Wall: add instances for Polar

move some instances around,
remove some imports

src/Diagrams/Direction.hs

@@ -16,10 +16,10 @@ module Diagrams.Direction
        ( Direction
        , _Dir
        , direction, fromDirection
+       , angleBetweenDirs
        ) where
 
 import Control.Lens
-import Data.AffineSpace
 import Data.VectorSpace
 
 import Diagrams.Angle

src/Diagrams/TwoD/Arc.hs

@@ -32,7 +32,7 @@ import           Diagrams.Trail
 import           Diagrams.TrailLike
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (e, unitX, unitY, unit_Y, xDir)
+import           Diagrams.TwoD.Vector    (unitX, unitY, unit_Y, xDir)
 import           Diagrams.Util           (( # ))
 
 import           Control.Lens            ((^.))
@@ -98,7 +98,7 @@ arcT start sweep
     | sweep < zeroV = arcT start (sweep ^-^ (fromIntegral d @@ turn))
     | otherwise     = (if sweep >= fullTurn then glueTrail else id)
                     $ trailFromSegments bs
-  where end = start .+^ sweep
+  where
         bs    = map (rotate $ start .-. xDir) . bezierFromSweep $ sweep
         d      = floor (sweep^.turn) :: Integer
 
@@ -175,7 +175,6 @@ arcBetween p q ht = trailLike (a # rotate (v^._theta) # moveTo p)
     mid | ht >= 0    = direction unitY
         | otherwise  = direction unit_Y
     st  = mid .-^ th
-    end = mid .+^ th
     a | isStraight
       = fromOffsets [d *^ unitX]
       | otherwise

src/Diagrams/TwoD/Arrowheads.hs

@@ -54,7 +54,7 @@ module Diagrams.TwoD.Arrowheads
        , ArrowHT
        ) where
 
-import           Control.Lens            ((&), (.~), (^.), (%~), (-~), (+~))
+import           Control.Lens            ((&), (.~), (^.))
 import           Data.AffineSpace
 import           Data.Default.Class
 import           Data.Monoid             (mempty, (<>))
@@ -76,7 +76,7 @@ import           Diagrams.TwoD.Polygons
 import           Diagrams.TwoD.Shapes
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (e, unitX, unit_X, xDir)
+import           Diagrams.TwoD.Vector    (e, unit_X, xDir)
 import           Diagrams.Util           (( # ))
 
 -----------------------------------------------------------------------------

src/Diagrams/TwoD/Combinators.hs

@@ -18,7 +18,7 @@ module Diagrams.TwoD.Combinators
     (
       -- * Binary combinators
 
-      (===), (|||), atAngle
+      (===), (|||), atDirection
 
       -- * n-ary combinators
     , hcat, hcat'
@@ -45,7 +45,6 @@ import           Data.VectorSpace
 
 import           Diagrams.Core
 
-import           Diagrams.Angle
 import           Diagrams.BoundingBox
 import           Diagrams.Combinators
 import           Diagrams.Coordinates

src/Diagrams/TwoD/Ellipse.hs

@@ -22,8 +22,6 @@ module Diagrams.TwoD.Ellipse
     , ellipseXY
     ) where
 
-import           Data.AdditiveGroup
-
 import           Diagrams.Core
 
 import           Diagrams.Angle
@@ -32,7 +30,7 @@ import           Diagrams.TrailLike
 import           Diagrams.TwoD.Arc
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector
+import           Diagrams.TwoD.Vector    (xDir)
 import           Diagrams.Util
 
 -- | A circle of radius 1, with center at the origin.

src/Diagrams/TwoD/Transform/ScaleInv.hs

@@ -21,7 +21,6 @@ module Diagrams.TwoD.Transform.ScaleInv
     where
 
 import           Control.Lens            (makeLenses, view)
-import           Data.AdditiveGroup
 import           Data.AffineSpace        ((.-.))
 import           Data.Semigroup
 import           Data.Typeable
@@ -30,7 +29,6 @@ import           Diagrams.Angle
 import           Diagrams.Core
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector
 
 -- | The @ScaleInv@ wrapper creates two-dimensional /scale-invariant/
 --   objects.  Intuitively, a scale-invariant object is affected by

src/Diagrams/TwoD/Types.hs

@@ -28,13 +28,15 @@ module Diagrams.TwoD.Types
        ) where
 
 import           Control.Lens           (Iso', Rewrapped, Wrapped (..), iso,
-                                         lens, (^.), _1, _2)
+                                         (^.), (&), (<>~), _1, _2)
+
 
 import           Diagrams.Angle
 import           Diagrams.Direction
 import           Diagrams.Coordinates
 import           Diagrams.Core
 
+import           Data.AffineSpace
 import           Data.AffineSpace.Point
 import           Data.Basis
 import           Data.MemoTrie          (HasTrie (..))
@@ -182,11 +184,10 @@ instance HasY R2 where
     _y = r2Iso . _2
 
 instance HasTheta R2 where
-    _theta = lens (\v -> atanA (v^._y / v^._x))
-      (\v θ -> let r = magnitude v in R2 (r * cosA θ) (r * sinA θ))
+    _theta = polar._2
 
 instance HasR R2 where
-    _r = lens magnitude (\v r -> let s = r/magnitude v in s *^ v)
+    _r = polar._1
 
 instance HasTheta (Direction R2) where
     _theta = _Dir . _theta
@@ -252,3 +253,16 @@ instance HasTheta P2 where
 -- | Types which can be expressed in polar 2D coordinates, as a magnitude and an angle.
 class Polar t where
     polar :: Iso' t (Double, Angle)
+
+instance Polar R2 where
+    polar =
+        iso (\v -> ( magnitude v, atanA (v^._y / v^._x)))
+            (\(r,θ) -> R2 (r * cosA θ) (r * sinA θ))
+
+instance Polar P2 where
+    polar = _relative origin . polar
+
+instance AffineSpace (Direction R2) where
+    type Diff (Direction R2) = Angle
+    a .-. b = a^._theta ^-^ b^._theta
+    a .+^ θ = a & _theta <>~ θ

src/Diagrams/TwoD/Vector.hs

@@ -23,9 +23,8 @@ module Diagrams.TwoD.Vector
        , perp, leftTurn
        ) where
 
-import           Control.Lens         ((^.), (&), (<>~))
-import           Data.VectorSpace
 import           Data.AffineSpace
+import           Data.VectorSpace
 
 import           Diagrams.Angle
 import           Diagrams.Direction
@@ -48,11 +47,6 @@ unit_X = (-1) ^& 0
 unit_Y :: R2
 unit_Y = 0 ^& (-1)
 
-instance AffineSpace (Direction R2) where
-    type Diff (Direction R2) = Angle
-    a .-. b = a^._theta ^-^ b^._theta
-    a .+^ θ = a & _theta <>~ θ
-
 -- | The origin of the direction AffineSpace.  For all d, @d .-. xDir
 -- = d^._theta@.
 xDir :: Direction R2