           Data.Data        (Data)
+import           Data.Typeable    (Typeable)
 
 ------------------------------------------------------------
 --  Points  ------------------------------------------------
@@ -66,3 +67,23 @@
 -- | Scale a point by a scalar.
 (*.) :: VectorSpace v => Scalar v -> Point v -> Point v
 s *. P v = P (s *^ v)
+
+-- | Reflect a point through the 'origin'.
+mirror :: AdditiveGroup v => Point v -> Point v
+mirror = reflectThrough origin
+
+-- | Apply a transformation relative to the given point.
+relative :: AffineSpace p => p -> (Diff p -> Diff p) -> p -> p
+relative p f = (p .+^) . f . (.-. p)
+
+-- | Apply a transformation relative to the given point.
+relative2 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p) -> p -> p -> p
+relative2 p f x y = (p .+^) $ f (inj x) (inj y) where inj = (.-. p)
+
+-- | Apply a transformation relative to the given point.
+relative3 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p -> Diff p) -> p -> p -> p -> p
+relative3 p f x y z = (p .+^) $ f (inj x) (inj y) (inj z) where inj = (.-. p)
+
+-- | Mirror a point through a given point.
+reflectThrough :: AffineSpace p => p -> p -> p
+reflectThrough o = relative o negateV
diff --git a/vector-space-points.cabal b/vector-space-points.cabal
--- a/vector-space-points.cabal
+++ b/vector-space-points.cabal
@@ -1,5 +1,5 @@
 name:                vector-space-points
-version:             0.1.2.1
+version:             0.1.3
 synopsis:            A type for points, as distinct from vectors.
 description:         A type for points, as distinct from vectors, built on top
                      of Data.AffineSpace.