    {-# LANGUAGE FlexibleContexts          #-}
    {-# LANGUAGE NoMonomorphismRestriction #-}
    {-# LANGUAGE ScopedTypeVariables       #-}
    {-# LANGUAGE TypeFamilies              #-}
    {-# OPTIONS_GHC -fno-warn-unused-imports       #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Diagrams.TwoD.Arrowheads
    -- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
    -- License     :  BSD-style (see LICENSE)
    -- Maintainer  :  diagrams-discuss@googlegroups.com
    --
    -- Standard arrowheads and tails. Each arrowhead or tail is designed
    -- to be drawn filled, with a line width of 0, and is normalized to
    -- fit inside a circle of diameter 1.
    --
    -----------------------------------------------------------------------------

    module Diagrams.TwoD.Arrowheads
           (
           -- * Arrowheads
           -- ** Standard arrowheads
             tri
           , dart
           , halfDart
           , spike
           , thorn
           , lineHead
           , noHead

           -- ** Configurable arrowheads
           -- | Creates arrowheads of the same shape as the standard heads but
           --   where the angle parameter is used to specify the angle to the top
           --   left point of the arrowhead.
           , arrowheadTriangle
           , arrowheadDart
           , arrowheadHalfDart
           , arrowheadSpike
           , arrowheadThorn

           -- * Arrow tails
           -- ** Standard arrow tails
           , tri'
           , dart'
           , halfDart'
           , spike'
           , thorn'
           , lineTail
           , noTail
           , quill
           , block

           -- ** Configurable arrow tails

           , arrowtailQuill
           , arrowtailBlock

           -- * Internals
           , ArrowHT
           ) where

    import           Control.Lens            ((&), (.~), (<>~), (^.))
    import           Data.Default.Class
    import           Data.Monoid             (mempty, (<>))

    import           Diagrams.Angle
    import           Diagrams.Core

    import           Diagrams.Path
    import           Diagrams.Segment
    import           Diagrams.Trail
    import           Diagrams.TrailLike      (fromOffsets)
    import           Diagrams.TwoD.Align
    import           Diagrams.TwoD.Arc       (arc')
    import           Diagrams.TwoD.Path      ()
    import           Diagrams.TwoD.Polygons
    import           Diagrams.TwoD.Shapes
    import           Diagrams.TwoD.Transform
    import           Diagrams.TwoD.Types
    import           Diagrams.TwoD.Vector    (unitX, unit_X, xDir)
    import           Diagrams.Util           (( # ))

    import           Linear.Affine
    import           Linear.Metric
    import           Linear.Vector

    -----------------------------------------------------------------------------

    type ArrowHT n = n -> n -> (Path V2 n, Path V2 n)

    closedPath :: OrderedField n => Trail V2 n -> Path V2 n
    closedPath = pathFromTrail . closeTrail

    -- Heads ------------------------------------------------------------------
    --   > drawHead h = arrowAt' (with & arrowHead .~ h & shaftStyle %~ lw none
    --   >                             & headLength .~ local 0.5)
    --   >         origin (r2 (1, 0))
    --   >      <> square 0.5 # alignL # lw none # frame 0.1

    -- | Isoceles triangle style. The above example specifies an angle of `2/5 Turn`.

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg#diagram=tri25Ex&width=120>>

    --   > tri25Ex = arrowAt' (with & arrowHead .~ arrowheadTriangle (2/5 @@ turn)
    --   >                          & shaftStyle %~ lw none & headLength .~ local 0.5)
    --   >           origin (r2 (0.5, 0))
    --   >        <> square 0.6 # alignL # lw none # frame 0.1
    arrowheadTriangle :: RealFloat n => Angle n -> ArrowHT n
    arrowheadTriangle theta = aHead
      where
        aHead len _ = (p, mempty)
          where
            psi = pi - (theta ^. rad)
            r = len / (1 + cos psi)
            p = polygon (def & polyType .~ PolyPolar [theta, (-2) *^ theta]
                (repeat r) & polyOrient .~ NoOrient)  # alignL

    -- | Isoceles triangle with linear concave base. Inkscape type 1 - dart like.
    arrowheadDart :: RealFloat n => Angle n -> ArrowHT n
    arrowheadDart theta len shaftWidth = (hd # scale sz, jt)
      where
        hd = snugL . pathFromTrail . glueTrail $ fromOffsets [t1, t2, b2, b1]
        jt = pathFromTrail . glueTrail $ j <> reflectY j
        j = closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 (shaftWidth / 2)]
        v = rotate theta unitX
        (t1, t2) = (unit_X ^+^ v, V2 (-0.5) 0 ^-^ v)
        [b1, b2] = map (reflectY . negated) [t1, t2]
        psi = pi - negated t2 ^. _theta . rad
        jLength = shaftWidth / (2 * tan psi)

        -- If the shaft is too wide, set the size to a default value of 1.
        sz = max 1 ((len - jLength) / 1.5)

    -- | Top half of an 'arrowheadDart'.
    arrowheadHalfDart :: RealFloat n => Angle n -> ArrowHT n
    arrowheadHalfDart theta len shaftWidth = (hd, jt)
      where
        hd = fromOffsets [t1, t2]
           # closeTrail # pathFromTrail
           # translateX 1.5 # scale sz
           # translateY (-shaftWidth/2)
           # snugL
        jt = snugR . translateY (-shaftWidth/2) . pathFromTrail . closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 shaftWidth]
        v = rotate theta unitX
        (t1, t2) = (unit_X ^+^ v, (0.5 *^ unit_X) ^-^ v)
        psi = pi - negated t2 ^. _theta . rad
        jLength = shaftWidth / tan psi

        -- If the shaft is too wide, set the size to a default value of 1.
        sz = max 1 ((len - jLength) / 1.5)

    -- | Isoceles triangle with curved concave base. Inkscape type 2.
    arrowheadSpike :: RealFloat n => Angle n -> ArrowHT n
    arrowheadSpike theta len shaftWidth  = (hd # scale r, jt # scale r)
      where
        hd = snugL . closedPath $ l1 <> c <> l2
        jt = alignR . centerY . pathFromTrail
                    . closeTrail $ arc' 1 (xDir & _theta <>~ negated phi) (2 *^ phi)
        l1 = trailFromSegments [straight $ unit_X ^+^ v]
        l2 = trailFromSegments [reverseSegment . straight $ (unit_X ^+^ reflectY v)]
        c = arc' 1 (rotate α xDir) ((-2) *^ α)
        α = (1/2 @@ turn) ^-^ theta
        v = rotate theta unitX

        -- The length of the head without its joint is, -2r cos theta and
        -- the length of the joint is r - sqrt (r^2 - y^2). So the total
        -- length of the arrow head is given by r(1 - 2 cos theta)-sqrt (r^2-y^2).
        -- Solving the quadratic gives two roots, we want the larger one.

        -- 1/4 turn < theta < 2/3 turn.
        a = 1 - 2 * cos (theta ^. rad)
        y = shaftWidth / 2

        -- If the shaft is too wide for the head, we default the radius r to
        -- 2/3 * len by setting d=1 and phi=pi/2.
        d = max 1 (len**2 + (1 - a**2) * y**2)
        r = (a * len + sqrt d) / (a**2 -1)
        phi = asinA (min 1 (y/r))

    -- | Curved sides, linear concave base. Illustrator CS5 #3
    arrowheadThorn :: RealFloat n => Angle n -> ArrowHT n
    arrowheadThorn theta len shaftWidth = (hd # scale sz, jt)
      where
        hd = snugL . pathFromTrail . glueTrail $ hTop <> reflectY hTop
        hTop = closeTrail . trailFromSegments $ [c, l]
        jt = pathFromTrail . glueTrail $ j <> reflectY j
        j = closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 (shaftWidth / 2)]
        c = curvedSide theta
        v = rotate theta unitX
        l = reverseSegment . straight $ t
        t = v ^-^ V2 (-0.5) 0
        psi = fullTurn ^/ 2 ^-^ (negated t ^. _theta)
        jLength = shaftWidth / (2 * tanA psi)

        -- If the shaft if too wide, set the size to a default value of 1.
        sz = max 1 ((len - jLength) / 1.5)

    -- | Make a side for the thorn head.
    curvedSide :: Floating n => Angle n -> Segment Closed V2 n
    curvedSide theta = bezier3 ctrl1 ctrl2 end
      where
        v0    = unit_X
        v1    = rotate theta unitX
        ctrl1 = v0
        ctrl2 = v0 ^+^ v1
        end   = v0 ^+^ v1

    -- Standard heads ---------------------------------------------------------
    -- | A line the same width as the shaft.
    lineHead :: RealFloat n => ArrowHT n
    lineHead s w = (square 1 # scaleX s # scaleY w # alignL, mempty)

    noHead :: ArrowHT n
    noHead _ _ = (mempty, mempty)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg#diagram=triEx&width=100>>

    --   > triEx = drawHead tri
    tri :: RealFloat n => ArrowHT n
    tri = arrowheadTriangle (1/3 @@ turn)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg#diagram=spikeEx&width=100>>

    --   > spikeEx = drawHead spike
    spike :: RealFloat n => ArrowHT n
    spike = arrowheadSpike (3/8 @@ turn)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg#diagram=thornEx&width=100>>

    --   > thornEx = drawHead thorn
    thorn :: RealFloat n => ArrowHT n
    thorn = arrowheadThorn (3/8 @@ turn)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg#diagram=dartEx&width=100>>

    --   > dartEx = drawHead dart
    dart :: RealFloat n => ArrowHT n
    dart = arrowheadDart (2/5 @@ turn)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_halfDartEx.svg#diagram=halfDartEx&width=100>>

    --   > halfDartEx = drawHead halfDart
    halfDart :: RealFloat n => ArrowHT n
    halfDart = arrowheadHalfDart (2/5 @@ turn)

    -- Tails ------------------------------------------------------------------
    --   > drawTail t = arrowAt' (with  & arrowTail .~ t & shaftStyle %~ lw none
    --   >                              & arrowHead .~ noHead & tailLength .~ local 0.5)
    --   >         origin (r2 (1, 0))
    --   >      <> square 0.5 # alignL # lw none # frame 0.1

    -- | Utility function to convert any arrowhead to an arrowtail, i.e.
    --   attached at the start of the trail.
    headToTail :: OrderedField n => ArrowHT n -> ArrowHT n
    headToTail hd = tl
      where
        tl sz shaftWidth = (t, j)
          where
            (t', j') = hd sz shaftWidth
            t = reflectX t'
            j = reflectX j'

    arrowtailBlock :: forall n. (RealFloat n) => Angle n -> ArrowHT n
    arrowtailBlock theta = aTail
      where
       aTail len _ = (t, mempty)
          where
            t  = rect len (len * x) # alignR
            a' :: V2 n
            a' = rotate theta unitX
            a  = a' ^-^ reflectY a'
            x  = norm a

    -- | The angle is where the top left corner intersects the circle.
    arrowtailQuill :: OrderedField n => Angle n -> ArrowHT n
    arrowtailQuill theta = aTail
      where
       aTail len shaftWidth = (t, j)
          where
            t = closedPath (trailFromVertices [v0, v1, v2, v3, v4, v5, v0])
                  # scale sz # alignR
            sz = len / 0.6
            v0 = p2 (0.5, 0)
            v2 = origin .+^ (rotate theta unitX # scale 0.5)
            v1 = v2 # translateX (5/8)
            v3 = p2 (-0.1, 0)
            v4 = v2 # reflectY
            v5 = v4 # translateX (5/8)
            s = 1 - shaftWidth / norm (v1 .-. v5)
            n1 = v0 # translateY (0.5 * shaftWidth)
            n2 = v1 .-^ ((v1 .-. v0) # scale s)
            n3 = v5 .-^ ((v5 .-. v0) # scale s)
            n4 = n1 # reflectY
            j  = closedPath $ trailFromVertices [v0, n1, n2, v0, n3, n4, v0]

    -- Standard tails ---------------------------------------------------------
    -- | A line the same width as the shaft.
    lineTail :: RealFloat n => ArrowHT n
    lineTail s w = (square 1 # scaleY w # scaleX s # alignR, mempty)

    noTail :: ArrowHT n
    noTail _ _ = (mempty, mempty)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg#diagram=tri'Ex&width=100>>

    --   > tri'Ex = drawTail tri'
    tri' :: RealFloat n => ArrowHT n
    tri' = headToTail tri

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg#diagram=spike'Ex&width=100>>

    --   > spike'Ex = drawTail spike'
    spike' :: RealFloat n => ArrowHT n
    spike' = headToTail spike

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg#diagram=thorn'Ex&width=100>>

    --   > thorn'Ex = drawTail thorn'
    thorn' :: RealFloat n => ArrowHT n
    thorn' = headToTail thorn

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg#diagram=dart'Ex&width=100>>

    --   > dart'Ex = drawTail dart'
    dart' :: RealFloat n => ArrowHT n
    dart' = headToTail dart

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_halfDart'Ex.svg#diagram=halfDart'Ex&width=100>>

    --   > halfDart'Ex = drawTail halfDart'
    halfDart' :: RealFloat n => ArrowHT n
    halfDart' = headToTail halfDart

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg#diagram=quillEx&width=100>>

    --   > quillEx = drawTail quill
    quill :: (Floating n, Ord n) => ArrowHT n
    quill = arrowtailQuill (2/5 @@ turn)

    -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg#diagram=blockEx&width=100>>

    --   > blockEx = drawTail block
    block :: RealFloat n => ArrowHT n
    block = arrowtailBlock (7/16 @@ turn)