Add Direction type

src/Diagrams/Direction.hs

@@ -0,0 +1,54 @@
+{-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE RankNTypes                 #-}
+{-# LANGUAGE TypeFamilies               #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.Angle
+-- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Type for representing directions, polymorphic in vector space
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.Direction
+       ( Direction
+       , _Dir
+       , direction, fromDirection
+       ) where
+
+import Control.Lens
+import Data.AffineSpace
+import Data.VectorSpace
+
+import Diagrams.Angle
+
+--------------------------------------------------------------------------------
+-- Direction
+
+-- | A vector is described by a @Direction@ and a magnitude.  So we
+-- can think of a @Direction@ as a vector that has forgotten its
+-- magnitude.  @Direction@s can be used with 'fromDirection' and the
+-- lenses provided by its instances.
+data Direction v = Direction v
+
+-- | _Dir is provided to allow efficient implementations of functions
+-- in particular vector-spaces, but should be used with care as it
+-- exposes too much information.
+_Dir :: Iso' (Direction v) v
+_Dir = iso (\(Direction v) -> v) Direction
+
+-- | @direction v@ is the direction in which @v@ points.  Returns an
+--   unspecified value when given the zero vector as input.
+direction :: v -> Direction v
+direction = Direction
+
+-- | @fromDirection d@ is the unit vector in the direction @d@.
+fromDirection :: (InnerSpace v, Floating (Scalar v)) => Direction v -> v
+fromDirection (Direction v) = normalized v
+
+-- | compute the positive angle between the two directions in their common plane
+angleBetweenDirs  :: (InnerSpace v, Scalar v ~ Double) =>
+                     Direction v -> Direction v -> Angle
+angleBetweenDirs d1 d2 = angleBetween (fromDirection d1) (fromDirection d2)

src/Diagrams/Prelude.hs

@@ -88,6 +88,8 @@ module Diagrams.Prelude
        , module Diagrams.Angle
          -- | Convenience infix operators for working with coordinates.
        , module Diagrams.Coordinates
+         -- | Directions, distinguished from angles or vectors
+       , module Diagrams.Direction
 
          -- | A wide range of things (shapes, transformations,
          --   combinators) specific to creating two-dimensional
@@ -132,6 +134,7 @@ import           Diagrams.Combinators
 import           Diagrams.Coordinates
 import           Diagrams.CubicSpline
 import           Diagrams.Deform
+import           Diagrams.Direction
 import           Diagrams.Envelope
 import           Diagrams.Located
 import           Diagrams.Names