```{-# LANGUAGE FlexibleContexts
, TypeFamilies
#-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Diagrams.TwoD.Vector
--
-- Two-dimensional vectors.
--
-----------------------------------------------------------------------------
module Diagrams.TwoD.Vector
( -- * Special 2D vectors
unitX, unitY, unit_X, unit_Y

-- * Converting between vectors and angles
, direction, fromDirection,  e
) where

import Diagrams.TwoD.Types

-- | The unit vector in the positive X direction.
unitX :: R2
unitX = (1,0)

-- | The unit vector in the positive Y direction.
unitY :: R2
unitY = (0,1)

-- | The unit vector in the negative X direction.
unit_X :: R2
unit_X = (-1,0)

-- | The unit vector in the negative Y direction.
unit_Y :: R2
unit_Y = (0,-1)

-- | Compute the direction of a vector, measured counterclockwise from
--   the positive x-axis as a fraction of a full turn.  The zero
--   vector is arbitrarily assigned the direction 0.
direction :: Angle a => R2 -> a
direction (x,y) = convertAngle . Rad \$ atan2 y x

-- | Convert an angle into a unit vector pointing in that direction.
fromDirection :: Angle a => a -> R2
fromDirection a = (cos a', sin a')
where Rad a' = convertAngle a

-- | A convenient synonym for 'fromDirection'.
e :: Angle a => a -> R2
e = fromDirection
```