    {-
    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.
    -}
    module Data.Colour.RGB where

    import Data.List
    import Data.Colour.Matrix
    import Data.Colour.CIE.Chromaticity
    import Control.Applicative

    -- |An RGB triple for an unspecified colour space.
    data RGB a = RGB {RGB a -> a
    channelRed :: !a
                     ,RGB a -> a
    channelGreen :: !a
                     ,RGB a -> a
    channelBlue :: !a
                     } deriving (RGB a -> RGB a -> Bool
    (RGB a -> RGB a -> Bool) -> (RGB a -> RGB a -> Bool) -> Eq (RGB a)
    forall a. Eq a => RGB a -> RGB a -> Bool
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    /= :: RGB a -> RGB a -> Bool
    $c/= :: forall a. Eq a => RGB a -> RGB a -> Bool
    == :: RGB a -> RGB a -> Bool
    $c== :: forall a. Eq a => RGB a -> RGB a -> Bool
    Eq, Int -> RGB a -> ShowS
    [RGB a] -> ShowS
    RGB a -> String
    (Int -> RGB a -> ShowS)
    -> (RGB a -> String) -> ([RGB a] -> ShowS) -> Show (RGB a)
    forall a. Show a => Int -> RGB a -> ShowS
    forall a. Show a => [RGB a] -> ShowS
    forall a. Show a => RGB a -> String
    forall a.
    (Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
    showList :: [RGB a] -> ShowS
    $cshowList :: forall a. Show a => [RGB a] -> ShowS
    show :: RGB a -> String
    $cshow :: forall a. Show a => RGB a -> String
    showsPrec :: Int -> RGB a -> ShowS
    $cshowsPrec :: forall a. Show a => Int -> RGB a -> ShowS
    Show, ReadPrec [RGB a]
    ReadPrec (RGB a)
    Int -> ReadS (RGB a)
    ReadS [RGB a]
    (Int -> ReadS (RGB a))
    -> ReadS [RGB a]
    -> ReadPrec (RGB a)
    -> ReadPrec [RGB a]
    -> Read (RGB a)
    forall a. Read a => ReadPrec [RGB a]
    forall a. Read a => ReadPrec (RGB a)
    forall a. Read a => Int -> ReadS (RGB a)
    forall a. Read a => ReadS [RGB a]
    forall a.
    (Int -> ReadS a)
    -> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
    readListPrec :: ReadPrec [RGB a]
    $creadListPrec :: forall a. Read a => ReadPrec [RGB a]
    readPrec :: ReadPrec (RGB a)
    $creadPrec :: forall a. Read a => ReadPrec (RGB a)
    readList :: ReadS [RGB a]
    $creadList :: forall a. Read a => ReadS [RGB a]
    readsPrec :: Int -> ReadS (RGB a)
    $creadsPrec :: forall a. Read a => Int -> ReadS (RGB a)
    Read)

    instance Functor RGB where
     fmap :: (a -> b) -> RGB a -> RGB b
    fmap f :: a -> b
    f (RGB r :: a
    r g :: a
    g b :: a
    b) = b -> b -> b -> RGB b
    forall a. a -> a -> a -> RGB a
    RGB (a -> b
    f a
    r) (a -> b
    f a
    g) (a -> b
    f a
    b)

    instance Applicative RGB where
     pure :: a -> RGB a
    pure c :: a
    c = a -> a -> a -> RGB a
    forall a. a -> a -> a -> RGB a
    RGB a
    c a
    c a
    c
     (RGB fr :: a -> b
    fr fg :: a -> b
    fg fb :: a -> b
    fb) <*> :: RGB (a -> b) -> RGB a -> RGB b
    <*> (RGB r :: a
    r g :: a
    g b :: a
    b) = b -> b -> b -> RGB b
    forall a. a -> a -> a -> RGB a
    RGB (a -> b
    fr a
    r) (a -> b
    fg a
    g) (a -> b
    fb a
    b)

    -- |Uncurries a function expecting three r, g, b parameters.
    uncurryRGB :: (a -> a -> a -> b) -> RGB a -> b
    uncurryRGB :: (a -> a -> a -> b) -> RGB a -> b
    uncurryRGB f :: a -> a -> a -> b
    f (RGB r :: a
    r g :: a
    g b :: a
    b) = a -> a -> a -> b
    f a
    r a
    g a
    b

    -- |Curries a function expecting one RGB parameter.
    curryRGB :: (RGB a -> b) -> a -> a -> a -> b
    curryRGB :: (RGB a -> b) -> a -> a -> a -> b
    curryRGB f :: RGB a -> b
    f r :: a
    r g :: a
    g b :: a
    b = RGB a -> b
    f (a -> a -> a -> RGB a
    forall a. a -> a -> a -> RGB a
    RGB a
    r a
    g a
    b)

    -- |An 'RGBGamut' is a 3-D colour &#8220;cube&#8221; that contains all the
    -- colours that can be displayed by a RGB device.
    -- The &#8220;cube&#8221; is normalized so that white has
    -- 'Data.Colour.CIE.luminance' 1.
    data RGBGamut = RGBGamut {RGBGamut -> RGB (Chromaticity Rational)
    primaries :: !(RGB (Chromaticity Rational))
                             ,RGBGamut -> Chromaticity Rational
    whitePoint :: !(Chromaticity Rational)
                             } deriving (RGBGamut -> RGBGamut -> Bool
    (RGBGamut -> RGBGamut -> Bool)
    -> (RGBGamut -> RGBGamut -> Bool) -> Eq RGBGamut
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    /= :: RGBGamut -> RGBGamut -> Bool
    $c/= :: RGBGamut -> RGBGamut -> Bool
    == :: RGBGamut -> RGBGamut -> Bool
    $c== :: RGBGamut -> RGBGamut -> Bool
    Eq)

    instance Show RGBGamut where
      showsPrec :: Int -> RGBGamut -> ShowS
    showsPrec d :: Int
    d gamut :: RGBGamut
    gamut = Bool -> ShowS -> ShowS
    showParen (Int
    d Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    app_prec) ShowS
    showStr
       where
        showStr :: ShowS
    showStr = String -> ShowS
    showString "mkRGBGamut"
                ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . String -> ShowS
    showString " " ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> RGB (Chromaticity Rational) -> ShowS
    forall a. Show a => Int -> a -> ShowS
    showsPrec (Int
    app_precInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +1) (RGBGamut -> RGB (Chromaticity Rational)
    primaries RGBGamut
    gamut))
                ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . String -> ShowS
    showString " " ShowS -> ShowS -> ShowS
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> Chromaticity Rational -> ShowS
    forall a. Show a => Int -> a -> ShowS
    showsPrec (Int
    app_precInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +1) (RGBGamut -> Chromaticity Rational
    whitePoint RGBGamut
    gamut))

    instance Read RGBGamut where
      readsPrec :: Int -> ReadS RGBGamut
    readsPrec d :: Int
    d r :: String
    r = Bool -> ReadS RGBGamut -> ReadS RGBGamut
    forall a. Bool -> ReadS a -> ReadS a
    readParen (Int
    d Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    app_prec)
                      (\r :: String
    r -> [(RGB (Chromaticity Rational) -> Chromaticity Rational -> RGBGamut
    mkRGBGamut RGB (Chromaticity Rational)
    p Chromaticity Rational
    w,String
    t)
                             |("mkRGBGamut",s :: String
    s) <- ReadS String
    lex String
    r
                             ,(p :: RGB (Chromaticity Rational)
    p,s0 :: String
    s0) <- Int -> ReadS (RGB (Chromaticity Rational))
    forall a. Read a => Int -> ReadS a
    readsPrec (Int
    app_precInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +1) String
    s
                             ,(w :: Chromaticity Rational
    w,t :: String
    t)  <- Int -> ReadS (Chromaticity Rational)
    forall a. Read a => Int -> ReadS a
    readsPrec (Int
    app_precInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +1) String
    s0]) String
    r

    -- |An RGB gamut is specified by three primary colours (red, green, and
    -- blue) and a white point (often 'Data.Colour.CIE.Illuminant.d65').
    mkRGBGamut :: RGB (Chromaticity Rational) -- ^ The three primaries
               -> Chromaticity Rational       -- ^ The white point
               -> RGBGamut
    mkRGBGamut :: RGB (Chromaticity Rational) -> Chromaticity Rational -> RGBGamut
    mkRGBGamut = RGB (Chromaticity Rational) -> Chromaticity Rational -> RGBGamut
    RGBGamut

    {- not for export -}

    primaryMatrix :: (Fractional a) => (RGB (Chromaticity a)) -> [[a]]
    primaryMatrix :: RGB (Chromaticity a) -> [[a]]
    primaryMatrix p :: RGB (Chromaticity a)
    p =
      [[a
    xr, a
    xg, a
    xb]
      ,[a
    yr, a
    yg, a
    yb]
      ,[a
    zr, a
    zg, a
    zb]]
     where
      RGB (xr :: a
    xr, yr :: a
    yr, zr :: a
    zr)
          (xg :: a
    xg, yg :: a
    yg, zg :: a
    zg)
          (xb :: a
    xb, yb :: a
    yb, zb :: a
    zb) = (Chromaticity a -> (a, a, a))
    -> RGB (Chromaticity a) -> RGB (a, a, a)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap Chromaticity a -> (a, a, a)
    forall a. Fractional a => Chromaticity a -> (a, a, a)
    chromaCoords RGB (Chromaticity a)
    p

    rgb2xyz :: RGBGamut -> [[Rational]]
    rgb2xyz :: RGBGamut -> [[Rational]]
    rgb2xyz space :: RGBGamut
    space =
      [[Rational]] -> [[Rational]]
    forall a. [[a]] -> [[a]]
    transpose ((Rational -> [Rational] -> [Rational])
    -> [Rational] -> [[Rational]] -> [[Rational]]
    forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
    zipWith ((Rational -> Rational) -> [Rational] -> [Rational]
    forall a b. (a -> b) -> [a] -> [b]
    map ((Rational -> Rational) -> [Rational] -> [Rational])
    -> (Rational -> Rational -> Rational)
    -> Rational
    -> [Rational]
    -> [Rational]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Rational -> Rational -> Rational
    forall a. Num a => a -> a -> a
    (*)) [Rational]
    as ([[Rational]] -> [[Rational]]
    forall a. [[a]] -> [[a]]
    transpose [[Rational]]
    matrix))
     where
      (xn :: Rational
    xn, yn :: Rational
    yn, zn :: Rational
    zn) = Chromaticity Rational -> (Rational, Rational, Rational)
    forall a. Fractional a => Chromaticity a -> (a, a, a)
    chromaCoords (RGBGamut -> Chromaticity Rational
    whitePoint RGBGamut
    space)
      matrix :: [[Rational]]
    matrix = RGB (Chromaticity Rational) -> [[Rational]]
    forall a. Fractional a => RGB (Chromaticity a) -> [[a]]
    primaryMatrix (RGBGamut -> RGB (Chromaticity Rational)
    primaries RGBGamut
    space)
      as :: [Rational]
    as = [[Rational]] -> [Rational] -> [Rational]
    forall b. Num b => [[b]] -> [b] -> [b]
    mult ([[Rational]] -> [[Rational]]
    forall a. Fractional a => [[a]] -> [[a]]
    inverse [[Rational]]
    matrix) [Rational
    xnRational -> Rational -> Rational
    forall a. Fractional a => a -> a -> a
    /Rational
    yn, 1, Rational
    znRational -> Rational -> Rational
    forall a. Fractional a => a -> a -> a
    /Rational
    yn]

    xyz2rgb :: RGBGamut -> [[Rational]]
    xyz2rgb :: RGBGamut -> [[Rational]]
    xyz2rgb = [[Rational]] -> [[Rational]]
    forall a. Fractional a => [[a]] -> [[a]]
    inverse ([[Rational]] -> [[Rational]])
    -> (RGBGamut -> [[Rational]]) -> RGBGamut -> [[Rational]]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . RGBGamut -> [[Rational]]
    rgb2xyz

    hslsv :: (Fractional a, Ord a) => RGB a -> (a,a,a,a,a)
    hslsv :: RGB a -> (a, a, a, a, a)
    hslsv (RGB r :: a
    r g :: a
    g b :: a
    b) | a
    mx a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    == a
    mn  = (0,0,a
    mx,0 ,a
    mx)
                      | Bool
    otherwise = (a
    h,a
    s,a
    l ,a
    s0,a
    mx)
     where
      mx :: a
    mx = [a] -> a
    forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
    maximum [a
    r,a
    g,a
    b]
      mn :: a
    mn = [a] -> a
    forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
    minimum [a
    r,a
    g,a
    b]
      l :: a
    l = (a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    +a
    mn)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /2
      s :: a
    s | a
    l a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    <= 0.5 = (a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    -a
    mn)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /(a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    +a
    mn)
        | Bool
    otherwise = (a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    -a
    mn)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /(2a -> a -> a
    forall a. Num a => a -> a -> a
    -(a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    +a
    mn))
      s0 :: a
    s0 = (a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    -a
    mn)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /a
    mx
      -- hue calcuation
      [x :: a
    x,y :: a
    y,z :: a
    z] = Int -> [a] -> [a]
    forall a. Int -> [a] -> [a]
    take 3 ([a] -> [a]) -> [a] -> [a]
    forall a b. (a -> b) -> a -> b
    $ (a -> Bool) -> [a] -> [a]
    forall a. (a -> Bool) -> [a] -> [a]
    dropWhile (a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    /=a
    mx) [a
    r,a
    g,a
    b,a
    r,a
    g]
      Just o :: Int
    o = a -> [a] -> Maybe Int
    forall a. Eq a => a -> [a] -> Maybe Int
    elemIndex a
    mx [a
    r,a
    g,a
    b]
      h0 :: a
    h0 = 60a -> a -> a
    forall a. Num a => a -> a -> a
    *(a
    ya -> a -> a
    forall a. Num a => a -> a -> a
    -a
    z)a -> a -> a
    forall a. Fractional a => a -> a -> a
    /(a
    mxa -> a -> a
    forall a. Num a => a -> a -> a
    -a
    mn) a -> a -> a
    forall a. Num a => a -> a -> a
    + 120a -> a -> a
    forall a. Num a => a -> a -> a
    *(Int -> a
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    o)
      h :: a
    h | a
    h0 a -> a -> Bool
    forall a. Ord a => a -> a -> Bool
    < 0 = a
    h0 a -> a -> a
    forall a. Num a => a -> a -> a
    + 360
        | Bool
    otherwise = a
    h0

    -- |The 'hue' coordinate of an 'RGB' value is in degrees. Its value is
    -- always in the range 0-360.
    hue :: (Fractional a, Ord a) => RGB a -> a
    hue :: RGB a -> a
    hue rgb :: RGB a
    rgb = a
    h
     where
      (h :: a
    h,_,_,_,_) = RGB a -> (a, a, a, a, a)
    forall a. (Fractional a, Ord a) => RGB a -> (a, a, a, a, a)
    hslsv RGB a
    rgb

    mod1 :: p -> p
    mod1 x :: p
    x | p
    pf p -> p -> Bool
    forall a. Ord a => a -> a -> Bool
    < 0 = p
    pfp -> p -> p
    forall a. Num a => a -> a -> a
    +1
           | Bool
    otherwise = p
    pf
     where
      (_,pf :: p
    pf) = p -> (Integer, p)
    forall a b. (RealFrac a, Integral b) => a -> (b, a)
    properFraction p
    x