Coordinate lenses for R2, P2, R3, P3, using type classes

src/Diagrams/Coordinates.hs

@@ -18,7 +18,11 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Coordinates
-    ( (:&)(..), Coordinates(..) )
+    ( (:&)(..), Coordinates(..)
+
+    -- * Lenses for particular axes
+    , HasX(..), HasY(..), HasZ(..)
+    )
     where
 
 import           Diagrams.Core.Points
@@ -104,3 +108,12 @@ instance Coordinates v => Coordinates (Point v) where
 
   x & y        = P (x & y)
   coords (P v) = coords v
+
+class HasX t where
+    _x :: Functor f => (Double -> f Double) -> t -> f t
+
+class HasY t where
+    _y :: Functor f => (Double -> f Double) -> t -> f t
+
+class HasZ t where
+    _z :: Functor f => (Double -> f Double) -> t -> f t

src/Diagrams/ThreeD/Types.hs

@@ -40,7 +40,7 @@ module Diagrams.ThreeD.Types
        ) where
 
 import           Control.Applicative
-import           Control.Lens           (Iso', iso, over)
+import           Control.Lens           (Iso', iso, over, _1, _2, _3)
 
 import           Diagrams.Coordinates
 import           Diagrams.Core
@@ -99,10 +99,13 @@ type P3 = Point R3
 p3 :: (Double, Double, Double) -> P3
 p3 = P . R3
 
--- | Convert a 2D point back into a triple of coordinates.
+-- | Convert a 3D point back into a triple of coordinates.
 unp3 :: P3 -> (Double, Double, Double)
 unp3 = unR3 . unPoint
 
+p3Iso :: Iso' P3 (Double, Double, Double)
+p3Iso = iso unp3 p3
+
 -- | Transformations in R^3.
 type T3 = Transformation R3
 
@@ -149,3 +152,21 @@ instance (Angle a) => Direction (Spherical a) where
 -- intermediate type would be ambiguous.
 asSpherical :: Spherical Turn -> Spherical Turn
 asSpherical = id
+
+instance HasX R3 where
+    _x = r3Iso . _1
+
+instance HasX P3 where
+    _x = p3Iso . _1
+
+instance HasY R3 where
+    _y = r3Iso . _2
+
+instance HasY P3 where
+    _y = p3Iso . _2
+
+instance HasZ R3 where
+    _z = r3Iso . _3
+
+instance HasZ P3 where
+    _z = p3Iso . _3

src/Diagrams/TwoD/Types.hs

@@ -20,8 +20,8 @@
 
 module Diagrams.TwoD.Types
        ( -- * 2D Euclidean space
-         R2(..), r2, unr2
-       , P2, p2, unp2
+         R2(..), r2, unr2, r2Iso
+       , P2, p2, unp2, p2Iso
        , T2
 
          -- * Angles
@@ -40,7 +40,7 @@ import           Data.NumInstances.Tuple ()
 import           Data.VectorSpace
 
 import           Data.Typeable
-
+import           Control.Lens           (Iso', iso, _1, _2)
 ------------------------------------------------------------
 -- 2D Euclidean space
 
@@ -151,6 +151,15 @@ instance Coordinates R2 where
   x & y           = R2 x y
   coords (R2 x y) = x :& y
 
+r2Iso :: Iso' R2 (Double, Double)
+r2Iso = iso unr2 r2
+
+instance HasX R2 where
+    _x = r2Iso . _1
+
+instance HasY R2 where
+    _y = r2Iso . _2
+
 -- | Points in R^2.  This type is intentionally abstract.
 --
 --   * To construct a point, use 'p2', or '&' (see
@@ -190,6 +199,14 @@ type T2 = Transformation R2
 instance Transformable R2 where
   transform = apply
 
+p2Iso :: Iso' P2 (Double, Double)
+p2Iso = iso unp2 p2
+
+instance HasX P2 where
+    _x = p2Iso . _1
+
+instance HasY P2 where
+    _y = p2Iso . _2
 ------------------------------------------------------------
 -- Angles