{-# LANGUAGE FlexibleContexts , TypeFamilies , ViewPatterns #-} ----------------------------------------------------------------------------- -- | -- Module : Diagrams.ThreeD.Vector -- Copyright : (c) 2013 diagrams-lib team (see LICENSE) -- License : BSD-style (see LICENSE) -- Maintainer : diagrams-discuss@googlegroups.com -- -- Three-dimensional vectors. -- ----------------------------------------------------------------------------- module Diagrams.ThreeD.Vector ( -- * Special 2D vectors unitX, unitY, unitZ, unit_X, unit_Y, unit_Z, -- * Converting between vectors and angles direction, fromDirection, angleBetween, angleBetweenDirs ) where import Control.Lens ((^.)) import Data.VectorSpace import Data.Cross import Diagrams.ThreeD.Types import Diagrams.Coordinates -- | The unit vector in the positive X direction. unitX :: R3 unitX = 1 ^& 0 ^& 0 -- | The unit vector in the positive Y direction. unitY :: R3 unitY = 0 ^& 1 ^& 0 -- | The unit vector in the positive Z direction. unitZ :: R3 unitZ = 0 ^& 0 ^& 1 -- | The unit vector in the negative X direction. unit_X :: R3 unit_X = (-1) ^& 0 ^& 0 -- | The unit vector in the negative Y direction. unit_Y :: R3 unit_Y = 0 ^& (-1) ^& 0 -- | The unit vector in the negative Z direction. unit_Z :: R3 unit_Z = 0 ^& 0 ^& (-1) -- | @direction v@ is the direction in which @v@ points. Returns an -- unspecified value when given the zero vector as input. direction :: Direction d => R3 -> d direction v | r == 0 = fromSpherical \$ Spherical zero zero | otherwise = fromSpherical \$ Spherical θ φ where r = magnitude v (x,y,z) = unr3 v φ = asin (z / r) @@ rad θ = atan2 y x @@ rad zero = 0 @@ rad -- | @fromDirection d@ is the unit vector in the direction @d@. fromDirection :: Direction d => d -> R3 fromDirection (toSpherical -> (Spherical θ' φ')) = r3 (x,y,z) where θ = θ'^.rad φ = φ'^.rad x = cos θ * cos φ y = sin θ * cos φ z = sin φ -- | compute the positive angle between the two vectors in their common plane angleBetween :: R3 -> R3 -> Angle angleBetween v1 v2 = atan2 (magnitude \$ cross3 v1 v2) (v1 <.> v2) @@ rad -- | compute the positive angle between the two vectors in their common plane angleBetweenDirs :: Direction d => d -> d -> Angle angleBetweenDirs d1 d2 = angleBetween (fromDirection d1) (fromDirection d2)