{-# LANGUAGE DeriveFunctor #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE UndecidableInstances #-} ----------------------------------------------------------------------------- -- | -- Module : Diagrams.Direction -- Copyright : (c) 2014 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, dir, fromDirection, fromDir , angleBetweenDirs , dirBetween ) where import Control.Lens (Iso', iso) import Diagrams.Angle import Diagrams.Core import Linear.Affine import Linear.Vector import Linear.Metric -------------------------------------------------------------------------------- -- 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. newtype Direction v n = Dir (v n) deriving (Read, Show, Eq, Ord, Functor) -- todo: special instances type instance V (Direction v n) = v type instance N (Direction v n) = n instance (V (v n) ~ v, N (v n) ~ n, Transformable (v n)) => Transformable (Direction v n) where transform t (Dir v) = Dir (transform t v) instance HasTheta v => HasTheta (Direction v) where _theta = _Dir . _theta instance HasPhi v => HasPhi (Direction v) where _phi = _Dir . _phi -- | _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 n) (v n) _Dir = iso (\(Dir v) -> v) Dir -- | @direction v@ is the direction in which @v@ points. Returns an -- unspecified value when given the zero vector as input. direction :: v n -> Direction v n direction = Dir -- | Synonym for 'direction'. dir :: v n -> Direction v n dir = Dir -- | @fromDirection d@ is the unit vector in the direction @d@. fromDirection :: (Metric v, Floating n) => Direction v n -> v n fromDirection (Dir v) = signorm v -- | Synonym for 'fromDirection'. fromDir :: (Metric v, Floating n) => Direction v n -> v n fromDir (Dir v) = signorm v -- | compute the positive angle between the two directions in their common plane angleBetweenDirs :: (Metric v, Floating n) => Direction v n -> Direction v n -> Angle n angleBetweenDirs d1 d2 = angleBetween (fromDirection d1) (fromDirection d2) -- | @dirBetween p q@ returns the directions from @p@ to @q@ dirBetween :: (Additive v, Num n) => Point v n -> Point v n -> Direction v n dirBetween p q = dir \$ p .-. q