    {-# LANGUAGE TypeFamilies #-}
    {-# OPTIONS_GHC -fno-warn-orphans #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Diagrams.ThreeD.Types
    -- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
    -- License     :  BSD-style (see LICENSE)
    -- Maintainer  :  diagrams-discuss@googlegroups.com
    --
    -- Basic types for three-dimensional Euclidean space.
    --
    -----------------------------------------------------------------------------

    module Diagrams.ThreeD.Types
           ( -- * 3D Euclidean space
             r3, unr3, mkR3
           , p3, unp3, mkP3
           , r3Iso, p3Iso, project
           , r3SphericalIso, r3CylindricalIso
           , V3 (..), P3,      T3
           , R1 (..), R2 (..), R3 (..)

           ) where

    import           Control.Lens        (Iso', iso, _1, _2, _3)

    import           Diagrams.Angle
    import           Diagrams.Core
    import           Diagrams.Points
    import           Diagrams.TwoD.Types

    import           Linear.Metric
    import           Linear.V3           as V

    ------------------------------------------------------------
    -- 3D Euclidean space

    -- Basic R3 types

    type P3 = Point V3
    type T3 = Transformation V3

    r3Iso :: Iso' (V3 n) (n, n, n)
    r3Iso = iso unr3 r3

    -- | Construct a 3D vector from a triple of components.
    r3 :: (n, n, n) -> V3 n
    r3 (x,y,z) = V3 x y z

    -- | Curried version of `r3`.
    mkR3 :: n -> n -> n -> V3 n
    mkR3 = V3

    -- | Convert a 3D vector back into a triple of components.
    unr3 :: V3 n -> (n, n, n)
    unr3 (V3 x y z) = (x,y,z)

    -- | Construct a 3D point from a triple of coordinates.
    p3 :: (n, n, n) -> P3 n
    p3 = P . r3

    -- | Convert a 3D point back into a triple of coordinates.
    unp3 :: P3 n -> (n, n, n)
    unp3 (P (V3 x y z)) = (x,y,z)

    p3Iso :: Iso' (P3 n) (n, n, n)
    p3Iso = iso unp3 p3

    -- | Curried version of `r3`.
    mkP3 :: n -> n -> n -> P3 n
    mkP3 x y z = p3 (x, y, z)

    type instance V (V3 n) = V3
    type instance N (V3 n) = n

    instance Transformable (V3 n) where
      transform = apply

    r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n)
    r3SphericalIso = iso
      (\v@(V3 x y z) -> (norm v, atan2A y x, acosA (z / norm v)))
      (\(r,θ,φ)   -> V3 (r * cosA θ * sinA φ) (r * sinA θ * sinA φ) (r * cosA φ))

    r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n)
    r3CylindricalIso = iso
      (\(V3 x y z) -> (sqrt $ x*x + y*y, atan2A y x, z))
      (\(r,θ,z)    -> V3 (r*cosA θ) (r*sinA θ) z)

    instance HasR V3 where
      _r = r3SphericalIso . _1

    instance HasTheta V3 where
      _theta = r3CylindricalIso . _2

    instance HasPhi V3 where
      _phi = r3SphericalIso . _3