    {-
    Copyright (c) 2008, 2009
    Russell O'Connor

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the "Software"), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
    THE SOFTWARE.
    -}
    -- |Colour operations defined by the International Commission on
    -- Illumination (CIE).
    module Data.Colour.CIE
     (Colour
     ,cieXYZ, cieXYZView, luminance
     ,toCIEXYZ -- depricated

     ,Chromaticity
     ,mkChromaticity, chromaCoords
     ,chromaX, chromaY, chromaZ
     ,chromaConvert
     ,chromaColour

     ,lightness, cieLABView, cieLAB --cieLuv
     )
    where

    import Data.List (foldl1')
    import Data.Colour
    import Data.Colour.RGB
    import Data.Colour.SRGB.Linear
    import Data.Colour.CIE.Chromaticity
    import Data.Colour.Matrix

    -- |Construct a 'Colour' from XYZ coordinates for the 2&#176; standard
    -- (colourimetric) observer.
    cieXYZ :: (Fractional a) => a -> a -> a -> Colour a
    cieXYZ :: forall a. Fractional a => a -> a -> a -> Colour a
    cieXYZ a
    x a
    y a
    z = a -> a -> a -> Colour a
    forall a. Fractional a => a -> a -> a -> Colour a
    rgb a
    r a
    g a
    b
     where
      [a
    r,a
    g,a
    b] = [[a]] -> [a] -> [a]
    forall {b}. Num b => [[b]] -> [b] -> [b]
    mult [[a]]
    matrix [a
    x,a
    y,a
    z]
      matrix :: [[a]]
    matrix = ([Rational] -> [a]) -> [[Rational]] -> [[a]]
    forall a b. (a -> b) -> [a] -> [b]
    map ((Rational -> a) -> [Rational] -> [a]
    forall a b. (a -> b) -> [a] -> [b]
    map Rational -> a
    forall a. Fractional a => Rational -> a
    fromRational) [[Rational]]
    xyz2rgb709

    -- |Returns the XYZ colour coordinates for the 2&#176; standard
    -- (colourimetric) observer.
    cieXYZView :: (Fractional a) => Colour a -> (a,a,a)
    cieXYZView :: forall a. Fractional a => Colour a -> (a, a, a)
    cieXYZView Colour a
    c = (a
    x,a
    y,a
    z)
     where
      RGB a
    r a
    g a
    b = Colour a -> RGB a
    forall a. Fractional a => Colour a -> RGB a
    toRGB Colour a
    c
      [a
    x,a
    y,a
    z] = [[a]] -> [a] -> [a]
    forall {b}. Num b => [[b]] -> [b] -> [b]
    mult [[a]]
    matrix [a
    r,a
    g,a
    b]
      matrix :: [[a]]
    matrix = ([Rational] -> [a]) -> [[Rational]] -> [[a]]
    forall a b. (a -> b) -> [a] -> [b]
    map ((Rational -> a) -> [Rational] -> [a]
    forall a b. (a -> b) -> [a] -> [b]
    map Rational -> a
    forall a. Fractional a => Rational -> a
    fromRational) [[Rational]]
    rgb7092xyz

    {-# DEPRECATED toCIEXYZ "`toCIEXYZ' has been renamed `cieXYZView'" #-}
    toCIEXYZ :: Colour a -> (a, a, a)
    toCIEXYZ Colour a
    x = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    cieXYZView Colour a
    x

    {- CIE luminance -}
    -- |Returns the Y colour coordinate (luminance) for the 2&#176; standard
    -- (colourimetric) observer.
    luminance :: (Fractional a) => Colour a -> a
    luminance :: forall a. Fractional a => Colour a -> a
    luminance Colour a
    c = a
    y
     where
      (a
    x,a
    y,a
    z) = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    toCIEXYZ Colour a
    c

    instance AffineSpace Chromaticity where
     affineCombo :: forall a.
    Num a =>
    [(a, Chromaticity a)] -> Chromaticity a -> Chromaticity a
    affineCombo [(a, Chromaticity a)]
    l Chromaticity a
    z =
       (Chromaticity a -> Chromaticity a -> Chromaticity a)
    -> [Chromaticity a] -> Chromaticity a
    forall a. HasCallStack => (a -> a -> a) -> [a] -> a
    foldl1' Chromaticity a -> Chromaticity a -> Chromaticity a
    forall {a}.
    Num a =>
    Chromaticity a -> Chromaticity a -> Chromaticity a
    chromaAdd [a -> Chromaticity a -> Chromaticity a
    forall {a}. Num a => a -> Chromaticity a -> Chromaticity a
    chromaScale a
    w Chromaticity a
    a | (a
    w,Chromaticity a
    a) <- (a
    1a -> a -> a
    forall a. Num a => a -> a -> a
    -a
    total,Chromaticity a
    z)(a, Chromaticity a)
    -> [(a, Chromaticity a)] -> [(a, Chromaticity a)]
    forall a. a -> [a] -> [a]
    :[(a, Chromaticity a)]
    l]
      where
       total :: a
    total = [a] -> a
    forall a. Num a => [a] -> a
    forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
    sum ([a] -> a) -> [a] -> a
    forall a b. (a -> b) -> a -> b
    $ ((a, Chromaticity a) -> a) -> [(a, Chromaticity a)] -> [a]
    forall a b. (a -> b) -> [a] -> [b]
    map (a, Chromaticity a) -> a
    forall a b. (a, b) -> a
    fst [(a, Chromaticity a)]
    l
       (Chroma a
    x0 a
    y0) chromaAdd :: Chromaticity a -> Chromaticity a -> Chromaticity a
    `chromaAdd` (Chroma a
    x1 a
    y1) = a -> a -> Chromaticity a
    forall a. a -> a -> Chromaticity a
    Chroma (a
    x0a -> a -> a
    forall a. Num a => a -> a -> a
    +a
    x1) (a
    y0a -> a -> a
    forall a. Num a => a -> a -> a
    +a
    y1)
       a
    s chromaScale :: a -> Chromaticity a -> Chromaticity a
    `chromaScale` (Chroma a
    x a
    y) = a -> a -> Chromaticity a
    forall a. a -> a -> Chromaticity a
    Chroma (a
    sa -> a -> a
    forall a. Num a => a -> a -> a
    *a
    x) (a
    sa -> a -> a
    forall a. Num a => a -> a -> a
    *a
    y)

    -- |Constructs a colour from the given 'Chromaticity' and 'luminance'.
    chromaColour :: (Fractional a) =>
                    Chromaticity a
                 -> a              -- ^ 'luminance'
                 -> Colour a
    chromaColour :: forall a. Fractional a => Chromaticity a -> a -> Colour a
    chromaColour Chromaticity a
    ch a
    y = a -> a -> a -> Colour a
    forall a. Fractional a => a -> a -> a -> Colour a
    cieXYZ (a
    sa -> a -> a
    forall a. Num a => a -> a -> a
    *a
    ch_x) a
    y (a
    sa -> a -> a
    forall a. Num a => a -> a -> a
    *a
    ch_z)
     where
      (a
    ch_x, a
    ch_y, a
    ch_z) = Chromaticity a -> (a, a, a)
    forall a. Fractional a => Chromaticity a -> (a, a, a)
    chromaCoords Chromaticity a
    ch
      s :: a
    s = a
    ya -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    ch_y

    -- |Returns the lightness of a colour with respect to a given white point.
    -- Lightness is a perceptually uniform measure.
    lightness :: (Ord a, Floating a) => Chromaticity a -- ^White point
                                     -> Colour a -> a
    lightness :: forall a. (Ord a, Floating a) => Chromaticity a -> Colour a -> a
    lightness Chromaticity a
    white_ch Colour a
    c | (a
    6a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    29)a -> Integer -> a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^Integer
    3 a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    < a
    y' = a
    116a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    y'a -> a -> a
    forall a. Floating a => a -> a -> a
    **(a
    1a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    3) a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    16
                         | Bool
    otherwise = (a
    29a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    3)a -> Integer -> a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^Integer
    3a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    y'
     where
      white :: Colour a
    white = Chromaticity a -> a -> Colour a
    forall a. Fractional a => Chromaticity a -> a -> Colour a
    chromaColour Chromaticity a
    white_ch a
    1.0
      y' :: a
    y' = (Colour a -> a
    forall a. Fractional a => Colour a -> a
    luminance Colour a
    ca -> a -> a
    forall a. Fractional a => a -> a -> a
    /Colour a -> a
    forall a. Fractional a => Colour a -> a
    luminance Colour a
    white)

    -- |Returns the CIELAB coordinates of a colour, which is a
    -- perceptually uniform colour space.
    -- The first coordinate is 'lightness'.
    -- If you don't know what white point to use, use
    -- 'Data.Colour.CIE.Illuminant.d65'.
    cieLABView :: (Ord a, Floating a) => Chromaticity a -- ^White point
                                  -> Colour a -> (a,a,a)
    cieLABView :: forall a.
    (Ord a, Floating a) =>
    Chromaticity a -> Colour a -> (a, a, a)
    cieLABView Chromaticity a
    white_ch Colour a
    c = (Chromaticity a -> Colour a -> a
    forall a. (Ord a, Floating a) => Chromaticity a -> Colour a -> a
    lightness Chromaticity a
    white_ch Colour a
    c, a
    a, a
    b)
     where
      white :: Colour a
    white = Chromaticity a -> a -> Colour a
    forall a. Fractional a => Chromaticity a -> a -> Colour a
    chromaColour Chromaticity a
    white_ch a
    1.0
      (a
    x,a
    y,a
    z) = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    toCIEXYZ Colour a
    c
      (a
    xn,a
    yn,a
    zn) = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    toCIEXYZ Colour a
    white
      (a
    fx, a
    fy, a
    fz) = (a -> a
    forall {a}. (Floating a, Ord a) => a -> a
    f (a
    xa -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    xn), a -> a
    forall {a}. (Floating a, Ord a) => a -> a
    f (a
    ya -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    yn), a -> a
    forall {a}. (Floating a, Ord a) => a -> a
    f (a
    za -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    zn))
      a :: a
    a = a
    500a -> a -> a
    forall a. Num a => a -> a -> a
    *(a
    fx a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    fy)
      b :: a
    b = a
    200a -> a -> a
    forall a. Num a => a -> a -> a
    *(a
    fy a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    fz)
      f :: a -> a
    f a
    x | (a
    6a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    29)a -> Integer -> a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^Integer
    3 a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    < a
    x = a
    xa -> a -> a
    forall a. Floating a => a -> a -> a
    **(a
    1a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    3)
          | Bool
    otherwise = a
    841a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    108a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    x a -> a -> a
    forall a. Num a => a -> a -> a
    + a
    4a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    29

    -- |Returns the colour for given CIELAB coordinates, which is a
    -- perceptually uniform colour space.
    -- If you don't know what white point to use, use
    -- 'Data.Colour.CIE.Illuminant.d65'.
    cieLAB :: (Ord a, Floating a) => Chromaticity a -- ^White point
                                  -> a              -- ^L* coordinate (lightness)
                                  -> a              -- ^a* coordinate
                                  -> a              -- ^b* coordinate
                                  -> Colour a
    cieLAB :: forall a.
    (Ord a, Floating a) =>
    Chromaticity a -> a -> a -> a -> Colour a
    cieLAB Chromaticity a
    white_ch a
    l a
    a a
    b = a -> a -> a -> Colour a
    forall a. Fractional a => a -> a -> a -> Colour a
    cieXYZ (a
    xna -> a -> a
    forall a. Num a => a -> a -> a
    *a -> a
    transform a
    fx)
                                   (a
    yna -> a -> a
    forall a. Num a => a -> a -> a
    *a -> a
    transform a
    fy)
                                   (a
    zna -> a -> a
    forall a. Num a => a -> a -> a
    *a -> a
    transform a
    fz)
     where
      white :: Colour a
    white = Chromaticity a -> a -> Colour a
    forall a. Fractional a => Chromaticity a -> a -> Colour a
    chromaColour Chromaticity a
    white_ch a
    1.0
      (a
    xn,a
    yn,a
    zn) = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    toCIEXYZ Colour a
    white
      fx :: a
    fx = a
    fy a -> a -> a
    forall a. Num a => a -> a -> a
    + a
    aa -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    500
      fy :: a
    fy = (a
    l a -> a -> a
    forall a. Num a => a -> a -> a
    + a
    16)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    116
      fz :: a
    fz = a
    fy a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    ba -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    200
      delta :: a
    delta = a
    6a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    29
      transform :: a -> a
    transform a
    fa | a
    fa a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    > a
    delta = a
    faa -> Integer -> a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^Integer
    3
                   | Bool
    otherwise = (a
    fa a -> a -> a
    forall a. Num a => a -> a -> a
    - a
    16a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    116)a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    3a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    deltaa -> Integer -> a
    forall a b. (Num a, Integral b) => a -> b -> a
    ^Integer
    2

    -- |Returns the CIELUV coordinates of a colour, which is a
    -- perceptually uniform colour space.
    -- If you don't know what white point to use, use
    -- 'Data.Colour.CIE.Illuminant.d65'.
    cieLuv :: (Ord a, Floating a) => Chromaticity a -- ^White point
                                  -> Colour a -> (a,a,a)
    cieLuv :: forall a.
    (Ord a, Floating a) =>
    Chromaticity a -> Colour a -> (a, a, a)
    cieLuv Chromaticity a
    white_ch Colour a
    c = (a
    l, a
    13a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    la -> a -> a
    forall a. Num a => a -> a -> a
    *(a
    u'a -> a -> a
    forall a. Num a => a -> a -> a
    -a
    un'), a
    13a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    la -> a -> a
    forall a. Num a => a -> a -> a
    *(a
    v'a -> a -> a
    forall a. Num a => a -> a -> a
    -a
    vn'))
     where
      white :: Colour a
    white = Chromaticity a -> a -> Colour a
    forall a. Fractional a => Chromaticity a -> a -> Colour a
    chromaColour Chromaticity a
    white_ch a
    1.0
      (a
    u', a
    v') = Colour a -> (a, a)
    forall a. (Ord a, Floating a) => Colour a -> (a, a)
    u'v' Colour a
    c
      (a
    un', a
    vn') = Colour a -> (a, a)
    forall a. (Ord a, Floating a) => Colour a -> (a, a)
    u'v' Colour a
    white
      l :: a
    l = Chromaticity a -> Colour a -> a
    forall a. (Ord a, Floating a) => Chromaticity a -> Colour a -> a
    lightness Chromaticity a
    white_ch Colour a
    c
    --------------------------------------------------------------------------
    {- not for export -}
    u'v' :: (Ord a, Floating a) => Colour a -> (a,a)
    u'v' :: forall a. (Ord a, Floating a) => Colour a -> (a, a)
    u'v' Colour a
    c = (a
    4a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    xa -> a -> a
    forall a. Fractional a => a -> a -> a
    /(a
    xa -> a -> a
    forall a. Num a => a -> a -> a
    +a
    15a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    ya -> a -> a
    forall a. Num a => a -> a -> a
    +a
    3a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    z), a
    9a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    ya -> a -> a
    forall a. Fractional a => a -> a -> a
    /(a
    xa -> a -> a
    forall a. Num a => a -> a -> a
    +a
    15a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    ya -> a -> a
    forall a. Num a => a -> a -> a
    +a
    3a -> a -> a
    forall a. Num a => a -> a -> a
    *a
    z))
     where
      (a
    x,a
    y,a
    z) = Colour a -> (a, a, a)
    forall a. Fractional a => Colour a -> (a, a, a)
    toCIEXYZ Colour a
    c

    rgb7092xyz :: [[Rational]]
    rgb7092xyz = (RGBGamut -> [[Rational]]
    rgb2xyz RGBGamut
    sRGBGamut)

    xyz2rgb709 :: [[Rational]]
    xyz2rgb709 = [[Rational]] -> [[Rational]]
    forall {a}. Fractional a => [[a]] -> [[a]]
    inverse [[Rational]]
    rgb7092xyz