{-# 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